Dispersion relation for hadronic light-by-light scattering: theoretical foundations

作者：Colangelo Gilberto^*; Hoferichter Martin; Procura Massimiliano; Stoffer Peter

来源：The Journal of High Energy Physics, 2015, 2015(9): 074.

DOI：10.1007/JHEP09(2015)074

• Chiral Lagrangians
• QCD

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)(mu). 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 doubledispersive representation; and the explicit relation for the HLbL contribution to (g - 2)(mu) 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.

• 出版日期2015-9-14