University of Turin DEPARTMENT OF PHYSICSUniversity of Turin DEPARTMENT OF PHYSICS Master’s Degree...

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University of Turin DEPARTMENT OF PHYSICS Master’s Degree in Nuclear and Subnuclear Physics Measurement of the relative phase between EM and strong amplitudes in ψ(2s) p ¯ p Candidate: Barbara Passalacqua Supervisor: Prof. Marco Maggiora Co-Supervisor: Prof. Marco Giovanni Maria Destefanis Reviewer: Prof. Margherita Obertino Academic Year 2018-2019

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  • University of TurinDEPARTMENT OF PHYSICS

    Master’s Degree in Nuclear and Subnuclear Physics

    Measurement of the relative phase between EM and strongamplitudes in ψ(2s)→ pp̄

    Candidate:

    Barbara Passalacqua

    Supervisor:

    Prof. Marco Maggiora

    Co-Supervisor:

    Prof. Marco Giovanni Maria Destefanis

    Reviewer:

    Prof. Margherita Obertino

    Academic Year 2018-2019

  • Alle notti insonni superate grazie al

    sostegno dei miei professori, della mia

    famiglia e dei miei amici.

  • Enthusiasm is followed by disappoint-

    ment and even depression, and then by

    renewed enthusiasm.

    Murray Gell-Man

  • Abstract

    The investigation of the measurement of the relative phase between strong and electro-

    magnetic resonant and non-resonant amplitudes could shed new light on many different

    open questions for Charmonia. Recently a relative phase of |∆φ| = 90◦ for J/ψ has beenobserved by BESIII Collaboration, and the relation suggests the hypothesis that the J/ψ

    and ψ(2S) could be a combination of two resonances, one decaying solely through EM

    processes and another one decaying strongly; in this work the process ψ(2s) → pp̄ isinvestigated.

    After an initial focus on the related theoretical issues, the experimental scenario, the

    BESIII spectrometer and BOSS, the official software framework adopted for reconstruc-

    tion and event selection, will be described in detail. After the reconstruction and the

    event selection are performed, the number of the pp̄ pairs are evaluated by means of p

    and p̄ simultaneous fit of momenta distributions. The pp̄ pairs produced in the investi-

    gated channel should be emitted back-to-back in the center of mass frame, once taken

    into account possible misalignments, detector resolution and contribution of Initial State

    Radiation, which was naively implemented by mean of a custom algorithm. The com-

    plete procedure to extract the cross section and the branching fraction for the inclusive

    process will be reported, from the event selection to the final result. Finally the relative

    phase between the strong and electromagnetic (resonant and non-resonant) amplitudes,

    has been extracted considering the pp̄ final state. This analysis has been performed on

    the full set of events collected in 2018, to perform both the ψ(2S) lineshape scan and a

    detailed investigation of the off-resonance interference pattern.

    5

  • Contents

    1 Introduction 1

    1.1 The Standard Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1

    1.2 Quantum ChromoDynamics . . . . . . . . . . . . . . . . . . . . . . . . . . 2

    1.3 Running Coupling Constant and Confinement . . . . . . . . . . . . . . . . 2

    1.4 Charmonium . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3

    1.5 Cross Section . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4

    1.6 Initial State Radiation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5

    1.7 Phase Measurement . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7

    1.8 A Different Theoretical Approach . . . . . . . . . . . . . . . . . . . . . . . 8

    2 The BESIII Experiment 9

    2.1 The BEPCII . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9

    2.2 The BESIII Spectrometer . . . . . . . . . . . . . . . . . . . . . . . . . . . 10

    2.2.1 The Superconductor Solenoid Magnet . . . . . . . . . . . . . . . . . 11

    2.2.2 Multilayer Drift Chamber . . . . . . . . . . . . . . . . . . . . . . . 11

    2.2.3 The Time-Of-Flight System . . . . . . . . . . . . . . . . . . . . . . 12

    2.2.4 Electromagnetic Calorimeter . . . . . . . . . . . . . . . . . . . . . . 14

    2.2.5 Muon Identifier . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14

    2.2.6 Triggers and Data Acquisition . . . . . . . . . . . . . . . . . . . . . 15

    2.3 The BESIII Offline Software System . . . . . . . . . . . . . . . . . . . . . 16

    2.3.1 Simulation, Reconstruction and Analysis . . . . . . . . . . . . . . . 16

    2.3.2 Event Generation . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16

    2.3.3 Particle Transport and Digitalization . . . . . . . . . . . . . . . . . 17

    2.3.4 Reconstruction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17

    2.4 BESIII Physics Program . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18

    2.4.1 Charmonium Spectroscopy . . . . . . . . . . . . . . . . . . . . . . . 18

    2.4.2 Open Charm Decays . . . . . . . . . . . . . . . . . . . . . . . . . . 18

    2.4.3 Light Hadron Spectroscopy . . . . . . . . . . . . . . . . . . . . . . 18

    2.4.4 τ , R, and QCD Studies . . . . . . . . . . . . . . . . . . . . . . . . . 19

    2.4.5 New Physics beyond the Standard Model . . . . . . . . . . . . . . . 19

    3 Data Analysis 21

    3.1 Experimental Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21

    3.2 Event Selection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22

    3.3 Simulations Efficiency . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28

    7

  • 3.4 ISR Correction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29

    3.5 Background Studies . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30

    3.6 Simultaneous Fit . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32

    3.7 Systematic Uncertanties . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38

    3.8 Inclusive Simulations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40

    4 Results 43

    4.1 Cross Section . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43

    4.2 Relative Phase Evaluation . . . . . . . . . . . . . . . . . . . . . . . . . . . 44

    5 Conclusions 47

    List of Figures 49

    List of Tables 51

    Bibliography 53

  • Chapter 1

    Introduction

    Elementary particle physics is trying to address the question, “What is matter made of?”

    on the most fundamental level. There are just three fundamental forces in nature: the

    strong force, carried by gluons, the electroweak force, carried by photons and W and

    Z bosons, and the gravitational force, dominant at macroscopic scale. Each of these

    forces is described by a (sometimes unfortunately different) physical theory. According

    to the Standard Model, the strong interaction acts on particles carrying color charge e.g.

    quarks and gluons. Together the elementary quarks and gluons form hadrons, a class of

    composite particles that interact via the strong force. In this work, the strong interaction is

    investigated by observing decays into hadrons of quarkonium states, produced in electron-

    positron collision provided by the Beijing Electron-Positron Collider II (BEPCII), and

    observed by mean of the Beijing Electromagnetic Spectrometer III (BESIII).

    1.1 The Standard Model

    The Standard Model of fundamental interactions is a theoretical model that led to the uni-

    fication of Quantum Electro-Dynamics (QED) and Quantum Chromodynamics (QCD).

    QED describes both electromagnetic and weak forces, while QCD the strong force (for

    more details see Section 1.2) [1–3]. The Standard Model is mathematically formulated

    in terms of renormalizable gauge theories. A gauge theory is a quantum field theory

    (QFT) where gauge fields emerge as a consequence of the internal symmetries [4]. In the

    Standard Model, these gauge fields are the force mediators.

    The basic Lagrangian may be expressed as:

    L = Lvct + LHiggs + Llep + Lquark,

    where Lvct corresponds to gauge bosons, LHiggs to Higgs scalar, Llep to leptonicfermions and Lquark to hadronic fermions, respectively.

    The total gauge group of the Standard Model is:

    SU(3)C × SU(2)L × U(1)Y (1.1)

    The symmetry group of the electroweak interaction is SU(2)L × U(1)Y , while the gaugesymmetry of the strong interaction is SU(3)C .

    1

  • The theory is commonly viewed as containing the fundamental set of particles: the

    leptons, quarks, gauge bosons and the Higgs particle.

    The fermions, spin 1/2 particles which follow the Fermi-Dirac statistics, are divided

    into quarks and leptons. Leptons l can be subdivided in three families, each one composed

    of one of the three electrically charged leptons — the electron (e), the muon (µ) and the

    tauon (τ) — and of one of the three electrically neutral leptons — the electron-neutrino

    (νe), the muon-neutrino (νµ) and the tau-neutrino (ντ ). All the charged leptons have

    electric charge −e while their antiparticles have charge +e. All leptons interact via theweak interaction while only the charged ones interact also electromagnetically. None of

    the leptons interact via the strong interaction.

    Quarks q come in six flavours: down (d), up (u), strange (s), charm (c), bottom (b)

    and top (t). In contrast to the charged leptons, the quarks carry fractional electric charge:

    −13e for d, s and b, and +2

    3e for u, c and t. In addition to the electric charge, quarks also

    carry color charge, a further degree of freedom. While electric charge is either positive or

    negative, color charge comes in three varieties. The color charges are commonly referred

    to as red (r), green (g) and blue (b). For each color charge there is also an anticolor

    charge. Combining all three colors, or anticolors, the color neutral states can be obtained

    [3].

    1.2 Quantum ChromoDynamics

    QCD is a gauge field theory that describes the strong interaction by means of the color-

    charged gluons and quarks and represents the SU(3) component of the Standard Model.

    QCD Lagrangian is given by

    L(x) = −14F aµν F

    aµν +∑q

    q̄q,a (iD −mq) q (1.2)

    where repeated indices are summed over. The term F aµν encodes the dynamics of the

    gluon fields, D is the gauge covariant derivative [5–7]. The q̄q,a are quark field spinors fora quark of flavor q and mass mq. The color-index a runs from 1 to Nc = 3, where Nc is

    the number of colors. This degree of freedom is called color, in analogy with the three

    color (R,G,B) with which one can build images. Each quark can appear in one of the

    three colors that is the same degree of freedom predicted by Han and Nambu [7].

    Indication of the nature of the constituent masses can be found considering sponta-

    neous and explicit breaking of the chiral symmetry of the QCD Lagrangian. This feature

    influences also an important characteristic of the QCD: the confinement. There is no

    experimental evidence of free colored quarks or gluons: as observed so far, they bound

    together to form color-singlet (hadrons).

