Quark Action Research Articles

Nucleon form factors in Nf=2+1 lattice QCD at the physical point: Finite lattice spacing effect on the root-mean-square radii

We present results for the nucleon form factors: electric (GE), magnetic (GM), axial (FA), induced pseudoscalar (FP), and pseudoscalar (GP) form factors, using the second PACS10 ensemble that is one of three sets of 2+1 flavor lattice QCD configurations at physical quark masses in large spatial volumes [exceeding (10 fm)3]. The second PACS10 gauge configurations are generated by the PACS Collaboration with the six stout-smeared O(a) improved Wilson quark action and Iwasaki gauge action at the second gauge coupling β=2.00 corresponding to the lattice spacing of a=0.063 fm. We determine the isovector electric, magnetic and axial radii, and magnetic moment from the corresponding form factors, as well as the axial-vector coupling gA. Combining our previous results for the coarser lattice spacing [E. Shintani , ; ], the finite lattice spacing effects on the isovector radii, magnetic moment, and axial-vector coupling are investigated using the difference between the two results. It was found that the effect on gA is kept smaller than the statistical error of 2% while the effect on the isovector radii was observed as a possible discretization error of about 10%, regardless of the channel. We also report the partially conserved axial-vector current relation using a set of nucleon three-point correlation functions in order to verify the effect by O(a) improvement of the axial-vector current. Published by the American Physical Society 2024

Pion screening mass at finite chemical potential

We present a method to compute the responses of meson screening masses to the chemical potential by Taylor expanding the correlator using lattice QCD simulation. We start by comparing the free theory lattice results with the analytical expression. Then, using symmetry arguments, we obtain an expression for the correlator in a series of the chemical potential at finite temperature. Using this, we obtain the lowest order correction to the screening mass at a finite chemical potential for temperatures around 2.5 GeV. Our lattice analysis is limited to isoscalar chemical potential for the pseudoscalar channel. The calculations were performed using (2+1)-flavors of the Highly Improved Staggered Quark (HISQ/tree) action, with the ratio of the strange quark mass to the light quark mass ms/mℓ = 20 corresponding to pion masses of 160 MeV.

Study of Quarkonium in QGP from Unquenched Lattice QCD

This paper discusses the charmonium and bottomonium correlators in the pseudoscalar channel and the corresponding spectral reconstruction on the lattice. The absence of a transport peak in the pseudoscalar channel spectral function allows for an easier study of the in-medium modification of bound states. However, extracting spectral information from Euclidean correlators is still a numerically ill-posed problem. To constrain the spectral reconstruction, we use an ansatz motivated from perturbation theory. The perturbative model spectral function has two main contributions: a thermal part around the threshold obtained from pNRQCD and the vacuum part well above the threshold. These two regions are matched continuously, and the model spectral function is obtained by introducing parameters that control the overall thermal shift of the peak and the overall amplitude. The lattice correlator data is computed using clover-improved Wilson valence fermions on large and fine gauge field configurations generated using N_f=2+1 flavors Highly Improved Staggered Quark action with physical strange quark mass m_s, and slightly heavy degenerate up and down quark masses m_l=m_s/5 that correspond to m_pi simeq 320 MeV. Our results obtained at T=220 MeV and T=251 MeV suggest that no resonance peaks are needed to describe the charmonium lattice data at these temperatures, while for bottomonium thermally broadened resonance peaks persists.

