Low energy e - annihilation and τ -lepton decays as a ...

O. Shekhovtsova KIPT Kharkov

Ukraine

Cracow, 23.11.2017

NATIONAL SCIENCE CENTERKharkov Institute of Physics and Technology,NAS of Ukraine

Low energy e+ e− - annihilationand τ -lepton decays as a source

information about hadronic interaction

OUTLINE

Muon (g-2): the test of the Standard Model. Current status

Low energy hadronic interaction and Effective Field Theory. Chiral Perturbation Theory and inclusion of resonances

e+e- annihilation into a meson pair, e+e- scattering and hadronic decay modes of �-lepton. Theoretical results and fit to data

Conclusions and perspectives

Standard Model of Elementary Particles

Neutrino oscillations and neutrino masses

Matter-antimatter asymmetry in the Universe

Dark matter and dark energy

…. 2012 by Atlas and CMS the last missing block

the Higgs boson

New Physics ?

Direct search in high energy experiments → no direct signals from LHC so farPrecise low energy measurement of SM parameters

Anomalous Magnetic Momentum of muon: for more than 10 years SM – experiment ~ (2.5 – 4) �

Muon (g-2): the test of the Standard Model.

The magnetic moment of a particle is related to its spin

μ⃗= ge ℏ

2mcS⃗

For Dirac pointlike particle :

g=2

Current status AMM

based on e+e- data → 3.6σ

based on tau – data → 2.4σ

Anomalous magnetic moment (AMM)



μ⃗= ge ℏ

2mcS⃗


g=2


Current status AMMBNL E821 experiment,completed 2001, published 2006

δaμexp=54⋅10−11

New experiment: Fermilab Muon g-2

Assuming no changes in the (g-2) central value the (exp - theory) discrepancy increases 5σ



μ⃗= ge ℏ

2mcS⃗


g=2


Current status AMM

What are the SM contributions and their errors? → to get the same precision?

SM VALUE FOR MUON AMM: QED

1 loop

2 loop graphs

………

Recently several independent checks of 4- and 5-loop diagrams: agree with Kinoshita’ results

PRL 109 (2012) 111807

is already reached

SM VALUE FOR MUON AMM: Electro-Weak

is already reached

SM VALUE FOR MUON AMM: Hadronic contribution

L(eading)O(rder) diagrams

H(adronic)V(acuum)P(olarization) H(adronic)L(ight)b(y)L(ight)

... non-perturbative QCD region, the limiting factor of the SM (g-2) prediction

TO APPLY EXPERIMENTAL LOW ENERGY DATA

(LO) Relies on measurements of T(ransition)F(orm)F(actor) in (two-photon) scattering e+e- → e+e- +’

aμHLbL

=(10 .5±26 )⋅10−11

SM VALUE FOR MUON AMM: Hadronic contribution

L(eading)O(rder) diagrams

H(adronic)V(acuum)P(olarization) H(adronic)L(ight)b(y)L(ight)

... non-perturbative QCD region, the limiting factor of the SM (g-2) prediction

TO APPLY EXPERIMENTAL LOW ENERGY DATA

e+e-- → → hadrons(τ→ hadrons + ν

)

dispersion relation+ optical theorem

CVC data

Current status AMM. Summary

692.3 (4.2)

The SM value

Total:(on e+e-)

3.6σ Diff: 28.2 · 10-10

HADRONIC uncertainty dominates!

It is heavy to expect a missed SM effect as large as (200-300)·10 -11 , i.e. logical posibilities:

Some experimental issue → new independent measurement by Fermilab Muon g-2


692.3 (4.2)

The SM value

Total:(on e+e-)

3.6σ Diff: 28.2 · 10-10




NP beyond the Standard Model → no evidence about NP from LHC


692.3 (4.2)

The SM value

Total:(on e+e-)

3.6σ Diff: 28.2 · 10-10




NP beyond the Standard Model → no evidence about NP from LHC

Coherent combination of small effects in theory and experiment that reduces the discrepancy - mainly due to hadronic contribution: non direct estimation based on e+e- (tau) data - model dependent data analysis of hadronic interaction at low energies more precise experimental results and reliable theoretical model

Measured experimental distributions

“Bare” hadronic form factors/ cross section

Theoretical Model inspired by QCD :

hadronic form factors

Low energy data as input in HVP and HLbL

HVP and HLbL

estimation

Low energy hadronic interaction and Effective Field Theory

The QCD Lagrangian

with covariant derivative

The behaviour of the QCD strong coupling :

1 = (2 n

f – 33)/6

1 < 0 for n

f < 17

the coupling increases when the energy decreases :- asymptotic freedom at high energies - confiment at low energies: below ~1 GeV is to big to apply perturbative theory methods

For low energies (quark, gluons) → (new objects?/ light mesons) QCD → EFT ChPT that rem

The QCD Lagrangian

For u/d/s quarks for the energy about 1GeV the main part

with a small perturbation

For the chiral components

[the chiral components mixed only in ] Chiral invariant

is invariant under

whereas the ground state shows

Spontaneous symmetry breaking of chiral symmetry → 8 Goldstone bosons

The light pseudoscalar octet (, K, ) the best candidates for them.

