Old and new results HLbL results OLD AND NEW RESULTS FOR Johan Bijnens HADRONIC-LIGHT-BY-LIGHT Overview Main contributions HLbL Future Johan Bijnens Conclusions Lund University bijnens@thep.lu.se http://www.thep.lu.se/ ∼ bijnens http://www.thep.lu.se/ ∼ bijnens/chpt.html Hadronic Probes of Fundamental Symmetries, Amherst, 6-8 March 2014 1/64
Overview Overview Old and new 1 results HLbL results Main contributions 2 Johan Bijnens QED HO hadronic Overview Main HLbL 3 contributions General properties HLbL π 0 -exchange Future π -loop: new stuff is here Conclusions Quark-loop Scalar a 1 -exchange Summary Future 4 Theory Experiment Conclusions 5 2/64
Literature Old and new results HLbL Final experimental paper: results G. W. Bennett et al. [Muon G-2 Collaboration], “Final Johan Bijnens Report of the Muon E821 Anomalous Magnetic Moment Overview Measurement at BNL,” Phys. Rev. D 73 (2006) 072003 Main [hep-ex/0602035]. contributions HLbL Review 1: Future F. J. M. Farley and Y. K. Semertzidis, “The 47 years of Conclusions muon g-2,” Prog. Part. Nucl. Phys. 52 (2004) . Review 2: J. P. Miller, E. de Rafael and B. L. Roberts, “Muon (g-2): Experiment and theory,” Rept. Prog. Phys. 70 (2007) 795 [hep-ph/0703049]. Review 3: F. Jegerlehner and A. Nyffeler, “The Muon g-2,” Phys. Rept. 477 (2009) 1 [arXiv:0902.3360 [hep-ph]]. 3/64
Literature Old and new results HLbL Lectures: results M. Knecht, Lect. Notes Phys. 629 (2004) 37 Johan Bijnens [hep-ph/0307239]. Overview “Final” HLBL number: Main contributions J. Bijnens and J. Prades, Mod. Phys. Lett. A 22 (2007) HLbL 767 [hep-ph/0702170]. J. Prades, E. de Rafael and A. Vainshtein, “Hadronic Future Light-by-Light Scattering Contribution to the Muon Conclusions Anomalous Magnetic Moment,” (Advanced series on directions in high energy physics. 20) [arXiv:0901.0306 [hep-ph]]. New stuff here: JB, Mehran Zahiri Abyaneh, Johan Relefors HLbL pion loop contribution arXiv:1208.3548, arXiv:1208.2554, arXiv:1308.2575 and to be published 4/64
Muon g − 2: measurement Old and new results HLbL results Johan Bijnens Overview Main contributions HLbL Future Conclusions 5/64
Muon g − 2: measurement Old and new results HLbL results Johan Bijnens Overview Main contributions HLbL Future Conclusions 6/64
Muon g − 2: measurement Old and new results HLbL results Johan Bijnens Overview Main contributions HLbL Future Conclusions Phys.Rev. D73 (2006) 072003 [hep-ex/0602035] 7/64
Muon g − 2: measurement Old and new results HLbL results Johan Bijnens Overview Main contributions HLbL Future Conclusions Phys.Rev. D73 (2006) 072003 [hep-ex/0602035] 2001: µ − , others µ + 8/64
Muon g − 2: overview Old and new results HLbL in terms of the anomaly a µ = ( g − 2) / 2 results Johan Bijnens Data dominated by BNL E821 (statistics)(systematic) a exp µ + = 11659204(6)(5) × 10 − 10 Overview a exp µ − = 11659215(8)(3) × 10 − 10 Main contributions a exp = 11659208 . 9(5 . 4)(3 . 3) × 10 − 10 HLbL µ Future Theory is off somewhat (electroweak)(LO had)(HO had) Conclusions = 11659180 . 2(0 . 2)(4 . 2)(2 . 6) × 10 − 10 a SM µ = 28 . 7(6 . 3)(4 . 9) × 10 − 10 (PDG) ∆ a µ = a exp − a SM µ µ E821 goes to Fermilab, expect factor of four in precision Note: g agrees to 3 10 − 9 with theory Many BSM models CAN predict a value in this range (often a lot more or a lot less) Numbers taken from PDG2012, see references there 9/64
Summary of Muon g − 2 contributions Old and new results HLbL Error on LO had results all e + e − based OK 10 10 a µ Johan Bijnens τ based 2 σ exp 11 659 208.9 6.3 Overview Error on HLbL theory 11 659 180.2 5.0 Main contributions Errors added QED 11 658 471.8 0.0 HLbL EW 15.4 0.2 quadratically Future LO Had 692.3 4.2 3.5 σ Conclusions HO HVP − 9.8 0.1 Difference: HLbL 10.5 2.6 4% of LO Had difference 28.7 8.1 270% of HLbL 1% of leptonic LbL � 2 Generic SUSY: 12 . 3 × 10 − 10 � 100 GeV tan β M SUSY M SUSY ≈ 66 GeV √ tan β 10/64
Muon g − 2: QED � α � α � 2 + 24 . 05050964(43) � 3 a QED = α Old and new 2 π + 0 . 765857410(27) µ π π results HLbL � α � 4 + 663(20) � α � 5 + · · · results +130 . 8055(80) π π Johan Bijnens First three loops known analytically Overview four-loops fully done numerically Main contributions Five loops estimate QED HO hadronic Kinoshita, Laporta, Remiddi, Schwinger,. . . HLbL α fixed from the electron g − 2: α = 1 / 137 . 035999084(51) Future a QED = 11658471 . 809(0 . 015) × 10 − 10 Conclusions µ Light-by-light surprisingly large: 2670 × 10 − 10 e = 20 . 95 , µ = 0 . 37 , τ = 0 . 002 11/64