D -meson semileptonic decays to pseudoscalars from four-flavor lattice QCD

We present lattice-QCD calculations of the hadronic form factors for the semileptonic decays $D\to\pi\ell\nu$, $D\to K\ell\nu$, and $D_s\to K\ell\nu$. Our calculation uses the highly improved staggered quark (HISQ) action for all valence and sea quarks and includes $N_f=2+1+1$ MILC ensembles with lattice spacings ranging from $a\approx0.12$ fm down to $0.042$ fm. At most lattice spacings, an ensemble with physical-mass light quarks is included. The HISQ action allows all the quarks to be treated with the same relativistic light-quark action, allowing for nonperturbative renormalization using partial conservation of the vector current. We combine our results with experimental measurements of the differential decay rates to determine $|V_{cd}|^{D\to\pi}=0.2238(11)^{\rm Expt}(15)^{\rm QCD}(04)^{\rm EW}(02)^{\rm SIB}[22]^{\rm QED}$ and $|V_{cs}|^{D\to K}=0.9589(23)^{\rm Expt}(40)^{\rm QCD}(15)^{\rm EW}(05)^{\rm SIB}[95]^{\rm QED}$ This result for $|V_{cd}|$ is the most precise to date, with a lattice-QCD error that is, for the first time for the semileptonic extraction, at the same level as the experimental error. Using recent measurements from BES III, we also give the first-ever determination of $|V_{cd}|^{D_s\to K}=0.258(15)^{\rm Expt}(01)^{\rm QCD}[03]^{\rm QED}$ from $D_s\to K \ell\nu$. Our results also furnish new Standard Model calculations of the lepton flavor universality ratios $R^{D\to\pi}=0.98671(17)^{\rm QCD}[500]^{\rm QED}$, $R^{D\to K}=0.97606(16)^{\rm QCD}[500]^{\rm QED}$, and $R^{D_s\to K}=0.98099(10)^{\rm QCD}[500]^{\rm QED}$, which are consistent within $2\sigma$ with experimental measurements. Our extractions of $|V_{cd}|$ and $|V_{cs}|$, when combined with a value for $|V_{cb}|$, provide the most precise test of second-row CKM unitarity, finding agreement with unitarity at the level of one standard deviation.

Muon g-2 with overlap valence fermions

We present a lattice calculation of the leading order (LO) hadronic vacuum polarization (HVP) contribution to the muon anomalous magnetic moment for the connected light and strange quarks, $a^{\rm W}_{{\rm con}, l/s}$ in the widely used window $t_0=0.4~\mathrm{fm}$, $t_1=1.0~\mathrm{fm}$, $\Delta=0.15~\mathrm{fm}$, and also of $a^{\rm S}_{{\rm con}, l/s}$ in the short distance region. We use overlap fermions on 4 physical-point ensembles. Two 2+1 flavor RBC/UKQCD ensembles use domain wall fermions (DWF) and Iwasaki gauge actions at $a = 0.084$ and 0.114 fm, and two 2+1+1 flavor MILC ensembles use the highly improved staggered quark (HISQ) and Symanzik gauge actions at $a = 0.088$ and 0.121 fm. We have incorporated infinite volume corrections from 3 additional DWF ensembles at ${\rm L}$ = 4.8, 6.4 and 9.6 fm and physical pion mass. For $a^{\rm W}_{{\rm con}, l}$, we find that our results on the two smaller lattice spacings are consistent with those using the unitary setup, but those at the two coarser lattice spacings are slightly different. Eventually, we predict $a^{\rm W}_{{\rm con}, l}=206.7(1.5)(1.0)$ and $a^{\rm W}_{{\rm con}, s}=26.8(0.1)(0.3)$, using linear extrapolation in $a^2$, with systematic uncertainties estimated from the difference of the central values from the RBC/UKQCD and MILC ensembles.

Kaon semileptonic form factors at the physical quark masses on large volumes in Nf = 2 + 1 lattice QCD

We present our results for the kaon semileptonic form factors calculated by using two sets of the PACS10 configuration, whose physical volumes are more than (10 fm)4 at the physical light and strange quark masses in the Nf = 2+1 lattice QCD. The configurations were generated using the Iwasaki gauge action and Nf = 2 + 1 stout-smeared clover quark action. The form factors near zero momentum transfer q 2 can be calculated thanks to the large volume. Using our data, a q 2 interpolation and continuum extrapolation are carried out simultaneously. The value of |Vus | is determined using the result of the form factors at q 2 = 0 in the continuum limit. Our result of |Vus| is compared with the one determined from the CKM matrix unitarity and with those determined using recent lattice results.

