# Relaxing the $W'$ constraint on compactified extra-dimension

## TL;DR

This paper investigates how allowing brane fluctuations (branons) to relax the $W'$ constraint on extra dimensions, showing that lower compactification scales are compatible with current collider data when branons form dark matter.

## Contribution

It demonstrates that relaxing the $W'$ constraint with brane fluctuations permits smaller compactification scales, expanding the parameter space for extra-dimensional models.

## Key findings

- Compactification scales as low as ~1 TeV are allowed.
- Branon dark matter influences collider constraints.
- Relaxed constraints differ from rigid brane scenarios.

## Abstract

It has been known for some time that the inclusion of brane fluctuations, namely branons, helps in the suppression of KK-mode couplings to brane localised matter fields. In this paper we study the constraint on brane tension and compactification scale for such models using the results from the direct search of $W'$ at 13 TeV LHC, with an integrated luminosity of $36.1 fb^{-1}$, in the case for which branon forms the entire cold dark matter. Unlike the rigid brane scenario, where the compactification scale gets constrained to $\frac{1}{R} \gtrsim 5.2$ TeV, here we show that compactification scales as small as $\sim 1$ TeV are allowed for brane tensions of similar strength.