We determine the strange and light quark condensates in full lattice QCD for the first time. This is done by direct calculation of the expectation value of the trace of the quark propagator followed by subtraction of the appropriate perturbative contribution to convert to a value for the condensate in the MS-bar scheme at 2 GeV. We use lattice QCD configurations including u, d, s and c quarks in the sea with u/d quark masses going down to the physical value. We find the ratio of the strange to the light quark condensate to be 1.08(16).
The evolution of the chiral condensate with the temperature is studied using SU(3) Chiral Perturbation Theory and the virial expansion. We observe a large decrease of the melting temperature of the non-strange condensate compared with the SU(2) case. Due to the larger mass of the strange quark we also find an slower temperature evolution of the strange condensate compared with the non-strange condensate.
The temperature evolution of the chiral condensates in a gas made of pions, kaons and etas is studied within the framework of SU(2) and SU(3) Chiral Perturbation Theory. We describe the temperature dependence of the quark condensates by using the meson meson scattering phase shifts in a second order virial expansion. We find that the SU(3) formalism yields an extrapolated melting temperature for the non-strange condensates which is lower by about 20-30 MeV than within SU(2). In addition our results show that the strange condensate melting is slower than that of the non-strange, due to the diff…
Lattice calculations of the mass of the strange quark are reviewed. In particular, the reason for the spread in values is explained with emphasis on the effects that recently implemented improvements have had on the lattice determinations.
We calculate the "strange quark content of the nucleon", <N| s s_bar |N>, which is important for interpreting the results of some dark matter detection experiments. The method is to evaluate quark-line disconnected correlations on the MILC lattice ensembles, which include the effects of dynamical strange quarks. After continuum and chiral extrapolations, the result is <N |s s_bar |N> = 0.69 +- 0.07(statistical) +- 0.09(systematic), in the modified minimal subtraction scheme (2 GeV), or for the renormalization scheme invariant form, m_s partial{M_N}/partial{m_s} = 59(6)(8) MeV.
We determine the strange quark condensate from lattice QCD for the first time and compare its value to that of the light quark and chiral condensates. The results come from a direct calculation of the expectation value of the trace of the quark propagator followed by subtraction of the appropriate perturbative contribution, derived here, to convert the non-normal-ordered $m\barψψ$ to the $\bar{MS}$ scheme at a fixed scale. This is then a well-defined physical `nonperturbative' condensate that can be used in the Operator Product Expansion of current-current correlators. The perturbative subtrac…
We propose and apply a new approach to determining $|V_{us}|$ using dispersion relations with weight functions having poles at Euclidean (space-like) momentum which relate strange hadronic $τ$ decay distributions to hadronic vacuum polarization functions (HVPs) obtained from lattice QCD. We show examples where spectral integral contributions from the region where experimental data have large errors or do not exist are strongly suppressed but accurate determinations of the relevant lattice HVP combinations remain possible. The resulting $|V_{us}|$ agrees well with determinations from $K$ physic…
We compute the light and strange quark masses m_l = (m_u+m_d)/2 and m_s, respectively, in full lattice QCD with N_f=2 flavors of light dynamical quarks. The renormalization constants, which convert bare quark masses into renormalized quark masses, are computed nonperturbatively, including the effect of quark-line disconnected diagrams. We obtain m_l=4.7(2)(3) MeV and m_s=119(5)(8) MeV in the MSbar scheme at the scale 2 GeV.
The strange quark scalar content plays an important role in both the description of nucleon structure and in the determination of dark matter direct detection cross sections. As a measure of the strange-quark contribution to the nucleon mass, the strange-quark sigma term (σ_s) provides important insight into the nature of mass generation in QCD. The phenomenological determination of σ_s exhibits a wide range of variation, with values suggesting that the strange quark contributes anywhere between 0 and more than 30% of the nucleon mass. In the context of dark matter searches, coupled with relat…
The strange quark content of the nucleon, as well as other matrix elements, can be calculated on the lattice by examining correlations between the nucleon propagator and the quark condensate. The largest contribution to statistical error comes from fluctuations in the condensate far from the propagation region that contribute only noise. We will report on a technique for considering only the condensate near the propagation region, significantly reducing the statistical error.