    1.3 Running Coupling Constant and Confinement

    Similarly to QED, in the pure QCD [5, 8] Lagrangian description loops lead to divergent

    contributions. They appear in vertices and in the boson propagator. The issue of the

    2

  • infinite contributions by the loops was solved by a mechanism that is now addressed as

    renormalization: the coupling constant becomes function of a nonphysical parameter [2]:

    αs(|q2|) =12π

    21ln(|q2|/Λ2), (1.3)

    where Λ is the renormalization scale, and q is the energy scale. In this way the

    divergent contribution can be cut-off from the calculations. The introduction of a scale

    results in a modification of the coupling strength at different values of this scale, while the

    QED coupling constant is αQED ∼ 1/137. The coupling strenght changes according tothe energy scale. In QCD, the possible contributions to the gluon propagator are two: the

    first one is the analogous of the QED term, while the second one is due to the gluon-gluon

    interaction.

    The coupling strength (αs =g2s4π

    ) is a function of the energy scale (µR):

    the coupling strength in QCD decreases at higher energies (e.g. αs = 0.1185 at the

    energy of the Z0 and αs ≈ 0.4 at the 1 GeV scale). This feature is called asymptoticfreedom: in high energy processes quarks and gluons can be considered as free particles

    during the interaction, thus the rules of the perturbation theory, well tested in QED, can

    be applied for QCD as well. This is the core concept of the so-called perturbative QCD

    (pQCD) [7].

    On the other hand, for very low energies, the coupling constant becomes so large that

    any perturbative approach becomes unfeasible. This effect is called confinement and it is

    the origin of the binding of quarks and gluons inside the hadrons.

    The mathematical expression of QCD potential takes into account both confinement

    and asymptotic freedom, and it is usually defined as:

    V (r) = −4αs3r

    + σr, (1.4)

    where αs is the QCD coupling constant,43

    is a color factor, r is the distance between

    the cc̄ pair, and σ is the factor which takes into account the confinement effect.

    1.4 Charmonium

    Charmonium is a flavorless meson whose constituents are a heavy quark pair: a charm

    quark and its own antiquark [8]. The Charmonium system was discovered in Novem-

    ber 1974, when two experimental groups at Brookhaven and SLAC announced almost

    simultaneously the discovery of a new, narrow resonance, later addressed as J/ψ [8]. The

    resonance was characterized by a mass ∼ 3100 MeV/c2 and an extremely narrow width.Its current values from PDG are [9]:

    MJ/ψ = (3096.916± 0.011) MeV/c2,

    Γ = (92.9± 2.8) keV.

    Another narrow state was soon discovered at SLAC [8], later addressed as ψ(2S). Its

    resonance parameters from PDG are [9]:

    3

  • Mψ(2S) = (3686.093± 0.034) MeV/c2,

    Γ = (294± 8) keV.

    The J/ψ and the ψ(2S) can be formed directly in e+e− annihilations, therefore they have

    the same quantum numbers of the photon Jpc = 1−− (Figure 1.1).

    Figure 1.1: The J/ψ and the ψ(2S) formation diagram.

    Their extremely narrow widths discourage an interpretation of these new states in

    terms of the light u, d, s quarks. They were interpreted as bound states of a new quark

    (c) and its antiquark (c̄), whose existence had been predicted in 1970 to account for the

    non existence of Strangeness Changing Neutral Currents [6, 10].

    Charmonium is a powerful tool for the understanding of the strong interaction. The

    high mass of the c quark (mc ≈ 1.5 GeV/c2) allows to attempt a description of thedynamical properties of the cc̄ system in terms of non-relativistic potential models, in

    which the functional form of the potential is chosen to reproduce the known asymptotic

    properties of the strong interaction, as explained in Sections 1.2 and 1.3, and in Equation

    1.4.

    One of the decay features of the Charmonium states below DD̄ threshold is the narrow

    width. These states decay violating the OZI rule. According to the OZI rule, branching

    fractions related to diagrams with unconnected quark lines are suppressed. States above

    threshold can generally decay to open charm (see Section 2.4.2), except when forbidden

    by some conservation rule (and in such cases these states are narrow as well). These

    strong decays are described within QCD, and hence when the value of αs becomes larger,

    they cannot always be described within a perturbative approach.

    1.5 Cross Section

    Resonant cross sections are generally described by the Breit-Wigner formula [1]:

    σ(E) =2J + 1

    (2S1 + 1)(2S2 + 1)

    k2

    [Γ2/4

    (E − E0)2 + Γ2/4

    ]BinBout

    where E is the center of mass (CM) energy, J is the spin of the resonance, the number

    of polarization states of the two incident particles are 2S1 + 1 and 2S2 + 1, k is the CM

    momentum in the initial state, E0 is in the resonance peak CM energy, Γ is the full width at

    half maximum height of the resonance, Bin is the branching fraction for the resonance into

    4

  • the initial-state channel and Bout is the one into the final-state channel. The differential

    production cross section of point-like, spin 1/2 fermions in e+e− annihilation through a

    virtual photon, e+e− → γ∗ → ff̄ , at CM energy squared s is given by [3]:

    dΩ= Nc

    α2

    4sβ[1 + cos2θ] + (1− β2)[sin2θ]Q2f , (1.5)

    where β is v/c for the produced fermions in the CM frame, θ is the CM scattering angle,

    Qf is the charge of the fermion, and the factor Nc is 1 for charged leptons. In the ultra-

    relativistic limit β → 1, the cross section integrated over the solid angle is:

    σ = NcQ2f

    4πα2

    3s= NcQ

    2f

    86.8nb

    s(GeV 2)(1.6)

    This formula is useful in Section 3.5 for the investigation of the background. The total

    cross section for a squared CM energy√s can be expressed as:

    σ =N

    L�(1 + δ), (1.7)

    where N is the number of events, L is the integrated luminosity, � is the efficiency, and(1+δ) is the ISR correction factor, as explained in Section 1.6.

    The resonance mass MR, the total width ΓR and the product of branching ratios into

    the initial and final state Bin and Bout can be extracted by measuring the formation rate

    for that resonance as a function of the CM energy E.

    1.6 Initial State Radiation

    In an e+e− collision each one of the inciding leptons e+ or e−, or both, can radiate one

    or more photons. This process is known as Initial State Radiation (ISR) [11, 12]. The

    radiated energy reduces the effective CM energy of the e+e− annihilation. The ISR process

    is shown in Figure 1.2.

    Figure 1.2: An electron radiating a ISR photon γISR.

    Let’s consider a process e+e− → X at a CM energy E0 and its cross section as afunction of the CM energy σ(E). The integrated luminosity is L0, and the data sampleare collected at the nominal CM energy E0. Because of the ISR process, the collisions

    actually occur at lower CM energies E < E0. The probability of radiating an ISR photon

    is described by the radiator function W (x) [12], where x is the fraction of the beam energy

    carried by the ISR photon.

    5

  • The two kinematic paramenters x and E are related by:

    x = 1− E2

    E20. (1.8)

    We can consider W (x) as a probability distribution function, hence∫ 1

    0W (x)dx = 1,

    and express the cross section as a function of x: σ0 ≡ σ(E = E0) = σ(x = 0). Theexperimental efficiency to detect the process e+e− → X at a CM energy E0 is a functionof x: �(x). In the no ISR case, we can define �0 ≡ �(0).

    The number of observed events is then:

    N = L′∫ 1

    0

    �(x)σ(x)W (x)dx, (1.9)

    where L′ is the luminosity for the case of no ISR.The cross section σ0 can be determined in two steps.

    First, one can define an effective efficiency �′:

    �′ ≡ NreconstructedNgenerated

    =LMC

    ∫ 10�(x)σ(x)W (x)dx

    LMC∫ 1

    0σ(x)W (x)dx

    , (1.10)

    where LMC is the luminosity of the MonteCarlo. To account for the ISR we need thena correction factor 1 + δ defined as:

    1 + δ ≡∫ 1

    0

    σ(x)

    σ0W (x)dx, (1.11)

    that can be evaluated exploiting MonteCarlo simulations.

    The cross section is hence:

    σ0 =N

    L0�′(1 + δ). (1.12)

    Taking into account Eq. 1.10 and 1.11 one can evaluate the product:

    �′(1 + δ) =1

    σ0

    ∫ 10

    �(x)σ(x)W (x)dx, (1.13)

    where the integral can be limited to any value of x where either �(x) or σ(x) become

    negligible and compatible with zero. The actual values for �′ and (1 + δ) might depend

    on the cut-off, but their product, and hence the final value of σ0, does not.

    If one considers the process near the threshold, the integrals in Eq. 1.10 and 1.11 can

    be cut off at small x, corresponding to a threshold xT

  • they still need to be accounted for in the calculation of 1 + δ:

    1 + δ ≡∫ 1

    0

    σ(x)

    σ0W (x)dx =

    σ0σ0

    ∫ xT0

    W (x)dx. =

    ∫ xT0

    W (x)dx

    The role of the ISR is particularly relevant for the cross section evaluation, as explained

    in Section 1.5.

    1.7 Phase Measurement

    An interference pattern between the J/ψ decay and non-resonant amplitudes was observed

    in e+e− → µ+µ− final states [13–15]. Close to resonance, the annihilation of e+e− intohadronic final states may proceed via three processes: strong and EM decays and the

    continuum process, respectively mediated by gluons or virtual photon for the resonant

    diagrams, and by a virtual photon for the non-resonant one, as shown in Figure 1.3.

    Figure 1.3: The Feynman diagrams for the process e+e− → hadrons (a) strong A3g, (b)electromagnetic Aγ and (c) Acont continuum.

    In a perturbative QCD approach all amplitudes are expected to be almost real, and,

    with these assumptions, maximal interference should occur between the above mentioned

    amplitudes corresponding to a 0◦/180◦ relative phase. On the contrary experimental data

    suggest a phase ∼ 90◦. Such a behaviour has been previously explained by means ofSU(3) symmetry breaking and subsequent restoration [16].

    The relative phase could be extracted investigating the interference pattern of e+e−

    reaction cross section as a function of CM energy (W) near the resonance [17]. The full

    Born cross section for processes including the strong and EM amplitudes can be expressed

    as:

    σ0 ∝ |Ag(W )eiφg,EM + Aγ(W ) + Acont(W )|2, (1.14)

    where φg,EM is the phase between the strong and the full EM amplitudes. The total cross

    section becomes hence:

    σ[nb] = 12πBinBout

    [ cW

    ]2· 107 ·

    [C1 + C2e

    Wris −W − iΓ2+ C3e

    ]2, (1.15)

    where C1, C2 and C3 are proportional to the strong, the electromagnetic and the non-

    resonant amplitudes respectivetely, φ is the relative phase and Bout is the branching ratio

    of the final states [16].

