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Physical review / D 107(5), 054503 (2023). doi:10.1103/PhysRevD.107.054503, We present a simultaneous extraction of the moments of $F_2$ and $F_L$ structure functions of the proton for a range of photon virtuality, $Q_2$. This is achieved by computing the forward Compton amplitude on the lattice utilizing the second-order Feynman-Hellmann theorem. Our calculations are performed on configurations with two different lattice spacings and volumes, all at the $SU(3)$ symmetric point. We find the moments of $F_2$ and $F_L$ in good agreement with experiment. Power corrections turn out to be significant. This is the first time the $Q^2$ dependence of the lowest moment of $F_2$ has been quantified., Published by Inst., Woodbury, NY

DIS2022 conference presentation

We present results for the decay constants of the $D$ and $D_s$ mesons computed in lattice QCD with $N_f=2+1$ dynamical flavours. The simulations are based on RBC/UKQCD's domain wall ensembles with both physical and unphysical light-quark masses and lattice spacings in the range 0.11--0.07$\,$fm. We employ the domain wall discretisation for all valence quarks. The results in the continuum limit are $f_D=208.7(2.8)_\mathrm{stat}\left(^{+2.1}_{-1.8}\right)_\mathrm{sys}\,\mathrm{MeV}$ and $f_{D_{s}}=246.4(1.3)_\mathrm{stat}\left(^{+1.3}_{-1.9}\right)_\mathrm{sys}\,\mathrm{MeV}$ and $f_{D_s}/f_D=1.1667(77)_\mathrm{stat}\left(^{+57}_{-43}\right)_\mathrm{sys}$. Using these results in a Standard Model analysis we compute the predictions $|V_{cd}|=0.2185(50)_\mathrm{exp}\left(^{+35}_{-37}\right)_\mathrm{lat}$ and $|V_{cs}|=1.011(16)_\mathrm{exp}\left(^{+4}_{-9}\right)_\mathrm{lat}$ for the CKM matrix elements.

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., 10 pages

In the framework of relativistic SU(2)_f baryon chiral perturbation theory we calculate the volume dependence of the nucleon mass up to and including O(p^4). Since the parameters in the resulting finite size formulae are fixed from the pion mass dependence of the large volume nucleon masses and from phenomenology, we obtain a parameter-free prediction of the finite size effects. We present mass data from the recent N_f=2 simulations of the UKQCD and QCDSF collaborations and compare these data as well as published mass values from the dynamical simulations of the CP-PACS and JLQCD collaborations with the theoretical expectations. Remarkable agreement between the lattice data and the predictions of chiral perturbation theory in a finite volume is found., 23 pages, 5 figures; references added + minor corrections; one more reference added, typo in eq.(25) corrected, additional clarifying remarks

I discuss strategies to determine hadronic decay couplings from lattice studies. As a check of the methods, I explore the decay of a vector meson to two pseudoscalar mesons with $N_f=2$ flavours of sea quark. Although we are working with quark masses that do not allow a physical decay, I show how the transition rate can be evaluated from the amplitude for $\rho \to \pi \pi$ and from the annihilation component of $\pi \pi \to \pi \pi$. I explore the decay amplitude for two different pion momenta and find consistent results. The coupling strength found is in agreement with experiment. I also find evidence for a shift in the $\rho$ mass caused by mixing with two pion states. I also present results for the decay of a hybrid meson, for the case of heavy valence quarks., Comment: 10 pages, 7 ps figures, proc LHP03, Cairns

A possible explanation of the apparent disrepency between the theoretical prediction and experimental measurement of the ratio of lifetimes $\tau(\Lambda_b)/\tau(B_d)$ is that ``spectator effects'', which appear at $O(1/m_b^3)$ in the heavy quark expansion, contribute significantly. We investigate this possibility by computing the corresponding operator matrix elements in a lattice simulation. We find that spectator effects are indeed significant, but do not appear to be sufficiently large to account for the full discrepency. We stress, however, that this is an exploratory study, and it is important to check our conclusions on a larger lattice and using a larger sample of gluon configurations., Comment: 12 pages, Latex. One correction: in the original version of the paper, in eqs.10, 11, 12 and 39, the values of the pion masses appeared interchanged

