We calculate the nucleon sigma term in two-flavor lattice QCD utilizing the Feynman-Hellman theorem. Both sea and valence quarks are described by the overlap fermion formulation, which preserves exact chiral and flavor symmetries on the lattice. We analyse the lattice data for the nucleon mass using the analytical formulae derived from the baryon chiral perturbation theory. From the data at valence quark mass set different from sea quark mass, we may extract the sea quark contribution to the sigma term, which corresponds to the strange quark content. We find that the strange quark content is much smaller than the previous lattice calculations and phenomenological estimates.
Lattice QCD calculations with chiral fermions of the $π$N sigma term $σ_{πN}$ and strangeness sigma term $σ_{sN}$ including chiral interpolation with continuum and volume corrections are provided in this work, with the excited-state contaminations subtracted properly. We calculate the scalar matrix element for the light/strange quark directly and find $σ_{πN}=45.9(7.4)(2.8)$ MeV, with the disconnected insertion part contributing 20(12)(4)\%, and $σ_{sN}=40.2(11.7)(3.5)$ MeV, which is somewhat smaller than $σ_{πN}$. The ratio of the strange/light scalar matrix elements is $y$ = 0.09(3)(1).
We present results on the scalar strangeness and charm contents of the nucleon and of the disconnected contributions to the nucleon spin. These are obtained on two flavour non-perturbatively improved Sheikholeslami-Wilson configurations at a pseudoscalar mass of 290 MeV. We quote f_{T_s} = m_s<N|ss|N>/m_N< = 0.070(22) as our preliminary value for the strange quark fraction of the nucleon mass and a modified minimal subtraction scheme value Delta s = -0.015(10), with as yet unknown systematics, for the strangeness contribution to the spin.
We study the nucleon matrix elements of the quark scalar-density operator using maximally twisted mass fermions with dynamical light ($u$,$d$), strange and charm degrees of freedom. We demonstrate that in this setup the nucleon matrix elements of the light and strange quark densities can be obtained with good statistical accuracy, while for the charm quark counterpart only a bound can be provided. The present calculation which is performed at only one value of the lattice spacing and pion mass serves as a benchmark for a future more systematic computation of the scalar quark content of the nuc…
Results for the disconnected contributions to matrix elements of the vector current and scalar density have been obtained for the nucleon from the Wilson action at beta=6 using a stochastic estimator technique and 2000 quenched configurations. Various methods for analysis are employed and chiral extrapolations are discussed.
We calculate the strange magnetic moment of the nucleon on a quenched $16^3 \times 24$ lattice at $β= 6.0$, and with Wilson fermions at $κ$ = 0.148, 0.152, and 0.154. The strange quark contribution from the disconnected insertion is estimated stochastically by employing the $Z_2$ noise method. Using an unbiased subtraction along with the help of charge conjugation and hermiticity, we reduce the error by a factor of 2 with negligible overhead. Our result is $G_{M}^{s} = -0.28\pm0.10 μ_{N}$.
In current lattice simulations of nucleon properties, the up and down quark masses are significantly larger than their physical values, while the strange quark can be included in simulations with its physical mass. When the up and down quark masses are much smaller than the strange-quark mass the chiral extrapolation of strange-quark matrix elements in the nucleon from the lattice up and down quark masses to their physical values can be performed with two-flavor chiral perturbation theory, thereby avoiding the slow convergence problem of the three-flavor chiral expansion. We explore the chiral…
Contributions of strange quarks to the mass and spin of the nucleon, characterized by the observables f_Ts and Delta s, respectively, are investigated within lattice QCD. The calculation employs a 2+1-flavor mixed-action lattice scheme, thus treating the strange quark degrees of freedom in dynamical fashion. Numerical results are obtained at three pion masses, m_pi = 495 MeV, 356 MeV, and 293 MeV, renormalized, and chirally extrapolated to the physical pion mass. The value extracted for Delta s at the physical pion mass in the MSbar scheme at a scale of 2 GeV is Delta s = -0.031(17), whereas t…
I review recent studies of strangeness content in the nucleon pertaining to the flavor-singlet $g_A^0$, the $\bar{s}s$ matrix element and the strangeness electric and magnetic form factors $G_E^s(q^2)$ and $G_M^s(q^2)$, based on lattice QCD calculations. I shall also discuss the relevance of incorporating the strangeness content in nuclei in regard to strange baryon-antibaryon productions from proton-nucleus and nucleus-nucleus collisions at SPS and RHIC energies.
