Search

An accurate determination of the leading-order hadronic vacuum polarisation (HVP) contribution to the anomalous magnetic moment of the muon is critical to understanding the size and significance of any discrepancy between the Standard Model prediction and experimental results being obtained by the Muon g-2 experiment at Fermilab. The Standard Model prediction is currently based on a data-driven approach to the HVP using experimental results for $\sigma(e^+e^-\rightarrow\,\mathrm{hadrons})$. Lattice QCD aims to provide a result with similar uncertainty from calculated vector-vector correlation functions, but the growth of statistical and systematic errors in the $u/d$ quark correlation functions at large Euclidean time has made this difficult to achieve. We show that restricting the lattice contributions to a one-sided window $0

We review the present status of the Standard Model calculation of the anomalous magnetic moment of the muon. This is performed in a perturbative expansion in the fine-structure constant $\alpha$ and is broken down into pure QED, electroweak, and hadronic contributions. The pure QED contribution is by far the largest and has been evaluated up to and including $\mathcal{O}(\alpha^5)$ with negligible numerical uncertainty. The electroweak contribution is suppressed by $(m_\mu/M_W)^2$ and only shows up at the level of the seventh significant digit. It has been evaluated up to two loops and is known to better than one percent. Hadronic contributions are the most difficult to calculate and are responsible for almost all of the theoretical uncertainty. The leading hadronic contribution appears at $\mathcal{O}(\alpha^2)$ and is due to hadronic vacuum polarization, whereas at $\mathcal{O}(\alpha^3)$ the hadronic light-by-light scattering contribution appears. Given the low characteristic scale of this observable, these contributions have to be calculated with nonperturbative methods, in particular, dispersion relations and the lattice approach to QCD. The largest part of this review is dedicated to a detailed account of recent efforts to improve the calculation of these two contributions with either a data-driven, dispersive approach, or a first-principle, lattice-QCD approach. The final result reads $a_\mu^\text{SM}=116\,591\,810(43)\times 10^{-11}$ and is smaller than the Brookhaven measurement by 3.7$\sigma$. The experimental uncertainty will soon be reduced by up to a factor four by the new experiment currently running at Fermilab, and also by the future J-PARC experiment. This and the prospects to further reduce the theoretical uncertainty in the near future-which are also discussed here-make this quantity one of the most promising places to look for evidence of new physics., Comment: 196 pages, 103 figures, version published in Phys. Rept., bib files for the citation references are available from: https://muon-gm2-theory.illinois.edu

We present an update on the ongoing calculations by the Fermilab Lattice, HPQCD, and MILC Collaboration of the leading-order (in electromagnetism) hadronic vacuum polarization contribution to the anomalous magnetic moment of the muon. Our project employs ensembles with four flavors of highly improved staggered fermions, physical light-quark masses, and four lattice spacings ranging from $a \approx 0.06$ to 0.15 fm for most of the results thus far., Comment: LATTICE 2019, 7 pages, 7 figures

We calculate the contribution to the muon anomalous magnetic moment hadronic vacuum polarization from {the} connected diagrams of up and down quarks, omitting electromagnetism. We employ QCD gauge-field configurations with dynamical $u$, $d$, $s$, and $c$ quarks and the physical pion mass, and analyze five ensembles with lattice spacings ranging from $a \approx 0.06$ to~0.15~fm. The up- and down-quark masses in our simulations have equal masses $m_l$. We obtain, in this world where all pions have the mass of the $\pi^0$, $10^{10} a_\mu^{ll}({\rm conn.}) = 637.8\,(8.8)$, in agreement with independent lattice-QCD calculations. We then combine this value with published lattice-QCD results for the connected contributions from strange, charm, and bottom quarks, and an estimate of the uncertainty due to the fact that our calculation does not include strong-isospin breaking, electromagnetism, or contributions from quark-disconnected diagrams. Our final result for the total $\mathcal{O}(\alpha^2)$ hadronic vacuum polarization to the muon's anomalous magnetic moment is~$10^{10}a_\mu^{\rm HVP,LO} = 699(15)_{u,d}(1)_{s,c,b}$, where the errors are from the light-quark and heavy-quark contributions, respectively. Our result agrees with both {\it ab-initio} lattice-QCD calculations and phenomenological determinations from experimental $e^+e^-$-scattering data. It is $1.3\sigma$ below the "no new physics" value of the hadronic-vacuum-polarization contribution inferred from combining the BNL E821 measurement of $a_\mu$ with theoretical calculations of the other contributions., Comment: 19 pages, 12 figures, 6 tables; updated to correct a small mistake in the finite volume correction resulting in small changes to the results, matches published version