We discuss strategies to determine hadronic decay couplings from lattice studies. As an application, we explore the decay of a vector meson to two pseudoscalar mesons with $N_f=2$ flavours of sea quark. Although we are working with quark masses that do not allow a physical decay, we show how the transition rate can be evaluated from the amplitude for $\rho \to \pi \pi$ and from the annihilation component of $\pi \pi \to \pi \pi$. We explore the decay amplitude for two different pion momenta and find consistent results. The coupling strength we find is in agreement with experiment. We also find evidence for a shift in the $\rho$ mass caused by mixing with two pion states., Comment: Proc. Latt03 (spectrum), 3 pages, 4 figs

Using an SU(3) flavour symmetry breaking expansion in the quark mass, we determine the QCD component of the neutron-proton, Sigma and Xi mass splittings of the baryon octet due to up-down (and strange) quark mass differences. Provided the average quark mass is kept constant, the expansion coefficients in our procedure can be determined from computationally cheaper simulations with mass degenerate sea quarks and partially quenched valence quarks. Full details and numerical results are given in ref 1., Comment: Talk presented at the XXX International Symposium on Lattice Field Theory (Lattice 2012), June 24-29, 2012, Cairns, Australia

Simulations that use the clover action in quenched QCD calculations have a lower limit to the quark mass that can be reached, because of the fluctuations caused by exceptional configurations. From this low statistics study, we find that the twisted clover action, recently introduced by the ALPHA collaboration, can be used to simulate quenched QCD at quark masses below those attainable by simulations that use the clover action., Comment: Lattice2001(spectrum)

The coupling gB ∗ Bπ is related to the form factor at zero momentum of the axial between B ∗ and B states. Moreover it is related to the effective coupling between heavy mesons and pions that appears in the heavy meson chiral Lagrangian. This coupling has been evaluated on the lattice using static heavy quarks and light quark propagators determined by a stochastic inversion of the fermionic bilinear. We found the value g = 0.42(4)(8). Besides its theoretical interest, this quantity has phenomenological implications in B → π + l l decays.

We investigate a number of algorithms that calculate the quark propagators for the overlap-Dirac fermion operator. The QCD simulations were performed at beta = 5.9 with a lattice volume of 16**3*32., Comment: LATTICE99(Chiral Fermions) 3 pages, 2 figures. A problem with the incorrect definition of the overlap mass has been corrected. The results have changed, but not the conclusions of the paper

We present a calculation of f_B and of the form factors for the semi-leptonic decay B -> D l nu in the quenched approximation to QCD. Results are generated on lattices at beta = 6.2, using an O(a)-improved fermion action, with the clover coefficient determined non-perturbatively., LATTICE98(heavyqk); corrected some errors in figures

We present results of a lattice computation of the matrix elements of the vector currents which are relevant for the semileptonic decays of D to K, D to pi and B to pi. The computations are performed in the quenched approximation on a 24^3x48 lattice at beta=6.2, using an O(a) non-perturbatively improved fermionic action., 3 pages, 3 figures (LATTICE 98 matrixelement) Corrections to figures and tables

This is a follow-up to our earlier work on the energies and radial distributions of heavy-light mesons. The heavy quark is taken to be static (infinitely heavy) and the light quark has a mass about that of the strange quark. We now concentrate on the energies of the excited states with higher angular momentum and with a radial node. A new improvement is the use of hypercubic blocking in the time direction. The calculation is carried out with dynamical fermions on a 16 cubed times 32 lattice with a lattice spacing approximately 0.1 fm generated using a non-perturbatively improved clover action. In nature the closest equivalent of this heavy-light system is the B_s meson, which allows us to compare our lattice calculations to experimental results (where available) or to give a prediction where the excited states, particularly P-wave states, should lie. We pay special attention to the spin-orbit splitting, to see which one of the states (for a given angular momentum L) has the lower energy. An attempt is made to understand these results in terms of the Dirac equation., Comment: 35 pages. v3: Data from two new lattices added. New results in several chapters

