Search

We calculate the bag parameters for neutral $B$-meson mixing in and beyond the Standard Model, in full four-flavour lattice QCD for the first time. We work on gluon field configurations that include the effect of $u$, $d$, $s$ and $c$ sea quarks with the Highly Improved Staggered Quark (HISQ) action at three values of the lattice spacing and with three $u/d$ quark masses going down to the physical value. The valence $b$ quarks use the improved NRQCD action and the valence light quarks, the HISQ action. Our analysis was blinded. Our results for the bag parameters for all five operators are the most accurate to date. For the Standard Model operator between $B_s$ and $B_d$ mesons we find: $\hat{B}_{B_s}=1.232(53)$, $\hat{B}_{B_d}=1.222(61)$. Combining our results with lattice QCD calculations of the decay constants using HISQ quarks from the Fermilab/MILC collaboration and with experimental values for $B_s$ and $B_d$ oscillation frequencies allows determination of the CKM elements $V_{ts}$ and $V_{td}$. We find $V_{ts} = 0.04189(93)$, $V_{td} = 0.00867(23)$ and $V_{ts}/V_{td} = 0.2071(27)$. Our results agree well (within $2\sigma$) with values determined from CKM unitarity constraints based on tree-level processes (only). Using a ratio to $\Delta M$ in which CKM elements cancel in the Standard Model, we determine the branching fractions ${\text{Br}}(B_s\rightarrow \mu^+\mu^-) = 3.81(18) \times 10^{-9}$ and ${\text{Br}}(B_d\rightarrow \mu^+\mu^-) = 1.031(54) \times 10^{-10}$. We also give results for matrix elements of the operators $R_0$, $R_1$ and $\tilde{R}_1$ that contribute to neutral $B$-meson width differences., Comment: 27 pages, 16 figures. Slight changes to text to clarify arguments. Updated Figure 10. Version accepted by Physical Review D

We present a lattice quantum chromodynamics determination of the ratio of the scalar and vector form factors for two semileptonic decays of the ${B}_{s}$ meson: ${B}_{s}\ensuremath{\rightarrow}K\ensuremath{\ell}\ensuremath{\nu}$ and ${B}_{s}\ensuremath{\rightarrow}{D}_{s}\ensuremath{\ell}\ensuremath{\nu}$. In conjunction with future experimental data, our results for these correlated form factors will provide a new method to extract $|{V}_{ub}/{V}_{cb}|$, which may elucidate the current tension between exclusive and inclusive determinations of these Cabibbo-Kobayashi-Maskawa mixing matrix parameters. In addition to the form factor results, we determine the ratio of the differential decay rates, and forward-backward and polarization asymmetries, for the two decays.

We present a lattice quantum chromodynamics determination of the scalar and vector form factors for the ${B}_{s}\ensuremath{\rightarrow}{D}_{s}\ensuremath{\ell}\ensuremath{\nu}$ decay over the full physical range of momentum transfer. In conjunction with future experimental data, our results will provide a new method to extract $|{V}_{cb}|$, which may elucidate the current tension between exclusive and inclusive determinations of this parameter. Combining the form factor results at nonzero recoil with recent HPQCD results for the $B\ensuremath{\rightarrow}D\ensuremath{\ell}\ensuremath{\nu}$ form factors, we determine the ratios ${f}_{0}^{{B}_{s}\ensuremath{\rightarrow}{D}_{s}}({M}_{\ensuremath{\pi}}^{2})/{f}_{0}^{B\ensuremath{\rightarrow}D}({M}_{K}^{2})=1.000(62)$ and ${f}_{0}^{{B}_{s}\ensuremath{\rightarrow}{D}_{s}}({M}_{\ensuremath{\pi}}^{2})/{f}_{0}^{B\ensuremath{\rightarrow}D}({M}_{\ensuremath{\pi}}^{2})=1.006(62)$. These results give the fragmentation fraction ratios ${f}_{s}/{f}_{d}=0.310(30{)}_{\text{stat}}(21{)}_{\text{syst}}(6{)}_{\text{theor}}(38{)}_{\text{latt}}$ and ${f}_{s}/{f}_{d}=\phantom{\rule{0ex}{0ex}}0.307(16{)}_{\text{stat}}(21{)}_{\text{syst}}(23{)}_{\text{theor}}(44{)}_{\text{latt}}$, respectively. The fragmentation fraction ratio is an important ingredient in experimental determinations of ${B}_{s}$ meson branching fractions at hadron colliders, in particular for the rare decay $\mathcal{B}({B}_{s}\ensuremath{\rightarrow}{\ensuremath{\mu}}^{+}{\ensuremath{\mu}}^{\ensuremath{-}})$. In addition to the form factor results, we make the first prediction of the branching fraction ratio $R({D}_{s})=\mathcal{B}({B}_{s}\ensuremath{\rightarrow}{D}_{s}\ensuremath{\tau}\ensuremath{\nu})/\mathcal{B}({B}_{s}\ensuremath{\rightarrow}{D}_{s}\ensuremath{\ell}\ensuremath{\nu})=0.301(6)$, where $\ensuremath{\ell}$ is an electron or muon. Current experimental measurements of the corresponding ratio for the semileptonic decays of $B$ mesons disagree with Standard Model expectations at the level of nearly four standard deviations. Future experimental measurements of $R({D}_{s})$ may help understand this discrepancy.

