Light hadrons at e+e- colliders

Transcription

1 Light hadrons at e+e- colliders Andrzej Kupsc Experiment: e+e- colliders Dispersive methods for hadronic contribution to muon g-2 Two hadrons: Pion form factor / η,η -> π+π-γ Three hadrons: Dalitz Plot / η,ω,η -> π+π-π 0... IU, June 13th, 2017

2 Lightest neutral mesons J P =0 - π 0 lightest hadron Vector Mesons Dominance: V 0 γ Pseudo Goldstone bosons: stable Low energy QCD degrees of freedom

3 Low Energy QCD processes Even # pseudoscalars PPPP u-d quark masses π-π,π-η (re-)scattering Odd intrinsic parity: PVV/Pγγ, PPPV TFF Vector Meson Dominance

4 Content Light hadrons at e+e- colliders Hadronic contribution to muon g-2 (using dispersive methods) Pion vector form factor e + e - π + π - (τ π + π - ν τ ) Anomalous processes/transition form factors η,η π + π - γ Dalitz decays η,η e + e - γ ω π + π - π 0 (e + e - π + π - π 0 ) Even P processes η,η π + π - π 0...an example of amplitude analysis...

5 e+e- colliders AdA 1961, LNF Frascati VEP , Novosibirsk

6 November revolution 1974 Charmonia SPEAR (c c) BS

7 BaBar: ISR s 3.0 GeV, Belle/BelleII e+e- colliders s BEPC II DAΦNE VEPP 2000 s ISR W< s γγ e+e- colliders in operation: BEPCII L= cm -2 s -1 at Ψ(3.77) DAΦNE L= cm -2 s -1 at Φ VEPP2000 L= cm -2 s -1 at 2GeV BESIII KLOE-2 CMD-3,SND

8 e+e- colliders s BEPC II ISR DAΦNE VEPP 2000 s W< s γγ e+e- colliders in operation: BEPCII L= cm -2 s -1 at Ψ(3.77) DAΦNE L= cm -2 s -1 at Φ VEPP2000 L= cm -2 s -1 at 2GeV BESIII KLOE-2 CMD-3,SND e+ e- soon?... η'/η c /χ c1

9 Muon anomalous magnetic moment puzzle x10-11 BNL FNAL 3.6 σ SM Present D.Hertzog, arxiv: Goal

10 Anomalous magnetic moment of elementary fermions Single non trivial parameter coming from loops in QFT QED: ae = (28) ( ) QED test or α em determination aμ = (63) ( ) Sensitive test of the Standard Model PRL 100, (2008) E821, PRD 73, (2006) a τ = 0.018(17) or < a τ < %CL (DELPHI), EPJC 35, 159 (2004) Theory: (5) 10 8, Eidelman, Passera, MPL A 22, 159 (2007) aμ much more sensitive to NP than ae (mμ/me)

11 Muon g-2 measurements sensitivity Had LbL HVP h.o. HVP 1st Weak 2nd Weak 1st +/-a µ uncertainty abs(a µ ) contribution QED 5th QED 4th QED 3rd QED 2nd QED 1st Slide: David Hertzog a µ in units of α 2π 11

12 BNL result a μ BNL = ( ±63) a μ exp a μ SM =(249 ± 87) (3σ) hadronic vacuum polarization (HVP) hadronic light-by-light scattering (HLbL) a μ HVP =(6 923 ± 42) a μ HLbL =(116 ± 40) a μ exp a μ SM :4% HVP 215% HLbL (1% of leptonic LbL)

13 HVP dispersive approach: precision predictions from precision data J. Phys. Radium 22,121 (1961) K(s): kernel 0.63< KK(s)<1 Phys.Rept. 477, 1

14 CMD-2, SND (scan at s < 1.4 GeV) KLOE (ISR at s < 1.0 GeV) S.Eidelman,F.Jegerlehner

15 BaBar e + e - π + π - J.P. Lees et al., Phys. Rev. D86 (2012)

16 HVP Phys.Lett. B753 (2016) 629 CMD3 prel. e + e - π + π -

17 Excercise: pion vector form factor fits

18 Gounaris-Sakurai PRL,21,244 (1968) P-wave I=1 ππ scattering phase-shift generalized effective-range Chew- Mandelstam formula

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22 π-π phase shifts I=1 (P wave) Phys.Rev. D71 (2005)

23 Omnes function fits isospin violation I=0 (ρ-ω mixing) EPJC77 (2017) 98

24 Phys.Rev. D86 (2012)

25 η/η decays at e + e - colliders KK BR = 83% η ' (960) BR = η(550) BR = 1.3% π 0 BR = φ (1020) ρ(770) BR = 15% a 0 (980) f 0 (980) BR ~ O(10 4 ) J/Ψ η ( ) γ (BESIII) φ η ( ) γ (KLOE) 1.31x10 9 J/Ψ events 6x10 6 η

