Two-flavor Lattice Research Articles

Preparations for quantum simulations of quantum chromodynamics in 1+1 dimensions. II. Single-baryon β -decay in real time

A framework for quantum simulations of real-time weak decays of hadrons and nuclei in a two-flavor lattice theory in one spatial dimension is presented. A single generation of the Standard Model is found to require 16 qubits per spatial lattice site after mapping to spin operators via the Jordan-Wigner transformation. Both quantum chromodynamics and flavor-changing weak interactions are included in the dynamics, the latter through four-Fermi effective operators. Quantum circuits that implement time evolution in this lattice theory are developed and run on Quantinuum's H1-1 20-qubit trapped ion system to simulate the $\ensuremath{\beta}$-decay of a single baryon on one lattice site. These simulations include the initial state preparation and are performed for both one and two Trotter time steps. The potential intrinsic error-correction properties of this type of lattice theory are discussed, and the leading lattice Hamiltonian required to simulate $0\ensuremath{\nu}\ensuremath{\beta}\ensuremath{\beta}$-decay of nuclei induced by a neutrino Majorana mass term is provided.

Neural-network preconditioners for solving the Dirac equation in lattice gauge theory

This work develops neural-network--based preconditioners to accelerate solution of the Wilson-Dirac normal equation in lattice quantum field theories. The approach is implemented for the two-flavor lattice Schwinger model near the critical point. In this system, neural-network preconditioners are found to accelerate the convergence of the conjugate gradient solver compared with the solution of unpreconditioned systems or those preconditioned with conventional approaches based on even-odd or incomplete Cholesky decompositions, as measured by reductions in the number of iterations and/or complex operations required for convergence. It is also shown that a preconditioner trained on ensembles with small lattice volumes can be used to construct preconditioners for ensembles with many times larger lattice volumes, with minimal degradation of performance. This volume-transferring technique amortizes the training cost and presents a pathway towards scaling such preconditioners to lattice field theory calculations with larger lattice volumes and in four dimensions.

Decay constant of B_s and B^*_s mesons from mathrm{N_f}=2 lattice QCD

We report on a two-flavor lattice QCD estimate of the B_s and B^*_s leptonic decays parameterized by the decay constants f_{B_s} and f_{B^*_s}. In addition to their relevance for phenomenology, their extraction has allowed us to investigate whether the “step scaling in mass” strategy is suitable with Wilson–Clover fermions to smoothly extrapolate quantities of the heavy-strange sector up to the bottom scale. From the central value of f_{D_s} quoted by FLAG at N_f=2 and our ratio frac{f_{B_s}}{f_{D_s}}, we obtain f_{B_s}=215(10)(2)(^{+2}_{-5}) MeV and f_{B^*_s}/f_{B_s}=1.02(2)(^{+2}_{-0}).

Nucleon generalized form factors from two-flavor lattice QCD

We determine the generalized form factors, which correspond to the second Mellin moment (i.e., the first $x$-moment) of the generalized parton distributions of the nucleon at leading twist. The results are obtained using lattice QCD with $N_f=2$ nonperturbatively improved Wilson fermions, employing a range of quark masses down to an almost physical value with a pion mass of about 150 MeV. We also present results for the isovector quark angular momentum and for the first $x$-moment of the transverse quark spin density. We compare two different fit strategies and find that directly fitting the ground state matrix elements to the functional form expected from Lorentz invariance and parametrized in terms of form factors yields comparable, and usually more stable results than the traditional approach where the form factors are determined from an overdetermined linear system based on the fitted matrix elements.

Isovector axial form factors of the nucleon in two-flavor lattice QCD

We present a lattice calculation of the nucleon isovector axial and induced pseudoscalar form factors on the CLS ensembles using [Formula: see text] dynamical flavors of nonperturbatively [Formula: see text]-improved Wilson fermions and an [Formula: see text]-improved axial current together with the pseudoscalar density. Excited-state effects in the extraction of the form factors are treated using a variety of methods, with a detailed discussion of their respective merits. The chiral and continuum extrapolation of the results is performed both using formulae inspired by Heavy Baryon Chiral Perturbation Theory (HBChPT) and a global approach to the form factors based on a chiral effective field theory (EFT) including axial vector mesons. Our results indicate that careful treatment of excited-state effects is important in order to obtain reliable results for the axial form factors of the nucleon, and that the main remaining error stems from the systematic uncertainties of the chiral extrapolation. As final results, we quote [Formula: see text], [Formula: see text], and [Formula: see text] for the axial charge, axial charge radius and induced pseudoscalar charge, respectively, where the first error is statistical and the second is systematic.

