Light flavor at e + e − colliders: Impact of hadronic cross sections on g µ − 2 Andreas Hafner (hafner@slac.stanford.edu) Mainz University On behalf of the B A B A R Collaboration FPCP May 23, 2013 Andreas Hafner (Mainz University) ISR at BABA FPCP 2013 1 / 24 R
Outline Motivation: muon-anomaly ( g − 2) µ 1 Initial State Radiation (ISR) analyses at B A B A 2 R Status of Hadronic Cross Section Measurements 3 e + e − → p ¯ p e + e − → π + π − π + π − e + e − → K + K − Summary 4 Andreas Hafner (Mainz University) ISR at BABA FPCP 2013 2 / 24 R
Motivation: muon-anomaly ( g − 2) µ Introduction and direct measurement The anomalous magnetic moment of the muon ( g − 2) µ gyromagnetic ratio: g 2 mc · � µ = g e � � S spin 1 2 → Dirac theory: g = 2 QFT: g � = 2 Andreas Hafner (Mainz University) ISR at BABA FPCP 2013 3 / 24 R
Motivation: muon-anomaly ( g − 2) µ Introduction and direct measurement The anomalous magnetic moment of the muon ( g − 2) µ gyromagnetic ratio: g 2 mc · � µ = g e � � S spin 1 2 → Dirac theory: g = 2 QFT: g � = 2 muon anomaly: a µ = ( g − 2) µ / 2 Brookhaven National Laboratory (BNL) a theory = a QED + a weak + a had µ µ µ µ [G.W. Bennett et al. , PRD 73 , 072003 (2006)] BNL E821 11 659 208 . 9 ± 6 . 4 a µ units in 10 − 10 Andreas Hafner (Mainz University) ISR at BABA FPCP 2013 3 / 24 R
Motivation: muon-anomaly ( g − 2) µ Introduction and direct measurement The anomalous magnetic moment of the muon ( g − 2) µ gyromagnetic ratio: g QED weak 2 mc · � µ = g e � � S γ γ spin 1 2 → Dirac theory: g = 2 QFT: g � = 2 µ + µ + µ + µ + muon anomaly: a µ = ( g − 2) µ / 2 γ Z 0 a theory = a QED + a weak + a had µ µ µ µ BNL E821 11 659 208 . 9 ± 6 . 4 [T.Kinoshita et al. , PRD 73 , 013003 (2006)] QED 11 658 471 . 809 ± 0 . 015 weak 15 . 4 ± 0 . 2 [A.Czarnecki et al. , PRD 67 , 073006 (2003) Erratum-ibid. D 73 , 119901 (2006)] [M.Knecht et al. , JHEP 0211, 003 (2002)] a µ units in 10 − 10 Andreas Hafner (Mainz University) ISR at BABA FPCP 2013 3 / 24 R
Motivation: muon-anomaly ( g − 2) µ Introduction and direct measurement The anomalous magnetic moment of the muon ( g − 2) µ gyromagnetic ratio: g hadronic 2 mc · � µ = g e � � S γ spin 1 had. vacuum polarisation 2 → Dirac theory: g = 2 q α QCD QFT: g � = 2 ¯ q q µ + µ + muon anomaly: a µ = ( g − 2) µ / 2 α QCD ≈ O (1) ¯ q a theory = a QED + a weak + a had µ µ µ µ optical theorem BNL E821 11 659 208 . 9 ± 6 . 4 e − QED 11 658 471 . 809 ± 0 . 015 hadrons weak 15 . 4 ± 0 . 2 had 693 . 0 ± 4 . 9 e + had. cross section hadro a µ units in 10 − 10 Andreas Hafner (Mainz University) ISR at BABA FPCP 2013 3 / 24 R