In this paper we investigate the benefits of using Z(2)xZ(2) single timeslice stochastic sources for the calculation of light quark physics on the lattice. Meson 2-point correlators measured using sources stochastic in only spin and those stochastic in both spin and colour indices are compared to point source correlators on the unit gauge and on a 16^3 x 32 Domain Wall QCD ensemble. It is found that the use of stochastic sources gives a considerable improvement in statistics for the same computational cost. The neutral kaon mixing matrix element B_K is also calculated on this ensemble with stochastic sources, but we conclude that the stochastic method offers no significant advantage over the traditional gauge-fixed wall source approach which already offers an exact volume average. We also discuss the application to semileptonic form factors in conjunction with partially twisted boundary conditions., Comment: 26 pages, 7 figures. Version accepted by JHEP

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., 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

In order to enhance our understanding of spectral functions in lattice QCD obtained with the help of the Maximum Entropy Method, we study meson spectral functions for lattice fermions with chiral symmetry. In particular we analyse lattice artefacts for standard overlap, overlap hypercube and domain wall fermions in the free field limit. We also present first results for pseudoscalar spectral functions in dynamical QCD with 2+1 flavours of domain wall fermions, using data generated by the UKQCD and RBC collaborations on QCDOC machines., Comment: 25 pages, two sentences added; to appear in JHEP

We compute the masses of the flavor singlet 0{sup ++} mesons using (n{sub 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{sup ++} meson is suppressed relative to the mass of the 0{sup ++} glueball in quenched QCD at an equivalent lattice spacing. The low value for mass of the lightest flavor singlet 0{sup ++} meson obtained in our calculation could be due to either: that the mass of the meson is much lower than that of the 0{sup ++} glueball in quenched QCD, or due to the effect of lattice artifacts. We present arguments for the first option, but we are unable to rule out the explanation due to lattice artifacts.

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 exploratory results for the hadron mass spectrum and pseudoscalar meson decay constants using mixed actions. We use improved staggered sea quarks and HYP-smeared overlap valence quarks. We obtain good signals on 10 configurations at one lattice spacing and two different sets of sea quark masses., Comment: Lattice2004(spectrum), 3pages, 4 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 calculate finite size effects on nucleon masses in chiral perturbation theory. We confront the theoretical predictions with N_f=2 lattice results and discuss chiral extrapolation formulae., Comment: talk at Lattice 03 (spectrum), 3 pages latex, 3 figures. Assignment of 2 data points to incorrect data sets in plot 1 and of 1 data point in plot 2 corrected. 1 fm lattice result updated. Conclusions unchanged

We determine the mass of the charm quark ($m_c$) from lattice QCD with two flavors of dynamical quarks with a mass around the strange quark. We compare this to a determination in quenched QCD which has the same lattice spacing (0.1 fm). We investigate different formulations of the quark mass, based on the Vector Ward Identity, PCAC relation and the FNAL heavy quark formalism. Based on these preliminary results we find no effects due to sea quarks with a mass around strange., Comment: Presented at 21st International Symposium on Lattice Field Theory (LATTICE 2003), Tsukuba, Japan, 15-19 July, 2003

We discuss the allowed decays of a hybrid meson in the heavy quark limit. We deduce that an important decay will be into a heavy quark non-hybrid state and a light quark meson, in other words, the de-excitation of an excited gluonic string by emission of a light quark-antiquark pair. We discuss the study of hadronic decays from the lattice in the heavy quark limit and apply this approach to explore the transitions from a spin-exotic hybrid to $\chi_b \eta$ and $\chi_b S$ where $S$ is a scalar meson. We obtain a signal for the transition emitting a scalar meson and we discuss the phenomenological implications., Comment: 18 pages, LATEX, 3 ps figures

