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We calculate the form factors for the $B \to D^*\ell\nu_\ell$ decay in 2+1 flavor lattice QCD. For all quark flavors, we employ the M\"obius domain-wall action, which preserves chiral symmetry to a good precision. Our gauge ensembles are generated at three lattice cutoffs $a^{-1} \sim 2.5$, 3.6 and 4.5 GeV with pion masses as low as $M_\pi \sim 230$ MeV. The physical lattice size $L$ satisfies the condition $M_\pi L \geq 4$ to control finite volume effects (FVEs), while we simulate a smaller size at the smallest $M_\pi$ to directly examine FVEs. The bottom quark masses are chosen in a range from the physical charm quark mass to $0.7 a^{-1}$ to control discretization effects. We extrapolate the form factors to the continuum limit and physical quark masses based on heavy meson chiral perturbation theory at next-to-leading order. Then the recoil parameter dependence is parametrized using a model independent form leading to our estimate of the decay rate ratio between the tau ($\ell = \tau$) and light lepton ($\ell = e,\mu$) channels $R(D^*) = 0.252(22)$ in the Standard Model. A simultaneous fit with recent data from the Belle experiment yields $|V_{cb}| = 39.19(91)\times 10^{-3}$, which is consistent with previous exclusive determinations, and shows good consistency in the kinematical distribution of the differential decay rate between the lattice and experimental data., Comment: 45 pages, 19 figures; v2: version published in PRD

The $\beta$ decays of the ground state (gs) and isomeric state (m) of $^{96}$Y have been studied with the total absorption $\gamma$-ray spectroscopy technique at the Ion Guide Isotope Separator On-Line facility. The separation of the 8$^{+}$ isomeric state from the 0$^{-}$ ground state was achieved thanks to the purification capabilities of the JYFLTRAP double Penning trap system. The $\beta$-intensity distributions of both decays have been independently determined. In the analyses the de-excitation of the 1581.6 keV level in $^{96}$Zr, in which conversion electron emission competes with pair production, has been carefully considered and found to have significant impact on the $\beta$-detector efficiency, influencing the $\beta$-intensity distribution obtained. Our results for $^{96\text{gs}}$Y (0$^+$) confirm the large ground state to ground state $\beta$-intensity probability, although a slightly larger value than reported in previous studies was obtained, amounting to $96.6_{-2.1}^{+0.3}\%$ of the total $\beta$ intensity. Given that the decay of $^{96\text{gs}}$Y is the second most important contributor to the reactor antineutrino spectrum between 5 and 7 MeV, the impact of the present results on reactor antineutrino summation calculations has been evaluated. In the decay of $^{96\text{m}}$Y (8$^{+}$), previously undetected $\beta$ intensity in transitions to states above 6 MeV has been observed. This shows the importance of total absorption $\gamma$-ray spectroscopy measurements of $\beta$ decays with highly fragmented de-excitation patterns. $^{96\text{m}}$Y (8$^{+}$) is a major contributor to reactor decay heat in uranium-plutonium and thorium-uranium fuels around 10 s after fission pulses, and the newly measured average $\beta$ and $\gamma$ energies differ significantly from the previous values in evaluated databases (...)

The precision of lattice QCD calculations has been steadily improving for some time and is now approaching, or has surpassed, the 1% level for multiple quantities. At this level QED effects, i.e. the fact that quarks carry electric as well as color charge, come into play. In this report we will summarise results from the first lattice QCD+QED computations of the properties of ground-state charmonium and bottomonium mesons by the HPQCD Collaboration., Comment: Contribution to the proceedings of the 19th International Conference on Hadron Spectroscopy and Structure (HADRON 2021). Accepted for publication in Suplemento de la Revista Mexicana de F\'isica

We calculate the $B \to D^{(*)} \ell \nu$ form factors in 2+1 flavor relativistic lattice QCD by employing the M\"obius domain-wall action for all quark flavors. Our simulations are carried out at lattice cut-offs $a^{-1} \sim 2.5$, 3.6 and 4.5 GeV with the bottom quark masses up to 0.7 $a^{-1}$ to control discretization effects. We extrapolate the form factors to the continuum limit and physical quark masses, and discuss systematic uncertainties of the form factors., Comment: 9 pages, 4 figures, talk presented at the 38th International Symposium on Lattice Field Theory (LATTICE2021), 26th-30th July, 2021, Zoom/Gather@MIT, USA

As tests of QCD in the bottomonium system, we give the most accurate results to date for the ground-state hyperfine splitting and the $\Upsilon$ leptonic width from full lattice QCD. These quantities are both accurately known from experiment, so can provide a good test of $b$ physics, but previous lattice results have been rather imprecise. We also test the impact on these quantities of the $b$ quark's electric charge. Our results are: $M_{\Upsilon}-M_{\eta_b} = $ 57.5(2.3)(1.0) MeV (where the second uncertainty comes from neglect of quark-line disconnected correlation functions) and decay constants, $f_{\eta_b} =$ 724(12) MeV and $f_{\Upsilon} =$ 677.2(9.7) MeV, giving $\Gamma(\Upsilon \rightarrow e^+e^-) =$ 1.292(37)(3) keV. We also give a new determination of the ratio of the masses for $b$ and $c$ quarks that is completely nonperturbative in lattice QCD and includes the calculation of QED effects for the first time. This gives a result for the $b$ quark mass of $\overline{m}_b(\overline{m}_b,n_f=5) =$ 4.202(21) GeV., Comment: 6 pages, The 38th International Symposium on Lattice Field Theory, LATTICE2021 26th-30th July, 2021 Zoom/Gather@Massachusetts Institute of Technology