We present a lattice QCD calculation of the $B\ensuremath{\rightarrow}Dl\ensuremath{\nu}$ semileptonic decay form factors ${f}_{+}({q}^{2})$ and ${f}_{0}({q}^{2})$ for the entire physical ${q}^{2}$ range. Nonrelativistic QCD bottom quarks and highly improved staggered quark charm and light quarks are employed together with ${N}_{f}=2+1$ MILC gauge configurations. A joint fit to our lattice and BABAR experimental data allows an extraction of the Cabibbo-Kobayashi-Maskawa matrix element $|{V}_{cb}|$. We also determine the phenomenologically interesting ratio $R(D)=\mathcal{B}(B\ensuremath{\rightarrow}D\ensuremath{\tau}{\ensuremath{\nu}}_{\ensuremath{\tau}})/\mathcal{B}(B\ensuremath{\rightarrow}Dl{\ensuremath{\nu}}_{l})$ ($l=e,\ensuremath{\mu}$). We find $|{V}_{cb}{|}_{\text{excl}}^{B\ensuremath{\rightarrow}D}=0.0402(17)(13)$, where the first error consists of the lattice simulation errors and the experimental statistical error and the second error is the experimental systematic error. For the branching fraction ratio we find $R(D)=0.300(8)$.

We report the first lattice QCD calculation of the form factors for the standard model tree-level decay B s → K l ν . In combination with future measurement, this calculation will provide an alternative exclusive semileptonic determination of | V u b | . We compare our results with previous model calculations, make predictions for differential decay rates and branching fractions, and predict the ratio of differential branching fractions between B s → K τ ν and B s → K μ ν . We also present standard model predictions for differential decay rate forward-backward asymmetries and polarization fractions and calculate potentially useful ratios of B s → K form factors with those of the fictitious B s → η s decay. Our lattice simulations utilize nonrelativistic QCD b and highly improved staggered light quarks on a subset of the MILC Collaboration 2 + 1 asqtad gauge configurations, including two lattice spacings and a range of light quark masses.

We present a quenched lattice calculation of heavy-light meson decay constants, using non-relativistic (NRQCD) heavy quarks in the mass region of the $b$ quark and heavier, and clover-improved light quarks. The NRQCD Hamiltonian and the heavy-light current include the corrections at first order in the expansion in the inverse heavy quark mass. We study the dependence of the decay constants on the heavy meson mass $M$, for light quarks with the tree level ($c_{SW}$ = 1), as well as the tadpole improved clover coefficient. We compare decay constants from NRQCD with results from clover ($c_{SW}=1$) heavy quarks. Having calculated the current renormalisation constant $Z_A$ in one-loop perturbation theory, we demonstrate how the heavy mass dependence of the pseudoscalar decay constants changes after renormalisation. For the first time, we quote a result for $f_B$ from NRQCD including the full one-loop matching factors at $O(\alpha/M)$., Comment: 45 pages, latex, 24 postscript figures

We present a new determination of the strong coupling constant from lattice QCD simulations. We use four different short-distance quantities to obtain the coupling, three different (infrared) meson splittings to tune the simulation parameters, and a wide range of lattice spacings, quark masses, and lattice volumes to test for systematic errors. Our final result consists of ten different determinations of $\alpha^{(3)}_{P}(8.2 GeV)$, which agree well with each other and with our previous results. The most accurate of these, when evolved perturbatively to the $Z^0$ mass, gives $\alpha^{(5)}_{\msbar}(M_Z) = .1174(24)$. We compare our results with those obtained from other recent lattice simulations.

