Hadronic Light-By-Light Scattering Contribution to the Muon<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi mathvariant="italic">g</mml:mi><mml:mi/><mml:mo>−</mml:mo><mml:mi/><mml:mn>2</mml:mn></mml:math>: An Effective Field Theory Approach

The correction to the muon anomalous magnetic moment from the pion-pole contribution to the hadronic light-by-light scattering is considered using a description of the π 0 − γ * − γ * transition form factor based on the large-N C and short-distance properties of QCD. The resulting twoloop integrals are treated by first performing the angular integration analytically, using the method of Gegenbauer polynomials, followed by a numerical evaluation of the remaining twodimensional integration over the moduli of the Euclidean loop momenta. The value obtained, a LbyL;π 0 µ = +5.8 (1.0) × 10 −10 , disagrees with other recent calculations. In the case of the vector meson dominance form factor, the result obtained by following the same procedure reads a LbyL;π 0 µ | V M D = +5.6 × 10 −10 , and differs only by its overall sign from the value obtained by previous authors. The inclusion of the η and η ′ poles gives a total value a LbyL;PS µ = +8.3 (1.2) × 10 −10 for the three pseudoscalar states. This result substantially reduces the difference between the experimental value of a µ and its theoretical counterpart in the standard model.

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“…(6.2), involving the positive definite weight function w f 1 (Q 1 , Q 2 ), contributes. This integral is divergent, and behaves as [49,51] lim…”

Section: Discussionmentioning

confidence: 99%

Hadronic light-by-light corrections to the muong−2:The pion-pole contribution

Knecht

Nyffeler²

2002

Phys. Rev. D

428

720

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“…Current estimates for HLbL scattering in (g − 2) µ are largely based on hadronic models [16][17][18][19][20][21][22][23][24][25][26][27], which despite implementing different limits of QCD, such as large-N c , chiral symmetry, or constraints from perturbative QCD, all involve a certain amount of uncontrollable uncertainties without offering a systematic path forward. In order to improve the determination of the HLbL contribution, we proposed a dispersive framework [28], based on the fundamental principles of analyticity, unitarity, gauge invariance, and crossing symmetry, which opens up a path towards a data-driven evaluation [29].…”

Section: Introductionmentioning

confidence: 99%

Dispersion relation for hadronic light-by-light scattering: two-pion contributions

Colangelo

Hoferichter

Procura

et al. 2017

J. High Energ. Phys.

385

257

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In this third paper of a series dedicated to a dispersive treatment of the hadronic light-by-light (HLbL) tensor, we derive a partial-wave formulation for two-pion intermediate states in the HLbL contribution to the anomalous magnetic moment of the muon (g − 2) µ , including a detailed discussion of the unitarity relation for arbitrary partial waves. We show that obtaining a final expression free from unphysical helicity partial waves is a subtle issue, which we thoroughly clarify. As a by-product, we obtain a set of sum rules that could be used to constrain future calculations of γ * γ * → ππ. We validate the formalism extensively using the pion-box contribution, defined by two-pion intermediate states with a pion-pole left-hand cut, and demonstrate how the full known result is reproduced when resumming the partial waves. Using dispersive fits to high-statistics data for the pion vector form factor, we provide an evaluation of the full pion box, a π-box µ = −15.9(2)×10 −11 . As an application of the partial-wave formalism, we present a first calculation of ππ-rescattering effects in HLbL scattering, with γ * γ * → ππ helicity partial waves constructed dispersively using ππ phase shifts derived from the inverse-amplitude method. In this way, the isospin-0 part of our calculation can be interpreted as the contribution of the f 0 (500) to HLbL scattering in (g − 2) µ . We argue that the contribution due to charged-pion rescattering implements corrections related to the corresponding pion polarizability and show that these are moderate. Our final result for the sum of pion-box contribution and its S-wave rescattering corrections reads a π-box µ + a ππ,π-pole LHC µ,J=0 = −24(1) × 10 −11 .

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“…Another caveat is that, although large values of the magnetic susceptibility χ 0 are disfavored, in the absence of stronger bounds on χ 0 , an additional (10 − 15)% systematic uncertainty on the previous value for a π 0 μ cannot be excluded. Modified ENJL [26][27][28] 59(9) VMD/HLS [29][30][31][32] 57(4) VMD+V (h 2 = 0) [33] 58(10) VMD+V (h 2 = −10 GeV 2 ) [33] 63(10) VMD+V (const.F π 0 γ * γ ) [37] 77(7) DSE [34,36] 58(7) Non local χQM [38] 65(2) AdS/QCD [21,39] 69 AdS/QCD/DIP [2] 65.4(2.5) RχT [40] 65.8(1.2) CχQM [41] 68(3) Table 3 shows a partial list of values of a π 0 μ obtained using different models, some of them discussed in other talks at this conference. Our numerical analysis showed also that the values of χ 0 hovered around 2 GeV −2 , as in the case shown in (18), with higher values disfavored although not definitely excluded.…”

Section: Numerical Resultsmentioning

confidence: 99%

What does Holographic QCD predict for anomalous (g− 2)_μ?

Cappiello

2016

EPJ Web of Conferences

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Abstract. In this talk we discuss how holographic models of QCD have been applied to the study of the lightby-light contribution to the muon anomalous magnetic moment. After a review of the holographic procedure, we discuss the approach we followed in a previous work, in which, using a certain set of holographic model as a "Theory Space", we gave our estimate for the π 0 exchange diagram. Our result depended also on the value of the quark magnetic susceptibility. Thus, in the last part of the talk, we concentrate on the attempts which have been done in the literature to apply holographic methods to the evaluation of this important order parameter of QCD.

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Hadronic Light-By-Light Scattering Contribution to the Muong−2: An Effective Field Theory Approach

Cited by 241 publications

References 32 publications

Hadronic light-by-light corrections to the muong−2:The pion-pole contribution

Hadronic light-by-light corrections to the muong−2:The pion-pole contribution

Dispersion relation for hadronic light-by-light scattering: two-pion contributions

What does Holographic QCD predict for anomalous (g− 2)_μ?

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Hadronic Light-By-Light Scattering Contribution to the Muong−2: An Effective Field Theory Approach

Cited by 241 publications

References 32 publications

Hadronic light-by-light corrections to the muong−2:The pion-pole contribution

Hadronic light-by-light corrections to the muong−2:The pion-pole contribution

Dispersion relation for hadronic light-by-light scattering: two-pion contributions

What does Holographic QCD predict for anomalous (g− 2)μ?

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What does Holographic QCD predict for anomalous (g− 2)_μ?