    7

  • 1.8 A Different Theoretical Approach

    A possible explanation by Freund and Nambu is that Quarkonium violates the OZI Rule in

    its decay [8, 18]. One can interpret quarkonium as a superposition of a narrow resonance

    ν, not directly decaying into hadrons, and a wide resonance (a glueball O), not coupled

    to leptons but strongly coupled to hadrons, as shown by the diagrams in Figure 1.4.

    Figure 1.4: The scheme suggested by Freund and Nambu [8], the process being iterated

    in f .

    In this scenario f is the coupling constant between ν and O. In this model, assuming

    Γ >> ΓJ/ψ and f2 ∼ Γo(ΓJ/ψ − Γν), the strong and electromagnetic amplitudes can be

    expressed as:

    Astrong ∼i√BeeMνf

    √Bh

    M2J/ψ −W 2 − iMJ/ψΓJΨ(1.16)

    Aem =

    √BeeMνΓJ/ψ

    √Bem

    M2J/ψ −W 2 − iMJ/ψΓJψ(1.17)

    where Bee, Bh and Bem are the branching fractions related to electron-positron pairs,

    to hadrons and to the continuum respectivetely, Mν and MJ/ψ are the masses of the narrow

    ν and J/ψ, W is the energy in the CM frame, and the factor i in the strong amplitude

    makes it imaginary. The J/ψ shape can be properly reproduced when |f | ∼ 0.012 GeV ,Mo ∼ MJ/ψ, and Γo ∼ 0.5 GeV , where Mo and Γo are the mass and the width of theglueball.

    8

  • Chapter 2

    The BESIII Experiment

    The experimental data analyzed in this work were collected by the Beijing Spectrometer

    III (BESIII) [19]. BESIII is a multipurpose particle spectrometer hosted on the Beijing

    Electron-Positron Collider II (BEPCII) at the Institute for High Energy Physics (IHEP)

    in Beijing, China. The BESIII Collaboration is an international collaboration which

    involves more than 500 members from 72 institutions from 15 countries, including IHEP

    and INFN.

    2.1 The BEPCII

    The Beijing Electron Positron Collider II (BEPCII) is a double-ring e+e− collider with

    two interaction points (IPs). BEPCII is also exploited for synchrotron radiation, taking

    advance of photons emitted in a direction tangential to the particle trajectory. The

    upgrade of BEPC to BEPCII increased the design peak luminosity by two orders of

    magnitude from L ≈ 1031fb−1 to L ≈ 1033fb−1, where L was evaluated in both cases atthe optimal beam energies of 1.89 GeV.

    The luminosity for a circular e+e− collider is given by:

    L0[fb−1] = 2.17 · 1010(1 + r)ξyeE0(GeV )NbNeT0(s)β∗y(cm)

    Fh,

    where E0 is the nominal energy, Ne is the e+e− bunch population, Nb is the bunch num-

    ber, T0 is the revolution time, β∗y is the vertical betatron function at the interaction point,

    r is the interaction point (IP) beam size ratio σ∗y/σ∗x, and ξy is the vertical beam-beam

    tune shift. Fh is the luminosity reduction factor due to the hourglass effect. The values of

    beam-beam tune shifts and the luminosity reduction factor are calculated by beam-beam

    simulations. The storage rings of BEPCII are 237.5 m long and are installed in the tun-

    nels that previously hosted BEPC. In BEPCII, electrons and positrons are accelerated

    from 1.0 GeV up to maximum energy of 2.3 GeV in the linear accelerator Linac, that is

    1.2 km long, before they are injected into the storage rings. The electrons and positron

    circulate in separate vacuum tubes and are therefore brought to collide at a small angle

    of 22 mrad at the interaction point inside the BESIII detector, as shown in Figure 2.1.

    9

  • Figure 2.1: Schematic layout of the Beijing Electron Positron Collider II.

    Both storage rings hold 93 electron/positron bunches each with a bunch spacing of

    8 ns, giving a total beam current of 2× 910 mA (see [20–22]).

    2.2 The BESIII Spectrometer

    The purpose of the BESIII spectrometer, shown schematically in Figure 2.2, is to detect

    particles created in e+e− interactions and their charged and neutral decay products. It is

    composed of different detectors, each one with its peculiar capabilities.

    Figure 2.2: Schematic layout of the BESIII Spectrometer.

    As particles traverse the different BESIII subsystem, signals are collected and used to

    reconstruct the tracks and to perform particle identification (PID). The spectrometer,

    cylindrically symmetric, is mainly hosted inside the 1 T superconducting solenoid, pro-

    viding a geometrical acceptance ∆Ω/4π = 0.93. The main characteristics of each detector

    system will be briefly addressed in the following Sections (see [23–25]).

    10

  • 2.2.1 The Superconductor Solenoid Magnet

    The 1 T magnetic field provided by the superconductor solenoid magnet (SSM) [23] bends

    the trajectories of charged particles inside the detector volume via the Lorentz force.

    The magnetic field enables the determination of momenta of charged particles by

    means of the measurement of curvatures of the trajectories in the MDC. Typically the

    momentum of the particle is given by:

    p = 0.3Bρ,

    where ρ is the radius of the curved paths and B is the magnetic field. In order to

    establish the γ or β factors together with the particle momenta, the other components of

    the spectrometer are used to identify the particles and their masses.

    2.2.2 Multilayer Drift Chamber

    The Multilayer Drift Chamber (MDC) [21, 23] is situated in the central region of BESIII

    surrounding the beam pipe, as shown in Figure 2.3.

    Figure 2.3: Scheme of BESIII MDC.

    The inner radius of the MDC is 60 mm and the outer radius is 810 mm, with a polar

    angle acceptance of |cosθ| < 0.93. The MDC consists of an inner tracker and an outerchamber filled with a gas mixture of 60% He and 40% C3H8. The multilayer drift chamber

    is a gaseous detector used to track the paths of charged particles in the magnetic field

    provided by the SSM. The MDC also provides information of particle energy loss due to

    ionization of the gas (dEdx

    ). The evaluated dEdx

    can be used as input for particle identification

    (PID), since each different kind of particle shows a characteristic correlation among its dEdx

    11

  • and momentum. The basic operating principle of a drift chamber is the following: when a

    charged particle passes through a suitable gas, some of the gas molecules become ionized

    and the charged particle loses parts of its energy.

    Drift chambers, developed in the early ’70s, can be used as well to estimate the lon-

    gitudinal position of a track by exploiting the arrival time of electrons at the anodes if

    the interaction time is known. A drift cell, the basic unit of the drift chamber, consists

    of a sense wire (anode) with a large positive voltage, surrounded by grounded field wires

    (cathodes). As the passage of a charged particle in a drift cell ionizes the gas, electrons

    will start to drift towards the anode. Electrons are collected at the sense wire and thereby

    cause an electric pulse which is amplified by the front-end electronics. After amplifica-

    tion, the signal is branched for timing, charge measurement and for the first level (L1)

    trigger. Signals from different drift cells are combined by pattern matching algorithms to

    form track candidates. Momentum and energy loss per distance traveled in the detector

    (dEdx

    ) are determined for each track. In total, there are 6796 sense wires in the BESIII

    MDC. The BESIII drifts cells consist of a gold-plated tungsten sense wire surrounded by 8

    aluminum field wires. The position resolution, measured at the interaction vertex, in the

    rφ-plane of the MDC is better than 120 µm, and in the z-axis is ∼ 2 mm. The momentumresolution is better than 5% for a particle with transverse momentum of 1 GeV/c. The

    transverse momentum resolution can be expressed as:

    σptpt

    =

    √(σwireptpt

    )2+

    (σmsptpt

    )2,

    where σwirept is the momentum resolution provided by each individual wire spatial resolu-

    tion, and σmspt is the momentum resolution due to multiple scattering. The factors which

    contribute to the dEdx

    resolution are the fluctuation of the number of primary ionizations

    along the track, the recombination loss of electron-ion pair, and the fluctuations in the

    avalanche process.

    2.2.3 The Time-Of-Flight System

    The Time Of Flight System (TOF) [21–23] is located outside the MDC: its barrel section

    covers |cosθ| < 0.83 and its end-cap section 0.85 < |cosθ| < 0.95. The TOF systemconsists of a two staggered-layer barrel sections and two one-layer end-cap sections. The

    two barrel layers are composed of 88 plastic scintillators each and the end-caps of 48

    scintillators. The total lenght of the TOF system is 2.3 m, with a radius of 0.81 m.

    The purpose of the time-of-flight system (TOF) is to provide flight-time measurements

    of charged particles, to be exploited for particle identification (PID). The basic component

    of the TOF system is the scintillation counter. There are two main types of scintillator

    materials, inorganic crystals and organic materials. Common inorganic crystals used

    in scintillation detectors are CsI(T l) and CsI(Na). As a charged particle crosses the

    scintillation material, molecules in the material are excited. Scintillation light is hence

    emitted when the molecules de-excite. As the scintillation light hits the base cathode

    of the photo-multiplier tubes (PMT), electrons are knocked out via the photoelectric

    effect. The electrons are then accelerated in a 2000 V potential over about 5 cm in

    12

  • Figure 2.4: Scheme of BESIII TOF

    the Hamamatsu R5924-70 PMTs, used in the TOF. As electrons hit the dynodes in the

    PMT, additional electrons are knocked out. The subsequent knock-out and acceleration

    of electrons result in a cascade of electrons reaching the anode, producing an electric pulse

    with the charge proportional to the light collected at the photocathode. Each scintillation

    counter consists of a block of plastic scintillator material with two PMTs attached directly

    at the two end faces of the block. Signals from the PMTs are amplified and fed to the

    Front End Electronics (FEE) which splits the signal for timing and charge measurements.

    The time resolution of the TOF system depends on several variables, the single layer

    resolution being in the range 100−110 ps. The main contribution to the uncertainty in thetime measurement comes from the intrinsic time resolution of the scintillation counters.

