Loops In QCD Research Articles

Exact quark-mass dependence of the Higgs-gluon form factor at three loops in QCD

We determine the three-loop form factor parameterising the amplitude for the production of an off-shell Higgs boson in gluon fusion in QCD with a single massive quark. The result is obtained via a numerical solution of a system of differential equation for the occurring master integrals. The solution is also used to determine the high-energy and threshold expansions of the form factor. Our findings may be used for the evaluation of virtual corrections generated by top-quark and b-quark loops in Higgs boson hadroproduction cross sections at next-to-next-to-leading order.

The full four-loop cusp anomalous dimension in mathcal{N} = 4 super Yang-Mills and QCD

We present the complete formula for the cusp anomalous dimension at four loops in QCD and in maximally supersymmetric Yang-Mills. In the latter theory it is given by {left.{Gamma}_{mathrm{cusp},mathrm{A}}right|}_{alpha_s^4}=-{left(frac{alpha_sN}{pi}right)}^4left[frac{73{pi}^6}{20160}+frac{zeta_3^2}{8}+frac{1}{N^2}left(frac{31{pi}^6}{5040}+frac{9{zeta}_3^2}{4}right)right]. Our approach is based on computing the correlation function of a rectangular light-like Wilson loop with a Lagrangian insertion, normalized by the expectation value of the Wilson loop. In maximally supersymmetric Yang-Mills theory, this ratio is a finite function of a cross-ratio and the coupling constant. We compute it to three loops, including the full colour dependence. Integrating over the position of the Lagrangian insertion gives the four-loop Wilson loop. We extract its leading divergence, which determines the four-loop cusp anomalous dimension. Finally, we employ a supersymmetric decomposition to derive the last missing ingredient in the corresponding QCD result.

Three loop QCD corrections to heavy quark form factors

Higher order calculations in perturbative Quantum Field Theories often produce coupled linear systems of differential equations which factorize to first order. Here we present an algorithm to solve such systems in terms of iterated integrals over an alphabet the structure of which is implied by the coefficient matrix of the given system. We apply this method to calculate the master integrals in the color–planar and complete light quark contributions to the three-loop massive form factors.

Calculation of disconnected quark loops in lattice QCD * * Supported by National Natural Science Foundation of China (11335001)

Calculation of disconnected quark loops in lattice QCD is very time consuming. Stochastic noise methods are generally used to estimate these loops. However, stochastic estimation gives large errors in the calculations of disconnected diagrams. We use the symmetric multi-probing source (SMP) method to estimate the disconnected quark loops, and compare the results with the noise method and the spin-color explicit (SCE) method on a quenched lattice QCD ensemble with lattice volume and lattice spacing fm. The results show that the SMP method is very suitable for the calculation of pseudoscalar disconnected quark loops. However, the SMP and SCE methods do not have an obvious advantage over the noise method in the evaluation of the scalar disconnected loops.

On QCD RFT corrections to the propagator of reggeized gluons

We calculate an one loop QCD Regge Field Theory (RFT) correction to the propagator of reggeized gluons basing on the QCD effective action of Lipatov, [1–6], and results of [7] where Dyson-Schwinger hierarchy of the equations for the correlators of reggeized gluon fields was derived. The correction is calculated entirely in the framework of RFT with the use of the obtained expressions for the RFT bare triple Reggeon vertices and propagator of reggeized gluons, the cases of bare propagator and propagator calculated to one-loop precision are considered separately. In both results the obtained correction represents non-eikonal contributions to the propagator kinematically suppressed by 1/s factor in comparison to the usual LLA contributions. The further application of the obtained results is discussed as well.

Multi-quark colour decompositions from unitarity

Any loop QCD amplitude at full colour is constructed from kinematic and gauge-group building blocks. In a unitarity-based on-shell framework, both objects can be reconstructed from their respective counterparts in tree-level amplitudes. This procedure is at its most powerful when aligned with flexible colour decompositions of tree-level QCD amplitudes. In this note we derive such decompositions for amplitudes with an arbitrary number of quarks and gluons from the same principle that is used to bootstrap kinematics— unitarity factorisation. In the process we formulate new multi-quark bases and provide closed-form expressions for the new decompositions. We then elaborate upon their application in colour decompositions of loop multi-quark amplitudes.

