Flavors Of Domain Wall Fermions Research Articles

Simulating rare kaon decays K+→π+ℓ+ℓ− using domain wall lattice QCD with physical light quark masses

We report the first calculation using physical light-quark masses of the electromagnetic form factor $V(z)$ describing the long-distance contributions to the ${K}^{+}\ensuremath{\rightarrow}{\ensuremath{\pi}}^{+}{\ensuremath{\ell}}^{+}{\ensuremath{\ell}}^{\ensuremath{-}}$ decay amplitude. The calculation is performed on a $2+1$ flavor domain wall fermion ensemble with inverse lattice spacing ${a}^{\ensuremath{-}1}=1.730(4)\text{ }\text{ }\mathrm{GeV}$. We implement a Glashow-Iliopoulos-Maiani cancellation by extrapolating to the physical charm-quark mass from three below-charm masses. We obtain $V(z=0.013(2))=\ensuremath{-}0.87(4.44)$, achieving a bound for the value. The large statistical error arises from stochastically estimated quark loops.

Search for b¯b¯us and b¯c¯ud tetraquark bound states using lattice QCD

We use lattice QCD to investigate the existence of strong-interaction-stable antiheavy-antiheavy-light-light tetraquarks. We study the $\overline{b}\overline{b}us$ system with quantum numbers ${J}^{P}={1}^{+}$ as well as the $\overline{b}\overline{c}ud$ systems with quantum numbers $I({J}^{P})=0({0}^{+})$ and $I({J}^{P})=0({1}^{+})$. We carry out computations on five gauge-link ensembles with $2+1$ flavors of domain-wall fermions, including one at the physical pion mass. The bottom quarks are implemented using lattice nonrelativistic QCD, and the charm quarks using an anisotropic clover action. In addition to local diquark-antidiquark and local meson-meson interpolating operators, we include nonlocal meson-meson operators at the sink, which facilitates the reliable determination of the low-lying energy levels. We find clear evidence for the existence of a strong-interaction-stable $\overline{b}\overline{b}us$ tetraquark with binding energy $(\ensuremath{-}86\ifmmode\pm\else\textpm\fi{}22\ifmmode\pm\else\textpm\fi{}10)\text{ }\text{ }\mathrm{MeV}$ and mass $(10609\ifmmode\pm\else\textpm\fi{}22\ifmmode\pm\else\textpm\fi{}10)\text{ }\text{ }\mathrm{MeV}$. For the $\overline{b}\overline{c}ud$ systems we do not find any indication for the existence of bound states, but cannot rule out their existence either.

Λb→Λc*(2595,2625)ℓ−ν¯ form factors from lattice QCD

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

Roper state from overlap fermions

The Roper state is extracted with valence overlap fermions on a $2+1$-flavor domain-wall fermion lattice (spacing $a = 0.114$ fm and $m_{\pi} = 330$ MeV) using both the Sequential Empirical Bayes (SEB) method and the variational method. The results are consistent, provided that a large smearing-size interpolation operator is included in the variational calculation to have better overlap with the lowest radial excitation. Similar calculations carried out for an anisotropic clover lattice with similar parameters find the Roper $\approx 280$ MeV higher than that of the overlap fermion. The fact that the prediction of the Roper state by overlap fermions is consistently lower than those of clover fermions, chirally improved fermions, and twisted-mass fermions over a wide range of pion masses has been dubbed a "Roper puzzle." To understand the origin of this difference, we study the hairpin $Z$-diagram in the isovector scalar meson ($a_0$) correlator in the quenched approximation. Comparing the $a_0$ correlators for clover and overlap fermions, at a pion mass of 290 MeV, we find that the spectral weight of the ghost state with clover fermions is smaller than that of the overlap at $a = 0.12$ fm and $0.09$ fm, whereas the whole $a_0$ correlators of clover and overlap at $a = 0.06$ fm coincide within errors. This suggests that chiral symmetry is restored for clover at $a \le 0.06$ fm and that the Roper should come down at and below this $a$. We conclude that this work supports a resolution of the "Roper puzzle" due to $Z$-graph type chiral dynamics. This entails coupling to higher components in the Fock space (e.g. $N\pi$, $N\pi\pi$ states) to induce the effective flavor-spin interaction between quarks as prescribed in the chiral quark model, resulting in the parity-reversal pattern as observed in the experimental excited states of $N, \Delta$ and $\Lambda$.

