Recent Hadronic Cross Section Measurements from B A B A R Konrad Griessinger on behalf of the B A B A R Collaboration Institute for Nuclear Physics Mainz University International Workshop on e + e − Collisions from Phi to Psi, June 2017 π + π − π 0 π 0 and π + π − η at BABA K. Griessinger (U Mainz) June 2017 1 / 20 R
Outline Introduction 1 Cross section e + e − → π + π − π 0 π 0 2 Cross section e + e − → π + π − η 3 Cross sections e + e − → K S K L π 0 , K S K L π 0 π 0 , K S K L η 4 π + π − π 0 π 0 and π + π − η at BABA K. Griessinger (U Mainz) June 2017 2 / 20 R
Introduction The contributions to a µ and its uncertainty g e � µ = 2 m � s a SM = a QED + a weak + a hadronic ( g µ − 2) / 2 =: µ µ µ µ Contribution [ · 10 − 11 ] Uncertainty [ · 10 − 11 ] Interaction QED [1] 116 584 718 . 951 0 . 080 EW [9] 153 . 6 1 hadronic VP [6, 12] 6837 43 hadronic LbL [11, 2] 119 41 total theory 116 591 828 60 E821 experiment [15] 116 592 089 63 deviation exp-theo 261 87 π + π − π 0 π 0 and π + π − η at BABA K. Griessinger (U Mainz) June 2017 3 / 20 R
Introduction Discrepancy between SM prediction and direct measurement from Eur.Phys.J., C71:1515, 2011 [6] . BNL-E821 2004 HMNT 07 (e + e – -based) –285 ± 51 JN 09 (e + e – ) –299 ± 65 Davier et al. 09/1 ( τ -based) –157 ± 52 Davier et al. 09/1 (e + e – ) –312 ± 51 Davier et al. 09/2 (e + e – w/ BABAR) –255 ± 49 HLMNT 10 (e + e – w/ BABAR) –259 ± 48 DHMZ 10 ( τ newest) –195 ± 54 DHMZ 10 (e + e – newest) –287 ± 49 BNL-E821 (world average) 0 ± 63 -700 -600 -500 -400 -300 -200 -100 0 × 10 –11 exp a µ – a µ Just a fluctuation? 3 σ effect, thus reduction of uncertainties necessary! π + π − π 0 π 0 and π + π − η at BABA K. Griessinger (U Mainz) June 2017 4 / 20 R
Introduction Connection between a µ and σ had � ∞ 1 a had ≈ K µ ( s ) · σ e + e − → had ( s ) d s µ 4 π 3 m 2 π Kernel function cross section π + π − π 0 π 0 and π + π − η at BABA K. Griessinger (U Mainz) June 2017 5 / 20 R
Introduction Connection between a µ and σ had � ∞ 1 a had ≈ K µ ( s ) · σ e + e − → had ( s ) d s µ 4 π 3 m 2 π π + π - γ π + π - π 0 π + π - π 0 π 0 preliminary cross sections, nb Courtesy of F. Ignatov π + π - π + π - π + π π - + π - π 0 3 10 2 π + 2 π - 2 π 0 π + π - 3 3 - K + K γ + - + - K K K K + - K K π 0 + - π 0 π 0 K K - K + K π + π - 2 10 + - π π - π K K + 0 - K + K π + π - π + π - K K S L K K π + π - S L +- π K K -+ S ± K K π ± η S ± π ± π K K 0 10 S K K K + K - S S π π - K K + S S η K + K - (not φ ) η + - π π - K K + η π + π - η π π π π + - + - 1 ppbar − 1 10 − 2 10 0.5 1 1.5 2 2.5 3 3.5 4 4.5 2E, GeV π + π − π 0 π 0 and π + π − η at BABA K. Griessinger (U Mainz) June 2017 5 / 20 R