    Other major contributions to the resolution come from uncertainty in vertex position of

    colliding 15 mm bunches, from the time resolution of the readout electronics, and from

    the error propagation to the expected time of flight from flight path length and momen-

    tum measurements. The overall time resolution σ of the spectrometer can be expressed as:

    σ =√σ2i + σ

    2b + σ

    2l + σ

    2z + σ

    2e + σ

    2t + σ

    2w

    where the value of each term is reported in Table 2.1.

    σ Barrel[ps] EndCap[ps]]

    σi: counter intrinsic time resolution 80 ∼ 90 80σl: uncertainty from 15 mm bunch length 35 35

    σb: uncertainty from clock system ∼20 ∼ 20σθ: uncertainty from θ-angle 25 50

    σe: uncertainty from electronics 25 25

    σt: uncertainty in expected flight time 30 30

    σw: uncertainty from time walk 10 10

    σ1: total time resolution, one layer 100-110 110

    combined time resolution, two layers 80-90 -

    Table 2.1: TOF time resolution performance for 1 GeV/c particles.

    13

  • 2.2.4 Electromagnetic Calorimeter

    The main purpose of the electromagnetic calorimeter (EMC) [21] is to precisely measure

    the energy and position of electrons, positrons and photons. It also provides input to the

    L1 trigger. The EMC is similar to the TOF in terms of operationg principles. However, it

    differs in the choice of scintillator material and light-readout from the scintillator. Since

    one of the main purposes of the EMC is to detect photons, the scintillator needs to be

    composed of a material with large atomic number (Z). This is because the total cross

    section of photons with matter scales with Z. In the typical energy range of photons at

    BESIII, from 25 MeV to 2000 MeV , the main interaction mechanisms with the detector

    material are Compton scattering and pair production.

    As photons or charged particles interact with a scintillator crystal they initialize elec-

    tromagnetic showers. An electromagnetic shower is a process that occurs when highly

    energetic (> a few MeV ) particle give away its energy in the form of e.g. pair production

    (if a photon) or bremsstrahlung (if a charged particle). This initilizes a cascade of events

    where the highly energetic particles undergo bremsstrahlung and pair production, hence

    creating a shower-like process. The electromagnetic shower starting in a seed crystal

    can spread to adjacent crystals, creating a cluster. Each kind of particle have different

    shower pattern characteristics and can therefore be used as input for PID. By the end

    of the process, all the energy of the initial high-energetic particle has been converted

    into a large number of low-energetic photons i.e. into visible light. The light from the

    crystals is converted to electrical signals by photodiodes attached to the back faces of the

    crystals. Photodiodes are compact semiconductor detectors. Like the TOF, the EMC in

    BESIII consists of a barrel section covering |cosθ| < 0.83 and the two end-cap sectionscovering 0.85 < |cosθ| < 0.93. The EMC consists of 6240 CsI(T l) scintillating crystals,each crystal covers approximately 3◦ in the φ direction and 1.5 ÷ 3◦ in the θ direction.The crystals are 28 cm long, with a pyramidal shape. The front and back faces of the

    crystals are square shaped with side lengths of 5.2 cm and 6.4 cm, respectively. The

    main contributions to the energy resolution are imperfections in the crystals and light

    leakage. The design range for photon energy measurement is approximately in the range

    20÷ 2000 MeV , with an energy resolution of 2.5% at 1 GeV and a position resolution ofσxy ≤ 6mm/

    √E(GeV ).

    2.2.5 Muon Identifier

    Since muons and pions have similar masses, 105 MeV/c2 and 139MeV/c2 respectivetely,

    they are difficult to be resolved exploting to perform the PID the TOF and MDC systems

    only. However, muons interact only electromagnetically and weakly.

    Muons can therefore penetrate large amounts of matter without being heavily dis-

    torted. This allows to single them out from the strongly interacting pions. Most pions

    are in fact stopped in either the EMC or in the SSC coil. By placing specialized detec-

    tors inside the SSC coil, in this case resistive plate chambers (RPC), one can combine

    information from the muon chambers (MUC), which is shown in Figure 2.5, the MDC,

    the EMC and the TOF system to tag muons[26].

    RPCs are gaseous detectors where high voltage is applied between two electrodes of

    14

  • Figure 2.5: BESIII Muon Chamber.

    highly resistive bakelite slabs, separated by a compartment filled with a gas mixture con-

    sisting of 50% Ar, 42% C2F4H2 and 8% C4HC10. As muons pass through the gas, they

    ionize the molecules of the gas along their trajectories. The electrons start to drift towards

    the anode (+HV ) in the strong electric field. However, since the electrodes are highly

    resistive, they are essentially ”invisible” to the electrons which are collected by readout

    strips. The readout strips have a width of about 4 cm. In total, there are 9 layers of RPC

    units in the barrel and 8 layers in the end-caps, each layer alternating the direction of the

    readout strips to allow for 2D position measurement.

    2.2.6 Triggers and Data Acquisition

    The goal of the BESIII trigger system [21] is to select relevant Physics events and to

    suppress background from sources other than the e+e− annihilation process. Background

    from cosmic rays, Bhabha scattering (e+e− → e+e−) and beam interactions are expectedto contribute with more than 100 kHz to the total event rate. To suppress the total

    event rate and to keep as many of the Physics events as possible, a two-level trigger

    system is employed. This system consist of the L1 hardware trigger system, and the

    L3 software trigger system. The L1 trigger system is ”online”, i.e. it performs event

    filtering in real time using fast electronics and fast algorithms. The L3 trigger is ”offline”

    and uses more sophisticated algorithms whose computational load is heavier and hence

    require more time. An L1 trigger decision, based on signals from the trigger sub-systems

    of the detector modules’ FEE, is performed every clock cycle. The L1 trigger frequency

    is 41.65 MHz, i.e. the cycle is 24 ns long. The reference time for the L1 timing is

    the accelerator radio frequency (RF) clock with a frequency of 499.8 MHz (2 ns). The

    subsystems that provide input for the L1 trigger are the TOF, the MDC, the EMC and

    the MUC. The final trigger decision is handled with the Global Trigger Logic (GLT).

    Once the L3 trigger filtering has been applied, background events are reduced to below

    1 Hz, while keeping the signal event rate basically constant.

    15

  • 2.3 The BESIII Offline Software System

    The BESIII Offline Software System (BOSS) [27] is a software framework that integrates

    full custom algorithms developed for the BESIII experiment with external algorithms.

    BOSS aims to streamline the analysis chain from interactions in the detector to recon-

    struction and selection of data. BOSS is coded in C++ and builds upon the GAUDI

    framework, originally developed by the LHCb collaboration. The ROOT scientific soft-

    ware framework from CERN, also coded in C++, is heavily exploited in the BOSS frame-

    work. ROOT is also used for visualization, selection and fitting of data. Depending on

    the release, BOSS runs on Scientific Linux versions SLC5 for older versions (< 6.6.4.p01)

    and SLC6 for newer releases. The main tools integrated into BOSS used in the analy-

    ses performed within my thesis are described in the following sections. This work was

    performed within BOSS version 7.0.4.

    2.3.1 Simulation, Reconstruction and Analysis

    Monte Carlo simulations are used to estimate detection efficiency and background, as well

    as to optimize selection criteria. The simulation-to-analysis chain consists of five main

    stages:

    • event generation;

    • transport through detector materials;

    • digitization to simulate detector and trigger response;

    • reconstruction;

    • analysis.

    Reconstruction and analysis of simulated and real data is performed by the same

    algorithms. The only difference is that in the simulations the un-digitized MonteCarlo

    information is retained in parallel to the digitized simulated events [27, 28].

    2.3.2 Event Generation

    The EvtGen framework, coded in C++ as well [21], models all decay distributions cor-

    rectly, and allows at the same time the implementation of new physical models.

    There are approximately 70 models implemented that simulate a large variety of phys-

    ical processes. The modularity of the code allows for easy implementation of additional

    models and all particles property are contained. The decay table contained in the EvtGen

    package provides an extensive list of decays for resonances, and the table is updated with

    the available experimental and theoretical information on a regular basis. There are three

    main components needed to specify a decay channel: the branching ratio, the list of final

    state particles, and the model used to simulate the decay. In this work, the J1BB1 model

    is used, and it is explained in detail in Section 3.1.

    16

  • 2.3.3 Particle Transport and Digitalization

    The particles generated in the previous step are propagated through the BESIII detector

    model implemented in Geant4 [27, 29]. The propagation through the detector material

    takes into account energy loss (ionization), multiple scattering, and magnetic field effects.

    When a particle enters on active detector material, where it interacts, a hit point with

    a perfect resolution is registered. The output from the particle transport is a collection

    of hit points containing information about hit location, time and energy deposit. After

    the particle transport, the collection of hits is digitized. The task of the digitization code

    is to simulate output signals from the readout electronics corresponding to the hits posi-

    tion, smearing hence the initially simulated resolution. Here, energy losses are converted

    into pulse heights and the hit points are converted into hits, whose spatial resolution

    corresponds to the granularity of the detector. The digitized output from the simulated

    detector sub-systems is then feeded to a trigger simulation. After the trigger simulation,

    the events firing the trigger condition are saved as raw data, containing all the information

    output from the detector sub-systems that gave signals during the event. At this stage,

    the simulated data should provide the same information as the real data. During the final

    reconstruction, simulated data and real data are treated by the same algorithms. The

    representation of the BESIIII detector geometry and materials used by Geant4 is stored

    using the Geometry Markup Design Language (GDML) [27]. GMDL is an application-

    independent persistent data format based on XML for describing geometries and materials

    involved in Physics experiments.

    2.3.4 Reconstruction

    The reconstruction algorithm takes as inout the raw data and processes them in order

    to construct more accessible objects for Physics analysis. Such objects are MDC tracks,

    EMC clusters and MUC hits.

    For charged tracks, track reconstruction is performed in two stages. Tracks in the MDC

    are reconstructed by fast pattern recognition algorithms together with TOF information

    for the L1 trigger decisions. Track matching is also performed on the L1 trigger level,

    i.e. information from all detector sub-systems is combined to find matching hits and

    tracks. Information about drift times is taken into account already at trigger level. Then,

    a Kalman track fit is performed by iterating over the hits in the MDC by solving the

    equations of motions. After each step of the fit the track parameters and their covariance

    matrix as well as the χ2 of the fit are updated. Two iterative processes are applied:

    one starting from the interaction vertex of the e+e− as pivot in a forward fit, and the

    other from the last hit in a backward fit, the procedure being performed for the particle

    hypotheses. After the Kalman track fit is completed, a track object is created and stored.

