Light Sea Quark Masses Research Articles

Correlated Dirac Eigenvalues and Axial Anomaly in Chiral Symmetric QCD.

We introduce novel relations between the derivatives [∂^{n}ρ(λ,m_{l})/∂m_{l}^{n}] of the Dirac eigenvalue spectrum [ρ(λ,m_{l})] with respect to the light sea quark mass (m_{l}) and the (n+1)-point correlations among the eigenvalues (λ) of the massless Dirac operator. Using these relations we present lattice QCD results for ∂^{n}ρ(λ,m_{l})/∂m_{l}^{n} (n=1, 2, 3) for m_{l} corresponding to pion masses m_{π}=160-55 MeV and at a temperature of about 1.6 times the chiral phase transition temperature. Calculations were carried out using (2+1) flavors of highly improved staggered quarks with the physical value of strange quark mass, three lattice spacings a=0.12, 0.08, 0.06fm, and lattices having aspect ratios 4-9. We find that ρ(λ→0,m_{l}) develops a peaked structure. This peaked structure arises due to non-Poisson correlations within the infrared part of the Dirac eigenvalue spectrum, becomes sharper as a→0, and its amplitude is proportional to m_{l}^{2}. We demonstrate that this ρ(λ→0,m_{l}) is responsible for the manifestations of axial anomaly in two-point correlation functions of light scalar and pseudoscalar mesons. After continuum and chiral extrapolations we find that axial anomaly remains manifested in two-point correlation functions of scalar and pseudoscalar mesons in the chiral limit.

Splittings of low-lying charmonium masses at the physical point

We present high-precision results from lattice QCD for the mass splittings of the low-lying charmonium states. For the valence charm quark, the calculation uses Wilson-clover quarks in the Fermilab interpretation. The gauge-field ensembles are generated in the presence of up, down, and strange sea quarks, based on the improved staggered (asqtad) action, and gluon fields, based on the one-loop, tadpole-improved gauge action. We use five lattice spacings and two values of the light sea quark mass to extrapolate the results to the physical point. An enlarged set of interpolating operators is used for a variational analysis to improve the determination of the energies of the ground states in each channel. We present and implement a continuum extrapolation within the Fermilab interpretation, based on power-counting arguments, and thoroughly discuss all sources of systematic uncertainty. We compare our results for various mass splittings with their experimental values, namely, the 1S hyperfine splitting, the 1P-1S splitting and the P-wave spin-orbit and tensor splittings. Given the uncertainty related to the width of the resonances, we find excellent agreement.

Quark chiral condensate from the overlap quark propagator**Supported by National Natural Science Foundation of China (11575197, 11575196, 11335001, 11405178), joint funds of NSFC (U1632104, U1232109), YC and ZL acknowledge the support of NSFC and DFG (CRC110)

From the overlap lattice quark propagator calculated in the Landau gauge, we determine the quark chiral condensate by fitting operator product expansion formulas to the lattice data. The quark propagators are computed on domain wall fermion configurations generated by the RBC-UKQCD Collaborations with Nf = 2+1 flavors. Three ensembles with different light sea quark masses are used at one lattice spacing 1/a = 1.75(4) GeV. We obtain in the SU(2) chiral limit.

Diquark mass differences from unquenched lattice QCD**Supported by National Science Foundation of China (11575197, 10835002, 11405178, 11335001), joint funds of NSFC (U1232109), MG and ZL are partially supported by the Youth Innovation Promotion Association of CAS (2015013, 2011013), YC and ZL acknowledge support of NSFC and DFG (CRC110)

We calculate diquark correlation functions in the Landau gauge on the lattice using overlap valence quarks and 2+1-flavor domain wall fermion configurations. Quark masses are extracted from the scalar part of quark propagators in the Landau gauge. The scalar diquark quark mass difference and axial vector scalar diquark mass difference are obtained for diquarks composed of two light quarks and of a strange and a light quark. The light sea quark mass dependence of the results is examined. Two lattice spacings are used to check the discretization effects. The coarse and fine lattices are of sizes 243 × 64 and 323 × 64 with inverse spacings 1/a = 1.75(4) GeV and 2.33(5) GeV, respectively.