We present a lattice investigation of the heavy-light meson decay constants using Wilson light quarks and NRQCD heavy quarks, partially including the effects of dynamical sea quarks. We calculate the pseudoscalar and vector decay constants over a wide range in heavy quark mass and are able to perform a detailed analysis of heavy quark symmetry. We find consistency between the extrapolation of the NRQCD results and the static case, as expected. We find the slope of the decay constants with $1/M$ is significantly larger than naive expectations and the results of previous lattice calculations. For the first time we extract the non-perturbative coefficients of the slope arising from the $O(1/M)$ heavy quark interactions separately and show the kinetic energy of the heavy quark is dominant and responsible for the large slope. In addition, we find that significant systematic errors remain in the decay constant extracted around the $B$ meson mass due to truncating the NRQCD series at $O(1/M)$. We estimate the higher order contributions to $f_B$ are approximately $20\%$; roughly the same size as the systematic errors introduced by using the Wilson action for light quarks., Comment: 30 pages, Latex, 14 postscript figures

We calculate, for the first time using unquenched lattice QCD, form factors for the rare decay B→Kl+l− in and beyond the Standard Model. Our lattice QCD calculation utilizes a nonrelativistic QCD formulation for the b valence quarks and the highly improved staggered quark formulation for the light valence quarks. We employ the MILC 2+1 asqtad ensembles. The form factor results, based on the z expansion, are valid over the full kinematic range of q2. We construct the ratios f0/f+ and fT/f+, which are useful in constraining new physics and verifying effective theory form factor symmetry relations. We also discuss the calculation of Standard Model observables.

We match the continuum and lattice axial-vector and vector currents at one loop in perturbation theory. For the heavy quarks we use the nonrelativistic QCD (NRQCD) action and for the light quarks the highly improved staggered quark (HISQ) action. We present results for both massless and massive HISQ quarks and as part of the matching procedure we include a discussion of the one loop HISQ renormalization parameters.

We present a lattice investigation, partially including the effects of dynamical quarks, of the heavy-light mesons using NRQCD for the heavy quark and the Wilson action for the light quark. We performed an extensive calculation of the spectrum employing a multi-state, multi-exponential fitting analysis which enabled us to extract the $2S{-}1S$ splitting as well as the $^1P_1{-}\bar{S}$ and hyperfine splittings. The Wilson action introduces a large systematic error into the calculation, and within this uncertainty we obtain agreement with experiment. We performed a comprehensive calculation of the heavy-light meson mass, investigating three methods and their range of validity. The agreement found between these methods confirms that Lorentz invariance can be restored at this order in NRQCD by a constant shift to all masses. We calculated spectroscopic quantities over a wide range in heavy quark mass and were able to perform a detailed investigation of heavy quark symmetry around the $b$ quark mass. In particular, we extracted the nonperturbative coefficients of terms in the heavy quark expansion of the meson binding energy. We demonstrate the importance of using tadpole-improved operators in such a calculation., 34 pages, latex, 40 postscript figures

We present a lattice investigation of heavy-light mesons in the quenched approximation, using non-relativistic QCD for the heavy quark and a clover improved Wilson formulation for the light quark. A comprehensive calculation of the heavy-light spectrum has been performed for various heavy quark masses around the $b$. Our results for the $B_s-B_d$ splitting agree well with the experimental value. We find the $\Lambda_b-B$ splitting to be compatible with experiment, albeit with large error bars. Our $B^*-B$ splitting is slightly low, which could be explained as an effect of quenching. For the first time, we are able to estimate the mass of $P$ states at the $B$ and compare them with experiment., Comment: 24 pages, latex, 10 figures in uuencoded compressed postscript

We present an update of the D meson decay constant fD using the highly improved staggered quark action for valence charm and light quarks on MILC Nf=2+1 lattices. The new determination incorporates HPQCD’s improved scale r1Nf=2+1=0.3133(23) fm, accurately retuned bare charm quark masses and data from an ensemble that is more chiral than in our previous calculations. We find fD=208.3(3.4) MeV. Combining the new fD with D→μνμ branching fraction data from CLEO-c, we extract the Cabibbo-Kobayashi-Maskawa matrix element |Vcd|=0.223(10)exp(4)lat. This value is in excellent agreement with |Vcd| from D semileptonic decays and from neutrino scattering experiments and has comparable total errors. We determine the ratio between semileptonic form factor and decay constant and find [f+D→π(0)/fD]lat=3.20(15) GeV-1 to be compared with the experimental value of [f+D→π(0)/fD]exp=3.19(18) GeV-1. Finally, we mention recent preliminary but already more accurate D→μνμ branching fraction measurements from BES III and discuss their impact on precision |Vcd| determinations in the future.