    The track object is used in higher level track selection and as an input to kinematic and

    vertex fits and PID algorithms. The TOF timing is determined by extrapolating tracks

    from the MDC and matching with hits in the TOF.

    17

  • 2.4 BESIII Physics Program

    The BESIII physics program is quite wide and it can be roughly subdived into five topics:

    Charmonium spectroscopy, open Charm decay, light hadron spectroscopy, τ −R−QCDstudies, and new Physics searches. For a more detailed description of the BESIII physics,

    please refer to the BESIII Physics Book [21].

    2.4.1 Charmonium Spectroscopy

    Firstly predicted by the Glashow-Iliopoulos-Maiani (GIM) mechanism [3], the existence

    of the charm quark was confirmed by the J/ψ discovery in the early 70s [8]. Very soon

    its first radial exctitation as well, the ψ(2S), was identified. The discovery of the two

    resonances in the Charmonium spectrum confirmed the possibility to describe these states

    in a spectroscopic approach, as for the atomic structure. Other excited states where hence

    soon predicted. This very simplified model worked properly until the beginning of the

    XXI Century, leading even to the suspect that all the missing states had not yet been

    detected just due to the limited statistics available in literature. In 2003, the discovery

    by the BELLE Collaboration of a very narrow resonance above the open charm threshold

    decaying mostly in π+π−J/ψ changed completely the picture [19]. The X(3872), as it is

    called nowadays, was only the first of several new states unpredicted by the simple Quark

    Model. Most of these states show exotic features (charged Charmonia decay preferentially

    in other Charmonia, rather than into charmed mesons) and nowadays they are usually

    addressed as XY Z states [30].

    2.4.2 Open Charm Decays

    In the past, the interest in the investigation of open charm mesons was limited, since most

    of the more interesting phenomena that can be observed in B meson Physics (Cabibbo-

    Kobayashi-Maskawa transitions, CP violation, D0 − D̄0 oscillation) are weak or verysmall in D spectrum. However, the interest in these processes increased significantly in

    the recent years. On one side, the discovery of the Dsj states revived the interest in

    the charmed meson spectroscopy. On the other side, being the weak forces well-known

    in the SM, it is possible to reach unprecedented precision in the investigation of the

    interplay between strong and weak interaction. Moreover, the tools previously developed

    for the B physics can be tuned and employed in an environment with less background. In

    addition, thanks to the high luminosity of the e+e− colliders, it is possible to be sensitive

    to discrepancies between the SM predictions and experimental data, eventually gaining

    access to New Physics [31].

    2.4.3 Light Hadron Spectroscopy

    Light hadron spectroscopy is a broad sector which includes the search for glueballs (full

    gluonic states), the characterization of η/η′, the search for new resonances of conven-

    tional baryons and mesons. The common issue among all these different branches is the

    18

  • interpretation of the strong interaction in the low energy regime, where the perturbative

    approach cannot be extended [32].

    2.4.4 τ , R, and QCD Studies

    The main Physics goal is the precise measurement of different key parameters of the Stan-

    dard Model (τ properties, muon anomalous magnetic moment), and the investigation of

    the QCD perturbative (determination of the R value) and non-perturbative regime. Even

    though the QCD is a well tested theory, a better knowledge of several parameters requires

    extremely precise measurements, far more precise w.r.t. those available in literature: BE-

    SIII can measure with unprecedented precision hadronic contribution to the muon anoma-

    lous magnetic moment. A working group is dedicated to such precise studies in both the

    perturbative and non-perturbative sections of the QCD spectrum. While electrons and

    muons properties are well understood, τ leptons are yet less known. Such measurements

    are quite challenging, since τ can decay hadronically into a large number of different final

    states, being heavier than many hadrons (Mτ = (1776.86 ± 0.12) MeV/c2). The mainchallenge in such studies arises from the presence of at least one neutrino in each decay

    (ντ , for lepton number conservation), so the kinematic variables of the event can not be

    completely determined, leading to a lower precision in the experimental measurement.

    BESIII took advantage of the possibility to produce the τ pairs at or near the threshold,

    and to scan the line-shape to precisely measure the mass opening providing the most

    precise single measurement of the τ lepton mass. The last data taking was scheduled in

    the data taking period 2017-2018, in order to further improve this measurement.

    In the early years of the investigation of the strong interaction, a key measurement was

    the ratio between the e+e− → hadrons and the e+e− → µ+µ−, addressed R− value. Bydetermining such a ratio, physicist confirmed the existence of a further degree of freedom

    [2], the color, and thus provided the first confirmation of the theory nowadays known

    as Quantum Chromodynamics. After more than 40 years, the precise measurement of

    this ratio it is still an important parameter to be determined when investigating QCD,

    as previously explained in Section 1.2, and to eventually spot any possible discrepancy

    means to gain access to New Physics beyond the Standard Model.

    2.4.5 New Physics beyond the Standard Model

    Although the Standard Model represents the most complete theory to understand the

    world at quantum level, there are several experimental evidences suggesting that there are

    still some open questions and that there are issues not yet fully understood, e.g. neutrino

    masses, naturalness, dark matter, dark energy completeness. The typical energy regime

    in which such issues can be addressed is usually extimated to be in the range between

    ∼ 1 TeV and ∼ 100 TeV . Such high energy ranges leaves most of these searches to thehigher energy accelerators, as LHC [33], and in the future to the possibly-forthcoming

    Circular Electron Positron Collider(CEPC) [22] in China, International Linear Collider

    (ILC)[34] in Japan and Future Circular Collider (FCC) at CERN [19].

    However, in recent years, thanks to the high luminosity delivered by the e+e− colliders,

    19

  • tests for new Physics became available also in the lower energy regime. Among the

    different theories, one foresees the existence of a massive partner of the photon, called

    Dark Photon. This new vector boson behaves as a portal between standard and dark

    particles, it couples directly to the SM photon, and it can decay both in SM electron or in

    supersymmetric partners, like the neutralino of the WIMPs (Weakly Interacting Massive

    Particles) [21].

    20

  • Chapter 3

    Data Analysis

    3.1 Experimental Data

    The process investigated in this work is e+e− → X → pp̄, in the ψ(2S) energy regime. Thedata collected during the 2018 run were analysed using BOSS version 7.0.4, considering

    the data collected at CM energies in the 3.4÷3.8 GeV range by the BESIII Collaborationclose to the ψ(2S) resonance (Mψ(2S) = 3.686 GeV ). These data were collected to perform

    a ψ(2s) lineshape scan and will be also used to evaluate the relative phase between strong

    and electromagnetic decay amplitudes [16, 35]. The nominal energies, the real energies

    with their spread and the integrated luminosities of each collected CM energy data sample

    are shown in Table 3.1

    Nominal E[MeV ] E σE L[pb−1]3580.0 3581.543 0.060 85.7

    3670.0 3670.158 0.063 84.7

    3681.0 3680.144 0.061 84.8

    3683.0 3682.752 0.115 28.7

    3684.0 3684.224 0.119 28.7

    3685.5 3685.264 0.105 26.0

    3686.6 3686.496 0.120 25.1

    3690.0 3691.363 0.075 69.4

    3710.0 3709.755 0.074 70.3

    Table 3.1: Data set collected by BESIII during the 2018 data taking.

    MonteCarlo simulations are used to define proper selection criteria and to estimate

    the reconstruction efficiency. ROOT version 5.34 was used for the analysis. To perform

    efficiency corrections, I have also used the 400M MonteCarlo ψ(2S) inclusive samples,

    provided by the Collaboration and analysed with the BOSS version 7.0.4.

    In this inclusive samples, all the ψ(2S) decays are simulated with their respective

    branching ratios (BR). To generate Charmonium decay events produced from the e+e−

    annihilation, the KKMC+BesEvtGen event generators were used, following the scheme de-

    picted in Figure 3.1.

    21

  • Figure 3.1: Scheme of e+e− annihilation into Charmonia.

    The KKMC [27] was used to simulate the e+e− annihilation into a Charmonium including

    ISR effects, as previously explained in Section 1.6, together with the beam energy spread.

    Then the Charmonium decays have been generated with BesEvtGen, adopting in this work

    the J1BB1 model to simulate the final states. The J1BB1 model distributes the final states

    particle according to the theoretical model described in [2], with an angular distribution

    1 + αcos2θ, where α = 0.68 is a value specific for Charmonium, and assumed to be same

    both at the peak and at the continuum. Events were generated in the e+e− CM [36].

    In total 104 events were generated for each energy value and for each e+e− → γ∗ → pp̄process.

    3.2 Event Selection

    In order to reconstruct Charmonia from the pp̄ final state, the event selection must identify

    events with two good charged tracks reconstructed in the MDC and zero net charge. To

    increase the signal over backround ratio, the following kinematic cuts are required for the

    proton tracks:

    • the point of closest approach to the Interaction Point must be inside a cylinder ofradius 1 cm and longitudinally 10 cm long;

    • proton momentum p ≤ 2 GeV/c, so to have a total event momentum not largerthan Mψ(2S);

    • proton polar angle |cosθ| < 0.8 in the LAB frame, in order to select the barrel regionof the spectrometer, where the sample is more clean;

    • Epp< 0.5, where Ep is the energy deposited in the EMC.

    Moreover the following cuts are applied to both the proton and the antiproton tracks:

    • 178◦ < θ < 180◦, where theta is the angle among the two p and p̄ tracks, in orderto select back-to-back tracks;

    22

  • • PID tags selecting proton and antiproton;

    • specific momentum p cuts, for both proton and antiproton, tuned considering theMonteCarlo simulations.

    In detail, PID information allows to identify the tracks exploiting the probability den-

    sity function method. To be identified as a proton a track candidate: must be associated

    with a probability > 0.001 to be a proton; and this probability must be larger than the

    one to be a kaon or a pion.

    Figures 3.2, 3.3, 3.4, and 3.5 show the MonteCarlo pp̄ pairs angular distributions,

    Eshow/p proton spectra, and 3-momenta distribution of the tracks, respectively, plotted

    for the 9 investigated CM energies listed in Table 3.1.