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 $\alpha_s^2$ multiplying $\langle\overline{\psi}\psi\rangle/M^3$ and terms in $\alpha_s$ multiplying $\langle \alpha_s G^2 \rangle/M^4$, 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 strange-quark condensate to the time-moments is very substantial. We use our lattice QCD time-moments and the OPE to determine a value for the condensate, fitting the 4th, 6th, 8th and 10th time-moments simultaneously. Our result, $\langle \overline{s}s \rangle^{\overline{\text{MS}}}(2 \text{GeV}) = -(296(11) \,\mathrm{MeV})^3$, agrees well with HPQCD's earlier, more direct, lattice QCD determination~\cite{McNeile:2012xh}. As well as confirming that the $s$ quark condensate is close in value to the light quark condensate, this demonstrates clearly the consistency of the Operator Product Expansion for fully nonperturbative calculations of matrix elements of short-distance operators in lattice QCD., Comment: 14 pages, 4 figures

All lattice-QCD calculations of the hadronic-vacuum-polarization contribution to the muon's anomalous magnetic moment to-date have been performed with degenerate up- and down-quark masses. Here we calculate directly the strong-isospin-breaking correction to $a_\mu^{\rm HVP}$ for the first time with physical values of $m_u$ and $m_d$ and dynamical $u$, $d$, $s$, and $c$ quarks, thereby removing this important source of systematic uncertainty. We obtain a relative shift to be applied to lattice-QCD results obtained with degenerate light-quark masses of $\delta a_\mu^{{\rm HVP,} m_u \neq m_d}$= +1.5(7)%, in agreement with estimates from phenomenology and a recent lattice-QCD calculation with unphysically heavy pions., Comment: v2: 6 pages, 2 tables, 2 figures. Additional references and expanded discussion of systematic errors. Version accepted to Physical Review Letters

We present a new lattice QCD analysis of heavy-quark pseudoscalar-pseudoscalar correlators, using gluon configurations from the MILC collaboration that include vacuum polarization from $u$, $d$, $s$ and $c$~quarks($n_f=4$). We extract new values for the QCD coupling and for the $c$ quark's $\overline{\mathrm{MS}}$ mass: $\alpha_{\overline{\mathrm{MS}}}(M_Z,n_f=5) = 0.11822(74)$ and $m_c(3\mathrm{GeV}, n_f=4) = 0.9851(63)$GeV. These agree well with our earlier simulations using $n_f=3$ sea quarks, vindicating the perturbative treatment of $c$ quarks in that analysis. We also obtain a new nonperturbative result for the ratio of $c$~and $s$~quark masses: $m_c/m_s=11.652(65)$. This ratio implies $m_s(2\,\mathrm{GeV}, n_f=3)=93.6(8)$MeV when it is combined with our new~$c$~mass. Combining $m_c/m_s$ with our earlier $m_b/m_c$ gives $m_b/m_s=52.55(55)$, which is several standard deviations (but only 4%) away from the Georgi-Jarlskop prediction from certain GUTs. Finally we obtain an $n_f=4$ estimate for $m_b/m_c=4.528(54)$ which agrees well with our earlier $n_f=3$ result. The new ratio implies~$m_b(m_b,n_f=5)=4.162(48)$GeV., Comment: 16 pages, 9 figures, 6 tables

We have developed two methods for handling $b$ quarks in lattice QCD. One uses NRQCD (now improved to include radiative corrections) and the other uses Highly Improved Staggered Quarks (HISQ), extrapolating to the $b$ quark from lighter masses and using multiple lattice spacings to control discretisation errors. Comparison of results for the two different methods gives confidence in estimates of lattice QCD systematic errors, since they are very different in these two cases. Here we show results for heavyonium hyperfine splittings and vector current-current correlator moments using HISQ quarks, to add to earlier results testing the heavy HISQ method with pseudoscalar mesons. We also show the form factor for $B \rightarrow \pi l \nu$ decay at zero recoil using NRQCD $b$ quarks and $u/d$ quarks with physical masses. This allows us to test the soft pion theorem relation ($f_0(q^2_{max})=f_B/f_{\pi}$) accurately and we find good agreement as $M_{\pi} \rightarrow 0$. }, Comment: 5 pages, 3 figures, Proceedings of Lattice2013