We present a new determination of the B and Bs meson decay constants using nonrelativistic quantum chromodynamics (NRQCD) b-quarks, highly improved staggered quark (HISQ) light and strange valence quarks and the MILC collaboration Nf=2+1 lattices. The new calculations improve on HPQCD’s earlier work with NRQCD b-quarks by replacing AsqTad with HISQ valence quarks, by including a more chiral MILC fine ensemble in the analysis, and by employing better tuned quark masses and overall scale. We find fB=0.191(9) GeV, fBs=0.228(10) GeV and fBs/fB=1.188(18). Combining the new value for fBs/fB with a recent very precise determination of the Bs meson decay constant based on HISQ b-quarks, fBs=0.225(4) GeV, leads to fB=0.189(4) GeV. With errors of just 2.1% this represents the most precise fB available today.

We illustrate a technique for fitting lattice QCD correlators to sums of exponentials that is significantly faster than traditional fitting methods --- 10--40 times faster for the realistic examples we present. Our examples are drawn from a recent analysis of the Upsilon spectrum, and another recent analysis of the D -> pi semileptonic form factor. For single correlators, we show how to simplify traditional effective-mass analyses., 5 pages, 4 figures

The spectrum of the \ensuremath{\Upsilon} system is investigated using the nonrelativistic lattice QCD approach to heavy quarks and ignoring light quark vacuum polarization. We find good agreement with experiment for the \ensuremath{\Upsilon},\ensuremath{\Upsilon}',\ensuremath{\Upsilon}'' and for the center of mass and fine structure of the ${\mathrm{\ensuremath{\chi}}}_{\mathit{b}}$ states. The lattice calculations predict bb\ifmmode\bar\else\textasciimacron\fi{} D states with a center of mass at (10.20\ifmmode\pm\else\textpm\fi{}0.07\ifmmode\pm\else\textpm\fi{}0.03) GeV. Fitting procedures aimed at extracting both ground and excited state energies are developed. We calculate a nonperturbative dispersion mass for the \ensuremath{\Upsilon}(1S) and compare it with tadpole-improved lattice perturbation theory.

We present a new calculation of the D→π, lν semileptonic form factor f+D→π(q2) at q2=0 based on “highly improved staggered quark” charm and light valence quarks on MILC Nf=2+1 lattices. Using methods developed recently for HPQCD’s study of D→K, lν decays, we find f+D→π(0)=0.666(29). This signifies a better than factor 2 improvement in errors for this quantity compared to previous calculations. Combining the new result with CLEO-c branching fraction data, we extract the Cabibbo-Kobayashi-Maskawa matrix element |Vcd|=0.225(6)exp(10)lat, where the first error comes from experiment and the second from theory. With a total error of ∼5.3% the accuracy of the direct determination of |Vcd| from D semileptonic decays has become comparable to (and in good agreement with) that from neutrino scattering. We also check for second row unitarity using this new |Vcd|, HPQCD’s earlier |Vcs|, and |Vcb| from the Fermilab Lattice and MILC collaborations. We find |Vcd|2+|Vcs|2+|Vcb|2=0.976(50), improving on the current PDG2010 value.

We give the first accurate results for $B$ and ${B}_{s}$ meson masses from lattice QCD including the effect of $u$, $d$, and $s$ sea quarks, and we improve an earlier value for the ${B}_{c}$ meson mass. By using the highly improved staggered quark (HISQ) action for $u/d$, $s$, and $c$ quarks and NRQCD for the $b$ quarks, we are able to achieve an accuracy in the masses of around 10 MeV. Our results are: ${m}_{B}=5.291(18)\text{ }\text{ }\mathrm{GeV}$, ${m}_{{B}_{s}}=5.363(11)\text{ }\text{ }\mathrm{GeV}$, and ${m}_{{B}_{c}}=6.280(10)\text{ }\text{ }\mathrm{GeV}$. Note that all QCD parameters here are tuned from other calculations, so these are parameter free-tests of QCD against experiment. We also give scalar, ${B}_{s0}^{*}$ and axial-vector, ${B}_{s1}$ meson masses. We find these to be slightly below threshold for decay to $BK$ and ${B}^{*}K$, respectively.