Semileptonic $D \to{}K \ell \nu$ decays provide one angle of attack to get at the CKM matrix element $V_{cs}$, complementary to the study of leptonic $D_s$ decays. Here, HPQCD present the results of a recently published, improved determination of $V_{cs}$. We discuss a new, precise determination of $D\to K$ scalar and vector form factors from a lattice calculation on eight different $N_f=2+1+1$ MILC gluon field ensembles using the HISQ action, including three with physical light quark masses. When combined with experimental results, we are able to extract $|V_{cs}|=0.9663(80)$ to a sub percent level of precision for the first time. This is achieved using three different methods, which each combine our form factors with different sets of experimental results in different ways, with the results in very good agreement. Our primary method is to use $q^2$-binned data for the differential decay rate, but we also calculate $V_{cs}$ from the total branching fraction and from the value $|V_{cs}|f_+(0)$, which is also quoted by some experiments., Comment: 9 pages, 7 figures. Proceedings of the 38th International Symposium on Lattice Field Theory - LATTICE2021

We provide a 0.8\%-accurate determination of $V_{cs}$ from combining experimental results for the differential rate of $D \rightarrow K$ semileptonic decays with precise form factors that we determine from lattice QCD. This is the first time that $V_{cs}$ has been determined with an accuracy that allows its difference from 1 to be seen. Our lattice QCD calculation uses the Highly Improved Staggered Quark (HISQ) action for all valence quarks on gluon field configurations generated by the MILC collaboration that include the effect of $u$, $d$, $s$ and $c$ HISQ quarks in the sea. We use eight gluon field ensembles with five values of the lattice spacing ranging from 0.15 fm to 0.045 fm and include results with physical $u/d$ quarks for the first time. Our calculated form factors cover the full $q^2$ range of the physical decay process and enable a Standard Model test of the shape of the differential decay rate as well as the determination of $V_{cs}$ from a correlated weighted average over $q^2$ bins. We obtain $|V_{cs}|= 0.9663(53)_{\text{latt}}(39)_{\text{exp}}(19)_{\eta_{EW}}(40)_{\text{EM}}$, where the uncertainties come from lattice QCD, experiment, short-distance electroweak and electromagnetic corrections, respectively. This last uncertainty, neglected for $D \rightarrow K \ell \nu$ hitherto, now needs attention if the uncertainty on $V_{cs}$ is to be reduced further. We also determine $V_{cs}$ values in good agreement using the measured total branching fraction and the rates extrapolated to $q^2=0$. Our form factors enable tests of lepton flavour universality violation. We find the ratio of branching fractions for $D^0 \rightarrow K^-$ with $\mu$ and $e$ in the final state to be $R_{\mu/e}=0.9779(2)_{\text{latt}}(50)_{\mathrm{EM}}$ in the Standard Model, with the uncertainty dominated by that from electromagnetic corrections., Comment: 27 pages, 28 figures. Small changes to text to improve readability. Updated to include the BES average for the D to K branching fraction from 2104.08081

We extend HPQCD's earlier $n_f=4$ lattice-QCD analysis of the ratio of $\overline{\mathrm{MSB}}$ masses of the $b$ and $c$ quark to include results from finer lattices (down to 0.03fm) and a new calculation of QED contributions to the mass ratio. We find that $\overline{m}_b(\mu)/\overline{m}_c(\mu)=4.586(12)$ at renormalization scale $\mu=3$\,GeV. This result is nonperturbative. Combining it with HPQCD's recent lattice QCD$+$QED determination of $\overline{m}_c(3\mathrm{GeV})$ gives a new value for the $b$-quark mass: $\overline{m}_b(3\mathrm{GeV}) = 4.513(26)$GeV. The $b$-mass corresponds to $\overline{m}_b(\overline{m}_b, n_f=5) = 4.202(21)$GeV. These results are the first based on simulations that include QED., Comment: 8 pages, 4 figures

We calculate the mass difference between the $\Upsilon$ and $\eta_b$ and the $\Upsilon$ leptonic width from lattice QCD using the Highly Improved Staggered Quark formalism for the $b$ quark and including $u$, $d$, $s$ and $c$ quarks in the sea. We have results for lattices with lattice spacing as low as 0.03 fm and multiple heavy quark masses, enabling us to map out the heavy quark mass dependence and determine values at the $b$ quark mass. Our results are: $M_{\Upsilon} -M_{\eta_b} = 57.5(2.3)(1.0) \,\mathrm{MeV}$ (where the second uncertainty comes from neglect of quark-line disconnected correlation functions) and decay constants, $f_{\eta_b}=724(12)$ MeV and $f_{\Upsilon} =677.2(9.7)$ MeV, giving $\Gamma(\Upsilon \rightarrow e^+e^-) = 1.292(37)(3) \,\mathrm{keV}$. The hyperfine splitting and leptonic width are both in good agreement with experiment, and provide the most accurate lattice QCD results to date for these quantities by some margin. At the same time results for the time moments of the vector-vector correlation function can be compared to values for the $b$ quark contribution to $\sigma(e^+e^- \rightarrow \mathrm{hadrons})$ determined from experiment. Moments 4--10 provide a 2\% test of QCD and yield a $b$ quark contribution to the anomalous magnetic moment of the muon of 0.300(15)$\times 10^{-10}$. Our results, covering a range of heavy quark masses, may also be useful to constrain QCD-like composite theories for beyond the Standard Model physics., Comment: 16 pages, 9 figures Version accepted by PRD: Appendix with tables of fit parameters that allow the dependence on heavy quark mass of the hyperfine splitting and decay constants to be reconstructed added

