Two-Loop g -> gg Splitting Amplitudes in QCD

Splitting amplitudes are universal functions governing the collinear behavior of scattering amplitudes for massless particles. We compute the two-loop g -> gg splitting amplitudes in QCD, N=1, and N=4 super-Yang-Mills theories, which describe the limits of two-loop n-point amplitudes where two gluon momenta become parallel. They also represent an ingredient in a direct x-space computation of DGLAP evolution kernels at next-to-next-to-leading order. To obtain the splitting amplitudes, we use the unitarity sewing method. In contrast to the usual light-cone gauge treatment, our calculation does not rely on the principal-value or Mandelstam-Leibbrandt prescriptions, even though the loop integrals contain some of the denominators typically encountered in light-cone gauge. We reduce the integrals to a set of 13 master integrals using integration-by-parts and Lorentz invariance identities. The master integrals are computed with the aid of differential equations in the splitting momentum fraction z. The epsilon-poles of the splitting amplitudes are consistent with a formula due to Catani for the infrared singularities of two-loop scattering amplitudes. This consistency essentially provides an inductive proof of Catani's formula, as well as an ansatz for previously-unknown 1/epsilon pole terms having non-trivial color structure. Finite terms in the splitting amplitudes determine the collinear behavior of finite remainders in this formula.Comment: 100 pages, 33 figures. Added remarks about leading-transcendentality argument of hep-th/0404092, and additional explanation of cut-reconstruction uniquenes

Supersymmetric Regularization, Two-Loop QCD Amplitudes and Coupling Shifts

We present a definition of the four-dimensional helicity (FDH) regularization scheme valid for two or more loops. This scheme was previously defined and utilized at one loop. It amounts to a variation on the standard 't Hooft-Veltman scheme and is designed to be compatible with the use of helicity states for "observed" particles. It is similar to dimensional reduction in that it maintains an equal number of bosonic and fermionic states, as required for preserving supersymmetry. Supersymmetry Ward identities relate different helicity amplitudes in supersymmetric theories. As a check that the FDH scheme preserves supersymmetry, at least through two loops, we explicitly verify a number of these identities for gluon-gluon scattering (gg to gg) in supersymmetric QCD. These results also cross-check recent non-trivial two-loop calculations in ordinary QCD. Finally, we compute the two-loop shift between the FDH coupling and the standard MS-bar coupling, alpha_s. The FDH shift is identical to the one for dimensional reduction. The two-loop coupling shifts are then used to obtain the three-loop QCD beta function in the FDH and dimensional reduction schemes.Comment: 44 pages, minor corrections and clarifications include

What Can Be Learned with an Iodine Solar-Neutrino Detector?

We study the potential benefits of an iodine-based solar-neutrino detector for testing hypotheses that involve neutrino oscillations. We argue that such a detector will have a good chance of distinguishing the two allowed regions of $\Delta m^2$ -- $\sin^22\theta$ parameter space if neutrino conversion is occurring in the sun. It should also be able to detect seasonal variations in the signal due to vacuum oscillations and might be sensitive enough to detect day/night variations due to MSW transitions in the earth. Although it would need to be calibrated, a working iodine detector could be completed before more ambitious projects that seek to accomplish the same things.Comment: 8 pages, RevTex, 2 uuencoded figures, submittted to Phys. Rev.

Search for single top quark production in ppbar collisions at sqrt(s)=1.96 TeV

We present a search for electroweak production of single top quarks in the s-channel and t-channel using neural networks for signal-background separation. We have analyzed 230 pb$^{-1}$ of data collected with the D0 detector at the Fermilab Tevatron Collider at a center-of-mass energy of 1.96 TeV and find no evidence for a single top quark signal. The resulting 95% confidence level upper limits on the single top quark production cross sections are 6.4 pb in the s-channel and 5.0 pb in the t-channel.Comment: 9 pages, 4 figure