The polarized three-loop anomalous dimensions from on-shell massive operator matrix elements

We calculate all contributions ∝TF to the polarized three–loop anomalous dimensions in the M–scheme using massive operator matrix elements and compare to results in the literature. This includes the complete anomalous dimensions γqq(2),PS and γqg(2). We also obtain the complete two–loop polarized anomalous dimensions in an independent calculation. While for most of the anomalous dimensions the usual direct computation methods in Mellin N–space can be applied since all recurrences factorize at first order, this is not the case for γqg(2). Due to the necessity of deeper expansions of the master integrals in the dimensional parameter ε=D−4, we had to use the method of arbitrary high moments to eliminate elliptic contributions in intermediate steps. 4000 moments were generated to determine this anomalous dimension and 2640 moments turned out to be sufficient. As an aside, we also recalculate the contributions ∝TF to the three–loop QCD β–function.

Gluon jet function at three loops in QCD

We present here the first result on the three-loop gluon jet function in perturbative QCD. Using the three-loop coefficient functions [1,2] for deep-inelastic scattering via the exchange of a virtual photon that couples to quarks or a scalar that couples to gluons and employing the KG equation, renormalization group invariance and factorization theorem, we obtain both the quark and the gluon jet functions up to the three-loop level. The former agrees with the recent result [3]. These jet functions being universal ingredients for many collider and decay processes, will play an important role in the phenomenological studies at the Large Hadron Collider.

Heavy quark form factors at three loops in the planar limit

We compute the color-planar and complete light quark non-singlet contributions to the heavy quark form factors in the case of the axialvector, scalar and pseudoscalar currents at three loops in perturbative QCD. We evaluate the master integrals applying a new method based on differential equations for general bases, which is applicable for all first order factorizing systems. The analytic results are expressed in terms of harmonic polylogarithms and real-valued cyclotomic harmonic polylogarithms.

First Look at Two-Loop Five-Gluon Scattering in QCD.

We compute the leading-color contributions to five-gluon scattering at two loops in massless QCD. The integrands of all independent helicity amplitudes are evaluated using d-dimensional generalized unitarity cuts and finite field reconstruction techniques. Numerical evaluation of the integral basis is performed with sector decomposition methods to obtain the first benchmark results for all helicity configurations of a 2→3 scattering process in QCD.

Three-loop quark form factor at high energy: The leading mass corrections

We compute the leading mass corrections to the high-energy behavior of the massive quark vector form factor to three loops in QCD in the double-logarithmic approximation.

Symmetric point four-point functions at one loop in QCD

We evaluate the quartic ghost and quark Green's functions as well as the gluon-ghost, gluon-quark and ghost-quark four-point functions of quantum chromodynamics at one loop at the fully symmetric point in a linear covariant gauge. Similar expressions for the analogous Green's functions in quantum electrodynamics are also provided.

Heavy-quark Form Factors at Two Loops in Perturbative QCD

We present the results for heavy quark form factors at two-loop order in perturbative QCD for different currents, namely vector, axial-vector, scalar and pseudo-scalar currents, up to second order in the dimensional regularization parameter. We outline the necessary computational details, ultraviolet renormalization and corresponding universal infrared structure.

Vector-Boson Fusion Higgs Production at Three Loops in QCD.

We calculate the next-to-next-to-next-to-leading-order (N^{3}LO) QCD corrections to inclusive vector-boson fusion Higgs production at proton colliders, in the limit in which there is no color exchange between the hadronic systems associated with the two colliding protons. We also provide differential cross sections for the Higgs transverse momentum and rapidity distributions. We find that the corrections are at the 1‰-2‰ level, well within the scale uncertainty of the next-to-next-to-leading-order calculation. The associated scale uncertainty of the N^{3}LO calculation is typically found to be below the 2‰ level. We also consider theoretical uncertainties due to missing higher order parton distribution functions, and provide an estimate of their importance.

Spin-2 form factors at three loop in QCD

Spin-2 fields are often candidates in physics beyond the Standard Model namely the models with extra-dimensions where spin-2 Kaluza-Klein gravitons couple to the fields of the SM. Also, in the context of Higgs searches, spin-2 fields have been studied as an alternative to the scalar Higgs boson. In this article, we present the complete three loop QCD radiative corrections to the spin-2 quark-antiquark and spin-2 gluon-gluon form factors in SU(N) gauge theory with $n_f$ light flavors. These form factors contribute to both quark-antiquark and gluon-gluon initiated processes involving spin-2 particle in the hadronic reactions at the LHC. We have studied the structure of infrared singularities in these form factors up to three loop level using Sudakov integro-differential equation and found that the anomalous dimensions originating from soft and collinear regions of the loop integrals coincide with those of the electroweak vector boson and Higgs form factors confirming the universality of the infrared singularities in QCD amplitudes.