We present a new study of $D$ semileptonic decays on the lattice which employs the highly improved staggered quark action for both the charm and the light valence quarks. We work with MILC unquenched ${N}_{f}=2+1$ lattices and determine the scalar form factor ${f}_{0}({q}^{2})$ for $D\ensuremath{\rightarrow}K$, $l\ensuremath{\nu}$ semileptonic decays. The form factor is obtained from a scalar current matrix element that does not require any operator matching. We develop a new approach to carrying out chiral/continuum extrapolations of ${f}_{0}({q}^{2})$. The method uses the kinematic ``$z$''variable instead of ${q}^{2}$ or the kaon energy ${E}_{K}$ and is applicable over the entire physical ${q}^{2}$ range. We find ${f}_{0}^{D\ensuremath{\rightarrow}K}(0)\ensuremath{\equiv}{f}_{+}^{D\ensuremath{\rightarrow}K}(0)=0.747(19)$ in the chiral plus continuum limit and hereby improve the theory error on this quantity by a factor of $\ensuremath{\sim}4$ compared to previous lattice determinations. Combining the new theory result with recent experimental measurements of the product ${f}_{+}^{D\ensuremath{\rightarrow}K}(0)*|{V}_{cs}|$ from BABAR and CLEO-c leads to a very precise direct determination of the CKM matrix element $|{V}_{cs}|$, $|{V}_{cs}|=0.961(11)(24)$, where the first error comes from experiment and the second is the lattice QCD theory error. We calculate the ratio ${f}_{+}^{D\ensuremath{\rightarrow}K}(0)/{f}_{{D}_{s}}$ and find $2.986\ifmmode\pm\else\textpm\fi{}0.087\text{ }\text{ }{\mathrm{GeV}}^{\ensuremath{-}1}$ and show that this agrees with experiment.

It has been recognized for some time that quantization on a null plane has several unique and remarkable advantages for the elucidation of quantum field theories. To date these unique features have not been exploited to solve strongly coupled, four-dimensional gauge theories. This is the first in a series of papers aimed at systematically formulating renormalizable gauge theories on the null plane. In order to lay down the groundwork for upcoming nonperturbative studies, it is indispensable to gain control over the perturbative treatment first. A discussion of one-loop renormalization of QED in the Hamiltonian formalism is presented. In this approach, one is faced with severe infrared divergences characteristic of the light-cone gauge. We show how to treat these divergences in a coherent fashion, and thus recover the usual results of the renormalization procedure such as Ward identities and coupling-constant renormalizations.

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 ${\ensuremath{\alpha}}_{V}(7.5\text{ }\text{ }\mathrm{GeV},{n}_{f}=3)=0.2120(28)$, which is equivalent to ${\ensuremath{\alpha}}_{\overline{\mathrm{MS}}}({M}_{Z},{n}_{f}=5)=0.1183(8)$. We compare this with our previous result from Wilson loops, which differs by one standard deviation.

We present one-loop matching coefficients between continuum and lattice QCD for the heavy-light four-fermion operators relevant for neutral B meson mixing both within and beyond the standard model. For the lattice theory we use nonrelativistic QCD (NRQCD) to describe b quarks and improved staggered fermions (AsqTad) for light quarks. The gauge action is the tree-level Symanzik improved gauge action. Matching to full QCD is carried out through order {alpha}{sub s}, {lambda}{sub QCD}/M{sub b}, and {alpha}{sub s}/(aM{sub b})

We determine hadronic matrix elements relevant for the mass and width differences, $\ensuremath{\Delta}{M}_{s}$ and $\ensuremath{\Delta}{\ensuremath{\Gamma}}_{s}$, in the ${B}_{s}^{0}\ensuremath{-}{\overline{B}}_{s}^{0}$ meson system using fully unquenched lattice QCD. We employ the MILC Collaboration gauge configurations that include $u$, $d$, and $s$ sea quarks using the improved staggered quark (AsqTad) action and a highly improved gluon action. We implement the valence $s$ quark also with the AsqTad action and use nonrelativistic QCD for the valence $b$ quark. For the nonperturbative QCD input into the standard model expression for $\ensuremath{\Delta}{M}_{s}$ we find ${f}_{{B}_{s}}\sqrt{{\stackrel{^}{B}}_{{B}_{s}}}=0.281(21)\text{ }\text{ }\mathrm{GeV}$. Results for four-fermion operator matrix elements entering standard model formulas for $\ensuremath{\Delta}{\ensuremath{\Gamma}}_{s}$ are also presented.