Nucleon isovector couplings in Nf=2+1 lattice QCD at the physical point

We present results for the scalar and tensor isovector-couplings ($g_S$ and $g_T$) of the nucleon measured at the physical point ($M_{\pi}=135$ MeV) with a single lattice spacing of $0.085\ \mathrm{fm}$ in 2+1 flavor QCD. Our calculations are carried out with two ensembles of gauge configurations generated by the PACS Collaboration with nonperturbatively ${\cal O}(a)$ improved Wilson quark action and Iwasaki gauge action on $(10.9\ {\rm fm})^4$ and $(5.5\ {\rm fm})^4$ lattices, where the finite-size effect on the nucleon mass was not shown at the level of the statistical precision less than 0.5%. We compute the nucleon three-point correlation functions in the vector, axial, scalar, and tensor channels. We confirm that our previous result of the nucleon axial coupling on the large spatial volume of $(10.9\ {\rm fm})^4$ has no finite-size effect at the level of the statistical precision of 1.9%. For the renormalization, we first renormalize $g_S$ and $g_T$ nonperturbatively using the RI/SMOM$_{(\gamma_\mu)}$ scheme, a variant of Rome-Southampton RI/MOM scheme with reduced systematic errors, as the intermediate scheme. We evaluate our final results at the renormalization scale of 2 GeV in the $\overline{\rm MS}$ scheme through matching procedure between the RI/SMOM$_{(\gamma_\mu)}$ and $\overline{\rm MS}$ schemes with the help of perturbation theory, and then obtain $g_S=0.927(71)_{\rm stat}(22)_{\rm syst}$ and $g_T=1.036(6)_{\rm stat}(20)_{\rm syst}$.

Kℓ3 form factors at the physical point: Toward the continuum limit

We present updated results for the form factors of the kaon semileptonic $(K_{\ell 3})$ decay process calculated with $N_f = 2 + 1$ nonperturbatively $O(a)$-improved Wilson quark action and Iwasaki gauge action at the physical point on large volumes of more than (10 fm)$^4$. In addition to our previous calculation at the lattice spacing $a = 0.085$ fm, we perform a calculation at the second lattice spacing of $0.063$ fm. Using the results for the form factors extracted from 3-point functions with the local and also conserved vector currents at the two lattice spacings, continuum extrapolation and interpolation of the momentum transfer are carried out simultaneously to obtain the value of the form factor $f_+(0)$ at the zero momentum transfer in the continuum limit. After investigation of stability of $f_+(0)$ against several fit forms and different data, we obtain $f_+(0) = 0.9615(10)(^{+47}_{\ -3})(5)$, where the first, second, and third errors are statistical, systematic errors from choice of the fit forms and isospin breaking effect, respectively. Combining our value of $f_+(0)$ and experimental input of the $K_{\ell 3}$ decay, one of the Cabibbo-Kobayashi-Maskawa matrix elements $|V_{us}|$ is determined as $|V_{us}| = 0.2252(^{\ +5}_{-12})$, whose error contains the experimental one as well as that in the lattice calculation. This value is reasonably consistent with the ones determined from recent lattice QCD results of $f_+(0)$ and also the one determined through the kaon leptonic decay process. We observe some tension between our value and $|V_{us}|$ evaluated from the unitarity of the CKM matrix with $|V_{ud}|$, while it depends on the size of the error of $|V_{ud}|$. It is also found that $|V_{us}|$ determined with our phase space integrals through six $K_{\ell 3}$ decay processes is consistent with the above one using $f_+(0)$.

Preliminary results on deconfinement phase transition in full QCD

We explore the profiles of the flux tube connecting a quark and an antiquark in hightemperature SU(3) lattice gauge theory in close vicinity to the critical temperature of thephase transition. In this work, we consider the more realistic case of the flux tube withdynamical quarks, extending the previous study to SU(3) gauge group and making use ofthe Gradient flow method in smoothing procedure for noise reduction. The profiles of thechromoelectric and chromomagnetic field strengths in the flux tube have been measuredfrom Polyakov loop-plaquette correlations using the highly improved staggered quark(HISQ) action on a lattice with temporal extent.