Calculations of pseudoscalar decay constants of B, Bs, K and pi mesons with physical light quarks are presented. We use HISQ ensembles that include u,d,s and c sea quarks at three lattice spacings. HISQ is used for the valence light quarks and a radiatively improved NRQCD action for the heavy quarks. The key results are f_{B^+}=0.184(4)$ GeV, f_{B_s}=0.224(4) GeV, f_{B_s}/f_{B^+}=1.217(8), f_{K^+}/f_{pi^+}=1.1916(21), f_{K^+}=155.37(34) MeV, giving a significant improvement over previous results that required chiral extrapolation. We also calculate the Wilson flow scale w_0, finding w_0=0.1715(9) fm., Comment: 7 pages, 8 figures, presented at the 31st International Symposium on Lattice Field Theory

We determine the decay constants of the pi and K mesons on gluon field configurations from the MILC collaboration including u, d, s and c quarks. We use three values of the lattice spacing and u/d quark masses going down to the physical value. We use the w_0 parameter to fix the relative lattice spacing and f_pi to fix the overall scale. This allows us to obtain a value for f{K^+}/f{pi^+} = 1.1916(21). Comparing to the ratio of experimental leptonic decay rates gives |Vus| = 0.22564(28){Br(K^+)}(20){EM}(40){latt}(5){Vud} and the test of unitarity of the first row of the Cabibbo-Kobayashi-Maskawa matrix: |Vud|^2+|Vus|^2+|Vub|^2 - 1 = 0.00009(51)., Comment: 9 pages, 5 figures. Updated to include more discussion of different checks of our fitting procedures and error analysis. Added a figure on autocorrelations. Published version

We show results from calculations in full lattice QCD of the mass, leptonic width and radiative decay rate to eta_c of the J/psi meson. These provide few % tests of QCD. Another (1.5%) test comes from comparison of time-moments of the vector charmonium correlator with results derived from the experimental values of R(e+e- to hadrons) in the charm region., Comment: 3 pages, 4 figures, Proceedings of Confinement2012

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)., Comment: 4 pages, 4 figures, Proceedings of Confinement2012

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 $m\bar{\psi}\psi$ 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 subtraction is calculated through $\mathcal{O}(\alpha_s)$ and estimates of higher order terms are included through fitting results at multiple lattice spacing values. The gluon field configurations used are `second generation' ensembles from the MILC collaboration that include 2+1+1 flavors of sea quarks implemented with the Highly Improved Staggered Quark action and including $u/d$ sea quarks down to physical masses. Our results are : $<\bar{s}{s}>^{\bar{MS}}(2 \mathrm{GeV})= -(290(15) \mathrm{MeV})^3$, $<\bar{l}{l}>^{\bar{MS}}(2\, \mathrm{GeV})= -(283(2) \mathrm{MeV})^3$, where $l$ is a light quark with mass equal to the average of the $u$ and $d$ quarks. The strange to light quark condensate ratio is 1.08(16). The light quark condensate is significantly larger than the chiral condensate in line with expectations from chiral analyses. We discuss the implications of these results for other calculations., Comment: 21 pages, 13 figures

We calculate the J/{\psi} mass, leptonic width and radiative decay rate to \gamma \eta_c from lattice QCD including u, d and s quarks in the sea for the first time. We use the Highly Improved Staggered Quark formalism and nonperturbatively normalised vector currents for the leptonic and radiative decay rates. Our results are: M_{J/\psi} -M_{\eta_c} = 116.5(3.2) MeV; \Gamma(J/{\psi} to e^+e^-) = 5.48(16) keV; \Gamma(J/{\psi} to \gamma \eta_c) = 2.49(19) keV. The first two are in good agreement with experiment, with \Gamma(J/{\psi} to e^+e^-) providing a test of a decay matrix element in QCD, independent of CKM uncertainties, to 2%. At the same time results for the time moments of the correlation function can be compared to values from the charm contribution to \Gamma(e^+e^- to hadrons), giving a 1.5% test of QCD. Our results show that an improved experimental error would enable a similarly strong test from \Gamma(J/{\psi} to \gamma \eta_c)., Comment: 20 pages, 16 figures. Added some text plus a figure and two tables comparing the time moments of the charmonium vector correlator to results extracted from experiment for the charm contribution to e^+e^- -> hadrons. This allows a 1.5% test of QCD. Further minor amendments to the text. Version accepted for publication by Physical Review D

We use a variational technique to study heavy glueballs on gauge configurations generated with 2+1 flavours of ASQTAD improved staggered fermions. The variational technique includes glueball scattering states. The measurements were made using 2150 configurations at 0.092 fm with a pion mass of 360 MeV. We report masses for 10 glueball states. We discuss the prospects for unquenched lattice QCD calculations of the oddballs., Comment: 19 pages, 4 tables and 8 figures. One figure added. Now matches the published version

