arXiv subjects

C. R. Allton

Publications and source records attributed to C. R. Allton.

47 records · Page 3Linked to original sources

arXiv1996

Lattice Monte Carlo Data versus Perturbation Theory

The differences between lattice Monte Carlo data and perturbation theory are usually associated with the ``bad'' behaviour of the bare lattice coupling g_0 due to the effects of large (and unknown) higher order coefficients in the g_0 perturbative series. In this philosophy a new, renormalised coupling g' is defined with the aim of reducing the higher order coefficients of the perturbative series in g'. An improvement in the agreement between lattice data and this new perturbation series is generally observed. In this paper an alternative scenario is discussed where lattice artifacts are proposed as the cause of the disagreement between lattice data and the g_0-perturbative series. We find that this interpretation provides excellent agreement between lattice data and perturbation theory in g_0 corrected for lattice artifacts. We show that this viewpoint leads typically to an order of magnitude improvement in the agreement between lattice data and perturbation theory, compared to typical g' perturbation expansions. The success of this procedure leads to a determination of Lambda_MSbar^{N_f=0} of 220 +- 20 MeV. Lattice data studied includes quenched values of the string tension, the hadronic scale r_0, the discrete beta function Deltaβ, M_rho, f_pi and the 1P-1S splitting in charmonium. The new 3-loop term of the lattice beta- function has been incorporated in this study. A discussion of the implication of this result for lattice calculations is presented.

hep-lat↗

arXiv1996

Lattice Monte Carlo Data versus Perturbation Theory

Differences between lattice Monte Carlo data and perturbation theory (for example the lack of asymptotic scaling) are usually associated with the `bad' behaviour of the bare lattice coupling g_0 due to the effects of large (and unknown) higher order terms in g_0. In this philosophy a new, renormalised coupling g' is defined with the aim of making the higher order coefficients of the perturbative series in g' as small as possible. In this paper an alternative scenario is discussed where lattice artifacts are proposed as the cause of the disagreement between Monte Carlo data and the g_0-perturbative series. We find that with the addition of a lattice artifact term, the usual asymptotic scaling expression in g_0 is in excellent agreement with Monte Carlo data. Lattice data studied includes the string tension, the hadronic scale r_0, the discrete beta function, M_rho, f_pi and the 1P-1S splitting in charmonium.

hep-lat↗

arXiv1996

Light Quenched Hadron Spectrum and Decay Constants on different Lattices

We present a study of ${\cal O}(2000)$ (quenched) lattice configurations from the APE collaboration, for $6.0\leβ\le 6.4$ using both the Wilson and the SW-Clover fermion action. We determine the light hadronic spectrum and meson decay constants. We extract the inverse lattice spacing using data at the simulated values of the quark mass. We find an agreement with the experimental data of $\sim 5%$ for mesonic masses and $\sim 10%-15%$ for baryonic masses and pseudoscalar decay constants. A larger deviation is present for the vector decay constants.

hep-lat↗

arXiv1995

RESULTS FOR THE B-MESON DECAY CONSTANT FROM THE APE COLLABORATION

The decay constant for the B-meson in the static limit is calculated using the Wilson and clover actions at various lattice spacings. We show that both the contamination of our results by excited states and the effects finite lattice spacing are at most the order of the statistical uncertainties. A comparison is made of our results and those obtained in other studies. Values for $f^{stat}_{B_S}/f^{stat}_B$ and $M_{B_S} - M_B$ are also given.

hep-lat↗

arXiv1994

Lattice Calculation of D- and B-meson Semileptonic Decays, using the Clover Action at beta=6.0 on APE

We present the results of a high statistics lattice calculation of hadronic form factors relevant for $D-$ and $B-$meson semi-leptonic decays into light pseudoscalar and vector mesons. The results have been obtained by averaging over 170 gauge field configurations, generated in the quenched approximation, at $β=6.0$, on a $18^3 \times 64$ lattice, using the $O(a)$-improved SW-Clover action.From the study of the matrix element $ $, we obtain $f_+ (0)=0.78\pm 0.08$ and from the matrix element $<\bar K^{* 0}\vert J_μ\vert D^+>$ we obtain $V(0)=1.08\pm 0.22$, $A_1(0)=0.67\pm 0.11$ and $A_2(0)=0.49\pm 0.34$. We also obtain the ratios $V(0)/A_1(0)=1.6\pm 0.3$ and $A_2(0)/A_1(0)= 0.7\pm 0.4$. Our predictions for the different form factors are in good agreement with the experimental data, although, in the case of $A_2(0)$, the errors are still too large to draw any firm conclusion. With the help of the Heavy Quark Effective Theory (HQET) we have also extrapolated the lattice results to $B$-meson decays. The form factors follow a behaviour compatible with the HQET predictions. Our results are in agreement with a previous lattice calculation, performed at $β=6.4$, using the standard Wilson action.

hep-lat↗

arXiv1994

The continuum limit of $f_B$ from the lattice in the static approximation

We present an analysis of the continuum extrapolation of $f_B$ in the static approximation from lattice data. The method described here aims to uncover the systematic effects which enter in this extrapolation and has not been described before. Our conclusions are that we see statistical evidence for scaling of $f_B^{stat}$ for inverse lattice spacings $\gtap 2$ GeV but not for $\ltap 2$ GeV. We observe a lack of {\em asymptotic} scaling for a variety of quantities, including $f_B^{stat}$, at all energy scales considered. This can be associated with finite lattice spacing systematics. Once these effects are taken into account, we obtain a value of 230(35) MeV for $f_B^{stat}$ in the continuum where the error represents uncertainties due to both the statistics and the continuum extrapolation. In this method there is no error due to uncertainties in the renormalization constant connecting the lattice and continuum effective theories.