We measure the spectrum of low-lying nucleon resonances using Bayesian fitting methods. We compare the masses obtained in the quenched approximation to those obtained with two flavours of dynamical fermions at a matched lattice spacing. At the pion masses employed in our simulations, we find that the mass of the first positive-parity nucleon excitation is always greater than that of the parity partner of the nucleon., Comment: Lattice2002(spectrum) 3 pages, 4 figures

We compute the mass of the singlet 0++ state using both (psi_bar psi) and Wilson loop operators from a N_f=2 lattice QCD calculation., Comment: Lattice2002(spectrum)

For lattice calculations with light dynamical quarks, finite size effects have become an important aspect. We study finite size effects in nucleon masses on N_f=2 dynamical lattices of 1-2 fm. Predictions for the finite size effects are obtained in one-loop chiral perturbation theory., Comment: 3 pages, 7 eps figures, Lattice 2002 (matrixel)

We study the flavor singlet mesons from first principles using lattice QCD. We explore the splitting between flavor singlet and nonsinglet mesons for vector and axial mesons as well as the more commonly studied cases of the scalar and pseudoscalar mesons.

We present results of quenched lattice calculations of the matrix elements relevant for B_d-\bar B_d and B_s-\bar B_s mixing in the Standard Model. Results for the corresponding SU(3)-breaking ratios, which can be used to constrain or determine |V_{td}|, are also given. The calculations are performed at two values of the lattice spacing, corresponding to \beta = 6.0 and \beta = 6.2, with quarks described by a mean-field-improved Sheikholeslami-Wohlert action. As a by-product, we obtain the leptonic decay constants of B and D mesons. We also present matrix elements relevant for D^0-\bar D^0 mixing. Our results are summarized in the Introduction., Comment: 27 pages (RevTeX), 26 figures, version published in Phys. Rev. D: improved estimate of the systematic error associated with the uncertainty on the strange quark mass and other small improvements to analysis (results change only slightly); correction of typos and minor changes to text; RevTeX formatting

In nuclear many-body problems the short-range correlation between two nucleons is well described by the corresponding correlation in the {two}-body problem. Therefore, as a first step in any attempt at an analogous description of many-quark systems, it is necessary to know the two-quark correlation. With this in mind, we study the light quark distribution in a heavy-light meson with a static heavy quark. The charge and matter radial distributions of these heavy-light mesons are measured on a lattice with a light quark mass about that of the strange quark. Both distributions can be well fitted upto r approx 0.7 fm with the exponential form w_i^2(r), where w_i(r)=A exp(-r/r_i). For the charge(c) and matter(m) distributions r_c approx 0.32(2) fm and r_m \approx 0.24(2) fm. We also discuss the normalisation of the total charge (defined to be unity in the continuum limit) and matter integrated over all space, finding 1.30(5) and 0.4(1) respectively for a lattice spacing approx 0.17 fm., Comment: 8 pages, 3 ps figures

We present the results of a calculation of semileptonic form factors of D and B mesons. The calculation uses nonperturbatively order a improved quenched lattice QCD and two values of the coupling. Results for charm mesons show reasonable agreement with experiment. The lattice results for B -> rho l nu are compared with high q^2 experimental results., Contribution to Lattice 2001 (heavy quarks); 3 pages, 4 figures. Typo corrected

The h+, h_A1 form factors for the semi-leptonic B->D and B->D* decays are evaluated in quenched lattice QCD with beta=6.2. The action and the operators are fully O(a) non-perturbatively improved. The Isgur-Wise function is evaluated and fitted to extract its slope; the latter is found to be rho^2=1.1(2)(3) from the B->D* decay and rho^2=1.0(2)(3) from the B->D decay. The form factors ratios R_1, R_2 are evaluated and found to be in agreement with experimental determinations., Lattice 2001 proc., 3 pages, 3 figures

We describe the bottomonium spectrum obtained on the UKQCD dynamical ensembles and its comparison to quenched results. We include a determination of alpha_s and m_b from the dynmaical results., Comment: Lattice 2000 (Heavy Quark Physics)