Some hadronic parameters of charmonia in varvec{N_{text {f}}=2} lattice QCD

The phenomenology of leptonic decays of quarkonia holds many interesting features: for instance, it can establish constraints on scenarios beyond the Standard Model with the Higgs sector enriched by a light CP-odd state. In the following paper, we report on a two-flavor lattice QCD study of the eta _c and J/psi decay constants, f_{eta _c}=387(3)(3), {mathrm{MeV}} and f_{J/psi }=399(4)(2), {mathrm{MeV}}. We also examine some properties of the first radial excitation eta _c(2S) and psi (2S).

Axial U(1) symmetry at high temperature in 2-flavor lattice QCD

We investigate the axial U(1)A symmetry breaking above the critical temperature in two-flavor lattice QCD. The ensembles are generated with dynamical Möbius domain-wall or reweighted overlap fermions. The U(1)A susceptibility is extracted from the low-modes spectrum of the overlap Dirac eigenvalues. We show the quark mass and temperature dependences of U(1)A susceptibility. Our results at T = 220MeV imply that the U(1)A symmetry is restored in the chiral limit. Its coincidence with vanishing topological susceptibility is observed.

Can axial U(1) anomaly disappear at high temperature?

In our recent study of two-flavor lattice QCD using chiral fermions, we find strong suppression of axial U(1) anomaly above the critical temperature of chiral phase transition. Our simulation data also indicate suppression of topological susceptibility. In this talk, we present both of our theoretical and numerical evidence for disappearance of axial U(1) anomaly, emphasizing the importance of controlling lattice chiral symmetry violation, which is enhanced at high temperature.

Evidence of effective axialU(1)symmetry restoration at high temperature QCD

We study the axial U(1) symmetry at finite temperature in two-flavor lattice QCD. Employing the Mobius domain-wall fermions, we generate gauge configurations slightly above the critical temperature Tc with different lattice sizes L = 2-4 fm. Our action allows frequent topology tunneling while keeping good chiral symmetry close enough to that of overlap fermions. This allows us to recover full chiral symmetry by an overlap/domain-wall reweighting. Above the phase transition, a strong suppression of the low-lying modes is observed in both of overlap and domain-wall Dirac spectra. We, however, find a sizable violation of the Ginsparg-Wilson relation in the Mobius domain-wall Dirac eigenmodes, which dominates the signals of the axial U(1) symmetry breaking near the chiral limit. We also find that the use of overlap fermion only in the valence sector is dangerous since it suffers from the artifacts due to partial quenching. Reweighting the Mobius domain-wall fermion determinant to that of the overlap fermion, we observe the axial U(1) breaking to vanish in the chiral limit, which is stable against the changes of the lattice volume and lattice spacing.

Symmetry restoration at high-temperature in two-color and two-flavor lattice gauge theories

We consider the SU(2) gauge theory with Nf = 2 flavors of Dirac fundamental fermions. We study the high-temperature behavior of the spectra of mesons, discretizing the theory on anisotropic lattices, and measuring the two-point correlation functions in the temporal direction as well as screening masses in various channels. We identify the (pseudo-)critical temperature as the temperature at which the susceptibility associated with the Polyakov loop has a maximum. At high temperature both the spin-1 and spin-0 sectors of the light meson spectra exhibit enhanced symmetry properties, indicating the restoration of both the global SU(4) and the axial U(1)A symmetries of the model.

Role of the strange quark in theρ(770) meson

Recently, the GWU lattice group has evaluated high-precision phase-shift data for $\pi\pi$ scattering in the $I = 1$, $J = 1$ channel. Unitary Chiral Perturbation Theory describes these data well around the resonance region and for different pion masses. Moreover, it allows to extrapolate to the physical point and estimate the effect of the missing $K\bar{K}$ channel in the two-flavor lattice calculation. The absence of the strange quark in the lattice data leads to a lower $\rho$ mass, and the analysis with U$\chi$PT shows that the $K \bar{K}$ channel indeed pushes the $\pi\pi$-scattering phase shift upward, having a surprisingly large effect on the $\rho$-mass. The inelasticity is shown to be compatible with the experimental data. The analysis is then extended to all available two-flavor lattice simulations and similar mass shifts are observed. Chiral extrapolations of $N_f = 2 + 1$ lattice simulations for the $\rho(770)$ are also reported.

