Search

We present a direct calculation for the first derivative of the isovector nucleon form factors with respect to the momentum transfer ${q}^{2}$ using the lower moments of the nucleon 3-point function in the coordinate space. Our numerical simulations are performed using the ${N}_{f}=2+1$ nonperturbatively $O(a)$-improved Wilson quark action and Iwasaki gauge action near the physical point, corresponding to the pion mass ${M}_{\ensuremath{\pi}}=138\text{ }\text{ }\mathrm{MeV}$, on a $(5.5\text{ }\text{ }\mathrm{fm}{)}^{4}$ lattice at a single lattice spacing of $a=0.085\text{ }\text{ }\mathrm{fm}$. In the momentum derivative approach, we can directly evaluate the mean square radii for the electric, magnetic, and axial-vector form factors, and also the magnetic moment without the ${q}^{2}$ extrapolation to the zero momentum point. These results are compared with the ones determined by the standard method, where the ${q}^{2}$ extrapolations of the corresponding form factors are carried out by fitting models. We find that the new results from the momentum derivative method are obtained with a larger statistical error than the standard method, but with a smaller systematic error associated with the data analysis. Within the total error range of the statistical and systematic errors combined, the two results are in good agreement. On the other hand, two variations of the momentum derivative of the induced pseudoscalar form factor at the zero momentum point show some discrepancy. It seems to be caused by a finite volume effect, since a similar trend is not observed on a large volume, but seen on a small volume in our pilot calculations at a heavier pion mass of ${M}_{\ensuremath{\pi}}=510\text{ }\text{ }\mathrm{MeV}$. Furthermore, we discuss an equivalence between the momentum derivative method and the similar approach with the point splitting vector current.

We have performed a study of the isovector, octet, and singlet axial charges of the proton in an extended chiral constituent quark model, where all the possible uudqq¯ (q=u, d, s) five-quark Fock components in the proton wave function are taken into account. The P03 quark-antiquark creation mechanism is assumed to account for the transition coupling between three- and five-quark components in proton, and the corresponding transition coupling strength is fixed by fitting the intrinsic sea flavor asymmetry d¯−u¯ data for proton. Accordingly, with all the parameters fixed by empirical values, the probabilities of the intrinsic five-quark Fock components in proton wave function should be ∼30–50%, which lead to the numerical results for quark spin Δu, Δd, and Δs, as well the axial charges of proton consistent with the experimental data and predictions by other theoretical approaches.

We present an $\mathcal{O}(\ensuremath{\alpha})$ Standard Model calculation of the inner radiative corrections to Gamow-Teller $\ensuremath{\beta}$ decays. We find that a priori contributions arise from the photonic vertex correction and $\ensuremath{\gamma}W$ box diagram. Upon evaluation most elastic contributions vanish due to crossing symmetry or cancellation between isoscalar and isovector photonic contributions, leaving only the polarized parity-odd contribution, i.e., the Gamow-Teller equivalent of the well-known axial $\ensuremath{\gamma}W$ box contribution for Fermi decays. We show that weak magnetism contributes significantly to the Born amplitude, and consider additional hadronic contributions at low energy using a holomorphic continuation of the polarized Bjorken sum rule constrained by experimental data. We perform the same procedure for the Fermi inner radiative correction through a combination of the running of Bjorken and Gross-Llewellyn Smith sum rules. We discuss heavy flavor, higher-twist, and target mass corrections and find a significant increase at low momentum from the latter. We find ${\mathrm{\ensuremath{\Delta}}}_{R}^{A}=0.02532(22)$ and ${\mathrm{\ensuremath{\Delta}}}_{R}^{V}=0.02473(27)$ for axial and vector inner radiative corrections, respectively, resulting in ${\mathrm{\ensuremath{\Delta}}}_{R}^{A}\ensuremath{-}{\mathrm{\ensuremath{\Delta}}}_{R}^{V}=0.60(5)\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}3}$, which allows us to extract ${g}_{A}^{0}$ for the first time to our knowledge. We discuss consequences for comparing experimental data to lattice calculations in beyond Standard Model fits. Further, we show how some traditional $\ensuremath{\beta}$ decay calculations contain part of this effect but fail to account for cancellations in the full $\mathcal{O}(\ensuremath{\alpha})$ result. Finally, we correct for a double-counting instance in the isospin $T=1/2$ mirror decay extraction of $|{V}_{ud}|$, the up-down matrix element of the Cabibbo-Kobayashi-Maskawa matrix element, resolving a long-standing tension and leading to increased precision.

The mass spectra of isovector ϒ, ψ, ϕ, and ω meson resonances are investigated, in the AdS/QCD and information entropy setups. The differential configurational entropy is employed to obtain the mass spectra of radial S-wave resonances, with higher excitation levels, in each one of these meson families, whose respective first undisclosed states are discussed and matched up to candidates in the Particle Data Group.

Quantum chromodynamics presents a series of exact and approximate symmetries which can be exploited to predict new hadrons from previously known ones. The ${Z}_{c}(3900)$ and ${Z}_{c}(4020)$, which have been theorized to be isovector ${D}^{*}\overline{D}$ and ${D}^{*}{\overline{D}}^{*}$ molecules [${I}^{G}({J}^{PC})={1}^{\ensuremath{-}}({1}^{+\ensuremath{-}})$], are no exception. Here we argue that from SU(3)-flavor symmetry, we should expect the existence of strange partners of the ${Z}_{c}$'s with hadronic molecular configurations ${D}^{*}{\overline{D}}_{s}\ensuremath{-}D{\overline{D}}_{s}^{*}$ and ${D}^{*}{\overline{D}}_{s}^{*}$ (or, equivalently, quark content $c\overline{c}s\overline{q}$, with $q=u$, $d$). The quantum numbers of these ${Z}_{cs}$ and ${Z}_{cs}^{*}$ structures would be $I({J}^{P})=\frac{1}{2}({1}^{+})$. The predicted masses of these partners depend on the details of the theoretical scheme used, but they should be around the ${D}^{*}{\overline{D}}_{s}\ensuremath{-}D{\overline{D}}_{s}^{*}$ and ${D}^{*}{\overline{D}}_{s}^{*}$ thresholds, respectively. Moreover, any of these states could be either a virtual pole or a resonance. We show that, together with a possible triangle singularity contribution, such a picture nicely agrees with the very recent BESIII data of the ${e}^{+}{e}^{\ensuremath{-}}\ensuremath{\rightarrow}{K}^{+}({D}_{s}^{\ensuremath{-}}{D}^{*0}+{D}_{s}^{*\ensuremath{-}}{D}^{0})$.

The low-lying $sQ\overline{q}\overline{q}$ ($q=u$, $d$, $Q=c$, $b$) tetraquark states with ${J}^{P}={0}^{+}$, ${1}^{+}$, and ${2}^{+}$, and in the isoscalar and isovector sectors, are systematically investigated in the framework of the real- and complex-scaling range of a chiral quark model, whose parameters are fixed in advance describing hadron, hadron-hadron, and multiquark phenomenology, and thus, all results presented here are pure predictions. Each tetraquark configuration compatible with the quantum numbers studied is taken into account; this includes meson-meson, diquark-antidiquark, and K-type arrangements of quarks with all possible color wave functions in the four-body sector. Among the different numerical techniques to solve the Schr\"odinger-like four-body bound-state equation, we use a variational method in which the trial wave function is expanded in complex-range Gaussian basis functions because of its simplicity and flexibility. Several compact bound states and narrow resonances are found in both charm-strange $cs\overline{q}\overline{q}$ and bottom-strange $bs\overline{q}\overline{q}$ tetraquark sectors, most of them as a product of the strong coupling between the different channels. In regard to the so-called ${X}_{0,1}(2900)$ structures recently discovered with good statistical significance by the LHCb Collaboration, whose properties point out to be $cs\overline{u}\overline{d}$ tetraquarks, we find that they are unstable in our formalism with several candidates in the single-channel computations. We distinguish four cases with $I({J}^{P})=0({0}^{+})$ quantum numbers: three K-type configurations with masses at 2.89, 2.96, and 2.97 GeV, and one hidden-color coupled-channel calculation delivering a mass 2.86 GeV. With quantum numbers $I({J}^{P})=0({1}^{+})$, only one candidate can be found in the hidden-color coupled-channel calculation with mass 2.94 GeV.

