Manifestly Soft Gauge Invariant Formulation of vNRQCD

Abstract

Homogeneous power counting in Non-Relativistic QCD (NRQCD) implies the simultaneous existence of both soft and ultrasoft gluons. In the velocity renormalization group (vNRQCD) formalism we show that operators involving soft fields interacting with heavy potential quarks can be put in a manifestly gauge invariant form by utilizing gluon and quark building blocks which contain Wilson lines, and are analogous to those used in the soft collinear effective theory. This leads to several simplifications, in particular significantly reducing the size of the operator basis, which stream-lines matching and anomalous dimension calculations at subleading order in the velocity expansion. Also, soft ghosts no longer couple via potential like interactions to the heavy quark fields, and hence do not appear until two loops. Furthermore the the color structures that appear at each order in ${\alpha }_s$ in the static potential are only those which should arise according to non-Abelian exponentiation. We also discuss how zero-bin subtractions clarify the role of $i\epsilon$ terms in the heavy quark propagator poles carrying soft momenta. Even though the choice of the direction of the soft Wilson lines in our building blocks does not matter, there is still a limited set of consistent choices, and the predicted form of the eikonal poles does influence results at two-loops and beyond.

arXiv comment29 pages, 7 figures

References in corpus (43)

• Rigorous QCD Analysis of Inclusive Annihilation and Production of Heavy Quarkonium
• An effective field theory for collinear and soft gluons: heavy to light decays
• Soft-Collinear Factorization in Effective Field Theory
• Asymptotic expansion of Feynman integrals near threshold
• Summing Sudakov logarithms in B -> X_s + gamma in effective field theory
• Invariant Operators in Collinear Effective Theory
• An Effective Field Theory of Gravity for Extended Objects
• Potential NRQCD: an effective theory for heavy quarkonium
• Effective field theories for heavy quarkonium
• Effective Field Theory for Ultrasoft Momenta in NRQCD and NRQED
• The static potential in QCD to two loops
• The Zero-Bin and Mode Factorization in Quantum Field Theory
• The static quark-antiquark potential in QCD to three loops
• The HQET/NRQCD Lagrangian to order alpha/m^3
• Three-loop static potential
• Renormalization group scaling in nonrelativistic QCD
• The infrared behaviour of the static potential in perturbative QCD
• Static QCD potential at three-loop order
• Potential NRQED: The Positronium Case
• Bound States and Power Counting in Effective Field Theories
• Fermionic contributions to the three-loop static potential
• The Renormalization Group Improvement of the QCD Static Potentials
• Effective Field Theory and Matching in Non-Relativistic Gauge Theories
• On the Apparent Ambiguities in the Post-Newtonian Expansion for Binary Systems
• TASI Lectures on Effective Field Theories
• Renormalization group improvement of the NRQCD Lagrangian and heavy quarkonium spectrum
• The QCD heavy-quark potential to order v^2: one loop matching conditions
• Renormalization group analysis of the QCD quark potential to order v^2
• Next-to-leading-log renormalization-group running in heavy-quarkonium creation and annihilation
• Running of the heavy quark production current and 1/k potential in QCD
• Renormalization Group Scaling of the 1/m^2 HQET Lagrangian
• Ultrasoft Renormalization in Non-Relativistic QCD
• Three-Loop Anomalous Dimension of the Heavy Quark Pair Production Current in Non-Relativistic QCD
• Logarithms of alpha in QED bound states from the renormalization group
• Threshold Expansion and Dimensionally Regularised NRQCD
• The Running Coulomb Potential and Lamb Shift in QCD
• Heavy Quarkonium Dynamics
• The renormalization group for correlated scales: one-stage versus two-stage running
• Ultrasoft NLL Running of the Nonrelativistic O(v) QCD Quark Potential
• Next-to-leading ultrasoft running of the heavy quarkonium potentials and spectrum: Spin-independent case
• Two-Loop Ultrasoft Running of the O(v^2) QCD Quark Potentials
• On different ways to quantize Soft-Collinear Effective Theory
• The static quark potential to three loops in perturbation theory

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