# Monte-Carlo study of the $\Delta\rho$ parameter

## TL;DR

This study uses Monte Carlo simulations to analyze the electroweak rho-parameter within a lattice SU(2)×U(1) chiral Yukawa model, confirming perturbation theory predictions and highlighting cut-off effects.

## Contribution

It provides a numerical verification of the rho-parameter behavior in a lattice model, including the impact of finite cut-off effects on the parameter's value.

## Key findings

- Numerical data agree with one-loop perturbation theory.
- Finite cut-off can significantly alter the rho-parameter.
- Decoupling of species doublers is confirmed.

## Abstract

We present results concerning a lattice study of the electroweak $\rho$-parameter. We have used an SU(2)$\times$U(1) symmetric chiral Yukawa model built with Zaragoza fermions. The decoupling of the species doublers in this model is verified numerically. We find that the numerical data for $\Delta\rho$ are well described by one-loop perturbation theory with the same finite volume and with the same finite cut-off. However, a finite cut-off can cause substantial deviations of $\Delta\rho$ from the standard value, even in infinite volume.