arXiv : $\mathrm{D}$ and $\mathrm{D_s}$ decay constants in $N_{\rm f}=2+1$ QCD with Wilson fermions

Kuberski, Simon; Collins, Sara; Söldner, Wolfgang; Joswig, Fabian; Heitger, Jochen

doi:10.1007/JHEP07(2024)090

Article
Report number	arXiv:2405.04506 ; CERN-TH-2024-052 ; MITP-24-047 ; MS-TP-24-09
Title	$\mathrm{D}$ and $\mathrm{D_s}$ decay constants in $N_{\rm f}=2+1$ QCD with Wilson fermions
Author(s)	Kuberski, Simon (CERN ; Mainz U., Inst. Phys. ; Darmstadt, GSI) ; Joswig, Fabian (Edinburgh U.) ; Collins, Sara (Regensburg U.) ; Heitger, Jochen (Munster U., ITP) ; Söldner, Wolfgang (Regensburg U.)
Collaboration	RQCD Collaboration ; ALPHA Collaboration
Publication	2024-07-10
Imprint	2024-05-07
Number of pages	44
Note	44 pages, 12 figures, 7 tables
In:	JHEP 2407 (2024) 090
DOI	10.1007/JHEP07(2024)090
Subject category	hep-lat ; Particle Physics - Lattice
Abstract	We present results for the leptonic decay constants of the D and D$_{\rm s}$ mesons from $N_{\rm f}=2+1$ lattice QCD. We employ a set of 49 high statistics gauge ensembles generated by the Coordinated Lattice Simulations (CLS) effort utilising non-perturbatively improved Wilson fermions and the tree-level Symanzik improved gauge action at six values of the lattice spacing in the range $a = 0.098\,$fm down to $a = 0.039\,$fm, with pion masses varying from around $420\,$MeV down to below the physical point. The ensembles lie on three trajectories in the quark mass plane, two trajectories intersecting close to the physical quark mass point and the third one approaching the SU(3) chiral limit, enabling tight control of the light and strange quark mass dependence. We obtain $f_{\mathrm{D_s}}=246.8(1.3)\,$MeV, $f_\mathrm{D}=208.4(1.5)\,$MeV and $f_{\mathrm{D_s}}/f_\mathrm{D}=1.1842(36)$, where the precision of our results is mostly limited by the determination of the scale.
Copyright/License	preprint: (License: CC BY 4.0) publication: © 2024-2025 The Authors (License: CC-BY-4.0), sponsored by SCOAP³

$Overview of the ensembles used in this work in the plane of (renormalised) light and strange quark masses: the chiral trajectory where $\Tr M = \text{const.}$ approaches the physical point from below (blue line) and meets the trajectory with renormalised strange quark mass $\widehat{m}_{\rm s} \approx \text{const.}$ (orange line) at the physical point by construction. A third trajectory for which the light and strange quark masses are equal, $m_{\rm l}=m_{\rm s}$ (yellow line), approaches the SU(3) chiral limit. The orange line is obtained by setting $8t_0 (m_{\rm K}^2 - \frac{1}{2}m_\pi^2)$ to its physical value, analogously the blue line is defined by fixing~$\Mbarsq \equiv 8 t_0 \big(2m_\mathrm{K}^2 + m_\pi^2\big) / 3= \bar{\mathbb{M}}^2_{\rm phys}$.$ $Overview of the ensembles entering the present study: three different quark mass trajectories (left: $m_{\rm l}=m_{\rm s}$, centre: $\Tr M =\text{const.}$, right: $\widehat{m}_{\rm s} \approx \text{const.}$) have been analysed at six (four for $\widehat{m}_{\rm s} \approx \text{const.}$) different lattice spacings. Additional ensembles with different spatial volumes exist for selected parameter sets. From these dedicated ensembles, the small volumes (S100, S201, U101, U102, U103, X252, X253) do not enter the final extrapolation. Also the ensembles B452 and N300 have been excluded. For these two cases the rather small temporal extent, in view of the given statistics, did not allow for a reliable extraction of the ground state.$ $Results from our combined fits to the $\tilde{P}\tilde{P}$ and $A_0\tilde{P}$ two-point functions for the heavy-strange meson on ensemble E300 (left, $m_\pi=175$\,MeV, $a=0.049\,$fm) and the heavy-light meson on ensemble E250 (right, $m_\pi=130$\,MeV, $a=0.064\,$fm). Note that the results displayed are for the second charm hopping parameter ($\kappa_{c^2}$), see table \ref{t:hopping} in appendix \ref{a:tables}. {\it Top}: The fit result for the meson mass $m_{\mathrm{D}_{(\rm s)}}$ (blue band) is shown together with the effective masses of the two correlation functions. The lower end of the fit range~($t_{\rm min}$) in each case is indicated by a dashed line. {\it Bottom}: The result for the decay constant obtained from the fit (grey band) is displayed along with the effective decay constant (eq.~\eqref{eq:efff}). The dashed line indicates the $t_{\rm min}$ of the $A_0\tilde{P}$ two-point function.$ Show more plots

Corresponding record in: Inspire

Element opprettet 2024-05-09, sist endret 2024-12-05

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