[Paper Review] High-energy frontier of the muon g-2 at a muon collider

Paride Paradisi, Olcyr Sumensari+1 more|arXiv (Cornell University)|Mar 11, 2022

Particle physics theoretical and experimental studies4 citations

TL;DR

This paper validates the connection between the muon g-2 anomaly and high-energy muon collider processes by performing full one-loop calculations of $\mu^+\mu^- \to h\gamma$ in simplified models with chirally enhanced contributions. It confirms that this process provides a model-independent probe of new physics at multi-TeV energies, with cross sections scaling quadratically with center-of-mass energy, and demonstrates that $2\to3$ processes like $\mu^+\mu^- \to h\bar{\Psi}\Psi$ offer stronger correlations with $\Delta a_\mu$ than $2\to2$ processes, enabling model discrimination at the high-energy frontier.

ABSTRACT

The long-standing muon g-2 anomaly can be explained by heavy new physics particles through chirally enhanced contributions. It has been recently proposed that a muon collider running at center-of-mass energies of several TeV could test these new physics scenarios in a model-independent way, through the study of high-energy processes such as mu+ mu- --> h gamma. In this work, we validate these findings, based on effective field theories, by considering selected renormalizable simplified models and by computing this one-loop process in full generality. Furthermore, we explore the interplay of direct and indirect high-energy searches to pin down the details of the underlying new physics model accommodating the muon g-2 anomaly.

Motivation & Objective

• To validate effective field theory (EFT) predictions that $\mu^+\mu^- \to h\gamma$ at high energies can probe the muon $g$-2 anomaly.
• To perform full one-loop calculations of $\mu^+\mu^- \to h\gamma$ in simplified models with chirally enhanced $\Delta a_\mu$ contributions.
• To assess the validity limit of the EFT description for this process in the context of new physics at multi-TeV scales.
• To explore the interplay between direct high-energy searches and indirect $\Delta a_\mu$ constraints to disentangle underlying new physics models.
• To identify $2\to3$ processes such as $\mu^+\mu^- \to h\bar{\Psi}\Psi$ as more sensitive probes of the $g$-2 anomaly than $2\to2$ processes.

Proposed method

• The study employs renormalizable simplified models with new scalars and vectorlike fermions in $SU(2)_L \times U(1)_Y$ representations, preserving a $Z_2$ symmetry to stabilize dark matter candidates.
• One-loop amplitudes for $\mu^+\mu^- \to h\gamma$ are computed in full generality, including all momentum-dependent and mass-dependent contributions beyond the EFT regime.
• The phase space for $2\to3$ processes is decomposed into $2\to2$ sub-processes and $1\to2$ decays, with kinematics evaluated in both center-of-mass and rest frames using Lorentz-invariant phase-space parametrizations.
• The $R$-matrix transformation is used to relate momenta between the $2\to2$ and $1\to2$ frames, enabling consistent evaluation of scalar products in the amplitude.
• Renormalization group equations (RGEs) are derived for gauge, Yukawa, and quartic couplings, with $\beta$-function coefficients computed for each model to assess running effects.
• The cross sections are evaluated numerically across a range of $\sqrt{s}$ values to compare with EFT predictions and determine the energy scale where EFT breaks down.

Experimental results

Research questions

• RQ1 Can full one-loop calculations in simplified models confirm the EFT prediction that $\mu^+\mu^- \to h\gamma$ cross section scales quadratically with $\sqrt{s}$?
• RQ2 What is the energy scale beyond which the EFT description for $\mu^+\mu^- \to h\gamma$ becomes invalid in these models?
• RQ3 How do $2\to3$ processes like $\mu^+\mu^- \to h\bar{\Psi}\Psi$ correlate with $\Delta a_\mu$ compared to $2\to2$ processes?
• RQ4 Can the interplay of direct high-energy signals and indirect $\Delta a_\mu$ constraints uniquely identify the underlying new physics model?
• RQ5 To what extent do $2\to3$ processes provide a more robust and model-discriminating probe of the muon $g$-2 anomaly than $2\to2$ processes?

Key findings

• The full one-loop calculation confirms that the $\mu^+\mu^- \to h\gamma$ cross section grows quadratically with $\sqrt{s}$, validating the EFT prediction across a wide energy range.
• The EFT description breaks down at $\sqrt{s} \sim \Lambda/2$ for $\Lambda \sim 10$ TeV, indicating a clear energy window where direct collider measurements can probe the $g$-2 anomaly.
• The $2\to3$ process $\mu^+\mu^- \to h\bar{\Psi}\Psi$ exhibits a stronger correlation with $\Delta a_\mu$ than $2\to2$ processes, making it a superior probe for model discrimination.
• The $\mu^+\mu^- \to h\gamma$ process is shown to be equivalent to measuring $\Delta a_\mu$ at high energies, providing a direct link between high-energy and high-intensity frontiers.
• The inclusion of $2\to3$ processes significantly improves the ability to distinguish between different simplified models that explain the $g$-2 anomaly.
• The results demonstrate that a multi-TeV muon collider can perform a model-independent test of the muon $g$-2 anomaly through high-energy $\mu^+\mu^-$ scattering.