# Hadron-Hadron Interactions from $N_f=2+1+1$ Lattice QCD: isospin-1 $KK$ scattering length

## TL;DR

This study computes the isospin-1 kaon-kaon scattering length using lattice QCD with $N_f=2+1+1$ flavors, providing a precise extrapolation to the physical point and continuum limit.

## Contribution

It presents the first lattice QCD calculation of the $I=1$ $KK$ scattering length with $N_f=2+1+1$ flavors, including systematic error analysis and physical extrapolation.

## Key findings

- Scattering length $a_0^{I=1} = -0.154(6)_{stat}(^{+0}_{-5})_{m_s}(^{+0}_{-2})_{Z_P}(2)_{r_f} ext{ fm}
- Results are consistent with chiral perturbation theory predictions
- Provides a benchmark for future lattice and experimental studies

## Abstract

We present results for the interaction of two kaons at maximal isospin. The calculation is based on $N_f=2+1+1$ flavour gauge configurations generated by the European Twisted Mass Collaboration with pion masses ranging from about $230$ to $450\,\textrm{MeV}$ at three values of the lattice spacing. The elastic scattering length $a_0^{I=1}$ is calculated at several values of the bare strange and light quark masses. We find $M_K a_0 = -0.385(16)_{\textrm{stat}} (^{+0}_{-12})_{m_s}(^{+0}_{-5})_{Z_P}(4)_{r_f}$ as the result of a combined extrapolation to the continuum and to the physical point, where the first error is statistical, and the three following are systematical. This translates to $a_0 = -0.154(6)_{\textrm{stat}}(^{+0}_{-5})_{m_s} (^{+0}_{-2})_{Z_P}(2)_{r_f}\,\textrm{fm}$.