Lattice QCD investigation of a doubly-bottom b¯b¯ud tetraquark with quantum numbers I(JP)=0(1+)

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

Strong Running Coupling from the Gauge Sector of Domain Wall Lattice QCD with Physical Quark Masses.

We report on the first computation of the strong running coupling at the physical point (physical pion mass) from the ghost-gluon vertex, computed from lattice simulations with three flavors of domain wall fermions. We find α_{MS[over ¯]}(m_{Z}^{2})=0.1172(11), in remarkably good agreement with the world-wide average. Our computational bridge to this value is the Taylor-scheme strong coupling, which has been revealed of great interest by itself because it can be directly related to the quark-gluon interaction kernel in continuum approaches to the QCD bound-state problem.

Gluon Quasi-Parton-Distribution Functions from Lattice QCD.

We present the first attempt to access the x dependence of the gluon unpolarized parton-distribution function (PDF), based on lattice simulations using the large-momentum effective theory approach. The lattice calculation is carried out with pion masses of 340 and 678MeV on a (2+1)-flavor domain-wall fermion configuration with lattice spacing a=0.111 fm, for the gluon quasi-PDF matrix element with the nucleon momentum up to 0.93GeV. Taking the normalization from similar matrix elements in the rest frame of the nucleon and pion, our results for these matrix elements are consistent with the Fourier transform of the global fit CT14 and PDF4LHC15 NNLO of the gluon PDF, within statistical uncertainty and the systematic one up to power corrections, perturbative O(α_{s}) matching and the mixing from the quark PDFs.

Λc→N form factors from lattice QCD and phenomenology of Λc→nℓ+νℓ and Λc→pμ+μ− decays

A lattice QCD determination of the $\Lambda_c \to N$ vector, axial vector, and tensor form factors is reported. The calculation was performed with $2+1$ flavors of domain wall fermions at lattice spacings of $a\approx 0.11\:{\rm fm},\:0.085\:{\rm fm}$ and pion masses in the range $230\:{\rm MeV} \lesssim m_\pi \lesssim 350$ MeV. The form factors are extrapolated to the continuum limit and the physical pion mass using modified $z$ expansions. The rates of the charged-current decays $\Lambda_c \to n\, e^+ \nu_e$ and $\Lambda_c \to n\, \mu^+ \nu_\mu$ are predicted to be $\left( 0.405 \pm 0.016_{\,\rm stat} \pm 0.020_{\,\rm syst} \right)|V_{cd}|^2 \:{\rm ps}^{-1}$ and $\left( 0.396 \pm 0.016_{\,\rm stat} \pm 0.020_{\,\rm syst} \right)|V_{cd}|^2 \:{\rm ps}^{-1}$, respectively. The phenomenology of the rare charm decay $\Lambda_c \to p\, \mu^+ \mu^-$ is also studied. The differential branching fraction, the fraction of longitudinally polarized dimuons, and the forward-backward asymmetry are calculated in the Standard Model and in an illustrative new-physics scenario.

αs from the Hadronic Vacuum Polarisation

We present our result for the strong coupling constant computed from the u-d vector Hadronic Vacuum Polarisation function. We use nf = 2 + 1 flavours of Domain Wall fermions at 3 lattice spacings, generated by the RBC-UKQCD collaboration. We identify several possible pitfalls in this method for determining the coupling and illustrate how to resolve them.

Neutral kaon mixing beyond the Standard Model with nf = 2 + 1 chiral fermions. Part 2: non perturbative renormalisation of the \u0394F = 2 four-quark operators

We compute the renormalisation factors (Z-matrices) of the ΔF = 2 four-quark operators needed for Beyond the Standard Model (BSM) kaon mixing. We work with nf = 2+1 flavours of Domain-Wall fermions whose chiral-flavour properties are essential to maintain a continuum-like mixing pattern. We introduce new RI-SMOM renormalisation schemes, which we argue are better behaved compared to the commonly-used corresponding RI-MOM one. We find that, once converted to overline{mathrm{MS}} , the Z-factors computed through these RI-SMOM schemes are in good agreement but differ significantly from the ones computed through the RI-MOM scheme. The RI-SMOM Z-factors presented here have been used to compute the BSM neutral kaon mixing matrix elements in the companion paper [1]. We argue that the renormalisation procedure is responsible for the discrepancies observed by different collaborations, we will investigate and elucidate the origin of these differences throughout this work.

