arXiv subjects

C. Bernard

Publications and source records attributed to C. Bernard.

At least 19 recordsLinked to original sources

arXiv2021

Electromechanical properties of ferroelectric polymers: Finsler geometry modeling and a Monte Carlo study

Polyvinylidene difluoride (PVDF) is a ferroelectric polymer characterized by negative strain along the direction of the applied electric field. However, the electromechanical response mechanism of PVDF remains unclear due to the complexity of the hierarchical structure across the length scales. As described in this letter, we employ the Finsler geometry model as a new solution to the aforementioned problem and demonstrate that the deformations observed through Monte Carlo simulations on 3D tetrahedral lattices are nearly identical to those of real PVDF. Specifically, the simulated mechanical deformation and polarization are similar to those observed experimentally.

cond-mat.soft↗

arXiv2019

$B$- and $D$-meson leptonic decay constants from four-flavor lattice QCD

We calculate the leptonic decay constants of heavy-light pseudoscalar mesons with charm and bottom quarks in lattice quantum chromodynamics on four-flavor QCD gauge-field configurations with dynamical $u$, $d$, $s$, and $c$ quarks. We analyze over twenty isospin-symmetric ensembles with six lattice spacings down to $a\approx 0.03$~fm and several values of the light-quark mass down to the physical value $\frac{1}{2}(m_u+m_d)$. We employ the highly-improved staggered-quark (HISQ) action for the sea and valence quarks; on the finest lattice spacings, discretization errors are sufficiently small that we can calculate the $B$-meson decay constants with the HISQ action for the first time directly at the physical $b$-quark mass. We obtain the most precise determinations to-date of the $D$- and $B$-meson decay constants and their ratios, $f_{D^+} = 212.7(0.6)$~MeV, $f_{D_s} = 249.9(0.4)$~MeV, $f_{D_s}/f_{D^+} = 1.1749(16)$, $f_{B^+} = 189.4 (1.4)$~MeV, $f_{B_s} = 230.7(1.3)$~MeV, $f_{B_s}/f_{B^+} = 1.2180(47)$, where the errors include statistical and all systematic uncertainties. Our results for the $B$-meson decay constants are three times more precise than the previous best lattice-QCD calculations, and bring the QCD errors in the Standard-Model predictions for the rare leptonic decays $\overline{\mathcal{B}}(B_s \to μ^+μ^-) = 3.64(11) \times 10^{-9}$, $\overline{\mathcal{B}}(B^0 \to μ^+μ^-) = 1.00(3) \times 10^{-10}$, and $\overline{\mathcal{B}}(B^0 \to μ^+μ^-)/\overline{\mathcal{B}}(B_s \to μ^+μ^-) = 0.0273(9)$ to well below other sources of uncertainty. As a byproduct of our analysis, we also update our previously published results for the light-quark-mass ratios and the scale-setting quantities $f_{p4s}$, $M_{p4s}$, and $R_{p4s}$. We obtain the most precise lattice-QCD determination to date of the ratio $f_{K^+}/f_{π^+} = 1.1950(^{+16}_{-23})$~MeV.

hep-lat↗

arXiv2019

$|V_{us}|$ from $K_{\ell 3}$ decay and four-flavor lattice QCD

Using HISQ $N_f=2+1+1$ MILC ensembles with five different values of the lattice spacing, including four ensembles with physical quark masses, we have performed the most precise computation to date of the $K\toπ\ellν$ vector form factor at zero momentum transfer, $f_+^{K^0π^-}(0)=0.9696(15)_\text{stat}(12)_\text{syst}$. This is the first calculation that includes the dominant finite-volume effects, as calculated in chiral perturbation theory at next-to-leading order. Our result for the form factor provides a direct determination of the Cabibbo-Kobayashi-Maskawa matrix element $|V_{us}|=0.22333(44)_{f_+(0)}(42)_\text{exp}$, with a theory error that is, for the first time, at the same level as the experimental error. The uncertainty of the semileptonic determination is now similar to that from leptonic decays and the ratio $f_{K^+}/f_{π^+}$, which uses $|V_{ud}|$ as input. Our value of $|V_{us}|$ is in tension at the 2--$2.6σ$ level both with the determinations from leptonic decays and with the unitarity of the CKM matrix. In the test of CKM unitarity in the first row, the current limiting factor is the error in $|V_{ud}|$, although a recent determination of the nucleus-independent radiative corrections to superallowed nuclear $β$ decays could reduce the $|V_{ud}|^2$ uncertainty nearly to that of $|V_{us}|^2$. Alternative unitarity tests using only kaon decays, for which improvements in the theory and experimental inputs are likely in the next few years, reveal similar tensions. As part of our analysis, we calculated the correction to $f_+^{Kπ}(0)$ due to nonequilibrated topological charge at leading order in chiral perturbation theory, for both the full-QCD and the partially-quenched cases. We also obtain the combination of low-energy constants in the chiral effective Lagrangian $[C_{12}^r+C_{34}^r-(L_5^r)^2](M_ρ)=(2.92\pm0.31)\cdot10^{-6}$.