Finite u/d/s quark masses → finite masses of Goldstone bosons

Stefan Scherer, hep-ph/0210398Introduction to Chiral Perturbation Theory

A theory that obeys for Lagrangian

and

for the ground states → Chiral Perturbation Theory

A natural choice the lightest pseudoscalar octet (, K, )

Chiral Perturbation Theory and inclusion of resonances

+ … , 10 terms

, 97 terms

p2/(4 F)2 < 1 p < M

770 MeV

p ~ Mresonance has to be included

The object is SU(3) matrix

Nambu-Goldstone boson of SSB of massless QCD

A series by a small parameter p2/(4 F)2

Chiral and gauge invariant Lagrangian with the minimal number of derivatives

LEC’s determined by low energy phenomenology, high energy behaviour of Green functions.

e.g. : →

Inclusion of resonances. Resonance Chiral Theory

From p ~ Mthe resonances have to be included

80’s Gasser&Leutwyler O(p2) chiral invariant Lagrangian with -resonance → generalization V, A, S, P in 90’s → Resonance Chiral Theory

R= V, A, S, P

Satisfies low (ChPT, by constraction) and high (QCD, by LEC’ resonance) energy limits → was applied for study of e+e- →hadrons and hadronic decays of tau-lepton

2 ways to realize A, V: vector and tensor formalisms, LEC’s depend on a chosen formalism

Tensor formalism

chiral and gauge invariant Lagrangian with the minimal number of derivatives

Single, lightest octet resonances(two-pion FF → p4 GB LECs = 0)


Monte Carlo generators:a technique to integrate restricted phase space;

a quality depends on used input (both theory and exp

data



fitting procedure:

limitations: syst err., reduced dimensionality, folded backgrounds

Theo

r diff

dis

tr li

mita

tions

:

unce

rtain

ass

umpt

ions

Fitt

ed m

odel

par

amet

ers do results of fitted theoretical model

represent results of measurements ???

Study of low energy hadronic data

Application of RChL for hadronic FFs

Hadronic Light by Light → Transition Form factors

LO

0

Experimentally measured TFF

Ti(x,y,z) kinematical functions

Where to measure TFF’s

Two-photon exchange in e+e- collisions

Single-Tag measurements (BaBar, Belle)

Double-Tag measurementsReconstruct both scattered lepton. Not measured yet!

For any setup: Measured cross section → MC (th. model) → TFF

TFF model for both virtualities

RChL with n resonance octets vector formulation n = 1, 2, 3

P = 0’

Chiral approach with vector resonances for pion and eta (eta’) mesons

H. Czyz, S. Ivashyn, A. Korchin, O.S., PRD 85 (2012) 094010

QCD driven behaviour(n+1) equations → 2n – (n+1) = (n-1) to be fitted

One-octet ansatz

no free parameters

116 exp points

Two-octet ansatz

1 parameter to fit →

PDG

Fit 116 exp points

Three-octet ansatz

2 parameters to fit strong correlation!!!

Two-octet ansatz included in EKHARAhttp://prac.us.edu.pl/~ekhara/

Contradictsother exp.

Belle2012 , to be included !

BaBar arXiv: 0905.4778

Influence of BaBar selection rules on the measured cross section

d(full) – d(approx)) /d(approx)

d(approx) = d(q22 = 0)

Dependence on Q2 for TFF’s. Not taking into account → a fake Q2 dependence for TFF

TFF of - mesons bigger (up to 6.5% ) than BaBar claims (4.6%)

EKHARA installed in BES III

Hadronic Vacuum Polarization → Hadronic e+e- cross section

How to estimate HVP

above ~ 1.8 GeV QCD is applied + narrow resonances ( J/ , Y)

Below ~ 1.8 GeV data for e+e-

had have to be “bare” → without RC

Two ways to measure (/ scan) had :

- direct scanning (Novosibirsk)

- radiative return (KLOE Frascati : + –)

