Calculation of the quark and gluon form factors to three loops in QCD

186

We compute a class of diagrams contributing to the multi-leg soft anomalous dimension through three loops, by renormalizing a product of semi-infinite non-lightlike Wilson lines in dimensional regularization. Using non-Abelian exponentiation we directly compute contributions to the exponent in terms of webs. We develop a general strategy to compute webs with multiple gluon exchanges between Wilson lines in configuration space, and explore their analytic structure in terms of α ij , the exponential of the Minkowski cusp angle formed between the lines i and j. We show that beyond the obvious inversion symmetry α ij → 1/α ij , at the level of the symbol the result also admits a crossing symmetry α ij → −α ij , relating spacelike and timelike kinematics, and hence argue that in this class of webs the symbol alphabet is restricted to α ij and 1 − α 2 ij . We carry out the calculation up to three gluons connecting four Wilson lines, finding that the contributions to the soft anomalous dimension are remarkably simple: they involve pure functions of uniform weight, which are written as a sum of products of polylogarithms, each depending on a single cusp angle. We conjecture that this type of factorization extends to all multiple-gluon-exchange contributions to the anomalous dimension.

Section: Jhep04(2014)044mentioning

confidence: 99%

Section: Jhep04(2014)044mentioning

confidence: 99%

From webs to polylogarithms

Gardi

2014

186

“…Following the derivation of the three-loop virtual corrections [27][28][29][30][31], of the required renormalization and factorization counterterm contributions [32,33], and of expansions of single and multiple real radiation contributions around the soft limit [25,26,[34][35][36], the threshold approximation of this coefficient function was computed earlier this year [37]. We use our results for the two-loop splitting amplitudes to derive a closed analytic expression for the two-loop single-real contribution to the inclusive N 3 LO coefficient function for Higgs production.…”

Section: Jhep02(2015)077mentioning

confidence: 99%

“…the ℓ-loop gluon and quark form factors, known up to three loops in QCD [27][28][29][30][31]. As a consequence, if we know the the matrix elements in the left-hand side in CDR through O(ǫ) up to two loops, we can immediately extract the corresponding splitting amplitudes through O(ǫ).…”

Section: Jhep02(2015)077mentioning

confidence: 99%

Two-loop splitting amplitudes and the single-real contribution to inclusive Higgs production at N3LO

Duhr

Gehrmann

Jaquier

2015

The factorisation of QCD matrix elements in the limit of two external partons becoming collinear is described by process-independent splitting amplitudes, which can be expanded systematically in perturbation theory. Working in conventional dimensional regularisation, we compute the two-loop splitting amplitudes for all simple collinear splitting processes, including subleading terms in the regularisation parameter. Our results are then applied to derive an analytical expression for the two-loop single-real contribution to inclusive Higgs boson production in gluon fusion to fourth order (N 3 LO) in perturbative QCD.

“…Motivated by future four-loop calculations, the authors of Ref. [10] presented one more term of the ǫ-expansion for all the master integrals but A 9,1 , A 9,2 and A 9,4 . For A 9,1 , this was done in [4].…”

Section: Introductionmentioning

confidence: 99%

Analytic epsilon expansion of three-loop on-shell master integrals up to four-loop transcendentality weight

Lee

Smirnov

2011

We evaluate analytically higher terms of the ǫ-expansion of the threeloop master integrals corresponding to three-loop quark and gluon form factors and to the three-loop master integrals contributing to the electron g−2 in QED up to the transcendentality weight typical to four-loop calculations, i.e. eight and seven, respectively. The calculation is based on a combination of a method recently suggested by one of the authors (R.L.) with other techniques: sector decomposition implemented in FIESTA, the method of Mellin-Barnes representation, and the PSLQ algorithm.