arXiv subjects

Robert M. Schabinger

Publications and source records attributed to Robert M. Schabinger.

31 records · Page 2Linked to original sources

arXiv2016

On the Computation of Form Factors in Massless QCD with Finite Master Integrals

We present the bare one-, two-, and three-loop form factors in massless Quantum Chromodynamics as linear combinations of finite master integrals. Using symbolic integration, we compute their $ε$ expansions and thereby reproduce all known results with an independent method. Remarkably, in our finite basis, only integrals with a less-than-maximal number of propagators contribute to the cusp anomalous dimensions. We report on indications of this phenomenon at four loops, including the result for a finite, irreducible, twelve-propagator form factor integral. Together with this article, we provide our automated software setup for the computation of finite master integrals.

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arXiv2015

A novel approach to integration by parts reduction

Integration by parts reduction is a standard component of most modern multi-loop calculations in quantum field theory. We present a novel strategy constructed to overcome the limitations of currently available reduction programs based on Laporta's algorithm. The key idea is to construct algebraic identities from numerical samples obtained from reductions over finite fields. We expect the method to be highly amenable to parallelization, show a low memory footprint during the reduction step, and allow for significantly better run-times.

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arXiv2015

Soft-virtual corrections to Higgs production at N$^3$LO

In this paper, we compute the soft-virtual corrections to Higgs boson production in gluon fusion for infinite top quark mass at next-to-next-to-next-to-leading order in QCD. In addition, we present analogous soft-virtual terms for both Drell-Yan lepton production in QCD and scalar pair production in N = 4 super Yang-Mills theory. The result for Drell-Yan lepton production is derived from the result for Higgs boson production using Casimir scaling arguments together with well-known results available in the literature. For scalar pair production in the N = 4 model, we show by explicit calculation that the result is equal to the part of the Higgs boson soft-virtual term which is of maximal transcendentality weight.

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arXiv2015

The two-loop soft function for heavy quark pair production at future linear colliders

We report on the calculation of the threshold soft function for heavy quark pair production in e+ e- annihilation at two-loop order. Our main result is a generalization of the familiar Drell-Yan threshold soft function to the case of non-zero primary quark mass. We set up a framework based on the method of differential equations which allows for the straightforward calculation of the bare soft function to arbitrarily high orders in the dimensional regularization parameter. Remarkably, we find that we can obtain the bare two-loop Drell-Yan soft function from the heavy quark soft function to the order in epsilon required for a two-loop calculation by making simple replacements. We expect that our results will be of use, both as an important input for precision physics calculations at linear colliders and, more formally, as a first step towards a better understanding of the connection between vacuum matrix elements of massive soft Wilson lines and vacuum matrix elements of massless soft Wilson lines.

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arXiv2015

Scattering on the Moduli Space of N=4 Super Yang-Mills

We calculate one-loop scattering amplitudes in N=4 super Yang-Mills theory away from the origin of the moduli space and demonstrate that the results are extremely simple, in much the same way as in the conformally invariant theory. Specifically, we consider the model where an SU(2) gauge group is spontaneously broken down to U(1). The complete component Lagrange density of the model is given in a form useful for perturbative calculations. We argue that the scattering amplitudes with massive external states deserve further study. Finally, our work shows that loop corrections can be readily computed in a mass-regulated N=4 theory, which may be relevant in trying to connect weak-coupling results with those at strong coupling, as discussed recently by Alday and Maldacena.