We review the present status of the Standard Model calculation of the anomalous magnetic moment of the muon. This is performed in a perturbative expansion in the fine-structure constant $\alpha$ and is broken down into pure QED, electroweak, and hadronic contributions. The pure QED contribution is by far the largest and has been evaluated up to and including $\mathcal{O}(\alpha^5)$ with negligible numerical uncertainty. The electroweak contribution is suppressed by $(m_\mu/M_W)^2$ and only shows up at the level of the seventh significant digit. It has been evaluated up to two loops and is known to better than one percent. Hadronic contributions are the most difficult to calculate and are responsible for almost all of the theoretical uncertainty. The leading hadronic contribution appears at $\mathcal{O}(\alpha^2)$ and is due to hadronic vacuum polarization, whereas at $\mathcal{O}(\alpha^3)$ the hadronic light-by-light scattering contribution appears. Given the low characteristic scale of this observable, these contributions have to be calculated with nonperturbative methods, in particular, dispersion relations and the lattice approach to QCD. The largest part of this review is dedicated to a detailed account of recent efforts to improve the calculation of these two contributions with either a data-driven, dispersive approach, or a first-principle, lattice-QCD approach. The final result reads $a_\mu^\text{SM}=116\,591\,810(43)\times 10^{-11}$ and is smaller than the Brookhaven measurement by 3.7$\sigma$. The experimental uncertainty will soon be reduced by up to a factor four by the new experiment currently running at Fermilab, and also by the future J-PARC experiment. This and the prospects to further reduce the theoretical uncertainty in the near future-which are also discussed here-make this quantity one of the most promising places to look for evidence of new physics., Comment: 196 pages, 103 figures, version published in Phys. Rept., bib files for the citation references are available from: https://muon-gm2-theory.illinois.edu

In $\beta$-decay studies the determination of the decay probability to the ground state of the daughter nucleus often suffers from large systematic errors. The difficulty of the measurement is related to the absence of associated delayed $\gamma$-ray emission. In this work we revisit the $4\pi\gamma-\beta$ method proposed by Greenwood and collaborators in the 1990s, which has the potential to overcome some of the experimental difficulties. Our interest is driven by the need to determine accurately the $\beta$-intensity distributions of fission products that contribute significantly to the reactor decay heat and to the antineutrinos emitted by reactors. A number of such decays have large ground state branches. The method is relevant for nuclear structure studies as well. Pertinent formulae are revised and extended to the special case of $\beta$-delayed neutron emitters, and the robustness of the method is demonstrated with synthetic data. We apply it to a number of measured decays that serve as test cases and discuss the features of the method. Finally, we obtain ground state feeding intensities with reduced uncertainty for four relevant decays that will allow future improvements in antineutrino spectrum and decay heat calculations using the summation method.

We have performed the first $n_f = 2+1+1$ lattice QCD computations of the properties (masses and decay constants) of ground-state charmonium mesons. Our calculation uses the HISQ action to generate quark-line connected two-point correlation functions on MILC gluon field configurations that include $u/d$ quark masses going down to the physical point, tuning the $c$ quark mass from $M_{J/\psi}$ and including the effect of the $c$ quark's electric charge through quenched QED. We obtain $M_{J/\psi}-M_{\eta_c}$ (connected) = 120.3(1.1) MeV and interpret the difference with experiment as the impact on $M_{\eta_c}$ of its decay to gluons, missing from the lattice calculation. This allows us to determine $\Delta M_{\eta_c}^{\mathrm{annihiln}}$ =+7.3(1.2) MeV, giving its value for the first time. Our result of $f_{J/\psi}=$ 0.4104(17) GeV, gives $\Gamma(J/\psi \rightarrow e^+e^-)$=5.637(49) keV, in agreement with, but now more accurate than experiment. At the same time we have improved the determination of the $c$ quark mass, including the impact of quenched QED to give $\overline{m}_c(3\,\mathrm{GeV})$ = 0.9841(51) GeV. We have also used the time-moments of the vector charmonium current-current correlators to improve the lattice QCD result for the $c$ quark HVP contribution to the anomalous magnetic moment of the muon. We obtain $a_{\mu}^c = 14.638(47) \times 10^{-10}$, which is 2.5$\sigma$ higher than the value derived using moments extracted from some sets of experimental data on $R(e^+e^- \rightarrow \mathrm{hadrons})$. This value for $a_{\mu}^c$ includes our determination of the effect of QED on this quantity, $\delta a_{\mu}^c = 0.0313(28) \times 10^{-10}$., Comment: Added extra discussion on QED setup, some new results to study the effects of strong isospin breaking in the sea (including new Fig. 1) and a fit stability plot for the hyperfine splitting (new Fig. 7). Version accepted for publication in PRD

We analyze the inclusive semileptonic $B \to X_c \ell\nu$ structure functions in 2+1-flavor lattice QCD. The M\"obius domain-wall fermion action is used for light, strange, charm and bottom quarks. The structure function receives contributions from various exclusive modes, including the dominant S-wave states $D^{(*)}_s$ as well as the P-wave states $D_s^{**}$. We can identify them in the lattice data, from which we put some constraints on the $B_s \to D_s^{**}\ell\nu$ form factors., Comment: 7 pages, 3 figures, talk presented at the 37th International Symposium on Lattice Field Theory (Lattice2019), 16-22 June 2019, Wuhan, China

We report on our calculation of the B \to D^(*) \ell \nu form factors in 2+1 flavor lattice QCD. The M\"obius domain-wall action is employed for light, strange, charm and bottom quarks. At lattice cutoffs 1/a \sim 2.4, 3.6 and 4.5 GeV, we simulate bottom quark masses up to 0.7/a to control discretization errors. The pion mass is as low as 230 MeV. We extrapolate the form factors to the continuum limit and physical quark masses, and make a comparison with recent phenomenological analyses., Comment: 7 pages, 4 figures, talk presented at the 37th International Symposium on Lattice Field Theory (Lattice2019), 16-22 June 2019, Wuhan, China

