Quark Pesanti Spettroscopia del Charmoniobettoni/particelle/charmonium.pdf · 2005. 6. 1. · Diego...

Quark PesantiSpettroscopia del Charmonio

Diego Bettoni Charmonium 2

The Discovery of Charm

The charmonium system was discovered in November 1974, when two experimental groups at Brookhaven and SLAC announced almostsimultaneously the discovery of a new, narrow resonance, later to becalled J/ψ.

The new resonance had a mass of roughly 3100 MeV/c2 and anextremely narrow width. Present values from PDG 2004 edition:

M(J/ψ)=(3096.916 ± 0.011) MeV/c2

Γ(J/ψ) =(91.0±3.2) keVThis was followed very shortly by the discovery, by the SLAC group, ofanother narrow state, called ψ′.

M(ψ′)=(3686.093 ± 0.034) MeV/c2

Γ(ψ′) =(277±22) keV


The Brookhaven Signal

XeeBepJ

++→+ −+321


The SLAC Signals

hadronsee →→−+ ψ

−+−+ →→ µµψee

−+−+ →→ eeee ψ


Measurement of the J/ψ Total Width - I

The cross section for the process a+b→R→c+d is given by the Breit-Wigner formula:

where k, s1 and s2 are the CMS momentum and spins of a and b; J, MR and Γ are the resonance spin and mass and total width, E is theCMS energy, Γab and Γcd are the partial widths for R→ab and R→cd.If G(E) is the beam distribution function, the measured cross section is:

4)()12)(12(

12)( 22

221 Γ+−

ΓΓ++

+=R

cdabBW

MEkssJE πσ

∫∞ ′−′′= 0 )()()( EdEEGEE BWσσ


The area under the resonance is given by:

where σpeak is the value of the Breit-Wigner cross section at E=MR. The area under the resonance is thus independent of the form of G(E):if G(E) is unknown, then the value of the resonance width Γ can beobtained from the measured area (indirect determination of Γ). This ishow the J/ψψψψ and ψ′ψ′ψ′ψ′ total widths were determined at SLAC.On the other hand, if G(E) is known, than Γ can be determined directlyfrom the analysis of the shape of the measured excitation function (i.e. the measured cross section as a function of the CMS energy).

Measurement of the J/ψ Total Width - II

∫∞ Γ== 0 2

)( peakdEEA σπσ


The J/ψ and ψ′ as c c states

The J/ψ and the ψ′ are formed directly in e+e- annihilation, therefore they have the quantum numbers of the photon: JPC=1--.

Their extremely narrow width makes it impossible to understand these new states in terms of the light u,d,s quarks.They are interpreted as bound states of a new quark (c) and itsantiquark ( c), whose existence had been predicted in 1970 to accountfor the non existence of Strangeness Changing Neutral Currents.

e-

e

γ+

e-

e+

,µ

µ

+

-,

J/ ψ


The J/ψ Width and the OZI rule

Decay rates described by diagrams with unconnected quark lines aresuppressed.

c-

u

d-

d-

u-

3 g

π+

π0

-π

ψc

d

d

J/d

-D

D+

-g

J/

c

-c

c

-c

ψd

OZI suppressedOZI allowedforbidden by energy conservation


Why is Charmonium Interesting ?

Charmonium is a powerful tool for the understanding of the stronginteraction. The high mass of the c quark (mc ~ 1.5 GeV/c2) makes itplausible to attempt a description of the dynamical properties of the(c c) system in terms of non-relativistic potential models, in which thefunctional form of the potential is chosen to reproduce the known asymptotic properties of the strong interaction. The free parameters inthese models are determined from a comparison with experimental data.

Non-relativistic potential models + Relativistic corrections + PQCD

β2 ≈ 0.2 αs ≈ 0.3


The Non-Relativistic Potential

The functional form of the potential is chosen to reproduce the knownasymptotic properties of the strong interaction.