The strange contribution to the electric and magnetic form factors of the nucleon is determined at a range of discrete values of $Q^2$ up to $1.4$ GeV$^2$. This is done by combining recent lattice QCD results for the electromagnetic form factors of the octet baryons with experimental determinations of those quantities. The most precise result is a small negative value for the strange magnetic moment: $G_M^s(Q^2=0) = -0.07\pm0.03\,μ_N$. At larger values of $Q^2$ both the electric and magnetic form factors are consistent with zero to within $2$-sigma.
We present results for the light, strange and charm quark masses using $N_f=2+1+1$ twisted mass fermion ensembles at three values of the lattice spacing, including two ensembles simulated with the physical value of the pion mass. The analysis is done both in the meson and baryon sectors. The difference in the mean values found in the two sectors is included as part of the systematic error. The presentation is based on the work of Ref. [1], where more details can be found.
A fully non-perturbative lattice determination of the up/down and strange quark masses is given for quenched QCD using both, $O(a)$ improved Wilson fermions and ordinary Wilson fermions. For the strange quark mass with $O(a)$ improved fermions we obtain $m^{\msbar}_s(μ=2 {GeV}) = 105(4) {MeV}$, using the interquark force scale $r_0$. Due to quenching problems fits are only possible for quark masses larger than the strange quark mass. If we extrapolate our fits to the up/down quark mass we find for the average mass $m^{\msbar}_l(μ=2 {GeV}) = 4.4(2) {MeV}$.
Using the O(a) Symanzik improved action an estimate is given for the strange quark mass for unquenched (nf=2) QCD. The determination is via the axial Ward identity (AWI) and includes a non-perturbative evaluation of the renormalisation constant. Numerical results have been obtained at several lattice spacings, enabling the continuum limit to be taken. Results indicate a value for the strange quark mass (in the MSbar-scheme at a scale of 2GeV) in the range 100 - 130MeV.
In this work we present a precise and model-independent dispersive determination from data of the existence and parameters of the lightest strange resonance $κ/K_0^*(700)$. We use both subtracted and unsubtracted partial-wave hyperbolic and fixed-$t$ dispersion relations as constraints on combined fits to $πK\rightarrowπK$ and $ππ\rightarrow K\bar K$ data. We then use the hyperbolic equations for the analytic continuation of the isospin $I=1/2$ scalar partial wave to the complex plane, in order to determine the $κ/K_0^*(700)$ and $K^*(892)$ associated pole parameters and residues.
Two strategies are taken into account to determine the $f_1(1420)$-$f_1(1285)$ mixing angle $θ$. (i) First, using the Gell-Mann-Okubo mass formula together with the $K_1(1270)$-$K_1(1400)$ mixing angle $θ_{K_1}=(-34\pm 13)^\circ$ extracted from the data for ${\cal B}(B\to K_1(1270) γ), {\cal B}(B\to K_1(1400) γ), {\cal B}(τ\to K_1(1270) ν_τ)$, and ${\cal B}(τ\to K_1(1420) ν_τ)$, gave $θ= (23^{+17}_{-23})^\circ$. (ii) Second, from the study of the ratio for $f_1(1285) \to ϕγ$ and $f_1(1285) \to ρ^0γ$ branching fractions, we have two-fold solution $θ=(19.4^{+4.5}_{-4.6})^\circ$ or $(51.1^{+4.5}_…
The gluon condensate, $\langle \frac{α_s}π G^2 \rangle$, i.e. the leading order power correction in the operator product expansion of current correlators in QCD at short distances, is determined from $e^+ e^-$ annihilation data in the charm-quark region. This determination is based on finite energy QCD sum rules, weighted by a suitable integration kernel to (i) account for potential quark-hadron duality violations, (ii) enhance the contribution of the well known first two narrow resonances, the $J/ψ$ and the $ψ(2S)$, while quenching substantially the data region beyond, and (iii) reinforce the…
The SU(2) and SU(3) chiral phase transitions in a hot gas made of pions, kaons and etas are studied within the framework of Chiral Perturbation Theory. By using the meson meson scattering phase shifts in a second order virial expansion, we are able to describe the temperature dependence of the quark condensates. We have estimated the critical temperatures where the different condensates melt. In particular, the SU(3) formalism yields a lower critical temperature for the non-strange condensates than within SU(2), and also suggests that the strange condensate may melt at a somewhat higher temper…