The decays of the $\beta$-delayed neutron emitters $^{137}$I and $^{95}$Rb have been studied with the total absorption $\gamma$-ray spectroscopy technique. The purity of the beams provided by the JYFLTRAP Penning trap at the ion guide isotope separator on-line facility in Jyv\"askyl\"a allowed us to carry out a campaign of isotopically pure measurements with the decay total absorption $\gamma$-ray spectrometer, a segmented detector composed of eighteen NaI(Tl) modules. The contamination coming from the interaction of neutrons with the spectrometer has been carefully studied, and we have tested the use of time differences between prompt $\gamma$-rays and delayed neutron interactions to eliminate this source of contamination. Due to the sensitivity of our spectrometer, we have found a significant amount of $\beta$-intensity to states above the neutron separation energy that de-excite by $\gamma$-rays, comparable to the neutron emission probability. The competition between $\gamma$ de-excitation and neutron emission has been compared with Hauser-Feshbach calculations, and it can be understood as a nuclear structure effect. In addition, we have studied the impact of the $\beta$-intensity distributions determined in this work on reactor decay heat and reactor antineutrino spectrum summation calculations. The robustness of our results is demonstrated by a thorough study of uncertainties, and with the reproduction of the spectra of the individual modules and the module-multiplicity gated spectra. This work represents the state-of-the-art of our analysis methodology for segmented total absorption spectrometers.

We present a lattice QCD determination of the $B_s \to D_s \ell\nu$ scalar and vector form factors over the full physical range of momentum transfer. The result is derived from correlation functions computed using the Highly Improved Staggered Quark (HISQ) formalism, on the second generation MILC gluon ensembles accounting for up, down, strange and charm contributions from the sea. We calculate correlation functions for three lattice spacing values and an array of unphysically light $b$-quark masses, and extrapolate to the physical value. Using the HISQ formalism for all quarks means that the lattice current coupling to the $W$ can be renormalized non-perturbatively, giving a result free from perturbative matching errors for the first time. Our results are in agreement with, and more accurate than, previous determinations of these form factors. From the form factors we also determine the ratio of branching fractions that is sensitive to violation of lepton universality: $R(D_s) = \mathcal{B}(B_s\to D_s \tau \nu_{\tau})/\mathcal{B}(B_s\to D_s \ell \nu_{l})$, where $\ell$ is an electron or a muon. We find $R(D_s) = 0.2987(46)$, which is also more accurate than previous lattice QCD results. Combined with a future measurement of $R(D_s)$, this could supply a new test of the Standard Model. We also compare the dependence on heavy quark mass of our form factors to expectations from Heavy Quark Effective Theory., Comment: 22 pages, 17 figures

The $\beta$ intensity distributions of the decays of $^{100\text{gs},100\text{m}}$Nb and $^{102\text{gs},102\text{m}}$Nb have been determined using the Total Absorption $\gamma$-Ray Spectroscopy technique. The JYFLTRAP double Penning trap system was employed to disentangle the isomeric states involved, lying very close in energy, in a campaign of challenging measurements performed with the Decay Total Absorption $\gamma$-ray Spectrometer at the Ion Guide Isotope Separator On-Line facility in Jyv\"askyl\"a. The low-spin isomeric state of each niobium case was populated through the decay of the zirconium parent, that was treated as a contaminant. We have applied a method to extract this contamination, and additionally we have obtained $\beta$ intensity distributions for these zirconium decays. The $\beta$-strength distributions evaluated with these results were compared with calculations in quasiparticle random-phase approximation, suggesting a prolate configuration for the ground states of $^{100,102}$Zr. The footprint of the Pandemonium effect was found when comparing our results for the analyses of the niobium isotopes with previous decay data. The $\beta$-intensities of the decay of $^{102\text{m}}$Nb were obtained for the first time. A careful evaluation of the uncertainties was carried out, and the consistency of our results was validated taking advantage of the segmentation of our spectrometer. The final results were used as input in reactor summation calculations. A large impact on antineutrino spectrum calculations was already reported and here we detail the significant impact on decay heat calculations.

We present details of a lattice QCD calculation of the $B_s\to D_s^*$ axial form factor at zero recoil using the Highly Improved Staggered Quark (HISQ) formalism on the second generation MILC gluon ensembles that include up, down, strange and charm quarks in the sea. Using the HISQ action for all valence quarks means that the lattice axial vector current that couples to the $W$ can be renormalized fully non-perturbatively, giving a result free of the perturbative matching errors that previous lattice QCD calculations have had. We calculate correlation functions at three values of the lattice spacing, and multiple `$b$'-quark masses, for physical $c$ and $s$. The functional dependence on the $b$-quark mass can be determined and compared to Heavy Quark Effective Theory expectations, and a result for the form factor obtained at the physical value of the $b$-quark mass. We find $\mathcal{F}^{B_s\to D_s^*}(1) = h^s_{A_1}(1) = 0.9020(96)_{\text{stat}}(90)_{\text{sys}}$. This is in agreement with earlier lattice QCD results, which use NRQCD $b$ quarks, with a total uncertainty reduced by more than a factor of two. We discuss implications of this result for the $B\to D^*$ axial form factor at zero recoil and for determinations of $V_{cb}$., Comment: 18 pages, 9 figures

We present a nearly final analysis of the $u/d$ and $s$ quark masses, extracted using the PCAC quark masses reported in [PRD 95 (2017) 074504]. The data is based on the CLS $N_f = 2 + 1$ simulations with Wilson/Clover quarks and L\"uscher-Weisz gauge action, at four $\beta$ values (i.e. lattice spacings) and a range of quark masses. We use the ALPHA results of [EPJC 78 (2018) 387] for non-perturbative quark mass renormalisation and RG-running from hadronic to electroweak scales in the Schr\"odinger Functional scheme. Quark masses are quoted both in the $\overline{\rm MS}$ scheme and as RGI quantities., Comment: Talk presented at the 36th Annual International Symposium on Lattice Field Theory (Lattice 2018), 22-28 July 2018, Michigan, USA

