2015/06/30 by Gilberto Colangelo, Martin Hoferichter, Massimiliano Procura +1 · 1 citation
Physics and Astronomy · #hep-ph #hep-ex #hep-lat #nucl-th
paper · pdf · doi:10.1007/jhep09(2015)074
59 pages, 11 figures. Draws on and substantially extends arXiv:1412.5171 [hep-ph] and arXiv:1402.7081 [hep-ph]. Version accepted for publication in JHEP
arxiv created 2015/09/22 · arxiv updated 2015/09/23
In this paper we make a further step towards a dispersive description of the hadronic light-by-light (HLbL) tensor, which should ultimately lead to a data-driven evaluation of its contribution to (g-2)μ. We first provide a Lorentz decomposition of the HLbL tensor performed according to the general recipe by Bardeen, Tung, and Tarrach, generalizing and extending our previous approach, which was constructed in terms of a basis of helicity amplitudes. Such a tensor decomposition has several advantages: the role of gauge invariance and crossing symmetry becomes fully transparent; the scalar coefficient functions are free of kinematic singularities and zeros, and thus fulfill a Mandelstam double-dispersive representation; and the explicit relation for the HLbL contribution to (g-2)μ in terms of the coefficient functions simplifies substantially. We demonstrate explicitly that the dispersive approach defines both the pion-pole and the pion-loop contribution unambiguously and in a model-independent way. The pion loop, dispersively defined as pion-box topology, is proven to coincide exactly with the one-loop scalar QED amplitude, multiplied by the appropriate pion vector form factors.