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…
Quenched lattice QCD simulations and quenched chiral perturbation theory are used together for this study of strangeness in the nucleon. Dependences of the matrix elements on strange quark mass, valence quark mass and momentum transfer are discussed in both the lattice and chiral frameworks. The combined results of this study are in good agreement with existing experimental data and predictions are made for upcoming experiments. Possible future refinements of the theoretical method are suggested.
We investigate the transverse quark spin densities of the nucleon with the lowest moment within the framework of the SU(3) chiral quark-soliton model, emphasizing the strange quark spin density. Based on previous results of the vector and tensor form factors, we are able to determine the impact-parameter dependent probability densities of transversely polarized quarks in an unpolarized nucleon as well as those of unpolarized quarks in a transversely polarized nucleon. We find that the present numerical results for the transverse spin densities of the up and down quarks are in good agreement wi…
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.
Effective quark magnetic moments are extracted from experimental measurements as a function of the strangeness magnetic moment of the nucleon. Assumptions made in even the most general quark model analyses are ruled out by this investigation. Ab initio QCD calculations demand a non-trivial role for strange quarks in the nucleon. The effective moments from QCD calculations are reproduced for a strangeness magnetic moment contribution to the proton of 0.11 $μ_N$, which corresponds to $F_2^s(0) = -0.33\ μ_N$.
We study the sigma term and the strange quark content of nucleon in 2+1-flavor QCD with dynamical overlap fermions. We analyze the lattice data of nucleon mass taken at two different strange quark masses with five values of up and down quark masses each. Using the reweighting technique, we study the strange quark mass dependence of the nucleon and extract the strange quark content.
We calculate the strange quark content of the nucleon in 2+1-flavor lattice QCD. Chirally symmetric overlap fermion formulation is used to avoid the contamination from up and down quark contents due to an operator mixing between strange and light scalar operators, \bar{s}s and \bar{u}u+\bar{d}d. At a lattice spacing a=0.112(1) fm, we perform calculations at four values of degenerate up and down quark masses, which cover a range of the pion mass M_pi \simeq 300-540 MeV. We employ two different methods: one is a direct method where we calculate the strange quark content by directly inserting the…
By using lattice QCD computations we determine the sigma terms and strangeness content of all octet baryons by means of an application of the Hellmann-Feynman theorem. In addition to polynomial and rational expressions for the quark mass dependence of octet members, we use SU(3) covariant baryon chiral perturbation theory to perform the extrapolation to the physical up and down quark masses. Our N_f=2+1 lattice ensembles include pion masses down to about 190 MeV in large volumes (M_πL > 4), and three values of the lattice spacing. Our main results are the nucleon sigma term σ_{πN} = 39(4)(^{+1…
We present a non-perturbative calculation of the strangeness of the nucleon $y_N$ within the framework of lattice QCD. This observable is known to be an important cornerstone to interpret results from direct dark matter detection experiments. We perform a lattice computation for $y_N$ with an analysis of systematic effects originating from discretization, finite size, chiral extrapolation and excited state effects leading to the value of $y_N= 0.173(50)$. The rather large uncertainty of this value of $y_N$ is dominated by systematic uncertainties which we were able to quantify in this work.
The contributions of strange quarks to the nucleon mass and the nucleon spin are investigated in a mixed action scheme employing domain wall valence quarks and quark loops on MILC asqtad dynamical fermion ensembles. Results are presented for pion masses 495 MeV and 356 MeV.