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arXiv2015

One-Loop N = 4 Super Yang-Mills Scattering Amplitudes to All Orders in the Dimensional Regularization Parameter

In this paper we discuss in detail computational methods and new results for one-loop virtual corrections to N = 4 super Yang-Mills scattering amplitudes calculated to all orders in epsilon, the dimensional regularization parameter. It is often the case that one-loop gauge theory computations are carried out to order epsilon^0, since higher order in epsilon contributions vanish in the small epsilon limit. We will show, however, that the higher order contributions are actually quite useful. In the context of maximally supersymmetric Yang-Mills, we consider two examples in detail to illustrate our point. First we will concentrate on computations with gluonic external states and argue that N = 4 supersymmetry implies a simple relation between all-orders-in-epsilon one-loop N = 4 super Yang-Mills amplitudes and the first and second stringy corrections to analogous tree-level superstring amplitudes. For our second example we will derive a new result for the all-orders-in-epsilon one-loop superamplitude for planar six-particle NMHV scattering, an object which allows one to easily obtain six-point NMHV amplitudes with arbitrary external states. We will then discuss the relevance of this computation to the evaluation of the ratio of the planar two-loop six-point NMHV superamplitude to the planar two-loop six-point MHV superamplitude, a quantity which is expected to have remarkable properties and has been the subject of much recent investigation. To make the presentation as self-contained as possible, we extensively review the prerequisites necessary to understand the main results of this work.

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arXiv2015

One-loop N = 4 super Yang-Mills scattering amplitudes in d dimensions, relation to open strings and polygonal Wilson loops

In this review we discuss some recent developments related to one-loop N = 4 super Yang-Mills scattering amplitudes calculated to all orders in epsilon. It is often the case that one-loop gauge theory computations are carried out to order epsilon^0, since higher order in epsilon contributions vanish in the limit as epsilon goes to zero. We will show, however, that the higher order contributions are actually quite useful. In the context of maximally supersymmetric Yang-Mills, we consider two examples in detail to illustrate our point. First we concentrate on computations with gluonic external states and argue that N = 4 supersymmetry implies a simple relation between all-orders-in-epsilon one-loop N = 4 super Yang-Mills amplitudes and the first and second stringy corrections to analogous tree-level superstring amplitudes. For our second example we will derive a new result for the all-orders-in-epsilon one-loop superamplitude for planar six-particle NMHV scattering, an object which allows one to easily obtain six-point NMHV amplitudes with arbitrary external states. We will then discuss the relevance of this computation to the evaluation of the ratio of the planar two-loop six-point NMHV superamplitude to the planar two-loop six-point MHV superamplitude, a quantity which is expected to have remarkable properties and has been the subject of much recent investigation.

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arXiv2015

The Complete Two-Loop Integrated Jet Thrust Distribution In Soft-Collinear Effective Theory

In this work, we complete the calculation of the soft part of the two-loop integrated jet thrust distribution in e+e- annihilation. This jet mass observable is based on the thrust cone jet algorithm, which involves a veto scale for out-of-jet radiation. The previously uncomputed part of our result depends in a complicated way on the jet cone size, r, and at intermediate stages of the calculation we actually encounter a new class of multiple polylogarithms. We employ an extension of the coproduct calculus to systematically exploit functional relations and represent our results concisely. In contrast to the individual contributions, the sum of all global terms can be expressed in terms of classical polylogarithms. Our explicit two-loop calculation enables us to clarify the small r picture discussed in earlier work. In particular, we show that the resummation of the logarithms of r that appear in the previously uncomputed part of the two-loop integrated jet thrust distribution is inextricably linked to the resummation of the non-global logarithms. Furthermore, we find that the logarithms of r which cannot be absorbed into the non-global logarithms in the way advocated in earlier work have coefficients fixed by the two-loop cusp anomalous dimension. We also show that, given appropriate L-loop contributions to the integrated hemisphere soft function, one can straightforwardly predict a number of potentially large logarithmic contributions at L loops not controlled by the factorization theorem for jet thrust.

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arXiv2014

N$^3$LO Higgs and Drell-Yan production at threshold: the one-loop two-emission contribution

In this paper, we study phenomenologically interesting soft radiation distributions in massless QCD. Specifically, we consider the emission of two soft partons off of a pair of light-like Wilson lines, in either the fundamental or the adjoint representation, at next-to-leading order. Our results are an essential component of the next-to-next-to-next-to-leading order threshold corrections to both Higgs boson production in the gluon fusion channel and Drell-Yan lepton production. Our calculations are consistent with the recently published results for Higgs boson production. As a non-trivial cross-check on our analysis, we rederive a recent prediction for the Drell-Yan threshold cross section using a completely different strategy. Our results are compact, valid to all orders in the dimensional regularization parameter, and expressed in terms of pure functions.