Density distributions in the B meson

We report on a two-flavor lattice QCD study of the axial, charge and matter distributions of the $B$ meson and its first radial excitation. As our framework is the static limit of Heavy Quark Effective Theory (HQET), taking their Fourier transform gives access to several form factors at the kinematical point $q^2=0$. Moreover they provide some useful information on the nature of an excited state, i.e. a radial excitation of a quark-antiquark bound state or a multihadron state.

Chiral and deconfining phase transitions from holographic QCD study

A preliminary quantitative study to match the lattice QCD simulation on the chiral and deconfining phase transitions of QCD in the bottom-up holographic framework is given. We constrain the relation between dilaton field ϕ and metric warp factor Ae and get several reasonable models in the Einstein-Dilaton system. Using the potential reconstruction approach, we solve the corresponding gravity background. Then we fit the background-related parameters by comparing the equation of state with the two-flavor lattice QCD results. After that we study the temperature dependent behavior of Polyakov loop and chiral condensate under those background solutions. We find that the results are in good agreement with the two-flavor lattice results. All the studies about the equation of state, the Polyakov loop and the chiral condensate signal crossover behavior of the phase transitions, which are consistent with the current understanding on the QCD phase transitions with physical quark mass. Furthermore, the extracted transition temperatures are comparable with the two-flavor lattice QCD results.

Pion couplings to the scalar $$B$$ B meson

We present two-flavor lattice QCD estimates of the hadronic couplings $g_{B^*_0 B \pi}$ and $g_{B_1^* B_0^* \pi}$ that parametrise the non leptonic decays $B^*_0 \to B \pi$ and $B^*_1 \to B_0^* \pi$. We use CLS two-flavour gauge ensembles. Our framework is the Heavy Quark Effective Theory (HQET) in the static limit and solving a Generalized Eigenvalue Problem (GEVP) reveals crucial to disentangle the $B^*_0$($B^*_1$) state from the $B \pi$($B^*\pi$) state. This work brings us some experience on how to treat the possible contribution from multihadronic states to correlation functions calculated on the lattice, especially when $S$-wave states are involved.

Vector screening masses in the quark–gluon plasma and their physical significance

Static and non-static thermal screening states that couple to the conserved vector current are investigated in the high-temperature phase of QCD . Their masses and couplings to the current are determined at weak coupling, as well as using two-flavor lattice QCD simulations. A consistent picture emerges from the comparison, providing evidence that non-static Matsubara modes can indeed be treated perturbatively. We elaborate on the physical significance of the screening masses.

Deconfinement transition in two-flavor lattice QCD with dynamical overlap fermions in an external magnetic field

We study the influence of an external magnetic field on the deconfinement transition in two-flavour lattice QCD with physical quark charges. We use dynamical overlap fermions without any approximation such as fixed topology and perform simulations on a $16^3 \times 6$ lattice and at a pion mass around $500MeV$. The pion mass (as well as the lattice spacing) was determined in independent runs on $12^3 \times 24$ lattices. We consider two temperatures, one of which is close to the deconfinement transition and one which is above. Within our limited statistics the dependence of the Polyakov loop and chiral condensate on the magnetic field supports the "inverse magnetic catalysis" scenario in which the transition temperature decreases as the field strength grows for temperature not to far above the critical temperature.

Scalar pion form factor in two-flavor lattice QCD

We calculate the scalar form factor of the pion using two dynamical flavors of non-perturbatively $\mathcal{O}(a)$-improved Wilson fermions, including both the connected and the disconnected contribution to the relevant correlation functions. We employ the calculation of all-to-all propagators using stochastic sources and a generalized hopping parameter expansion. From the form factor data at vanishing momentum transfer, $Q^2=0$, and two non-vanishing $Q^2$ we obtain an estimate for the scalar radius $\left<r^2\right>^\pi_{_{\rm S}}$ of the pion at one value of the lattice spacing and for five different pion masses. Using Chiral Perturbation Theory at next-to-leading order, we find $\left<r^2\right>^\pi_{_{\rm S}}=0.635\pm0.016$ fm$^2$ at the physical pion mass (statistical error only). This is in good agreement with the phenomenological estimate from $\pi\pi$-scattering. The inclusion of the disconnected contribution is essential for achieving this level of agreement.

