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

Colangelo, Gilberto; Hoferichter, Martin; Procura, Massimiliano; Stoffer, Peter (2015). Dispersion relation for hadronic light-by-light scattering: theoretical foundations. Journal of High Energy Physics, 2015(9), pp. 1-75. Springer 10.1007/JHEP09(2015)074

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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.

Item Type:

Journal Article (Original Article)

Division/Institute:

10 Strategic Research Centers > Albert Einstein Center for Fundamental Physics (AEC)
08 Faculty of Science > Institute of Theoretical Physics

UniBE Contributor:

Colangelo, Gilberto; Hoferichter, Martin; Procura, Massimiliano and Stoffer, Peter

Subjects:

500 Science > 530 Physics

ISSN:

1029-8479

Publisher:

Springer

Language:

English

Submitter:

Esther Fiechter

Date Deposited:

20 Nov 2015 16:14

Last Modified:

20 Nov 2015 16:14

Publisher DOI:

10.1007/JHEP09(2015)074

ArXiv ID:

1506.01386v2

BORIS DOI:

10.7892/boris.73160

URI:

https://boris.unibe.ch/id/eprint/73160

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