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On the new physics in Bhabha luminometry at future $e^+e^-$ colliders

Clara L. Del Pio, Francesco P. Ucci

TL;DR

The paper addresses the risk that unknown heavy new physics could bias luminosity measurements at future $e^+e^-$ colliders, which rely on small-angle Bhabha scattering (SABS). It employs Standard Model Effective Field Theory (SMEFT) to quantify heavy NP effects on SABS, computing LO interference and including NLO corrections, across FCC-ee, CEPC, ILC, and CLIC benchmarks, and expresses the cross-section shift as $\delta_{SMEFT} = (1/\sigma_{SM})(\sigma^{(6)} \pm \sqrt{\sum_i \sigma_i^{(6)} V_{ij} \sigma_j^{(6)}})$ with $\sigma^{(6)} = \sum_i (C_i/\Lambda_{NP}^2) \sigma_i^{(6)}$. The results show that SMEFT-induced deviations can reach $\mathcal{O}(10^{-4})$–$\mathcal{O}(10^{-3})$, particularly near the $Z$ pole, and that NLO corrections do not erase these effects, motivating a luminosity-independent strategy. To mitigate, the authors propose using LABS and polarization-based asymmetries to constrain four-electron operators, achieving residual shifts as small as $\sim 5\times 10^{-6}$ to $10^{-5}$ and thereby preserving the targeted luminosity precision. This approach informs the design of future collider programs and suggests extensions to other processes such as $e^+e^- \to \gamma\gamma$ and potentially muon colliders.

Abstract

The absolute machine luminosity is a key quantity to achieve the high-precision physics program of future $e^+e^-$ collider. It is determined by measuring a theoretically well-known process, which, ideally, can be computed with arbitrary precision in the perturbation theory. However, yet undiscovered new physics could give a non-negligible contribution to the cross section of the luminosity monitoring process, thus invalidating the uncertainty determination of measured quantities. We assess the theoretical error of non-Standard Model origin to the small-angle Bhabha scattering in various future colliders scenarios. In addition, a possible running strategy to constrain unknown heavy interactions is proposed, relying on asymmetries that do not depend on the absolute luminosity.

On the new physics in Bhabha luminometry at future $e^+e^-$ colliders

TL;DR

The paper addresses the risk that unknown heavy new physics could bias luminosity measurements at future colliders, which rely on small-angle Bhabha scattering (SABS). It employs Standard Model Effective Field Theory (SMEFT) to quantify heavy NP effects on SABS, computing LO interference and including NLO corrections, across FCC-ee, CEPC, ILC, and CLIC benchmarks, and expresses the cross-section shift as with . The results show that SMEFT-induced deviations can reach –, particularly near the pole, and that NLO corrections do not erase these effects, motivating a luminosity-independent strategy. To mitigate, the authors propose using LABS and polarization-based asymmetries to constrain four-electron operators, achieving residual shifts as small as to and thereby preserving the targeted luminosity precision. This approach informs the design of future collider programs and suggests extensions to other processes such as and potentially muon colliders.

Abstract

The absolute machine luminosity is a key quantity to achieve the high-precision physics program of future collider. It is determined by measuring a theoretically well-known process, which, ideally, can be computed with arbitrary precision in the perturbation theory. However, yet undiscovered new physics could give a non-negligible contribution to the cross section of the luminosity monitoring process, thus invalidating the uncertainty determination of measured quantities. We assess the theoretical error of non-Standard Model origin to the small-angle Bhabha scattering in various future colliders scenarios. In addition, a possible running strategy to constrain unknown heavy interactions is proposed, relying on asymmetries that do not depend on the absolute luminosity.
Paper Structure (4 sections, 10 equations, 3 figures, 1 table)

This paper contains 4 sections, 10 equations, 3 figures, 1 table.

Table of Contents

  1. Introduction
  2. New physics in SABS
  3. Asymmetries
  4. Conclusions and outlook

Figures (3)

  • Figure 1: Diagrams contributing to the SABS cross section. The first diagram is the SM $t$-channel photon exchange. The second two are LO SMEFT diagrams representing a modified $Zee$ vertex and a four-fermion interaction. The latter two are next-to-leading-order (NLO) diagrams in the SMEFT.
  • Figure 2: Differential deviation of the SABS cross section as computed in the SMEFT, according to Eq. \ref{['eq:deltasmeft']}.
  • Figure 3: The first panel shows the absolute difference between the SMEFT and SM $A_\text{FB}$ as a function of the energy. The latter three panels are the projection on $(C_i,C_j)$ planes of the $\chi^2\leq1$ region (Eq.\ref{['chi2']}) for polarisation asymmetries.