Chiralspin symmetry and confinement

Interesting lattice QCD simulations at high temperature in QCD and particular truncated studies have shown the emergence of an unexpected group symmetry, so called chiralspin. However this is not a symmetry of the QCD action for free quarks, which makes unclear the transition to deconfinement at high temperature in QCD. Therefore we try to redefine this group so that is a symmetry of free quark action and it is consistent with the presence of deconfinement in QCD.

Strong coupling constant from moments of quarkonium correlators revisited

We revisit previous determination of the strong coupling constant from moments of quarkonium correlators in (2 + 1)-flavor QCD. We use previously calculated moments obtained with Highly Improved Staggered Quark (HISQ) action for five different quark masses and several lattice spacings. We perform a careful continuum extrapolations of the moments and from the comparison of these to the perturbative result we determine the QCD Lambda parameter, varLambda _{overline{MS}}^{n_f=3}=332 pm 17 pm 2(scale) MeV. This corresponds to alpha _s^{n_f=5}(mu =M_Z)=0.1177(12).

Nucleon scalar and tensor couplings from lattice QCD at the physical points

We present results for the axial, scalar and tensor isovector-couplings (gA, gS and gT) of the nucleon obtained from 2+1 flavor QCD with the physical light quark masses (Mπ = 135 MeV). Our calculations are performed at a single lattice spacing of 0.085 fm, but with two large volumes of (10.9 fm)4 and (5.5 fm)4. The configurations are generated by the PACS Collaboration with nonperturbatively 𝒪(a) improved Wilson quark action and Iwasaki gauge action. The result of gA is a good indicator for determination of gS and gT with respect to accuracy and precision. Our result of gA well reproduces the experimental value within a statistical error of less than 2%. As for gS and gT, we compute the renormalization constants at the scale of 2 GeV in the ̅M̅S scheme through the RI/SMOM(γμ) intermediate scheme, and then obtain gS = 0.927(83)stat(22)syst and gT = 1.036(6)stat(20)syst.

Pion-Nucleon Sigma Term from Lattice QCD.

We present an analysis of the pion-nucleon σ-term σ_{πN} using six ensembles with 2+1+1-flavor highly improved staggered quark action generated by the MILC Collaboration. The most serious systematic effect in lattice calculations of nucleon correlation functions is the contribution of excited states. We estimate these using chiral perturbation theory (χPT) and show that the leading contribution to the isoscalar scalar charge comes from Nπ and Nππ states. Therefore, we carry out two analyses of lattice data to remove excited-state contamination, the standard one and a new one including Nπ and Nππ states. We find that the standard analysis gives σ_{πN}=41.9(4.9) MeV, consistent with previous lattice calculations, while our preferred χPT-motivated analysis gives σ_{πN}=59.6(7.4) MeV, which is consistent with phenomenological values obtained using πN scattering data. Our data on one physical pion mass ensemble were crucial for exposing this difference, therefore, calculations on additional physical mass ensembles are needed to confirm our result and resolve the tension between lattice QCD and phenomenology.

Linking continuum and lattice quark mass functions via an effective charge

The quark mass function is computed both by solving the quark propagator Dyson-Schwinger equation and from lattice simulations implementing overlap and Domain-Wall fermion actions for valence and sea quarks, respectively. The results are confronted and seen to produce a very congruent picture, showing a remarkable agreement for the explored range of current-quark masses. The effective running-interaction is based on a process-independent charge rooted on a particular truncation of the Dyson-Schwinger equations in the gauge sector, establishing thus a link from there to the quark sector and inspiring a correlation between the emergence of gluon and hadron masses.