Motivation: muon-anomaly ( g − 2) µ Introduction and direct measurement The anomalous magnetic moment of the muon ( g − 2) µ dispersion relation: gyromagnetic ratio: g 2 mc · � µ = g e � � S � ∞ a had 1 µ, LO = π 0 ds K ( s ) σ had ( s ) 4 π 3 m 2 spin 1 2 → Dirac theory: g = 2 QFT: g � = 2 K ( s ) ∼ 1 / s & σ had ( s ) ∼ 1 / s →∼ 1 / s 2 (low energies important!) muon anomaly: a µ = ( g − 2) µ / 2 a theory = a QED + a weak + a had µ µ µ µ exp. input BNL E821 11 659 208 . 9 ± 6 . 4 e − QED 11 658 471 . 809 ± 0 . 015 hadrons weak 15 . 4 ± 0 . 2 had 693 . 0 ± 4 . 9 e + had. cross section BNL − SM 28 . 7 ± 8 . 0 hadro ⇓ a µ units in 10 − 10 3 . 6 σ [M. Davier et al. , EPJ C 71, 1515 (2011)] Andreas Hafner (Mainz University) ISR at BABA FPCP 2013 3 / 24 R
ISR at BABA R PEP-II and the B A B A R detector at SLAC asymmetric e + e − -collider: 9 GeV ( e − ) and 3.1 GeV ( e + ) √ s = 10 . 58 GeV ⇒ Υ (4 S ) ⇒ above BB -threshold main purpose: B -physics multi purpose detector data taken from 1999 – 2008 integrated luminosity: 531 fb − 1 on Υ (4 S ): 454 fb − 1 ≈ 600 · 10 6 BB -pairs Andreas Hafner (Mainz University) ISR at BABA FPCP 2013 4 / 24 R
ISR at BABA R Initial State Radiation (ISR) events at B A B A R γ e − (9 GeV ) γ hadrons √ hadrons s ′ = E CM e + (3 GeV ) ISR selection Detected high energy photon: E γ > 3 GeV → defines E CM & provides strong background rejection Event topology: γ ISR back-to-back to hadrons → high acceptance Kinematic fit including γ ISR → very good energy resolution (4 – 15 MeV ) e + e − -boost into the laboratory reference frame → high efficiency at production threshold of hadronic system Continuous measurement from threshold to ∼ 4.5 GeV → provides common, consistent systematic uncertainties Andreas Hafner (Mainz University) ISR at BABA FPCP 2013 5 / 24 R
ISR at BABA R ISR analyses at B A B A R published e + e − → π + π − PRD 86 (2012) 032013, PRL 103 (2009) 231801 e + e − → φ f 0 (980) PRD 74 (2006) 091103, PRD 76 (2007) 012008 e + e − → π + π − π 0 PRD 70 (2004) 072004 e + e − → K + K − η, K + K − π 0 , K 0 S K ± π ∓ PRD 77 (2008) 092002, PRD 71 (2005) 052001 e + e − → 2( π + π − ) PRD 85 (2012) 112009, PRD 76 (2007) 012008 e + e − → K + K − π 0 π 0 , K + K − π + π − , 2( K + K − ) PRD 86 (2012) 012008, PRD 76 (2007) 012008 e + e − → 2( π + π − ) π 0 , 2( π + π − ) η, K + K − π + π − π 0 , K + K − π + π − η PRD 76 (2007) 092005 e + e − → 3( π + π − ) , 2( π + π − π 0 ) , 2( π + π − ) K + K − PRD 73 (2006) 052003 e + e − → p ¯ p PRD 87 (2013) 092005, PRD 73 (2006) 012005 Σ 0 , Σ 0 ¯ e + e − → Λ ¯ Λ, Λ ¯ Σ 0 PRD 76 (2007) 092006 e + e − → c ¯ c → . . . . . . . . . about to be submitted for publication to PRD e + e − → K + K − ongoing analyses e + e − → K 0 S K 0 L , π + π − π 0 π 0 , K 0 S K ± π ∓ π 0 /η Andreas Hafner (Mainz University) ISR at BABA FPCP 2013 6 / 24 R
