arXiv subjects
Publications and source records attributed to Robert M. Schabinger.
We present analytical results for all master integrals for massless three-point functions, with one off-shell leg, at four loops. Our solutions were obtained using differential equations and direct integration techniques. We review the methods and provide additional details.
We compute the four-loop corrections to the Higgs-bottom vertex within massless QCD and present analytic results for all color structures. The infrared poles of the renormalized form factor agree with the predicted four-loop pattern. Furthermore, we use the results for the Higgs-bottom, photon-quark, and Higgs-gluon form factors to provide hard matching coefficients in soft-collinear effective theory up to four-loop accuracy.
We compute the photon-quark and Higgs-gluon form factors to four-loop order within massless perturbative Quantum Chromodynamics. Our results constitute ready-to-use building blocks for N${}^4$LO cross sections for Drell-Yan processes and gluon-fusion Higgs boson production at the LHC. We present complete analytic expressions for both form factors and show several of the most complicated master integrals.
We present the Sudakov form factor in full color $\mathcal{N}=4$ supersymmetric Yang-Mills theory to four loop order and provide uniformly transcendental results for the relevant master integrals through to weight eight.
We analytically compute all four-loop QCD corrections to the photon-quark and Higgs-gluon form factors involving a closed massless fermion loop. Our calculation of non-planar vertex integrals confirms a previous conjecture for the analytical form of the non-fermionic contributions to the collinear anomalous dimensions of quarks and gluons.
We calculate the collinear anomalous dimensions in massless four-loop QCD and $\mathcal{N} = 4$ supersymmetric Yang-Mills theory from the infrared poles of vertex form factors. We give very precise numerical approximations and a conjecture for the complete analytic results in both models we consider.
We perform a dedicated study of the $q \bar{q}$-initiated two-loop electroweak-QCD Drell-Yan scattering amplitude in dimensional regularization schemes for vanishing light quark and lepton masses. For the relative order $α$ and $α_s$ one-loop Standard Model corrections, details of our comparison to the original literature are given. The infrared pole terms of the mixed two-loop amplitude are governed by a known generalization of the dipole formula and we show explicitly that exactly the same two-loop polarized hard scattering functions are obtained in both the standard 't Hooft-Veltman-Breitenlohner-Maison $γ_5$ scheme and Kreimer's anticommuting $γ_5$ scheme.
We consider Feynman integrals with algebraic leading singularities and total differentials in $ε\,\mathrm{d}\ln$ form. We show for the first time that it is possible to evaluate integrals with singularities involving unrationalizable roots in terms of conventional multiple polylogarithms, by either parametric integration or matching the symbol. As our main application, we evaluate the two-loop master integrals relevant to the $αα_s$ corrections to Drell-Yan lepton pair production at hadron colliders. We optimize our functional basis to allow for fast and stable numerical evaluations in the physical region of phase space.
We calculate the complete quark and gluon cusp anomalous dimensions in four-loop massless QCD analytically from first principles. In addition, we determine the complete matter dependence of the quark and gluon collinear anomalous dimensions. Our approach is to Laurent expand four-loop quark and gluon form factors in the parameter of dimensional regularization. We employ finite field and syzygy techniques to reduce the relevant Feynman integrals to a basis of finite integrals, and subsequently evaluate the basis integrals directly from their standard parametric representations.
We present an analytic derivation of the full four-loop cusp anomalous dimension of $\mathcal{N}=4$ supersymmetric Yang-Mills theory from the Sudakov form factor. To extract the cusp anomalous dimension, we calculate the $ε^{-2}$ pole of the form factor using parametric integrations of finite integrals. We provide uniformly transcendental results for the master integrals through to weight six and confirm a very recent independent analytic result for the full four-loop cusp anomalous dimension of the $\mathcal{N}=4$ model.