The strange and charm quark contributions to the anomalous magnetic moment of the muon from lattice QCD

We describe a new technique (published in [1]) to determine the contribution to the anomalous magnetic moment of the muon coming from the hadronic vacuum polarisation using lattice QCD. Our method uses Padé approximants to reconstruct the Adler function from its derivatives at q2=0. These are obtained simply and accurately from time-moments of the vector current-current correlator at zero spatial momentum. We test the method using strange quark correlators calculated on MILC Collaboration's nf=2+1+1 HISQ ensembles at multiple values of the lattice spacing, multiple volumes and multiple light sea quark masses (including physical pion mass configurations). We find the (connected) contribution to the anomalous moment from the strange quark vacuum polarisation to be aμs=53.41(59)×10−10, and the contribution from charm quarks to be aμc=14.42(39)×10−10−1% accuracy is achieved for the strange quark contribution. The extension of our method to the light quark contribution and to that from the quark-line disconnected diagram is straightforward.

Lattice calculation of the leading strange quark-connected contribution to the muon g − 2

We present results for the leading hadronic contribution to the muon anomalous magnetic moment due to strange quark-connected vacuum polarisation effects. Simulations were performed using RBC--UKQCD's $N_f=2+1$ domain wall fermion ensembles with physical light sea quark masses at two lattice spacings. We consider a large number of analysis scenarios in order to obtain solid estimates for residual systematic effects. Our final result in the continuum limit is $a_\mu^{(2)\,{\rm had},\,s}=53.1(9)\left(^{+1}_{-3}\right)\times10^{-10}$.

Kaon BSMB-parameters using improved staggered fermions fromNf=2+1unquenched QCD

We present results for the matrix elements of the additional $\Delta S=2$ operators that appear in models of physics beyond the Standard Model (BSM), expressed in terms of four BSM $B$-parameters. Combined with experimental results for $\Delta M_K$ and $\epsilon_K$, these constrain the parameters of BSM models. We use improved staggered fermions, with valence HYP-smeared quarks and $N_f=2+1$ flavors of "asqtad" sea quarks. The configurations have been generated by the MILC collaboration. The matching between lattice and continuum four-fermion operators and bilinears is done perturbatively at one-loop order. We use three lattice spacings for the continuum extrapolation: $a\approx 0.09$, $0.06$ and $0.045\;$fm. Valence light-quark masses range down to $\approx m_s^{\rm phys}/13$ while the light sea-quark masses range down to $\approx m_s^{\rm phys}/20$. Compared to our previous published work, we have added four additional lattice ensembles, leading to better controlled extrapolations in the lattice spacing and sea-quark masses. We report final results for two renormalization scales, $\mu=2\;\text{GeV}$ and $3\;\text{GeV}$, and compare them to those obtained by other collaborations. Agreement is found for two of the four BSM $B$-parameters ($B_2$ and $B_3^\text{SUSY}$). The other two ($B_4$ and $B_5$) differ significantly from those obtained using RI-MOM renormalization as an intermediate scheme, but are in agreement with recent preliminary results obtained by the RBC-UKQCD collaboration using RI-SMOM intermediate schemes.

Charmed and light pseudoscalar meson decay constants from four-flavor lattice QCD with physical light quarks

We compute the leptonic decay constants $f_{D^+}$, $f_{D_s}$, and $f_{K^+}$, and the quark-mass ratios $m_c/m_s$ and $m_s/m_l$ in unquenched lattice QCD using the experimentally determined value of $f_{\pi^+}$ for normalization. We use the MILC highly improved staggered quark (HISQ) ensembles with four dynamical quark flavors---up, down, strange, and charm---and with both physical and unphysical values of the light sea-quark masses. The use of physical pions removes the need for a chiral extrapolation, thereby eliminating a significant source of uncertainty in previous calculations. Four different lattice spacings ranging from $a\approx 0.06$ fm to $0.15$ fm are included in the analysis to control the extrapolation to the continuum limit. Our primary results are $f_{D^+} = 212.6(0.4)({}^{+1.0}_{-1.2})\ \mathrm{MeV}$, $f_{D_s} = 249.0(0.3)({}^{+1.1}_{-1.5})\ \mathrm{MeV}$, and $f_{D_s}/f_{D^+} = 1.1712(10)({}^{+29}_{-32})$, where the errors are statistical and total systematic, respectively. The errors on our results for the charm decay constants and their ratio are approximately two to four times smaller than those of the most precise previous lattice calculations. We also obtain $f_{K^+}/f_{\pi^+} = 1.1956(10)({}^{+26}_{-18})$, updating our previous result, and determine the quark-mass ratios $m_s/m_l = 27.35(5)({}^{+10}_{-7})$ and $m_c/m_s = 11.747(19)({}^{+59}_{-43})$. When combined with experimental measurements of the decay rates, our results lead to precise determinations of the CKM matrix elements $|V_{us}| = 0.22487(51) (29)(20)(5)$, $|V_{cd}|=0.217(1) (5)(1)$ and $|V_{cs}|= 1.010(5)(18)(6)$, where the errors are from this calculation of the decay constants, the uncertainty in the experimental decay rates, structure-dependent electromagnetic corrections, and, in the case of $|V_{us}|$, the uncertainty in $|V_{ud}|$, respectively.