This work continues our program of lattice-QCD baryon physics using staggered fermions for both the sea and valence quarks. We present a proof-of-concept study that demonstrates, for the first time, how to calculate baryon matrix elements using staggered quarks for the valence sector. We show how to relate the representations of the continuum staggered flavor-taste group $\text{SU}(8)_{FT}$ to those of the discrete lattice symmetry group. The resulting calculations yield the normalization factors relating staggered baryon matrix elements to their physical counterparts. We verify this methodology by calculating the isovector vector and axial-vector charges $g_V$ and $g_A$. We use a single ensemble from the MILC Collaboration with 2+1+1 flavors of sea quark, lattice spacing $a\approx 0.12$ fm, and a pion mass $M_\pi\approx305$ MeV. On this ensemble, we find results consistent with expectations from current conservation and neutron beta decay. Thus, this work demonstrates how highly-improved staggered quarks can be used for precision calculations of baryon properties, and, in particular, the isovector nucleon charges., Comment: 19 pages, 9 figures

The QCD axion remains experimentally viable in the mass range of $\mathcal{O}(10\text{ }\text{ }\mathrm{MeV})$ if (i) it couples predominantly to the first generation of SM fermions; (ii) it decays to ${e}^{+}{e}^{\ensuremath{-}}$ with a short lifetime ${\ensuremath{\tau}}_{a}\ensuremath{\lesssim}4\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}14}\text{ }\text{ }\mathrm{s}$; and (iii) it has suppressed isovector couplings, i.e., if it is piophobic. Remarkably, these are precisely the properties required to explain recently observed anomalies in nuclear deexcitations, to wit: the ${e}^{+}{e}^{\ensuremath{-}}$ emission spectra of isoscalar magnetic transitions of $^{8}\mathrm{Be}$ and $^{4}\mathrm{He}$ nuclei showed a ``bumplike'' feature peaked at ${m}_{{e}^{+}{e}^{\ensuremath{-}}}\ensuremath{\sim}17\text{ }\text{ }\mathrm{MeV}$. In this paper, we argue that on-shell emission of the QCD axion (with the aforementioned properties) provides an extremely well-motivated, compatible explanation for the observed excesses in these nuclear deexcitations. The absence of anomalous features in other measured transitions is also naturally explained: piophobic axion emission is strongly suppressed in isovector magnetic transitions and forbidden in electric transitions. This QCD axion hypothesis is further corroborated by an independent observation: a $\ensuremath{\sim}2--3\ensuremath{\sigma}$ deviation in the measurement of $\mathrm{\ensuremath{\Gamma}}({\ensuremath{\pi}}^{0}\ensuremath{\rightarrow}{e}^{+}{e}^{\ensuremath{-}})$ from the Standard Model theoretical expectation. This paper also includes detailed estimations of various axionic signatures in rare light meson decays, which take into account contributions from low-lying QCD resonance exchange, and, in the case of rare kaon decays, the possible effective implementations of $\mathrm{\ensuremath{\Delta}}S=1$ octet enhancement in chiral perturbation theory. These inherent uncertainties of the effective description of the strong interactions at low energies result in large variations in the predictions for hadronic signals of the QCD axion; in spite of this, the estimated ranges for rare meson decay rates obtained here can be probed in the near future in $\ensuremath{\eta}/{\ensuremath{\eta}}^{\ensuremath{'}}$ and kaon factories.

A light boson $U$ from an extra $U(1)$ interpolates between a generalized dark photon coupled to $Q$, $B$, and ${L}_{i}$ (or $B\ensuremath{-}L$), plus possibly dark matter, a dark $Z$ coupled to the $Z$ current, and one axially coupled to quarks and leptons. We identify the corresponding $U(1{)}_{F}$ symmetries, with $F={\ensuremath{\gamma}}_{Y}Y+{\ensuremath{\gamma}}_{B}B+{\ensuremath{\gamma}}_{{L}_{i}}{L}_{i}+{\ensuremath{\gamma}}_{A}{F}_{A}+{\ensuremath{\gamma}}_{{F}^{\ensuremath{'}}}{F}^{\ensuremath{'}}+{\ensuremath{\gamma}}_{d}{F}_{d}$, ${F}_{d}$ acting in a dark sector and ${F}^{\ensuremath{'}}$ on possible semi-inert Brout-Englert-Higgs (BEH) doublets uncoupled to quarks and leptons. The $U$ current is obtained from the $U(1{)}_{F}$ and $Z$ currents, with a mixing determined by the spin-0 BEH fields. The charge ${Q}_{U}$ of chiral quarks and leptons is a combination of $Q$, $B$, ${L}_{i}$, and ${T}_{3L}$ with the axial ${F}_{A}$. It involves in general isovector and isoscalar axial terms, in the presence of two BEH doublets. A longitudinal $U$ with axial couplings has enhanced interactions and behaves much as an axionlike particle. Its axial couplings ${g}_{A}$, usually restricted to $\ensuremath{\lesssim}\text{ }2\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}7}\text{ }\text{ }{m}_{U}(\mathrm{MeV})$, lead to effective pseudoscalar ones ${g}_{P}={g}_{A}\ifmmode\times\else\texttimes\fi{}2{m}_{q,l}/{m}_{U}={2}^{1/4}{G}_{F}^{1/2}{m}_{q,l}\text{ }{A}_{\ifmmode\pm\else\textpm\fi{}}$. ${A}_{\ifmmode\pm\else\textpm\fi{}}$ is proportional to an invisibility parameter $r=\mathrm{cos}{\ensuremath{\theta}}_{A}$ induced by a singlet v.e.v., possibly large and allowing the $U$ to be very weakly interacting. This allows for a very small gauge coupling, expressed with two doublets and a singlet as ${g}^{\ensuremath{'}\ensuremath{'}}/4\ensuremath{\simeq}2\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}6}\text{ }\text{ }{m}_{U}(\mathrm{MeV})\text{ }r/\mathrm{sin}2\ensuremath{\beta}$. We discuss phenomenological implications for meson decays, neutrino interactions, atomic-physics parity violation, naturally suppressed ${\ensuremath{\pi}}^{0}\ensuremath{\rightarrow}\ensuremath{\gamma}U$ decays, etc. The $U$ boson fits within the grand unification framework, in symbiosis with a $SU(4{)}_{\mathrm{es}}$ electrostrong symmetry broken at the grand unification scale, with ${Q}_{U}$ depending on $Q$, $B\ensuremath{-}L$, ${F}_{A}$, and ${T}_{3A}$ through three parameters ${\ensuremath{\gamma}}_{Y}$, ${\ensuremath{\gamma}}_{A}$, and $\ensuremath{\eta}$.

