arXiv subjects
Publications and source records attributed to Stefan Meinel.
We present a Lattice QCD calculation of the second Mellin moments of the nucleon axial, vector and tensor parton distribution functions (PDFs). The calculation is performed at the physical pion mass with two different lattice spacings, and includes both zero and non-zero nucleon momenta. In our preliminary analysis, we identify operators that greatly reduce excited-state contamination.
$V_{ub}$ is the smallest and least known of all CKM matrix elements; the community currently determines its magnitude primarily through the exclusive process $B\toπ\ell\barν$. Here we present our progress toward a lattice QCD determination of the $V_{ub}$ matrix element from a novel transition -- $B\toππ\ell\barν$ process, where the $ππ$ system is in a $P$ wave and scattering features the $ρ(770)$ resonance as an enhancement. We perform our calculation on $N_f=2+1$ isotropic clover fermions on a lattice of $L\approx 3.6$ fm and a pion mass of $\approx 320$ MeV; for the $b$-quark we use the anisotropic clover action. After a brief overview of the theoretical framework, we will discuss some preliminary results.
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 $D_s^+ \to \ell^+ νγ$. 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 $D_s^+ \to \ell^+ νγ$ 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.
The Heavy Quark Expansion (HQE) gives an expansion of inclusive decay rates of $b$-hadrons as a simultaneous series in $α_s$ and $1/m_b$, in terms of perturbatively defined coefficients and non-perturbative matrix elements. Spectator effects arise from the dimension-$6$ operators in the HQE in which along with the heavy quark, a light spectator quark from the hadron participates in the weak decay. In this work, we provide a lattice determination of the bare matrix elements that contribute to the spectator effects for the $B^+$-meson, $B_d$-meson and the $Λ_b$-baryon. The computations were performed on two separate lattice spacings of the RBC-UKQCD (2+1)-flavor Domain Wall Fermion ensembles. Renormalization and continuum extrapolation of the matrix elements have not yet been computed, and are left to future work.
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} $.
We present first results of a recently started lattice QCD investigation of antiheavy-antiheavy-light-light tetraquark systems including scattering interpolating operators in correlation functions both at the source and at the sink. In particular, we discuss the importance of such scattering interpolating operators for a precise computation of the low-lying energy levels. We focus on the $\bar b \bar b u d$ four-quark system with quantum numbers $I(J^P) = 0(1^+)$, which has a ground state below the lowest meson-meson threshold. We carry out a scattering analysis using Lüscher's method to extrapolate the binding energy of the corresponding QCD-stable tetraquark to infinite spatial volume. Our calculation uses clover $u$, $d$ valence quarks and NRQCD $b$ valence quarks on gauge-link ensembles with HISQ sea quarks that were generated by the MILC collaboration.
Contribution from the USQCD Collaboration to the Proceedings of the US Community Study on the Future of Particle Physics (Snowmass 2021).
Lattice gauge theory continues to be a powerful theoretical and computational approach to simulating strongly interacting quantum field theories, whose applications permeate almost all disciplines of modern-day research in High-Energy Physics. Whether it is to enable precision quark- and lepton-flavor physics, to uncover signals of new physics in nucleons and nuclei, to elucidate hadron structure and spectrum, to serve as a numerical laboratory to reach beyond the Standard Model, or to invent and improve state-of-the-art computational paradigms, the lattice-gauge-theory program is in a prime position to impact the course of developments and enhance discovery potential of a vibrant experimental program in High-Energy Physics over the coming decade. This projection is based on abundant successful results that have emerged using lattice gauge theory over the years: on continued improvement in theoretical frameworks and algorithmic suits; on the forthcoming transition into the exascale era of high-performance computing; and on a skillful, dedicated, and organized community of lattice gauge theorists in the U.S. and worldwide. The prospects of this effort in pushing the frontiers of research in High-Energy Physics have recently been studied within the U.S. decadal Particle Physics Planning Exercise (Snowmass 2021), and the conclusions are summarized in this Topical Report.
Precision measurements in weak decays of heavy flavored hadrons can test in unique ways our understanding of the fundamental interactions and of the observed baryon asymmetry in the Universe. The high sensitivity of such decays to beyond-Standard-Model physics, combined with the lack of major discoveries in direct production of new particles, motivates the continuation of a strong heavy-flavor program in the next decades. The observation of several anomalies by the BaBar, Belle and LHCb experiments in such decays, including evidence for violation of lepton universality, provides particular motivation to vigorously pursue this program. While the mass scales probed by direct searches for non-Standard-Model phenomena at the energy frontier will only marginally increase in the near future, a substantial advancement is expected in the study of weak decays of $b$ and $c$ quarks. The next 10 to 20 years will see the development of a highly synergistic program of experiments at both $pp$ and $e^+e^-$ colliders. This program will be complemented by advancements in theory, including both lattice and continuum calculations. Experimental measurements and theory predictions of several key observables will reach unprecedented precision and will allow to test the Standard Model in ways that have not been possible thus far. With a strong participation in this program, the US high-energy-physics community will remain at the forefront of indirect searches for new physics and retain its leading role in expanding humankind's understanding of fundamental interactions.
Lattice quantum chromodynamics has proven to be an indispensable method to determine nonperturbative strong contributions to weak decay processes. In this white paper for the Snowmass community planning process we highlight achievements and future avenues of research for lattice calculations of weak $b$ and $c$ quark decays, and point out how these calculations will help to address the anomalies currently in the spotlight of the particle physics community. With future increases in computational resources and algorithmic improvements, percent level (and below) lattice determinations will play a central role in constraining the standard model or identifying new physics.
