Anomalous dimensions from soft Regge constants

Self Cite

The high energy (Regge) limit provides a playground for understanding all loop structures of scattering amplitudes, and plays an important role in the description of many phenomenologically relevant cross-sections. While well understood in the planar limit, the structure of non-planar corrections introduces many fascinating complexities, for which a general organizing principle is still lacking. We study the structure of multi-reggeon exchanges in the context of the effective field theory for forward scattering, and derive their factorization into collinear operators (impact factors) and soft operators. We derive the structure of the renormalization group consistency equations in the effective theory, showing how the anomalous dimensions of the soft operators are related to those of the collinear operators, allowing us to derive renormalization group equations in the Regge limit purely from a collinear perspective. The rigidity of the consistency equations provides considerable insight into the all orders organization of Regge amplitudes in the effective theory, as well as its relation to other approaches. Along the way we derive a number of technical results that improve the understanding of the effective theory. We illustrate this collinear perspective by re-deriving all the standard BFKL equations for two-Glauber exchange from purely collinear calculations, and we show that this perspective provides a number of conceptual and computational advantages as compared to the standard view from soft or Glauber physics. We anticipate that this formulation in terms of collinear operators will enable a better understanding of the relation between BFKL and DGLAP in gauge theories, and facilitate the analysis of renormalization group evolution equations describing Reggeization beyond next-to-leading order.

Section: Jhep05(2024)328mentioning

confidence: 67%

“…The explanation for the need to distinguish them beyond the lowest order loop graphs, and send η ′ → 0 prior to η → 0, was given in ref. [57].…”

Section: Factorization Into Multi-glauber Operatorsmentioning

confidence: 99%

Section: Vanishing Of 1 → J Glauber Transitions In the Eftmentioning

confidence: 99%

Section: Simplifications In the Planar Limit From Glauber Instantaneitymentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

A collinear perspective on the Regge limit

Gao,

Moult,

Raman

et al. 2024

Self Cite

Projected transverse momentum resummation in top-antitop pair production at LHC

Schoenherr

2023

The transverse momentum distribution of the $$ t\overline{t} $$ t t ¯ system is of both experimental and theoretical interest. In the presence of azimuthally asymmetric divergences, pursuing resummation at high logarithmic precision is rather demanding in general. In this paper, we propose the projected transverse momentum spectrum $$ \textrm{d}{\sigma}_{t\overline{t}}/\textrm{d}{q}_{\tau } $$ d σ t t ¯ / d q τ , which is derived from the classical $$ {\overrightarrow{q}}_{\textrm{T}} $$ q → T spectrum by integrating out the rejection component $$ {q}_{\tau_{\perp }} $$ q τ ⊥ with respect to a reference unit vector $$ \overrightarrow{\tau} $$ τ → , to serve as an alternative solution to remove these asymmetric divergences, in addition to the azimuthally averaged case $$ \textrm{d}{\sigma}_{t\overline{t}}/\textrm{d}\mid {\overrightarrow{q}}_{\textrm{T}}\mid $$ d σ t t ¯ / d ∣ q → T ∣ . In the context of the effective field theories, SCETII and HQET, we will demonstrate that in spite of the $$ {q}_{\tau_{\perp }} $$ q τ ⊥ integrations, the leading asymptotic terms of $$ \textrm{d}{\sigma}_{t\overline{t}}/\textrm{d}{q}_{\tau } $$ d σ t t ¯ / d q τ still observe the factorisation pattern in terms of the hard, beam, and soft functions in the vicinity of qτ = 0 GeV. Then, with the help of the renormalisation group equation techniques, we carry out the resummation at NLL+NLO, N2LL+N2LO, and approximate N2LL′+N2LO accuracy on three observables of interest, $$ \textrm{d}{\sigma}_{t\overline{t}}/d{q}_{\textrm{T},\textrm{in}},\textrm{d}{\sigma}_{t\overline{t}}/\textrm{d}{q}_{\textrm{T},\textrm{out}} $$ d σ t t ¯ / d q T , in , d σ t t ¯ / d q T , out , and $$ \textrm{d}{\sigma}_{t\overline{t}}/d\Delta {\phi}_{t\overline{t}} $$ d σ t t ¯ / d Δ ϕ t t ¯ , within the domain $$ {M}_{t\overline{t}} $$ M t t ¯ ≥ 400 GeV. The first two cases are obtained by choosing $$ \overrightarrow{\tau} $$ τ → parallel and perpendicular to the top quark transverse momentum, respectively. The azimuthal de-correlation $$ \Delta {\phi}_{t\overline{t}} $$ Δ ϕ t t ¯ of the $$ t\overline{t} $$ t t ¯ pair is evaluated through its kinematical connection to qT,out. This is the first time the azimuthal spectrum $$ \Delta {\phi}_{t\overline{t}} $$ Δ ϕ t t ¯ is appraised at or beyond the N2LL level including a consistent treatment of both beam collinear and soft radiation.

Dissecting polytopes: Landau singularities and asymptotic expansions in 2 → 2 scattering

Gardi,

Herzog,

Jones

et al. 2024

Parametric representations of Feynman integrals have a key property: many, frequently all, of the Landau singularities appear as endpoint divergences. This leads to a geometric interpretation of the singularities as faces of Newton polytopes, which facilitates algorithmic evaluation by sector decomposition and asymptotic expansion by the method of regions. Here we identify cases where some singularities appear instead as pinches in parametric space for general kinematics, and we then extend the applicability of sector decomposition and the method of regions algorithms to such integrals, by dissecting the Newton polytope on the singular locus. We focus on 2 → 2 massless scattering, where we show that pinches in parameter space occur starting from three loops in particular nonplanar graphs due to cancellation between terms of opposite sign in the second Symanzik polynomial. While the affected integrals cannot be evaluated by standard sector decomposition, we show how they can be computed by first linearising the graph polynomial and then splitting the integration domain at the singularity, so as to turn it into an endpoint divergence. Furthermore, we demonstrate that obtaining the correct asymptotic expansion of such integrals by the method of regions requires the introduction of new regions, which can be systematically identified as facets of the dissected polytope. In certain instances, these hidden regions exclusively govern the leading power behaviour of the integral. In momentum space, we find that in the on-shell expansion for wide-angle scattering the new regions are characterised by having two or more connected hard subgraphs, while in the Regge limit they are characterised by Glauber modes.