Muon g − 2: HO hadronic Old and new results HLbL results Two main types of contributions Johan Bijnens Overview Main contributions QED HO hadronic HLbL Future HO HVP HLbL Conclusions HO HVP is like LO Had, can be derived from e + e − → hadrons. a HO HVP = − 9 . 84(0 . 06) × 10 − 10 µ HLbL is the real problem: best estimate now: a HLbL = 10 . 5(2 . 6) × 10 − 10 µ Note that the sum is very small: but not an indication of the error 12/64
HLbL: the main object to calculate Old and new β p 3 results HLbL results Johan Bijnens Overview Main α q ρ p 2 contributions ν p 1 HLbL General properties π 0-exchange p ′ p 4 p 5 p π -loop Quark-loop Scalar a 1-exchange Muon line and photons: well known Summary Future The blob: fill in with hadrons/QCD Conclusions Trouble: low and high energy very mixed Double counting needs to be avoided: hadron exchanges versus quarks 13/64
A separation proposal: a start Old and new results HLbL results Johan Bijnens E. de Rafael, “Hadronic contributions to the muon g-2 and low-energy QCD,” Overview Phys. Lett. B322 (1994) 239-246. [hep-ph/9311316]. Main Use ChPT p counting and large N c contributions HLbL p 4 , order 1: pion-loop General properties p 8 , order N c : quark-loop and heavier meson exchanges π 0-exchange π -loop Quark-loop p 6 , order N c : pion exchange Scalar a 1-exchange Summary Does not fully solve the problem Future only short-distance part of quark-loop is really p 8 Conclusions but it’s a start 14/64
A separation proposal: a start Old and new results HLbL E. de Rafael, “Hadronic contributions to the muon g-2 and low-energy QCD,” results Phys. Lett. B322 (1994) 239-246. [hep-ph/9311316]. Johan Bijnens Use ChPT p counting and large N c Overview p 4 , order 1: pion-loop Main contributions p 8 , order N c : quark-loop and heavier meson exchanges HLbL General p 6 , order N c : pion exchange properties π 0-exchange π -loop Implemented by two groups in the 1990s: Quark-loop Scalar a 1-exchange Hayakawa, Kinoshita, Sanda: meson models, pion loop using Summary hidden local symmetry, quark-loop with VMD, calculation Future in Minkowski space Conclusions JB, Pallante, Prades: Try using as much as possible a consistent model-approach, ENJL, calculation in Euclidean space 14/64
General properties Old and new results HLbL results Johan Bijnens p 1 p 2 Overview Main contributions Π ρναβ ( p 1 , p 2 , p 3 ) = HLbL General properties q p 3 π 0-exchange π -loop Quark-loop Scalar a 1-exchange Summary Future Conclusions Actually we really need δ Π ρναβ ( p 1 , p 2 , p 3 ) � � � δ p 3 λ � p 3 =0 15/64
General properties Old and new results HLbL results Π ρναβ ( p 1 , p 2 , p 3 ): Johan Bijnens In general 138 Lorentz structures (but only 28 contribute Overview to g − 2) Main contributions Using q ρ Π ρναβ = p 1 ν Π ρναβ = p 2 α Π ρναβ = p 3 β Π ρναβ = 0 HLbL 43 gauge invariant structures General properties π 0-exchange Bose symmetry relates some of them π -loop Quark-loop All depend on p 2 1 , p 2 2 and q 2 , but before derivative and Scalar a 1-exchange p 3 → 0 also p 2 3 , p 1 · p 2 , p 1 · p 3 Summary Future Compare HVP: one function, one variable Conclusions General calculation from experiment difficult to see how In four photon measurement: lepton contribution 16/64
General properties Old and new results HLbL d 4 p 1 d 4 p 2 � � plus loops inside the hadronic part results (2 π ) 4 (2 π ) 4 Johan Bijnens 8 dimensional integral, three trivial, Overview 5 remain: p 2 1 , p 2 2 , p 1 · p 2 , p 1 · p µ , p 2 · p µ Main Rotate to Euclidean space: contributions Easier separation of long and short-distance HLbL General Artefacts (confinement) in models smeared out. properties π 0-exchange π -loop More recent: can do two more using Gegenbauer Quark-loop techniques Knecht-Nyffeler, Scalar a 1-exchange Summary Jegerlehner-Nyffeler,JB–Zahiri-Abyaneh–Relefors Future 2 and Q 2 remain P 2 1 , P 2 Conclusions dl P 1 dl P 2 dl Q a XLLQ study a X � dl P 1 dl P 2 a XLL � µ = = µ µ l P = ln ( P / G eV ), to see where the contributions are Study the dependence on the cut-off for the photons 17/64
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