• At small distances asymptotic freedom, the potential is coulomb-like:

• At large distances confinement:

rrrV s

r)(

34)( 0

α−→ →

krrV r → ∞→)(


The Non-Relativistic Potential II

)ln()3211(

4)(2

2

Λ−

=µ

πµαf

s

n

nf = number of flavoursΛ ~ 0.2 GeV QCD scale parameterk string constant (~ 1 GeV/fm)


The Spin-Dependent Potential

TSSLSSD VVVH ++=

−⋅=

drdV

drdV

rmSLV SV

cLS 3

2)(

2

rr

( ) )(3

2 22

21 rVm

SSV Vc

SS ∇⋅=rr

( )( )[ ]

−−⋅⋅= 2

2

2

2 112

ˆˆ32dr

Vddr

dVrm

SrSrSV VV

cT

rr

spin-orbit(fine structure)

spin-spin(hyperfine structure)

tensor

VS and VV are the scalar and vector components of the non-relativistic potential


The Spin-Dependent Potential II

• The Coulomb-like part of V(r) corresponds to one-gluon exchange and contributes only to the vector part of the potential VV. The scalar part is due to the linear confining potential. This could in principle contribute to both VS and VV, but the fit to the χcJ masses suggests that the VV contribution is small.

• The charmonium mass spectrum can be computed also within the framework of Lattice QCD (LQCD), which is essentially QCD applied to a discreet 4-dimensional space with given spacing a.

• Non Relativistic QCD (NRQCD) provides another framework for the calculation of the heavy quarkonium spectrum. In NRQCD the various dynamical scales m, mv, mv2 in the production and decay processes are well separated.


Charmonium Decay

• One of the key features of charmonium states below D D threshold is the narrow width. These states decay violating the OZI rule.

• States above threshold can generally decay to open charm, except if forbidden by some conservation rule: in this case these states are also narrow.

• Electromagnetic decays are calculable with high accuracy in QED, but it is the strong interaction which describes the c c bound state. – e+e- decay of vector states.– γγdecay of J-even states.– γγγdecay – radiative transitions

• Strong decays must be calculated in QCD. Due to the high value of αs, QCD cannot always be treated as a perturbative theory.


Electromagnetic Decays - I

Charmonium decay to lepton pairs or to a pairof light quarks (u,d,s). Only possible for vectorstates (JPC=1--), e.g. the J/ψ or the ψ′. Van Royen – Weisskopf formula (at LO in αs):

( )

−

Ψ=→Γ −+

παπαψ

3161

4)0(

16/ 2

222 s

cc m

eeeJ

where |Ψ(0)| is the module of the c c wave function at the origin.

Three-photon decay. Only possible for C-odd states. This decay is notobserved experimentally for any c c state because of the small branchingratio. NLO in α and LO in αs.

( ) ( )

−

Ψ−=→Γ

πααπγγγ s

cc m

eS 6.121)0(

93

162

2632

13


Electromagnetic Decays - II

Two-photon decay. Forbidden for J=1 states byYang’s theorem. Partial widths can be calculatedusing QED in analogy to positronium decay to γγ.(R′(0) is the derivative of the non relativistic P-wave function at the origin)

( )

−

Ψ=→Γ

παπαγγη s

ccc m

e 4.31)0(

12 2

242

( )

+

′=→Γ

πααγγχ s

ccc m

Re 2.01

)0(27 4

242

0

( )

−

′=→Γ

πααγγχ

3161

)0(5

364

242

2s

ccc m

Re


Radiative Transitions

• Electric dipole (E1) transitions obey the selection rules ∆L=±1, ∆S=0. The transitions widths are given by:

where k is the photon momentum, i and f denote initial and final staterespectively and Eif is the transition dipole matrix element.

• Magnetic dipole (M1) transitions obey ∆L=0, ∆S=±1.

232

94

1212

)( ifci

f EkeJJ

PS αγ ⋅++

=+→Γ

232

94)( ifc EkeSP αγ =+→Γ

2

220

12

01

13

)(/134)( if

cc I

kSMkk

mkeSS

++=+→Γ αγ


Hadronic Decays - I

Annihilation of the c c pair in theappropriate number of hard gluonsor q q pairs (gg, ggg, g(q q ) etc.)

Can be treated perturbatively.Charmonium decay to light hadrons.

Hadronic de-excitation of charmonium (emission of soft gluons). The low momentumcarried by the gluons makes thisprocess non perturbative.e.g. ψ′→J/ψππ.


Hadronic Decays – II

( )

+

Ψ=→Γ

παπαη s

csc m

gg 8.41)0(

38

2

22

( )

+

′=→Γ

πααχ s

csc m

Rgg 5.91

)0(6 4

22

0

( )

−

′=→Γ

πααχ s

csc m

Rgg 2.21

)0(58

4

22

2

( ) ( )

−

Ψ−=→Γ

πααπψ s

cs m

gggJ 7.31)0(

98140/ 2

232

For these states theratio of the γγwidthto the hadronic widthcan be used to estimate αs.