hep-lat↗

arXiv2019

Lattice computation of the electromagnetic contributions to kaon and pion masses

We present a lattice calculation of the electromagnetic (EM) effects on the masses of light pseudoscalar mesons. The simulations employ 2+1 dynamical flavors of asqtad QCD quarks, and quenched photons. Lattice spacings vary from $\approx 0.12$ fm to $\approx 0.045$ fm. We compute the quantity $ε$, which parameterizes the corrections to Dashen's theorem for the $K^+$-$K^0$ EM mass splitting, as well as $ε_{K^0}$, which parameterizes the EM contribution to the mass of the $K^0$ itself. An extension of the nonperturbative EM renormalization scheme introduced by the BMW group is used in separating EM effects from isospin-violating quark mass effects. We correct for leading finite-volume effects in our realization of lattice electrodynamics in chiral perturbation theory, and remaining finite-volume errors are relatively small. While electroquenched effects are under control for $ε$, they are estimated only qualitatively for $ε_{K^0}$, and constitute one of the largest sources of uncertainty for that quantity. We find $ε= 0.78(1)_{\rm stat}({}^{+\phantom{1}8}_{-11})_{\rm syst}$ and $ε_{K^0}=0.035(3)_{\rm stat}(20)_{\rm syst}$. We then use these results on 2+1+1 flavor pure QCD HISQ ensembles and find $m_u/m_d = 0.4529(48)_{\rm stat}( {}_{-\phantom{1}67}^{+150})_{\rm syst}$.

hep-lat↗

arXiv2019

$B_s\to K\ellν$ decay from lattice QCD

We use lattice QCD to calculate the form factors $f_+(q^2)$ and $f_0(q^2)$ for the semileptonic decay $B_s\to K\ellν$. Our calculation uses six MILC asqtad 2+1 flavor gauge-field ensembles with three lattice spacings. At the smallest and largest lattice spacing the light-quark sea mass is set to 1/10 the strange-quark mass. At the intermediate lattice spacing, we use four values for the light-quark sea mass ranging from 1/5 to 1/20 of the strange-quark mass. We use the asqtad improved staggered action for the light valence quarks, and the clover action with the Fermilab interpolation for the heavy valence bottom quark. We use SU(2) hard-kaon heavy-meson rooted staggered chiral perturbation theory to take the chiral-continuum limit. A functional $z$ expansion is used to extend the form factors to the full kinematic range. We present predictions for the differential decay rate for both $B_s\to Kμν$ and $B_s\to Kτν$. We also present results for the forward-backward asymmetry, the lepton polarization asymmetry, ratios of the scalar and vector form factors for the decays $B_s\to K\ellν$ and $B_s\to D_s \ellν$. Our results, together with future experimental measurements, can be used to determine the magnitude of the Cabibbo-Kobayashi-Maskawa matrix element $|V_{ub}|$.

hep-lat↗

arXiv2018

Up-, down-, strange-, charm-, and bottom-quark masses from four-flavor lattice QCD