Excited-state spectroscopy of triply bottom baryons from lattice QCD

The spectrum of baryons containing three $b$ quarks is calculated in nonperturbative QCD, using the lattice regularization. The energies of ten excited $bbb$ states with ${J}^{P}=\frac{1}{2}{\text{ }}^{+}$, $\frac{3}{2}{\text{ }}^{+}$, $\frac{5}{2}{\text{ }}^{+}$, $\frac{7}{2}{\text{ }}^{+}$, $\frac{1}{2}{\text{ }}^{\ensuremath{-}}$, and $\frac{3}{2}{\text{ }}^{\ensuremath{-}}$ are determined with high precision. A domain-wall action is used for the up, down, and strange quarks, and the bottom quarks are implemented with nonrelativistic QCD. The computations are done at lattice spacings of $a\ensuremath{\approx}0.11\text{ }\text{ }\mathrm{fm}$ and $a\ensuremath{\approx}0.08\text{ }\text{ }\mathrm{fm}$, and the results demonstrate the improvement of rotational symmetry as $a$ is reduced. A large lattice volume of $(2.7\text{ }\text{ }\mathrm{fm}{)}^{3}$ is used, and extrapolations of the $bbb$ spectrum to realistic values of the light sea-quark masses are performed. All spin-dependent energy splittings are resolved with total uncertainties of order 1 MeV, and the dependence of these splittings on the couplings in the nonrelativistic QCD action is analyzed.

Probing the chiral regime ofNf=2QCD with mixed actions

We report on our first experiences with a mixed action setup with overlap valence quarks and non-perturbatively O(a) improved Wilson sea quarks. For the latter we employ CLS Nf=2 configurations with light sea quark masses at small lattice spacings. Exact chiral symmetry allows to consider very light valence quarks and explore the matching to (partially quenched) Chiral Perturbation Theory (ChPT) in a mixed epsilon/p-regime. We compute the topological susceptibility and the low-lying spectrum of the massless Neuberger-Dirac operator for three values of the sea quark mass, and compare the sea quark mass dependence to NLO ChPT in the mixed regime. This provides two different determinations of the chiral condensate, as well as information about some NLO low-energy couplings. Our results allow to test the consistency of the mixed-regime approach to ChPT, as well as of the mixed action framework.

BKusing HYP-smeared staggered fermions inNf=2+1unquenched QCD

We present results for kaon mixing parameter $B_K$ calculated using HYP-smeared improved staggered fermions on the MILC asqtad lattices. We use three lattice spacings ($a\approx 0.12$, $0.09$ and $0.06\;$fm), ten different valence quark masses ($m\approx m_s/10-m_s$), and several light sea-quark masses in order to control the continuum and chiral extrapolations. We derive the next-to-leading order staggered chiral perturbation theory (SChPT) results necessary to fit our data, and use these results to do extrapolations based both on SU(2) and SU(3) SChPT. The SU(2) fitting is particularly straightforward because parameters related to taste-breaking and matching errors appear only at next-to-next-to-leading order. We match to the continuum renormalization scheme (NDR) using one-loop perturbation theory. Our final result is from the SU(2) analysis, with the SU(3) result providing a (less accurate) cross check. We find $B_K(\text{NDR}, \mu = 2 \text{GeV}) = 0.529 \pm 0.009 \pm 0.032$ and $\hat{B}_K =B_K(\text{RGI})= 0.724 \pm 0.012 \pm 0.043$, where the first error is statistical and the second systematic. The error is dominated by the truncation error in the matching factor. Our results are consistent with those obtained using valence domain-wall fermions on lattices generated with asqtad or domain-wall sea quarks.