We use perturbative Symanzik improvement to create a new staggered-quark action (HISQ) that has greatly reduced one-loop taste-exchange errors, no tree-level order a^2 errors, and no tree-level order (am)^4 errors to leading order in the quark's velocity v/c. We demonstrate with simulations that the resulting action has taste-exchange interactions that are at least 3--4 times smaller than the widely used ASQTAD action. We show how to estimate errors due to taste exchange by comparing ASQTAD and HISQ simulations, and demonstrate with simulations that such errors are no more than 1% when HISQ is used for light quarks at lattice spacings of 1/10 fm or less. The suppression of (am)^4 errors also makes HISQ the most accurate discretization currently available for simulating c quarks. We demonstrate this in a new analysis of the psi-eta_c mass splitting using the HISQ action on lattices where a m_c=0.43 and 0.66, with full-QCD gluon configurations (from MILC). We obtain a result of~111(5) MeV which compares well with experiment. We discuss applications of this formalism to D physics and present our first high-precision results for D_s mesons., Comment: 21 pages, 8 figures, 5 tables

One-loop matching of heavy-light currents is carried out for a highly improved lattice action, including the effects of mixings with dimension $4O(1/M)$ and $O(a)$ operators. We use the NRQCD action for heavy quarks, the Asqtad improved naive action for light quarks, and the Symanzik improved glue action. As part of the matching procedure we also present results for the NRQCD self-energy and for massless Asqtad quark wave function renormalization with improved glue.

We report on an investigation of the LANL method for determining the O(a) improvement coefficient c(A) nonperturbatively. We find we are able to extract reliable estimates for the coefficient using this method. However, our study of systematic errors shows that for very accurate determinations of c(A), the smearing function must be tuned to keep the O(a) ambiguity in c(A) fixed as beta varies. Consistency was found with previous results from the LANL group and (within fairly large errors) 1-loop perturbation theory; c(A) does not change significantly over the range beta=5.93- 6.2. The big difference between our results and those of the ALPHA Collaboration, around beta=6.0, shows that the O(a) differences in c(A) between the different methods can be large. We find that the lattice spacing dependence of f(pi) and the renormalized quark mass is much smaller using our values of c(A) compared to those of the ALPHA Collaboration.

Semileptonic, B→pi l (ν) over bar, decays are studied on quenched anisotropic lattices using tree-level tadpole improved Symanzik glue, nonrelativistic QCD heavy quark and D234 light quark actions. Constrained fitting methods are applied to extract ground state contributions to two-point and three-point correlators. We agree with previous lattice determinations of the form factors. The major source of systematic error here, as in previous work, comes from the chiral extrapolation to the physical pion mass. Future calculations must work at lighter quark masses to resolve this.

An investigation of the \ensuremath{\lambda}${\ensuremath{\varphi}}^{4}$ theory coupled via Yukawa couplings to fermions has been initiated on the lattice. Dynamical fermions are taken fully into account, using hybrid-molecular-dynamic algorithms. Different ways of transcribing Yukawa couplings onto the lattice are discussed. It is found that the lattice phase diagram is very sensitive to the manner in which this interaction is regularized. Some results for scalar and fermionic correlation functions are also presented.

String dynamics, the heavy-quark potential, and the restoration of rotational symmetry in lattice gauge theory are studied using Hamiltonian methods. We find that off-axis strings experience unbounded transverse fluctuations at all finite couplings. A fermion formulation of lattice strings is used to do systematic calculations. The heavy-quark potential is seen to have power-law corrections to linear confinement. Rotational symmetry in the string sector of the theory is restored in two stages. There is a finite coupling g/sub R/ (''roughening'') where the equipotential surfaces of the heavy-quark potential become well-approximated by spheres, and there is the bulk critical point g = 0 where short-distance violations of rotational symmetry disappear. A new order parameter, the ''kink'' mass, is introduced to distinguish the smooth and rough phases of the string sector of any lattice gauge theory. Roughening coupling constants are determined using the kink mass for a variety of theories. These results are compared against more traditional width calculations. In the Hamiltonian formulation of SU(3) lattice gauge theory the roughening point lies inside the weak-coupling region.