We present the first Monte Carlo based global QCD analysis of spin-averaged and spin-dependent parton distribution functions (PDFs) that includes nucleon isovector matrix elements in coordinate space from lattice QCD. We investigate the degree of universality of the extracted PDFs when the lattice and experimental data are treated under the same conditions within the Bayesian likelihood analysis. For the unpolarized sector, we find rather weak constraints from the current lattice data on the phenomenological PDFs, and difficulties in describing the lattice matrix elements at large spatial distances. In contrast, for the polarized PDFs we find good agreement between experiment and lattice data, with the latter providing significant constraints on the spin-dependent isovector quark and antiquark distributions., Comment: 23 pages, 4 figures

The axial-vector form factors of the $\mathrm{spin}\ensuremath{-}{\frac{3}{2}}^{+}$ decuplet baryons are investigated in the chiral constituent quark model using their explicit quark spin polarizations. The quark sea arises from the chiral symmetry breaking, which results in the Goldstone bosons mediating the interaction between constituent quarks. The axial-vector form factors, which have some physical significance corresponding to the flavor singlet current, flavor isovector (triplet) current, and the flavor hypercharge axial (octet) current at zero momentum transfer, are, respectively ${G}_{\mathrm{AV},{B}^{*\frac{3}{2}}}^{0}(0)$, ${G}_{\mathrm{AV},{B}^{*\frac{3}{2}}}^{3}(0)$, and ${G}_{\mathrm{AV},{B}^{*\frac{3}{2}}}^{8}(0)$. In order to further understand the ${Q}^{2}$ dependence of these form factors, we have used the dipole form of parametrization. The qualitative and quantitative contribution of the quark sea has also been investigated by varying the transition probability of the chiral fluctuation.

We present results on the isovector momentum fraction, $⟨x{⟩}_{u\ensuremath{-}d}$, helicity moment, $⟨x{⟩}_{\mathrm{\ensuremath{\Delta}}u\ensuremath{-}\mathrm{\ensuremath{\Delta}}d}$, and the transversity moment, $⟨x{⟩}_{\ensuremath{\delta}u\ensuremath{-}\ensuremath{\delta}d}$, of the nucleon obtained using nine ensembles of gauge configurations generated by the MILC Collaboration using $2+1+1$-flavors of dynamical highly improved staggered quarks. The correlation functions are calculated using the Wilson-Clover action, and the renormalization of the three operators is carried out nonperturbatively on the lattice in the ${\mathrm{RI}}^{\ensuremath{'}}\text{\ensuremath{-}}\text{MOM}$ scheme. The data have been collected at lattice spacings $a\ensuremath{\approx}0.15$, 0.12, 0.09, and 0.06 fm and ${M}_{\ensuremath{\pi}}\ensuremath{\approx}310$, 220, and 135 MeV, which are used to obtain the physical values using a simultaneous chiral-continuum-finite-volume fit. The final results, in the $\overline{\mathrm{MS}}$ scheme at 2 GeV, are $⟨x{⟩}_{u\ensuremath{-}d}=0.173(14)(07)$, $⟨x{⟩}_{\mathrm{\ensuremath{\Delta}}u\ensuremath{-}\mathrm{\ensuremath{\Delta}}d}=0.213(15)(22)$, and $⟨x{⟩}_{\ensuremath{\delta}u\ensuremath{-}\ensuremath{\delta}d}=0.208(19)(24)$, where the first error is the overall analysis uncertainty and the second is an additional systematic uncertainty due to possible residual excited-state contributions. These results are consistent with other recent lattice calculations and phenomenological global fit values.

In this work, we consider a non-quadratic dilaton $\Phi(z)=(\kappa\,z)^{2-\alpha}$ in the context of the static soft wall model to describe the mass spectrum of a wide range of vector mesons from the light up to the heavy sectors. The effect of this non-quadratic approach is translated into non-linear Regge trajectories with the generic form $M^2=a\,(n+b)^\nu$. We apply this sort of fits for the isovector states of $\omega$, $\phi$, $J/\psi$ and $\Upsilon$ mesons and compare with the corresponding holographic duals. We also extend these ideas to the heavy-light sector by using the isovector set of parameters to extrapolate the proper values of $\kappa$ and $\alpha$ through the average constituent mass $\bar{m}$ for each mesonic specie considered. In the same direction, we address the description of possible non-$q\,\bar{q}$ candidates using $\bar{m}$ as a holographic threshold, associated with the structure of the exotic state, to define the values of $\kappa$ and $\alpha$. We study the $\pi_1$ mesons in the light sector, and the $Z_c$, $Y$ and $Z_b$ mesons in the heavy sector as possible exotic vector states. Finally, the RMS error for describing these twenty-seven states with fifteen parameters (four values for $\kappa$ and $\alpha$ respectively and seven values for $\bar{m}$) is $12.61\%$., Comment: 12 pages, 4 figures, 7 tables

We study the possible bound states of the $D_1D$ system in the Bethe-Salpeter (BS) formalism in the ladder and instantaneous approximations. By solving the BS equation numerically with the kernel containing one-particle exchange diagrams and introducing three different form factors (monopole, dipole, and exponential form factors) at the vertices, we investigate whether the isoscalar and isovector $D_1D$ bound states may exist, respectively. We find that $Y(4260)$ could be accommodated as a $D_1D$ molecule, whereas the interpretation of $Z_2^+(4250)$ as a $D_1D$ molecule is disfavored. The bottom analog of $Y(4260)$ may exist but that of $Z_2^+(4250)$ does not., 17 pages, 6 figures, and 4 tables

We have applied isovector and isoscalar tensor current to evaluate the tensor form factors of the $ N(1535) \rightarrow N $ transition with the help of the light-cone QCD sum rule method. In numerical computations, have used the most general forms of the interpolating current for the nucleon and the tensor current together with two different sets of the input parameters in the DAs of the $N(1535)$ state. We have obtained that the values of $N(1535) \rightarrow N$ transition tensor form factors very sensitive to the input parameters of the distribution amplitudes of the $N(1535)$ state. We have acquired that the $Q^2$ dependence of $N(1535) \rightarrow$ transition tensor form factors is well defined by a p-pole fit function.

We report nucleon mass, isovector vector and axial-vector charges, and tensor and scalar couplings, calculated using two recent 2+1-flavor dynamical domain-wall fermions lattice-QCD ensembles generated jointly by the RIKEN-BNL-Columbia and UKQCD collaborations. These ensembles were generated with Iwasaki $\times$ dislocation-suppressing-determinant-ratio gauge action at inverse lattice spacing of 1.378(7) GeV and pion mass values of 249.4(3) and 172.3(3) MeV. The nucleon mass extrapolates to a value $m_N = 0.950(5)$ GeV at physical point. The isovector vector charge renormalizes to unity in the chiral limit, narrowly constraining excited-state contamination in the calculation. The ratio of the isovector axial-vector to vector charges shows a deficit of about ten percent. The tensor coupling no longer depends on mass and extrapolates to 1.04(5) in $\overline {\rm MS}$ 2-GeV renormalization at physical point, in a good agreement with the value obtained at the lightest mass in our previous calculations and other calculations that followed. The scalar charge, though noisier, does not show mass dependence and is in agreement with other calculations.

Results are presented for the nucleon isovector electromagnetic form factors using 11 ensembles generated by the MILC collaboration using the 2+1+1-flavors HISQ action. They span 4 lattice spacings $a \sim$ 0.06, 0.09, 0.12 and 0.15~fm and 3 values of $M_\pi \sim 135, 225$ and 315 MeV. High-statistics estimates are used to perform a simultaneous extrapolation in the lattice spacing, lattice volume and light-quark masses. The $Q^2$ dependence over the range 0.05-1.4 ${\rm GeV}^2$ is investigated using both the $z$-expansion and the dipole form. Final $z$-expansion estimates for the isovector r.m.s. radius are $r_E = 0.769(27)(30)$ fm $r_M = 0.671(48)(76)$ fm and $\mu^{p-n} = 3.939(86)(138)$ Bohr magneton. The first error is the combined uncertainty from the leading-order analysis, and the second is an estimate of the additional uncertainty due to using the leading order chiral-continuum-finite-volume fits. The dipole estimates, $r_E = 0.765(11)(8)$ fm, $r_M = 0.704(21)(29)$ fm and $\mu^{p-n} = 3.975(84)(125)$, are consistent with those from the $z$-expansion but with smaller errors. Our analysis highlights three points. First, all data from the eleven ensembles and existing lattice data on, or close to, physical mass ensembles from other collaborations collapses more clearly onto a single curve when plotted versus $Q^2/M_N^2$ as compared to $Q^2$ with the scale set by quantities other than $M_N$. The difference between these two analyses is indicative of discretization errors, some of which presumably cancel when the data are plotted versus $Q^2/M_N^2$. Second, the size of the remaining deviation of this common curve from the Kelly curve is small and can be accounted for by statistical and possible systematic uncertainties. Third, to improve lattice estimates, high statistics data for $Q^2 < 0.1$ ${\rm GeV}^2$ are needed.