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.
We determine the strangeness and light quark fractions of the nucleon mass by computing the quark line connected and disconnected contributions to the matrix elements m_q <N|qbar q|N> in lattice QCD, using the non-perturbatively improved Sheikholeslami-Wohlert Wilson Fermionic action. We simulate n_F=2 mass degenerate sea quarks with a pion mass of about 285 MeV and a lattice spacing a approx 0.073 fm. The renormalization of the matrix elements involves mixing between contributions from different quark flavours. The pion-nucleon sigma-term is extrapolated to physical quark masses exploiting th…
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.
We revisit the classical relation between the strangeness content of the nucleon, the pion-nucleon sigma term and the $SU(3)_F$ breaking of the baryon masses in the context of Lorentz covariant chiral perturbation theory with explicit decuplet-baryon resonance fields. We find that a value of the pion-nucleon sigma term of $\sim$60 MeV is not necessarily at odds with a small strangeness content of the nucleon, in line with the fulfillment of the OZI rule. Moreover, this value is indeed favored by our next-to-leading order calculation. We compare our results with earlier ones and discuss the con…
The scalar strangeness content of the nucleon, characterized by the so-called strangeness-nucleon sigma term, is of fundamental importance in understanding its sea-quark flavor structure. We report a determination of the octet baryon sigma terms via the Feynman-Hellmann theorem by analyzing the latest high-statistics $n_f=2+1$ lattice QCD simulations with covariant baryon chiral perturbation theory up to next-to-next-to-next-to-leading order. In particular, we predict $σ_{πN}=55(1)(4)$ MeV and $σ_{sN}=27(27)(4)$ MeV, while the first error is statistical and the second systematic due to differe…
We discuss methods for the calculation of disconnected diagrams and their application to various form factors of the nucleon. In particular, we present preliminary results for the strange contribution to the scalar and axial form factors, calculated with N_f=2 dynamical flavors of Wilson fermions on an anisotropic lattice.
We report a lattice QCD calculation of the strange quark contribution to the nucleon's magnetic moment and charge radius. This analysis presents the first direct determination of strange electromagnetic form factors including at the physical pion mass. We perform a model-independent extraction of the strange magnetic moment and the strange charge radius from the electromagnetic form factors in the momentum transfer range of $0.051 \,\text{GeV}^2 \lesssim Q^2 \lesssim 1.31 \,\text{GeV}^2 $. The finite lattice spacing and finite volume corrections are included in a global fit with $24$ valence q…
We report on our ongoing study of nucleon properties, the nucleon mass and the strange quark content (<N|ss|N>) in particular. These calculations are done on (2+1)-flavor Domain Wall Fermion (DWF) ensembles with Iwasaki gauge action with 2 different lattice spacings (a ~ 0.08, 0.11fm) and DWF with Dislocation Suppressing Determinant Ratio(DSDR) (a ~ 0.14fm), generated by RBC/UKQCD collaborations.
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.
