Scalar one-loop integrals for QCD

By R. Ellis, G. Zanderighi. 2007

456 citations recorded by the source corpus.

We construct a basis set of infra-red and/or collinearly divergent scalar one-loop integrals and give analytic formulas, for tadpole, bubble, triangle and box integrals, regulating the divergences (ultra-violet, infra-red or collinear) by regularization in D = 4−2 dimensions. For scalar triangle integrals we give results for our basis set containing 6 divergent integrals. For scalar box integrals we give results for our basis set containing 16 divergent integrals. We provide analytic results for the 5 divergent box integrals in the basis set which are missing in the literature. Building on the work of van Oldenborgh, a general, publicly available code has been constructed, which calculates both finite and divergent one-loop integrals. The code returns the coefficients of 1/2,1/1 and 1/0 as complex numbers for an arbitrary tadpole, bubble, triangle or box integral.

Subfields: Nuclear and High Energy Physics

View Paper: https://www.semanticscholar.org/paper/fa0e1023669fafc24649d83e1f7bd8c16ca85543

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In Nuclear and High Energy Physics

Citations in the corpus

Two-loop planar master integrals for Higgs → 3 partons with full heavy-quark mass dependence (2016, background): “However in our case all the divergent integrals are factorisable into products of one-loop integrals, which are known analytically [24, 79].”
Associated production of a Higgs boson at NNLO (2016, methodology): “In the notation of the QCDLoop library [82], which we use to evaluate the integrals, I3(s, t,m 2 t ) ≡ I3(s, t, 0;m(2)t ,m(2)t ,m(2)t ) and I2(s,m(2)t ) ≡ I2(s;m(2)t ,m(2)t ) .”
Single-top Wt-channel production matched with parton showers using the POWHEG method (2010, methodology): “[51]) is computed numerically, using the package QCDloop [59] to evaluate the finite part of the scalar integrals.”
Higgs boson production in association with a jet at next-to-next-to-leading order in perturbative QCD (2013, methodology): “The one-loop integrals that are required for this calculation are computed using QCDloops [73].”
GoSam-2.0: a tool for automated one-loop calculations within the Standard Model and beyond (2014, background): “ [35,36]. Alternatively, tensorial reconstruction [27] is also available, based on the library Golem95C [30,59,60]. The scalar loop integrals can be evaluated using OneLOop [61], Golem95C, or QCDLoop [62,63]. It should be emphasized that all the reduction- and integral libraries used in GoSam-2.0 ar”
Spinning black hole binary dynamics, scattering amplitudes, and effective field theory (2020, background): “In any case, since the one-loop Feynman integrals are known [87], we can also simply extract the classical limit directly from these from these.”
The automation of next-to-leading order electroweak calculations (2018, unknown): “nly with 1-point and 2-point scalar integrals, and the former do not pose any problems. As far as the latter are concerned, the basic results we need to consider are the following [92] (see also ref. [93]): 1 iˇ2 B 0(p2;0;0) = 1 + 2 log p2 i0 2 ; (5.33) 1 iˇ 2 B 0(p2;0;2 2) = 1 + 2 + log 2 2 2 + 2”
Two-loop integrand decomposition into master integrals and surface terms (2015, background): “) Higher polygons are reducible using Gram-determinant identities [54, 55] and we do not considered them explicitly.”
Revisiting the second post-Minkowskian eikonal and the dynamics of binary black holes (2019, background): “In the ultrarelativistic case one recovers the massless results that can be found for instance in [32].”
Automation of one-loop QCD computations (2011, methodology): “and by using the well-known expressions for scalar loop integrals [27–29].”