Lattice calculation of nucleon isovector axial charge with improved currents

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.

Glue Spin and Helicity in the Proton from Lattice QCD.

We report the first lattice QCD calculation of the glue spin in the nucleon. The lattice calculation is carried out with valence overlap fermions on 2+1 flavor domain-wall fermion gauge configurations on four lattice spacings and four volumes including an ensemble with physical values for the quark masses. The glue spin S_{G} in the Coulomb gauge in the modified minimal subtraction (MS[over ¯]) scheme is obtained with one-loop perturbative matching. We find the results fairly insensitive to lattice spacing and quark masses. We also find that the proton momentum dependence of S_{G} in the range 0≤|p[over →]|<1.5 GeV is very mild, and we determine it in the large-momentum limit to be S_{G}=0.251(47)(16) at the physical pion mass in the MS[over ¯] scheme at μ^{2}=10 GeV^{2}. If the matching procedure in large-momentum effective theory is neglected, S_{G} is equal to the glue helicity measured in high-energy scattering experiments.

Neutron and proton electric dipole moments fromNf=2+1domain-wall fermion lattice QCD

We present a lattice calculation of the neutron and proton electric dipole moments (EDM's) with $N_f=2+1$ flavors of domain-wall fermions. The neutron and proton EDM form factors are extracted from three-point functions at the next-to-leading order in the $\theta$ vacuum of QCD. In this computation, we use pion masses 0.33 and 0.42 GeV and 2.7 fm$^3$ lattices with Iwasaki gauge action and a 0.17 GeV pion and 4.6 fm$^3$ lattice with I-DSDR gauge action, all generated by the RBC and UKQCD collaborations. The all-mode-averaging technique enables an efficient and high statistics calculation. Chiral behavior of lattice EDM's is discussed in the context of baryon chiral perturbation theory. In addition, we also show numerical evidence on relationship of three- and two-point correlation function with local topological distribution.

Charm and strange quark masses andfDsfrom overlap fermions

We use overlap fermions as valence quarks to calculate meson masses in a wide quark mass range on the $2+1$-flavor domain-wall fermion gauge configurations generated by the RBC and UKQCD Collaborations. The well-defined quark masses in the overlap fermion formalism and the clear valence quark mass dependence of meson masses observed from the calculation facilitate a direct derivation of physical current quark masses through a global fit to the lattice data, which incorporates $O(a^2)$ and $O(m_c^4a^4)$ corrections, chiral extrapolation, and quark mass interpolation. Using the physical masses of $D_s$, $D_s^*$ and $J/\psi$ as inputs, Sommer's scale parameter $r_0$ and the masses of charm quark and strange quark in the $\overline{\rm MS}$ scheme are determined to be $r_0=0.465(4)(9)$ fm, $m_c^{\overline{\rm MS}}(2\,{\rm GeV})=1.118(6)(24)$ GeV (or $m_c^{\overline{\rm MS}}(m_c)=1.304(5)(20)$ GeV), and $m_s^{\overline{\rm MS}}(2\,{\rm GeV})=0.101(3)(6)\,{\rm GeV}$, respectively. Furthermore, we observe that the mass difference of the vector meson and the pseudoscalar meson with the same valence quark content is proportional to the reciprocal of the square root of the valence quark masses. The hyperfine splitting of charmonium, $M_{J/\psi}-M_{\eta_c}$, is determined to be 119(2)(7) MeV, which is in good agreement with the experimental value. We also predict the decay constant of $D_s$ to be $f_{D_s}=254(2)(4)$ MeV. The masses of charmonium $P$-wave states $\chi_{c0}, \chi_{c1}$ and $h_c$ are also in good agreement with experiments.