Introduction The B A B A R Experiment Experimental specifications Energy: √ s ≈ 10 . 58 GeV ( E e − ≈ 9 . 0 GeV , E e + ≈ 3 . 1 GeV), Luminosity: L ≈ 500 fb − 1 ( Υ (4 S )) π + π − π 0 π 0 and π + π − η at BABA K. Griessinger (U Mainz) June 2017 6 / 20 R
Introduction The B A B A R Experiment Experimental specifications Energy: √ s ≈ 10 . 58 GeV ( E e − ≈ 9 . 0 GeV , E e + ≈ 3 . 1 GeV), Luminosity: L ≈ 500 fb − 1 ( Υ (4 S )) π + π − π 0 π 0 and π + π − η at BABA K. Griessinger (U Mainz) June 2017 6 / 20 R
Introduction Initial State Radiation (ISR) events at B A B A R γ ISR e − (9GeV) γ hadrons hadrons √ s ′ = E CM e + (3GeV) ISR selection Detected high energy photon: E γ > 3GeV → 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 – 15MeV) Continuous measurement from threshold to ∼ 5GeV → provides common, consistent systematic uncertainties π + π − π 0 π 0 and π + π − η at BABA K. Griessinger (U Mainz) June 2017 7 / 20 R
Cross section e + e − → π + π − π 0 π 0 e + e − → π + π − π 0 π 0 PRELIMINARY π + π − π 0 π 0 and π + π − η at BABA K. Griessinger (U Mainz) June 2017 8 / 20 R
Cross section e + e − → π + π − π 0 π 0 Resulting cross section e + e − → π + π − π 0 π 0 σ (nb) 35 P 30 R E L I M 25 dominant ISR-bkg π + π − 3 π 0 I N A R 20 Y removed using data 15 most precise measurement to 10 date 5 widest energy range 0 0 . 85 < E CM < 4 . 5 GeV 0.5 1 1.5 2 2.5 3 3.5 4 4.5 M 4 π (GeV/c 2 ) E CM (GeV) Syst. unc. 1 . 2 – 2 . 7 3 . 1% 2 . 7 – 3 . 2 6 . 7% > 3 . 2 7 . 1% π + π − π 0 π 0 and π + π − η at BABA K. Griessinger (U Mainz) June 2017 9 / 20 R
Cross section e + e − → π + π − π 0 π 0 Resulting cross section e + e − → π + π − π 0 π 0 σ (nb) σ (0) (nb) σ (0) (nb) 35 8 Y P R 30 R 7 A E N L I I M M 6 25 I I L N E A R R 5 P 20 Y 4 15 3 10 2 5 1 0 0 0.84 0.86 0.88 0.9 0.92 0.94 0.96 0.98 1 1.02 1.04 0.5 1 1.5 2 2.5 3 3.5 4 4.5 M 4 π (GeV/c 2 ) M 4 π (GeV/c 2 ) M 4 π (GeV/c 2 ) E CM (GeV) Syst. unc. Comparison to Chiral Pert. Theo. 1 . 2 – 2 . 7 3 . 1% (Eur.Phys.J., C24:535–545, 2002 [8]) 2 . 7 – 3 . 2 6 . 7% > 3 . 2 7 . 1% π + π − π 0 π 0 and π + π − η at BABA K. Griessinger (U Mainz) June 2017 9 / 20 R
Cross section e + e − → π + π − π 0 π 0 Contribution of π + π − 2 π 0 to g µ − 2 50 σ (e + e - → π + π - 2 π 0 ) (nb) � 1 − 4 m 2 � ∞ 45 SND e 1 s ADONE γγ 2 a had = K µ ( s ) σ ( s ) d s ADONE MEA 40 4 π 3 1 + 2 m 2 µ ACO e m 2 π 0 s DCI-M3N 35 ND OLYA 30 Before B A B A R (Eur.Phys.J.,C31:503,2003) [5] a µ (1 . 02 < √ s < 1 . 8 GeV) = 25 20 (16 . 76 ± 1 . 31 ± 0 . 20 rad ) × 10 − 10 15 10 5 0 1 1.5 2 2.5 3 3.5 4 4.5 E CM (GeV) π + π − π 0 π 0 and π + π − η at BABA K. Griessinger (U Mainz) June 2017 10 / 20 R