We study the flavour singlet pseudoscalar mesons from first principles using lattice QCD. We explore the quark content of the $��$ and $��'$ mesons and we discuss their decay constants., Figure 1 corrected

The construction of operators and calculational methods for the determination of the N* spectrum are discussed. The masses of the parity partners of the nucleon and delta are computed from the O(a)-improved data of the UKQCD Collaboration, and a clear splitting observed between the mass of the nucleon and its parity partner., Comment: Lattice 2000 (subject), 4 pages, 5 postscript figures

We present results for the semi-leptonic and leptonic decays of B mesons. These non-perturbative matrix elements are important for constraining the CKM matrix. Results are presented for the pseudoscalar and vector decay constants, as well as flavour breaking ratios and heavy quark symmetry relations. We consider the chiral and momentum dependence of the semi-leptonic form factors of the decay B-> pi l nu and the soft pion relation (SPR) on the lattice. These calculations were performed in the quenched approximation at two values of the coupling with non-perturbatively order a improved action and currents., LAT2000 (Heavy quarks) 4 pages 4 figures

We present the first results for the static quark potential and the light hadron spectrum using dynamical fermions at $\beta=5.2$ using an O(a) improved Wilson fermion action together with the standard Wilson plaquette action for the gauge part. Sea quark masses were chosen such that the pseudoscalar-vector mass ratio, m_PS/m_V$, varies from 0.86 to 0.67. Finite-size effects are studied by using three different volumes, 8^3\cdot 24, 12^3\cdot 24 and 16^3\cdot 24. Comparing our results to previous ones obtained using the quenched approximation, we find evidence for sea quark effects in quantities like the static quark potential and the vector-pseudoscalar hyperfine splitting., Comment: 38 pages, 14 Postscript figure, LaTeX

We present results of a lattice study of the form factors in the decay B-> pi l nu. We attempt to disentangle the the dependence of the form factors on the light quark masses and the momentum transfer. Using models of the q^2 dependence we calculate the total decay rate, and compare to the experimental measure to extract Vub. This study was performed in the quenched approximation at beta=6.2 on a 24^3 X 48 lattice, with a non-perturbatively improved SW fermion action., 3 pages, 2 figures, (LATTICE 99 - Heavy Quarks)

We present UKQCD's latest results for the static quark potential and light hadron spectrum obtained from matched simulations using two flavours of dynamical quarks. We report that using matched ensembles helps disentangle screening effects from discretisation errors in the static quark potential., Comment: LATTICE99(QCD spectrum), corrected a typo

We derive the form factors relevant for decays of pseudo-scalar mesons corresponding to the semi-leptonic decay B->D l nu. The simulations are performed in the quenched approximation at beta=6.0 and beta=6.2 using a non-perturbatively improved clover action. The slope of the Isgur Wise function and |Vcb| are extracted from the form factors., LaTeX. 6 PostScript figures. Contribution to LATTICE99(Heavy Quarks)

The potential between two heavy-light mesons as a function of the heavy quark separation is calculated in quenched SU(3) lattice QCD. We study the case of heavy-light mesons with a static heavy quark and light quarks of mass close to the strange quark mass. We explore the case of light quarks with the same and with different flavours, classified according to the light quark isospin. We evaluate the appropriate light quark exchange contributions and explore the spin-dependence of the interaction. Comparison is made with meson exchange., Comment: 31 pages, 10 figures; error bars in Fig. 2 corrected (now smaller)

The coupling $g_{B^\ast B \pi}$ is related to the form factor at zero momentum of the axial current between $B^\ast$- and $B$-states. This form factor is evaluated on the lattice using static heavy quarks and light quark propagators determined by a stochastic inversion of the fermionic bilinear. The $\gBBP$ coupling is related to the coupling $g$ between heavy mesons and low-momentum pions in the effective heavy meson chiral lagrangian. The coupling of the effective theory can therefore be computed by numerical simulations. We find the value $g = 0.42(4)(8)$. Besides its theoretical interest, the phenomenological implications of such a determination are discussed.