We use a hadron resonance gas model to calculate the quark-antiquark condensates for light (up and down) and strange quark flavors at finite temperatures and chemical potentials. At zero chemical potentials, we find that at the temperature where the light quark-antiquark condensates entirely vanish the strange quark-antiquark condensate still keeps a relatively large fraction of its value in the vacuum. This is in agreement with results obtained in lattice simulations and in chiral perturbation theory at finite temperature and zero chemical potentials. Furthermore, we find that this effect slo…
We compute the strange quark mass $m_s$ and the average of the $u$ and $d$ quark masses $\hat m$ using full lattice QCD with three dynamical quarks combined with experimental values for the pion and kaon masses. The simulations have degenerate $u$ and $d$ quarks with masses $m_u=m_d\equiv \hat m$ as low as $m_s/8$, and two different values of the lattice spacing. The bare lattice quark masses obtained are converted to the $\msbar$ scheme using perturbation theory at $O(alpha_s)$. Our results are: $m_s^\msbar$(2 GeV) = 76(0)(3)(7)(0) MeV, $\hat m^\msbar$(2 GeV) = 2.8(0)(1)(3)(0) MeV and $m_s/\h…
We calculate the chiral condensate of QCD with 2, 2+1 and 3 flavors of sea quarks. Lattice QCD simulations are performed employing dynamical overlap fermions with up and down quark masses covering a range between 3 and 100 MeV. On L ~ 1.8-1.9 fm lattices at a lattice spacing ~ 0.11 fm, we calculate the eigenvalue spectrum of the overlap-Dirac operator. By matching the lattice data with the analytical prediction from chiral perturbation theory at the next-to-leading order, the chiral condensate in the massless limit of up and down quarks is determined.
We present a lattice QCD determination of the average up-down, strange and charm quark masses based on simulations performed by the European Twisted Mass Collaboration with $N_f = 2 + 1 + 1$ dynamical fermions. We simulated at three different values of the lattice spacing, the smallest being approximately $0.06fm$, and with pion masses as small as $210 \text{MeV}$. Our results are: $m_{ud}(2\text{GeV})=3.70(17)\text{MeV}$, $m_s(2\text{GeV})=99.2(3.9)\text{MeV}$, $m_c(m_c)=1.350(49)\text{GeV}$, $m_s/m_{ud}=26.64(30)$ and $m_c/m_s=11.65(12)$.
We determine the non-perturbative gluon condensate of four-dimensional SU(3) gauge theory in a model independent way. This is achieved by carefully subtracting high order perturbation theory results from non-perturbative lattice QCD determinations of the average plaquette. No indications of dimension two condensates are found. The value of the gluon condensate turns out to be of a similar size as the intrinsic ambiguity inherent to its definition.
We present a determination of the strange quark mass for two flavours (nf=2) of light dynamical quarks using the axial Ward identity. The calculations are performed on the lattice using O(a) improved Wilson fermions and include a fully non-perturbative determination of the renormalisation constant. In the continuum limit we find in the MSbar scheme at 2GeV, ms = 111(6)(4)(6)MeV using the force scale r0 = 0.467fm, where the first error is statistical, the second and third are systematic due to the fit and scale uncertainties respectively. Results are also presented for the light quark mass and …
We give the hyperasymptotic expansion of the plaquette with a precision that includes the terminant associated to the leading renormalon. Subleading effects are also considered. The perturbative series is regulated using the principal value prescription for its Borel integral. We use this analysis to give a determination of the gluon condensate in SU(3) pure gluodynamics that is independent of the scale and renormalization scheme used for the coupling constant: $\langle G^2 \rangle_{\rm PV} (n_f=0)=3.15(18)\; r_0^{-4}$.