Erratum: Determination of the Chiral Condensate from (2+1)-Flavor Lattice QCD [Phys. Rev. Lett.104, 122002 (2010)

We perform a precise calculation of the chiral condensate in QCD using lattice QCD with 2+1 flavors of dynamical overlap quarks. Up and down quark masses cover a range between 3 and 100 MeV on a 16^3x48 lattice at a lattice spacing around 0.11 fm. At the lightest sea quark mass, the finite volume system on the lattice is in the epsilon-regime. By matching the low-lying eigenvalue spectrum of the Dirac operator with the prediction of chiral perturbation theory at the next-to-leading order, we determine the chiral condensate in 2+1-flavor QCD with strange quark mass fixed at its physical value as Sigma (MS-bar at 2 GeV) = [242(04)(^+19_-18}) MeV}]^3, where the errors are statistical and systematic, respectively.

NeutralB-meson mixing from unquenched lattice QCD with domain-wall light quarks and staticbquarks

We demonstrate a method for calculating the neutral B-meson decay constants and mixing matrix elements in unquenched lattice QCD with domain-wall light quarks and static b-quarks. Our computation is performed on the "2+1" flavor gauge configurations generated by the RBC and UKQCD Collaborations with a lattice spacing of a approx 0.11 fm (a^-1 = 1.729 GeV) and a lattice spatial volume of approximately (1.8 fm)^3. We simulate at three different light sea quark masses with pion masses down to approximately 430 MeV, and extrapolate to the physical quark masses using a phenomenologically-motivated fit function based on next-to-leading order heavy-light meson SU(2) chiral perturbation theory. For the b-quarks, we use an improved formulation of the Eichten-Hill action with static link-smearing to increase the signal-to-noise ratio. We also improve the heavy-light axial current used to compute the B-meson decay constant to O(alpha_s p a) using one-loop lattice perturbation theory. We present initial results for the SU(3)-breaking ratios f_{B_s}/f_{B_d} and xi = f_{B_s} sqrt{B_{B_s}}/f_{B_d} sqrt{B_{B_d}}, thereby demonstrating the viability of the method. For the ratio of decay constants, we find f_{B_s}/f_{B_d} = 1.15(12) and for the ratio of mixing matrix elements, we find xi = 1.13(12), where in both cases the errors reflect the combined statistical and systematic uncertainties, including an estimate of the size of neglected O(1/m_b) effects.

Determination of the Chiral Condensate from (2+1)-Flavor Lattice QCD

We perform a precise calculation of the chiral condensate in QCD using lattice QCD with 2+1 flavors of dynamical overlap quarks. Up and down quark masses cover a range between 3 and 100 MeV on a 16{3}x48 lattice at a lattice spacing approximately 0.11 fm. At the lightest sea quark mass, the finite volume system on the lattice is in the regime. By matching the low-lying eigenvalue spectrum of the Dirac operator with the prediction of chiral perturbation theory at the next-to-leading order, we determine the chiral condensate in (2+1)-flavor QCD with strange quark mass fixed at its physical value as Sigma;{MS[over ]}(2 GeV)=[242(04)(+19/-18) MeV]{3} where the errors are statistical and systematic, respectively.

Topological susceptibility in [formula omitted] flavors lattice QCD with domain-wall fermions

We measure the topological charge and its fluctuation for the gauge configurations generated by the RBC and UKQCD Collaborations using 2+1 flavors of domain-wall fermions on the 163×32 lattice (L≃2 fm) with length 16 in the fifth dimension at the inverse lattice spacing a−1≃1.62 GeV. From the spectral flow of the Hermitian operator Hw(2+γ5Hw)−1, we obtain the topological charge Qt of each gauge configuration in the three ensembles with light sea quark masses mqa=0.01, 0.02, and 0.03, and with the strange quark mass fixed at msa=0.04. From our result of Qt, we compute the topological susceptibility χt=〈Qt2〉/Ω, where Ω is the volume of the lattice. In the small mq regime, our result of χt agrees with the chiral effective theory. Using the formula χt=Σ/(mu−1+md−1+ms−1) by Leutwyler–Smilga, we obtain the chiral condensate ΣMS¯(2 GeV)=[259(6)(9) MeV]3.

