B- and D-meson decay constants from three-flavor lattice QCD (1112.3051v1)

Abstract: We calculate the leptonic decay constants of B_{(s)} and D_{(s)} mesons in lattice QCD using staggered light quarks and Fermilab bottom and charm quarks. We compute the heavy-light meson correlation functions on the MILC asqtad-improved staggered gauge configurations which include the effects of three light dynamical sea quarks. We simulate with several values of the light valence- and sea-quark masses (down to ~m_s/10) and at three lattice spacings (a ~ 0.15, 0.12, and 0.09 fm) and extrapolate to the physical up and down quark masses and the continuum using expressions derived in heavy-light meson staggered chiral perturbation theory. We renormalize the heavy-light axial current using a mostly nonperturbative method such that only a small correction to unity must be computed in lattice perturbation theory and higher-order terms are expected to be small. We obtain f_{B^+} = 196.9(8.9) MeV, f_{B_s} = 242.0(9.5) MeV, f_{D^+} = 218.9(11.3) MeV, f_{D_s} = 260.1(10.8) MeV, and the SU(3) flavor-breaking ratios f_{B_s}/f_{B} = 1.229(26) and f_{D_s}/f_{D} = 1.188(25), where the numbers in parentheses are the total statistical and systematic uncertainties added in quadrature.

An Analysis of $B$- and $D$-Meson Decay Constants from Three-Flavor Lattice QCD

This paper presents a detailed investigation into calculating the leptonic decay constants of $B_{(s)}$ and $D_{(s)}$ mesons using three-flavor lattice Quantum Chromodynamics (QCD). The research employs staggered light quarks paired with Fermilab’s approach for bottom and charm quarks, leveraging the MILC Collaboration’s asqtad-improved staggered gauge configurations. These configurations take into account three light dynamical sea quarks, an essential component for achieving accurate simulations within the QCD framework.

Key Methodology

The paper outlines the computation of heavy-light meson correlation functions on MILC configurations, covering a range of valence- and sea-quark masses—down to approximately $m_s/10$—and lattice spacings of approximately 0.15, 0.12, and 0.09 fm. The results are extrapolated to the physical quark masses and the continuum limit using heavy-light meson staggered chiral perturbation theory (HMS$\chi$PT).

Lattice QCD techniques rely heavily on the renormalization of the heavy-light axial current. The researchers utilize a mostly nonperturbative method, ensuring that only a minimal correction requires computation in lattice perturbation theory, thereby minimizing higher-order term contributions. Systematic uncertainties are meticulously calculated and considered via a comprehensive chiral-continuum extrapolation approach, integrating Bayesian methods to handle lattice-spacing-dependent corrections and potential heavy-quark discretization errors systematically.

Numerical Results and Implications

The paper presents the extracted decay constants for the charged $B$ and $D$ mesons, with $f_{B^+} = 196.9(8.9)$ MeV and $f_{D^+} = 218.9(11.3)$ MeV, and for the $B_s$ and $D_s$ mesons, obtaining $f_{B_s} = 242.0(9.5)$ MeV and $f_{D_s} = 260.1(10.8)$ MeV. The flavor breaking ratios $f_{B_s}/f_{B} = 1.229(26)$ and $f_{D_s}/f_{D} = 1.188(25)$ further illustrate the effect of flavor symmetry breaking in these systems. These results are presented with the total combined statistical and systematic uncertainties, encompassing aspects such as scale determination, perturbative corrections, finite-volume effects, and discretization errors.

Theoretical and Practical Insights

The determinations of the decay constants presented represent a vital input for precision tests of the Standard Model through their role in extracting the Cabibbo-Kobayashi-Maskawa (CKM) matrix elements from experimental decay data. The sensitivity of these calculations to potential new physics is underscored by the current tensions observed in the CKM unitarity triangle, where even slight deviations from Standard Model predictions provide scenarios where new physics may manifest.

The methodology highlights areas where future improvements can have a significant impact, emphasizing the necessity for enhanced statistics, finer lattice spacings, and potentially improved actions like the Highly Improved Staggered Quark (HISQ) action for charm quarks. The ongoing advancements in computational resources and methods are likely to mitigate the current leading uncertainties, thereby enhancing the precision of future determinations.

Conclusion

This paper robustly contributes to understanding heavy meson decay constants in lattice QCD, offering a comprehensive approach that carefully addresses the multifaceted challenges inherent in such calculations. The research paves the way for future enhancements that could further delimit our knowledge of fundamental interactions, supporting ongoing and forthcoming precision tests of the Standard Model, and exploring avenues for discovering new phenomena in flavor physics.