$D_s \rightarrow \eta, \eta'$ semileptonic decay form factors with disconnected quark loop contributions

TL;DR

This study computes the form factors for $D_s$ meson semi-leptonic decays to $ ext{eta}$ and $ ext{eta'}$ using lattice QCD, including disconnected quark loop contributions, providing new insights into meson structure.

Contribution

It is the first lattice QCD calculation of these form factors including disconnected contributions, with improved noise reduction techniques and results at different pion masses.

Findings

Scalar form factors at zero momentum transfer are quantified.

Disconnected quark loop contributions are successfully incorporated.

Results show specific form factor values with statistical errors.

Abstract

We calculate for the first time the form factors of the semi-leptonic decays of the $D_s$ meson to $\eta$ and $\eta^\prime$ using lattice techniques. As a by-product of the calculation we obtain the masses and leading distribution amplitudes of the $\eta$ and $\eta^\prime$ mesons. We use $N_f=2+1$ non-perturbatively improved clover fermions on configurations with a lattice spacing $a\sim 0.075$ fm. We are able to obtain clear signals for relevant matrix elements, using several noise reduction techniques, both for the connected and disconnected contributions. This includes a new method for reducing the variance of pseudoscalar disconnected two-point functions. At zero momentum transfer, we obtain for the scalar form factors, $|f_0^{D_s\to \eta}|=0.564(11)$ and $|f_0^{D_s\to \eta'}|=0.437(18)$ at $M_\pi\approx 470\, {\rm MeV}$, as well as $|f_0^{D_s\to \eta}|=0.542(13)$ and $|f_0^{D_s\to \eta'}|=0.404(25)$ at $M_\pi\approx 370\, {\rm MeV}$, where the errors are statistical only.