Radiator function = QED RC analytically / by MC destroyed by FSR (models)

IDEAL

FSR is suppressed for small angle analysis < 15 ; 45 <

< 135

is not suppressed for large angle analysis 45 < < 135

Photon radiation in e+ e-- → P1 P2

ISR defined only by 1 Lorentz structure

(multiplied the pion FF)

FSRdefined by ? Lorentz structures

(multiplied by hadronic FF )

FSR tensor: general structure

charge congjugation, photon crossing symmetry, gauge invariance and one photon real → 3 Lorentz structures → Hadronic Form factors

Hadronic Form factors model dependent

Final state radiation in e+ e-- → P1 P2

below and about 1GeV

Vector resonance contribution

Scalar resonance contribution

Bremsstrahlung process (only for + – )

P1 P2 = (+ 000)

Calculation was done within RChL

S. Dubinsky et al. EPJC 40; S. Eidelman et al EPJC 69;G. Pancheri et al PLB 642; O. S. Comp. Phys. Comm 18-

Numerical results

neutral modes

Clear signal of Vector resonance mechanism

~ no Vector resonance mechanism

Numerical results +

PHOKHARA 6.1: KLOE study

PHOKHARA 6.1 MC of KLOE to study FSR; syst uncertainty related with FSR in a_mu^had

Forward- Backward asymmetry, large angle analysis

NLO HVP to muon AMM

aμhad ,γ=

α 2

3π2 ∫4mπ

2

smax

dss

R γ ( s )K ( s ) , R γ ( s )=σπ +π− ,γ (s )

σ μ+ μ−(s )

much below current experimental precision

diff sQED and RChL

>Ecut

estimation within sQED·VMD : 4.3·10 -11 (exp 4.9·10 -11)

- CVC to estimate HVP of AMM

to estimate HVP of AMM

TAUOLA (Monte Carlo generator for tau decay modes)

R. Decker, S.Jadach, M.Jezabek, J.H.Kuhn, Z. Was, Comp. Phys. Comm. 76 (1993) 361; ibid 70 (1992) 69, ibid 64 (1990) 275

Later: Cleo parametrization for 0 0 (Phys Rev D61, 012002)

Hadronic FF within VMD

3 scalar modes BW(V1)*BW(V2) , reproduces LO ChPT limit

RChL hadronic form factors for main 2P and 3P modes

KK →88% of tau hadronic width

Hadronic Decay Modes of tau

2P: 2 FFs (Lorentz structures)3P : 4 FFs (Lorentz structures)

RChL

RChL vs VMD

VMD

ChPT at least up to NLO + correct QCD behaviour

ChPT LO + correct QCD behaviour

wrong ChPT NLO

O.S, T. Przedzinski, P. Roig, Z. Was PRD D86

Based on the theoretically predicted values for the RChL

Deviation from the PDG central values 1-20% (exception 25-40% for KK mode)

Adding (1400) and (1700)

Fitting to BaBar preliminary data for mode

Fitting to Belle data for 0mode

RChL TAUOLA is used by LHCb

…… Belle II

Belle parametrization RChL

To get agreement we HAD to add sigma meson (phenomenologically)

I.Nugent et al PRD 88 OS JETP 102

CONCLUSIONS:

Hadronic contribution to muon AMM is the main restriction to its SM estimation

HVP and HlLbL estimated on the basis of experimental data

e+ e-- → hadrons ( →

+ hadrons) and e+ e-- →e+ e-- + hadrons

Data analysis equires theoretical calculations of Hadronic FF within

a QCD inspired model Resonance Chiral Lagrangian approach:

e+ e-- → (FSR) ; e+ e-- → ;) ;

t → nt + (2 ; 3 ; K K )

Implementation of the Hadronic FF in : PHOKHARA, EKHARA, TAUOLA

BaBar, KLOE BES Belle, LHCb

Fit of theoretical spectra within RChL to KLOE, Belle, BaBar data

PERSPECTIVES:

Belle II : Phase III Early 2019 start of data taking with the complete Belle II detectorintegrated luminosity: 50 ab -1 (50 x Belle)

Wide physics program: WG 8 “Low multiplicity & tau ” - gamma-gamma physics (TFF 1 and 2 mesons) - tau physics - low energy e + e -- → hadrons (radiative return)

Official MC: EKHARA, PHOKHARA, TAUOLA

Continuous work on: new theoretical results update of MC based on new theoretical results advanced fitting strategy to get hadronic model parameters

Update our knowledge about hadronic interactions (pole masses and vertex constants) → more precise estimation of HVP and HlbL of muon AMM to be compatible