We determine masses and decay constants of heavy-heavy and heavy-charm pseudoscalar mesons as a function of heavy quark mass using a fully relativistic formalism known as Highly Improved Staggered Quarks for the heavy quark. We are able to cover the region from the charm quark mass to the bottom quark mass using MILC ensembles with lattice spacing values from 0.15 fm down to 0.044 fm. We obtain f_{B_c} = 0.427(6) GeV; m_{B_c} = 6.285(10) GeV and f_{\eta_b} = 0.667(6) GeV. Our value for f_{\eta_b} is within a few percent of f_{\Upsilon} confirming that spin effects are surprisingly small for heavyonium decay constants. Our value for f_{B_c} is significantly lower than potential model values being used to estimate production rates at the LHC. We discuss the changing physical heavy-quark mass dependence of decay constants from heavy-heavy through heavy-charm to heavy-strange mesons. A comparison between the three different systems confirms that the B_c system behaves in some ways more like a heavy-light system than a heavy-heavy one. Finally we summarise current results on decay constants of gold-plated mesons., Comment: 16 pages, 12 figures

Scale setting is of central importance in lattice QCD. It is required to predict dimensional quantities in physical units. Moreover, it determines the relative lattice spacings of computations performed at different values of the bare coupling, and this is needed for extrapolating results into the continuum. Thus, we calculate a new quantity, $w_0$, for setting the scale in lattice QCD, which is based on the Wilson flow like the scale $t_0$ (M. Luscher, JHEP 1008 (2010) 071). It is cheap and straightforward to implement and compute. In particular, it does not involve the delicate fitting of correlation functions at asymptotic times. It typically can be determined on the few per-mil level. We compute its continuum extrapolated value in 2+1-flavor QCD for physical and non-physical pion and kaon masses, to allow for mass-independent scale setting even away from the physical mass point. We demonstrate its robustness by computing it with two very different actions (one of them with staggered, the other with Wilson fermions) and by showing that the results agree for physical quark masses in the continuum limit., Comment: 15 pages, 7 figures, 2 tables; Version published in JHEP

We present a new determination of the $B_s$ leptonic decay constant from lattice QCD simulations that use gluon configurations from MILC and a highly improved discretization of the relativistic quark action for both valence quarks. Our result, $f_{B_s} = 0.225(4)$\,GeV, is almost three times more accurate than previous determinations. We analyze the dependence of the decay constant on the heavy quark's mass and obtain the first empirical evidence for the leading $1/\sqrt{m_h}$ dependence predicted by Heavy Quark Effective Theory (HQET). As a check, we use our analysis technique to calculate the $m_{B_s}-m_{\eta_b}/2$ mass difference. Our result agrees with experiment to within errors of $11\,\mathrm{MeV}$ (better than 2%). We discuss how to extend our analysis to other quantities in $B_s$ and $B$ physics, making 2%-precision possible for the first time., Comment: 5 pages, 3 figures

We study the spectra of heavy-light and heavy-heavy mesons containing charm quarks, including higher spin states. We use two sets of $N_f = 2 + 1$ gauge configurations, one set from QCDSF using the SLiNC action, and the other configurations from the Budapest-Marseille-Wuppertal collaboration, using the HEX smeared clover action. To extract information about the excited states, we choose a suitable basis of operators to implement the variational method., Comment: 7 pages, 5 figures, Talk presented at the XXIX International Symposium on Lattice Field Theory, Lattice2011, July 11-16, 2011, The Village at Squaw Valley, California, USA

Indirect CP violation in K \rightarrow {\pi}{\pi} decays plays a central role in constraining the flavor structure of the Standard Model (SM) and in the search for new physics. For many years the leading uncertainty in the SM prediction of this phenomenon was the one associated with the nonperturbative strong interaction dynamics in this process. Here we present a fully controlled lattice QCD calculation of these effects, which are described by the neutral kaon mixing parameter B_K . We use a two step HEX smeared clover-improved Wilson action, with four lattice spacings from a\approx0.054 fm to a\approx0.093 fm and pion masses at and even below the physical value. Nonperturbative renormalization is performed in the RI-MOM scheme, where we find that operator mixing induced by chiral symmetry breaking is very small. Using fully nonperturbative continuum running, we obtain our main result B_K^{RI}(3.5GeV)=0.531(6)_{stat}(2)_{sys}. A perturbative 2-loop conversion yields B_K^{MSbar-NDR}(2GeV)=0.564(6)_{stat}(3)_{sys}(6)_{PT}, which is in good agreement with current results from fits to experimental data., Comment: 10 pages, 7 figures. v2: Added one reference and one figure, replaced 2 figures for better readability and updated ensembles, conclusions unchanged. Final, published version

