A Numerical Study of Partially Twisted Boundary Conditions

We investigate the use of partially twisted boundary conditions in a lattice simulation with two degenerate flavours of improved Wilson sea quarks. The use of twisted boundary conditions on a cubic volume (L^3) gives access to components of hadronic momenta other than integer multiples of 2*pi/L. Partial twisting avoids the need for new gluon configurations for every choice of momentum, while, as recently demonstrated, keeping the finite-volume errors exponentially small for the physical quantities investigated in this letter. In this study we focus on the spectrum of pseudo scalar and vector mesons, on their leptonic decay constants and on Z_P, the matrix element of the pseudo scalar density between the pseudo scalar meson and the vacuum. The results confirm the momentum shift imposed by these boundary conditions and in addition demonstrate that they do not introduce any appreciable noise. We therefore advocate the use of partially twisted boundary conditions in applications where good momentum resolution is necessary.Comment: 10 pages, 3 figure

First Lattice Study of the Form Factors A_0 and A_3 in the Decay Bbar^0 to rho^+ l^- nubar_l

We report on a lattice calculation of the form factors A_0 and A_3 for the pseudoscalar to vector meson semileptonic decay Bbar^0 to rho^+ l^- nubar_l. We find that resonant (or pole-type) contributions alone are unable to describe these two form factors simultaneously. For the quantity A_0(q^2=0), which is important phenomenologically for the determination of |Vub|, we extract a range of values, A_0(q^2=0) = (0.16--0.35) +0.09-0.06, where the range is due to systematic uncertainty and the quoted error is statistical. We have also determined A_2(q^2=0) = 0.28 +0.09-0.06 +0.04-0.05.Comment: 14 pages LaTeX209 with 5 figures from 11 encapsulated PostScript files, using epsf.sty. Also available from http://wwwhep.phys.soton.ac.uk/hepwww/papers/shep9601

An Investigation of the Soft Pion Relation in Quenched Lattice QCD

A lattice determination of the form factor and decay constants for the semileptonic decay of heavy pseudoscalar (PS) mesons at zero recoil is presented from which the soft pion relation is satisfied. Chiral extrapolation of the form factor is performed at constant $q^2$. Pole dominance is used to extrapolate the form factor in heavy quark mass. At the B mass, the form factor at zero recoil lies somewhat below the ratio of decay constants; the relation remains satisfied within error.Comment: 3 pages, 2 figure

Excited Baryons from the FLIC Fermion Action

Masses of positive and negative parity excited nucleons and hyperons are calculated in quenched lattice QCD using an O(a^2) improved gluon action and a fat-link clover fermion action in which only the irrelevant operators are constructed with fat links. The results are in agreement with earlier N* simulations with improved actions, and exhibit a clear mass splitting between the nucleon and its parity partner, as well as a small mass splitting between the two low-lying J^P={1/2}^- N* states. Study of different Lambda interpolating fields suggests a similar splitting between the lowest two {1/2}^- Lambda* states, although the empirical mass suppression of the Lambda*(1405) is not seen.Comment: 3 pages, 3 figures, Lattice2002(QCD Spectrum and Quark Masses

Low-lying spectrum of the Y-string three-quark potential using hyper-spherical coordinates

We calculate the energies of three-quark states with definite permutation symmetry (i.e. of SU(6) multiplets) in the N=0,1,2 shells, confined by the Y-string three-quark potential. The exact Y-string potential consists of one, so-called three-string term, and three angle-dependent two-string terms. Due to this technical complication we treat the problem at three increasingly accurate levels of approximation: 1) the (approximate) three-string potential expanded to first order in trigonometric functions of hyper-spherical angles; 2) the (approximate) three-string potential to all orders in the power expansion in hyper-spherical harmonics, but without taking into account the transition(s) to two-string potentials; 3) the exact minimal-length string potential to all orders in power expansion in hyper-spherical harmonics, and taking into account the transition(s) to two-string potentials. We show the general trend of improvement %convergence of these approximations: The exact non-perturbative corrections to the total energy are of the order of one per cent, as compared with approximation 2), yet the exact energy differences between the $[20,1^{+}], [70,2^{+}], [56,2^{+}], [70,0^{+}]$-plets are shifted to 2:2:0.9, from the Bowler and Tynemouth separation rule 2:2:1, which is obeyed by approximation 2) at the one per cent level. The precise value of the energy separation of the first radial excitation ("Roper") $[56^{\prime},0^{+}]$-plet from the $[70,1^{-}]$-plet depends on the approximation, but does not become negative, i.e. the "Roper" remains heavier than the odd-parity $[70,1^{-}]$-plet in all of our approximations.Comment: 19 pages, 6 figure

Lattice Study of the Decay B^0-bar -> rho^+ l^- nu_l-bar: Model-Independent Determination of |V_{ub}|

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.Comment: 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

B→ϕπB\to \phi \pi and B0→ϕϕB^0 \to \phi\phi in the Standard Model and new bounds on R parity violation

We study the pure penguin decays $B \to \phi\pi$ and $B^0 \to \phi\phi$. Using QCD factorization, we find ${\cal B}(B^\pm \to\phi\pi^{\pm} )=2.0^{+0.3}_{-0.1}\times 10^{-8}$. For the pure penguin annihilation process $B^0 \to \phi\phi$, analyzed here for the first time, ${\cal B}(B^0 \to\phi\phi)=2.1^{+1.6}_{-0.3}\times 10^{-9}$. The smallness of these decays in the Standard Model makes them sensitive probes for new physics. From the upper limit of $B\to \phi\pi$,we find constraints on R parity violating couplings, $| \lambda{''}_{i23}\lambda{''}_{i21}|<6\times10^{-5}$, $| \lambda'_{i23}\lambda'_{i21}|<4\times10^{-4}$ and $| \lambda'_{i32}\lambda'_{i12}|<4\times10^{-4}$ for $i=1,2,3$. Our new bounds on $|\lambda{''}_{i23}\lambda{''}_{i21}|$ are one order of magnitude stronger than before. Within the available upper bounds for $| \lambda{''}_{i23}\lambda{''}_{i21}|$, $|\lambda'_{i23}\lambda'_{i21}|$ and $|\lambda'_{i32}\lambda'_{i12}|$, we find that ${\cal B}(B\to\phi\phi)$ could be enhanced to $10^{-8}\sim 10^{-7}$. Experimental searches for these decays are strongly urged.Comment: 5 pages, 3 figures embede

Come back Marshall, all is forgiven? : Complexity, evolution, mathematics and Marshallian exceptionalism

Marshall was the great synthesiser of neoclassical economics. Yet with his qualified assumption of self-interest, his emphasis on variation in economic evolution and his cautious attitude to the use of mathematics, Marshall differs fundamentally from other leading neoclassical contemporaries. Metaphors inspire more specific analogies and ontological assumptions, and Marshall used the guiding metaphor of Spencerian evolution. But unfortunately, the further development of a Marshallian evolutionary approach was undermined in part by theoretical problems within Spencer's theory. Yet some things can be salvaged from the Marshallian evolutionary vision. They may even be placed in a more viable Darwinian framework.Peer reviewedFinal Accepted Versio