Functional Methods for Heavy Quark Effective Theory

Abstract

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.

arXiv comment42 pages, extensive appendices

References in corpus (24)

• Rigorous QCD Analysis of Inclusive Annihilation and Production of Heavy Quarkonium
• An effective field theory for collinear and soft gluons: heavy to light decays
• Heavy Quark Symmetry
• Soft-Collinear Factorization in Effective Field Theory
• Asymptotic expansion of Feynman integrals near threshold
• Invariant Operators in Collinear Effective Theory
• The Standard Model as an Effective Field Theory
• Reparameterisation Invariance Constraints on Heavy Particle Effective Field Theories
• The Universal One-Loop Effective Action
• Integrating out heavy particles with functional methods: a simplified framework
• Non-perturbative Heavy Quark Effective Theory
• Covariant diagrams for one-loop matching
• Effective Field Theory and Matching in Non-Relativistic Gauge Theories
• Extending the Universal One-Loop Effective Action: Heavy-Light Coefficients
• Mixed Heavy-Light Matching in the Universal One-Loop Effective Action
• The NRQED lagrangian at order 1/M^4
• Completing the scalar and fermionic Universal One-Loop Effective Action
• Lorentz invariance in heavy particle effective theories
• HQET at order 1/m: I. Non-perturbative parameters in the quenched approximation
• Reparameterization Invariance Revisited
• Reparameterization Invariance to all Orders in Heavy Quark Effective Theory
• Short-Distance Expansion of Heavy-Light Currents at Order 1/m
• Extending the Universal One-Loop Effective Action by Regularization Scheme Translating Operators
• Renormalization of Heavy Quark Effective Field Theory: Quantum Action Principles and Equations of Motion

Cited by in corpus (16)

• Matching scalar leptoquarks to the SMEFT at one loop
• The Fermionic Universal One-Loop Effective Action
• STrEAMlining EFT Matching
• Functional Prescription for EFT Matching
• Evanescent Operators in One-Loop Matching Computations
• SuperTracer: A Calculator of Functional Supertraces for One-Loop EFT Matching
• Complete One-loop Matching of the Type-I Seesaw Model onto the Standard Model Effective Field Theory
• One-loop Matching of the Type-II Seesaw Model onto the Standard Model Effective Field Theory
• Neutrino seesaw models at one-loop matching: Discrimination by effective operators
• Axion Effective Action
• Two-loop matching of renormalizable operators: general considerations and applications
• One-loop Matching of Scotogenic Model onto Standard Model Effective Field Theory up to Dimension 7
• Electroweak phase transition triggered by fermion sector
• Complete One-loop Structure of the Type-(I+II) Seesaw Effective Field Theory
• Anomalies From the Covariant Derivative Expansion
• Effective description of Nelson-Barr models and the theta parameter