Meson mass decomposition from lattice QCD

Hadron masses can be decomposed as a sum of quark and glue components which are defined through hadronic matrix elements of QCD operators. The components consist of the quark mass term, the quark energy term, the glue energy term, and the trace anomaly term. We calculate these components for mesons with lattice QCD for the first time. The calculation is carried out with overlap fermion on $2+1$ flavor domain-wall fermion gauge configurations. We confirm that $\sim 50\%$ of the light pion mass comes from the quark mass term and $\sim 10\%$ comes from the quark energy; whereas, while for the $\rho$ meson, the quark energy contributes roughly half of its mass but the quark mass term contributes little. The combined glue components contribute $\sim 40 - 50\%$ for both mesons. It is interesting to observe that the quark mass contribution to the mass of the vector meson is almost linear in quark mass over a large quark mass region below the charm quark mass. For heavy mesons, the quark mass term dominates the masses, while the contribution from the glue components is about $200$ MeV (a bare value around 2GeV) for the heavy pseudoscalar and vector mesons. The charmonium hyperfine splitting is found to be dominated by the quark energy term which is consistent with the picture of the quark potential model.

Lattice simulations with eight flavors of domain wall fermions in SU(3) gauge theory

We study an SU(3) gauge theory with ${N}_{f}=8$ degenerate flavors of light fermions in the fundamental representation. Using the domain wall fermion formulation, we investigate the light hadron spectrum, chiral condensate $⟨\overline{\ensuremath{\psi}}\ensuremath{\psi}⟩$ and electroweak $S$ parameter. We consider a range of light fermion masses on two lattice volumes at a single gauge coupling chosen so that IR scales approximately match those from our previous studies of the two- and six-flavor systems. Our results for the ${N}_{f}=8$ spectrum suggest spontaneous chiral symmetry breaking, though fits to the fermion mass dependence of spectral quantities do not strongly disfavor the hypothesis of mass-deformed infrared conformality. Compared to ${N}_{f}=2$ we observe a significant enhancement of $⟨\overline{\ensuremath{\psi}}\ensuremath{\psi}⟩$ relative to the symmetry breaking scale $F$, similar to the situation for ${N}_{f}=6$. The reduction of the $S$ parameter, related to parity doubling in the vector and axial-vector channels, is also comparable to our six-flavor results.

Nonperturbative renormalization of overlap quark bilinears on2+1-flavor domain wall fermion configurations

We present renormalization constants of overlap quark bilinear operators on $2+1$-flavor domain wall fermion configurations. This setup is being used by the $\ensuremath{\chi}\mathrm{QCD}$ Collaboration in calculations of physical quantities such as strangeness in the nucleon and the strange and charm quark masses. The scale-independent renormalization constant for the axial-vector current is computed using the Ward identity. The renormalization constants for scalar, pseudoscalar, and vector currents are calculated in the RI-MOM scheme. Results in the $\overline{\mathrm{MS}}$ scheme are also given. The step scaling function of quark masses in the RI-MOM scheme is computed as well. The analysis uses, in total, six different ensembles of three sea quarks, each on two lattices with sizes ${24}^{3}\ifmmode\times\else\texttimes\fi{}64$ and ${32}^{3}\ifmmode\times\else\texttimes\fi{}64$ at spacings $a=(1.73\text{ }\text{ }\mathrm{GeV}{)}^{\ensuremath{-}1}$ and $(2.28\text{ }\text{ }\mathrm{GeV}{)}^{\ensuremath{-}1}$, respectively.

Λb→Λℓ+ℓ−form factors and differential branching fraction from lattice QCD

We present the first lattice QCD determination of the ${\ensuremath{\Lambda}}_{b}\ensuremath{\rightarrow}\ensuremath{\Lambda}$ transition form factors that govern the rare baryonic decays ${\ensuremath{\Lambda}}_{b}\ensuremath{\rightarrow}\ensuremath{\Lambda}{\ensuremath{\ell}}^{+}{\ensuremath{\ell}}^{\ensuremath{-}}$ at leading order in heavy-quark effective theory. Our calculations are performed with $2+1$ flavors of domain-wall fermions, at two lattice spacings and with pion masses down to 227 MeV. Three-point functions with a wide range of source-sink separations are used to extract the ground-state contributions. The form factors are extrapolated to the physical values of the light-quark masses and to the continuum limit. We use our results to calculate the differential branching fractions for ${\ensuremath{\Lambda}}_{b}\ensuremath{\rightarrow}\ensuremath{\Lambda}{\ensuremath{\ell}}^{+}{\ensuremath{\ell}}^{\ensuremath{-}}$ with $\ensuremath{\ell}=e$, $\ensuremath{\mu}$, $\ensuremath{\tau}$ within the standard model. We find agreement with a recent CDF measurement of the ${\ensuremath{\Lambda}}_{b}\ensuremath{\rightarrow}\ensuremath{\Lambda}{\ensuremath{\mu}}^{+}{\ensuremath{\mu}}^{\ensuremath{-}}$ differential branching fraction.

