Two-loop quark and gluon form factors in dimensional regularisation

By Thomas Gehrmann, T. Huber, D. Maître. 2005

209 citations recorded by the source corpus.

Abstract We compute the two-loop corrections to the massless quark form factor γ ∗ → q q ¯ and gluon form factor H → g g to all orders in the dimensional regularisation parameter e = ( 4 − d ) / 2 . The two-loop contributions to the form factors are reduced to linear combinations of master integrals, which are computed in a closed form, expressed as Γ-functions and generalised hypergeometric functions of unit argument. Using the newly developed HypExp -package, these can be expanded to any desired order, yielding Laurent expansions in e. We provide expansions of the form factors to order e 2 , as required for ultraviolet renormalisation and infrared factorisation of the three-loop form factors.

Subfields: Nuclear and High Energy Physics

View Paper: https://www.semanticscholar.org/paper/b446dc60d326277f2675b4ad0ef67b55e616a3ca

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In Nuclear and High Energy Physics

Citations in the corpus

Antenna subtraction at NNLO with hadronic initial states: initial-final configurations (2009, background): “J H E P 0 1 ( 2 0 1 0 ) 1 1 8 The functions F (i) g (i = 1, 2) are the gluon form factor at one- respectively two-loop given in [129].”
Factorization at the LHC: From parton distribution functions to initial state jets (2010, background): “[41, 118] from the known two-loop quark form factor [100, 130, 144, 145].”
Factorization at the LHC: From PDFs to Initial State Jets (Ph.D. thesis) (2009, background): “ C(q2;) = 1 + s()C F 4ˇ ln2 q2 i0 2 + 3ln q2 i0 2 8 + ˇ2 6 : (7.79) The vector current coecient at two loops was obtained in Refs. [41, 118] from the known two-loop quark form factor [100, 130, 144, 145]. Starting at three loops, it can have a contribution that is not diagonal in avor, i.e., i”
On the resolution of singularities of multiple Mellin–Barnes integrals (2009, background): “Now, results of expansion up to ε(2) [11], up to ε(4) [12] and even a result for general ε [12] are available.”
A quasi-finite basis for multi-loop Feynman integrals (2014, background): “10) with the exact results presented in reference [39].”
Calculation of the quark and gluon form factors to three loops in QCD (2010, methodology): “The one-loop and two-loop master integrals appearing in the form factors at these loop orders are displayed in figure 1. Their expansions to finite order have been known for a long time, all-orders expressions were derived in [ 37 ], they can for example be expanded using HypExp [77].”