New E989 (g-2)_mu in Fermilab (first physics run 2018, late 2018 - early 2019 BNL to

reproduce statistics ) with precision 1.6 · 10 -11


Monte Carlo generators:a technique to integrate restricted phase space;

a quality depends on used input (both theory and exp

data



My participation in study of hadronization

details can be found in ….

fitting procedure:

List of publications:

BACK SLIDES


692.3 (4.2)

The SM value

Total:(on e+e-)

3.6σ

New experiment: Fermilab Muon g-2

Assuming no changes in the (g-2) central value the (exp - theory) discrepancy increases 5σ

Diff: 28.2 · 10-10

HADRONIC uncertainty dominates! Non direct estimation!!

NP beyond the Standard Model


Some experimental issue → new measurement by Fermilab Muon g-2

Coherent combination of small effects in theory and experiment that reduces the discrepancy - mainly due to hadronic contribution: non direct estimation based on e+e- (tau) data

Hadronic Light by Light

F.Jegerlehner&A.Nyfeller https://arxiv.org/pdf/0902.3360.pdf

n resonance octet

Similar for and H. Czyz et al, PRD 85 (2012) 094010

High energy behaviour of TFF

leads to restrictions for couplings

(n+1) equations → 2n – (n+1) = (n-1) constants to be fitted to data

n = 1 all parameters fixed, n = 2 - ONE to fit

The resonance masses from PDG

The slope of TFF’s at the origin

E799 experiment

Crystall Ball

SINDRUM I

NA60

http://prac.us.edu.pl/~ekhara/

Monte Carlo generator EKHARA

As a default two-octet parametrization

Not done yet

Comparison with measured cross section

BABAR event selection 0 : q22< 0.18 GeV2 q2

2< 0.38 GeV2

Discrepancy only with BaBar 2009

Bremsstrahlung (sQEDVMD)

But how good is

this approximation?

F(s) F(s)

F(s)

RChL

sQEDsQED

Beyond sQEDBeyond sQED

sQED VMD is reasonable for the final state

But what about final state ?

Can we use for FSR the same value of F(s) as for

S. Dubinsky et al, EPJC40(2005) 41

Charge asymmetry

big enough contribution due to RPT !

almost negligiblealmost negligible

s=1 GeV2FSR as background to ISR

RT parametrization

Tauola 2013 : inclusion of sigma meson

Tauola 2013 : inclusion of sigma meson

* alpha, beta are related for PT - correct inclusion based on PT structure* inclusion tensor resonances in RT framework J.J Sanz Cillero, O.S.

CLEO parametrization

F5

V

RT parametrization

OZI

Also K*(1400), (1450)

Also No yet and KKK modes with RT TAUOLA CPC

I. Nugent (BaBar Colaboration)

Tau Workshop, Cracow, 2013

RT TAUOLA (default) no OZI contribution

Not in TAUOLA

Goal of Fermilab E989

• A factor of 4 reduction in total error in aover BNL (0.54 ppm)

± 0.54 ppm total error

• Two things to notice:– statistical error dominates– systematic error is only 2.5 to 3 times larger than E989 goal

• How to improve:– get a hotter beam (Fermilab) (21 × statistics of BNL)– improve everything in systematics, which have many contributing factors

• Fermilab Goal: Equal statistical and systematic errors– ± 70 ppb for a and p. total: ± 100 ppb

– ± 100 ppb for statistics– Total error 140 ppb ( 0.14 ppm)

B. Lee Roberts - PhiPsi 2016- Mainz 26 June 2017 72

Fermilab Timescale

• This Year:– We are in first commissioning now until 7 July– We will turn back on in November and finish comissioning– US budget willing, we will then move to production running

• Anticipated results: (≃ 1, 5, 25 × BNL data set)– A BNL level data set should obtained relative quickly.

• We will stop data collection, and re-blind and keep running.• BNL level result perhaps by late 2018, early 2019.

– The next data set should give us half the BNL error– The final data set should give us one-fourth the BNL error.


June 2017 ~ 700,000 positrons (~2 weeks)


Particle: q = Qe moving in a magnetic field: momentum turns with cyclotron frequency C,

spin turns with S

Spin turns relative to the momentum with a


Spin Motion in a Magnetic Field

In a storage ring, we need vertical focusing


With an electric quadrupole field for vertical focusing and the magic 0

Measure two quantities

where B is expressed in terms of the Larmor frequency of a free proton

Low energy e - annihilation and τ -lepton decays as a ...

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