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Register a new userRegularization Schemes and Higher Order Corrections
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Authors
William B. Kilgore
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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.
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We present a simple formalism for the evolution of timelike jets in which tree-level matrix element corrections can be systematically incorporated, up to arbitrary parton multiplicities and over all of phase space, in a way that exponentiates the matching corrections. The scheme is cast as a shower Markov chain which generates one single unweighted event sample, that can be passed to standard hadronization models. Remaining perturbative uncertainties are estimated by providing several alternative weight sets for the same events, at a relatively modest additional overhead. As an explicit example, we consider Z -> q qbar evolution with unpolarized, massless quarks and include several formally subleading improvements as well as matching to tree-level matrix elements through alpha_s^4. The resulting algorithm is implemented in the publicly available VINCIA plugin to the PYTHIA 8 event generator.
We compute the inclusive jet spectrum in the presence of a dense QCD medium by going beyond the single parton energy loss approximation. We show that higher-order corrections are important yielding large logarithmic contributions that must be resummed to all orders. This reflects the fact that jet quenching is sensitive to fluctuations of the jet substructure.
We calculate higher-order corrections to the quenching factor of heavy-quark jets due to hard, in-medium splittings in the framework of the BDMPS-Z formalism. These corrections turn out to be sensitive to a single mass-scale $m_ast = (hat q L)^{1/2}$, where $hat q$ is the medium transport coefficient and $L$ the path length, and allow to draw a distinction between the way light, with $m < m_ast$ (in contrast to massless $m=0$), and genuinely heavy, with $m > m_ast$, quark jets are quenched in the medium. We show that the corrections to the quenching factor at high energies are double-logarithmic and qualitatively of the same order as for the massless quark jet.
The QCD corrections to photon structure functions are defined in a way consistent with the factorization scheme invariance. It is shown that the conventional DIS$_{gamma}$ factorization scheme does not respect this invariance and is thus deeply flawed. The origins of the divergent behavior of photonic coefficient function at large $x$ are analyzed and recipe to remove it is suggested.
We present results for higher-order corrections to exclusive $mathrm{J}/psi$ production. This includes the first relativistic correction of order $v^2$ in quark velocity, and next-to-leading order corrections in $alpha_s$ for longitudinally polarized production. The relativistic corrections are found to be important for a good description of the HERA data, especially at small values of the photon virtuality. The next-to-leading order results for longitudinal production are evaluated numerically. We also demonstrate how the vector meson production provides complementary information to the structure functions for extracting the initial condition for the small-$x$ evolution of the dipole-proton scattering amplitude.
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