One-loop Single Real Emission Contributions to Inclusive Higgs Production at NNNLO

I discuss the contributions of the one-loop single-real-emission amplitudes, $ggto H g$, $qgto H q$, etc. to inclusive Higgs boson production through next-to-next-to-next-to-leading order in the strong coupling.

One-Loop Single-Real-Emission Contributions to $ppto H + X$ at Next-to-Next-to-Next-to-Leading Order

I compute the contributions of the one-loop single-real-emission amplitudes, $ggto H g$, $qgto H q$, etc., to inclusive Higgs boson production through next-to-next-to-next-to-leading order (N^3LO) in the strong coupling $alpha_s$. The next-to-leading (NLO) and next-to-next-to-leading order (NNLO) terms are computed in closed form, in terms of $Gamma$-functions and the hypergeometric functions ${}_{2}F_{1}$ and ${}_{3}F_{2}$. I compute the nnlo terms as Laurent expansions in the dimensional regularization parameter through order $(epsilon^{1})$. To obtain the nnlo terms, I perform an extended threshold expansion of the phase space integrals and map the resulting coefficients onto a basis of harmonic polylogarithms.

The Two-Loop Infrared Structure of Amplitudes with Mixed Gauge Groups

The infrared structure of (multi-loop) scattering amplitudes is determined entirely by the identities of the external particles participating in the scattering. The two-loop infrared structure of pure qcd amplitudes has been known for some time. By computing the two-loop amplitudes for $bar{f},flongrightarrow X$ and $bar{f},flongrightarrow V_1,V_2$ scattering in an $SU(N)times SU(M)times U(1)$ gauge theory, I determine the anomalous dimensions which govern the infrared structure for any massless two-loop amplitude.

The Four Dimensional Helicity Scheme Beyond One Loop

I describe a procedure by which one can transform scattering amplitudes computed in the four dimensional helicity scheme into properly renormalized amplitudes in the t Hooft-Veltman scheme. I describe a new renormalization program, based upon that of the dimensional reduction scheme and explain how to remove both finite and infrared-singular contributions of the evanescent degrees of freedom to the scattering amplitude.

Regularization Schemes and Higher Order Corrections

I apply commonly used regularization schemes to a multi-loop calculation to examine the properties of the schemes at higher orders. I find complete consistency between the conventional dimensional regularization scheme and dimensional reduction, but I find that the four dimensional helicity scheme produces incorrect results at next-to-next-to-leading order and singular results at next-to-next-to-next-to-leading order. It is not, therefore, a unitary regularization scheme.

One-loop Integral Coefficients from Generalized Unitarity

I describe a method for determining the coefficients of scalar integrals for one-loop amplitudes in quantum field theory. The method is based upon generalized unitarity and the behavior of amplitudes when the free parameters of the cut momenta approach infinity. The method works for arbitrary masses of both external and internal legs of the amplitudes. It therefore applies not only to QCD but also to the Electroweak theory and to quantum field theory in general.