[Paper Review] Charmed and light pseudoscalar meson decay constants from HISQ simulations

Alexei Bazavov, C. Bérnard+21 more|arXiv (Cornell University)|Nov 10, 2014

Particle physics theoretical and experimental studies27 references4 citations

TL;DR

This lattice QCD study computes the leptonic decay constants of charmed and light pseudoscalar mesons using unquenched HISQ fermions on MILC ensembles with four dynamical quarks. The authors report $f_{D^+} = 212.6(0.4)^{+1.0}_{-1.2}$ MeV and $f_{D_s} = 249.0(0.3)^{+1.1}_{-1.5}$ MeV, enabling precise determinations of CKM matrix elements and stringent tests of CKM unitarity.

ABSTRACT

We compute the leptonic decay constants $f_{D^+}$, $f_{D_s}$, and $f_{K^+}$, and the quark-mass ratios $m_c/m_s$ and $m_s/m_l$ in unquenched lattice QCD. We use the MILC highly improved staggered quark (HISQ) ensembles with four dynamical quark flavors. Our primary results are $f_{D^+} = 212.6(0.4)({}^{+1.0}_{-1.2})\ \mathrm{MeV}$, $f_{D_s} = 249.0(0.3)({}^{+1.1}_{-1.5})\ \mathrm{MeV}$, and $f_{D_s}/f_{D^+} = 1.1712(10)({}^{+29}_{-32})$, where the errors are statistical and total systematic, respectively. We also obtain $f_{K^+}/f_{π^+} = 1.1956(10)({}^{+26}_{-18})$, updating our previous result, and determine the quark-mass ratios $m_s/m_l = 27.35(5)({}^{+10}_{-7})$ and $m_c/m_s = 11.747(19)({}^{+59}_{-43})$. When combined with experimental measurements of the decay rates, our results lead to precise determinations of the CKM matrix elements $|V_{us}| = 0.22487(51) (29)(20)(5)$, $|V_{cd}|=0.217(1) (5)(1)$ and $|V_{cs}|= 1.010(5)(18)(6)$, where the errors are from this calculation of the decay constants, the uncertainty in the experimental decay rates, structure-dependent electromagnetic corrections, and, in the case of $|V_{us}|$, the uncertainty in $|V_{ud}|$, respectively.

Motivation & Objective

• To compute the leptonic decay constants $f_{D^+}$, $f_{D_s}$, and $f_{K^+}$ with high precision using unquenched lattice QCD.
• To determine the quark-mass ratios $m_c/m_s$ and $m_s/m_l$ from lattice simulations with four dynamical quark flavors.
• To improve the precision of CKM matrix element determinations $|V_{us}|$, $|V_{cd}|$, and $|V_{cs}|$ by combining lattice results with experimental decay rates.
• To test the unitarity of the first and second rows of the CKM matrix using updated decay constant and branching fraction inputs.
• To estimate and quantify systematic uncertainties, particularly from structure-dependent electromagnetic corrections in charm meson decays.

Proposed method

• Utilizes unquenched lattice QCD simulations with the MILC highly improved staggered quark (HISQ) action and a one-loop tadpole-improved Symanzik gauge action.
• Employs a large set of ensembles with four dynamical quark flavors ($n_f=2+1+1$) and four lattice spacings (0.15–0.06 fm) to control continuum extrapolation.
• Performs a physical-mass analysis using ensembles with valence quark masses tuned to physical values, avoiding chiral extrapolation.
• Applies chiral perturbation theory in a combined fit to physical and unphysical mass ensembles to reduce statistical errors on $f_{D^+}$ and $f_{D_s}$.
• Uses $f_{\pi^+} = 130.41$ MeV to set the lattice scale and determines the tuned light-quark mass via the physical $M_\pi^2/f_{\pi^+}^2$ ratio.
• Estimates systematic errors by comparing results from the physical-mass analysis and the chiral fit, particularly for $f_{D^+}$ and $f_{D_s}$.

Experimental results

Research questions

• RQ1 What are the precise values of the leptonic decay constants $f_{D^+}$, $f_{D_s}$, and $f_{K^+}$ from unquenched lattice QCD with four dynamical quarks?
• RQ2 How do the quark-mass ratios $m_c/m_s$ and $m_s/m_l$ compare to experimental and theoretical expectations?
• RQ3 What is the impact of improved decay constant precision on the determination of CKM matrix elements $|V_{us}|$, $|V_{cd}|$, and $|V_{cs}|$?
• RQ4 To what extent do the results support CKM matrix unitarity, and what tensions, if any, exist in the first and second rows?
• RQ5 How significant are the uncertainties from structure-dependent electromagnetic corrections in charm meson decays?

Key findings

• The study reports $f_{D^+} = 212.6(0.4)^{+1.0}_{-1.2}$ MeV, with statistical and total systematic errors.
• The value of $f_{D_s} = 249.0(0.3)^{+1.1}_{-1.5}$ MeV is obtained with high precision, and $f_{D_s}/f_{D^+} = 1.1712(10)^{+29}_{-32}$.
• The ratio $f_{K^+}/f_{\pi^+} = 1.1956(10)^{+26}_{-18}$ is updated and used to determine $|V_{us}|/|V_{ud}|$.
• The quark-mass ratios are determined as $m_s/m_l = 27.35(5)^{+10}_{-7}$ and $m_c/m_s = 11.747(19)^{+59}_{-43}$.
• The result $|V_{us}| = 0.22487(51)^{+29}_{-20}(5)_{V_{ud}}$ is consistent with CKM unitarity to within $0.026\%$.
• The values $|V_{cd}| = 0.217(1)^{+5}_{-1}$ and $|V_{cs}| = 1.010(5)^{+18}_{-6}$ show tensions with unitarity, though within current uncertainties.