The Drell-Yan production of charged lepton pairs is one of the key processes measured at hadron colliders. The QCD corrections to the cross section are known to order $α_s^2$ and electroweak corrections are known to order $α$. The next important step for a better theoretical understanding is the complete calculation of the mixed QCD-EW corrections of order $α_sα$. In my talk, I report on the first complete calculation of the virtual two-loop corrections of order $αα_s$ to the lepton-pair production cross section. The calculation is carried out analytically using tensor reduction, integration-by-parts relations and the method of differential equations. We validate a previous calculation of the subset of mixed QCD-QED corrections and show how the jet and soft functions of that reference can be used to subtract the infrared divergences of the complete mixed QCD-electroweak virtual corrections.
We present the complete set of planar master integrals relevant to the calculation of three-point functions in four-loop massless Quantum Chromodynamics. Employing direct parametric integrations for a basis of finite integrals, we give analytic results for the Laurent expansion of conventional integrals in the parameter of dimensional regularization through to terms of weight eight.
We calculate the four-loop massless QCD corrections with two closed quark lines to quark and gluon form factors. The results for the gluon form factor and the singlet part of the quark form factor are given for the first time. From our analytic expressions for the form factors, we determine the corresponding cusp anomalous dimensions. The relevant Feynman integrals are obtained with novel integral reduction techniques and direct integration methods.
The infrared exponentiation properties of dimensionally-regularized multi-loop scattering amplitudes are typically hidden at the level of the integrand, materializing only after integral evaluation. We address this long-standing problem by introducing an appropriate integral basis which is simultaneously finite and uniform weight. As an example, we cast the integrand for the QCD corrections to the two-loop massless quark electromagnetic form factor into a form where it is manifest that the $ε^{-4}$ and $ε^{-3}$ pole terms arise from the $ε$ expansion of the square of our one-loop master integral.
We study a recently-proposed approach to the numerical evaluation of multi-loop Feynman integrals using available sector decomposition programs. As our main example, we consider the two-loop integrals for the $αα_s$ corrections to Drell-Yan lepton production with up to one massive vector boson in physical kinematics. As a reference, we evaluate these planar and non-planar integrals by the method of differential equations through to weight five. Choosing a basis of finite integrals for the numerical evaluation with SecDec3 leads to tremendous performance improvements and renders the otherwise problematic seven-line topologies numerically accessible. As another example, basis integrals for massless QCD three loop form factors are evaluated with FIESTA4. Here, employing a basis of finite integrals results in an overall speedup of more than an order of magnitude.
We develop a general framework for the evaluation of $d$-dimensional cut Feynman integrals based on the Baikov-Lee representation of purely-virtual Feynman integrals. We implement the generalized Cutkosky cutting rule using Cauchy's residue theorem and identify a set of constraints which determine the integration domain. The method applies equally well to Feynman integrals with a unitarity cut in a single kinematic channel and to maximally-cut Feynman integrals. Our cut Baikov-Lee representation reproduces the expected relation between cuts and discontinuities in a given kinematic channel and furthermore makes the dependence on the kinematic variables manifest from the beginning. By combining the Baikov-Lee representation of maximally-cut Feynman integrals and the properties of periods of algebraic curves, we are able to obtain complete solution sets for the homogeneous differential equations satisfied by Feynman integrals which go beyond multiple polylogarithms. We apply our formalism to the direct evaluation of a number of interesting cut Feynman integrals.
We present a new method for the decomposition of multi-loop Euclidean Feynman integrals into quasi-finite Feynman integrals. These are defined in shifted dimensions with higher powers of the propagators, make explicit both infrared and ultraviolet divergences, and allow for an immediate and trivial expansion in the parameter of dimensional regularization. Our approach avoids the introduction of spurious structures and thereby leaves integrals particularly accessible to direct analytical integration techniques. Alternatively, the resulting convergent Feynman parameter integrals may be evaluated numerically. Our approach is guided by previous work by the second author but overcomes practical limitations of the original procedure by employing integration by parts reduction.
We calculate the four-loop massless QCD corrections with three closed quark lines to quark and gluon form factors. We apply a novel integration by parts algorithm based on modular arithmetic and compute all relevant master integrals for arbitrary values of the space-time dimension. This is the first calculation of a gluon form factor at this perturbative order in QCD.