Lattice QCD can provide a direct determination of meson electromagnetic form factors, making predictions for upcoming experiments at Jefferson Lab. The form factors are a reflection of the bound-state nature of the meson and so these calculations give information about how confinement by QCD affects meson internal structure. The region of high squared (space-like) momentum-transfer, $Q^2$, is of particular interest because perturbative QCD predictions take a simple form in that limit that depends on the meson decay constant. We previously showed in\cite{jonnaff} that, up to $Q^2$ of 6 $\mathrm{GeV}^2$, the form factor for a `pseudo-pion' made of strange quarks was significantly larger than the asymptotic perturbative QCD result and showed no sign of heading towards that value at higher $Q^2$. Here we give predictions for real mesons, the $K^+$ and $K^0$, in anticipation of JLAB results for the $K^+$ in the next few years. We also give results for a heavier meson, the $\eta_c$, up to $Q^2$ of 25 $\mathrm{GeV}^2$ for a comparison to perturbative QCD in a higher $Q^2$ regime., Comment: 6 pages, 5 figures, Proceedings of LATTICE2018

We present progress on an ongoing calculation of the $B_s\to D_s^{(*)} l \nu$ form factors calculated on the $n_f=2+1+1$ MILC ensembles and using the Highly Improved Staggered Quark action for all valence quarks. We perform the calculation at a range of $b$ quark masses (and lattice spacings) so that we can extrapolate to the physical $b$-quark mass., Comment: 6 pages, 3 figures, proceedings of the 36th Annual International Symposium on Lattice Field Theory - LATTICE2018

We derive the Operator Product Expansion whose vacuum expectation value gives the time-moments of the pseudoscalar heavy-light current-current correlator up to and including terms in $\alpha_s^2$ multiplying $\langle\overline{\psi}\psi\rangle/M^3$ and terms in $\alpha_s$ multiplying $\langle \alpha_s G^2 \rangle/M^4$, where $M$ is the heavy-quark mass. Using lattice QCD results for heavy-strange correlators obtained for a variety of heavy quark masses on gluon field configurations including $u$, $d$ and $s$ quarks in the sea at three values of the lattice spacing, we are able to show that the contribution of the strange-quark condensate to the time-moments is very substantial. We use our lattice QCD time-moments and the OPE to determine a value for the condensate, fitting the 4th, 6th, 8th and 10th time-moments simultaneously. Our result, $\langle \overline{s}s \rangle^{\overline{\text{MS}}}(2 \text{GeV}) = -(296(11) \,\mathrm{MeV})^3$, agrees well with HPQCD's earlier, more direct, lattice QCD determination~\cite{McNeile:2012xh}. As well as confirming that the $s$ quark condensate is close in value to the light quark condensate, this demonstrates clearly the consistency of the Operator Product Expansion for fully nonperturbative calculations of matrix elements of short-distance operators in lattice QCD., Comment: 14 pages, 4 figures

DTAS is a segmented total absorption {\gamma}-ray spectrometer developed for the DESPEC experiment at FAIR. It is composed of up to eighteen NaI(Tl) crystals. In this work we study the performance of this detector with laboratory sources and also under real experimental conditions. We present a procedure to reconstruct offline the sum of the energy deposited in all the crystals of the spectrometer, which is complicated by the effect of NaI(Tl) light-yield non-proportionality. The use of a system to correct for time variations of the gain in individual detector modules, based on a light pulse generator, is demonstrated. We describe also an event-based method to evaluate the summing-pileup electronic distortion in segmented spectrometers. All of this allows a careful characterization of the detector with Monte Carlo simulations that is needed to calculate the response function for the analysis of total absorption {\gamma}-ray spectroscopy data. Special attention was paid to the interaction of neutrons with the spectrometer, since they are a source of contamination in studies of \b{eta}-delayed neutron emitting nuclei.

Background: $\beta$-delayed multiple neutron emission has been observed for some nuclei with A$\leq$100, with $^{100}$Rb being the heaviest $\beta$2n emitter measured to date. So far, only 25 P$_{2n}$ values have been determined for the $\sim$300 nuclei that may decay in this way. Accordingly, it is of interest to measure P$_{2n}$ values for the other possible multiple neutron emitters throughout the chart of the nuclides. It is of particular interest to make such measurement for nuclei with A$>$100 to test the predictions of theoretical models and simulation tools for the decays of heavy nuclei in the region of very neutron-rich nuclei. In addition, the decay properties of these nuclei are fundamental for the understanding of astrophysical nucleosynthesis processes such as the $r$-process, and safety inputs for nuclear reactors. Purpose: To determine for the first time the two neutron branching ratio, P$_{2n}$ value, for $^{136}$Sb through a direct neutron measurement, and to provide precise P$_{1n}$ values for $^{136}$Sb and $^{136}$Te. Method: Pure beams were provided by the JYFLTRAP at the IGISOL facility of the University of Jyv\"askyl\"a, Finland. The purified ions were implanted into a moving tape at the end of the beam line. The detection setup consisted of a plastic scintillator placed right behind the implantation point, and the BELEN detector, based on neutron counters embedded in a polyethylene matrix. The analysis was based on the study of the $\beta$- and neutron- growth-and-decay curves and the $\beta$-one-neutron and $\beta$-two-neutron time correlations. Results: The P$_{2n}$ value of $^{136}$Sb was found to be 0.14(3)\% and the measured P$_{1n}$ values for $^{136}$Sb and $^{136}$Te were found to be 32.2(15)\% and 1.47(6)\%, respectively. The measured P$_{2n}$ value is a factor 44 smaller than predicted by the FRDM+QRPA model used for $r$-process calculations., Comment: 11 pages, 10 figures

All lattice-QCD calculations of the hadronic-vacuum-polarization contribution to the muon's anomalous magnetic moment to-date have been performed with degenerate up- and down-quark masses. Here we calculate directly the strong-isospin-breaking correction to $a_\mu^{\rm HVP}$ for the first time with physical values of $m_u$ and $m_d$ and dynamical $u$, $d$, $s$, and $c$ quarks, thereby removing this important source of systematic uncertainty. We obtain a relative shift to be applied to lattice-QCD results obtained with degenerate light-quark masses of $\delta a_\mu^{{\rm HVP,} m_u \neq m_d}$= +1.5(7)%, in agreement with estimates from phenomenology and a recent lattice-QCD calculation with unphysically heavy pions., Comment: v2: 6 pages, 2 tables, 2 figures. Additional references and expanded discussion of systematic errors. Version accepted to Physical Review Letters

The \b{eta}-decay of 100 Tc has been studied using the Total Absorption {\gamma}-Ray Spectroscopy technique at IGISOL. In this work the new DTAS spectrometer in coincidence with a cylindrical plastic \b{eta} detector has been employed. The \b{eta}-intensity to the ground state obtained from the analysis is in good agreement with previous high-resolution measurements. However, differences in the feeding to the first excited state as well as weak feeding to a new level at high excitation energy have been deduced from this experiment. Theoretical calculations performed in the quasiparticle random- phase approximation (QRPA) framework are also reported. Comparison of these calculations with our measurement serves as a benchmark for calculations of the double \b{eta}-decay of 100 Mo., Comment: submitted to Physical Review C

We compare correlators for pseudoscalar and vector mesons made from valence strange quarks using the clover quark and highly improved staggered quark (HISQ) formalisms in full lattice QCD. We use fully nonperturbative methods to normalise vector and axial vector current operators made from HISQ quarks, clover quarks and from combining HISQ and clover fields. This allows us to test expectations for the renormalisation factors based on perturbative QCD, with implications for the error budget of lattice QCD calculations of the matrix elements of clover-staggered $b$-light weak currents, as well as further HISQ calculations of the hadronic vacuum polarisation. We also compare the approach to the (same) continuum limit in clover and HISQ formalisms for the mass and decay constant of the $\phi$ meson. Our final results for these parameters, using single-meson correlators and neglecting quark-line disconnected diagrams are: $m_{\phi} =$ 1.023(6) GeV and $f_{\phi} = $ 0.238(3) GeV in good agreement with experiment. The results come from calculations in the HISQ formalism using gluon fields that include the effect of $u$, $d$, $s$ and $c$ quarks in the sea with three lattice spacing values and $m_{u/d}$ values going down to the physical point., Comment: 21 pages, 11 figures. Version published by Phys.Rev.D. Minor changes to text. HISQ Z_V value derived in Appendix B for a=0.06fm lattices changed slightly

We give an accurate determination of the vector (electromagnetic) form factor, $F(Q^2)$, for a light pseudoscalar meson up to squared momentum transfer $Q^2$ values of 6 $\mathrm{GeV}^2$ for the first time from full lattice QCD, including $u$, $d$, $s$ and $c$ quarks in the sea at multiple values of the lattice spacing. Our results show good control of lattice discretisation and sea quark mass effects. We study a pseudoscalar meson made of valence $s$ quarks but the qualitative picture obtained applies also to the $\pi$ meson, relevant to upcoming experiments at Jefferson Lab. We find that $Q^2F(Q^2)$ becomes flat in the region between $Q^2$ of 2 $\mathrm{GeV}^2$ and 6 $\mathrm{GeV}^2$, with a value well above that of the asymptotic perturbative QCD expectation, but well below that of the vector-meson dominance pole form appropriate to low $Q^2$ values. Our calculations show that we can reach higher $Q^2$ values in future to shed further light on where the perturbative QCD result emerges., Comment: 8 pages, 6 figures. Version accepted by Physical Review D. Includes results from a third value of the lattice spacing, change to the title and two additional figures in the appendix discussing analysis of systematic and statistical errors

Masses of $^{52}$Co, $^{52}$Co$^m$, $^{52}$Fe, $^{52}$Fe$^m$, and $^{52}$Mn have been measured with the JYFLTRAP double Penning trap mass spectrometer. Of these, $^{52}$Co and $^{52}$Co$^m$ have been experimentally determined for the first time and found to be more bound than predicted by extrapolations. The isobaric multiplet mass equation for the $T=2$ quintet at $A=52$ has been studied employing the new mass values. No significant breakdown (beyond the $3\sigma$ level) of the quadratic form of the IMME was observed ($\chi^2/n=2.4$). The cubic coefficient was 6.0(32) keV ($\chi^2/n=1.1$). The excitation energies for the isomer and the $T=2$ isobaric analogue state in $^{52}$Co have been determined to be 374(13) keV and 2922(13) keV, respectively. The $Q$ value for the proton decay from the $19/2^-$ isomer in $^{53}$Co has been determined with an unprecedented precision, $Q_{p} = 1558.8(17)$ keV. The proton separation energies of $^{52}$Co and $^{53}$Ni relevant for the astrophysical rapid proton capture process have been experimentally determined for the first time. \end{abstract}, Comment: 12 pages, 13 figures, submitted to Phys. Rev. C (26.9.2016)

In this work we report on the Monte Carlo study performed to understand and reproduce experimental measurements of a new plastic \b{eta}-detector with cylindrical geometry. Since energy deposition simulations differ from the experimental measurements for such a geometry, we show how the simulation of production and transport of optical photons does allow one to obtain the shapes of the experimental spectra. Moreover, taking into account the computational effort associated with this kind of simulation, we develop a method to convert the simulations of energy deposited into light collected, depending only on the interaction point in the detector. This method represents a useful solution when extensive simulations have to be done, as in the case of the calculation of the response function of the spectrometer in a total absorption {\gamma}-ray spectroscopy analysis., Comment: submitted to Nuclear Instruments and Methods A

We determine the contribution to the anomalous magnetic moment of the muon from the $\alpha^2_{\mathrm{QED}}$ hadronic vacuum polarization diagram using full lattice QCD and including $u/d$ quarks with physical masses for the first time. We use gluon field configurations that include $u$, $d$, $s$ and $c$ quarks in the sea at multiple values of the lattice spacing, multiple $u/d$ masses and multiple volumes that allow us to include an analysis of finite-volume effects. We obtain a result for $a_{\mu}^{\mathrm{HVP,LO}}$ of $667(6)(12)$, where the first error is from the lattice calculation and the second includes systematic errors from missing QED and isospin-breaking effects and from quark-line disconnected diagrams. Our result implies a discrepancy between the experimental determination of $a_{\mu}$ and the Standard Model of 3$\sigma$., Comment: 14 pages, 10 figures. Discussion of method extended with additional tests and figures added. Typographical errors corrected

The quark-line disconnected diagram is a potentially important ingredient in lattice QCD calculations of the hadronic vacuum polarization contribution to the anomalous magnetic moment of the muon. It is also a notoriously difficult one to evaluate. Here, for the first time, we give an estimate of this contribution based on lattice QCD results that have a statistically significant signal, albeit at one value of the lattice spacing and an unphysically heavy value of the $u/d$ quark mass. We use HPQCD's method of determining the anomalous magnetic moment by reconstructing the Adler function from time-moments of the current-current correlator at zero spatial momentum. Our results lead to a total (including $u$, $d$ and $s$ quarks) quark-line disconnected contribution to $a_{\mu}$ of $-0.15\%$ of the $u/d$ hadronic vacuum polarization contribution with an uncertainty which is 1\% of that contribution., Comment: 9 pages, 3 figures

The mass of $^{31}$Cl has been measured with the JYFLTRAP double Penning trap mass spectrometer at the Ion-Guide Isotope Separator On-Line (IGISOL) facility. The determined mass-excess value, -7034.7(34) keV, is 15 times more precise than in the Atomic Mass Evaluation 2012. The quadratic form of the isobaric multiplet mass equation for the T=3/2 quartet at A=31 fails ($\chi^2_n$=11.6) and a non-zero cubic term, d=-3.5(11) keV, is obtained when the new mass value is adopted. $^{31}$Cl has been found to be less proton-bound with a proton separation energy of $S_p$=265(4) keV. Energies for the excited states in $^{31}$Cl and the photodisintegration rate on $^{31}$Cl have been determined with significantly improved precision using the new $S_p$ value. The improved photodisintegration rate helps to constrain astrophysical conditions where $^{30}$S can act as a waiting point in the rapid proton capture process in type I x-ray bursts., Comment: 6 pages, 4 figures, submitted to Phys. Rev. C Rapid Comm

We present the first calculation of the electromagnetic form factor of the $\pi$ meson at physical light quark masses. We use configurations generated by the MILC collaboration including the effect of $u$, $d$, $s$ and $c$ sea quarks with the Highly Improved Staggered Quark formalism. We work at three values of the lattice spacing on large volumes and with $u$/$d$ quark masses going down to the physical value. We study scalar and vector form factors for a range in space-like $q^2$ from 0.0 to -0.1 $\mathrm{GeV}^2$ and from their shape we extract mean square radii. Our vector form factor agrees well with experiment and we find $\langle r^2 \rangle_V = 0.403(18)(6) \,\mathrm{fm}^2$. For the scalar form factor we include quark-line disconnected contributions which have a significant impact on the radius. We give the first results for SU(3) flavour-singlet and octet scalar mean square radii, obtaining: $\langle r^2 \rangle_S^{\mathrm{singlet}} = 0.506(38)(53) \mathrm{fm}^2$ and $\langle r^2 \rangle_S^{\mathrm{octet}} = 0.431(38)(46) \mathrm{fm}^2$. We discuss the comparison with expectations from chiral perturbation theory., Comment: 13 pages, 11 figures

The exclusive semileptonic decay $B \rightarrow \pi \ell \nu$ is a key process for the determination of the Cabibbo-Kobayashi-Maskawa matrix element $V_{ub}$ from the comparison of experimental rates as a function of $q^2$ with theoretically determined form factors. The sensitivity of the form factors to the $u/d$ quark mass has meant significant systematic uncertainties in lattice QCD calculations at unphysically heavy pion masses. Here we give the first lattice QCD calculations of this process for u/d quark masses going down to their physical values, calculating the $f_0$ form factor at zero recoil to 3\%. We are able to resolve a long-standing controversy by showing that the soft-pion theorem result $f_0(q^2_{max}) = f_B/f_{\pi}$ does hold as $m_{\pi} \rightarrow 0$. We use the Highly Improved Staggered Quark formalism for the light quarks and show that staggered chiral perturbation theory for the $m_{\pi}$ dependence is almost identical to continuum chiral perturbation theory for $f_0$, $f_B$ and $f_{\pi}$. We also give results for other processes such as $B_s \rightarrow K \ell \nu$., Comment: 16 pages, 6 figures

We extend the picture of $B$-meson decay constants obtained in lattice QCD beyond those of the $B$, $B_s$ and $B_c$ to give the first full lattice QCD results for the $B^*$, $B^*_s$ and $B^*_c$. We use improved NonRelativistic QCD for the valence $b$ quark and the Highly Improved Staggered Quark (HISQ) action for the lighter quarks on gluon field configurations that include the effect of $u/d$, $s$ and $c$ quarks in the sea with $u/d$ quark masses going down to physical values. For the ratio of vector to pseudoscalar decay constants, we find $f_{B^*}/f_B$ = 0.941(26), $f_{B^*_s}/f_{B_s}$ = 0.953(23) (both $2\sigma$ less than 1.0) and $f_{B^*_c}/f_{B_c}$ = 0.988(27). Taking correlated uncertainties into account we see clear indications that the ratio increases as the mass of the lighter quark increases. We compare our results to those using the HISQ formalism for all quarks and find good agreement both on decay constant values when the heaviest quark is a $b$ and on the dependence on the mass of the heaviest quark in the region of the $b$. Finally, we give an overview plot of decay constants for gold-plated mesons, the most complete picture of these hadronic parameters to date., Comment: 20 pages, 9 figures. Minor updates to the discussion in several places and some additional references

The charmonium system has several excited states below the energy threshold for decay into $D$ and $\bar{D}$ mesons, which can in principle be studied accurately in lattice QCD. Studies that include many states in the spectrum have typically only been done at one value of the lattice spacing and with relatively heavy light quarks in the sea. Here we give preliminary results for radial and orbital excitation energies for charmonium from a calculation on 2+1+1 MILC configurations at multiple lattice spacings and including physical values for $u/d$ quark masses. We use the HISQ formulation for $c$ to obtain small discretisation errors and smeared operators to improve excited state overlap., Comment: 7 pages, 4 figures. Presented at the 32nd International Symposium on Lattice Field Theory (Lattice 2014), 23-28 June 2014, New York, USA

We present a new lattice QCD analysis of heavy-quark pseudoscalar-pseudoscalar correlators, using gluon configurations from the MILC collaboration that include vacuum polarization from $u$, $d$, $s$ and $c$~quarks($n_f=4$). We extract new values for the QCD coupling and for the $c$ quark's $\overline{\mathrm{MS}}$ mass: $\alpha_{\overline{\mathrm{MS}}}(M_Z,n_f=5) = 0.11822(74)$ and $m_c(3\mathrm{GeV}, n_f=4) = 0.9851(63)$GeV. These agree well with our earlier simulations using $n_f=3$ sea quarks, vindicating the perturbative treatment of $c$ quarks in that analysis. We also obtain a new nonperturbative result for the ratio of $c$~and $s$~quark masses: $m_c/m_s=11.652(65)$. This ratio implies $m_s(2\,\mathrm{GeV}, n_f=3)=93.6(8)$MeV when it is combined with our new~$c$~mass. Combining $m_c/m_s$ with our earlier $m_b/m_c$ gives $m_b/m_s=52.55(55)$, which is several standard deviations (but only 4%) away from the Georgi-Jarlskop prediction from certain GUTs. Finally we obtain an $n_f=4$ estimate for $m_b/m_c=4.528(54)$ which agrees well with our earlier $n_f=3$ result. The new ratio implies~$m_b(m_b,n_f=5)=4.162(48)$GeV., Comment: 16 pages, 9 figures, 6 tables

We describe a new technique to determine the contribution to the anomalous magnetic moment of the muon coming from the hadronic vacuum polarization using lattice QCD. Our method reconstructs the Adler function, using Pad\'{e} approximants, from its derivatives at $q^2=0$ obtained simply and accurately from time-moments of the vector current-current correlator at zero spatial momentum. We test the method using strange quark correlators on large-volume gluon field configurations that include the effect of up and down (at physical masses), strange and charm quarks in the sea at multiple values of the lattice spacing and multiple volumes and show that 1% accuracy is achievable. For the charm quark contributions we use our previously determined moments with up, down and strange quarks in the sea on very fine lattices. We find the (connected) contribution to the anomalous moment from the strange quark vacuum polarization to be $a_\mu^s = 53.41(59) \times 10^{-10}$, and from charm to be $a_\mu^c = 14.42(39)\times 10^{-10}$. These are in good agreement with flavour-separated results from non-lattice methods, given caveats about the comparison. The extension of our method to the light quark contribution and to that from the quark-line disconnected diagram is straightforward., Comment: 7 pages, 4 figures. Updated to version accepted for publication, with additional clarification of the new method developed here

We have developed two methods for handling $b$ quarks in lattice QCD. One uses NRQCD (now improved to include radiative corrections) and the other uses Highly Improved Staggered Quarks (HISQ), extrapolating to the $b$ quark from lighter masses and using multiple lattice spacings to control discretisation errors. Comparison of results for the two different methods gives confidence in estimates of lattice QCD systematic errors, since they are very different in these two cases. Here we show results for heavyonium hyperfine splittings and vector current-current correlator moments using HISQ quarks, to add to earlier results testing the heavy HISQ method with pseudoscalar mesons. We also show the form factor for $B \rightarrow \pi l \nu$ decay at zero recoil using NRQCD $b$ quarks and $u/d$ quarks with physical masses. This allows us to test the soft pion theorem relation ($f_0(q^2_{max})=f_B/f_{\pi}$) accurately and we find good agreement as $M_{\pi} \rightarrow 0$. }, Comment: 5 pages, 3 figures, Proceedings of Lattice2013

We determine the rate for $D_s^* \rightarrow D_s \gamma$ for the first time from lattice QCD and include the full effect of $u$, $d$ and $s$ sea quarks. The valence quarks are implemented using the Highly Improved Staggered Quark (HISQ) formalism and we normalise the vector current nonperturbatively. We obtain $M(D_s^*)-M(D_s)$ of 148(4) MeV, in good agreement with experiment. The value of the decay constant of the $D_s^*$ we find to be 274(6) MeV, so that $f_{D_s^*}/f_{D_s} = 1.10(2)$. For the radiative decay we find $\Gamma(D_s^* \rightarrow D_s \gamma)$ = 0.066(26) keV. Given the experimental branching fraction for this decay we predict a total width for the $D_s^*$ of 0.070(28) keV, making this the longest lived charged vector meson., Comment: 5 pages, 3 figures

We determine the complete set of axial and vector form factors for the Ds to {\phi}l{\nu} decay from full lattice QCD for the first time. The valence quarks are implemented using the Highly Improved Staggered Quark action and we normalise the appropriate axial and vector currents fully nonperturbatively. The q^2 and angular distributions we obtain for the differential rate agree well with those from the BaBar experiment and, from the total branching fraction, we obtain Vcs = 1.017(63), in good agreement with that from D to Kl{\nu} semileptonic decay. We also find the mass and decay constant of the {\phi} meson in good agreement with experiment, showing that its decay to K{\bar{K}} (which we do not include here) has at most a small effect. We include an Appendix on nonperturbative renormalisation of the complete set of staggered vector and axial vector bilinears needed for this calculation., Comment: 19 pages, 13 figures