# Nonperturbative comparison of clover and HISQ quarks in lattice QCD and the properties of the phi meson

## TL;DR

This study compares clover and HISQ quark formalisms in lattice QCD, focusing on meson correlators and properties of the phi meson, using nonperturbative methods to assess renormalization and continuum limits.

## Contribution

It provides a nonperturbative comparison of clover and HISQ quarks, including renormalization factors and phi meson properties, with implications for lattice QCD calculations.

## Key findings

- Good agreement of phi meson mass and decay constant with experiment
- Nonperturbative renormalization factors consistent with perturbative QCD
- Comparison of continuum limit approaches for different formalisms

## Abstract

We compare correlators for pseudoscalar and vector mesons made from valence strange quarks using the clover quark and highly improved staggered quark (HISQ) formalisms in full lattice QCD. We use fully nonperturbative methods to normalise vector and axial vector current operators made from HISQ quarks, clover quarks and from combining HISQ and clover fields. This allows us to test expectations for the renormalisation factors based on perturbative QCD, with implications for the error budget of lattice QCD calculations of the matrix elements of clover-staggered $b$-light weak currents, as well as further HISQ calculations of the hadronic vacuum polarisation. We also compare the approach to the (same) continuum limit in clover and HISQ formalisms for the mass and decay constant of the $\phi$ meson. Our final results for these parameters, using single-meson correlators and neglecting quark-line disconnected diagrams are: $m_{\phi} =$ 1.023(6) GeV and $f_{\phi} = $ 0.238(3) GeV in good agreement with experiment. The results come from calculations in the HISQ formalism using gluon fields that include the effect of $u$, $d$, $s$ and $c$ quarks in the sea with three lattice spacing values and $m_{u/d}$ values going down to the physical point.