hep-lat↗

arXiv1994

Quark Masses from Lattice QCD at the Next-to-Leading Order

Using the results of several quenched lattice simulations, we predict the value of the strange and charm quark masses in the continuum at the next-to-leading order, $m^{\overline{MS}}_s(μ=2\,\, \rm{GeV})= (127 \pm 18)\,\, \rm{MeV}$ and $m^{\overline{MS}}_{ch}(μ=2 \,\,\rm{GeV})=(1.47 \pm 0.28)\,\, \rm{GeV}$. The errors quoted above have been estimated by taking into account the original statistical error of the lattice results and the uncertainties coming from the matching of the lattice to the continuum theory. A detailed presentation of the relevant formulae at the next-to-leading order and a discussion of the main sources of errors is also presented.

hep-ph↗

arXiv1994

A High Statistics Lattice Calculation of $f^{static}_B$ at $β=6.2$ Using the Clover Action

We present a calculation of $f_B$ in the static limit, obtained by numerical simulation of quenched QCD, at $β=6.2$ on a $18^3 \times 64$ lattice, using the SW-Clover quark action. The decay constant has been extracted by studying heavy(static)-light correlation functions of different smeared operators, on a sample of 220 gauge field configurations. We have obtained $f_B^{static}=(290 \pm 15 \pm 45)$ MeV, where the first error comes from the uncertainty in the determination of the matrix element and the second comes from the uncertainty in the lattice spacing. We also obtain $M_{B_s}-M_{B_d}= (70 \pm 10)$ MeV and $f^{stat}_{B_s}/f^{stat}_{B_d}=1.11(3)$. A comparison of our results with other calculations of the same quantity is made.

hep-ph↗

arXiv1993

Semi-leptonic Decays of Heavy Flavours on a Fine Grained Lattice

We present the results of a numerical calculation of semi-leptonic form factors relevant for heavy flavour meson decays into light mesons, at $β=6.4$ on a $24^3 \times 60$ lattice, using the Wilson action in the quenched approximation. We obtain $f^+_K(0)=0.65\pm 0.18$, $V(0)=0.95\pm 0.34$, $A_1(0)=0.63\pm 0.14 $ and $A_2(0)=0.45\pm 0.33 $. We also obtain $A_1(q^2_{max})=0.62\pm 0.09$, $V(0)/A_1(0)=1.5\pm 0.28 $ and $A_2(0)/A_1(0)=0.7\pm 0.4$. The results for $f^+_K(0)$, $V(0)$ and $A_1(0)$ are consistent with the experimental data and with previous lattice determinations with larger lattice spacings. In the case of $A_2(0)$ the errors are too large to draw any firm conclusion. We have also extrapolated the form factors to the B meson, showing a behaviour compatible with the predictions by the heavy quark effective theory (HQET). Within large uncertainties, our results suggest that $A_2/A_1$ increases with the heavy quark mass. We also get very rough estimates for the partial decay widths $B \rightarrow πl ν_l)=\vert V_{ub} \vert^2 (12 \pm 8) 10^{12} s^{-1}$ and $Γ(B \rightarrow ρl ν_l)=\vert V_{ub} \vert^2 (13 \pm12) 10^{12} s^{-1}$, which can be used to give upper bounds on the rates

hep-lat↗

arXiv1992

The Hyperfine Splitting in Charmonium: Lattice Computations Using the Wilson and Clover Fermion Actions

We compute the hyperfine splitting $m_{J/ψ}-m_{η_c}$ on the lattice, using both the Wilson and $O(a)$-improved (clover) actions for quenched quarks. The computations are performed on a $24^3\times48$ lattice at $β= 6.2$, using the same set of 18 gluon configurations for both fermion actions. We find that the splitting is 1.83\err{13}{15} times larger with the clover action than with the Wilson action, demonstrating the sensitivity of the spin-splitting to the magnetic moment term which is present in the clover action. However, even with the clover action the result is less than half of the physical mass-splitting. We also compute the decay constants $f_{η_c}$ and $f^{-1}_{J/ψ}$, both of which are considerably larger when computed using the clover action than with the Wilson action. For example for the ratio $f^{-1}_{J/ψ}/f^{-1}_ρ$ we find 0.32\err{1}{2} with the Wilson action and $0.48\pm 3$ with the clover action (the physical value is 0.44(2)).

hep-lat↗

arXiv1992

Quenched Hadrons using Wilson and O(a)-Improved Fermion Actions at beta=6.2

We present the first study of the light hadron spectrum and decay constants for quenched QCD using an O(a)-improved nearest-neighbour Wilson fermion action at β=6.2. We compare the results with those obtained using the standard Wilson fermion action, on the same set of 18 gauge field configurations of a 24^3 times 48 lattice. For pseudoscalar meson masses in the range 330-800 MeV, we find no significant difference between the results for the two actions. The scales obtained from the string tension and mesonic sector are consistent, but differ from that derived from baryon masses. The ratio of the pseudoscalar decay constant to the vector meson mass is roughly independent of quark mass as observed experimentally, and in approximate agreement with the measured value.

hep-lat↗