We present results for the moments of nucleon isovector vector and axial generalised parton distribution functions computed within lattice QCD. Three ensembles of maximally twisted mass clover-improved fermions simulated with a physical value of the pion mass are analyzed. Two of these ensembles are generated using two degenerate light quarks. A third ensemble is used having, in addition to the light quarks, strange and charm quarks in the sea. A careful analysis of the convergence to the ground state is carried out that is shown to be essential for extracting the correct nucleon matrix elements. This allows a controlled determination of the unpolarised, helicity and tensor second Mellin moments. The vector and axial-vector generalised form factors are also computed as a function of the momentum transfer square up to about 1 GeV$^2$. The three ensembles allow us to check for unquenching effects and to assess lattice finite volume effects., Comment: Published version. Typos corrected, references and figures added. 22 pages, 17 figures

There have been rapid developments in the direct calculation of the Bjorken-$x$ dependence of parton distribution functions (PDFs) using lattice QCD, and the technique shows promising results. Among various new methods, large-momentum effective theory (LaMET), which calculates boosted hadron matrix elements of multiple spatial displacements on the lattice, shows promising PDFs at physical pion mass by both ${\mathrm{LP}}^{3}$ and ETMC Collaborations. However, the finite-volume systematics have not yet been studied, and it has been suggested that such systematics can be more significant for LaMET-type operators than the traditional bilinear quark operators in charges and form factors. In this work, we present the first study of the finite-volume systematic for both isovector nucleon unpolarized and helicity matrix elements on three lattice volumes (2.88, 3.84, 4.8 fm) with lattice spacing 0.12 fm and 220-MeV pion mass. We perform two-state simultaneous fits using multiple source-sink separations to remove excited-state contamination and obtain reliable ground-state matrix elements. We then implement nonperturbative renormalization and Fourier transform the matrix elements to momentum-space quasi-PDFs. Overall, we do not see significant finite-volume systematics at the studied boost momenta of ${P}_{z}=1.3$ and 2.6 GeV.

The form-factors for the transition ${N}^{*}(1535)\ensuremath{\rightarrow}N$ induced by isovector and isoscalar axial currents within the framework of light cone QCD sum rules by using the most general form of the interpolating current are calculated. In numerical calculations, we use two sets of values of input parameters. It is observed that the ${Q}^{2}$ dependence of the form-factor ${G}_{A}$ can be described by the dipole form. Moreover, the form-factors ${G}_{P}^{(S)}$ are found to be highly sensitive to the variations in the auxiliary parameter $\ensuremath{\beta}$. The numerical calculations show that the form factor ${G}_{T}^{(S)}$ at all values of ${Q}^{2}$ and $\ensuremath{\beta}$ for both sets of values of the parameters are smaller than that one for ${G}_{A}^{(S)}$ and ${G}_{S}^{(S)}$.

We present results from a lattice QCD study of nucleon matrix elements at vanishing momentum transfer for local and twist-2 isovector operator insertions. Computations are performed on gauge ensembles with nonperturbatively improved ${N}_{f}=2+1$ Wilson fermions, covering four values of the lattice spacing and pion masses down to ${M}_{\ensuremath{\pi}}\ensuremath{\approx}200\text{ }\text{ }\mathrm{MeV}$. Several source-sink separations (typically $\ensuremath{\sim}1.0$ to $\ensuremath{\sim}1.5\text{ }\text{ }\mathrm{fm}$) allow us to assess excited-state contamination. Results on individual ensembles are obtained from simultaneous two-state fits across all observables and all available source-sink separations with the energy gap as a common fit parameter. Renormalization has been performed nonperturbatively using the Rome-Southampton method for all but the finest lattice spacing for which an extrapolation has been used. Physical results are quoted in the $\overline{\mathrm{MS}}$ scheme at a scale of $\ensuremath{\mu}=2\text{ }\text{ }\mathrm{GeV}$ and are obtained from a combined chiral, continuum, and finite-size extrapolation. For the nucleon isovector axial, scalar, and tensor charges we find physical values of ${g}_{A}^{u\ensuremath{-}d}=1.242(25{)}_{\mathrm{stat}}(\genfrac{}{}{0ex}{}{+00}{\ensuremath{-}31}{)}_{\mathrm{sys}}$, ${g}_{S}^{u\ensuremath{-}d}=1.13(11{)}_{\mathrm{stat}}(\genfrac{}{}{0ex}{}{+07}{\ensuremath{-}06}{)}_{\mathrm{sys}}$ and ${g}_{T}^{u\ensuremath{-}d}=0.965(38{)}_{\mathrm{stat}}(\genfrac{}{}{0ex}{}{+13}{\ensuremath{-}41}{)}_{\mathrm{sys}}$, respectively, where individual systematic errors in each direction from the chiral, continuum, and finite-size extrapolation have been added in quadrature. Our final results for the isovector average quark momentum fraction and the isovector helicity and transversity moments are given by $⟨x{⟩}_{u\ensuremath{-}d}=0.180(25{)}_{\mathrm{stat}}(\genfrac{}{}{0ex}{}{+14}{\ensuremath{-}06}{)}_{\mathrm{sys}}$, $⟨x{⟩}_{\mathrm{\ensuremath{\Delta}}u\ensuremath{-}\mathrm{\ensuremath{\Delta}}d}=0.221(25{)}_{\mathrm{stat}}(\genfrac{}{}{0ex}{}{+10}{\ensuremath{-}00}{)}_{\mathrm{sys}}$, and $⟨x{⟩}_{\ensuremath{\delta}u\ensuremath{-}\ensuremath{\delta}d}=0.212(32{)}_{\mathrm{stat}}(\genfrac{}{}{0ex}{}{+20}{\ensuremath{-}10}{)}_{\mathrm{sys}}$, respectively.

The comparison of the theoretical and experimental determinations of the anomalous magnetic moment of the muon $(g-2)_\mu$ constitutes one of the strongest tests of the Standard Model at low energies. In this article, we compute the leading hadronic contribution to $(g-2)_\mu$ using lattice QCD simulations employing Wilson quarks. Gauge field ensembles at four different lattice spacings and several values of the pion mass down to its physical value are used. We apply the O($a$) improvement programme with two discretizations of the vector current to better constrain the approach to the continuum limit. The electromagnetic current correlators are computed in the time-momentum representation. In addition, we perform auxiliary calculations of the pion form factor at timelike momenta in order to better constrain the tail of the isovector correlator and to correct its dominant finite-size effect. For the numerically dominant light-quark contribution, we have rescaled the lepton mass by the pion decay constant computed on each lattice ensemble. We perform a combined chiral and continuum extrapolation to the physical point, and our final result is $ a_\mu^{\rm hvp}=(720.0\pm12.4_{\rm stat}\,\pm9.9_{\rm syst})\cdot10^{-10}$. It contains the contributions of quark-disconnected diagrams, and the systematic error has been enlarged to account for the missing isospin-breaking effects.

