Thu·Aug 26, 2021Thursday·August 26, 2021

1. 01*

   Form factors for the processes $B_c^{+}\to D^0{\ell }^{+}{\nu }_{\ell }$ and $B_c^{+}\to D_s^{+}{\ell }^{+}{\ell }^{-}(\nu \overline{\nu })$ from lattice QCD

   Laurence J. Cooper🇬🇧 · Christine T. H. Davies🇬🇧 · Matthew Wingate🇬🇧

   We present results of the first lattice QCD calculations of the weak matrix elements for the decays $B_c^{+}\to D^0{\ell }^{+}{\nu }_{\ell }$, $B_c^{+}\to D_s^{+}{\ell }^{+}{\ell }^{-}$ and $B_c^{+}\to D_s^{+}\nu \overline{\nu }$. Form factors across the entire physical $q^2$ range are then extracted and extrapolated to the continuum limit with physical quark masses. Results are derived from correlation functions computed on MILC Collaboration gauge configurations with three different lattice spacings and including 2+1+1 flavours of sea quarks in the Highly Improved Staggered Quark (HISQ) formalism. HISQ is also used for all of the valence quarks. The uncertainty on the decay widths from our form factors is similar in size to that from the present value for $V_{ub}$. We obtain the ratio $\Gamma (B_c^{+}\to D^0{\mu }^{+}{\nu }_{\mu })/{\left|{\eta }_{\mathrm{EW}}{V}_{ub}\right|}^2=4.43(63)\times 10^{12}{\mathrm{s}}^{-1}$. Combining our form factors with those found previously by HPQCD for $B_c^{+}\to J/\psi {\mu }^{+}{\nu }_{\mu }$, we find ${\left|V_{cb}/V_{ub}\right|}^2\Gamma (B_c^{+}\to D^0{\mu }^{+}{\nu }_{\mu })/\Gamma (B_c^{+}\to J/\psi {\mu }^{+}{\nu }_{\mu })=0.257(36{)}_{B_c\to D}(18{)}_{B_c\to J/\psi }$. We calculate the differential decay widths of $B_c^{+}\to D_s^{+}{\ell }^{+}{\ell }^{-}$ across the full $q^2$ range, and give integrated results in $q^2$ bins that avoid possible effects from charmonium and $u\overline{u}$ resonances. For example, we find that the ratio of differential branching fractions integrated over the range $q^2=1{\mathrm{GeV}}^2-6{\mathrm{GeV}}^2$ for $B_c^{+}\to D_s^{+}{\mu }^{+}{\mu }^{-}$ and $B_c^{+}\to J/\psi {\mu }^{+}{\nu }_{\mu }$ is $5.23(73{)}_{B_c\to D_s}(54{)}_{B_c\to J/\psi }\times 10^{-6}$. We also give results for the branching fraction of $B_c^{+}\to D_s^{+}\nu \overline{\nu }$. Prospects for reducing our errors in the future are discussed.

   hep-lathep-phPRD(2022)·26 citations
2. 02*

   A Multilevel Approach to Variance Reduction in the Stochastic Estimation of the Trace of a Matrix

   Andreas Frommer🇩🇪 · Mostafa Nasr Khalil🇩🇪 · Gustavo Ramirez-Hidalgo🇩🇪

   The trace of a matrix function f(A), most notably of the matrix inverse, can be estimated stochastically using samples< x,f(A)x> if the components of the random vectors x obey an appropriate probability distribution. However such a Monte-Carlo sampling suffers from the fact that the accuracy depends quadratically of the samples to use, thus making higher precision estimation very costly. In this paper we suggest and investigate a multilevel Monte-Carlo approach which uses a multigrid hierarchy to stochastically estimate the trace. This results in a substantial reduction of the variance, so that higher precision can be obtained at much less effort. We illustrate this for the trace of the inverse using three different classes of matrices.

   ↳ math.NAcs.NAhep-latSIAM J.Sci.Comput.(2022)·15 citations

* Reconstructed cohort: no mailing for this day survives in the archive. Papers are grouped by their submission times and arXiv's announcement cut-off, assuming announcement without delay; positions follow identifier order. Validated at ~91% exact-day agreement against the archived era.