e + e − → p ¯ Recent results p e + e − → p ¯ p Based on 469 fb − 1 : PRD 87 (2013) 092005 Update of PRD 73 (2006) 012005 based on 232 fb − 1 Efficiency obtained from simulation [K¨ uhn et al. , EPJC 18 (2001),497] Measure Cross Section σ Extract effective form factor: � σ = 4 πα 2 β C | G M | 2 + 1 p | FF | 2 , | FF | = 2 τ | G E | 2 3 m 2 p ¯ Measure the ratio | G E / G M | from angular distributions dcos θ ∼ (1 + cos 2 θ ) + τ | G E d σ G M | 2 sin 2 θ Andreas Hafner (Mainz University) ISR at BABA FPCP 2013 7 / 24 R
e + e − → p ¯ Recent results p Form factor in comparison to other experiments 0.6 0.08 Proton form factor Proton form factor BABAR (a) BABAR (b) BES FENICE CLEO DM2 0.06 NU E835 0.4 DM1 E760 BES PS170 0.04 E835 0.2 E760 0.02 0 0 2 2.25 2.5 2.75 3 3 3.5 4 4.5 – (GeV/c 2 ) – (GeV/c 2 ) M pp M pp Proton form factor BABAR Steep rise at threshold seen by FENICE DM2 DM1 PS170 confirmed → tail of a BES CLEO resonance below threshold? -1 NU 10 PS170 E835 FF exhibits sharp drops at E760 p =2.2 GeV and 3 GeV M p ¯ Good fit to pQCD prediction: -2 10 Brodsky-Lepage [PRL 43 (1979) 545] : FF ∼ α 2 S ( M p ¯ p ) / c 2 ) ( M p ¯ p > 3 GeV 2 3 4 M 4 – (GeV/c 2 ) p ¯ p M pp Andreas Hafner (Mainz University) ISR at BABA FPCP 2013 8 / 24 R
e + e − → p ¯ Recent results p Time-like | G E / G M | measurements d σ ( G M ) ∼ 1 + cos 2 θ p dcos θ d σ ( G E ) dcos θ ∼ sin 2 θ p B A B A R measurement: Angular distributions from |G E /G M | threshold up to 3 GeV BABAR PS170 Observe maximum at 1.5 / c 2 M p ¯ p ≈ 2 GeV Inconsistent with PS170 measurement at LEAR 1 ISR method → weak angular dependence of detection efficiency 0.5 2 2.25 2.5 2.75 3 – (GeV/c 2 ) M pp Andreas Hafner (Mainz University) ISR at BABA FPCP 2013 9 / 24 R
e + e − → p ¯ Recent results p Contributions of Exclusive Final States to g µ − 2 Contributions of different energy regions to the dispersion integral 1 ρ, ω → E < 1 GeV region dominates 0.0 GeV, ∞ Υ 9.5 GeV → π + π − channel needed! ψ 3.1 GeV 2.0 GeV φ, . . . 1.0 GeV a had Integral µ Andreas Hafner (Mainz University) ISR at BABA FPCP 2013 10 / 24 R
e + e − → p ¯ Recent results p π + π − Cross Section σ π + π − [ nb ] σ π + π − [ nb ] TOF KLOE10 OLYA KLOE10 1400 1400 3 3 OLYA SND CMD SND 10 10 CMD DM1 CMD2 DM1 CMD2 DM2 1200 1200 KLOE08 BABAR 2 2 10 10 KLOE08 BABAR Average Average 1000 1000 10 10 800 800 1 1 600 600 + - + - e e → π π -1 -1 10 10 400 400 0.5 0.5 1 1 1.5 1.5 2 2 2.5 2.5 0.7 0.7 0.72 0.72 0.74 0.74 0.76 0.76 0.78 0.78 0.8 0.8 0.82 0.82 0.84 0.84 s s [GeV] [GeV] s s [GeV] [GeV] ρ peak Systematic Uncertainties ρ − ω interference R : 0.5% B A B A Dip at 1.6 GeV : excited ρ states CMD-2: 0.8% SND: 1.5% Dip at 2.2 GeV KLOE: 0.8% Contribution to a had µ : 75%! Andreas Hafner (Mainz University) ISR at BABA FPCP 2013 11 / 24 R
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