Tensor meson transition form factors in holographic QCD and the muon g − 2

Abstract

A bstract Despite the prominence of tensor mesons in photon-photon collisions, until recently their contribution to the hadronic light-by-light (HLbL) scattering part of the anomalous magnetic moment of the muon has been estimated to be at the level of only a few 10 − 12 , with an almost negligible contribution to the error budget of the Standard Model prediction. A recent reanalysis within the dispersive approach has found that after resolving the issue of kinematic singularities in previous approaches, a larger result is obtained, a few 10 − 11 , and with opposite sign as in previous results, when a simple quark model for the transition form factors is employed. In this paper, we present the first complete evaluation of tensor meson contributions within a hard-wall model in holographic QCD, which reproduces surprisingly well mass, two-photon width, and the observed singly virtual transition form factors of the dominant f 2 (1270), requiring only that the energy-momentum tensor correlator is matched to the leading OPE result of QCD. Due to a second structure function that is absent in the quark model and in lowest-order resonance chiral theory, the result for a μ turns out to be positive instead of negative, and also with a magnitude of a few 10 − 11 . We discuss both pole and non-pole contributions arising from tensor meson exchanges in the holographic HLbL amplitude, finding that keeping all contributions improves dramatically the convergence of a sum over excited tensor mesons and avoids unnaturally large contributions from the first few excited modes at low energies. Moreover, we find that the infinite tower of tensor mesons permits to fill the gap in the symmetric longitudinal short-distance constraint on the HLbL amplitude left by the contribution of axial vector mesons. Matching the corresponding leading-order OPE result leads to two-photon couplings consistent with the observed combined effects of the ground-state f 2 , a 2 , $$ {f}_2^{\prime } $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msubsup> <mml:mi>f</mml:mi> <mml:mn>2</mml:mn> <mml:mo>′</mml:mo> </mml:msubsup> </mml:math> multiplet and a total $$ {a}_{\mu}^{\textrm{Tensor}} $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msubsup> <mml:mi>a</mml:mi> <mml:mi>μ</mml:mi> <mml:mtext>Tensor</mml:mtext> </mml:msubsup> </mml:math> contribution of +12 . 4 × 10 − 11 ; with an F ρ fit this is reduced slightly to +11 . 1 × 10 − 11 . A contribution of this size from the tensor sector could explain the tension between the most recent dispersive and lattice results for $$ {a}_{\mu}^{\textrm{HLbL}} $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msubsup> <mml:mi>a</mml:mi> <mml:mi>μ</mml:mi> <mml:mtext>HLbL</mml:mtext> </mml:msubsup> </mml:math> .

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