The scalar strange-quark matrix element of the nucleon is computed with lattice QCD. A mixed-action scheme is used with domain-wall valence fermions computed on the staggered MILC sea-quark configurations. The matrix element is determined by making use of the Feynman-Hellmann theorem which relates this strange matrix element to the change in the nucleon mass with respect to the strange-quark mass. The final result of this calculation is m_s < N | s-bar s| N > = 49 +-10 +- 15 MeV and, correspondingly f_s = m_s < N | s-bar s |N > / m_N = 0.051 +- 0.011 +- 0.016. Given the lack of a quantitative …
We discuss the calculation of disconnected diagrams needed for determining the strange quark content of the nucleon on the lattice. We present results for the strange scalar form factor and the related parameter f_Ts, which enters into the cross-section for the scattering of dark matter off nuclei in supersymmetric extensions of the standard model. In addition, we present results for the strange contribution to the nucleon's axial and electromagnetic form factors. The calculations were performed with two dynamical flavors of Wilson fermions on a 24^3 x 64 anisotropic lattice with a_s = 3a_t = …
The role of the strange quarks on the low-energy interactions of the proton can be probed through the strange electromagnetic form factors. Knowledge of these form factors provides essential input for parity-violating processes and contributes to the understanding of the sea quark dynamics. We determine the strange electromagnetic form factors of the nucleon within the lattice formulation of Quantum Chromodynamics using simulations that include light, strange and charm quarks in the sea all tuned to their physical mass values. We employ state-of-the-art techniques to accurately extract the for…
We calculate the nucleon strange quark content directly from disconnected three-point functions. Numerical simulations are carried out in two-flavor QCD using the overlap quark action with up and down quark masses down to a fifth of the physical strange quark mass. To improve the statistical accuracy, we calculate the nucleon two-point functions with the low-mode averaging technique, whereas the all-to-all quark propagator is used for the disconnected quark loop. We obtain the y parameter, which is the ratio of the strange and light quark contents, y = 0.024(45) at the physical point. This is …
By combining the constraints of charge symmetry with new chiral extrapolation techniques and recent low mass lattice QCD simulations of the individual quark contributions to the magnetic moments of the nucleon octet, we obtain a precise determination of the strange magnetic moment of the proton. The result, namely G_M^s = -0.046 +/- 0.019 mu_N, is consistent with the latest experimental measurements but an order of magnitude more precise. This poses a tremendous challenge for future experiments.
The strangeness of the nucleon, <N|ss|N> - <0|ss|0>, is a quantity of interest for interpreting the results of dark matter detection experiments as well as for exploring the structure of the nucleon itself. We present a calculation of this quantity in 2+1 flavor lattice QCD using a range of lattice spacings and quark masses. The method is based on calculating quark-line disconnected contributions on the MILC lattice configurations, which include the effects of dynamical strange quarks. After continuum and chiral extrapolations, the value is <N|ss|N> - <0|ss|0> = 0.69 +/- 0.07(stat) +/- 0.09(sy…
We evaluate the matrix element of $\bar{q} q$ in hadron states on a lattice. We find substantial mixing of the connected and disconnected contributions so that the lattice result that the disconnected contribution to the nucleon is large does not imply that the $\bar{s} s$ content is large. This has implications for dark matter searches.
We present preliminary results for strange and charm contributions to nucleon charges and moments. The scalar, axial and tensor charges, and unpolarized first moments are calculated using clover-on-HISQ formulation and cover four lattice spacings, $a=\{0.06,0.09,0.12, 0.15\}$~fm, and three pion masses, $M_π=\{310,220,130\}$~MeV. The renormalization factors are calculated nonperturbatively using the RI-sMOM scheme. We carry out a chiral and continuum extrapolation to obtain physical results.
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…
We present a calculation of the nucleon sigma term on two-flavor QCD configurations with dynamical overlap fermions. We analyse the lattice data for the nucleon mass using the baryon chiral perturbation theory. Using partially quenched data sets, we extract the connected and disconnected contributions to the nucleon sigma term separately. Chiral symmetry on the lattice simplifies the determination of the disconnected contribution. We find that the strange quark content, which determines the neutralino dark matter reaction rate with nucleon through the Higgs boson exchange, is much smaller than…
We present results for the strangeness contribution to the nucleon, <N|ss|N>, and to the spin of the nucleon, Delta s. By combining several variance reduction techniques for all-to-all propagators we are able to obtain gains in terms of computer time of factors of 25-30 for the disconnected loop that is needed within the calculation of Delta s, relative to the standard approach of just employing time partitioning/dilution. For <N|ss|n>, the error is dominated by the gauge noise.
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）
We present the N_f=2+1 clover fermion lattice QCD calculation of the nucleon strangeness form factors. We evaluate disconnected insertions using the Z(4) stochastic method, along with unbiased subtractions from the hopping parameter expansion. We find that increasing the number of nucleon sources for each configuration improves the signal significantly. We obtain G_M^s(0) = -0.017(25)(07), where the first error is statistical, and the second is the uncertainties in Q^2 and chiral extrapolations. This is consistent with experimental values, and has an order of magnitude smaller error.