Syndrome de Segawa : étude clinique de 2 familles tunisiennes

The axial charge of the nucleon gA and the pion decay constant fπ are computed in two-flavor lattice QCD. The simulations are carried out on lattices of various volumes and lattice spacings. Results are reported for pion masses as low as mπ=130MeV. Both quantities, gA and fπ, suffer from large finite size effects, which to leading order ChEFT and ChPT turn out to be identical. By considering the naturally renormalized ratio gA/fπ, we observe a universal behavior as a function of decreasing quark mass. From extrapolating the ratio to the physical point, we find gAR=1.29(5)(3), using the physical value of fπ as input and r0=0.50(1) to set the scale. In a subsequent calculation we attempt to extrapolate gA and fπ separately to the infinite volume. Both volume and quark mass dependencies of gA and fπ are found to be well described by ChEFT and ChPT. We find at the physical point gAR=1.24(4) and fπR=89.6(1.1)(1.8)MeV. Both sets of results are in good agreement with experiment. As a by-product we obtain the low-energy constant l¯4=4.2(1).

Nucleon axial charge and pion decay constant from two-flavor lattice QCD

The axial charge of the nucleon gA and the pion decay constant fπ are computed in two-flavor lattice QCD. The simulations are carried out on lattices of various volumes and lattice spacings. Results are reported for pion masses as low as mπ=130 MeV. Both quantities, gA and fπ, suffer from large finite size effects, which to leading order ChEFT and ChPT turn out to be identical. By considering the naturally renormalized ratio gA/fπ, we observe a universal behavior as a function of decreasing quark mass. From extrapolating the ratio to the physical point, we find gAR=1.29(5)(3), using the physical value of fπ as input and r0=0.50(1) to set the scale. In a subsequent calculation we attempt to extrapolate gA and fπ separately to the infinite volume. Both volume and quark mass dependencies of gA and fπ are found to be well described by ChEFT and ChPT. We find at the physical point gAR=1.24(4) and fπR=89.6(1.1)(1.8) MeV. Both sets of results are in good agreement with experiment. As a by-product we obtain the low-energy constant l¯4=4.2(1).

Color screening potential at finite density in two-flavor lattice QCD with Wilson fermions

We investigate the chemical-potential ($\ensuremath{\mu}$) dependence of static-quark free energies in both the real and imaginary $\ensuremath{\mu}$ regions, performing lattice QCD simulations at imaginary $\ensuremath{\mu}$ and extrapolating the results to the real-$\ensuremath{\mu}$ region with analytic continuation. Lattice QCD calculations are done on a ${16}^{3}\ifmmode\times\else\texttimes\fi{}4$ lattice with the clover-improved two-flavor Wilson fermion action and the renormalization-group-improved Iwasaki gauge action. Static-quark potentials are evaluated from the Polyakov-loop correlation functions in the deconfinement phase. To perform the analytic continuation, the potential calculated at imaginary $\ensuremath{\mu}=i{\ensuremath{\mu}}_{\mathrm{I}}$ is expanded into a Taylor expansion series of $i{\ensuremath{\mu}}_{\mathrm{I}}/T$ up to fourth order and the pure imaginary variable $i{\ensuremath{\mu}}_{\mathrm{I}}/T$ is replaced by the real one ${\ensuremath{\mu}}_{\mathrm{R}}/T$. At real $\ensuremath{\mu}$, the fourth-order term sizably weakens the $\ensuremath{\mu}$ dependence of the potential. At long distance, all of the color-singlet and -nonsinglet potentials tend to twice the single-quark free energy, indicating that the interactions between static quarks are fully color screened for finite $\ensuremath{\mu}$. For both real and imaginary $\ensuremath{\mu}$, the color-singlet $q\overline{q}$ and the color-antitriplet $qq$ interactions are attractive, whereas the color-octet $q\overline{q}$ and the color-sextet $qq$ interactions are repulsive. The attractive interactions have a stronger $\ensuremath{\mu}/T$ dependence than the repulsive interactions. The color-Debye screening mass is extracted from the color-singlet potential at imaginary $\ensuremath{\mu}$, and the mass is extrapolated to real $\ensuremath{\mu}$ by analytic continuation. The screening mass thus obtained has a stronger $\ensuremath{\mu}$ dependence than the prediction of hard-thermal-loop perturbation theory at both real and imaginary $\ensuremath{\mu}$.