Fermionic Glauber Operators and Quark Reggeization

Abstract

We derive, in the framework of soft-collinear effective field theory (SCET), a Lagrangian describing the $t$-channel exchange of Glauber quarks in the Regge limit. The Glauber quarks are not dynamical, but are incorporated through non-local fermionic potential operators. These operators are power suppressed in $|t|/s$ relative to those describing Glauber gluon exchange, but give the first non-vanishing contributions in the Regge limit to processes such as $q\bar{q}\to gg$ and $q\bar{q}\to \gamma \gamma$. They therefore represent an interesting subset of power corrections to study. The structure of the operators, which describe certain soft and collinear emissions to all orders through Wilson lines, is derived from the symmetries of the effective theory combined with constraints from power and mass dimension counting, as well as through explicit matching calculations. Lightcone singularities in the fermionic potentials are regulated using a rapidity regulator, whose corresponding renormalization group evolution gives rise to the Reggeization of the quark at the amplitude level and the BFKL equation at the cross section level. We verify this at one-loop, deriving the Regge trajectory of the quark in the $3$ color channel, as well as the leading logarithmic BFKL equation. Results in the $\bar{6}$ and $15$ color channels are obtained by the simultaneous exchange of a Glauber quark and a Glauber gluon. SCET with quark and gluon Glauber operators therefore provides a framework to systematically study the structure of QCD amplitudes in the Regge limit, and derive constraints on higher order amplitudes.

31 pages, many figures

References in corpus (11)

• Bootstrapping a Five-Loop Amplitude Using Steinmann Relations
• Bootstrapping an NMHV amplitude through three loops
• Heptagons from the Steinmann Cluster Bootstrap
• Four-gluon scattering at three loops, infrared structure and Regge limit
• Next-to-soft corrections to high energy scattering in QCD and gravity
• A Subleading Operator Basis and Matching for $gg\to H$
• Adjoint BFKL at finite coupling: a short-cut from the collinear limit
• A Complete Basis of Helicity Operators for Subleading Factorization
• Two-parton scattering in the high-energy limit
• On the one-loop calculations with Reggeized quarks
• Regge meets collinear in strongly-coupled $\mathcal{N}=4$ super Yang-Mills

Cited by in corpus (20)

• 50 Years of Quantum Chromodynamics
• Subleading Power Rapidity Divergences and Power Corrections for $q_T$
• Transverse momentum dependent PDFs at N${}^3$LO
• Drell-Yan $q_T$ Resummation of Fiducial Power Corrections at N${}^3$LL
• First Subleading Power Resummation for Event Shapes
• Subleading Power Resummation of Rapidity Logarithms: The Energy-Energy Correlator in $\mathcal{N}=4$ SYM
• Subleading Power Factorization with Radiative Functions
• Resummed Photon Spectra for WIMP Annihilation
• The Energy-Energy Correlation in the back-to-back limit at N${}^3$LO and N${}^3$LL${}^{\prime }$
• TMD Fragmentation Functions at N${}^3$LO
• Factorization for Azimuthal Asymmetries in SIDIS at Next-to-Leading Power
• Infrared singularities of QCD scattering amplitudes in the Regge limit to all orders
• Sudakov resummation from the BFKL evolution
• Collinear expansion for color singlet cross sections
• Anomalous Dimensions from Soft Regge Constants
• The SAGEX Review on Scattering Amplitudes, Chapter 15: The Multi-Regge Limit
• A Collinear Perspective on the Regge Limit
• Higher Twists
• Effective Field Theory Factorization for Diffraction
• Quark-Gluon Backscattering in the Regge Limit at One-Loop