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The gamma gamma to gamma gamma process in the Standard and SUSY models at high energies

G. J. Gounaris, P. I. Porfyriadis, F. M. Renard

TL;DR

The paper analyzes high-energy $b3\u03b3\to\u03b3\u03b3$ scattering in the Standard Model and SUSY, showing that SM amplitudes arise at one loop mainly from the $W$ loop and that two helicity-conserving amplitudes dominate with largely imaginary phases. It derives simple high-energy 1-loop expressions for the relevant helicity amplitudes in terms of Passarino-Veltman functions and computes SUSY contributions from charginos and charged sleptons above their thresholds, highlighting their interference with SM amplitudes. Cross sections for polarized and unpolarized $b3\u03b3$ collisions are formulated using laser backscattering photon flux and are used to estimate observability at future linear colliders; unpolarized $\bar{\sigma}_0$ emerges as the most sensitive observable to SUSY effects, with potential several-sigma deviations for light states. The results indicate that $b3\u03b3$ scattering provides a clean, complementary NP probe to direct SUSY production, potentially revealing the presence and nature of charged superpartners if they lie in the 100--250 GeV range.

Abstract

We study the helicity amplitudes of the process γγ\to γγat high energy, which in the standard and SUSY models first arise at the one-loop order. In the standard model (SM), the diagrams involve W and charged quark and lepton loops, while in SUSY we also have contributions from chargino, charged sfermion and Higgs loop diagrams. The SUSY contributions are most important in the region above the threshold for producing the supersymmetric partners; since there, they interfere most effectively with the primarily imaginary SM amplitudes. Simple expressions for the relevant 1-loop functions are given, which provide a direct overview of the behaviour of the helicity amplitudes in the whole parameter space at high energies. The various characteristics of a large set of observables are studied in detail.

The gamma gamma to gamma gamma process in the Standard and SUSY models at high energies

TL;DR

The paper analyzes high-energy scattering in the Standard Model and SUSY, showing that SM amplitudes arise at one loop mainly from the loop and that two helicity-conserving amplitudes dominate with largely imaginary phases. It derives simple high-energy 1-loop expressions for the relevant helicity amplitudes in terms of Passarino-Veltman functions and computes SUSY contributions from charginos and charged sleptons above their thresholds, highlighting their interference with SM amplitudes. Cross sections for polarized and unpolarized collisions are formulated using laser backscattering photon flux and are used to estimate observability at future linear colliders; unpolarized emerges as the most sensitive observable to SUSY effects, with potential several-sigma deviations for light states. The results indicate that scattering provides a clean, complementary NP probe to direct SUSY production, potentially revealing the presence and nature of charged superpartners if they lie in the 100--250 GeV range.

Abstract

We study the helicity amplitudes of the process γγ\to γγat high energy, which in the standard and SUSY models first arise at the one-loop order. In the standard model (SM), the diagrams involve W and charged quark and lepton loops, while in SUSY we also have contributions from chargino, charged sfermion and Higgs loop diagrams. The SUSY contributions are most important in the region above the threshold for producing the supersymmetric partners; since there, they interfere most effectively with the primarily imaginary SM amplitudes. Simple expressions for the relevant 1-loop functions are given, which provide a direct overview of the behaviour of the helicity amplitudes in the whole parameter space at high energies. The various characteristics of a large set of observables are studied in detail.

Paper Structure

This paper contains 4 sections, 47 equations, 9 figures.

Table of Contents

  1. Introduction
  2. An overall view of the $\gamma \gamma \to \gamma \gamma$ amplitudes.
  3. The $\gamma \gamma \to \gamma \gamma$ Cross sections
  4. Conclusions

Figures (9)

  • Figure 1: Imaginary (solid) and real (dash) parts of the chargino (a,b) and slepton (c,d) contributions to the $\gamma \gamma \to \gamma \gamma$ helicity amplitudes at $\vartheta =90^0$ (a,c), and $\vartheta =30^0$ (b,d). The notation is: $F_{++++}$ (triangles), $F_{+++-}$ (circles), $F_{++--}$ (stars), $F_{+-+-}$ (rhombs). $F_{+--+}$, is identical to $F_{+-+-}$ for the (a,c) cases, while it is given by 'boxes' in the (b,d) ones.
  • Figure 2: $\bar{\sigma}_0$, $\bar{\sigma}_{22}$, $\bar{\sigma}_3$ and $\bar{\sigma}_{33}$ for SM (solid) and in the presence of a chargino (dash) or a charged slepton (circles) contribution.
  • Figure 2: $\bar{\sigma}_{33}^\prime$ and $\bar{\sigma}_{23}$ for SM (solid) and in the presence of a chargino (dash) or a charged slepton (circles) contribution.
  • Figure 3: $\bar{\sigma}_0$, $\bar{\sigma}_{22}$, $\bar{\sigma}_3$ and $\bar{\sigma}_{33}$ for SM (solid) and in the presence of a chargino (dash) or a charged slepton (circles) contribution.
  • Figure 3: $\bar{\sigma}_{33}^\prime$ and $\bar{\sigma}_{23}$ for SM (solid) and in the presence of a chargino (dash) or a charged slepton (circles) contribution.
  • ...and 4 more figures