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

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 $450\text{MeV}$ 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 $M_K{a}_0=-0.385(16{)}_{\text{stat}}{(}_{-12}^{+0}{)}_{m_s}{(}_{-5}^{+0}{)}_{Z_P}(4{)}_{r_f}$ 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 $a_0=-0.154(6{)}_{\text{stat}}{(}_{-5}^{+0}{)}_{m_s}{(}_{-2}^{+0}{)}_{Z_P}(2{)}_{r_f}\text{fm}$.

Comments: 28 pages, 18 tables, 14 figures