We update our previous determination of both the decay constant and the mass of the $D_s$ meson using the Highly Improved Staggered Quark formalism. We include additional results at two finer values of the lattice spacing along with improved determinations of the lattice spacing and improved tuning of the charm and strange quark masses. We obtain $m_{D_s}$ = 1.9691(32) GeV, in good agreement with experiment, and $f_{D_s}$ = 0.2480(25) GeV. Our result for $f_{D_s}$ is 1.6$\sigma$ lower than the most recent experimental average determined from the $D_s$ leptonic decay rate and using $V_{cs}$ from CKM unitarity. Combining our $f_{D_s}$ with the experimental rate we obtain a direct determination of $V_{cs} = 1.010(22)$, or alternatively $0.990 {+0.013 \atop -0.016}$ using a probability distribution for statistical errors for this quantity which vanishes above 1. We also include an accurate prediction of the decay constant of the $\eta_c$, $f_{\eta_c}$ = 0.3947(24) GeV, as a calibration point for other lattice calculations., Comment: 24 pages, 20 figures. Updated to include new experimental results from BaBar, new experimental averages from HFAG and consequent discussion of theory/experiment comparison. Other minor typographical changes. Version accepted by Phys. Rev. D

We extend our earlier lattice-QCD analysis of heavy-quark correlators to smaller lattice spacings and larger masses to obtain new values for the c mass and QCD coupling, and, for the first time, values for the b mass: m_c(3GeV,n_f=4)=0.986(6)GeV, alpha_msb(M_Z,n_f=5)=0.1183(7), and m_b(10GeV,n_f=5)=3.617(25)GeV. These are among the most accurate determinations by any method. We check our results using a nonperturbative determination of the mass ratio m_b(mu,n_f)/m_c(mu,n_f); the two methods agree to within our 1% errors and taken together imply m_b/m_c=4.51(4). We also update our previous analysis of alpha_msb from Wilson loops to account for revised values for r_1 and r_1/a, finding a new value alpha_\msb(M_Z,n_f=5)=0.1184(6); and we update our recent values for light-quark masses from the ratio m_c/m_s. Finally, in the Appendix, we derive a procedure for simplifying and accelerating complicated least-squares fits., Comment: 16 pages, 10 figures, 3 tables

We review various B meson decays that require knowledge of the transverse decay constant of the b1(1235) meson. We report on an exploratory lattice QCD calculation of the transverse decay constant of the b1 meson. The lattice QCD calculations used unquenched gauge configurations, at two lattice spacings, generated with two flavours of sea quarks. The twisted mass formalism is used., Comment: 11 pages, 3 figures. Fixed some typos, updated value of one of the sum rule results

By using a single formalism to handle charm, strange and light valence quarks in full lattice QCD for the first time, we are able to determine ratios of quark masses to 1%. For $m_c/m_s$ we obtain 11.85(16), an order of magnitude more precise than the current PDG average. Combined with 1% determinations of the charm quark mass now possible this gives $\bar{m}_s(2{\rm GeV}) =$ 92.4(1.5) MeV. The MILC result for $m_s/m_l = 27.2(3) $ yields $\bar{m}_l(2{\rm GeV})$ = 3.40(7) MeV for the average of $u$ and $d$ quark masses., Comment: 4 pages, 2 figures. Version accepted by Physical Review Letters. Changes include modifying the title, using the MILC value for m_s/m_l which changes slightly the resulting up and down quark masses and their average, adding some references and making other small adjustments to the text for space reasons.

We discuss the status of our ongoing efforts to improve on our calculation of the $D_s$ decay constant. We show preliminary results on the ratio of the charm to the strange quark mass. We also present preliminary results for spectroscopy, decay constants and bottom quark mass obtained by performing calculations with highly improved staggered quarks at masses above the c mass and close to the b mass., Comment: 8 pages. Contribution to 27th International Symposium on Lattice Field Theory, Beijing, China, 2009

