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A unified formulation of one-loop tensor integrals for finite volume effects

Ze-Rui Liang
(
- Hunan U.
)
,
De-Liang Yao
(
- Hunan U.
)

Jul 24, 2022

38 pages

Published in:

JHEP 12 (2022) 029

Published: Dec 6, 2022

e-Print:

2207.11750 [hep-ph]

DOI:

10.1007/JHEP12(2022)029

View in:

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Abstract: (Springer)

A unified formulation of one-loop tensor integrals is proposed for systematical calculations of finite volume corrections. It is shown that decomposition of the one-loop tensor integrals into a series of tensors accompanied by tensor coefficients is feasible, if a unit space-like four vector n

^{μ}

, originating from the discretization effects at finite volume, is introduced. A generic formula has been derived for numerical computations of all the involved tensor coefficients. For the vanishing external three-momenta, we also investigate the feasibility of the conventional Passarino-Veltmann reduction of the tensor integrals in a finite volume. Our formulation can be easily used to realize the automation of the calculations of finite volume corrections to any interesting quantities at one-loop level. Besides, it provides finite volume result in a unique and concise form, which is suited for, e.g., carrying out precision determination of physical observable from modern lattice QCD data.

Note:

Version accepted for publication in JHEP; 38 pages, 5 figures, 2 tables

Automation
Algorithms and Theoretical Developments
Effective Field Theories
Effective Field Theories of QCD
quantum chromodynamics: lattice
lattice field theory
finite size: effect
correction: finite size
effect: discrete
loop integral

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Figures(5)

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