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 a…
We derive the Operator Product Expansion whose vacuum expectation value gives the time-moments of the pseudoscalar heavy-light current-current correlator up to and including terms in $α_s^2$ multiplying $\langle\overlineψψ\rangle/M^3$ and terms in $α_s$ multiplying $\langle α_s G^2 \rangle/M^4$, where $M$ is the heavy-quark mass. Using lattice QCD results for heavy-strange correlators obtained for a variety of heavy quark masses on gluon field configurations including $u$, $d$ and $s$ quarks in the sea at three values of the lattice spacing, we are able to show that the contribution of the str…
We compute the strange and the average up/down quark masses in the quenched approximation of lattice QCD, by using the O(a)-improved Wilson action and operators and by implementing the non-perturbative renormalization. Our computation is performed at four values of the lattice spacing, from which we could extrapolate to the continuum limit. Our final result for the strange quark mass (in the MSbar scheme) is ms(2 GeV) = (106 +/- 2 +/- 8) MeV. For the average up/down quark mass we have ml(2 GeV) = (4.4 +/- 0.1 +/- 0.4) MeV. The ratio ms/ml = (24.3 +/- 0.2 +/- 0.6).
In this talk I summarize the recent lattice determinations of the decay constants and of the bag parameters of the heavy-light and heavy-strange neutral mesons.
While the standard model is the most successfully theory to describe all interactions and constituents in elementary particle physics, it has been constantly examined for over four decades. Weak decays of charm quarks can measure the coupling strength of quarks in different families and serve as an ideal probe for CP violation. As the lowest charm-strange baryons with three different flavors, $Ξ_c$ baryons (made of $csu$ or $csd$) have been extensively studied in experiments at the large hadron collider and in electron-positron collision. However the lack of reliable knowledge in theory become…
We study the effective monopole action obtained in the Maximal Abelian projection of quenched SU(2) lattice QCD. We determine the quadratic part of the lattice action using analytical blocking from continuum dual superconductor model to the lattice model. The leading contribution to the quadratic action depends explicitly on value of the monopole condensate. We show that the analytical monopole action matches the numerically obtained action in quenched SU(2) QCD with a good accuracy. The comparison of numerical and analytical results gives us the value of the monopole condensate in quenched SU…
We complete the non-perturbative calculations of the strange quark mass and the Lambda parameter in two flavor QCD by the ALPHA collaboration. The missing lattice scale is determined via the kaon decay constant, for whose chiral extrapolation complementary strategies are compared. We also give a value for the scale r_0 in physical units as well as an improved determination of the renormalization constant Z_A.
I use the technique of Hernandez, et al (hep-lat/0106011) to convert a recent calculation of the lattice-regulated quark condensate from an overlap action to a continuum-regulated number. I find Sigma(MSbar)(mu = 2 GeV) = (282(6) MeV)-cubed times (a-inverse/1766 MeV)-cubed from a calculation with the Wilson gauge action at beta=5.9.
We present a Lattice QCD determination of the chiral quark condensate based on a new method. We extract the quark condensate from the operator product expansion of the quark propagator at short euclidean distances, where it represents the leading contribution in the chiral limit. From this study we obtain <\bar q q>^ms(2 GeV)=-(265+-5+-22 MeV)^3$, in good agreement with determinations of this quantity based on different approaches. The simulation is performed by using the O(a)-improved Wilson action at beta=6.45 on a volume 32^3\times70 in the quenched approximation.
Using the O(a) Symanzik improved action an estimate is given for the strange quark mass for unquenched (n_f=2) QCD. The determination is via the axial Ward identity (AWI) and includes a non-perturbative evaluation of the renormalisation constant. Numerical results have been obtained at several lattice spacings, enabling the continuum limit to be taken. Our results indicate a value for the strange quark mass (in the MS-bar scheme at a scale of 2 GeV) in the range 100 - 130 MeV. A comparison is also made with other recent lattice determinations of the strange quark mass using dynamical sea quark…
We present a determination of the strange quark mass using lattice QCD. Particular focus is put on the definition and renormalization of the mass. The latter is done non-perturbatively, using a recursive finite-size scaling technique. The hadronic regime of QCD, where the kaon mass is used as input of the calculation, is connected with the perturbative regime, where the strange quark mass can be translated into the MSbar scheme. A summary plot of the present lattice computations using dynamical (sea) quarks is included.