26 η π + π - γ Acc corr Fit data uncorr χχ 2 NNddff=8367 Mππ= s WASA PLB707 (2012) 243 KLOE PLB718 (2013) 910

27 η/η π + π - γ PLB707 (2012) 184 η π + π - γ e + e - π + π - η' π + π - γ CBarrel PLB402,195 ('97); α=1.89±0.25 stat ±0.59 syst GeV -2 WASA PLB707 (2012) 243 α=1.31±0.08 stat ±0.40 syst GeV -2 KLOE PLB718 (2013) ±180 ev (S/B=0.3) Mππ= s s [GeV 2 ]

28 Model-dependent fit 1). fit with ρ(770)-ω 2). fit with ρ(770)-ω-ρ(1450) 3). fit with ρ(770)-ω-box anomaly χ 2 /ndf=3.0 χ 2 /ndf=2.0 Beside ρ(770) resonance, ω is needed ρ(770)-ω is not enough; Extra contribution (maybe ρ(1450) or box-anomaly, maybe both of them) is also necessary

29 Analysis: Liqing QIN SDU,IHEP Prel. analysis based on 9.7 x 10 5 η π+π-γ P(s ππ ) = 1+ α s ππ + β s 2 ππ P(s ππ ) = 1+ α s ππ + β s 2 ππ + δ BW ω PRD87,092001('13) ω contribution necessary Linear polynomial is insufficient... Crystal Barrel: α = (1.80±0.49±0.04)GeV -2 β = (0.04±0.36±0.03)GeV -4 GAMS-2000: α = (2.7±1.0)GeV -2

30 π 0,η,η Transition Form Factors (TFF) Low energy QCD l + l - spectra dark photon (U boson) Fπ 0 q 2 puzzle: BaBar HLbL for aµ φ π 0 γ* φ ηγ* ω π 0 γ* e + e - π 0 ω P γ * γ *

31 Single Dalitz decays η e + e - γ FF=1 η e + e - γ π 0 e + e - γ CB/TAPS: PRC89, (2014) Slope from ρ pole 1.69 GeV -2

32 PRD92 (2015)

33 g-2 Hadronic Light by Light Slide: J. Bijnens In general 138 Lorentz structures (only 28 contribute to a μ ) vs HVP: one function, one variable Low and high energy mixed Hadrons vs quarks γγ measurement? -- dominated by lepton contribution

34 Hadronic Light by Light Slide: J. Bijnens, A.Nyffeler must be calculated using hadronic models that correctly reproduce properties of QCD π ±,K-loop π 0, η,η' exchange quarkloop PdRV ( 1.9±1.9) (11.4±1.3) (0.8±1.1)

35 Hadronic contribution to a μ HVP HLbL e+e- γ* h KLOE-2 CMD3/SND BESIII BelleII Goal: reduce Δa μ (10-11 ) HVP HLbL 39/26 10 m h <1-2 GeV Hadrons γ ( * ) γ ( * ) h γ ( * ) hγ ( * ) + hadro- photoproduction exp

36 From e+e- π+π-π 0 to π 0 TFF ππ phase shifts + e+e- 3 π data Eur.Phys.J. C74 (2014) 3180 Similar strategy for η From e+e- π+π-η to η TFF arxiv:

37 Three body decays, Dalitz plot 3 body decay: s i (p 0 p i ) 2 = (m 0 m i ) 2-2T i m 0 η π+π-η

38 η πππ KLOE-2 JHEP 1605 (2016) 019 A(X,Y) 2 =N(1+aY+bY 2 +dx 2 +fy 3 +gx 2 Y)

39 η/η π + π - γ

40 Dalitz plot for ω π + π - π 0 PR,125 (1962)687

41 η πππ d-u quark masses Difficult/dubious: - other tree diagrams - rescattering U(3) CHPT, Borasoy, Nißler 2005: BR(η π + π π 0 ) 1.8% large ρ + π - + cc

42 η π 0 π 0 π 0 GAMS 235±45 ev (S:B=0.13) β=-0.59± ev PRD92 ( 15) β= 0.640± 0.046±0.047 Z=x 2 +y 2 PAN71,2124('08)

43 Analysis: Xiaolin KANG, IHEP BESIII, arxiv η π+π-π 0 η π 0 π 0 π 0

44 PWA η πππ arxiv B(η ρ+π- + cc) = (7.44 ± 0.60 ± 1.26 ± 1.84) 10 4 B(η π 0 π 0 π 0 ) puzzle CLEO PRL 102,061801( 09) B(η π 0 π 0 π 0 ) /B(η ηπ 0 π 0 ) from GAMS ( 84, 87, 08) (78±10) 10 4 vs BESIII (159±12) ±5 ev. BR= 3.7±

45 e+e- ->J/ψ-> Λ Λ Use spin correlations and polarization to extract hyperon decay parameters and test CP for baryons Revise assumption that hyperons from decays are unpolarized Göran Fäldt, AK arxiv: