Locality with staggered fermions

We address the locality problem arising in simulations, which take the square root of the staggered fermion determinant as a Boltzmann weight to reduce the number of dynamical quark tastes. A definition of such a theory necessitates an underlying local fermion operator with the same determinant and the corresponding Green's functions to establish causality and unitarity. We illustrate this point by studying analytically and numerically the square root of the staggered fermion operator. Although it has the correct weight, this operator is non-local in the continuum limit. Our work serves as a warning that fundamental properties of field theories might be violated when employing blindly the square root trick. The question, whether a local operator reproducing the square root of the staggered fermion determinant exists, is left open.Comment: 24 pages, 7 figures, few remarks added for clarity, accepted for publication in Nucl. Phys.

The locality problem for two tastes of staggered fermions

We address the locality problem arising in simulations, which take the square root of the staggered fermion determinant as a Boltzmann weight to reduce the number of dynamical quark tastes from four to two. We study analytically and numerically the square root of the staggered fermion operator as a candidate to define a two taste theory from first principles. Although it has the correct weight, this operator is non-local in the continuum limit. Our work serves as a warning that fundamental properties of field theories might be violated when employing blindly the square root trick. The question, whether a local operator reproducing the square root of the staggered fermion determinant exists, is left open.Comment: Talk presented at Lattice2004(theory), Fermilab, June 21-26, 200

Non-perturbative renormalization of quark mass in Nf=2+1 QCD with the Schroedinger functional scheme

We present an evaluation of the quark mass renormalization factor for Nf=2+1 QCD. The Schroedinger functional scheme is employed as the intermediate scheme to carry out non-perturbative running from the low energy region, where renormalization of bare mass is performed on the lattice, to deep in the high energy perturbative region, where the conversion to the renormalization group invariant mass or the MS-bar scheme is safely carried out. For numerical simulations we adopted the Iwasaki gauge action and non-perturbatively improved Wilson fermion action with the clover term. Seven renormalization scales are used to cover from low to high energy regions and three lattice spacings to take the continuum limit at each scale. The regularization independent step scaling function of the quark mass for the Nf=2+1 QCD is obtained in the continuum limit. Renormalization factors for the pseudo scalar density and the axial vector current are also evaluated for the same action and the bare couplings as two recent large scale Nf=2+1 simulations; previous work of the CP-PACS/JLQCD collaboration, which covered the up-down quark mass range heavier than $m_\pi\sim 500$ MeV and that of PACS-CS collaboration for much lighter quark masses down to $m_\pi=155$ MeV. The quark mass renormalization factor is used to renormalize bare PCAC masses in these simulations.Comment: 26 pages, 17 Postscript figures. Two tables are update

Non-perturbative renormalization of the static axial current in two-flavour QCD

We perform the non-perturbative renormalization of matrix elements of the static-light axial current by a computation of its scale dependence in lattice QCD with two flavours of massless O(a) improved Wilson quarks. The regularization independent factor that relates any running renormalized matrix element of the axial current in the static effective theory to the renormalization group invariant one is evaluated in the Schroedinger functional scheme, where in this case we find a significant deviation of the non-perturbative running from the perturbative prediction. An important technical ingredient to improve the precision of the results consists in the use of modified discretizations of the static quark action introduced earlier by our collaboration. As an illustration how to apply the renormalization of the static axial current presented here, we connect the bare matrix element of the current to the B_s-meson decay constant in the static approximation for one value of the lattice spacing, a ~ 0.08 fm, employing large-volume N_f=2 data at beta=5.3.Comment: 33 pages including figures and tables, latex2e, uses JHEP3.cls; version published in JHEP, small additions, results unchange

Relative Permeability Determination for Steam Injection Processes: An Analytical Approach

Due to the nature of bitumen and the inability to flow at reservoir conditions, it becomes necessary to alter the original state by imparting heat into the reservoir, thus lowering the viscosity to produce the fluid. The heat introduction is achieved through the utilization of steam assisted gravity drainage (SAGD) as well as solvent steam assisted gravity drainage (S-SAGD). However, the presence of three distinct fluid phases (oil, steam, and water) in the reservoir during steam injection has implications for the effective modeling of the complex fluid dynamics. Inherent complexity as a result of introducing a third phase (steam) in conjunction with temperature dependencies results in the inability to generate a comprehensive three phase relative permeability capable of adequately representing flow in the reservoir at all domains. In this study, experimental oil recovery data for two SAGD experiments, three S-SAGD experiments and one hot water flood are empirically modelled by manipulating relative permeabilities. Addition of a solvent during the steam injection (S-SAGD) takes advantage of a miscibility component with the bitumen in conjunction with the thermal mechanism of enhanced oil recovery which results in incremental recovery of bitumen along with a minimization of the environmental footprint. The two SAGD experiments are differentiated by different types of clay content while the three S-SAGD experiments vary due to the different solvent and injection strategy utilized during the experiment. The analytical approach implemented allows for the representation of fluid flow in the reservoir by achieving a pseudo-two phase relative permeability that results in comparable performance to the experiments. The assumption of a waterflood through the application of fractional flow theory allowed for the negation of the steam phase in the model and so two-phase flow was established. The sensitivity of the relative permeability curves to temperature change results in the inability to formulate a generic three-phase curve and so the pseudo-two phase curve is valuable for the analysis of the relative permeability behavior for different SAGD scenarios