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arXiv2011

Jet mass with a jet veto at two loops and the universality of non-global structure

We investigate the exclusive jet mass distribution in e+e- events, defined with a veto on the out-of-jet radiation, at two-loop order. In particular, we calculate the two-loop soft function, which is required to describe this distribution in the threshold region. When combined with other ingredients using soft-collinear effective theory, this generates the complete singular distribution for jet thrust, the sum of the jet masses, at two-loop order. The result is in excellent agreement with full QCD. The integrated jet thrust distribution is found to depend in an intricate way on both the finite jet cone size, R, and the jet veto scale. The result clarifies the structure of the potentially large logarithms (both global and non- global) which arise in jet observables for the first time at this order. Somewhat surprisingly, we find that, in the small R limit, there is a precise and simple correspondence between the non-global contribution to the integrated jet thrust distribution and the previously calculated non-global contribution to the integrated hemisphere soft function, including subleading terms. This suggests that the small R limit may provide a useful expansion for studying other exclusive jet substructure observables.

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arXiv2011

A New Algorithm For The Generation Of Unitarity-Compatible Integration By Parts Relations

Many multi-loop calculations make use of integration by parts relations to reduce the large number of complicated Feynman integrals that arise in such calculations to a simpler basis of master integrals. Recently, Gluza, Kajda, and Kosower argued that the reduction to master integrals is complicated by the presence of integrals with doubled propagator denominators in the integration by parts relations and they introduced a novel reduction procedure which eliminates all such integrals from the start. Their approach has the advantage that it automatically produces integral bases which mesh well with generalized unitarity. The heart of their procedure is an algorithm which utilizes the weighty machinery of computational commutative algebra to produce complete sets of unitarity-compatible integration by parts relations. In this paper, we propose a conceptually simpler algorithm for the generation of complete sets of unitarity-compatible integration by parts relations based on recent results in the mathematical literature. A striking feature of our algorithm is that it can be described entirely in terms of straightforward linear algebra.

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arXiv2011

The two-loop hemisphere soft function

The hemisphere soft function is calculated to order alpha_s^2. This is the first multi-scale soft function calculated to two loops. The renormalization scale dependence of the result agrees exactly with the prediction from effective field theory. This fixes the unknown coefficients of the singular parts of the two-loop thrust and heavy-jet mass distributions. There are four such coefficients, for 2 event shapes and 2 color structures, which are shown to be in excellent agreement with previous numerical extraction. The asymptotic behavior of the soft function has double logs in the CF CA color structure, which agree with non-global log calculations, but also has sub-leading single logs for both the CF CA and CF TF nf color structures. The general form of the soft function is complicated, does not factorize in a simple way, and disagrees with the Hoang-Kluth ansatz. The exact hemisphere soft function will remove one source of uncertainty on the alpha_s fits from e+e- event shapes.

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arXiv2009

The Imaginary Part of the N = 4 Super-Yang-Mills Two-Loop Six-Point MHV Amplitude in Multi-Regge Kinematics

The precise form of the multi-Regge asymptotics of the two-loop six-point MHV amplitude in N = 4 Super-Yang-Mills theory has been a subject of recent controversy. In this paper we utilize the amplitude/Wilson loop correspondence to obtain precise numerical results for the imaginary part of these asymptotics. The region of phase-space that we consider is interesting because it allowed Bartels, Lipatov, and Sabio Vera to determine that the two-loop six-point MHV amplitude is not fixed by the BDS ansatz. They proceeded by working in the framework of a high energy effective action, thus side-stepping the need for an arduous two-loop calculation. Our numerical results are consistent with the predictions of Bartels, Lipatov, and Sabio Vera for the leading-log asymptotics.

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