We calculate the up-, down-, strange-, charm-, and bottom-quark masses using the MILC highly improved staggered-quark ensembles with four flavors of dynamical quarks. We use ensembles at six lattice spacings ranging from $a\approx0.15$~fm to $0.03$~fm and with both physical and unphysical values of the two light and the strange sea-quark masses. We use a new method based on heavy-quark effective theory (HQET) to extract quark masses from heavy-light pseudoscalar meson masses. Combining our analysis with our separate determination of ratios of light-quark masses we present masses of the up, down, strange, charm, and bottom quarks. Our results for the $\overline{\text{MS}}$-renormalized masses are $m_u(2~\text{GeV}) = 2.130(41)$~MeV, $m_d(2~\text{GeV}) = 4.675(56)$~MeV, $m_s(2~\text{GeV}) = 92.47(69)$~MeV, $m_c(3~\text{GeV}) = 983.7(5.6)$~MeV, and $m_c(m_c) = 1273(10)$~MeV, with four active flavors; and $m_b(m_b) = 4195(14)$~MeV with five active flavors. We also obtain ratios of quark masses $m_c/m_s = 11.783(25)$, $m_b/m_s = 53.94(12)$, and $m_b/m_c = 4.578(8)$. The result for $m_c$ matches the precision of the most precise calculation to date, and the other masses and all quoted ratios are the most precise to date. Moreover, these results are the first with a perturbative accuracy of $α_s^4$. As byproducts of our method, we obtain the matrix elements of HQET operators with dimension 4 and 5: $\overlineΛ_\text{MRS}=555(31)$~MeV in the minimal renormalon-subtracted (MRS) scheme, $μ_π^2 = 0.05(22)~\text{GeV}^2$, and $μ_G^2(m_b)=0.38(2)~\text{GeV}^2$. The MRS scheme [Phys. Rev. D97, 034503 (2018), arXiv:1712.04983 [hep-ph]] is the key new aspect of our method.

hep-lat↗

arXiv2018

B- and D-meson leptonic decay constants and quark masses from four-flavor lattice QCD

We describe a recent lattice-QCD calculation of the leptonic decay constants of heavy-light pseudoscalar mesons containing charm and bottom quarks and of the masses of the up, down, strange, charm, and bottom quarks. Results for these quantities are of the highest precision to date. Calculations use 24 isospin-symmetric ensembles of gauge-field configurations with six different lattice spacings as small as approximately 0.03 fm and several values of the light quark masses down to physical values of the average up- and down-sea-quark masses. We use the highly-improved staggered quark (HISQ) formulation for valence and sea quarks, including the bottom quark. The analysis employs heavy-quark effective theory (HQET). A novel HQET method is used in the determination of the quark masses.

hep-lat↗

arXiv2018

The STEREO Experiment

The STEREO experiment is a very short baseline reactor antineutrino experiment aiming at testing the hypothesis of light sterile neutrinos as an explanation of the deficit of the observed neutrino interaction rate with respect to the predicted rate, known as the Reactor Antineutrino Anomaly. The detector center is located 10 m away from the compact, highly $^{235}$U enriched core of the research nuclear reactor of the Institut Laue Langevin in Grenoble, France. This paper describes the STEREO site, the detector components and associated shielding designed to suppress the external sources of background which were characterized on site. It reports the performances in terms of detector response and energy reconstruction.

physics.ins-det↗

arXiv2018

Effects of non-equilibrated topological charge distributions on pseudoscalar meson masses and decay constants

We study the effects of failure to equilibrate the squared topological charge $Q^2$ on lattice calculations of pseudoscalar masses and decay constants. The analysis is based on chiral perturbation theory calculations of the dependence of these quantities on the QCD vacuum angle $θ$. For the light-light partially quenched case, we rederive the known chiral perturbation theory results of Aoki and Fukaya, but using the nonperturbatively-valid chiral theory worked out by Golterman, Sharpe and Singleton, and by Sharpe and Shoresh. We then extend these calculations to heavy-light mesons. Results when staggered taste-violations are important are also presented. The derived $Q^2$ dependence is compared to that of simulations using the MILC collaboration's ensembles of lattices with four flavors of HISQ dynamical quarks. We find agreement, albeit with large statistical errors. These results can be used to correct for the leading effects of unequilibrated $Q^2$, or to make estimates of the systematic error coming from the failure to equilibrate $Q^2$. In an appendix, we show that the partially quenched chiral theory may be extended beyond a lower bound on valence masses discovered by Sharpe and Shoresh. Subtleties occurring when a sea-quark mass vanishes are discussed in another appendix.