A novel technique using machine learning (ML) to reduce the computational cost of evaluating lattice quantum chromodynamics (QCD) observables is presented. The ML is trained on a subset of background gauge field configurations, called the labeled set, to predict an observable $O$ from the values of correlated, but less compute-intensive, observables $\mathbf{X}$ calculated on the full sample. By using a second subset, also part of the labeled set, we estimate the bias in the result predicted by the trained ML algorithm. A reduction in the computational cost by about $7\%-38\%$ is demonstrated for two different lattice QCD calculations using the Boosted decision tree regression ML algorithm: (1) prediction of the nucleon three-point correlation functions that yield isovector charges from the two-point correlation functions, and (2) prediction of the phase acquired by the neutron mass when a small Charge-Parity (CP) violating interaction, the quark chromoelectric dipole moment interaction, is added to QCD, again from the two-point correlation functions calculated without CP violation., 8 pages, 5 figures

We present an analysis of two isovector scalar resonant contributions to the $B$ decays into charmonia plus $K\overline{K}$ or $\ensuremath{\pi}\ensuremath{\eta}$ pair in the perturbative QCD approach. The Flatt\'e model for the ${a}_{0}(980)$ resonance and the Breit Wigner formula for the ${a}_{0}(1450)$ resonance are adopted to parametrize the timelike form factors in the dimeson distribution amplitudes, which capture the important final state interactions in these processes. The predicted distribution in the ${K}^{+}{K}^{\ensuremath{-}}$ invariant mass as well as its integrated branching ratio for the ${a}_{0}(980)$ resonance in the ${B}^{0}\ensuremath{\rightarrow}J/\ensuremath{\psi}{K}^{+}{K}^{\ensuremath{-}}$ mode agree well with the current available experimental data. The obtained branching ratio of the quasi-two-body decay ${B}^{0}\ensuremath{\rightarrow}J/\ensuremath{\psi}{a}_{0}(980)(\ensuremath{\rightarrow}{\ensuremath{\pi}}^{0}\ensuremath{\eta})$ can reach the order of ${10}^{\ensuremath{-}6}$, letting the corresponding measurement appear feasible. For the ${a}_{0}(1450)$ component, our results could be tested by further experiments in the LHCb and Belle II. We also discuss some theoretical uncertainties in detail in our calculation.

Heavy-quark symmetry as applied to heavy hadron systems implies that their interactions are independent of their heavy-quark spin (heavy-quark spin symmetry) and heavy flavor contents (heavy flavor symmetry). In the molecular hypothesis the $X(3872)$ resonance is a ${1}^{++}$ ${D}^{*}\overline{D}$ bound state. If this is the case, the application of heavy-quark symmetry to a molecular $X(3872)$ suggests the existence of a series of partner states, the most obvious of which is a possible ${2}^{++}$ ${D}^{*}{\overline{D}}^{*}$ bound state for which the two-body potential is identical to that of the ${1}^{++}$ ${D}^{*}\overline{D}$ system, the reason being that these two heavy hadron-antihadron states have identical light-spin content. As already discussed in the literature, this leads to the prediction of a partner state at 4012 MeV, at least in the absence of other dynamical effects which might affect the location of this molecule. However the prediction of further heavy-quark symmetry partners cannot be made solely on the basis of symmetry and requires additional information. We propose to use the one-boson-exchange model to fill this gap, in which case we will be able to predict or discard the existence of other partner states. Besides the isoscalar ${2}^{++}$ ${D}^{*}{\overline{D}}^{*}$ bound state, we correctly reproduce the location and quantum numbers of the isovector hidden-bottom ${Z}_{b}(10610)$ and ${Z}_{b}(10650)$ molecular candidates. We also predict the hidden-bottom ${1}^{++}$ ${B}^{*}{\overline{B}}^{*}$ and ${2}^{++}$ ${B}^{*}{\overline{B}}^{*}$ partners of the $X(3872)$, in agreement with previous theoretical speculations, plus a series of other states. The isoscalar, doubly charmed ${1}^{+}\text{ }\text{ }D{D}^{*}$ and ${D}^{*}{D}^{*}$ molecules, and their doubly bottomed counterparts are likely to bind, providing a few instances of explicitly exotic systems.

We investigate the application of the distillation smearing approach, and the use of the variational method with an extended basis of operators facilitated by this approach, on the calculation of the nucleon isovector charges gSu−d, gAu−d, and gTu−d. We find that the better sampling of the lattice enabled through the use of distillation yields a substantial reduction in the statistical uncertainty in comparison with the use of alternative smearing methods, and furthermore, appears to offer better control over the contribution of excited states compared to use of a single, local interpolating operator. The additional benefit arising through the use of the variational method in the distillation approach is less dramatic, but nevertheless significant given that it requires no additional Dirac inversions. Dependence of our results on the rank of the distillation is space is also explored, and found to be mild.

In the molecular picture the hidden-charm, pentaquarklike ${P}_{c}(4450)$ resonance is a ${\overline{D}}^{*}{\mathrm{\ensuremath{\Sigma}}}_{c}$ bound state with quantum numbers $I=\frac{1}{2}$ and ${J}^{P}={\frac{3}{2}}^{\ensuremath{-}}$. If this happens to be the case, it will be natural to expect the existence of ${\overline{D}}^{*}{\overline{D}}^{*}{\mathrm{\ensuremath{\Sigma}}}_{c}$ three-body bound states. The most probable quantum numbers for a bound ${\overline{D}}^{*}{\overline{D}}^{*}{\mathrm{\ensuremath{\Sigma}}}_{c}$ trimer are the isoscalar ${J}^{P}={\frac{1}{2}}^{+}$, ${\frac{5}{2}}^{+}$ and the isovector ${J}^{P}={\frac{3}{2}}^{+}$, ${\frac{5}{2}}^{+}$ configurations. Calculations within a contact-range theory indicate a trimer binding energy ${B}_{3}\ensuremath{\sim}3--5\text{ }\text{ }\mathrm{MeV}$ and 14--16 MeV for the isoscalar ${\frac{1}{2}}^{+}$ and ${\frac{5}{2}}^{+}$ states and ${B}_{3}\ensuremath{\sim}1--3\text{ }\text{ }\mathrm{MeV}$ and 3--5 MeV for the isovector ${\frac{3}{2}}^{+}$ and ${\frac{5}{2}}^{+}$ states, respectively, with ${B}_{3}$ relative to the ${\overline{D}}^{*}{P}_{c}(4450)$ threshold. These predictions are affected by a series of error sources that we discuss in detail.

By using numerical stochastic perturbation theory, we carry out a quenched two-loop computation of the improvement coefficient cA associated to the isovector axial current. Within the Schrödinger functional formalism, we compute the bare partially conserved axial-vector current quark mass m and fix cA by requiring discretization corrections on m to be of order O(a2) in the lattice spacing a.

We present the nucleon form factors and root-mean-square (RMS) radii measured on a ${(10.8\text{ }\text{ }\mathrm{fm})}^{4}$ lattice at the physical point. We compute the form factors at small momentum transfer region in ${q}^{2}\ensuremath{\le}0.102\text{ }\text{ }{\mathrm{GeV}}^{2}$ with the standard plateau method choosing four source-sink separation times ${t}_{\mathrm{sep}}$ from 0.84 to 1.35 fm to examine the possible excited state contamination. We obtain the electric and magnetic form factors and their RMS radii for not only the isovector channel but also the proton and neutron ones without the disconnected diagram. We also obtain the axial-vector coupling and the axial radius from the axial-vector form factor. We find that these three form factors do not show large ${t}_{\mathrm{sep}}$ dependence in our lattice setup, and those RMS radii are consistent with the experimental values. On the other hand, the induced pseudoscalar and pseudoscalar form factors show the clear effects of the excited state contamination, which affect the generalized Goldberger-Treiman relation.