The recent chirally extrapolated result of Leinweber and Thomas [Phys. Rev. D {\bf 62}, 074505 (2000), or LT] for the nucleon strangeness form factor G_M^s(0)= -0.16 \pm 0.18 μ_N differs markedly from the earlier result -0.75 \pm 0.30 μ_N obtained by Leinweber [Phys. Rev. D {\bf 53}, 5115 (1996)] from the same lattice data. An unresolved problem in the LT analysis of lattice data is identified and addressed. A value of G_M^s(0) = -0.55 \pm 0.37 μ_N is obtained at R^s_d = 0.55 by extrapolating only the nucleon isoscalar lattice data.
By imposing the constraints of charge symmetry we show that the strangeness magnetic moment of the nucleon can be expressed in terms of empirical magnetic moments and ratios of valence quark magnetic moments. The latter are determined using modern chiral extrapolation techniques and recent low mass lattice QCD simulations of the individual quark contributions to the magnetic moments of the nucleon octet. The result is a precise determination of G_M^s, namely -0.043 +/- 0.026 mu_N, which is consistent with the latest experimental measurements.
We report on recent lattice QCD calculations of the strangeness magnetic moment of the nucleon and the nucleon electromagnetic form factors, when we allow the electromagnetic current to connect to quark loops as well as to the valence quarks. Our result for the strangeness magnetic moment is G_M^s(0)=-0.36+/-0.20. The sea contributions from the u and d quarks are about 80% larger. However, they cancel to a large extent due to their electric charges, resulting in a smaller net sea contribution of -0.097+/-0.037 mu_N to the nucleon magnetic moment. As far as the neutron to proton magnetic moment…
We study the strangeness electromagnetic form factors of the nucleon from the N_f=2+1 clover fermion lattice QCD calculation. The disconnected insertions are evaluated using the Z(4) stochastic method, along with unbiased subtractions from the hopping parameter expansion. In addition to increasing the number of Z(4) noises, we find that increasing the number of nucleon sources for each configuration improves the signal significantly. We obtain G_M^s(0) = -0.017(25)(07), where the first error is statistical, and the second is the uncertainties in Q^2 and chiral extrapolations. This is consisten…
We calculate the strange quark content of the nucleon directly from its disconnected three-point function in N_f=2+1 QCD. Chiral symmetry is crucial to avoid a possibly large contamination due to operator mixing, and is exactly preserved by employing the overlap quark action. We also use the all-to-all quark propagator and the low-mode averaging technique in order to accurately calculate the relevant nucleon correlator. Our preliminary result extrapolated to the physical point is f_{T_s} = 0.013(12)(16). This is in good agreement with our previous estimate in N_f=2 QCD as well as those from ou…
We study the strangeness contribution to nucleon matrix elements using Nf=2+1 dynamical clover fermion configurations generated by the CP-PACS/JLQCD collaboration. In order to evaluate the disconnected insertion (DI), we use the Z(4) stochastic method, along with unbiased subtraction from the hopping parameter expansion which reduces the off-diagonal noises in the stochastic method. Furthermore, we find that using many nucleon sources for each configuration is effective in improving the signal. Our results for the quark contribution to the first moment <x>_q in the DI, and the strangeness magn…
A status report is given for a joint project of the Budapest-Marseille-Wuppertal collaboration and the Regensburg group to study the quark mass-dependence of octet baryons in SU(3) Baryon XPT. This formulation is expected to extend to larger masses than Heavy-Baryon XPT. Its applicability is tested with 2+1 flavor data which cover three lattice spacings and pion masses down to about 190 MeV, in large volumes. Also polynomial and rational interpolations in M_π^2 and M_K^2 are used to assess the uncertainty due to the ansatz. Both frameworks are combined to explore the precision to be expected i…