The strangeness contribution to the electric and magnetic properties of the nucleon has been under investigation experimentally for many years. Lattice Quantum Chromodynamics (LQCD) gives theoretical predictions of these measurements by implementing the continuum gauge theory on a discrete, mathematical Euclidean space-time lattice which provides a cutoff removing the ultra-violet divergences. In this dissertation we will discuss effective methods using LQCD that will lead to a better determination of the strangeness contribution to the nucleon properties. Strangeness calculations are demandin…
The strange and flavor-singlet axial form factors of the nucleon from lattice QCD
Helmholtz-Institut Mainz, Johannes Gutenberg-Universität Mainz（美因茨亥姆霍兹研究所）；GSI Helmholtzzentrum für Schwerionenforschung（GSI重离子研究中心）；Theoretical Physics Department, CERN（欧洲核子研究中心理论物理部）；Helmholtz-Institut für Strahlen- und Kernphysik, Universität Bonn（波恩大学辐射与核物理亥姆霍兹研究所）
The status of lattice calculations in the light hadron sector is reviewed. Special emphasis is given to recent lattice determinations of the mass of the strange quark. The impact of non-perturbative renormalization and control over lattice artefacts on the attainable precision is discussed in detail. Furthermore the influence of dynamical quark effects is assessed.
We study the quark-gluon mixed condensate g<\bar{q} sigma G q>, using the SU(3)c lattice QCD with the Kogut-Susskind fermion at the quenched level. We generate 100 gauge configurations on the 16^4 lattice with β= 6.0, and perform the measurement of the mixed condensate at 16 points in each gauge configuration for each current quark mass of m_q=21, 36, 52 MeV. Using the 1600 data for each m_q, we find the ratio between the mixed condensate and the quark condensate, m_0^2 = g<\bar{q} sigma G q> / <\bar{q}q> \simeq 2.5 GeV^2 at the lattice scale of 1/a \simeq 2 GeV in the chiral limit. The large …
By combining the constraints of charge symmetry with new chiral extrapolation techniques and recent low-mass quenched lattice QCD simulations of the individual quark contributions to the electric charge radii of the baryon octet, we obtain an accurate determination of the strange electric charge radius of the proton. While this analysis provides a value for G_E^s(Q^2=0.1 GeV^2) in agreement with the best current data, the theoretical error is comparable with that expected from future HAPPEx results from JLab. Together with the earlier determination of G_M^s, this result considerably constrains…
Omega- correlators have been calculated on the MILC collaboration's archive of three flavor improved staggered quark lattices. The Omega- is stable under strong interactions (140 MeV below threshold). It provides a valuable consistency check on a combination of strange quark mass and lattice scale determination from other quantities. Alternatively, the Omega- mass could be used to fix the strange quark mass, which gives a check on computations of the strange quark mass based on the kaon mass.
We review the state of our knowledge concerning the contribution of strange quarks to various nucleon properties. In the case of the electric and magnetic form factors, the level of agreement between theory and experiment is very satisfactory and gives us considerable confidence in our capacity to make reliable calculations within non-perturbative QCD. In view of the importance of the scalar form factors to the detection of dark matter candidates such as neutralinos, we place a particular emphasis on the determination of the pi-N and strange quark sigma commutators.