Experimental Methods for the Study of Charmonium

• e+e- collisions (SLAC: Mark I, II, III, TPC, Crystall Ball; DESY: DASP and PLUTO; LEP; CESR: CLEO, CLEO-c; BEPC BES; B-factories: BaBar and Belle).– direct formation– two-photon production– initial state radiation– B meson decay– double charmonium

• p p annihilations (CERN R704, FNAL E760 E835, GSI PANDA)• hadroproduction (CDF, D0, LHC, BTEV)• electroproduction (HERA)


Direct Formation e+e-→c c

In e+e- annihilations direct formation is possibleonly for states with the quantum numbers of thephoton JPC=1--: J/ψ, ψ′ and ψ(3770).

All other states can be produced inthe radiative decays of the vectorstates. For example:

XSee +→′→+ −+ γψ )2(

Crystal Ball inclusive photon spectrum

The precision in the measurement of massesand widths is limited by the detector resolution.


Two-photon Production e+e-→e+e-+(c c)

J-even charmonium states can be produced in e+e- annihilations at higherenergies through γγcollisions. The (c c)state is usually identified by its hadronicdecays. The cross section for this processscales linearly with the γγpartial width ofthe (c c) state.

( )( ) ( ) ( )( )∫ →=→ −+−+ ccLdcceeee i γγσασ γγ5

( )( ) ( ) ( )22

212222

,128 qqFMMs

MMJcc

Γ+−ΓΓ+=→ γγπγγσ

Limititations: knowledge of hadronic branching ratios andform factors used to extract the γγpartial width.

L = Luminosity functionα= e.g. 4-momenta of out

going leptons.J,M,Γ = spin, mass ,total

width of c c state.s = cm energy of γγsystemΓγγ two-photon partial widthq1,q2 photon 4-momentaF = Form Factor describingevolution of cross section.


Initial State Radiation (ISR)

•Like in direct formation, only JPC=1– states can be formed in ISR.•This process allows a large mass range to be explored.•Useful for the measurement of R = σ(e+e-→hadrons)/σ(e+e-→µ+µ-).•Can be used to search for new vector states.


B-Meson Decay

J/ψ,ψ′,ψ(3770), ηc,η′ c,χc0,χc1,D(*), D(*),X(3872)

K±,KS,KL,K*(890),K(1270)...

Charmonium states can be produced at the B-factories in the decaysof the B-meson.The large data samples available make this a promising approach.States of any quantum numbers can be produced.η′ c and X(3872) discoveries illustrate the capabilities of the B-factoriesfor charmonium studies.


Double Charmonium

Discovered by Belle in e+e- → J/ψ + XThe measured cross section for this process is about one order ofmagnitude larger than predicted by NRQCD.

( ) ( ) ( )pbBJee c 009.0033.04/ 007.0006.0 ±=≥×+→ +

−−+ ηψσ

Enhances discovery potential of B-factories: states which so far areunobserved might be discovered in the recoil spectra of J/ψ and ηc.


pp Annihilation

In pp collisions the coherent annihilation of the 3 quarks inthe p with the 3 antiquarks in the p makes it possible to form directly states with all quantumnumbers.

The measurement of masses andwidths is very accurate because itdepends only on the beam parameters,not on the experimental detectorresolution, which determines only thesensitivity to a given final state.


Experimental Method

( ) 4/412

22

2

2RR

RoutinBW ME

BBk

JΓ+−

Γ+= πσ

The cross section for the process: pp → cc → final state

is given by the Breit-Wigner formula:

The production rate ν is a convolution of theBW cross section and the beam energy distribution function f(E,∆E):

{ }∫ +∆= bBW EEEdEfL σσεν )(),(0

The resonance mass MR, total width ΓR and product of branching ratiosinto the initial and final state BinBout can be extracted by measuring theformation rate for that resonance as a function of the cm energy E.


Beam Energy and Width Measurement

In pp annihilation the precision in the measurement of mass and widthis determined by the precision in the measurement of the beam energy and beam energy width, respectively.