We compare three different methods to determine the lattice spacing in lattice QCD and give results from calculations on the MILC ensembles of configurations that include the effect of $u$, $d$ and $s$ sea quarks. It is useful, for ensemble to ensemble comparison, to express the results as giving a physical value for $r_1$, a parameter from the heavy quark potential. Combining the three methods gives a value for $r_1$ in the continuum limit of 0.3133(23)(3) fm. Using the MILC values for $r_0/r_1$, this corresponds to a value for the $r_0$ parameter of 0.4661(38) fm. We also discuss how to use the $\eta_s$ for determining the lattice spacing and tuning the $s$-quark mass accurately, by giving values for $m_{\eta_s}$ (0.6858(40) GeV) and $f_{\eta_s}$ (0.1815(10) GeV)., Comment: 15 pages

We report results for the masses of the flavour non-singlet light 0++, 1--, and 1+- mesons from unquenched lattice QCD at two lattice spacings. The twisted mass formalism was used with two flavours of sea quarks. For the 0++ and 1+- mesons we look for the effect of decays on the mass dependence. For the light vector mesons we study the chiral extrapolations of the mass. We report results for the leptonic and transverse decay constants of the rho meson. We test the mass dependence of the KRSF relations., Comment: 35 pages, 14 figures. Added 2 references. Fixed small typos

We compare flavour singlet and non-singlet vector mesons from first principles using lattice QCD. With N_f=2 flavours of light quark, this addresses the omega-rho mass difference. Using maximally twisted-mass lattice QCD, we are able for the first time to determine this mass difference precisely and we compare with experiment. We also discuss omega-rho mixing effects arising within QCD through the u-d quark mass difference., Comment: 12 pages 4 figures

We present an update of results from the HPQCD collaboration on charm physics using the Highly Improved Staggered Quark action. This includes a precise determination of m_c using moments of current-current correlators combined with high-order continuum QCD perturbation theory. We also include an update on the determination of alpha_s from lattice QCD, preliminary results on the determination of m_b and a summary plot of the status of the gold-plated meson spectrum. There is an appendix on tackling systematic errors in fitting using the Bayesian approach., Comment: 14 pages, 7 figures, combined proceedings of talks by Christine Davies and Peter Lepage at the International Symposium on Lattice Field Theory 2008, Williamsburg

We present results for chiral extrapolations of the mass and decay constants of the rho meson. The data sets used are the nf=2 unquenched gauge configurations generated with twisted mass fermions by the European Twisted Mass Collaboration. We describe a calculation of three decay constants in charmonium and explain why they are required., Comment: 7 pages, 2 figures. Talk given at the XXVI International Symposium on Lattice Field Theory, July 14 - 19 2008, Williamsburg, Virginia, USA

We provide a new determination of the charm quark mass using the Highly Improved Staggered Quark (HISQ) action, finding m_c(3 GeV) = 0.983(23) GeV. Our determination makes extensive use of second order lattice perturbation theory in matching the bare lattice mass to the MSbar scheme. This matching utilises both traditional diagrammatic perturbation theory and weak coupling simulations. The second of these techniques allows us to extract perturbative coefficients from Monte-Carlo simulations and the process of doing this is laid out in some detail here., Comment: 7 pages, 4 figures, talk presented at the XXVI International Symposium on Lattice Field Theory, July 14-19, 2008, Williamsburg, Virginia, USA

We present some early results from a high statistics study of the scalar and pseudoscalar singlet sectors of lattice QCD using 2+1 flavours of Asqtad improved staggered fermions. The use of the Asqtad action has allowed us to generate an unprecedented number of configurations at 2 lattice spacings which on completion we hope will give us a significantly improved view of both the scalar and pseudoscalar singlet sectors., Comment: 7 pages, 3 figures, 1 table, to appear in the Proceedings of the XXVI International Symposium on Lattice Field Theory, July 14 - 19, 2008, Williamsburg, VA, USA

We use lattice QCD simulations, with MILC configurations (including vacuum polarization from u, d, and s quarks), to update our previous determinations of the QCD coupling constant. Our new analysis uses results from 6 different lattice spacings and 12 different combinations of sea-quark masses to significantly reduce our previous errors. We also correct for finite-lattice-spacing errors in the scale setting, and for nonperturbative chiral corrections to the 22 short-distance quantities from which we extract the coupling. Our final result is alpha_V(7.5GeV,nf=3) = 0.2120(28), which is equivalent to alpha_msbar(M_Z,n_f=5)= 0.1183(8). We compare this with our previous result, which differs by one standard deviation., Comment: 12 pages, 2 figures, 4 tables

