Charged Pion Polarizability & Muon g-2

Charged Pion Polarizability & Muon g-2 M.J. Ramsey-Musolf U Mass Amherst Amherst Center for Fundamental Interactions http://www.physics.umass.edu/acfi/ ACFI-J Lab Workshop! March 2014! 1

Outline I. Intro & Motivation: SM & Beyond II. Hadronic Light-by-Light: Review & Status III. Charged Pion Loops revisited IV. Summary and Outlook 2

Intro & Motivation: SM & Beyond 3

Muon Anomalous Magnetic Moment γ µ µ Z π QED Weak Had VP Had LbL Davier et al 11 ~ 3.5 σ! SM Loops ψ ϕ ϕ γ Smuon (SUSY) Leptoquark Dark photon Heavy Z Extended scalar sector µ 4

Theory Error Budget a µ (EW) = 154 (2) x 10-11 a µ (HVP-LO) = 7015 (47) x 10-11 a µ (HVP-NLO) = -98 (1) x 10-11 a µ (HLBL) = 116 (39) x 10-11 105 (26) x 10-11 δ a µ TH = + - 53 x 10-11 δ a µ EXP = + - 63 x 10-11 + - 15 x 10-11 BNL E821 FNAL New g-2 W. Marciano, arxiv: 1001.4528/hep-ph M. Davier et al, EPJ C 71 (2011) 1515 5

Theory Error Budget a µ (EW) = 154 (2) x 10-11 a µ (HVP-LO) = 7015 (47) x 10-11 a µ (HVP-NLO) = -98 (1) x 10-11 a µ (HLBL) = 116 (39) x 10-11 105 (26) x 10-11 δ a µ TH = + - 53 x 10-11 δ a µ EXP = + - 63 x 10-11 + - 15 x 10-11 BNL E821 FNAL New g-2 Δa µ = a µ EXP - a µ TH = 287 (83) x 10-11 W. Marciano, arxiv: 1001.4528/hep-ph M. Davier et al, EPJ C 71 (2011) 1515 6

Theory Error Budget a µ (EW) = 154 (2) x 10-11 a µ (HVP-LO) = 7015 (47) x 10-11 a µ (HVP-NLO) = -98 (1) x 10-11 a µ (HLBL) = 116 (39) x 10-11 105 (26) x 10-11 δ a µ TH = + - 53 x 10-11 δ a µ EXP = + - 63 x 10-11 + - 16 x 10-11 BNL E821 FNAL New g-2 Δa µ = a µ EXP - a µ TH = 287 (83) x 10-11 W. Marciano, arxiv: 1001.4528/hep-ph M. Davier et al, EPJ C 71 (2011) 1515 7

Theory Error Budget a µ (EW) = 154 (2) x 10-11 a µ (HVP-LO) = 7015 (47) x 10-11 a µ (HVP-NLO) = -98 (1) x 10-11 a µ (HLBL) = 116 (39) x 10-11 105 (26) x 10-11 Most challenging δ a µ TH = + - 53 x 10-11 δ a µ EXP = + - 63 x 10-11 + - 16 x 10-11 BNL E821 FNAL New g-2 Δa µ = a µ EXP - a µ TH = 287 (83) x 10-11 W. Marciano, arxiv: 1001.4528/hep-ph M. Davier et al, EPJ C 71 (2011) 1515 8

Hadronic Light-by-Light: Review & Status 9

HLBL Contributions Pseudoscalar Loops π +, K + π 0, η... Pseudoscalar Poles Quark Loops Hayakawa, Kinoshita, Sanda 95 10

Pseudoscalar Pole Contribution O (N C ) 11

Pseudoscalar Pole Contribution O (N C ) L WZW : ln 2 term! Sign error discovered by Knecht et al P! l + l - : ln term! Exp t (MRM, Wise) Overall LEC! Models, lattice QCD 12

Pseudoscalar Pole Contribution O (N C ) L WZW : ln 2 term! Sign error discovered by Knecht et al P! l + l - : ln term! Exp t (MRM, Wise) Overall LEC! Models, lattice QCD a µ (χpt) = (57 +50-60 + 31 C ) x 10-11 13

Pseudoscalar Pole Contribution O (N C ) L WZW : ln 2 term! Sign error discovered by Knecht et al P! l + l - : ln term! Exp t (MRM, Wise) Overall LEC! Models, lattice QCD Significantly reduced: KTeV 07 a µ (χpt) = (57 +50-60 + 31 C ) x 10-11 14