We carry out a systematic study of exotic $Q{Q}^{\ensuremath{'}}\overline{q}\overline{q}$ four-quark states containing distinguishable heavy flavors, $b$ and $c$. Different generic constituent models are explored in an attempt to extract general conclusions. The results are robust, predicting the same sets of quantum numbers as the best candidates to lodge bound states independently of the model used, the isoscalar ${J}^{P}={0}^{+}$ and ${J}^{P}={1}^{+}$ states. The first state would be strong and electromagnetic-interaction stable, while the second would decay electromagnetically to $\overline{B}D\ensuremath{\gamma}$. Isovector states are found to be unbound, preventing the existence of charged partners. The interest on exotic heavy-light tetraquarks with nonidentical heavy flavors comes reinforced by the recent estimation of the production rate of the isoscalar $bc\overline{u}\overline{d}$ ${J}^{P}={1}^{+}$ state, 2 orders of magnitude larger than that of the $bb\overline{u}\overline{d}$ analogous state.

The hidden charm $X(3872)$ resonance is usually thought to be a $D^{*0} \bar{D}^0$ meson-antimeson molecule with quantum numbers $J^{PC} = 1^{++}$. If this is the case, there is the possibility that there might be three body bound states with two charmed mesons and a charmed antimeson. Here we argue that the theoretical existence of this type of three body molecules is expected from heavy quark spin symmetry. If applied to the two body sector, this symmetry implies that the interaction of the $D^{*0} \bar{D}^{*0}$ meson-antimeson pair in the $J^{PC} = 2^{++}$ channel is the same as in the $J^{PC} = 1^{++}$ $D^{*0} \bar{D}^0$ case. From this we can infer that the $J^P = 3^{-}$ $D^{*0} D^{*0} \bar{D}^{*0}$ molecule will be able to display the Efimov effect if the scattering length of the $2^{++}$ channel is close enough to the unitary limit. Heavy quark spin symmetry also indicates that the $J^P = 2^{-}$ $D^{*0} D^{*0} \bar{D}^0$ molecule is analogous to the $J^P = 3^{-}$ $D^{*0} D^{*0} \bar{D}^{*0}$ one. That is, it can also have a geometric spectrum. If we consider these triply heavy trimers in the isospin symmetric limit, the Efimov effect disappears and we can in principle predict the fundamental state of the $2^-$ $D^*D^*\bar{D}$ and $3^-$ $D^* D^* \bar{D}^*$ systems. The same applies to the $B^*B^* \bar{B}^*$ system: if the $Z_b(10650)$ is an isovector $B^* \bar{B}^*$ molecule then the $0^-$ isodoublet and the $1^-$, $2^-$ isoquartet $B^* B^* \bar{B}^*$ trimers might bind, but do not display Efimov physics. Finally from heavy flavour symmetry it can be argued that scattering in the $B D$ two-body system might be resonant. This would in turn imply the possibility of Efimov physics in the $B B D$ three body system.

The recent precision measurement of the relative yield of $D^+D^-$ and $D^0 \bar D^0$ meson pairs at the $\psi(3770)$ peak in $e^+e^-$ annihilation is about 3.7 sigma away from a straightforward theoretical estimate. It is argued that combined with an even more significant deviation of similar ratio for the $B$ mesons at the $\Upsilon(4S)$ peak, this provides an insight into the structure of heavy mesons and requires both a form factor, corresponding to their finite `size', and a strong interaction between the mesons mesons in the isovector state $I^G(J^P) = 1^+(1^-)$. It is also argued that the data for the $D$ and $B$ mesons are possibly compatible with the heavy quark limit of the same meson-antimeson strong interaction in both systems.

Recently, a tetraquark mixing framework has been proposed for light mesons and applied more or less successfully to the isovector resonances, $a_0(980), a_0(1450)$, as well as to the isodoublet resonances, $K^*_0(800), K^*_0(1430)$. In this work, we present a more extensive view on the mixing framework and extend this to the isoscalar resonances, $f_0 (500)$, $f_0(980)$, $f_0 (1370)$, $f_0(1500)$. Tetraquarks in this framework can have two spin configurations containing either spin-0 diquark or spin-1 diquark and each configuration forms a nonet in flavor space. The two spin configurations are found to mix strongly through the color-spin interactions. Their mixtures, which diagonalize the hyperfine masses, can generate the physical resonances constituting the two nonets, which, in fact, coincide roughly with the experimental observation. We identify that $f_0 (500)$, $f_0(980)$ are the isoscalar members in the light nonet, and $f_0 (1370)$, $f_0(1500)$ are the similar members in the heavy nonet. This means that the spin configuration mixing, as it relates the corresponding members in the two nonets, can generate $f_0 (500), f_0 (1370)$ among the members in light mass, and $f_0(980), f_0(1500)$ in heavy mass. The complication arises because the isoscalar members of each nonet are subject to an additional flavor mixing known as OZI rule so that $f_0 (500), f_0 (980)$, and similarly $f_0 (1370), f_0 (1500)$, are the mixture of two isoscalar members belonging to an octet and a singlet in SU$_f$(3). The tetraquark mixing framework including the flavor mixing is tested for the isoscalar resonances in terms of the mass splitting and the fall-apart decay modes., Comment: 16 pages, 2 figures, slightly modified, 2 references added

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.

Semi-inclusive charge-changing neutrino reactions on targets of heavy water are investigated with the goal of determining the relative contributions to the total cross section of deuterium and oxygen in kinematics chosen to emphasize the former. The study is undertaken for conditions where the typical neutrino beam energies are in the few GeV region, and hence relativistic modeling is essential. For this, the previous relativistic approach for the deuteron is employed, together with a spectral function approach for the case of oxygen. Upon optimizing the kinematics of the final-state particles assumed to be detected (typically a muon and a proton) it is shown that the oxygen contribution to the total cross section is suppressed by roughly an order of magnitude compared with the deuterium cross section, thereby confirming that $\mathrm{CC}\ensuremath{\nu}$ studies of heavy water can effectively yield the cross sections for deuterium, with acceptable backgrounds from oxygen. This opens the possibility of using deuterium to determine the incident neutrino flux distribution, to have it serve as a target for which the nuclear structure issues are minimal, and possibly to use deuterium to provide improved knowledge of specific aspects of hadronic structure, such as to explore the momentum transfer dependence of the isovector axial-vector form factor of the nucleon.

The accuracy of the Gounaris-Sakurai pion electromagnetic form factor model at the elastic region, in which just the ${\ensuremath{\rho}}^{0}(770)$ resonance appears, is investigated by the particular analysis of the most accurate P-wave isovector $\ensuremath{\pi}\ensuremath{\pi}$ scattering phase shift ${\ensuremath{\delta}}_{1}^{1}(t)$ data, obtained by the Garcia-Martin-Kami\ifmmode \acute{n}\else \'{n}\fi{}ski-Pel\'aez-Yndurain approach, and by an application of the Unitary pion electromagnetic structure model to a description of the newest precise data on the ${e}^{+}{e}^{\ensuremath{-}}\ensuremath{\rightarrow}{\ensuremath{\pi}}^{+}{\ensuremath{\pi}}^{\ensuremath{-}}$ process.