    166 168 170 172 174 176 178 180

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    Cou

    nts

    Figure 3.2: pp̄ pairs angular distributions for the 165◦÷180◦ region for each CM energy.

    23

  • 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1/ppE

    0

    200

    400

    600

    800

    1000

    1200

    1400Co

    un

    ts

    0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1/ppE

    0

    200

    400

    600

    800

    1000

    1200

    1400

    1600

    1800

    2000

    2200

    Co

    un

    ts

    0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1/ppE

    0

    200

    400

    600

    800

    1000

    1200

    1400

    1600

    1800

    2000

    2200

    Co

    un

    ts

    0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1/p pE

    0

    200

    400

    600

    800

    1000

    1200

    1400

    1600

    1800

    2000

    2200

    2400

    Co

    un

    ts

    0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1/ppE

    0

    200

    400

    600

    800

    1000

    1200

    1400

    1600

    1800

    2000

    2200

    2400

    Co

    un

    ts

    0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1/ppE

    0

    200

    400

    600

    800

    1000

    1200

    1400

    1600

    1800

    2000

    2200

    2400

    Co

    un

    ts

    0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1/ppE

    0

    200

    400

    600

    800

    1000

    1200

    1400

    1600

    1800

    2000

    2200

    2400

    Co

    un

    ts

    0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1/ppE

    0

    200

    400

    600

    800

    1000

    1200

    1400

    1600

    1800

    2000

    2200

    2400

    Co

    un

    ts

    0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1/ppE

    0

    200

    400

    600

    800

    1000

    1200

    1400

    1600

    1800

    2000

    2200

    2400

    Co

    un

    ts

    Figure 3.3: Eshow/p proton spectra for each CM energy.

    24

  • 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1/p

    pE

    0

    200

    400

    600

    800

    1000

    Co

    un

    ts

    0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1/p

    pE

    0

    200

    400

    600

    800

    1000Co

    un

    ts

    0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1/p

    pE

    0

    200

    400

    600

    800

    1000

    1200

    Co

    un

    ts

    0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1/ppE

    0

    200

    400

    600

    800

    1000

    1200

    Co

    un

    ts

    0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1/p

    pE

    0

    200

    400

    600

    800

    1000

    1200

    Co

    un

    ts

    0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1/p

    pE

    0

    200

    400

    600

    800

    1000

    1200

    Co

    un

    ts

    0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1/p

    pE

    0

    200

    400

    600

    800

    1000

    1200

    Co

    un

    ts

    0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1/p

    pE

    0

    200

    400

    600

    800

    1000

    1200

    Co

    un

    ts

    0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1/ppE

    0

    200

    400

    600

    800

    1000

    1200

    Co

    un

    ts

    Figure 3.4: Eshow/p antiproton spectra for each CM energy.

    25

  • 1.2 1.3 1.4 1.5 1.6 1.7

    Mom p [Gev/c]

    1

    10

    210

    310

    Co

    un

    ts

    1.2 1.3 1.4 1.5 1.6 1.7

    Mom p [Gev/c]

    1

    10

    210

    310

    Co

    un

    ts

    1.2 1.3 1.4 1.5 1.6 1.7

    Mom p [Gev/c]

    1

    10

    210

    310

    Co

    un

    ts

    1.2 1.3 1.4 1.5 1.6 1.7

    Mom p [Gev/c]

    1

    10

    210

    310

    Co

    un

    ts

    1.2 1.3 1.4 1.5 1.6 1.7

    Mom p [Gev/c]

    1

    10

    210

    310

    Co

    un

    ts

    1.2 1.3 1.4 1.5 1.6 1.7

    Mom p [Gev/c]

    1

    10

    210

    310

    Co

    un

    ts

    1.2 1.3 1.4 1.5 1.6 1.7

    Mom p [Gev/c]

    1

    10

    210

    310

    Co

    un

    ts

    1.2 1.3 1.4 1.5 1.6 1.7

    Mom p [Gev/c]

    1

    10

    210

    310

    Co

    un

    ts

    1.2 1.3 1.4 1.5 1.6 1.7

    Mom p [Gev/c]

    1

    10

    210

    310

    Co

    un

    ts

    Figure 3.5: Proton momentum spectra for each CM energy; antiproton momentum spectra

    are analogous.

    Figure 3.4 shows clearly how different are the antiproton interactions in the EMC

    w.r.t. the proton ones. This is the reason why no cut has been applied for the antiproton

    26

  • Eshow/p.

    All these cuts were optimized in order to reduce the background in the real dataset

    when performing the analysis of 3-momenta distributions, shown in Figure 3.6. For more

    details see Section 3.5.

    1.2 1.3 1.4 1.5 1.6 1.7Mom p [Gev/c]

    210

    Cou

    nts

    1.2 1.3 1.4 1.5 1.6 1.7Mom p [Gev/c]

    20

    40

    60

    80

    100

    120

    140

    160

    180

    200

    Cou

    nts

    1.2 1.3 1.4 1.5 1.6 1.7Mom p [Gev/c]

    50

    100

    150

    200

    250

    Cou

    nts

    1.2 1.3 1.4 1.5 1.6 1.7Mom p [Gev/c]

    20

    40

    60

    80

    100

    120

    140

    160Cou

    nts

    1.2 1.3 1.4 1.5 1.6 1.7Mom p [Gev/c]

    0

    100

    200

    300

    400

    500

    600

    Cou

    nts

    1.2 1.3 1.4 1.5 1.6 1.7Mom p [Gev/c]

    0

    200

    400

    600

    800

    1000

    1200C

    ount

    s

    1.2 1.3 1.4 1.5 1.6 1.7Mom p [Gev/c]

    0

    200

    400

    600

    800

    1000

    1200Cou

    nts

    1.2 1.3 1.4 1.5 1.6 1.7Mom p [Gev/c]

    50

    100

    150

    200

    250

    300

    350

    Cou

    nts

    1.2 1.3 1.4 1.5 1.6 1.7Mom p [Gev/c]

    40

    60

    80

    100

    120

    Cou

    nts

    Figure 3.6: Proton momentum spectra for each CM energy; the cut on momentum is not

    applied.

    27

  • 3.3 Simulations Efficiency

    Signal events may go undetected due to: the not complete geometrical acceptance of

    BESIII; inefficiencies in the detection; failed or incorrect event reconstruction or event

    selection.

    The agreement between the real dataset and the performed MonteCarlo simulations

    must be carefully verified, in order to have full control of the acceptance corrections,

    which are needed and are crucial to evaluate the cross section. The efficiency is strictly

    connected to the choice of the MonteCarlo Generator, that mimics the underlying Physics

    as closely as possible to estimate detection efficiency, as explained in the previous sections.

    The efficiency is evaluated dividing the number of reconstructed ψ(2S) events by the total

    number of the generated ones.

    The statistical uncertainty in ε is estimated as binomial:

    σεε

    =

    √1− ε

    Ngenerated(3.1)

    The values of reconstructed events obtained from the MonteCarlo simulations for the

    different CM energies are reported in Table 3.2.

    Nominal Energy [MeV ] Nreconstructed Efficiency Error Efficiency

    3580.0 110 0.7025 0.0038

    3670.0 180 0.7002 0.0038

    3681.0 257 0.6941 0.0038

    3683.0 304 0.6981 0.0038

    3684.0 1408 0.6959 0.0038

    3685.5 3113 0.6944 0.0038

    3686.6 2955 0.6998 0.0038

    3690.0 622 0.6952 0.0038

    3710.0 300 0.6951 0.0038

    Table 3.2: Number of reconstructed events from the MonteCarlo simulations and efficiency

    for each CM energy.

    Figure 3.7 shows as an overall efficiency of 70% can be achieved.

    28

  • 3580 3600 3620 3640 3660 3680 3700 3720 E[MeV]

    0.6

    0.65

    0.7

    0.75

    0.8

    0.85

    0.9ε

    Figure 3.7: Efficiency, the red dashed line is at the fixed value of 0.70.

    3.4 ISR Correction

    Due to the nature of the ISR correction, an iterative process is needed. A custom algorithm

    was implemented, exploiting the Bonneau-Martin formula [11], and evaluating the ISR

    correction by mean of the hit-or-miss method. In detail, the nominal energy W of the

    process, with its spread (see Table 3.1), is the input for the extraction of the momenta

    of the ISR photon and for the evaluation of its effect on the collinearity. The probability

    distribution of the ISR photon p(k)dk = βkβ−1 is strictly correlated to the factor β:

    β = 4 · α/π · [ln(W1/me)− 0.5], (3.2)

    where α = 1/137 is the fine-structure constant, W1 is the energy after the spread, and

    me is the electron mass. Generally, the factor β is parametrized as:

    β = 2α

    π(ln(

    Q2

    m2)− 1), (3.3)

    where Q is the Q-value of the process, and the scale depends on the actual interaction

    process. For example, for a central production process, it can be defined as Q2 = s =

    4Ecm. According to Touscheck [37] the correction factor can be expressed as:

    C =∣∣1− E(1−β)n + 0.5E(2−β)n ∣∣ , (3.4)

    29

  • 900 1000 1100 1200 1300 1400 1500 1600 1700Mom p [GeV/c]

    50

    100

    150

    200

    250

    Cou

    nts

    Figure 3.8: Proton momenta distributions due to ISR effects for the nominal energy of

    E = 3.710 GeV .

    where R is the integral of the probability distribution and En = k/R is the energy after

    the correction. The correction factor from Equation 3.4 can be simulated by means of

    the hit-or-miss method. The hit-or-miss MonteCarlo method generates random points in

    a approximately bounded area and counts the number of ”hits” that contribute hence an

    estimation of the area one wants to evaluate.

    The energy after the ISR (W2) can be calculated as:

    W2 =√W 21 − 2 · k ·W1. (3.5)

    At a given energy W2, the momenta of both proton and antiproton can be finally

    determined with a Lorentz transformation assuming, as previously explained in Section

    3.1, an angular distribution 1 + αcos2(θ) in the LAB frame. An example of the ISR

    momenta distribution is shown in Figure 3.8.