Representative Models Hidden Local Symmetry (HLS) [1] Extended NJL (ENJL)/VMD[1,2] Constituent Chiral Quark Model (CχQM) [3] AdS/CFT [4] Dyson-Schwinger [5] [1] Hayakawa, Kinoshita, Sanda 95 [2] Bijnens, Pallante, Prades 96 [3] De Rafael 12; Boughezal & Melkinov 11 [4] Hong & Kim 09; Cappiello, Cata, D Ambrosio 11 [5] Goeke, Fischer, Williams 11, 12 16

Short Distance Constraints Vainshtein & Melnikov 04 O (N C ) L WZW : ln 2 term! Sign error discovered by Knecht et al P! l + l - : ln term! Exp t (MRM, Wise) Overall LEC! Models, lattice QCD Δ a µ (OPE) = 30 x 10-11 (! C = +1 ) 18

Charged Pion Loops Revisited 19

Charged Pion Contribution Kinoshita, Nizic, Okamoto 85 ; Hayakawa, Kinoshita, Sanda 95 O (N C0 ) Point-like pions: -0.0383 (19) (α /π) 3 = -48 (2) x 10-11 Include F π (q 2 ): -0.0125 (19) (α /π) 3 = -16 (2) x 10-11 HLS : -0.00355 (12) (α /π) 3 = -4.5 (0.2) x 10-11 ENJL: -0.015 (4) (α /π) 3 = -19 (5) x 10-11 20

Charged Pion Contribution Kinoshita, Nizic, Okamoto 85 ; Hayakawa, Kinoshita, Sanda 95 O (N C0 ) Substantial NLO impact Point-like pions: -0.0383 (19) (α /π) 3 = -48 (2) x 10-11 Include F π (q 2 ): -0.0125 (19) (α /π) 3 = -16 (2) x 10-11 HLS : -0.00355 (12) (α /π) 3 = -4.5 (0.2) x 10-11 ENJL: -0.015 (4) (α /π) 3 = -19 (5) x 10-11 21

Charged Pion Contribution: χpt Kevin Engel (Caltech), Hiren Patel (Wisconsin), MRM Chiral Perturbation Theory Pion: Goldstone boson of spont broken chiral symmetry SU(2) L x SU(2) R! SU(2) V Expand in p / Λ χ Λ χ ~ 1 GeV 22

Charged Pion Contribution: χpt Kevin Engel (Caltech), Hiren Patel (Wisconsin), MRM Beyond leading order: subgraphs Pion charge radius: first non-trivial term in expansion of F π (q 2 ) O (p 4 ) LEC: α 9 Pion polarizability: distinct physics from ff O (p 4 ) LEC: α 9 + α 10 + 23

Charged Pion Contribution: χpt Kevin Engel (Caltech), Hiren Patel (Wisconsin), MRM Beyond leading order: embedding subgraphs in full HLBL contribution d=8 ops PRD 86:037502 (2012) d=10 ops 24

Charged Pion Contribution: χpt Kevin Engel (Caltech), Hiren Patel (Wisconsin), MRM Beyond leading order: embedding subgraphs in full HLBL contribution PRD 86:037502 (2012) LO: suppressed 25

Charged Pion Contribution: χpt Kevin Engel (Caltech), Hiren Patel (Wisconsin), MRM Beyond leading order: embedding subgraphs in full HLBL contribution PRD 86:037502 (2012) Pol bility Charge radius 26

Charged Pion Contribution: χpt Kevin Engel (Caltech), Hiren Patel (Wisconsin), MRM Beyond leading order: embedding subgraphs in full HLBL contribution Currently Omitted Pol bility PRD 86:037502 (2012) Charge radius 27

Charged Pion Contribution: χpt Kevin Engel (Caltech), MRM Beyond leading order: embedding subgraphs in full HLBL contribution + 28

Charged Pion Contribution: χpt Kevin Engel (Caltech), MRM Beyond leading order: embedding subgraphs in full HLBL contribution Charge radius Pol bility + 29

Charged Pion Contribution: χpt Kevin Engel (Caltech), MRM Beyond leading order: embedding subgraphs in full HLBL contribution Charge radius Pol bility Pure EFT: Divergent! Modeling + required 30

Charged Pion Contribution: χpt Kevin Engel (Caltech), MRM Beyond leading order: embedding subgraphs in full HLBL contribution Charge radius Pol bility + Bijnens & Abyaneh 1208.3548 : Include α 9 +α 10 to k loop ~ 500 MeV! 10% increase in a µ (π loop) 31