The mass of the strange quark is determined from SU(3)-breaking effects in the tau hadronic width. Compared to previous analyses, the contributions from scalar and pseudoscalar spectral functions, which suffer from large perturbative corrections, are replaced by phenomenological parametrisations. This leads to a sizeable reduction of the uncertainties in the strange mass from tau decays. Nevertheless, the resulting m_s value is still rather sensitive to the moment of the invariant mass distribution which is used for the determination, as well as the size of the quark-mixing matrix element |V_u…
We present the first nonperturbative large-$N$ calculation of the $\mathcal{N}=1$ supersymmetric (SUSY) $\mathrm{SU}(N)$ Yang$-$Mills gluino condensate obtained by means of numerical simulations of the lattice-discretized theory, exploiting large-$N$ twisted volume reduction. We present two different determinations based, respectively, on the Banks$-$Casher formula and on the Gell-Mann$-$Oakes$-$Renner relation, both giving perfectly consistent results. By expressing the lattice results in the Novikov$-$Shifman$-$Vainshtein$-$Zakharov (NSVZ) scheme, we are able for the first time to compare nu…
We point out that the sum of the strange-quark-connected and full, three-flavor quark-disconnected contributions to the leading-order hadronic vacuum polarization contribution, $a_μ^{\mathrm{LO,HVP}}$, to the anomalous magnetic moment of the muon, is a physical observable, and provide a data-based determination of this quantity in the isospin limit. The result, $40.1(1.5)\times 10^{-10}$, or $38.7(2.0)\times 10^{-10}$, depending on which data compilation is used, serves as a target of comparison for lattice calculations of the same isospin-limit combination. Subtracting from this result the av…
We discuss the violation of quark-flavor symmetry at high temperatures, induced from nonperturbative thermal loop corrections and axial anomaly, based on a three-flavor linear-sigma model including an axial-anomaly induced-flavor breaking term. We employ a nonperturbative analysis following the Cornwall-Jackiw-Tomboulis formalism, and show that the model undergoes a chiral crossover with a pseudo-critical temperature, consistently with lattice observations. We find following features regarding the flavor breaking eminent around and above the pseudo-critical temperature: i) up-and down-quark co…
We present the results of our computation of the chiral condensate with $N_f=2$ and $N_f=2+1+1$ flavours of maximally twisted mass fermions. The condensate is determined from the Dirac operator spectrum, applying the spectral projector method proposed by Giusti and Luscher. We use 3 lattice spacings and several quark masses at each lattice spacing to perform the chiral and continuum extrapolations. We study the effect of the dynamical strange and charm quarks by comparing our results for $N_f=2$ and $N_f=2+1+1$ dynamical flavours.
We compute the chiral condensate in 2+1-flavor QCD through the spectrum of low-lying eigenmodes of Dirac operator. The number of eigenvalues of the Dirac operator is evaluated using a stochastic method with an eigenvalue filtering technique on the background gauge configurations generated by lattice QCD simulations including the effects of dynamical up, down and strange quarks described by the Mobius domain-wall fermion formulation. The low-lying spectrum is related to the chiral condensate, which is one of the leading order low-energy constants in chiral effective theory, as dictated by the B…
We investigate correlation functions of the Polyakov loop and static meson/diquark systems with the chiral condensate and the quark number density at finite temperature. In particular the latter observable can give insight in the mechanism of screening and string breaking at finite temperature. We use for our analysis gauge field configurations generated in 2+1 flavor QCD with an improved staggered fermion action with almost physical light quark masses and a physical value of the strange quark mass on lattices with temporal extent Nt=4 and 6.
Strangeness of nucleons from $N_f=2+1+1$ lattice QCD
Computation-based Science and Technology Research Center, The Cyprus Institute（塞浦路斯研究所计算科学与技术研究中心）；Department of Physics, University of Cyprus（塞浦路斯大学物理系）；Jülich Supercomputing Centre, Forschungzentrum Jülich（于利希超级计算中心，于利希研究中心）；Department of Physics, Bergische Universität Wuppertal（伍珀塔尔山岳大学物理系）
The eigenvalues of the Dirac operator at finite volume encode whether or not chiral symmetry is spontaneously broken in a massless theory. We apply this framework in a particular BSM context, namely SU(3) gauge theory with N_f=2 massless flavors in the 2-index symmetric (sextet) representation. Our first results are at a single lattice spacing. We find that both the density of near-zero eigenvalues and the renormalization group invariant mode number indicate spontaneous symmetry breaking. Quantitatively, there is a discrepancy between the determination of the fermion condensate in the chiral l…