The isovector bottomoniumlike exotic resonances $Z_b(10610)$ and $Z_b(10650)$ are very close to the thresholds of heavy meson pairs $B \bar B^* \, ( \bar B B^*)$ and $B^* \bar B^*$, and are naturally understood as `molecular' states made of the corresponding meson-antimeson pairs. The picture with a full separation of the two channels cannot be exact and a cross-feed between the states necessarily takes place. A simple model is considered here describing the mixing between the channels in terms of one parameter. The model reasonably describes the current data on the decays of the $Z_b$ resonances to bottomonium plus a pion and predicts the rate and a distinctive interference pattern for the decay $Z_b(10650) \to B \bar B^* \, ( \bar B B^*)$ as well as excess of the mass splitting between the resonances over the mass difference between $B^*$ and $B$ mesons., 8 pages, 2 figures

We present results on the nucleon axial and induced pseudoscalar form factors using an ensemble of two degenerate twisted mass clover-improved fermions with mass yielding a pion mass of ${m}_{\ensuremath{\pi}}=130\text{ }\text{ }\mathrm{MeV}$. We evaluate the isovector and the isoscalar, as well as the strange and the charm axial form factors. The disconnected contributions are evaluated using recently developed methods that include deflation of the lower eigenstates, allowing us to extract the isoscalar, strange, and charm axial form factors. We find that the disconnected quark loop contributions are nonzero and particularly large for the induced pseudoscalar form factor.

We employ dimension-4 operators to improve the local vector and axial-vector currents and calculate the nucleon isovector axial coupling $g^3_A$ with overlap valence on $2+1$-flavor Domain Wall Fermion sea. Using the equality of $g^3_A$ from the spatial and temporal components of the axial-vector current as a normalization condition, we find that $g_A^3$ is increased by a few percent towards the experimental value. The excited-state contamination has been taken into account with three time separations between the source and sink. The improved axial charges $g_A^{3}(24I)=1.22(4)$ and $g_A^{3}(32I)=1.21(3)$ are obtained on a $24^3\times 64$ lattice at pion mass of 330 MeV and a $32^3\times 64$ lattice at pion mass 300 MeV are increased by $3.4\%$ and $1.7\%$ from their unimproved values, respectively. We have also used clover fermion on the same DWF configurations and find the same behavior for the local axial charge as that of the overlap fermion., Comment: 25 pages, 11 figures, matched to the version accepted by PRD

New hidden particles could potentially be emitted and discovered in rare nuclear transitions. In this work, we investigate the production of hidden vector bosons with primarily axial couplings to light quarks in nuclear transitions, and we apply our results to the recent anomaly seen in $^{8}\mathrm{Be}$ decays. The relevant matrix elements for ${^{8}\mathrm{Be}}^{*}({1}^{+})\ensuremath{\rightarrow}^{8}\mathrm{Be}({0}^{+})$ transitions are calculated using ab initio methods with internucleon forces derived from chiral effective field theory and the in-medium similarity renormalization group. We find that the emission of a light axial vector with mass ${m}_{X}\ensuremath{\simeq}17\text{ }\text{ }\mathrm{MeV}$ can account for the anomaly seen in the ${1}^{+}\ensuremath{\rightarrow}{0}^{+}$ isoscalar transition together with the absence of a significant anomaly in the corresponding isovector transition. We also show that such an axial vector can be derived from an anomaly-free ultraviolet-complete theory that is consistent with current experimental data.

We present results for the isovector axial, scalar and tensor charges $g^{u-d}_A$, $g^{u-d}_S$ and $g^{u-d}_T$ of the nucleon needed to probe the Standard Model and novel physics. The axial charge is a fundamental parameter describing the weak interactions of nucleons. The scalar and tensor charges probe novel interactions at the TeV scale in neutron and nuclear $\beta$-decays, and the flavor-diagonal tensor charges $g^{u}_T$, $g^{d}_T$ and $g^{s}_T$ are needed to quantify the contribution of the quark electric dipole moment (EDM) to the neutron EDM. The 9 ensembles, generated by the MILC Collaboration using the HISQ action with 2+1+1 dynamical flavors, span three lattice spacings $a \approx 0.06, 0.09$ and 0.12 fm and light-quark masses corresponding to the pion masses $M_\pi \approx 135, 225$ and 315 MeV. High-statistics estimates on five ensembles using the all-mode-averaging method allow us to quantify all systematic uncertainties and perform a simultaneous extrapolation in the lattice spacing, lattice volume and light-quark masses for the connected contributions. Our final estimates, in the $\overline{\text{MS}}$ scheme at 2 GeV, of the isovector charges are $g_A^{u-d} = 1.195(33)(20)$, $g_S^{u-d} = 0.97(12)(6) $ and $g_T^{u-d} = 0.987(51)(20)$. The first error includes statistical and all systematic uncertainties except that due to the extrapolation Ansatz, which is given by the second error estimate. Combining our estimate for $g_S^{u-d}$ with the difference of light quarks masses $(m_d-m_u)^{\rm QCD}=2.67(35)$ MeV given by FLAG, we obtain $(M_N-M_P)^{\rm QCD} = 2.59(49)$ MeV. Estimates of the connected part of the flavor-diagonal tensor charges of the proton are $g^{u}_T=0.792(42)$ and $g^{d}_T=-0.194(14)$. Combining our new estimates with precision low-energy experiments, we update constraints on novel scalar and tensor interactions, $\epsilon_{S,T}$, at the TeV scale.

We employ leading order covariant chiral perturbation theory to compute the nucleon-pion-state contribution to the 3-point correlation functions one typically measures in lattice QCD to extract the isovector nucleon charges $g_A,g_T$ and $g_S$. We estimate the impact of the nucleon-pion-state contribution on both the plateau and the summation method for lattice simulations with physical pion masses. The nucleon-pion-state contribution results in an overestimation of all charges with both methods. The overestimation is roughly equal for the axial and the tensor charge, and about fifty percent larger for the scalar charge.

The D0 collaboration has recently reported a narrow peak structure in the ${B}_{s}^{0}{\ensuremath{\pi}}^{\ifmmode\pm\else\textpm\fi{}}$ invariant-mass spectrum, which is called $X(5568)$. Its proposed quantum numbers ${J}^{P}={0}^{+}/{1}^{+}$ are not determined unambiguously, and we show that one can fit the data assuming ${J}^{P}={1}^{\ensuremath{-}}$ with the same mass and width for the resonance signal. The corresponding isovector $P$-wave coupled-channel scattering involving the states ${B}_{s}\ensuremath{\pi}$, ${B}_{s}^{*}\ensuremath{\pi}$, $B\overline{K}$ and ${B}^{*}\overline{K}$ is studied employing leading-order heavy meson chiral perturbation theory, which is then unitarized making use of standard techniques from unitary chiral perturbation theory. The subtraction constants that appear in the unitarization process are determined by a $u$-channel crossing symmetry constraint or by naturalness arguments, being the numerical values obtained in both cases quite closed, and no further freedom is left in the model. A crucial point is that if the $X(5568)$ is ${1}^{\ensuremath{-}}$ and decaying into ${B}_{s}^{0}{\ensuremath{\pi}}^{\ifmmode\pm\else\textpm\fi{}}$ then it should appear as a pole in the $T$-matrix elements. It finally turns out that no $X(5568)$ pole is found that can be qualified as dynamically generated from the isovector $P$-wave coupled-channel dynamics. This result disfavors the interpretation of the $X(5568)$ within a ``molecular'' picture.

In this work, we perform a dynamical study of the ${B}^{(*)}$ and $\overline{K}$ interaction and show that the newly reported $X(5568)$ or $X(5616)$ cannot be assigned to be an isovector $B\overline{K}$ or ${B}^{*}\overline{K}$ molecular state. We continue to investigate the isoscalar ${B}^{(*)}\overline{K}$ systems, and the ${B}^{(*)}\overline{K}$ systems with isospin $I=0$, 1, and predict the existence of several isoscalar ${B}^{(*)}{\overline{K}}^{(*)}$ molecular states. A new task of exploring open-bottom molecular states will be created for future experiments.