hep-lat↗

arXiv2018

Short-distance matrix elements for $D^0$-meson mixing for $N_f=2+1$ lattice QCD

We calculate in three-flavor lattice QCD the short-distance hadronic matrix elements of all five $ΔC=2$ four-fermion operators that contribute to neutral $D$-meson mixing both in and beyond the Standard Model. We use the MILC Collaboration's $N_f = 2+1$ lattice gauge-field configurations generated with asqtad-improved staggered sea quarks. We also employ the asqtad action for the valence light quarks and use the clover action with the Fermilab interpretation for the charm quark. We analyze a large set of ensembles with pions as light as $M_π\approx 180$ MeV and lattice spacings as fine as $a\approx 0.045$ fm, thereby enabling good control over the extrapolation to the physical pion mass and continuum limit. We obtain for the matrix elements in the $\overline{\text{MS}}$-NDR scheme using the choice of evanescent operators proposed by Beneke \emph{et al.}, evaluated at 3 GeV, $\langle D^0|\mathcal{O}_i|\bar{D}^0 \rangle = \{0.0805(55)(16), -0.1561(70)(31), 0.0464(31)(9), 0.2747(129)(55), 0.1035(71)(21)\}~\text{GeV}^4$ ($i=1$--5). The errors shown are from statistics and lattice systematics, and the omission of charmed sea quarks, respectively. To illustrate the utility of our matrix-element results, we place bounds on the scale of CP-violating new physics in $D^0$~mixing, finding lower limits of about 10--50$\times 10^3$ TeV for couplings of $\mathrm{O}(1)$. To enable our results to be employed in more sophisticated or model-specific phenomenological studies, we provide the correlations among our matrix-element results. For convenience, we also present numerical results in the other commonly-used scheme of Buras, Misiak, and Urban.

hep-lat↗

arXiv2017

$B_s \to K \ellν$ form factors with 2+1 flavors

Using the MILC 2+1 flavor asqtad quark action ensembles, we are calculating the form factors $f_0$ and $f_+$ for the semileptonic $B_s \rightarrow K \ellν$ decay. A total of six ensembles with lattice spacing from $\approx0.12$ to 0.06 fm are being used. At the coarsest and finest lattice spacings, the light quark mass $m'_l$ is one-tenth the strange quark mass $m'_s$. At the intermediate lattice spacing, the ratio $m'_l/m'_s$ ranges from 0.05 to 0.2. The valence $b$ quark is treated using the Sheikholeslami-Wohlert Wilson-clover action with the Fermilab interpretation. The other valence quarks use the asqtad action. When combined with (future) measurements from the LHCb and Belle II experiments, these calculations will provide an alternate determination of the CKM matrix element $|V_{ub}|$.

hep-lat↗

arXiv2017

Semileptonic $B$-meson decays to light pseudoscalar mesons on the HISQ ensembles

We report the status of an ongoing lattice-QCD calculation of form factors for exclusive semileptonic decays of $B$ mesons with both charged currents ($B\toπ\ellν$, $B_s\to K\ellν$) and neutral currents ($B\toπ\ell^+\ell^-$, $B\to K\ell^+\ell^-$). The results are important for constraining or revealing physics beyond the Standard Model. This work uses MILC's (2+1+1)-flavor ensembles with the HISQ action for the sea and light valence quarks and the clover action in the Fermilab interpretation for the $b$ quark. Simulations are carried out at three lattice spacings down to $0.088$ fm, with both physical and unphysical sea-quark masses. We present preliminary results for correlation-function fits.

hep-lat↗

arXiv2016

Decay constants $f_B$ and $f_{B_s}$ and quark masses $m_b$ and $m_c$ from HISQ simulations

We present a progress report on our calculation of the decay constants $f_B$ and $f_{B_s}$ from lattice-QCD simulations with highly-improved staggered quarks. Simulations are carried out with several heavy valence-quark masses on $(2+1+1)$-flavor ensembles that include charm sea quarks. We include data at six lattice spacings and several light sea-quark masses, including an approximately physical-mass ensemble at all but the smallest lattice spacing, 0.03 fm. This range of parameters provides excellent control of the continuum extrapolation to zero lattice spacing and of heavy-quark discretization errors. Finally, using the heavy-quark effective theory expansion we present a method of extracting from the same correlation functions the charm- and bottom-quark masses as well as some low-energy constants appearing in the heavy-quark expansion.

hep-lat↗

arXiv2016

Kaon semileptonic decays with $N_f=2+1+1$ HISQ fermions and physical light-quark masses

