Search

Nucleon form factors at large momentum transfer are important for understanding the transition from nonperturbative to perturbative QCD and have been the focus of experiment and phenomenology. We calculate proton and neutron electromagnetic form factors GE,M (Q2) from first principles using nonperturbative methods of lattice QCD. We have accumulated large Monte Carlo statistics to study form factors up to momentum transfer Q2 ≲ 8 GeV2 with a range of lattice spacings as well as quark masses that approach the physical point. In this paper, results of initial analyses are presented and compared to experiment, and potential sources of systematic uncertainty are discussed.

We present a study of lattice-QCD methods to determine the relevant hadronic form factors for radiative leptonic decays of pseudoscalar mesons. We provide numerical results for $D_s^+ \to \ell^+ \nu \gamma$. Our calculation is performed using a domain-wall action for all quark flavors and on a single RBC/UKQCD lattice gauge-field ensemble. The first part of the study is how to best control two sources of systematic error inherent in the calculation, specifically the unwanted excited states created by the meson interpolating field, and unwanted exponentials in the sum over intermediate states. Using a 3d sequential propagator allows for better control over unwanted exponentials from intermediate states, while using a 4d sequential propagator allows for better control over excited states. We perform individual analyses of the 3d and 4d methods as well as a combined analysis using both methods, and find that the 3d sequential propagator offers good control over both sources of systematic uncertainties for the smallest number of propagator solves. From there, we further improve the use of a 3d sequential propagator by employing an infinite-volume approximation method, which allows us to calculate the relevant form factors over the entire allowed range of photon energies. We then study improvements gained by performing the calculation using a different three-point function, using ratios of three-point functions, averaging over positive and negative photon momentum, and using an improved method for extracting the structure-dependent part of the axial form factor. The optimal combination of methods yields results for the $D_s^+ \to \ell^+ \nu \gamma$ structure-dependent vector and axial form factors in the entire kinematic range with statistical plus fitting uncertainties of order 5%, using 25 gauge configurations with 64 samples per configuration., Comment: 31 pages, 14 figures

Two important sources of systematic errors in lattice QCD calculations of radiative leptonic decays are unwanted exponentials in the sum over intermediate states and unwanted excited states created by the meson interpolating field. Performing the calculation using a 3d sequential propagator allows for better control over the systematic uncertainties from intermediate states, while using a 4d sequential propagator allows for better control over the systematic uncertainties from excited states. We calculate form factors using both methods and compare how reliably each controls these systematic errors. We also employ a hybrid approach involving global fits to data from both methods., Comment: 10 pages, 4 figures, talk given at the 38th International Symposium on Lattice Field Theory (LATTICE2021), 26th-30th July 2021, Zoom/Gather@Massachusetts Institute of Technology

Understanding the properties of the strange Λ* baryon resonances is a long-standing and fascinating problem. Λc charm-baryon semileptonic weak decays to these resonances are highly sensitive to their internal structure and can be used to test theoretical models. We have performed the first lattice-QCD computation of the form factors governing Λc semileptonic decays to a Λ* resonance: the Λ*(1520), which has negative parity and spin 3/2. Here we present the resulting Standard Model predictions of the Λc→Λ*(1520)ℓ+νℓ differential and integrated decay rates as well as angular observables. Furthermore, by combining the recent BESIII measurement of the Λc→Xe+νe inclusive semipositronic branching fraction [Phys. Rev. Lett. 121, 251801 (2018)] with lattice-QCD predictions of the Λc→Λe+νe, Λc→ne+νe, and Λc→Λ*(1520)e+νe decay rates, we obtain an upper limit on the sum of the branching fractions to all other semipositronic final states. In particular, this upper limit constrains the Λc→Λ*(1405)e+νe branching fraction to be very small, which may be another hint for a molecular structure of the Λ*(1405).

We present our recent results on antiheavy-antiheavy-light-light tetraquark systems using lattice QCD. Our study of the $ \bar{b}\bar{b}us $ four-quark system with quantum numbers $ J^P=1^+ $ and the $ \bar{b}\bar{c}ud $ four-quark systems with $ I(J^P)=0(0^+) $ and $ I(J^P)=0(1^+) $ utilizes scattering operators at the sink to improve the extraction of the low-lying energy levels. We found a bound state for $ \bar{b}\bar{b}us $ with $ E_{\textrm{bind},\bar{b}\bar{b}us} = (-86 \pm 22 \pm 10)\,\textrm{MeV} $, but no indication for a bound state in both $ \bar{b}\bar{c}ud $ channels. Moreover, we show preliminary results for $ \bar{b}\bar{b}ud $ with $ I(J^P)=0(1^+) $, where we used scattering operators both at the sink and the source. We found a bound state and determined its infinite-volume binding energy with a scattering analysis, resulting in $ E_{\textrm{bind},\bar{b}\bar{b}ud} =(-103 \pm 8 )\,\textrm{MeV} $., Comment: 9 pages, 3 figures, talk given at "The 39th International Symposium on Lattice Field Theory", 08th-13th August 2022, Bonn, Germany

In this work we investigate the existence of bound states for doubly heavy tetraquark systems $ \bar{Q}\bar{Q}'qq' $ in a full lattice-QCD computation, where heavy bottom quarks are treated in the framework of non-relativistic QCD. We focus on three systems with quark content $ \bar{b}\bar{b}ud $, $ \bar{b}\bar{b}us $ and $ \bar{b}\bar{c}ud $. We show evidence for the existence of $ \bar{b}\bar{b}ud $ and $ \bar{b}\bar{b}us $ bound states, while no binding appears to be present for $ \bar{b}\bar{c}ud $. For the bound four-quark states we also discuss the importance of various creation operators and give an estimate of the meson-meson and diquark-antidiquark percentages., 9 pages, 9 figures, talk given at the 38th International Symposium on Lattice Field Theory (LATTICE2021), 26th-30th July 2021, Zoom/Gather@Massachusetts Institute of Technology

We present the first lattice-QCD determination of the form factors describing the semileptonic decays ${\mathrm{\ensuremath{\Lambda}}}_{b}\ensuremath{\rightarrow}{\mathrm{\ensuremath{\Lambda}}}_{c}^{*}(2595){\ensuremath{\ell}}^{\ensuremath{-}}\overline{\ensuremath{\nu}}$ and ${\mathrm{\ensuremath{\Lambda}}}_{b}\ensuremath{\rightarrow}{\mathrm{\ensuremath{\Lambda}}}_{c}^{*}(2625){\ensuremath{\ell}}^{\ensuremath{-}}\overline{\ensuremath{\nu}}$, where the ${\mathrm{\ensuremath{\Lambda}}}_{c}^{*}(2595)$ and ${\mathrm{\ensuremath{\Lambda}}}_{c}^{*}(2625)$ are the lightest charm baryons with ${J}^{P}={\frac{1}{2}}^{\ensuremath{-}}$ and ${J}^{P}={\frac{3}{2}}^{\ensuremath{-}}$, respectively. These decay modes provide new opportunities to test lepton flavor universality and also play an important role in global analyses of the strong interactions in $b\ensuremath{\rightarrow}c$ semileptonic decays. We determine the full set of vector, axial vector, and tensor form factors for both decays but only in a small kinematic region near the zero-recoil point. The lattice calculation uses three different ensembles of gauge-field configurations with $2+1$ flavors of domain-wall fermions, and we perform extrapolations of the form factors to the continuum limit and physical pion mass. We present Standard Model predictions for the differential decay rates and angular observables. In the kinematic region considered, the differential decay rate for the ${\frac{1}{2}}^{\ensuremath{-}}$ final state is found to be approximately 2.5 times larger than the rate for the ${\frac{3}{2}}^{\ensuremath{-}}$ final state. We also test the compatibility of our form-factor results with zero-recoil sum rules.

We determine the $\mathrm{\ensuremath{\Delta}}(1232)$ resonance parameters using lattice QCD and the L\"uscher method. The resonance occurs in elastic pion-nucleon scattering with ${J}^{P}=3/{2}^{+}$ in the isospin $I=3/2$, $P$-wave channel. Our calculation is performed with ${N}_{f}=2+1$ flavors of clover fermions on a lattice with $L\ensuremath{\approx}2.8\text{ }\text{ }\mathrm{fm}$. The pion and nucleon masses are ${m}_{\ensuremath{\pi}}=255.4(1.6)\text{ }\text{ }\mathrm{MeV}$ and ${m}_{N}=1073(5)\text{ }\text{ }\mathrm{MeV}$, respectively, and the strong decay channel $\mathrm{\ensuremath{\Delta}}\ensuremath{\rightarrow}\ensuremath{\pi}N$ is found to be above the threshold. To thoroughly map out the energy dependence of the nucleon-pion scattering amplitude, we compute the spectra in all relevant irreducible representations of the lattice symmetry groups for total momenta up to $\stackrel{\ensuremath{\rightarrow}}{P}=\frac{2\ensuremath{\pi}}{L}(1,1,1)$, including irreps that mix $S$ and $P$ waves. We perform global fits of the amplitude parameters to up to 21 energy levels, using a Breit-Wigner model for the $P$-wave phase shift and the effective-range expansion for the $S$-wave phase shift. From the location of the pole in the $P$-wave scattering amplitude, we obtain the resonance mass ${m}_{\mathrm{\ensuremath{\Delta}}}=1378(7)(9)\text{ }\text{ }\mathrm{MeV}$ and the coupling ${g}_{\mathrm{\ensuremath{\Delta}}\ensuremath{-}\ensuremath{\pi}N}=23.8(2.7)(0.9)$.

Generalized transverse momentum-dependent parton distributions (GTMDs) provide a comprehensive framework for imaging the internal structure of the proton. In particular, by encoding the simultaneous distribution of quark transverse positions and momenta, they allow one to directly access longitudinal quark orbital angular momentum, and, moreover, to correlate it with the quark helicity. The relevant GTMD is evaluated through a lattice calculation of a proton matrix element of a quark bilocal operator (the separation in which is Fourier conjugate to the quark momentum) featuring a momentum transfer (which is Fourier conjugate to the quark position), as well as the Dirac structure appropriate for capturing the quark helicity. The weighting by quark transverse position requires a derivative with respect to momentum transfer, which is obtained in unbiased fashion using a direct derivative method. The lattice calculation is performed directly at the physical pion mass, using domain wall fermions to mitigate operator mixing effects. Both the Jaffe-Manohar as well as the Ji quark spin-orbit correlations are extracted, yielding evidence for a strong quark spin-orbit coupling in the proton., Comment: 8 pages, 2 figures, to appear in the proceedings of the 38th International Symposium on Lattice Field Theory, LATTICE2021, PoS LATTICE2021, 413

We present a lattice-QCD determination of the elastic isospin-$1/2$ $S$-wave and $P$-wave $K\ensuremath{\pi}$ scattering amplitudes as a function of the center-of-mass energy using L\"uscher's method. We perform global fits of $K$-matrix parametrizations to the finite-volume energy spectra for all irreducible representations with total momenta up to $\sqrt{3}\frac{2\ensuremath{\pi}}{L}$; this includes irreducible representations (irreps) that mix the $S$- and $P$-waves. Several different parametrizations for the energy dependence of the $K$-matrix are considered. We also determine the positions of the nearest poles in the scattering amplitudes, which correspond to the broad $\ensuremath{\kappa}$ resonance in the $S$-wave and the narrow ${K}^{*}(892)$ resonance in the $P$-wave. Our calculations are performed with $2+1$ dynamical clover fermions for two different pion masses of 317.2(2.2) and 175.9(1.8) MeV. Our preferred $S$-wave parametrization is based on a conformal map and includes an Adler zero; for the $P$-wave, we use a standard pole parametrization including Blatt-Weisskopf barrier factors. The $S$-wave $\ensuremath{\kappa}$-resonance pole positions are found to be $[0.86(12)\ensuremath{-}0.309(50)i]\text{ }\text{ }\mathrm{GeV}$ at the heavier pion mass and $[0.499(55)\ensuremath{-}0.379(66)i]\text{ }\text{ }\mathrm{GeV}$ at the lighter pion mass. The $P$-wave ${K}^{*}$-resonance pole positions are found to be $[0.8951(64)\ensuremath{-}0.00250(21)i]\text{ }\text{ }\mathrm{GeV}$ at the heavier pion mass and $[0.8718(82)\ensuremath{-}0.0130(11)i]\text{ }\text{ }\mathrm{GeV}$ at the lighter pion mass, which corresponds to couplings of ${g}_{{K}^{*}K\ensuremath{\pi}}=5.02(26)$ and ${g}_{{K}^{*}K\ensuremath{\pi}}=4.99(22)$, respectively.

Two of the elements of the Cabibbo–Kobayashi–Maskawa quark mixing matrix, $$|V_{ub}|$$ | V ub | and $$|V_{cb}|$$ | V cb | , are extracted from semileptonic B decays. The results of the B factories, analysed in the light of the most recent theoretical calculations, remain puzzling, because for both $$|V_{ub}|$$ | V ub | and $$|V_{cb}|$$ | V cb | the exclusive and inclusive determinations are in clear tension. Further, measurements in the $$\tau $$ τ channels at Belle, Babar, and LHCb show discrepancies with the Standard Model predictions, pointing to a possible violation of lepton flavor universality. LHCb and Belle II have the potential to resolve these issues in the next few years. This article summarizes the discussions and results obtained at the MITP workshop held on April 9–13, 2018, in Mainz, Germany, with the goal to develop a medium-term strategy of analyses and calculations aimed at solving the puzzles. Lattice and continuum theorists working together with experimentalists have discussed how to reshape the semileptonic analyses in view of the much higher luminosity expected at Belle II, searching for ways to systematically validate the theoretical predictions in both exclusive and inclusive B decays, and to exploit the rich possibilities at LHCb.

Following updated and extended measurements of the full angular distribution of the decay ${\mathrm{\ensuremath{\Lambda}}}_{b}\ensuremath{\rightarrow}\mathrm{\ensuremath{\Lambda}}(\ensuremath{\rightarrow}p{\ensuremath{\pi}}^{\ensuremath{-}}){\ensuremath{\mu}}^{+}{\ensuremath{\mu}}^{\ensuremath{-}}$ by the LHCb collaborations, as well as a new measurement of the $\mathrm{\ensuremath{\Lambda}}\ensuremath{\rightarrow}p{\ensuremath{\pi}}^{\ensuremath{-}}$ decay asymmetry parameter by the BESIII collaboration, we study the impact of these results on searches for nonstandard effects in exclusive $b\ensuremath{\rightarrow}s{\ensuremath{\mu}}^{+}{\ensuremath{\mu}}^{\ensuremath{-}}$ decays. To this end, we constrain the Wilson coefficients ${\mathcal{C}}_{9}$ and ${\mathcal{C}}_{10}$ of the numerically leading dimension-six operators in the weak effective Hamiltonian, in addition to the relevant nuisance parameters. In stark contrast to previous analyses of this decay mode, the changes in the updated experimental results lead us to find very good compatibility with both the Standard Model and with the $b\ensuremath{\rightarrow}s{\ensuremath{\mu}}^{+}{\ensuremath{\mu}}^{\ensuremath{-}}$ anomalies observed in rare $B$-meson decays. We provide a detailed analysis of the impact of the partial angular distribution, the full angular distribution, and the ${\mathrm{\ensuremath{\Lambda}}}_{b}\ensuremath{\rightarrow}\mathrm{\ensuremath{\Lambda}}{\ensuremath{\mu}}^{+}{\ensuremath{\mu}}^{\ensuremath{-}}$ branching fraction on the Wilson coefficients. In this process, we are also able to constrain the size of the production polarization of the ${\mathrm{\ensuremath{\Lambda}}}_{b}$ baryon at LHCb.

A Lattice QCD approach to quark orbital angular momentum in the proton based on generalized transverse momentum-dependent parton distributions (GTMDs) is enhanced methodologically by incorporating a direct derivative technique. This improvement removes a significant numerical bias that had been seen to afflict results of a previous study. In particular, the value obtained for Ji quark orbital angular momentum is reconciled with the one obtained independently via Ji's sum rule, validating the GMTD approach. Since GTMDs simultaneously contain information about the quark impact parameter and transverse momentum, they permit a direct evaluation of the cross product of the latter. They are defined through proton matrix elements of a quark bilocal operator containing a Wilson line; the choice in Wilson line path allows one to continuously interpolate from Ji to Jaffe-Manohar quark orbital angular momentum. The latter is seen to be significantly enhanced in magnitude compared to Ji quark orbital angular momentum, confirming previous results., Comment: 12 pages, 6 figures

Based on lattice non-relativistic QCD (NRQCD) studies we present results for Bethe-Salpeter amplitudes for $\Upsilon(1S)$, $\Upsilon(2S)$ and $\Upsilon(3S)$ in vacuum as well as in quark-gluon plasma. Our study is based on 2+1 flavor $48^3 \times 12$ lattices generated using the Highly Improved Staggered Quark (HISQ) action and with a pion mass of $161$ MeV. At zero temperature the Bethe-Salpeter amplitudes follow the expectations based on non-relativistic potential models. At non-zero temperatures, the interpretation of Bethe-Salpeter amplitudes turns out to be more nuanced, but consistent with our previous lattice QCD study of excited Upsilons in quark-gluon plasma., Comment: RevTex, 10pages, 11 figures, minor changes, published version

Adding a hard photon to the final state of a leptonic pseudoscalar-meson decay lifts the helicity suppression and can provide sensitivity to a larger set of operators in the weak effective Hamiltonian. Furthermore, radiative leptonic $B$ decays at high photon energy are well suited to constrain the first inverse moment of the $B$-meson light-cone distribution amplitude, an important parameter in the theory of nonleptonic $B$ decays. We demonstrate that the calculation of radiative leptonic decays is possible using Euclidean lattice QCD, and present preliminary numerical results for $D_s^+ \to \ell^+ \nu\gamma$ and $K^- \to \ell^-\bar{\nu}\gamma$.

We present the first lattice QCD study of up to $3S$ and $2P$ bottomonia at non-zero temperatures. Correlation functions of bottomonia were computed using novel bottomonium operators and a variational technique, within the lattice non-relativistic QCD framework. We analyzed the bottomonium correlation functions based on simple physically-motivated spectral functions. We found evidence of sequential in-medium modifications, in accordance with the sizes of the bottomonium states., published version with ancillary files added

We present lattice non-relativistic QCD calculations of bottomonium correlation functions at temperatures $T \simeq 150-350$ MeV. The correlation functions were computed using extended bottomonium operators, and on background gauge-field configurations for 2+1-flavor QCD having physical kaon and nearly-physical pion masses. We analyzed these correlation functions based on simple theoretically-motivated parameterizations of the corresponding spectral functions. The results of our analyses are compatible with significant in-medium thermal broadening of the ground state S- and P-wave bottomonia., Comment: published version with ancillary files

Quark orbital angular momentum (OAM) in the proton can be calculated directly given a Wigner function encoding the simultaneous distribution of quark transverse positions and momenta. This distribution can be accessed via proton matrix elements of a quark bilocal operator (the separation in which is Fourier conjugate to the quark momentum) featuring a momentum transfer (which is Fourier conjugate to the quark position). To generate the weighting by quark transverse position needed to calculate OAM, a derivative with respect to momentum transfer is consequently required. This derivative is evaluated using a direct derivative method, i.e., a method in which the momentum derivative of a correlator is directly sampled in the lattice calculation, as opposed to extracting it a posteriori from the numerical correlator data. The method removes the bias stemming from estimating the derivative a posteriori that was seen to afflict a previous exploratory calculation. Data for Ji OAM generated on a clover ensemble at pion mass $m_{\pi } = 317\, \mbox{MeV} $ are seen to agree with the result obtained via the traditional Ji sum rule method. By varying the gauge connection in the quark bilocal operator, also Jaffe-Manohar OAM is extracted, and seen to be enhanced significantly compared to Ji OAM., Comment: 7 pages, 3 figures, to appear in the proceedings of the 23rd International Spin Physics Symposium (SPIN2018), 10-14 September 2018, Ferrara, Italy, and in the proceedings of the 36th Annual International Symposium on Lattice Field Theory (LATTICE2018), 22-28 July 2018, Michigan State University, East Lansing, Michigan, USA

It would be very useful to find a way of reducing excited-state effects in lattice QCD calculations of nucleon structure that has a low computational cost. We explore the use of hybrid interpolators, which contain a nontrivial gluonic excitation, in a variational basis together with the standard interpolator with tuned smearing width. Using the clover discretization of the field strength tensor, a calculation using a fixed linear combination of standard and hybrid interpolators can be done using the same number of quark propagators as a standard calculation, making this a cost-effective option. We find that such an interpolator, optimized by solving a generalized eigenvalue problem, reduces excited-state contributions in two-point correlators. However, the effect in three-point correlators, which are needed for computing nucleon matrix elements, is mixed: for some matrix elements such as the tensor charge, excited-state effects are suppressed, whereas for others such as the axial charge, they are enhanced. The results illustrate that the variational method is not guaranteed to reduce the net contribution from excited states except in its asymptotic regime, and suggest that it may be important to use a large basis of interpolators capable of isolating all of the relevant low-lying states., 12 pages, 8 figures

We use lattice QCD to investigate the spectrum of the $\overline{b}\overline{b}ud$ four-quark system with quantum numbers $I({J}^{P})=0({1}^{+})$. We use five different gauge-link ensembles with $2+1$ flavors of domain-wall fermions, including one at the physical pion mass, and treat the heavy $\overline{b}$ quark within the framework of lattice nonrelativistic QCD. Our work improves upon previous similar computations by considering in addition to local four-quark interpolators also nonlocal two-meson interpolators and by performing a L\"uscher analysis to extrapolate our results to infinite volume. We obtain a binding energy of $(\ensuremath{-}128\ifmmode\pm\else\textpm\fi{}24\ifmmode\pm\else\textpm\fi{}10)\text{ }\text{ }\mathrm{MeV}$, corresponding to the mass $(10476\ifmmode\pm\else\textpm\fi{}24\ifmmode\pm\else\textpm\fi{}10)\text{ }\text{ }\mathrm{MeV}$, which confirms the existence of a $\overline{b}\overline{b}ud$ tetraquark that is stable with respect to the strong and electromagnetic interactions.

We report on lattice QCD calculations of the nucleon isovector axial, scalar, and tensor charges. Our calculations are performed on two 2+1-flavor ensembles generated using a 2-HEX-smeared Wilson-clover action at the physical pion mass and lattice spacings $a\approx$ 0.116 and 0.093 fm. We use a wide range of source-sink separations - eight values ranging from roughly 0.4 to 1.4 fm on the coarse ensemble and three values from 0.9 to 1.5 fm on the fine ensemble - which allows us to perform an extensive study of excited-state effects using different analysis and fit strategies. To determine the renormalization factors, we use the nonperturbative Rome-Southampton approach and compare RI'-MOM and RI-SMOM intermediate schemes to estimate the systematic uncertainties. Our final results are computed in the MS-bar scheme at scale 2 GeV. The tensor and axial charges have uncertainties of roughly 4%, $g_T=0.972(41)$ and $g_A=1.265(49)$. The resulting scalar charge, $g_S=0.927(303)$, has a much larger uncertainty due to a stronger dependence on the choice of intermediate renormalization scheme and on the lattice spacing., Comment: 24 pages, 13 figures, 9 tables. v2: added references. v3: additional discussion of systematics and summary plot showing calculations by other groups

We use lattice QCD and the L\"uscher method to study elastic pion-nucleon scattering in the isospin $I = 3/2$ channel, which couples to the $\Delta(1232)$ resonance. Our $N_f=2+1$ flavor lattice setup features a pion mass of $m_\pi \approx 250$ MeV, such that the strong decay channel $\Delta \rightarrow \pi N$ is close to the threshold. We present our method for constructing the required lattice correlation functions from single- and two-hadron interpolating fields and their projection to irreducible representations of the relevant symmetry group of the lattice. We show preliminary results for the energy spectra in selected moving frames and irreducible representations, and extract the scattering phase shifts. Using a Breit-Wigner fit, we also determine the resonance mass $m_\Delta$ and the $g_{\Delta-\pi N}$ coupling.

In this project, we will compute the form factors relevant for $B \to K^*(\to K \pi)\ell^+\ell^-$ decays. To map the finite-volume matrix elements computed on the lattice to the infinite-volume $B \to K \pi$ matrix elements, the $K \pi$ scattering amplitude needs to be determined using Luscher's method. Here we present preliminary results from our calculations with $2+1$ flavors of dynamical clover fermions. We extract the $P$-wave scattering phase shifts and determine the $K^*$ resonance mass and the $K^* K \pi$ coupling for two different ensembles with pion masses of $317(2)$ and $178(2)$ MeV.

We present results on the nucleon electromagnetic form factors from Lattice QCD at momentum transfer up to about $12$~GeV$^2$. We analyze two gauge ensembles with the Wilson-clover fermion action, a lattice spacing of $a\approx 0.09$~fm and pion masses $m_\pi\approx 170$~MeV and $m_\pi\approx 280$~MeV. In our analysis we employ momentum smearing as well as a set of techniques to investigate excited state effects. Good agreement with experiment and phenomenology is found for the ratios $G_E/G_M$ and $F_2/F_1$, whereas discrepancies are observed for the individual form factors $F_1$ and $F_2$. We discuss various systematics that may affect our calculation., Comment: 7 pages, 7 figures. Conference: The 36th Annual International Symposium on Lattice Field Theory (LATTICE2018)

We present the results of our lattice QCD study of the $\pi\gamma\to\pi\pi$ process, where the $\rho$ resonance appears as an enhancement in the transition amplitude. We use $N_f=2+1$ clover fermions on a lattice of $L=3.6$ fm and a pion mass of $320$ MeV. Using a combination of forward, stochastic, and sequential propagators, we calculate the two-point and three-point functions that allow us to determine the $\pi\gamma\to\pi\pi$ matrix elements for several values of the invariant mass $s$ and momentum transfer $q^2$. To fit the $q^2$ and $s$ dependence of the $\pi\gamma\to\pi\pi$ amplitude, we explore a set of general parametrizations based on a Taylor expansion. By analytic continuation to the complex pole corresponding to the $\rho$ resonance, we determine the resonant form factors and calculate the radiative decay width of the $\rho$.

This document is one of a series of whitepapers from the USQCD collaboration. Here, we discuss opportunities for lattice QCD calculations related to the structure and spectroscopy of hadrons and nuclei. An overview of recent lattice calculations of the structure of the proton and other hadrons is presented along with prospects for future extensions. Progress and prospects of hadronic spectroscopy and the study of resonances in the light, strange and heavy quark sectors is summarized. Finally, recent advances in the study of light nuclei from lattice QCD are addressed, and the scope of future investigations that are currently envisioned is outlined., 45 pages

This document is one of a series of whitepapers from the USQCD collaboration. Here, we discuss opportunities for lattice QCD in quark and lepton flavor physics. New data generated at Belle II, LHCb, BES III, NA62, KOTO, and Fermilab E989, combined with precise calculations of the relevant hadronic physics, may reveal what lies beyond the Standard Model. We outline a path toward improvements of the precision of existing lattice-QCD calculations and discuss groundbreaking new methods that allow lattice QCD to access new observables., Comment: USQCD whitepaper

We report on our investigation of low-energy pion-nucleon scattering from lattice QCD with Wilson type fermions. Our focus is on the isospin I = 3/2 channel, which couples to the Delta resonance. We discuss our calculations aiming at the extraction of the Delta resonance mass, width and effective coupling at pion mass 250 MeV, using the Lüscher finite-volume method to extract the phase shift δJ=3/2,l=1.

We report a lattice QCD determination of the $\pi\gamma \to \pi\pi$ transition amplitude for the $P$-wave, $I=1$ two-pion final state, as a function of the photon virtuality and $\pi\pi$ invariant mass. The calculation was performed with $2+1$ flavors of clover fermions at a pion mass of approximately $320$ MeV, on a $32^3 \times 96$ lattice with $L\approx 3.6$ fm. We construct the necessary correlation functions using a combination of smeared forward, sequential and stochastic propagators, and determine the finite-volume matrix elements for all $\pi\pi$ momenta up to $|\vec{P}|= \sqrt{3} \frac{2\pi}{L}$ and all associated irreducible representations. In the mapping of the finite-volume to infinite-volume matrix elements using the Lellouch-Luscher factor, we consider two different parametrizations of the $\pi\pi$ scattering phase shift. We fit the $q^2$ and $s$ dependence of the infinite-volume transition amplitude in a model-independent way using series expansions, and compare multiple different truncations of this series. Through analytic continuation to the $\rho$ resonance pole, we also determine the $\pi\gamma \to \rho$ resonant transition form factor and the $\rho$ meson photocoupling, and obtain $|G_{\rho\pi\gamma}| = 0.0802(32)(20)$.

In this write-up we review and update our recent lattice QCD calculation of $B \to K^*$, $B_s \to \phi$, and $B_s \to K^*$ form factors [arXiv:1310.3722]. These unquenched calculations, performed in the low-recoil kinematic regime, provide a significant improvement over the use of extrapolated light cone sum rule results. The fits presented here include further kinematic constraints and estimates of additional correlations between the different form factor shape parameters. We use these form factors along with Standard Model determinations of Wilson coefficients to give Standard Model predictions for several observables [arXiv:1310.3887]. The modest improvements to the form factor fits lead to improved determinations of $F_L$, the fraction of longitudinally polarized vector mesons, but have little effect on most other observables., Comment: Contribution to the Proceedings of the 32nd International Symposium on Lattice Field Theory (LATTICE 2014), 23-28 June 2014, Columbia University. 13 pages (7 pp to appear in Proceedings of Science + 6 pp of supplementary details). Fits in v2 use block-diagonal correlations (results not significantly changed). v2 corrects a permutation of columns in Table 8/11 of v1/v2. Reference added

National Science Foundation [PHY-1520996, ACI-1053575]; RHIC Physics Fellow Program of the RIKEN BNL Research Center; National Energy Research Scientific Computing Center, a DOE Office of Science User Facility; Office of Science of the U.S. Department of Energy [DE-AC02-05CH11231]

We describe a procedure for extracting momentum derivatives of nucleon matrix elements on the lattice directly at ${Q}^{2}=0$. This is based on the Rome method for computing momentum derivatives of quark propagators. We apply this procedure to extract the nucleon isovector magnetic moment and charge radius as well as the isovector induced pseudoscalar form factor at ${Q}^{2}=0$ and the axial radius. For comparison, we also determine these quantities with the traditional approach of computing the corresponding form factors, i.e. ${G}_{E}^{v}({Q}^{2})$ and ${G}_{M}^{v}({Q}^{2})$ for the case of the vector current and ${G}_{P}^{v}({Q}^{2})$ and ${G}_{A}^{v}({Q}^{2})$ for the axial current, at multiple ${Q}^{2}$ values followed by $z$-expansion fits. We perform our calculations at the physical pion mass using a 2HEX-smeared Wilson-clover action. To control the effects of excited-state contamination, the calculations were done at three source-sink separations and the summation method was used. The derivative method produces results consistent with those from the traditional approach but with larger statistical uncertainties especially for the isovector charge and axial radii.

National Science Foundation [ACI-1053575, PHY-1520996]; RHIC Physics Fellow Program of the RIKEN BNL Research Center; U.S. Department of Energy Office of Nuclear Physics [DE-SC-0011090, DE-FC02-06ER41444]; European Union [642069]; HPC-LEAP joint doctorate program; Office of Science of the U.S. Department of Energy [DE-AC02-05CH11231]

In a recent paper we studied the effect of new-physics operators with different Lorentz structures on the semileptonic Λ b → Λ c τ ν ¯ τ $$ {\Lambda}_b\to {\Lambda}_c\tau {\overline{\nu}}_{\tau } $$ decay. This decay is of interest in light of the R(D (*)) puzzle in the semileptonic B ¯ → D ∗ τ ν ¯ τ $$ \overline{B}\to {D}^{\left(\ast \right)}\tau {\overline{\nu}}_{\tau } $$ decays. In this work we add tensor operators to extend our previous results and consider both model-independent new physics (NP) and specific classes of models proposed to address the R(D (*)) puzzle. We show that a measurement of R Λ c = ℬ Λ b → Λ c τ ν ¯ τ / ℬ Λ b → Λ c ℓ ν ¯ ℓ $$ R\left({\Lambda}_c\right)=\mathrm{\mathcal{B}}\left[{\Lambda}_b\to {\Lambda}_c\tau {\overline{\nu}}_{\tau}\right]/\mathrm{\mathcal{B}}\left[{\Lambda}_b\to {\Lambda}_c\ell {\overline{\nu}}_{\ell}\right] $$ can strongly constrain the NP parameters of models discussed for the R(D (*)) puzzle. We use form factors from lattice QCD to calculate all Λ b → Λ c τ ν ¯ τ $$ {\Lambda}_b\to {\Lambda}_c\tau {\overline{\nu}}_{\tau } $$ observables. The Λ b → Λ c tensor form factors had not previously been determined in lattice QCD, and we present new lattice results for these form factors here.

National Science Foundation [PHY-1520996, ACI-1053575]; RHIC Physics Fellow Program of the RIKEN BNL Research Center; National Energy Research Scientific Computing Center; U.S. Department of Energy [DE-AC02-05CH11231]

Physical review / D 95(11), 114502(2017). doi:10.1103/PhysRevD.95.114502, We report a calculation of the nucleon axial form factors $G^{q}_{A}(Q^{2})$ and $G^{q}_{P}(Q^{2})$ for all three light quark flavors $q ∈ {u,d,s}$ in the range $0 ≤ Q^2 ≲ 1.2 GeV^2$ using lattice QCD. This work was done using a single ensemble with pion mass 317 MeV and made use of the hierarchical probing technique to efficiently evaluate the required disconnected loops. We perform nonperturbative renormalization of the axial current, including a nonperturbative treatment of the mixing between light and strange currents due to the singlet-nonsinglet difference caused by the axial anomaly. The form factor shapes are fit using the model-independent z expansion. From $G^{q}_{A}(Q^{2})$, we determine the quark contributions to the nucleon spin and axial radii. By extrapolating the isovector $G^{u-d}_{P}(Q^{2})$, we obtain the induced pseudoscalar coupling relevant for ordinary muon capture and the pion-nucleon coupling constant. We find that the disconnected contributions to GP form factors are large, and give an interpretation based on the dominant influence of the pseudoscalar poles in these form factors., Published by APS, Woodbury, NY

We describe a lattice approach for directly computing momentum derivatives of nucleon matrix elements using the Rome method, which we apply to obtain the isovector magnetic moment and Dirac radius. We present preliminary results calculated at the physical pion mass using a 2HEX-smeared Wilson-clover action. For removing the effects of excited-state contamination, the calculations were done at three source-sink separations and the summation method was used.

Lattice QCD calculations of radiative transitions between hadrons have in the past been limited to processes of hadrons stable under the strong interaction. Recently developed methods for $1\to2$ transition matrix elements in a finite volume now enable the determination of radiative decay rates of strongly unstable particles. Our lattice QCD study focuses on the process $\pi \pi \to \pi \gamma^{\ast}$, where the $\rho$ meson is present as an enhancement in the cross-section. We use $2+1$ flavors of clover fermions at a pion mass of approximately $320$ MeV and a lattice size of approximately $3.6$ fm. The required $2$-point and $3$-point correlation functions are constructed from a set of forward, sequential and stochastic light quark propagators. In addition to determining the $\rho$ meson resonance parameters via the Luscher method, the scattering phase shift is used in conjunction with the $1\to2$ transition matrix element formalism of Brice\~no, Hansen and Walker-Loud \cite{Briceno:2014uqa} to compute the $\pi\pi\to\pi\gamma^{\ast}$ amplitude at several values of the momentum transfer and $\pi\pi$ invariant mass.

The first lattice QCD calculation of the form factors governing Λ_{c}→Λℓ^{+}ν_{ℓ} decays is reported. The calculation was performed with two different lattice spacings and includes one ensemble with a pion mass of 139(2) MeV. The resulting predictions for the Λ_{c}→Λe^{+}ν_{e} and Λ_{c}→Λμ^{+}ν_{μ} decay rates divided by |V_{cs}|^{2} are 0.2007(71)(74) and 0.1945(69)(72) ps^{-1}, respectively, where the two uncertainties are statistical and systematic. Taking the Cabibbo-Kobayashi-Maskawa (CKM) matrix element |V_{cs}| from a global fit and the Λ_{c} lifetime from experiments, this translates to branching fractions of B(Λ_{c}→Λe^{+}ν_{e})=0.0380(19)_{LQCD}(11)_{τ_{Λ_{c}}} and B(Λ_{c}→Λμ^{+}ν_{μ})=0.0369(19)_{LQCD}(11)_{τ_{Λ_{c}}}. These results are consistent with, and two times more precise than, the measurements performed recently by the BESIII Collaboration. Using instead the measured branching fractions together with the lattice calculation to determine the CKM matrix element gives |V_{cs}|=0.949(24)_{LQCD}(14)_{τ_{Λ_{c}}}(49)_{B}.

Experimental results for mesonic $b \to s \mu^+ \mu^-$ decays show a pattern of deviations from Standard-Model predictions, which could be due to new fundamental physics or due to an insufficient understanding of hadronic effects. Additional information on the $b \to s \mu^+ \mu^-$ transition can be obtained from $\Lambda_b$ decays. This was recently done using the process $\Lambda_b \to \Lambda \mu^+ \mu^-$, where the $\Lambda$ is the lightest strange baryon. A further interesting channel is $\Lambda_b \to p^+ K^- \mu^+ \mu^-$, where the $p^+ K^-$ final state receives contributions from multiple higher-mass $\Lambda$ resonances. The narrowest and most prominent of these is the $\Lambda(1520)$, which has $J^P=\frac32^-$. Here we present an ongoing lattice QCD calculation of the relevant $\Lambda_b \to \Lambda(1520)$ form factors. We discuss the choice of interpolating field for the $\Lambda(1520)$, and explain our method for extracting the fourteen $\Lambda_b \to \Lambda(1520)$ helicity form factors from correlation functions that are computed in the $\Lambda(1520)$ rest frame. We present preliminary numerical results at a pion mass of 340 MeV and a lattice spacing of 0.11 fm. This calculation uses a domain-wall action for the $u$, $d$, and $s$ quarks and a relativistic heavy-quark action for the $b$ quark, and is based on gauge-field configurations generated by the RBC and UKQCD Collaborations., Comment: 7 pages, 3 figures

We study the impact of including the baryonic decay ${\mathrm{\ensuremath{\Lambda}}}_{b}\ensuremath{\rightarrow}\mathrm{\ensuremath{\Lambda}}(\ensuremath{\rightarrow}p{\ensuremath{\pi}}^{\ensuremath{-}}){\ensuremath{\mu}}^{+}{\ensuremath{\mu}}^{\ensuremath{-}}$ in a Bayesian analysis of $|\mathrm{\ensuremath{\Delta}}B|=|\mathrm{\ensuremath{\Delta}}S|=1$ transitions. We perform fits of the Wilson coefficients ${\mathcal{C}}_{9}$, ${\mathcal{C}}_{{9}^{\ensuremath{'}}}$, ${\mathcal{C}}_{10}$ and ${\mathcal{C}}_{1{0}^{\ensuremath{'}}}$, in addition to the relevant nuisance parameters. Our analysis combines data for the differential branching fraction and three angular observables of ${\mathrm{\ensuremath{\Lambda}}}_{b}\ensuremath{\rightarrow}\mathrm{\ensuremath{\Lambda}}(\ensuremath{\rightarrow}p{\ensuremath{\pi}}^{\ensuremath{-}}){\ensuremath{\mu}}^{+}{\ensuremath{\mu}}^{\ensuremath{-}}$ with data for the branching ratios of ${B}_{s}\ensuremath{\rightarrow}{\ensuremath{\mu}}^{+}{\ensuremath{\mu}}^{\ensuremath{-}}$ and inclusive $b\ensuremath{\rightarrow}s{\ensuremath{\ell}}^{+}{\ensuremath{\ell}}^{\ensuremath{-}}$ decays. Newly available precise lattice QCD results for the full set of ${\mathrm{\ensuremath{\Lambda}}}_{b}\ensuremath{\rightarrow}\mathrm{\ensuremath{\Lambda}}$ form factors are used to evaluate the observables of the baryonic decay. Our fits prefer shifts to ${\mathcal{C}}_{9}$ that are opposite in sign compared to those found in global fits of only mesonic decays, and the posterior odds show no evidence of physics beyond the Standard Model. We investigate a possible hadronic origin of the observed tensions between theory and experiment.