Subleading Regge limit from a soft anomalous dimension

Vita

et al. 2018

101

158

We derive and analytically solve renormalization group (RG) equations of gauge invariant non-local Wilson line operators which resum logarithms for event shape observables τ at subleading power in the τ 1 expansion. These equations involve a class of universal jet and soft functions arising through operator mixing, which we call θ-jet and θ-soft functions. An illustrative example involving these operators is introduced which captures the generic features of subleading power resummation, allowing us to derive the structure of the RG to all orders in α s , and provide field theory definitions of all ingredients. As a simple application, we use this to obtain an analytic leading logarithmic result for the subleading power resummed thrust spectrum for H → gg in pure glue QCD. This resummation determines the nature of the double logarithmic series at subleading power, which we find is still governed by the cusp anomalous dimension. We check our result by performing an analytic calculation up to O(α 3 s ). Consistency of the subleading power RG relates subleading power anomalous dimensions, constrains the form of the θ-soft and θ-jet functions, and implies an exponentiation of higher order loop corrections in the subleading power collinear limit. Our results provide a path for carrying out systematic resummation at subleading power for collider observables.

Section: Contentsmentioning

confidence: 99%

First subleading power resummation for event shapes

Vita

et al. 2018

101

158

“…For some interesting recent progress for the particular case of the subleading power Regge behavior for massive scattering amplitudes in N = 4 super Yang-Mills theory, see ref [110]…”

mentioning

confidence: 99%

Subleading power rapidity divergences and power corrections for qT

Ebert

et al. 2019

138

182

A number of important observables exhibit logarithms in their perturbative description that are induced by emissions at widely separated rapidities. These include transverse-momentum (q T ) logarithms, logarithms involving heavy-quark or electroweak gauge boson masses, and small-x logarithms. In this paper, we initiate the study of rapidity logarithms, and the associated rapidity divergences, at subleading order in the power expansion. This is accomplished using the soft collinear effective theory (SCET). We discuss the structure of subleading-power rapidity divergences and how to consistently regulate them. We introduce a new pure rapidity regulator and a corresponding MS-like scheme, which handles rapidity divergences while maintaining the homogeneity of the power expansion. We find that power-law rapidity divergences appear at subleading power, which give rise to derivatives of parton distribution functions. As a concrete example, we consider the q T spectrum for colorsinglet production, for which we compute the complete q 2 T /Q 2 suppressed power corrections at O(α s ), including both logarithmic and nonlogarithmic terms. Our results also represent an important first step towards carrying out a resummation of subleading-power rapidity logarithms.

“…event shape observables [40-42, 54, 55], for power corrections in quark masses [56,57], and in the Regge limit [58]. To obtain an all loop understanding, and identify universal structures which persist at subleading powers, it is desirable to formulate subleading power factorization theorems whose renormalization group structure allows the prediction of higher loop results from lower loop data, as has been successful at leading power.…”

mentioning

confidence: 99%

Subleading power factorization with radiative functions

Vita

2019

The study of amplitudes and cross sections in the soft and collinear limits allows for an understanding of their all orders behavior, and the identification of universal structures. At leading power soft emissions are eikonal, and described by Wilson lines. Beyond leading power the eikonal approximation breaks down, soft fermions must be added, and soft radiation resolves the nature of the energetic partons from which they were emitted. For both subleading power soft gluon and quark emissions, we use the soft collinear effective theory (SCET) to derive an all orders gauge invariant bare factorization, at both amplitude and cross section level. This yields universal multilocal matrix elements, which we refer to as radiative functions. These appear from subleading power Lagrangians inserted along the lightcone which dress the leading power Wilson lines. The use of SCET enables us to determine the complete set of radiative functions that appear to O(λ 2 ) in the power expansion, to all orders in α s . For the particular case of event shape observables in e + e − → dijets we derive how the radiative functions contribute to the factorized cross section to O(λ 2 ).