We present the results of the first lattice study of semileptonic decays of baryons containing a b-quark. Predictions for the decay distributions are given and the Isgur-Wise functions for heavy baryons are computed, for values of the velocity transfer up to about omega=1.2. The computations are performed on a 24^3 x 48 lattice at beta=6.2 using the Sheikholeslami-Wohlert action in the quenched approximation., Comment: 55 pages, 17 ps figures, Latex 2.09, uses epsf

We have studied the O(mv^6) effects in NRQCD on the spectrum of heavy quarkonia and compare our results for different lattices (quenched and dynamical). We also report on an investigation into hybrid states within the framework of NRQCD. This suggests that the lowest lying hybrid is around the B^* \bar B threshold and 3 standard deviations above the B \bar B., Comment: 3 pages, LaTeX2e, 4 figures, uses styles [espcrc2, epsf], talk presented at Lattice 97

We explore the effect of higher order operators in the non-relativistic formulation of QCD (NRQCD). We calculated masses in the b \bar b spectrum using quenched gauge configurations at beta = 6.0 and two different NRQCD actions which have been corrected to order mv^4 and mv^6. The two-point functions are calculated in a gauge invariant fashion. We find the general structure of the spectrum to be the same in the two cases. Using the P - 3S1 splitting we determine the inverse lattice spacings to be 2.44(4) GeV and 2.44(5) GeV for the mv^4 and mv^6 actions, respectively. We do observe shifts in the spin splittings. The hyperfine splitting is reduced by approximately 4 MeV, while the fine splitting is down by up to 10 MeV, albeit with large statistical errors., Comment: 11 pages, LaTeX2e , 4 figures, uses styles [11pt, a4wide, epsf]. A minor typo in figure 2 has been corrected

We compare results obtained using the Sheikholeslami-Wohlert (SW) fermion action with tree-level and tadpole-improved coefficients for $5.7\le\beta\le 6.2$., Comment: Talk presented at LATTICE96(spectrum), 3 LaTeX pages plus 5 ps figures, espcrc2.sty (included)

We present a unified method for analysing form factors in B -> pi l nu-bar_l and B -> K* gamma decays. The analysis provides consistency checks on the q^2 and 1/M extrapolations necessary to obtain the physical decay rates. For the first time the q^2 dependence of the form factors is obtained at the B scale. In the B -> pi l nu-bar_l case, we show that pole fits to f^+ may not be consistent with the q^2 behaviour of f^0, leading to a possible factor of two uncertainty in the decay rate and hence in the value of |V_{ub}|^2 deduced from it. For B -> K* gamma, from the combined analysis of form factors T_1 and T_2, we find the hadronisation ratio R_{K^*} of the exclusive B -> K* gamma to the inclusive b -> s gamma rates is of order 35% or 15% for constant and pole-type behaviour of T_2 respectively., 13 pages, uuencoded compressed postscript file (including five figures). Also available from http://wwwhep.phys.soton.ac.uk/hepwww/papers/shep9509/

We present results of a lattice computation of the vector and axial-vector current matrix elements relevant for the semileptonic decay B^0-bar -> rho^+ l^- nu_l-bar. The computations are performed in the quenched approximation of lattice QCD on a 24^3 x 48 lattice at beta = 6.2, using an O(a) improved fermionic action. Our principal result is for the differential decay rate, dGamma/dq^2, for the decay B^0-bar -> rho^+ l^- nu_l-bar in a region beyond the charm threshold, allowing a model-independent extraction of |V_{ub}| from experimental measurements. Heavy quark symmetry relations between radiative and semileptonic decays of B-bar mesons into light vector mesons are also discussed., 22 pages LaTeX-209 (dependent on settings in a4.sty), 23 PostScript figures included with epsf.sty. Complete PostScript file including figures available at http://wwwhep.phys.soton.ac.uk/hepwww/papers/shep9518/