    The energy after the ISR, the proton and the antiproton momenta, their collinearity

    and the angle of pp̄ pairs in the CM frame can hence be easily determined. Theoretical pre-

    dictions suggest an ISR ptohon energy ∼ 50 MeV [12, 37], and its effect on the collinearityshould be hence 4◦ at most. A statistical approach would be useful for the qualitative

    understanding of the obtained results which are in agreement with the observations.

    3.5 Background Studies

    Due to the clear relevance of the background within the real dataset collected in the

    continuum region, an analysis of MonteCarlo simulated data is performed in order to

    qualitatively evaluate the impact of misidentified events on the event selection. The

    following background processes were investigated:

    e+e− → J/ψ → pp̄, (1)

    30

  • e+e− → e+e−, (2)

    e+e− → µ+µ−, (3)

    e+e− → K+K−, (4)

    e+e− → π+π−.(5)

    2.5 2.6 2.7 2.8 2.9 3 3.1 3.2 3.3 3.4 3.5]2 [GeV/cinvM

    0

    1

    2

    3

    4

    5

    Cou

    nts

    Figure 3.9: Invariant mass for (1) at nominal energy of 3.670 GeV , real dataset.

    Background studies aim to verify if the application of the same selection criteria

    adopted for the signal, and described in Section 3.2, is enough to clearly remove the back-

    ground. The considered channels have a Branching Ratio and a Cross Section greater

    by more than one order of magnitude with respect to the process analyzed [9]. More-

    over, the processes (2), (3), (4), (5) were selected due to the kinematic reasons. In a two

    body-decay, the particle 3-momenta can be obtained as:

    |p| =√M2 − 4m2x

    2, (3.6)

    where M is the invariant mass in the center of mass frame, and mx is the mass of the

    chosen candidate as final states.

    The background processes were investigated exploiting 104 simulated events, applying

    the same selection adopted for the analysis of the real data. Basically no event passed

    such selection in the momentum region relevant for our investigation for the processes

    (2) and (3); the processes (4) and (5) were excluded as well, as consequence of the PID

    tag, although PID can still sometime fail. Moreover the process (1) was useful for the

    optimization of the lower cuts on the 3-momenta. For the first CM energy, in particular,

    a lower cut on the momenta (Ppp̄ ≥ 1.2 GeV/c) was chosen, due to the kinematics of theevent. Figures 3.9, 3.10 and 3.11 clearly show how effective are the selection criteria to

    reject the considered backround processes both in the real and in the simulated datasets.

    An irreducible background is the pp̄γ final state, which can be considered as the

    principal radiative contribution to the background in our sample. But such a background

    31

  • 2 2.5 3 3.5 4 4.5 5

    Minv (GeV/c^2)

    0

    20

    40

    60

    80

    100

    120

    140

    160

    180

    200

    2 2.5 3 3.5 4 4.5 5

    Minv (GeV/c^2)

    0

    0.2

    0.4

    0.6

    0.8

    1

    Figure 3.10: Invariant mass for (2) at nominal energy 3.670 GeV , MonteCarlo simulations.

    2 2.5 3 3.5 4 4.5 5

    Minv (GeV/c^2)

    0

    20

    40

    60

    80

    100

    120

    140

    160

    180

    200

    2 2.5 3 3.5 4 4.5 5

    Minv (GeV/c^2)

    0

    0.2

    0.4

    0.6

    0.8

    1

    Figure 3.11: Invariant mass for (3) at nominal energy 3.670 GeV , MonteCarlo simulations.

    can be accounted for performing a simultaneous fit on the proton and the antiproton, as

    explained in Section 3.6.

    3.6 Simultaneous Fit

    In order to achieve the best signal over background ratio and to extract the number of pp̄

    pairs, a 2-dimensional fit of the pp̄ scatter plot was performed.

    32

  • 1.4 1.45 1.5 1.55 1.6 1.65 1.7

    Mom p (GeV/c)

    0

    200

    400

    600

    800

    1000

    1200

    1400

    Eve

    nts

    1.4 1.45 1.5 1.55 1.6 1.65 1.7

    Mom p (GeV/c)

    0

    200

    400

    600

    800

    1000

    1200

    1400

    Eve

    nts

    1.4 1.45 1.5 1.55 1.6 1.65 1.7

    Mom p (GeV/c)

    0

    200

    400

    600

    800

    1000

    1200

    1400

    Eve

    nts

    1.4 1.45 1.5 1.55 1.6 1.65 1.7

    Mom p (GeV/c)

    0

    200

    400

    600

    800

    1000

    1200

    1400

    Eve

    nts

    1.4 1.45 1.5 1.55 1.6 1.65 1.7

    Mom p (GeV/c)

    0

    200

    400

    600

    800

    1000

    1200

    1400

    Eve

    nts

    1.4 1.45 1.5 1.55 1.6 1.65 1.7

    Mom p (GeV/c)

    0

    200

    400

    600

    800

    1000

    1200

    1400

    Eve

    nts

    1.4 1.45 1.5 1.55 1.6 1.65 1.7

    Mom p (GeV/c)

    0

    200

    400

    600

    800

    1000

    1200

    1400

    Eve

    nts

    1.4 1.45 1.5 1.55 1.6 1.65 1.7

    Mom p (GeV/c)

    0

    200

    400

    600

    800

    1000

    1200

    1400

    Eve

    nts

    1.4 1.45 1.5 1.55 1.6 1.65 1.7

    Mom p (GeV/c)

    0

    200

    400

    600

    800

    1000

    1200

    1400

    Eve

    nts

    Figure 3.12: Proton momentum spectra for each CM energy, MonteCarlo simulations.

    Figures 3.12, 3.13, 3.14 and 3.15 show the p and p̄ momenta spectra for the signal

    simulation and for the experimental data, respectively. The distributions were fitted with

    a CrystalBall (CB) function [38] plus a flat background for the simulations, and a zero

    or first order polynomial for the real dataset (for the first two energies values). The

    3-momenta distributions are not symmetric, so the CB function is needed in order to

    consider possible ISR contributions. The CrystalBall function is a probability density

    33

  • 1.4 1.45 1.5 1.55 1.6 1.65 1.7

    (GeV/c)pMom

    0

    200

    400

    600

    800

    1000

    1200

    1400

    Eve

    nts

    1.4 1.45 1.5 1.55 1.6 1.65 1.7

    (GeV/c)pMom

    0

    200

    400

    600

    800

    1000

    1200

    1400

    1600

    Eve

    nts

    1.4 1.45 1.5 1.55 1.6 1.65 1.7

    (GeV/c)pMom

    0

    200

    400

    600

    800

    1000

    1200

    1400

    Eve

    nts

    1.4 1.45 1.5 1.55 1.6 1.65 1.7

    (GeV/c)pMom

    0

    200

    400

    600

    800

    1000

    1200

    1400

    Eve

    nts

    1.4 1.45 1.5 1.55 1.6 1.65 1.7

    (GeV/c)pMom

    0

    200

    400

    600

    800

    1000

    1200

    1400

    Eve

    nts

    1.4 1.45 1.5 1.55 1.6 1.65 1.7

    (GeV/c)pMom

    0

    200

    400

    600

    800

    1000

    1200

    1400

    Eve

    nts

    1.4 1.45 1.5 1.55 1.6 1.65 1.7

    (GeV/c)pMom

    0

    200

    400

    600

    800

    1000

    1200

    1400

    Eve

    nts

    1.4 1.45 1.5 1.55 1.6 1.65 1.7

    (GeV/c)pMom

    0

    200

    400

    600

    800

    1000

    1200

    1400

    Eve

    nts

    1.4 1.45 1.5 1.55 1.6 1.65 1.7

    (GeV/c)pMom

    0

    200

    400

    600

    800

    1000

    1200

    1400

    Eve

    nts

    Figure 3.13: Antiproton momentum spectra for each CM energy, MonteCarlo simulations.

    function, and is the convolution of Gaussian and a power-law low end tail below a certain

    threshold:

    f(x, α, n, x̄, σ) = N

    exp(− (x−x̄)

    2

    2σ2

    )forx−x̄

    σ> −α

    A ·(B − x−x̄

    σ

    )−nforx−x̄

    σ≤ −α

    (3.7)

    34

  • 1.4 1.45 1.5 1.55 1.6 1.65 1.7

    Mom p (GeV/c)

    0

    5

    10

    15

    20

    25

    30

    35

    40

    Eve

    nts

    1.4 1.45 1.5 1.55 1.6 1.65 1.7

    Mom p (GeV/c)

    0

    5

    10

    15

    20

    25

    30

    35

    Eve

    nts

    1.4 1.45 1.5 1.55 1.6 1.65 1.7

    Mom p (GeV/c)

    0

    20

    40

    60

    80

    100

    120

    Eve

    nts

    1.4 1.45 1.5 1.55 1.6 1.65 1.7

    Mom p (GeV/c)

    0

    10

    20

    30

    40

    50

    60

    70

    80

    90

    Eve

    nts

    1.4 1.45 1.5 1.55 1.6 1.65 1.7

    Mom p (GeV/c)

    0

    50

    100

    150

    200

    250

    300

    Eve

    nts

    1.4 1.45 1.5 1.55 1.6 1.65 1.7

    Mom p (GeV/c)

    0

    100

    200

    300

    400

    500

    600

    700

    Eve

    nts

    1.4 1.45 1.5 1.55 1.6 1.65 1.7

    Mom p (GeV/c)

    0

    100

    200

    300

    400

    500

    600

    Eve

    nts

    1.4 1.45 1.5 1.55 1.6 1.65 1.7

    Mom p (GeV/c)

    0

    20

    40

    60

    80

    100

    120

    140

    160

    Eve

    nts

    1.4 1.45 1.5 1.55 1.6 1.65 1.7

    Mom p (GeV/c)

    0

    5

    10

    15

    20

    25

    30

    35

    40

    45

    Eve

    nts

    Figure 3.14: Proton momentum spectra for each CM energy, real dataset.

    where

    A =

    (n

    |α|

    )nexp

    (−|α|

    2

    2

    ),

    B =n

    |α|− |α|,

    35

  • 1.4 1.45 1.5 1.55 1.6 1.65 1.7

    (GeV/c)pMom

    0

    5

    10

    15

    20

    25

    30

    Eve

    nts

    1.4 1.45 1.5 1.55 1.6 1.65 1.7

    (GeV/c)pMom

    0

    5

    10

    15

    20

    25

    30

    Eve

    nts

    1.4 1.45 1.5 1.55 1.6 1.65 1.7

    (GeV/c)pMom

    0

    20

    40

    60

    80

    100

    120

    Eve

    nts

    1.4 1.45 1.5 1.55 1.6 1.65 1.7

    (GeV/c)pMom

    0

    10

    20

    30

    40

    50

    60

    70

    80

    90

    Eve

    nts

    1.4 1.45 1.5 1.55 1.6 1.65 1.7

    (GeV/c)pMom

    0

    50

    100

    150

    200

    250

    300

    Eve

    nts

    1.4 1.45 1.5 1.55 1.6 1.65 1.7

    (GeV/c)pMom

    0

    100

    200

    300

    400

    500

    600Eve

    nts

    1.4 1.45 1.5 1.55 1.6 1.65 1.7

    (GeV/c)pMom

    0

    100

    200

    300

    400

    500

    600

    Eve

    nts

    1.4 1.45 1.5 1.55 1.6 1.65 1.7

    (GeV/c)pMom

    0

    20

    40

    60

    80

    100

    120

    140

    160

    Eve

    nts

    1.4 1.45 1.5 1.55 1.6 1.65 1.7

    (GeV/c)pMom

    0

    5

    10

    15

    20

    25

    30

    35

    40

    45

    Eve

    nts

    Figure 3.15: Antiproton momentum spectra for each CM energy, real dataset.