2)1(2 γ+= pcm mE21

1β

γ−

==p

beam

mE Lf ⋅=β

( )2232

12

+

+

=LL

ff

EE

cm

cm δδγ

γβδ

ff

pp δ

ηδ 1=

The beam revolution frequency f canbe measured to 1 part in 107 from thebeam current Schottky noise. In orderto measure the orbit length L to the required precision (better than 1 mm)it is necessary to calibrate using the known mass of a resonance, e.g. theψ′ for which ∆M = 34 keV.

ηηηη is a machine parameter which can be

measured to ~ 10 %


The Charmonium Spectrum

Spectroscopic Notation

n2S+1LJ


The J/ψ(13S0) and the ψ′(23S0)

•The masses of the triplet S states have been measured very precisely in e+e-

collision (using resonant depolarization)and in pp annihilation at Fermilab (E760)Accuracy of 11 keV/c2 for the J/ψ and of34 keV/c2 for the ψ′.

•The widths of these states were determined by the early e+e- experimentsby measuring the areas under the resonance curves.Direct measurement by E760 at Fermilab, which found larger values.

277 ± 22243 ± 43ψ′

91.0 ± 3.268±10J/ψPDG04PDG92Triplet S states

total widths (keV)


The ηC(11S0)


The ηc(21S0) discovery by BELLE

The Belle collaboration has recentlypresented a 6σ signal for B→KKSKπwhich they interpret as evidence forη′ c production and decay via the process:

with:

in disagreement with the Crystal Ballresult.

MeV)stat(2022MeV)stat(22978M

±=Γ±=

MeVstatcMeVstatM

)(2415/)(63654 2

±=Γ±=

−+→′′→ πηη KK;KB Scc

MeVcMeVM

c

c

55)(/863654)( 2

<′Γ±±=′

ηη


γγ → ηc(21S0)

M(η′ c) = 3637.7 ± 4.4 MeV/c2

BaBar

BaBar: Γ(η′ c) = 17.0 ± 8.3 ± 2.5 MeV


The χcJ(13PJ) States

χ0

•First observed by the early e+e- experiments, whichmeasured radiative decay widths, directly for χ1 andχ2, indirectly for χ0. Radiative decay important forrelativistic corrections and coupled channel effects.•Precision measurements of masses and widthsin pp experiments (R704, E760, E835). •χ1 width measured only by E760, most precisemeasurement of χ0 width by E835.

0.88 ± 0.143510.59 ± 0.12χ1

2.00 ± 0.183556.26 ± 0.11χ2

10.2 ± 0.93415.19 ± 0.34χ0

Width (MeV)Mass (MeV/c2) 1++

0++

2++


A signal in the hc region was seen by E760 in the process:

Due to the limited statistics E760 was only able to determine the massof this structure and to put an upperlimit on the width:

The hc(1P1) E760 observation

0c /Jhpp πψ +→→

)%90(1.1)(/2.015.02.3526)( 2

CLMeVhcMeVhM

c

c

<Γ±±=

( ) ( ) ( ) ( ) 707 106.05.2/104.08.1 −− ×±<<×± ψπJBppB

( )( ) ( )..%9018.0

//

0 LCJBJB ≤

ψπψππ


Observation of hc(1P1) by E835 and CLEO

E835

2/2.02.08.3525)( cMeVhM c ±±= pp →hc →ηcγ→γγγ

CLEO

e+e- →ψ′→π0hc →ηcγ→γγγhc →ηcγ ηc→hadrons

2/9.04.3524)( cMeVhM c ±=C. Patrignani, BEACH04 presentation A. Tomaradze, QWG04 presentation

2/2.015.02.3526)(:760 cMeVhME c ±±=


Meson States with 4 Flavours


Baryon States with 4 Flavours


Scoperta del Bottom (b)

XAp ++→+ −+ µµ−+→ µµΥ


Gli stessi dati con statistica triplicata

Fit con 2 o 3 risonanze:

26.3 ± 3.410355.2 ± 0.5Υ(3S)43 ± 610023.26 ± 0.31Υ(2S)

53.0 ± 1.59460.30 ± 0.26Υ(1S)Γ(keV)M(MeV/c2)

Quark Pesanti Spettroscopia del Charmoniobettoni/particelle/charmonium.pdf · 2005. 6. 1. · Diego...

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Transcript of Quark Pesanti Spettroscopia del Charmoniobettoni/particelle/charmonium.pdf · 2005. 6. 1. · Diego...