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We survey some of the recent developments in the extraction and application of heavy quark Parton Distribution Functions (PDFs). We also highlight some of the key HERA measurements which have contributed to these advances.
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We investigate a possible use of direct photon production in association with a heavy quark to test different models of intrinsic heavy quark parton distribution function (PDF) at the Tevatron, at the large hadron collider (LHC) and at RHIC.
We investigate the impact of displaced heavy quark matching scales in a global fit. The heavy quark matching scale $mu_{m}$ determines at which energy scale $mu$ the QCD theory transitions from $N_{F}$ to $N_{F}+1$ in the Variable Flavor Number Scheme (VFNS) for the evolution of the Parton Distribution Functions (PDFs) and strong coupling $alpha_S(mu)$. We study the variation of the matching scales, and their impact on a global PDF fit of the combined HERA data. As the choice of the matching scale $mu_{m}$ effectively is a choice of scheme, this represents a theoretical uncertainty; ideally, we would like to see minimal dependence on this parameter. For the transition across the charm quark (from $N_{F}=3$ to $4$), we find a large $mu_m=mu_{c}$ dependence of the global fit $chi^2$ at NLO, but this is significantly reduced at NNLO. For the transition across the bottom quark (from $N_{F}=4$ to $5$), we have a reduced $mu_{m}=mu_b$ dependence of the $chi^2$ at both NLO and NNLO as compared to the charm. This feature is now implemented in xFitter 2.0.0, an open source QCD fit framework.
We use functional methods to compute one-loop effects in Heavy Quark Effective Theory. The covariant derivative expansion technique facilitates the efficient extraction of matching coefficients and renormalization group evolution equations. This paper provides the first demonstration that such calculations can be performed through the algebraic evaluation of the path integral for the class of effective field theories that are (i) constructed using a non-trivial one-to-many mode decomposition of the UV theory, and (ii) valid for non-relativistic kinematics. We discuss the interplay between operators that appear at intermediate steps and the constraints imposed by the residual Lorentz symmetry that is encoded as reparameterization invariance within the effective description. The tools presented here provide a systematic approach for computing corrections to higher order in the heavy mass expansion; precision applications include predictions for experimental data and connections to theoretical tests via lattice QCD. A set of pedagogical appendices comprehensively reviews modern approaches to performing functional calculations algebraically, and derives contributions from a term with open covariant derivatives for the first time.
Conventional perturbative QCD calculations on the production of a heavy quark ``$H$ consist of two contrasting approaches: the usual QCD parton formalism uses the zero-mass approximation ($m_H=0$) once above threshold, and treats $H$ just like the other light partons; on the other hand, most recent ``NLO heavy quark calculations treat $m_H$ as a % large parameter and always consider $H$ as a heavy particle, never as a parton, irrespective of the energy scale of the physical process. By their very nature, both these approaches are limited in their regions of applicability. This dichotomy can be resolved in a unified general-mass variable-flavor-number scheme, which retains the $m_H$ dependence at all energies, and which naturally reduces to the two conventional approaches in their respective region of validity. Recent applications to lepto- and hadro-production of heavy quarks are briefly summarized.
We show that the Heavy Quark Effective Theory is renormalizable perturbatively. We also show that there exist renormalization schemes in which the infinite quark mass limit of any QCD Green function is exactly given by the corresponding Green function of the Heavy Quark Effective Theory. All this is accomplished while preserving BRS invariance.
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