Two-loop off-shell QCD amplitudes in FDR

We link the FDR treatment of ultraviolet (UV) divergences to dimensional regularization up to two loops in QCD. This allows us to derive the one-loop and two-loop coupling constant and quark mass shifts necessary to translate infrared finite quantities computed in FDR to the MSbar renormalization scheme. As a by-product of our analysis, we solve a problem analogous to the breakdown of unitarity in the Four Dimensional Helicity (FDH) method beyond one loop. A fix to FDH is then presented that preserves the renormalizability properties of QCD without introducing evanescent quantities.

Pseudo-scalar form factors at three loops in QCD

The coupling of a pseudo-scalar Higgs boson to gluons is mediated through a heavy quark loop. In the limit of large quark mass, it is described by an effective Lagrangian that only admits light degrees of freedom. In this effective theory, we compute the three-loop massless QCD corrections to the form factor that describes the coupling of a pseudo-scalar Higgs boson to gluons. Due to the axial anomaly, the pseudo-scalar operator for the gluonic field strength mixes with the divergence of the axial vector current. Working in dimensional regularization and using the 't~Hooft-Veltman prescription for the axial vector current, we compute the three-loop pseudo-scalar form factors for massless quarks and gluons. Using the universal infrared factorization properties, we independently derive the three-loop operator mixing and finite operator renormalisation from the renormalisation group equation for the form factors, thereby confirming recent results in the operator product expansion. The finite part of the three-loop form factor is an important ingredient to the precise prediction of the pseudo-scalar Higgs boson production cross section at hadron colliders. We discuss potential applications and derive the hard matching coefficient in soft-collinear effective theory.

Dilepton and photon production in the presence of a nontrivial Polyakov loop

We calculate the production of dileptons and photons in the presence of a nontrivial Polyakov loop in QCD. This is applicable to the semi-Quark Gluon Plasma (QGP), at temperatures above but near the critical temperature for deconfinement. The Polyakov loop is small in the semi-QGP, and near unity in the perturbative QGP. Working to leading order in the coupling constant of QCD, we find that there is a mild enhancement, ~ 20%, for dilepton production in the semi-QGP over that in the perturbative QGP. In contrast, we find that photon production is strongly suppressed in the semi-QGP, by about an order of magnitude, relative to the perturbative QGP. In the perturbative QGP photon production contains contributions from 2->2 scattering and collinear emission with the Landau- Pomeranchuk-Migdal (LPM) effect. In the semi-QGP we show that the two contributions are modified differently. The rate for 2->2 scattering is suppressed by a factor which depends upon the Polyakov loop. In contrast, in an SU(N) gauge theory the collinear rate is suppressed by 1/N, so that the LPM effect vanishes at infinite N. To leading order in the semi-QGP at large N, we compute the rate from 2->2 scattering to the leading logarithmic order and the collinear rate to leading order.

Higgs rapidity distribution in b b ¯ $$ b\overline{b} $$ annihilation at threshold in N3LO QCD

We present the rapidity distribution of the Higgs boson produced through bottom quark annihilation at third order in QCD using the threshold approximation. We provide a framework, based on the factorization properties of the QCD amplitudes along with Sudakov resummation and the renormalization group invariance, that allows one to perform the computation of the threshold corrections in a consistent, systematic and accurate way. The recent results on threshold N3LO correction in QCD for the Drell-Yan production and on three loop QCD correction to Higgs form factor with bottom anti-bottom quark are used to achieve this task. We also demonstrate the numerical impact of these corrections at the LHC.

Higgs boson production through b b ¯ $$ b\overline{b} $$ annihilation at threshold in N3LO QCD

We present threshold enhanced N3LO QCD corrections to inclusive Higgs production through bottom anti-bottom annihilation at hadron colliders using threshold resummed cross section. The resummed cross section is obtained using factorization properties and Sudakov resummation of the inclusive cross section. We use the recent results on threshold N3LO corrections in QCD for Drell-Yan production and three loop QCD corrections to Higgs form factor with bottom anti-bottom quark to achieve this task. This is the first step towards the evaluation of complete N3LO result. We have numerically demonstrated the importance of such corrections at the LHC.