Randall Kelley

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.

Electroweak corrections to high energy processes using effective field theory

Electroweak Sudakov logarithms at high energy, of the form ({alpha}/sin{sup 2}{theta}{sub W}){sup n}log{sup m}s/M{sub Z,W}{sup 2}, are summed using effective theory methods. The corrections are computed to processes involving two external particles in the standard model. The results include nonzero particle masses, such as the t-quark mass, electroweak mixing effects which lead to unequal W and Z masses, and radiative Higgs corrections proportional to the Yukawa couplings. We show that the matching at the scale M{sub W,Z} has a term at most linear in logs/{mu}{sup 2} to all orders. The effective theory formalism is compared with, and extends, previous work based on infrared evolution equations.

Soft-Collinear Factorization and Zero-Bin Subtractions

We study the Sudakov form factor for a spontaneously broken gauge theory using a (new) {delta}-regulator. To be well defined, the effective theory requires zero-bin subtractions for the collinear sectors. The zero-bin subtractions depend on the gauge boson mass M and are not scaleless. They have both finite and 1/{epsilon} contributions and are needed to give the correct anomalous dimension and low-scale matching contributions. We also demonstrate the necessity of zero-bin subtractions for soft-collinear factorization. We find that after zero-bin subtractions the form factor is the sum of the collinear contributions minus a soft mass-mode contribution, in agreement with a previous result of Idilbi and Mehen in QCD. This appears to conflict with the method-of-regions approach, where one gets the sum of contributions from different regions.

Resummation of Jet Mass at Hadron Colliders

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.

Electroweak Sudakov Corrections using Effective Field Theory

Electroweak Sudakov corrections of the form alphanlogms/MW,Z2 are summed using renormalization group evolution in soft-collinear effective theory. Results are given for the scalar, vector, and tensor form factors for fermion and scalar particles. The formalism for including massive gauge bosons in soft-collinear effective theory is developed.

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

One-Loop Matching and Next-to-Next-to-Leading Log Resummation for all Partonic 2→2 Processes in QCD

The Wilson coefficients for all 4-parton operators which arise in matching QCD to soft-collinear effective theory (SCET) are computed at 1-loop. Any dijet observable calculated in SCET beyond leading order will require these results. The Wilson coefficients are separated by spin and color, although most applications will involve only the spin-averaged hard functions. The anomalous dimensions for the Wilson coefficients are given to 2-loop order, and the renormalization group equations are solved explicitly. This will allow for analytical resummation of dijet observables to next-to-next-to-leading logarithmic accuracy. For each channel, there is a natural basis in which the evolution is diagonal in color space. The same basis also diagonalizes the color evolution for the soft function. Even though soft functions required for SCET calculations are observable dependent, it is shown that their renormalization group evolution is almost completely determined by a universal structure. With these results, it will be possible to calculate hadronic event shapes or other dijet observables to next-to-leading order with next-to-next-to-leading log resummation.

Soft and collinear functions for the standard model

Radiative corrections to high-energy scattering processes were given previously in terms of universal soft and collinear functions. This paper gives the collinear functions for all standard model particles, the general form of the soft function, and explicit expressions for the soft functions for fermion-fermion scattering, longitudinal and transverse gauge boson production, single

Non-Ohmic Variable-Range Hopping Transport in One-Dimensional Conductors

W/Z

Hidden fine tuning in the quark sector of little higgs models

production, and associated Higgs production. An interesting subtlety in the use of the Goldstone boson equivalence theorem for longitudinal