Charged Pion Polarizability & Muon g-2
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1 Charged Pion Polarizability & Muon g-2 M.J. Ramsey-Musolf U Mass Amherst Amherst Center for Fundamental Interactions ACFI-J Lab Workshop! March 2014! 1
2 Outline I. Intro & Motivation: SM & Beyond II. Hadronic Light-by-Light: Review & Status III. Charged Pion Loops revisited IV. Summary and Outlook 2
3 Intro & Motivation: SM & Beyond 3
4 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
5 Theory Error Budget a µ (EW) = 154 (2) x a µ (HVP-LO) = 7015 (47) x a µ (HVP-NLO) = -98 (1) x a µ (HLBL) = 116 (39) x (26) x δ a µ TH = x δ a µ EXP = x x BNL E821 FNAL New g-2 W. Marciano, arxiv: /hep-ph M. Davier et al, EPJ C 71 (2011)
6 Theory Error Budget a µ (EW) = 154 (2) x a µ (HVP-LO) = 7015 (47) x a µ (HVP-NLO) = -98 (1) x a µ (HLBL) = 116 (39) x (26) x δ a µ TH = x δ a µ EXP = x x BNL E821 FNAL New g-2 Δa µ = a µ EXP - a µ TH = 287 (83) x W. Marciano, arxiv: /hep-ph M. Davier et al, EPJ C 71 (2011)
7 Theory Error Budget a µ (EW) = 154 (2) x a µ (HVP-LO) = 7015 (47) x a µ (HVP-NLO) = -98 (1) x a µ (HLBL) = 116 (39) x (26) x δ a µ TH = x δ a µ EXP = x x BNL E821 FNAL New g-2 Δa µ = a µ EXP - a µ TH = 287 (83) x W. Marciano, arxiv: /hep-ph M. Davier et al, EPJ C 71 (2011)
8 Theory Error Budget a µ (EW) = 154 (2) x a µ (HVP-LO) = 7015 (47) x a µ (HVP-NLO) = -98 (1) x a µ (HLBL) = 116 (39) x (26) x Most challenging δ a µ TH = x δ a µ EXP = x x BNL E821 FNAL New g-2 Δa µ = a µ EXP - a µ TH = 287 (83) x W. Marciano, arxiv: /hep-ph M. Davier et al, EPJ C 71 (2011)
9 Hadronic Light-by-Light: Review & Status 9
10 HLBL Contributions Pseudoscalar Loops π +, K + π 0, η... Pseudoscalar Poles Quark Loops Hayakawa, Kinoshita, Sanda 95 10
11 Pseudoscalar Pole Contribution O (N C ) 11
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 12
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 a µ (χpt) = ( C ) x
14 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) = ( C ) x
15 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) = ( C ) x Models: C ~ 2 E821: C ~ 10 ~ 1σ 15
16 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
17 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 ρ pole 17
18 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 (! C = +1 ) 18
19 Charged Pion Loops Revisited 19
20 Charged Pion Contribution Kinoshita, Nizic, Okamoto 85 ; Hayakawa, Kinoshita, Sanda 95 O (N C0 ) Point-like pions: (19) (α /π) 3 = -48 (2) x Include F π (q 2 ): (19) (α /π) 3 = -16 (2) x HLS : (12) (α /π) 3 = -4.5 (0.2) x ENJL: (4) (α /π) 3 = -19 (5) x
21 Charged Pion Contribution Kinoshita, Nizic, Okamoto 85 ; Hayakawa, Kinoshita, Sanda 95 O (N C0 ) Substantial NLO impact Point-like pions: (19) (α /π) 3 = -48 (2) x Include F π (q 2 ): (19) (α /π) 3 = -16 (2) x HLS : (12) (α /π) 3 = -4.5 (0.2) x ENJL: (4) (α /π) 3 = -19 (5) x
22 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
23 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
24 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: (2012) d=10 ops 24
25 Charged Pion Contribution: χpt Kevin Engel (Caltech), Hiren Patel (Wisconsin), MRM Beyond leading order: embedding subgraphs in full HLBL contribution PRD 86: (2012) LO: suppressed 25
26 Charged Pion Contribution: χpt Kevin Engel (Caltech), Hiren Patel (Wisconsin), MRM Beyond leading order: embedding subgraphs in full HLBL contribution PRD 86: (2012) Pol bility Charge radius 26
27 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: (2012) Charge radius 27
28 Charged Pion Contribution: χpt Kevin Engel (Caltech), MRM Beyond leading order: embedding subgraphs in full HLBL contribution + 28
29 Charged Pion Contribution: χpt Kevin Engel (Caltech), MRM Beyond leading order: embedding subgraphs in full HLBL contribution Charge radius Pol bility + 29
30 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
31 Charged Pion Contribution: χpt Kevin Engel (Caltech), MRM Beyond leading order: embedding subgraphs in full HLBL contribution Charge radius Pol bility + Bijnens & Abyaneh : Include α 9 +α 10 to k loop ~ 500 MeV! 10% increase in a µ (π loop) 31
32 Beyond χpt: Modeling High Q 2 Analgous problem: Pseudoscalar EM mass splitting Donoghue, Holstein, Wyler 93 32
33 Beyond χpt: Modeling High Q 2 Analgous problem: Pseudoscalar EM mass splitting Donoghue, Holstein, Wyler 93 Pure EFT: Divergent! Modeling required 33
34 Beyond χpt: Modeling High Q 2 Analgous problem: Pseudoscalar EM mass splitting Donoghue, Holstein, Wyler 93 Quark counting rules 34
35 Beyond χpt: Modeling High Q 2 Analgous problem: Pseudoscalar EM mass splitting Donoghue, Holstein, Wyler 93 Quark counting rules ρ a 1 35
36 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
37 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
38 Charged Pion Contribution: Model Kevin Engel (Caltech), MRM arxiv: 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
39 Charged Pion Contribution: Model Kevin Engel (Caltech), MRM + ρ pole 39
40 Charged Pion Contribution: Model Kevin Engel (Caltech), MRM arxiv: 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
41 Pion Polarizability Experiment Rad π decay + r π 2 41
42 Pion Polarizability Experiment J Lab future γa! π + π - A Rad π decay + r π 2 42
43 Charged Pion Contribution: Results Kevin Engel (Caltech), MRM arxiv: (α 9 + α 10 ): Rad π decay γ p! γ π + n Recall: 43
44 Charged Pion Contribution: Results Kevin Engel (Caltech), MRM arxiv: (α 9 + α 10 ): Rad π decay γ p! γ π + n ~ 30 x spread from (α 9 + α 10 ) ~ 30 x spread from interpolation (modeling) 44
45 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
46 Back Up Slides 46
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 47
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 48
49 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
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 50
51 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
52 Nyffeler HLBL: Compilation 52
53 Nyffeler HLBL: Compilation 53
54 Nyffeler HLBL: Compilation HLS 54
55 Lattice QCD See A. Juttner (B1) Blum, Izubuchi, : QED + QCD Rakow (QCDSF): 4pt function 55
56 Aoyama, Hayakawa, Kinoshita, Nio 12 Tenth Order QED 56
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