    N =1

    σ(C +D),

    C =n

    |α|1

    n− 1exp

    (−|α|

    2

    2

    ),

    36

  • D =

    √π

    2

    (1 + erf(

    |α|√2

    )

    ),

    where N is a normalization factor, α, n, x̄ and σ are parameters which are fitted with

    the data in Figures 3.14 and 3.15. For each plot the blue line represents the fit on the

    data, the red dashed line only the signal distribution, and the light blue and brown dashed

    lines show the shape of the background on x axis convoluted with the CB shape along y

    axis and viceversa.

    Such an approach shows a good signal over background ratio at the energies closer

    to the resonance, while the contribution from background is comparable to the signal at

    lower energies. The fitting procedures always provide reasonable χ̃2 for each CM energy,

    as reported in Tables 3.3 and 3.4.

    Nominal Energy [MeV ] Nevents σE χ̃2x χ̃2y

    3580.0 6594 81 0.26 0.29

    3670.0 6543 81 0.20 0.42

    3681.0 6555 81 0.21 0.20

    3683.0 6536 81 0.18 0.13

    3684.0 6588 81 0.33 0.24

    3685.5 6572 81 0.18 0.17

    3686.6 6586 81 0.23 0.14

    3690.0 6581 81 0.23 0.38

    3710.0 6536 81 0.20 0.24

    Table 3.3: Number of pp̄ pairs selected at each CM energy for MonteCarlo simulations.

    Nominal Energy [MeV ] Nevents σE χ̃2x χ̃2y

    3580.0 81 9 0.12 0.08

    3670.0 63 8 0.12 0.11

    3681.0 537 23 0.18 0.24

    3683.0 350 19 0.10 0.10

    3684.0 1397 38 0.08 0.10

    3685.5 3098 56 0.14 0.12

    3686.6 2934 54 0.10 0.09

    3690.0 741 27 0.15 0.16

    3710.0 236 15 0.10 0.12

    Table 3.4: Number of pp̄ pairs selected at each CM energy for the real dataset.

    The number of pp̄ pairs is obtained by calculating the integral of each signal distribu-

    tion within 3σ from its peak value, as Npp̄ = I ∗ Nsignal, where I is the integral and Npp̄is the number of signal events from the fit.

    The errors where estimated assuming a poissonian distribution, thus σN =√Npp̄

    [39]. Once determined the number of signal events, the cross section can be evaluated as

    explained in Section 1.5.

    37

  • 3.7 Systematic Uncertanties

    Systematic uncertanties play an important role in the measurement of physical quantities,

    as they are often of comparable scale w.r.t. the statistical ones. They arise from different

    sources: the value of the parameters used to perform event selection and the specific

    values of the fit. In order to be more conservative as possible, a wide variation interval

    was chosen. From those variation, the number of pp̄ pairs was again calculated, performing

    simultaneous fits. The variations on the selection criteria are summarized in Table 3.5.

    Cut Value Variation

    Eshow/p 0.5 ± 0.05θpp̄ 178

    ◦ < < 180◦ −0.5◦ and +1◦

    fit −3σ < < 3σ ± 0.5PID 0.00 + 0.001

    Table 3.5: Parameter values used for the event selection and their variations to evaluate

    the systematic errors.

    A 1% per track was taken into account for the systematic error coming from tracking.

    To obtain an estimation of the systematic errors relative to each cut variation, the weighted

    average between the number of events of the analysis and the one with the parameter

    change was calculated.

    To be more specific the weighted average and its error has been evaluated by:

    x̄ =

    ∑ixiσ2xi∑

    i1σ2xi

    (3.8)

    and

    σ2x =1∑i

    1σ2xi

    (3.9)

    where xi are the measurements and σxi their errors. The total systematic error was

    obtained by summing in quadrature each single contribution:

    σsyst =

    √∑i

    σ2i (3.10)

    where σi is the weighted average error of the number of events extracted from the simul-

    taneous fit. The obtained values are shown in Table 3.6.

    In order to investigate the systematic errors due to the fitting function, the sideband

    method [40] was used. The sideband method allows to divide a 2-dimensional plot into

    areas: one for the signal, and eight for the background estimation. The three regions are

    defined, as shown in Figure 3.17.

    38

  • 1.4 1.45 1.5 1.55 1.6 1.65 1.7

    Mom p (GeV/c)

    0

    5

    10

    15

    20

    25

    30

    35

    40

    Eve

    nts

    1.4 1.45 1.5 1.55 1.6 1.65 1.7

    Mom p (GeV/c)

    0

    5

    10

    15

    20

    25

    30

    35

    Eve

    nts

    1.4 1.45 1.5 1.55 1.6 1.65 1.7

    Mom p (GeV/c)

    0

    20

    40

    60

    80

    100

    120

    Eve

    nts

    1.4 1.45 1.5 1.55 1.6 1.65 1.7

    Mom p (GeV/c)

    0

    10

    20

    30

    40

    50

    60

    70

    80

    90

    Eve

    nts

    1.4 1.45 1.5 1.55 1.6 1.65 1.7

    Mom p (GeV/c)

    0

    50

    100

    150

    200

    250

    300

    Eve

    nts

    1.4 1.45 1.5 1.55 1.6 1.65 1.7

    Mom p (GeV/c)

    0

    100

    200

    300

    400

    500

    600

    700

    Eve

    nts

    1.4 1.45 1.5 1.55 1.6 1.65 1.7

    Mom p (GeV/c)

    0

    100

    200

    300

    400

    500

    600

    Eve

    nts

    1.4 1.45 1.5 1.55 1.6 1.65 1.7

    Mom p (GeV/c)

    0

    20

    40

    60

    80

    100

    120

    140

    160

    Eve

    nts

    1.4 1.45 1.5 1.55 1.6 1.65 1.7

    Mom p (GeV/c)

    0

    5

    10

    15

    20

    25

    30

    35

    40

    45

    Eve

    nts

    Figure 3.16: Proton momentum spectra for each energy value with a different parameter

    of PID.

    The number of pp̄ events (N0) was extracted with the sideband method as:

    N0 = N −1

    2B +

    1

    4A, (3.11)

    where N is the number of events in the signal region, and A and B are the number of

    events in the corresponding regions, shown in Figure 3.17. For this study the 4σ − 10σregions were considered, and all the obtained distributions are similar to the one shown

    in Figure 3.18.

    39

  • Energy [MeV ] NEshow/p σEshow/p NT σT NPID σPID NF* σF σtot3580.0 80.03 5.19 6.05 0.94 80.55 8.97 93.51 5.36 9.84

    3670.0 62.77 4.57 10.94 2.54 62.77 7.92 122.54 5.23 9.28

    3681.0 537.38 13.38 27.02 3.29 537.38 23.18 531.39 13.11 25.11

    3683.0 349.42 10.80 12.73 2.38 350.28 18.72 349.87 10.71 20.31

    3684.0 1381.20 21.54 5.17 1.66 1396.93 37.38 1405.44 21.23 40.20

    3685.5 3076.45 32.09 45.88 4.06 3097.80 55.66 3126.30 31.87 60.09

    3686.6 2938.12 31.29 31.07 3.83 2094.12 54.17 3125.32 31.58 58.82

    3690.0 736.47 15.68 21.02 2.83 740.49 27.21 752.39 15.43 29.37

    3710.0 236.59 8.87 53.67 3.44 236.59 15.38 259.07 8.91 16.97

    Table 3.6: Number of events and their error for each parameter variation and total sys-

    tematic error.

    Figure 3.17: Example of sideband definition taken from [41].

    3.8 Inclusive Simulations

    The BESIII Collaboration provided a 400M events inclusive MonteCarlo sample, pro-

    duced for the analysis of the 2012 ψ(2S) data taking. The final states were generated

    according to the LUNDCHARM model [42], and the simulated events were reconstructed and

    analysed with the BOSS version 6.6.4.p03. The list of the processes considered in the

    production of the inclusive ψ(2S) dataset is reported in Table 3.7.

    The number of pp̄ in the final state was determined performing the same event selection

    procedure described above for the real dataset. Figure 3.19 shows the obtained spectrum.

    The advantage of this approach is that the detection efficiency of inclusive ψ(2S)

    decays can be extracted directly from the data sample already analyzed [43]. After ap-

    plying the same selection criteria as for the real data and using the sideband method,

    40

  • 1.4 1.45 1.5 1.55 1.6 1.65 1.7Mom p [GeV/c]

    1.4

    1.45

    1.5

    1.55

    1.6

    1.65

    1.7

    [GeV

    /c]

    pM

    om

    Figure 3.18: Bi-dimensional scatter plot of pp̄ at 3.684 GeV.

    Decay Branching Ratio

    pp̄π0 (1.53± 0.07)x10−4

    ηpp̄ (6.0± 0.4)x10−5

    ωpp̄ (6.9± 2.1)x1