Hua Xing Zhu

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.

Single soft gluon emission at two loops

A bstractWe study the single soft-gluon current at two loops with two energetic partons in massless perturbative QCD, which describes, for example, the soft limit of the two-loop amplitude for gg → Hg. The results are presented as Laurent expansions in ϵ in D = 4 − 2ϵ spacetime dimension. We calculate the expansion to order ϵ2 analytically, which is a necessary ingredient for Higgs production at hadron colliders at next-to-next-to-next-to-leading order in the soft-virtual approximation. We also give two-loop results of the single soft-gluon current in

Soft-virtual corrections to Higgs production at N 3 LO

\mathcal{N}=4

Resummation of Jet Mass at Hadron Colliders

Super-Yang-Mills theory, and find that it has uniform transcendentality. By iteration relation of splitting amplitudes, our calculations can determine the three-loop single soft-gluon current to order ϵ0 in

Jet mass with a jet veto at two loops and the universality of nonglobal structure

\mathcal{N}=4

Nonglobal logarithms at three loops, four loops, five loops, and beyond

Super-Yang-Mills theory in the limit of large Nc.

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

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.

The complete two-loop integrated jet thrust distribution in soft-collinear effective theory

A method is developed for calculating the jet mass distribution at hadron colliders using an expansion about the kinematic threshold. In particular, we consider the mass distribution of jets of size R produced in association with a hard photon at the Large Hadron Collider. Expanding around the kinematic threshold, where all the energy goes into the jet and the photon, provides a clean factorization formula and allows for the resummation of logarithms associated with soft and collinear divergences. All of the large logarithms of jet mass are resummed at next-to-leading logarithmic level (NLL), and all the global logarithms at next-to-next-to-leading logarithmic level (NNLL). A key step in the derivation is the factorization of the soft function into pieces associated with single scales and a remainder which contains non-global structure. This step, which is standard in traditional resummation, is implemented in effective field theory which is then used to resum the large logarithms using the renormalization group in a systematically improvable manner.

On the calculation of soft phase space integral

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.

Collinear factorization violation and effective field theory

We calculate the coefficients of the leading nonglobal logarithms for the hemisphere mass distribution analytically at 3, 4, and 5 loops at large N-c. We confirm that the integrand derived with the strong-energy-ordering approximation and fixed-order iteration of the Banfi-Marchesini-Syme (BMS) equation agree. Our calculation exploits a hidden PSL(2, R) symmetry associated with the jet directions, apparent in the BMS equation after a stereographic projection to the Poincare disk. The required integrals have an iterated form, leading to functions of uniform transcendentality. This allows us to extract the coefficients, and some functional dependence on the jet directions, by computing the symbols and coproducts of appropriate expressions involving classical and Goncharov polylogarithms. Convergence of the series to a numerical solution of the BMS equation is also discussed.