Continuum limit ofBKfrom2+1flavor domain wall QCD

We determine the neutral kaon mixing matrix element ${B}_{K}$ in the continuum limit with $2+1$ flavors of domain wall fermions, using the Iwasaki gauge action at two different lattice spacings. These lattice fermions have near exact chiral symmetry and therefore avoid artificial lattice operator mixing. We introduce a significant improvement to the conventional nonperturbative renormalization (NPR) method in which the bare matrix elements are renormalized nonperturbatively in the regularization invariant momentum scheme (RI-MOM) and are then converted into the $\overline{\mathrm{MS}}$ scheme using continuum perturbation theory. In addition to RI-MOM, we introduce and implement four nonexceptional intermediate momentum schemes that suppress infrared nonperturbative uncertainties in the renormalization procedure. We compute the conversion factors relating the matrix elements in this family of regularization invariant symmetric momentum schemes (RI-SMOM) and $\overline{\mathrm{MS}}$ at one-loop order. Comparison of the results obtained using these different intermediate schemes allows for a more reliable estimate of the unknown higher-order contributions and hence for a correspondingly more robust estimate of the systematic error. We also apply a recently proposed approach in which twisted boundary conditions are used to control the Symanzik expansion for off-shell vertex functions leading to a better control of the renormalization in the continuum limit. We control chiral extrapolation errors by considering both the next-to-leading order SU(2) chiral effective theory, and an analytic mass expansion. We obtain ${B}_{K}^{\overline{\mathrm{MS}}}(3\text{ }\text{ }\mathrm{GeV})=0.529(5{)}_{\mathrm{stat}}(15{)}_{\ensuremath{\chi}}(2{)}_{\mathrm{FV}}(11{)}_{\mathrm{NPR}}$. This corresponds to ${\stackrel{^}{B}}_{K}^{\overline{\mathrm{RGI}}}=0.749(7{)}_{\mathrm{stat}}(21{)}_{\ensuremath{\chi}}(3{)}_{\mathrm{FV}}(15{)}_{\mathrm{NPR}}$. Adding all sources of error in quadrature, we obtain ${\stackrel{^}{B}}_{K}^{\overline{\mathrm{RGI}}}=0.749(27{)}_{\mathrm{combined}}$, with an overall combined error of 3.6%.

Overlap valence on2+1flavor domain wall fermion configurations with deflation and low-mode substitution

The overlap fermion propagator is calculated on 2+1 flavor domain wall fermion gauge configurations on 16^3 x 32, 24^3 x 64 and 32^3 x 64 lattices. With HYP smearing and low eigenmode deflation, it is shown that the inversion of the overlap operator can be expedited by ~ 20 times for the 16^3 x 32 lattice and ~ 80 times for the 32^3 x 64 lattice. Through the study of hyperfine splitting, we found that the O(m^2a^2) error is small and these dynamical fermion lattices can adequately accommodate quark mass up to the charm quark. The low energy constant \Delta_{mix} which characterizes the discretization error of the pion made up of a pair of sea and valence quarks in this mixed action approach is calculated via the scalar correlator with periodic and anti-periodic boundary conditions. It is found to be small which shifts a 300 MeV pion mass by ~ 10 to 19 MeV on these sets of lattices. We have studied the signal-to-noise issue of the noise source for the meson and baryon. It is found that the many-to-all meson and baryon correlators with Z_3 grid source and low eigenmode substitution is efficient in reducing errors for the correlators of both mesons and baryons. With 64-point Z_3 grid source and low-mode substitution, it can reduce the statistical errors of the light quark (m_{\pi} ~ 200 - 300 MeV) meson and nucleon correlators by a factor of ~ 3-4 as compared to the point source. The Z_3 grid source itself can reduce the errors of the charmonium correlators by a factor of ~ 3.