We use lattice QCD simulations, with MILC gluon configurations and HISQ c-quark propagators, to make very precise determinations of moments of charm-quark pseudoscalar, vector and axial-vector correlators. These moments are combined with new four-loop results from continuum perturbation theory to obtain several new determinations of the MSbar mass of the charm quark and of the MSbar coupling. We find m_c(3GeV)=0.986(10)GeV, or, equivalently, m_c(m_c)=1.268(9)GeV, both for n_f=4 flavors; and alpha_msb(3GeV,n_f=4)=0.251(6), or, equivalently, alpha_\msb(M_Z,n_f=5)=0.1174(12). The new mass agrees well with results from continuum analyses of the vector correlator using experimental data for e+e- annihilation (instead of using lattice QCD simulations). These lattice and continuum results are the most accurate determinations to date of this mass. Ours is also one of the most accurate determinations of the QCD coupling by any method., Comment: 12 pages, 5 figures, 5 tables

The effect of Stout smearing is investigated in numerical simulations with twisted mass Wilson quarks. The phase transition near zero quark mass is studied on 12^3x24, 16^3x32 and 24^3x48 lattices at lattice spacings a = 0.1 - 0.125 fm., Comment: 7 pages, 5 figures, Poster presented at the XXV International Symposium on Lattice Field Theory, July 30 - August 4 2007, Regensburg, Germany

We present results of dynamical simulations with 2 flavours of degenerate Wilson twisted mass quarks at maximal twist in the range of pseudo scalar masses from 300 to 550 MeV. The simulations are performed at one value of the lattice spacing a \lesssim 0.1 fm. In order to have O(a) improvement and aiming at small residual cutoff effects, the theory is tuned to maximal twist by requiring the vanishing of the untwisted quark mass. Precise results for the pseudo scalar decay constant and the pseudo scalar mass are confronted with chiral perturbation theory predictions and the low energy constants F, \bar{l}_3 and \bar{l}_4 are evaluated with small statistical errors., Comment: 17 pages, 5 figures, references added, typos corrected

We compute the masses of the flavour singlet 0++ mesons using (n_f=2) unquenched lattice QCD with the Iwasaki and Wilson gauge actions. Both fermionic and glueball interpolating operators are used to create the states. The mass of the lightest 0++ meson is suppressed relative to the mass of the 0++ glueball in quenched QCD at an equivalent lattice spacing. We discuss two possible physical reasons for this.

We review the theory that predicts that the decay constant of the excited light pseudo-scalar mesons are suppressed in the chiral limit relative to the pion decay constant. We compute the decay constant of the first excited pion ($\pi^\prime$) using unquenched QCD at a fixed lattice spacing with sea quarks of mass as low as a third the mass of the strange quark. The final result is very sensitive to the improvement conditions. We obtain $f_{\pi^\prime} / f_{\pi}$ = 0.078(93) in the chiral limit., Comment: Updated references. Clarified discussion around equations 2 and 3

Lattice QCD with $N_f=2$ flavours of sea quark is used to explore the spectrum and decay of scalar mesons. We are able to determine the $b_1$ - $a_0$ mass difference and this leads to the conclusion that the lightest non-singlet scalar meson ($a_0$) has a mass of 1.01(4) GeV. We determine from the lattice the coupling strength to KK and $\pi \eta$. We compute the leptonic decay constant of the lightest non-singlet scalar meson. We discuss the impact of these lattice results on the interpretation of the $a_0(980)$ state. We also discuss $K^*_0$ states., Comment: version accepted by Phys Rev D

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: $f_{D_{s 0^+}} = 340(110)$ MeV using our normalisation conventions. We obtain the $f_{P_s}^{static}$ (static-strange P-wave) decay constant as $302(39)$ MeV., Comment: We have included a effective mass plot and a graph for the chiral extrapolation in the light quark mass. Some of the discussions are clarified. No change in results. Accepted for publication in Phys.Rev.D

Lattice QCD with $N_f=2$ flavours of sea quark is used to explore the spectrum and decay of a $J^{PC}=1^{-+}$ spin-exotic hybrid meson. We test lattice determination of S-wave decay amplitudes at threshold using $b_1 \to \pi \omega$ where agreement with data is found. We find a hybrid meson state at 2.2(2) GeV with a partial width to $\pi b_1$ of 400(120) MeV and to $\pi f_1$ of 90(60) MeV., Comment: 16 pages, 4 ps figures, version accepted for publication in Phys Rev D

