pith. sign in

arxiv: 1202.0814 · v2 · pith:L6JHG2X5new · submitted 2012-02-03 · ✦ hep-ph · hep-th

A Formalism for the Systematic Treatment of Rapidity Logarithms in Quantum Field Theory

classification ✦ hep-ph hep-th
keywords formalismobservablesresummationrapidityallowscrossrenormalizationsection
0
0 comments X
read the original abstract

Many observables in QCD rely upon the resummation of perturbation theory to retain predictive power. Resummation follows after one factorizes the cross section into the rele- vant modes. The class of observables which are sensitive to soft recoil effects are particularly challenging to factorize and resum since they involve rapidity logarithms. In this paper we will present a formalism which allows one to factorize and resum the perturbative series for such observables in a systematic fashion through the notion of a "rapidity renormalization group". That is, a Collin-Soper like equation is realized as a renormalization group equation, but has a more universal applicability to observables beyond the traditional transverse momentum dependent parton distribution functions (TMDPDFs) and the Sudakov form factor. This formalism has the feature that it allows one to track the (non-standard) scheme dependence which is inherent in any scenario where one performs a resummation of rapidity divergences. We present a pedagogical introduction to the formalism by applying it to the well-known massive Sudakov form factor. The formalism is then used to study observables of current interest. A factorization theorem for the transverse momentum distribution of Higgs production is presented along with the result for the resummed cross section at NLL. Our formalism allows one to define gauge invariant TMDPDFs which are independent of both the hard scattering amplitude and the soft function, i.e. they are uni- versal. We present details of the factorization and resummation of the jet broadening cross section including a renormalization in pT space. We furthermore show how to regulate and renormalize exclusive processes which are plagued by endpoint singularities in such a way as to allow for a consistent resummation.

This paper has not been read by Pith yet.

discussion (0)

Sign in with ORCID, Apple, or X to comment. Anyone can read and Pith papers without signing in.

Forward citations

Cited by 8 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score.

  1. Next-to-next-to-next-to-leading order QCD corrections to photon-pair production

    hep-ph 2026-04 unverdicted novelty 7.0

    N³LO QCD predictions for photon-pair production are presented, demonstrating perturbative convergence.

  2. Analytic structure of the high-energy gravitational amplitude: multi-H diagrams and classical 5PM logarithms

    hep-th 2025-11 unverdicted novelty 7.0

    Computes the leading double logarithm at 5PM in the high-energy gravitational amplitude via multi-H diagrams and dispersion relations, extracting the single-log imaginary part of the eikonal phase.

  3. The N$^3$LO Twist-2 Matching of Linearly Polarized Gluon TMDs

    hep-ph 2025-09 unverdicted novelty 7.0

    Computes N³LO twist-2 matching for linearly polarized gluon TMDs with NNLL small-x resummation for fragmentation functions.

  4. $B_c \to \eta_c$ form factors at large recoil: SCET analysis and a three-loop consistency check

    hep-ph 2026-05 unverdicted novelty 6.0

    SCET factorization confirms the double-logarithmic resummation for B_c to eta_c form factors up to three loops and derives the iterative structure from RG equations of light-cone distribution amplitudes with cutoff re...

  5. The Classical Gravitational Impulse at High Energies

    hep-th 2026-05 unverdicted novelty 6.0

    The gravitational impulse for ultrarelativistic massive scalars is resummed to all orders in G_N at fixed G_N s/mb, recovering post-Minkowski results and predicting the leading high-energy behavior to eleventh post-Mi...

  6. The Fate of Ultra-Collinear Modes in On-Shell Massive Sudakov Form Factors

    hep-ph 2026-04 unverdicted novelty 6.0

    Ultra-collinear modes cancel to all orders in on-shell massive Sudakov form factors by gauge invariance, preserving SCET_II factorization, with explicit two-loop soft and jet functions computed via eta regulator and N...

  7. Energy Correlators Resolving Proton Spin

    hep-ph 2025-09 unverdicted novelty 5.0

    The work establishes a correspondence between spin-dependent energy correlators and polarized TMDs/NECs using SCET, yielding N3LL/N2LL predictions for correlation patterns in current and target fragmentation regions.

  8. High-precision measurement of the W boson mass with the CMS experiment

    hep-ex 2024-12 unverdicted novelty 5.0

    CMS measures the W boson mass as 80360.2 ± 9.9 MeV from 2016 data, consistent with the Standard Model prediction.