We discuss the reduction of errors in the calculation of the form factor $f_+^{K π}(0)$ with HISQ fermions on the $N_f=2+1+1$ MILC configurations from increased statistics on some key ensembles, new data on ensembles with lattice spacings down to 0.042 fm and the study of finite-volume effects within staggered ChPT. We also study the implications for the unitarity of the CKM matrix in the first row and for current tensions with leptonic determinations of $\vert V_{us}\vert$.

hep-lat↗

arXiv2016

Fermi arcs and their topological character in the candidate type-II Weyl semimetal MoTe2

We report a combined experimental and theoretical study of the candidate type-II Weyl semimetal MoTe2. Using laser-based angle-resolved photoemission we resolve multiple distinct Fermi arcs on the inequivalent top and bottom (001) surfaces. All surface states observed experimentally are reproduced by an electronic structure calculation for the experimental crystal structure that predicts a topological Weyl semimetal state with 8 type-II Weyl points. We further use systematic electronic structure calculations simulating different Weyl point arrangements to discuss the robustness of the identified Weyl semimetal state and the topological character of Fermi arcs in MoTe2.

cond-mat.mtrl-sci↗

arXiv2016

Review of lattice results concerning low-energy particle physics

We review lattice results related to pion, kaon, D- and B-meson physics with the aim of making them easily accessible to the particle physics community. More specifically, we report on the determination of the light-quark masses, the form factor f+(0), arising in the semileptonic K -> pi transition at zero momentum transfer, as well as the decay constant ratio fK/fpi and its consequences for the CKM matrix elements Vus and Vud. Furthermore, we describe the results obtained on the lattice for some of the low-energy constants of SU(2)LxSU(2)R and SU(3)LxSU(3)R Chiral Perturbation Theory. We review the determination of the BK parameter of neutral kaon mixing as well as the additional four B parameters that arise in theories of physics beyond the Standard Model. The latter quantities are an addition compared to the previous review. For the heavy-quark sector, we provide results for mc and mb (also new compared to the previous review), as well as those for D- and B-meson decay constants, form factors, and mixing parameters. These are the heavy-quark quantities most relevant for the determination of CKM matrix elements and the global CKM unitarity-triangle fit. Finally, we review the status of lattice determinations of the strong coupling constant alpha_s.

hep-lat↗

arXiv2016

Electromagnetic effects on the light pseudoscalar mesons and determination of $m_u/m_d$

The MILC Collaboration has completed production running of electromagnetic effects on light mesons using asqtad improved staggered quarks. In these calculations, we use quenched photons in the noncompact formalism. We study four lattice spacings from $\approx\!0.12\:$fm to $\approx\!0.045\:$fm. To study finite-volume effects, we used six spatial lattice sizes $L/a=12$, 16, 20, 28, 40, and 48, at $a\!\approx\!0.12\:$fm. We update our preliminary values for the correction to Dashen's theorem ($ε$) and the quark-mass ratio $m_u/m_d$.

hep-lat↗

arXiv2016

Gradient flow and scale setting on MILC HISQ ensembles

We report on a scale determination with gradient-flow techniques on the $N_f=2+1+1$ highly improved staggered quark ensembles generated by the MILC Collaboration. The ensembles include four lattice spacings, ranging from approximately 0.15 to 0.06 fm, and both physical and unphysical values of the quark masses. The scales $\sqrt{t_0}/a$ and $w_0/a$ and their tree-level improvements, $\sqrt{t_{0,{\rm imp}}}$ and $w_{0,{\rm imp}}$, are computed on each ensemble using Symanzik flow and the cloverleaf definition of the energy density $E$. Using a combination of continuum chiral-perturbation theory and a Taylor-series ansatz for the lattice-spacing and strong-coupling dependence, the results are simultaneously extrapolated to the continuum and interpolated to physical quark masses. We determine the scales $\sqrt{t_0} = 0.1416({}_{-5}^{+8})$ fm and $w_0 = 0.1714({}_{-12}^{+15})$ fm, where the errors are sums, in quadrature, of statistical and all systematic errors. The precision of $w_0$ and $\sqrt{t_0}$ is comparable to or more precise than the best previous estimates, respectively. We then find the continuum mass dependence of $\sqrt{t_0}$ and $w_0$, which will be useful for estimating the scales of new ensembles. We also estimate the integrated autocorrelation length of $\langle E(t) \rangle$. For long flow times, the autocorrelation length of $\langle E \rangle$ appears to be comparable to that of the topological charge.

hep-lat↗