The nature of the bottomonium-like states ${Z}_{b}(10610)$ and ${Z}_{b}(10650)$ is studied by calculating the ${B}^{(*)}{\overline{B}}^{*}$ compositeness ($X$) in those resonances. We first consider uncoupled isovector $S$-wave scattering of ${B}^{(*)}{\overline{B}}^{*}$ within the framework of effective-range expansion (ERE). Expressions for the scattering length ($a$) and effective range ($r$) are derived exclusively in terms of the masses and widths of the two ${Z}_{b}$ states. We then develop compositeness within ERE for the resonance case and deduce the expression $X=1/\sqrt{2r/a\ensuremath{-}1}$, which is then applied to the systems of interest. Finally, the actual compositeness parameters are calculated in terms of resonance pole positions and their experimental branching ratios into ${B}^{(*)}{\overline{B}}^{*}$ by using the method of [U. G. Mei\ss{}ner and J. A. Oller, Phys. Lett. B 751, 59 (2015)]. We find the values $X=0.66\ifmmode\pm\else\textpm\fi{}0.11$ and $0.51\ifmmode\pm\else\textpm\fi{}0.10$ for the ${Z}_{b}(10610)$ and ${Z}_{b}(10650)$, respectively. We also compare the ERE with Breit-Wigner and Flatt\'e parametrizations to discuss the applicability of the last two for near-threshold resonances with explicit examples.

The strength of the amplitudes for the coupling between the bottomonium $\Upsilon(nS)$ states, the bottomonium-like isovector resonances $Z_b$ and a pion, $\Upsilon(nS) Z_b \pi$, is considered. These amplitudes describe the decays $Z_b \to \Upsilon(nS) \pi$ for $n=1,\,2,\,3$, and the processes $\Upsilon(nS) \to Z_b \pi$ for $n=5,\,6, \ldots$ with either $Z_b(10610)$ or $Z_b(10650)$. It is pointed out that analyticity and unitarity impose a sum rule for these couplings to each of the $Z_b$ resonances. With the currently available data it appears to be difficult or impossible to simultaneously satisfy the sum rules for the $Z_b(10610)$ and $Z_b(10650)$ resonances. This difficulty can be resolved if there is a considerable dissimilarity in the yield of the states $Z_b(10610) \pi$ and $Z_b(10650) \pi$ in the $e^+e^-$ annihilation at energies above the $\Upsilon(5S)$ resonance.

We introduce a stochastic sandwich method with low-mode substitution to evaluate the connected three-point functions. The isovector matrix elements of the nucleon for the axial-vector coupling $g_A^3$, scalar couplings $g_S^3$ and the quark momentum fraction $\langle x\rangle_{u -d}$ are calculated with overlap fermion on 2+1 flavor domain-wall configurations on a $24^3 \times 64$ lattice at $m_{\pi} = 330$ MeV with lattice spacing $a = 0.114$ fm., Comment: 15 pages, 13 figures, the version accepted by PRD

Within a nonlinear chiral Lagrangian framework, the underlying mixings among quark-antiquark, four-quark and glue components of ${f}_{0}(1500)$ and ${f}_{0}(1710)$ are studied in a global picture that includes all isosinglet scalar mesons below 2 GeV. The quark components are introduced in the Lagrangian in terms of two separate nonets (a quark-antiquark nonet and a four-quark nonet) which can mix with each other and with a scalar glueball. An iterative Monte Carlo simulation is developed to study the 14 free parameters of the Lagrangian by a simultaneous fit to more than 20 experimental data and constraints on the mass spectrum, decay widths, and decay ratios of the isosinglet scalars below 2 GeV. Moreover, constraints on the mass spectrum and decay widths of isodoublet and isovector scalars below 2 GeV as well as pion-pion scattering amplitude are also taken into account. In the leading order of the model and within the overall experimental uncertainties, the ranges of variation of the model parameters are determined. This leads to a set of points in the 14-dimensional parameter space at which the overall disagreement with experiment is no larger than the overall experimental uncertainties. The insights gained in this global picture, due to the complexities of the mixings as well as the experimental uncertainties, are mainly qualitative but are relatively robust, and reveal that the lowest scalar glueball hides between ${f}_{0}(1500)$ and ${f}_{0}(1710)$, resulting in a considerable mixing with various quark components of these two states. The overall current experimental and theoretical uncertainties do not allow us to pin down the exact glue components of isosinglet states; nevertheless it is shown that the ${f}_{0}(1500)$ and ${f}_{0}(1710)$ have the highest glue component. While this global study does not allow precision predictions for each individual state, it provides useful ``family'' correlations among the isosinglet states that are found insightful in probing the substructure of scalars, in general, and the isosinglets, in particular. Specifically, a close correlation between the substructure of isosinglets below and above 1 GeV is observed. It is shown that as the simulations approach the limit where the ${f}_{0}(500)$ and ${f}_{0}(980)$ become the two isosinglet members of an ideally mixed two-quark two-antiquark nonet (which is widely believed to be a good approximation), the ${f}_{0}(1500)$ develops a large glue component. The overall estimate of the scalar glueball mass is found to be $1.58\ifmmode\pm\else\textpm\fi{}0.18\text{ }\text{ }\mathrm{GeV}$.

In this paper it is proposed that the charged charmonium-like state ${Z}_{c}(3900)$ is a resonance above the threshold from the $D{\overline{D}}^{*}$ interaction. The $D{\overline{D}}^{*}$ interaction is described by the one-boson exchange model with light meson exchanges plus a short-range $J/\ensuremath{\psi}$ exchange. The scattering amplitude is calculated within a Bethe-Salpeter equation approach, and the poles near the $D{\overline{D}}^{*}$ threshold are searched. In the isoscalar sector, two poles found under the $D{\overline{D}}^{*}$ threshold---i.e., bound states---have the quantum numbers ${I}^{G}({J}^{\mathrm{PC}})={0}^{\ensuremath{-}}({1}^{+\ensuremath{-}})$ and ${0}^{+}({1}^{++})$. The latter can be related to the $X(3872)$. In the isovector sector, a bound state with ${I}^{G}({J}^{P})={1}^{+}({1}^{+})$ is found with a large cutoff at about 3 GeV. If a cutoff at about 2 GeV is adopted with which a pole carrying the quantum number of the $X(3872)$ is produced at an energy of about 3871 MeV, the pole for the bound state with ${1}^{+}({1}^{+})$ runs across the threshold to a second Riemann sheet and becomes a resonance above the $D{\overline{D}}^{*}$ threshold, which can be identified with the ${Z}_{c}(3900)$. With such a cutoff, the $D{\overline{D}}^{*}$ invariant mass spectrum is also investigated and the experimental results found by BESIII can be reproduced.

Recently, a new symmetry of mesons has been found upon truncation of the quasizero modes of the overlap Dirac operator in lattice simulations. Namely, the $\ensuremath{\rho}$, ${\ensuremath{\rho}}^{\ensuremath{'}}$, $\ensuremath{\omega}$, ${\ensuremath{\omega}}^{\ensuremath{'}}$, ${a}_{1}$, ${b}_{1}$, ${h}_{1}$, and possibly ${f}_{1}$ $J=1$ mesons get degenerate after removal of the quasizero modes. This emergent symmetry has been established to be $SU(4)\ensuremath{\supset}SU(2{)}_{\mathrm{L}}\ifmmode\times\else\texttimes\fi{}SU(2{)}_{\mathrm{R}}\ifmmode\times\else\texttimes\fi{}U(1{)}_{\mathrm{A}}$. It is higher than the symmetry of the QCD Lagrangian and provides not only a mixing of quarks of given chirality in the isospin space, but also the mixing of left-handed and right-handed components. Here we study, with the overlap Dirac operator, the isovector $J=2$ mesons upon the quasizero mode reduction and observe a similar degeneracy. This result further supports the $SU(4)$ symmetry in mesons of given spin $J\ensuremath{\ge}1$.