Beyond χpt: Modeling High Q 2 Analgous problem: Pseudoscalar EM mass splitting Donoghue, Holstein, Wyler 93 32

Beyond χpt: Modeling High Q 2 Analgous problem: Pseudoscalar EM mass splitting Donoghue, Holstein, Wyler 93 Pure EFT: Divergent! Modeling required 33

Beyond χpt: Modeling High Q 2 Analgous problem: Pseudoscalar EM mass splitting Donoghue, Holstein, Wyler 93 Quark counting rules 34

Beyond χpt: Modeling High Q 2 Analgous problem: Pseudoscalar EM mass splitting Donoghue, Holstein, Wyler 93 Quark counting rules ρ a 1 35

Beyond χpt: Modeling High Q 2 Analgous problem: Pseudoscalar EM mass splitting Donoghue, Holstein, Wyler 93 Finite Δ m π 2 requires additional form factors Quark counting rules See Donoghue & Perez 96 ρ a 1 36

Beyond χpt: Modeling High Q 2 Analgous problem: Pseudoscalar EM mass splitting Donoghue, Holstein, Wyler 93 Model: Expt: Δ m π 2 = 2 m π x 5.6 MeV Δ m π 2 = 2 m π x 4.6 MeV Quark counting rules ρ a 1 37

Charged Pion Contribution: Model Kevin Engel (Caltech), MRM arxiv: 1309.2225 Interpolating from chiral to high momentum regime: Match onto O (p 4 ) χpt results in low p regime Reproduce 1/q 2 asymptotic behavior for T µν Incorporate resonance saturation physics Produce finite a µ Reproduce EM Δm 2 π if possible Note: Δm π 2 receives contribution from 38

Charged Pion Contribution: Model Kevin Engel (Caltech), MRM + ρ pole 39

Charged Pion Contribution: Model Kevin Engel (Caltech), MRM arxiv: 1309.2225 Two Models: Finite Δ m π 2 for M A 2 = 2 M V 2 4 M A 2 (α 9 + α 10 ) = F A 2 40

Pion Polarizability Experiment Rad π decay + r π 2 41

Pion Polarizability Experiment J Lab future γa! π + π - A Rad π decay + r π 2 42

Charged Pion Contribution: Results Kevin Engel (Caltech), MRM arxiv: 1309.2225 (α 9 + α 10 ): Rad π decay γ p! γ π + n Recall: 43

Charged Pion Contribution: Results Kevin Engel (Caltech), MRM arxiv: 1309.2225 (α 9 + α 10 ): Rad π decay γ p! γ π + n ~ 30 x 10-11 spread from (α 9 + α 10 ) ~ 30 x 10-11 spread from interpolation (modeling) 44

Summary & Outlook Charged pion polarizability previously omitted from SM prediction for muon g-2 Inclusion tends to increase discrepancy between experimental value and SM prediction Parametric and modeling uncertainties are significant compared to expected precision of FNAL measurement J Lab polarizability measurement would eliminate parameteric uncertainty Future challenge: experimental test of interpolation with γ * momentum 45

Back Up Slides 46

Muon Anomalous Magnetic Moment γ µ µ Z π QED Weak Had VP Had LbL Davier et al 11 ~ 3.4 σ! SM Loops 47

Muon Anomalous Magnetic Moment γ µ µ Z π QED Weak Had VP Had LbL Davier et al 11 ~ 3.4 σ! SM Loops SUSY Loops 48

Muon Anomalous Magnetic Moment γ µ µ Z π QED Weak Had VP Had LbL Davier et al 11 ~ 3.4 σ! SM Loops SUSY Loops 49

Muon Anomalous Magnetic Moment γ µ µ Z π Future goal QED Weak Had VP Had LbL Davier et al 11 ~ 3.4 σ! SM Loops SUSY Loops 50

Muon Anomalous Magnetic Moment γ µ µ Z π Future goal QED Weak Had VP Had LbL Davier et al 11 ~ 3.4 σ! SM Loops SUSY Loops 51

Nyffeler 1001.3970 HLBL: Compilation 52

Nyffeler 1001.3970 HLBL: Compilation 53

Nyffeler 1001.3970 HLBL: Compilation HLS 54

Lattice QCD See A. Juttner (B1) Blum, Izubuchi, : QED + QCD Rakow (QCDSF): 4pt function 55

Aoyama, Hayakawa, Kinoshita, Nio 12 Tenth Order QED 56