Light-by-light scattering sum rules in light of new data

Danilkin, Igor; Vanderhaeghen, Marc

doi:10.1103/physrevd.95.014019

Cited by 112 publications

(102 citation statements)

References 28 publications

(63 reference statements)

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“…Hence, we can reverse the argument: with the assumption that sufficiently high partial waves are negligible, the included partial waves have to fulfill the sum rules, which also removes the dependence on the representation. This can be used as a check of or even a constraint on the input for the γ * γ * → ππ helicity partial waves, in a similar way as sum rules for forward HLbL scattering have been used to derive constraints on transition form factors of higher resonances [63,70,71].…”

Section: Approximate Partial-wave Sum Rulesmentioning

confidence: 99%

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

Colangelo

Hoferichter

Procura

et al. 2017

J. High Energ. Phys.

361

254

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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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Section: Approximate Partial-wave Sum Rulesmentioning

confidence: 99%

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

Colangelo

Hoferichter

Procura

et al. 2017

J. High Energ. Phys.

361

254

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“…Other approaches that combine phenomenological constraints with information from lattice QCD employ expansions of a hvp µ in terms of Mellin-Barnes moments [10][11][12] or finite energy sum rules [13,14]. The hadronic light-by-light scattering contribution has so far only been determined via model estimates (as reviewed in [5,[15][16][17]), although efforts have been undertaken to move towards a data-driven [18][19][20][21][22][23][24][25][26][27] approach as well.…”

Section: Jhep10(2017)020mentioning

confidence: 99%

The hadronic vacuum polarization contribution to the muon g − 2 from lattice QCD

Morte

Francis

Gülpers

et al. 2017

J. High Energ. Phys.

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We present a calculation of the hadronic vacuum polarization contribution to the muon anomalous magnetic moment, a hvp µ , in lattice QCD employing dynamical up and down quarks. We focus on controlling the infrared regime of the vacuum polarization function. To this end we employ several complementary approaches, including Padé fits, time moments and the time-momentum representation. We correct our results for finitevolume effects by combining the Gounaris-Sakurai parameterization of the timelike pion form factor with the Lüscher formalism. On a subset of our ensembles we have derived an upper bound on the magnitude of quark-disconnected diagrams and found that they decrease the estimate for a hvp JHEP10 (2017)020 10 −10 , where the first error is statistical, and the second denotes the combined systematic uncertainty. Based on our findings we discuss the prospects for determining a hvp µ with sub-percent precision.

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“…[8] for the full expression and extension to virtual photons. In order to satisfy the helicity sum rule, it was found in [5] that there is a quantitative cancellation between π 0 and a 2 in the low-lying isovector sector and a cancellation between η, η and f 2 (1270) in the low-lying isoscalar sector.…”

Section: Real Photon Helicity Sum Rule For Charmonium Statesmentioning

confidence: 99%

“…[8]. In applying these results to the charmonium states, the sum rules SR 2 and SR 3 can be expressed as a sum over the narrow charmonia bound states and a continuum contribution as:…”

Section: Virtual Photon Sum Rules For Charmonium Statesmentioning

confidence: 99%

Light-by-light forward scattering sum rules for charmonium states

Danilkin

Vanderhaeghen

2017

Phys. Rev. D

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We apply three forward light-by-light scattering sum rules to charmonium states. We show that these sum rules imply a cancellation between charmonium bound state contributions, which are mostly known from the γγ decay widths of these states, and continuum contributions above DD threshold, for which we provide a duality estimate. We also show that two of these sum rules allow to predict the yet unmeasured γ * γ coupling of the χc1(1P ) state, which can be tested at present high-luminosity e + e − colliders.

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Light-by-light scattering sum rules in light of new data

Cited by 112 publications

References 28 publications

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

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

The hadronic vacuum polarization contribution to the muon g − 2 from lattice QCD

Light-by-light forward scattering sum rules for charmonium states

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