Cross section e + e − → π + π − π 0 π 0 Contribution of π + π − 2 π 0 to g µ − 2 50 σ (e + e - → π + π - 2 π 0 ) (nb) 45 SND � 1 − 4 m 2 � ∞ ADONE γγ 2 e 1 ADONE MEA s 40 a had = K µ ( s ) σ ( s ) d s ACO 1 + 2 m 2 µ 4 π 3 DCI-M3N e m 2 35 π 0 ND s OLYA BaBar 30 Before B A B A R (Eur.Phys.J.,C31:503,2003) [5] 25 PRELIMINARY a µ (1 . 02 < √ s < 1 . 8 GeV) = 20 (16 . 76 ± 1 . 31 ± 0 . 20 rad ) × 10 − 10 15 10 New result in the same energy range 5 a µ (1 . 02 < √ s < 1 . 8 GeV) = 0 1 1.5 2 2.5 3 3.5 4 4.5 (17 . 4 ± 0 . 1 stat ± 0 . 6 syst ) × 10 − 10 E CM (GeV) π + π − π 0 π 0 and π + π − η at BABA K. Griessinger (U Mainz) June 2017 10 / 20 R
Cross section e + e − → π + π − π 0 π 0 Contribution of π + π − 2 π 0 to g µ − 2 50 σ (e + e - → π + π - 2 π 0 ) (nb) 45 SND � 1 − 4 m 2 � ∞ ADONE γγ 2 e 1 ADONE MEA s a had 40 = K µ ( s ) σ ( s ) d s ACO 4 π 3 1 + 2 m 2 µ DCI-M3N m 2 e 35 π 0 s ND OLYA BaBar 30 New result starting at lower limit 25 PRELIMINARY a µ (0 . 85 < √ s < 1 . 8 GeV) = 20 (17 . 9 ± 0 . 1 stat ± 0 . 6 syst ) × 10 − 10 15 10 New result in a wider energy range 5 a µ (0 . 85 < √ s < 3 . 0 GeV) = 0 1 1.5 2 2.5 3 3.5 4 4.5 E CM (GeV) (21 . 8 ± 0 . 1 stat ± 0 . 7 syst ) × 10 − 10 π + π − π 0 π 0 and π + π − η at BABA K. Griessinger (U Mainz) June 2017 11 / 20 R
Cross section e + e − → π + π − η e + e − → π + π − η PRELIMINARY π + π − π 0 π 0 and π + π − η at BABA K. Griessinger (U Mainz) June 2017 12 / 20 R
Cross section e + e − → π + π − η Cross section e + e − → π + π − η PRELIMINARY Y R A N I M I L E R P Most accurate σ ( e + e − → π + π − η ) measurement to date First measurement up to 3 . 5 GeV Especially above 1 . 6 GeV more precise than previous data π + π − π 0 π 0 and π + π − η at BABA K. Griessinger (U Mainz) June 2017 13 / 20 R
Cross section e + e − → π + π − η Fits to the cross section e + e − → π + π − η P Y R E R L I M A I N N A I R M Y I L E R P Model 1: ρ (770) − ρ (1450), fit: E CM < 1 . 7 GeV Model 2: ρ (770) − ρ (1450) − ρ (1700), fit: E CM < 1 . 9 GeV Model 3: ρ (770) − ρ (1450) + ρ (1700), fit: E CM < 1 . 9 GeV Model 4: ρ (770) − ρ (1450) + ρ (1700) + ρ (2150), fit: E CM < 2 . 2 GeV “+”: relative phase 0 ◦ , “-”: relative phase 180 ◦ π + π − π 0 π 0 and π + π − η at BABA K. Griessinger (U Mainz) June 2017 14 / 20 R
Cross section e + e − → π + π − η Contribution of π + π − η to g µ − 2 HLMNT 2011 [10] � 1 − 4 m 2 � ∞ a µ ( √ s < 1 . 8 GeV) = e 1 s a had = K µ ( s ) σ ( s ) d s 4 π 3 1 + 2 m 2 µ m 2 e (0 . 88 ± 0 . 10) × 10 − 10 π 0 s Y DHMZ 2011 [6] R a µ ( √ s < 1 . 8 GeV) = A N I M (1 . 15 ± 0 . 06 stat ± 0 . 08 syst ) × 10 − 10 I L E R P π + π − π 0 π 0 and π + π − η at BABA K. Griessinger (U Mainz) June 2017 15 / 20 R
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