2+1flavor domain wall QCD on a(2 fm)3lattice: Light meson spectroscopy withLs=16

We present results for light meson masses and pseudoscalar decay constants from the first of a series of lattice calculations with 2+1 dynamical flavors of domain wall fermions and the Iwasaki gauge action. The work reported here was done at a fixed lattice spacing of about 0.12 fm on a 16^3\times32 lattice, which amounts to a spatial volume of (2 fm)^3 in physical units. The number of sites in the fifth dimension is 16, which gives m_{res} = 0.00308(4) in these simulations. Three values of input light sea quark masses, m_l^{sea} \approx 0.85 m_s, 0.59 m_s and 0.33 m_s were used to allow for extrapolations to the physical light quark limit, whilst the heavier sea quark mass was fixed to approximately the physical strange quark mass m_s. The exact rational hybrid Monte Carlo algorithm was used to evaluate the fractional powers of the fermion determinants in the ensemble generation. We have found that f_\pi = 127(4) MeV, f_K = 157(5) MeV and f_K/f_\pi = 1.24(2), where the errors are statistical only, which are in good agreement with the experimental values.

Decay constants ofP-wave heavy-light mesons from unquenched lattice QCD

We review some decays that require knowledge of the decay constants of ${0}^{+}$ heavy-light mesons. We compute the decay constants of $P$-wave heavy-light mesons from unquenched lattice QCD, with two degenerate flavours of sea quarks, at a single lattice spacing. The lightest sea quark mass used in the calculation is a third of the strange quark mass. For the charm-strange meson we obtain the decay constant: ${f}_{{D}_{s{0}^{+}}}=340(110)\text{ }\text{ }\mathrm{MeV}$ using our normalization conventions. We obtain the ${f}_{{P}_{s}}^{\mathrm{static}}$ (static-strange $P$-wave) decay constant as $302(39)\text{ }\text{ }\mathrm{MeV}$.

Unquenched determination of the kaon parameterBKfrom improved staggered fermions

The use of improved staggered actions (HYP, Asqtad) has been proved to reduce the scaling corrections that affected previous calculations of ${B}_{K}$ with unimproved (standard) staggered fermions in the quenched approximation. This improved behavior allows us to perform a reliable calculation of ${B}_{K}$ including quark vacuum polarization effects, using the MILC configurations with ${n}_{f}=2+1$ flavors of sea fermions. We perform such a calculation for a single lattice spacing, $a=0.125\text{ }\text{ }\mathrm{fm}$, and with kaons made up of degenerate quarks with ${m}_{s}/2$. The valence strange quark mass ${m}_{s}$ is fixed to its physical value and we use two different values of the light sea quark masses. After a chiral extrapolation of the results to the physical value of the sea quark masses, we find ${\stackrel{^}{B}}_{K}=0.83\ifmmode\pm\else\textpm\fi{}0.18$, where the error is dominated by the uncertainty in the lattice to continuum matching at $\mathcal{O}({\ensuremath{\alpha}}_{s}^{2})$. The matching will need to be improved to get the precision needed to make full use of the experimental data on ${\ensuremath{\epsilon}}_{K}$ to constrain the unitarity triangle.

Topological susceptibility in lattice QCD with two flavors of dynamical quarks

We present a study of the topological susceptibility in lattice QCD with two degenerate flavors of dynamical quarks. The topological charge is measured on gauge configurations generated with a renormalization group improved gauge action and a mean field improved clover quark action at three values of $\beta=6/g^2$, corresponding to lattice spacings of $a \approx 0.22$, 0.16 and 0.11 fm, with four sea quark masses at each $\beta$. The study is supplemented by simulations of pure SU(3) gauge theory with the same gauge action at 5 values of $\beta$ with lattice spacings 0.09 fm$\simlt a \simlt$0.27 fm. We employ a field theoretic definition of the topological charge together with cooling. For the topological susceptibility in the continuum limit of pure SU(3) gauge theory we obtain $\chi_t^{1/4} = 197^{+13}_{-16}$ MeV where the error shows statistical and systematic ones added in quadrature. In full QCD $\chi_t$ at heavy sea quark masses is consistent with that of pure SU(3) gauge theory. A decrease of $\chi_t$ toward light quark masses, as predicted by the anomalous Ward-Takahashi identity for U(1) chiral symmetry, becomes clearer for smaller lattice spacings. The cross-over in the behavior of $\chi_t$ from heavy to light sea quark masses is discussed.