This is a follow-up to our earlier work [Phys. Rev. D 65, 014512 (2002); Eur. Phys. J. C 28, 79 (2003); Phys. Rev. D 69, 094505 (2004)] for the energies and the charge (vector) and matter (scalar) distributions for S-wave states in a heavy-light meson, where the heavy quark is static and the light quark has a mass about that of the strange quark. We study the radial distributions of higher angular momentum states, namely P- and D-wave states. In nature the closest equivalent of this heavy-light system is the B_s meson. The calculation is carried out with dynamical fermions on a 16^3 times 32 lattice with a lattice spacing of about 0.10 fm generated with the non-perturbatively improved clover action. It is shown that several features of the energies and radial distributions are in qualitative agreement with what one expects from a simple one-body Dirac equation interpretation., Comment: 6 pages, poster presented at Lattice 2005 (Heavy quarks)

Twisted mass fermions allow light quarks to be explored but with the consequence that there are mass splittings, such as between the neutral and charged pion. Using a direct calculation of the connected neutral pion correlator and stochastic methods to evaluate the disconnected correlations, we determine the neutral pion mass. We explore the dependence on lattice spacing and quark mass in quenched QCD. For dynamical QCD, we determine the sign of the splitting which is linked, via chiral PT, to the nature of the phase transition at small quark mass., Comment: 6 pages, poster (hadron spectrum and quark masses) at Lattice 2005,Dublin, July 25-30

We compute the mass of the charm quark using both quenched and dynamical lattice QCD calculations. We examine the effects of mass dependent lattice artifacts by comparing two different formalisms for the heavy quarks. We take the continuum limit of the charm mass in quenched QCD by extrapolating from three different lattice spacings. At a fixed lattice spacing, the mass of the charm quark is compared between quenched QCD and dynamical QCD with a sea quark mass around strange. In the continuum limit of quenched QCD, we find m_c(m_c)=1.29(7)(13) GeV. No evidence was seen for unquenching., Comment: Added NP analysis of quenched data, corrected error in PCAC RGI mass, updated strange quark mass discussion and references, unified notation and corrected typos. No change in final result. Version accepted for publication in JHEP

We study the flavour breaking effects appearing in the Wilson twisted mass formulation of lattice QCD. In this quenched study, we focus on the mass splitting between the neutral and the charged pion, determining the neutral pion mass with a stochastic noise method to evaluate the disconnected contributions. We find that these disconnected contributions are significant. Using the Osterwalder-Seiler interpretation of the connected piece of the neutral pion correlator, we compute the corresponding neutral pion mass to study with more precision the scaling behaviour of the mass splitting., Comment: 15 pages, 2 figures

Using the clover fermion action in unquenched QCD with pion masses as low as 420 MeV, we look for evidence for chiral logs in the static-light decay constant. There is some evidence for a chiral log term, if the original static theory of Eichten and Hill is used. However, the more precise data from the static action of the ALPHA collaboration do not show any evidence for non-linear dependence of the static-light decay constant on the light quark mass. We make some comments on the connection between chiral perturbation theory for decay constants of the pion and static-light meson.

We compute the charm quark mass in lattice QCD and compare different formulations of the heavy quark, and quenched data to that with dynamical sea quarks. We take the continuum limit of the quenched data by extrapolating from three different lattice spacings, and compare to data with two flavours of dynamical sea quarks with a mass around the strange at the coarsest lattice spacing. Both the FNAL and ALPHA formalism are used. We find the different heavy quark formulations have the same continuum limit in the quenched approximation, and limited evidence that this approximation overestimates the charm quark mass., Comment: Lattice2004(heavy) 3 pages, 2 figures

We compute the b quark mass from dynamical lattice QCD with clover quarks. The calculation is done at a fixed lattice spacing with sea quark masses as low as half the strange quark mass. Our final result is m_b(m_b} = 4.25(2)(11) GeV, where the first error is statistical and the last error is the systematic uncertainty., Comment: 10 pages

We explore the transitions B$(0^+)$ to B $\pi$ and B$_s(0^+)$ to B K from lattice QCD with $N_f=2$ flavours of sea quark, using the static approximation for the heavy quark. We evaluate the effective coupling constants, predicting a B$(0^+)$ to B $\pi$ width of around 160 MeV. Our result for the coupling strength adds to the evidence that the B$_s(0^+)$ meson is not predominantly a molecular state (BK)., Comment: 10 pages LATEX

We present results from simulations using 2 flavours of O(a)-improved Wilson quarks whose masses are about 1/3 of the physical strange quark mass. We present new data on the mass of the singlet pseudoscalar meson and evidence of the onset of chiral logarithms in the pion decay constant. The previously observed suppression of the topological susceptibility at lighter quark masses is confirmed. We report on the performance of the hybrid Monte Carlo algorithm at light quark masses., Comment: 9 pages, Revtex4, 10 figures