# Diphoton Higgs signal strength in universal extra dimensions

## TL;DR

This paper investigates how universal extra dimensions affect the Higgs boson signal strength in diphoton decay at the LHC, revealing divergence issues in Kaluza-Klein sums and deriving bounds on the compactification scale from experimental data.

## Contribution

It introduces a regularization method for divergent sums in UED models and analyzes their impact on Higgs signal predictions, providing new bounds on extra dimension parameters.

## Key findings

- Discrete sums diverge for n≥2, indicating genuine UV divergences.
- The SM prediction for H→γγ remains stable across UED models.
- Experimental data constrains the compactification scale to above 1.5 TeV for n=1 and higher for larger n.

## Abstract

The signal strength of the $gg \to H \to \gamma \gamma$ reaction in $pp$ collisions at the LHC is studied within the context of the SM with UED. The impact of an arbitrary number $n$ of UED on both the $gg\to H$ and $H\to \gamma \gamma$ subprocesses is studied. The 1-loop contributions of Kaluza-Klein excitations to these subprocesses are proportional to discrete and continuous sums, which can diverge. By implementing dimensional regularization, it is shown that discrete regularized sums can naturally be expressed as multidimensional Epstein functions, and that divergences, if exist, emerge through the poles of these functions. It is found that continuous sums converge, but the discrete ones diverge, with the exception of the $n=1$ case, in which the 1-dimensional Epstein function converges. It is argued that divergences that arise from discrete sums for $n\geq 2$ are genuine UV divergences, since they correspond to short-distance effects in the compact manifold. Then, the amplitudes are renormalized in a modern sense by incorporating interactions of canonical dimension higher than four that allow us to generate the required counterterms, which are determined using a $\overline{\rm MS}$-like renormalization scheme. We find that the $gg\to H$ subprocess is quite sensitive to both the size and the dimension of the compact manifold, but the SM prediction for $H\to \gamma \gamma$ subprocess is practically unchanged. In the $n=1$ case, it is found that the experimental constraint on the compactification scale $R^{-1}\geq 1.5$ TeV allow us to reproduce the experimental limit on the signal strength $1.01\leq \mu^{(1)}_{\gamma \gamma}\leq 1.2$. In the $n\geq 2$ cases, it is found that the experimental limit on $\mu^{(n)}_{\gamma \gamma}$ leads to stronger lower bounds for the compactification scale given by $R^{-1}\geq 1.55, 2.45, 3.57, 5.10, 7.25$ TeVs for $n=2, 4, 6, 8, 10$, respectively.