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Electroweak Sudakov form factors and nonfactorizable soft QED effects at NLC energies

P. Ciafaloni, D. Comelli

TL;DR

Problem: understanding leading infrared electroweak corrections at energies far above the EW scale, where the traditional separation of photonic and pure electroweak effects may fail. Approach: develop a soft-insertion, eikonal method that yields an operator-based LL expansion with a distinct EW piece H_EW(x) and a photon QED factor; apply to a two-fermion final state from a Z' neutral under the gauge group to expose the mixing effects. Findings: the photon and weak sectors do not decouple above M; nonabelian commutators and neutral-sector mixing prevent full exponentiation, leading to a small but non-negligible discrepancy relative to naive factorization (order of permille at 1 TeV). Significance: the framework is essential for accurate electroweak radiative corrections at NLC energies and can be extended to higher orders for precision collider phenomenology.

Abstract

We study the leading log infrared behavior of electroweak corrections at TeV scale energies, that will be reached by next generation of linear colliders (NLC). We show that, contrary to what happens at typical LEP energies, it is not anymore possible to disentangle ``pure electroweak'' from ``photonic'' corrections. This means that soft QED effects do not factorize and therefore cannot be treated in the usual ``naive'' way they were accounted for in the LEP-era. The nonfactorizable effects come up first at the two loop LL level, that we calculate explicitly for a fermion source that is neutral under the SU(2)$\otimes$U(1) gauge group (explicitly, a Z' decay into two fermions). The basic formalism we set up can be used to calculate LL effects at any order of perturbation theory. The results of this paper might be important for future calculations of electroweak corrections at NLC energies.

Electroweak Sudakov form factors and nonfactorizable soft QED effects at NLC energies

TL;DR

Problem: understanding leading infrared electroweak corrections at energies far above the EW scale, where the traditional separation of photonic and pure electroweak effects may fail. Approach: develop a soft-insertion, eikonal method that yields an operator-based LL expansion with a distinct EW piece H_EW(x) and a photon QED factor; apply to a two-fermion final state from a Z' neutral under the gauge group to expose the mixing effects. Findings: the photon and weak sectors do not decouple above M; nonabelian commutators and neutral-sector mixing prevent full exponentiation, leading to a small but non-negligible discrepancy relative to naive factorization (order of permille at 1 TeV). Significance: the framework is essential for accurate electroweak radiative corrections at NLC energies and can be extended to higher orders for precision collider phenomenology.

Abstract

We study the leading log infrared behavior of electroweak corrections at TeV scale energies, that will be reached by next generation of linear colliders (NLC). We show that, contrary to what happens at typical LEP energies, it is not anymore possible to disentangle ``pure electroweak'' from ``photonic'' corrections. This means that soft QED effects do not factorize and therefore cannot be treated in the usual ``naive'' way they were accounted for in the LEP-era. The nonfactorizable effects come up first at the two loop LL level, that we calculate explicitly for a fermion source that is neutral under the SU(2)U(1) gauge group (explicitly, a Z' decay into two fermions). The basic formalism we set up can be used to calculate LL effects at any order of perturbation theory. The results of this paper might be important for future calculations of electroweak corrections at NLC energies.

Paper Structure

This paper contains 5 sections, 32 equations, 1 figure.

Table of Contents

  1. Introduction
  2. Leading IR electroweak form factor
  3. Comparing with the "naive" approach
  4. Conclusions
  5. Appendix

Figures (1)

  • Figure 1: (a)-(b) :diagrams for soft boson insertion at 1 and n loops. Continuous lines are fermion lines, and dashed lines are $W,Z,\gamma$ gauge bosons.Crosses indicate that gauge bosons are close to mass-shell, and energies are such that $w_1\ll w_2\ll.....\ll w_n$ (see text). (c): Pictorial representation of eq. (\ref{['eqfig']})