We use lattice QCD to investigate the existence of strong-interaction-stable antiheavy-antiheavy-light-light tetraquarks. We study the $\bar b \bar b u s$ system with quantum numbers $J^P = 1^+$ as well as the $\bar b \bar c u d$ systems with quantum numbers $I(J^P) = 0(0^+)$ and $I(J^P) = 0(1^+)$. We carry out computations on five gauge-link ensembles with $2 + 1$ flavors of domain-wall fermions, including one at the physical pion mass. The bottom quarks are implemented using lattice nonrelativistic QCD, and the charm quarks using an anisotropic clover action. In addition to local diquark-antidiquark and local meson-meson interpolating operators, we include nonlocal meson-meson operators at the sink, which facilitates the reliable determination of the low-lying energy levels. We find clear evidence for the existence of a strong-interaction-stable $\bar b \bar b u s$ tetraquark with binding energy $(-86 \pm 22 \pm 10) \, \text{MeV}$ and mass $(10609 \pm 22 \pm 10) \, \text{MeV}$. For the $\bar b \bar c u d$ systems we do not find any indication for the existence of bound states, but cannot rule out their existence either.
We present the first lattice-QCD calculation of the form factors governing the charm-baryon semileptonic decays $Λ_c \to Λ^*(1520)\ell^+ν_\ell$. As in our previous calculation of the $Λ_b \to Λ^*(1520)$ form factors, we work in the $Λ^*(1520)$ rest frame, but here we use four different heavy-baryon momenta instead of just two. Because of the lower mass of the $Λ_c$, the moderately-sized momenta used here are sufficient to determine the form factors in the full kinematic range of the semileptonic decay. We also update the analysis of our lattice results for the $Λ_b \to Λ^*(1520)$ and $Λ_b \to Λ_c^*(2595,2625)$ form factors by imposing exact relations among the different form factors at zero recoil that follow from rotational symmetry. Imposing these relations ensures the correct behavior of the angular observables near the endpoint.
Understanding the properties of the strange $Λ^*$ baryon resonances is a long-standing and fascinating problem. $Λ_c$ 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 $Λ_c$ 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 $Λ_c\toΛ^*(1520)\ell^+ν_\ell$ differential and integrated decay rates as well as angular observables. Furthermore, by combining the recent BESIII measurement of the $Λ_c \to X e^+ ν_e$ inclusive semipositronic branching fraction [Phys. Rev. Lett. 121, 251801 (2018)] with lattice-QCD predictions of the $Λ_c \to Λe^+ ν_e$, $Λ_c \to n e^+ ν_e$, and $Λ_c \to Λ^*(1520) e^+ ν_e$ 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 $Λ_c\toΛ^*(1405)e^+ ν_e$ branching fraction to be very small, which may be another hint for a molecular structure of the $Λ^*(1405)$.
We report a lattice QCD determination of the $πγ\to ππ$ transition amplitude for the $P$-wave, $I=1$ two-pion final state, as a function of the photon virtuality and $ππ$ 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 $ππ$ momenta up to $|\vec{P}|= \sqrt{3} \frac{2π}{L}$ and all associated irreducible representations. In the mapping of the finite-volume to infinite-volume matrix elements using the Lellouch-Lüscher factor, we consider two different parametrizations of the $ππ$ 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 $ρ$ resonance pole, we also determine the $πγ\to ρ$ resonant transition form factor and the $ρ$ meson photocoupling, and obtain $|G_{ρπγ}| = 0.0802(32)(20)$.
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.
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.
Using $(2+1)$-flavor lattice QCD, we compute the 10 form factors describing the $Λ_b \to Λ$ matrix elements of the $b \to s$ vector, axial vector, and tensor currents. The calculation is based on gauge field ensembles generated by the RBC and UKQCD Collaborations with a domain-wall action for the $u$, $d$, and $s$ quarks and the Iwasaki gauge action. The $b$ quark is implemented using an anisotropic clover action, tuned nonperturbatively to the physical point, and the currents are renormalized with a mostly nonperturbative method. We perform simultaneous chiral, continuum, and kinematic extrapolations of the form factors through modified $z$ expansions. Using our form factor results, we obtain precise predictions for the $Λ_b \to Λ(\to p^+ π^-) μ^+ μ^-$ differential branching fraction and angular observables in the Standard Model.
A lattice QCD determination of the $Λ_c \to N$ vector, axial vector, and tensor form factors is reported. The calculation was performed with $2+1$ flavors of domain wall fermions at lattice spacings of $a\approx 0.11\:{\rm fm},\:0.085\:{\rm fm}$ and pion masses in the range $230\:{\rm MeV} \lesssim m_π\lesssim 350$ MeV. The form factors are extrapolated to the continuum limit and the physical pion mass using modified $z$ expansions. The rates of the charged-current decays $Λ_c \to n\, e^+ ν_e$ and $Λ_c \to n\, μ^+ ν_μ$ are predicted to be $\left( 0.405 \pm 0.016_{\,\rm stat} \pm 0.020_{\,\rm syst} \right)|V_{cd}|^2 \:{\rm ps}^{-1}$ and $\left( 0.396 \pm 0.016_{\,\rm stat} \pm 0.020_{\,\rm syst} \right)|V_{cd}|^2 \:{\rm ps}^{-1}$, respectively. The phenomenology of the rare charm decay $Λ_c \to p\, μ^+ μ^-$ is also studied. The differential branching fraction, the fraction of longitudinally polarized dimuons, and the forward-backward asymmetry are calculated in the Standard Model and in an illustrative new-physics scenario.