Nucleon isovector scalar charge from overlap fermions

We calculate the nucleon isovector scalar charge in lattice QCD using overlap fermions on five ensembles of gauge configurations generated by the RBC/UKQCD collaboration using the domain-wall quark action with $2+1$ dynamical flavors. The five ensembles cover five pion masses, $m_\pi \approx$ 139, 171, 302, 337 and 371 MeV, and four lattice spacings, $a \approx $ 0.06, 0.08, 0.11 and 0.14 fm. Three to six valence quark masses are computed on each ensemble to investigate the pion mass dependence. The extrapolation to the physical pion mass, continuum and infinite volume limits is obtained by a global fit of all data to a formula originated from partially quenched chiral perturbation theory. The excited-states contamination is carefully analyzed with 3--5 sink-source separations and multi-state fits. Our final result, in the $\overline{\text{MS}}$ scheme at 2 GeV, is $g_{S}^{u-d}= 0.94 (10)_{stat}(8)_{sys}$, where the first error is the statistical error and the second is the systematic error.

Calculation of the derivative of nucleon form factors in Nf=2+1 lattice QCD at Mπ=138 MeV on a (5.5 fm)3 volume

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.

Flux tubes in full QCD at high temperature

Chromoelectric and chromomagnetic field and energy density distributions produced by a quark-antiquark pair have been investigated in the presence of dynamical fermions in the close vicinity to the deconfinement phase transition. In our lattice simulation we have used highly improved staggered quark action and tree level improved Symanzik gauge (HISQ/tree) action on the lattices of two different sizes, exploiting the Gradient flow method for noise reduction. We find that, in full QCD with dynamical quarks, the dynamical fermions widen the flux tube in a short separation range of about R = 1 fm, after which an hadronization takes place due to the suppression by the dynamical fermions. Energy density and width of the flux tube vanish at about R = 1.8 fm and R = 1.5 fm, respectively, at all temperatures. The present results also suggest that the flux tube structure still persists in the deconfined phase and it melts gradually after certain temperature value is reached above the critical temperature.

Improved Vcs determination using precise lattice QCD form factors for D→Kℓν

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

Dibaryon with Highest Charm Number near Unitarity from Lattice QCD.

A pair of triply charmed baryons, Ω_{ccc}Ω_{ccc}, is studied as an ideal dibaryon system by (2+1)-flavor lattice QCD with nearly physical light-quark masses and the relativistic heavy-quark action with the physical charm quark mass. The spatial baryon-baryon correlation is related to their scattering parameters on the basis of the HAL QCD method. The Ω_{ccc}Ω_{ccc} in the ^{1}S_{0} channel, taking into account the Coulomb repulsion with the charge form factor of Ω_{ccc}, leads to the scattering length a_{0}^{C}≃-19 fm and the effective range r_{eff}^{C}≃0.45 fm. The ratio r_{eff}^{C}/a_{0}^{C}≃-0.024, whose magnitude is considerably smaller than that of the dineutron (-0.149), indicates that Ω_{ccc}Ω_{ccc} is located in the unitary regime.

Chiral properties of ( 2+1 )-flavor QCD in strong magnetic fields at zero temperature

We present lattice QCD results for masses and magnetic polarizabilities of light and strange pseudoscalar mesons, chiral condensates, decay constants of neutral pion, and neutral kaon in the presence of background magnetic fields with $eB$ ranging up to around 3.35 GeV$^2$ ($\sim70~M_\pi^2$) in the vacuum. The computations were carried out in (2+1)-flavor QCD mostly on $32^3 \times 96$ lattices using the highly improved staggered quark action with $M_{\pi} \approx $ 220 MeV at zero temperature. We find that the masses of neutral pseudoscalar mesons monotonously decrease as the magnetic field strength grows and then saturate at a nonzero value, while there exists a nonmonotonous behavior of charged pion and kaon masses in the magnetic field. We observe a $qB$ scaling of the up and down quark flavor components of neutral pion mass, neutral pion decay constant as well as the quark chiral condensates at 0.05 $\lesssim eB\lesssim$ 3.35 GeV$^2$. We show that the correction to the Gell-Mann-Oakes-Renner relation involving the neutral pion is less than 6% and the correction for the relation involving neutral kaon is less than 30% at $eB\lesssim$ 3.35 GeV$^2$. We also derive the Ward-Takahashi identities for QCD in the magnetic field in the continuum formulation including the relation between integrated neutral pseudoscalar meson correlators and chiral condensates.