Spectrum of quenched twisted mass lattice QCD at maximal twist

Hadron masses are computed from quenched twisted mass lattice QCD for a degenerate doublet of up and down quarks with the twist angle set to pi/2, since this maximally twisted theory is expected to be free of linear discretization errors. Two separate definitions of the twist angle are used, and the hadron masses for these two cases are compared. The flavor breaking, that can arise due to twisting, is discussed in the context of mass splittings within the Delta(1232) multiplet.Comment: 23 pages, 16 figures, added discussion of pion decay constan

HQET at order 1/m1/m: II. Spectroscopy in the quenched approximation

Using Heavy Quark Effective Theory with non-perturbatively determined parameters in a quenched lattice calculation, we evaluate the splittings between the ground state and the first two radially excited states of the $B_s$ system at static order. We also determine the splitting between first excited and ground state, and between the $B_s^*$ and $B_s$ ground states to order $1/m_b$. The Generalized Eigenvalue Problem and the use of all-to-all propagators are important ingredients of our approach.Comment: (1+18) pages, 3 figures (4 pdf files); pdflatex; v2: corrections to table 1, results unaffecte

Light quarks with twisted mass fermions

We investigate Wilson twisted mass fermions in the quenched approximation using different definitions of the critical bare quark mass m_c to realize maximal twist and, correspondingly, automatic O(a) improvement for physical observables. A particular definition of m_c is given by extrapolating the value of m_c obtained from the PCAC relation at non-vanishing bare twisted quark mass mu to mu=0. Employing this improved definition of the critical mass the Wilson twisted mass formulation provides the possibility to perform reliable simulations down to very small quark masses with correspondingly small pion masses of m_pi \simeq 250 MeV, while keeping the cutoff effects of O(a^2) under control.Comment: 10 pages, 8 figures, v2: version accepted for publication in PLB, minor correction

Hadronic Vacuum Polarization Contribution to g-2 from the Lattice

We give a short description of the present situation of lattice QCD simulations. We then focus on the computation of the anomalous magnetic moment of the muon using lattice techniques. We demonstrate that by employing improved observables for the muon anomalous magnetic moment, a significant reduction of the lattice error can be obtained. This provides a promising scenario that the accuracy of lattice calculations can match the experimental errors.Comment: Proceedings of the International Workshop on e+e- collisions from Phi to Psi (PHIPSI11), Sep. 19-22, 2011, BINP, Novosibirsk, Russi

Spatial correlators in strongly coupled plasmas

We numerically calculate the spatial correlators of the scalar and pseudoscalar operators $F^2$ and $F\tilde F$, in SU(3) Yang-Mills theory at zero and finite-temperature on the lattice. We compare the results over the distances $\frac{1}{2T}<r<\frac{3}{2T}$ to the free-field prediction, to the operator-product expansion as well as to the strongly coupled large-$N_c$ \sN=4 super-Yang-Mills theory, where results are obtained by AdS/CFT methods. For $T_c<T<1.15T_c$, both channels exhibit stronger spatial correlations than in the vacuum, and we give an explanation for this, using sum-rules and the operator-product expansion. The AdS/CFT calculation provides a semi-quantitatively successful description of the vacuum-subtracted $F^2$ correlator, renormalized in the 3-loop $\overline{\rm MS}$ scheme, in the interval of temperatures $1.2<T/T_c<1.9$, while the free-field prediction has the wrong sign. The $F\tilde F$ and $F^2$ correlators are predicted to have the same functional form both at weak coupling and in the strongly coupled SYM theory. The Yang-Mills plasma does not meet that expectation below $2T_c$. Instead we find that strong fluctuations of $F\tilde F$ are present at least up to that temperature. We discuss the impact of our results on our understanding of the quark-gluon plasma.Comment: 32 pages, 9 figures, 4 tables; added some references, more detailed captions, conclusions unchange