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C. T. Sachrajda

Publications and source records attributed to C. T. Sachrajda.

120 records · Page 7Linked to original sources
arXiv1995

First Lattice Calculation of The B-meson Binding and Kinetic Energies

We present the first lattice calculation of the B-meson binding energy $\labar$ and of the kinetic energy $-λ_1/2 m_Q$ of the heavy-quark inside the pseudoscalar B-meson. This calculation has required the non-perturbative subtraction of the power divergences present in matrix elements of the Lagrangian operator $\bar h D_4 h$ and of the kinetic energy operator $\bar h \vec D^2 h$. The non-perturbative renormalisation of the relevant operators has been implemented by imposing suitable renormalisation conditions on quark matrix elements, in the Landau gauge. Our numerical results have been obtained from several independent numerical simulations at $β=6.0$ and $6.2$, and using, for the meson correlators, the results obtained by the APE group at the same values of $β$. Our best estimate, obtained by combining results at different values of $β$, is $\labar =190 \err{50}{30}$ MeV. For the $\overline{MS}$ running mass, we obtain $\overline {m}_b(\overline {m}_b) =4.17 \pm 0.06$ GeV, in reasonable agreement with previous determinations. From a subset of 36 configurations, we were only able to establish a loose upper bound on the $b$-quark kinetic energy in a $B$-meson, $λ_1=\langle B \vert \bar h \vec{D}^{2} h \vert B \rangle /(2 M_B )<$~1\, GeV$^2$. This shows that a much larger statistical sample is needed to determine this important parameter.

hep-ph↗
arXiv1995

The Invisible Renormalon

We study the structure of renormalons in the Heavy Quark Effective Theory, by expanding the heavy quark propagator in powers of $1/m_Q$. We demonstrate that the way in which renormalons appear depends on the regularisation scheme used to define the effective theory. In order to investigate the relation between ultraviolet renormalons and power divergences of matrix elements of higher-dimensional operators in the heavy quark expansion, we perform calculations in dimensional regularisation and in three different cut-off regularisation schemes. In the case of the kinetic energy operator, we find that the leading ultraviolet renormalon which corresponds to a quadratic divergence, is absent in all but one (the lattice) regularisation scheme. The nature of this ``invisible renormalon'' remains unclear.

hep-ph↗
arXiv1995

Renormalons and the Heavy Quark Effective Theory

We propose a non-perturbative method for defining the higher dimensional operators which appear in the Heavy Quark Effective Theory (HQET), such that their matrix elements are free of renormalon singularities, and diverge at most logarithmically with the ultra-violet cut-off. Matrix elements of these operators can be computed numerically in lattice simulations of the HQET. We illustrate our procedures by presenting physical definitions of the binding energy ($\lb$) and of the kinetic energy (-$λ_1/2m_Q$) of the heavy quark in a hadron. This allows us to define a ``subtracted pole mass", whose inverse can be used as the expansion parameter in applications of the HQET.

hep-ph↗
arXiv1994

Renormalons on the Lattice

We present the first lattice calculation of the B-meson binding energy $\labar$ and of the kinetic energy $λ_1/2 m_Q$ of the heavy-quark inside the pseudoscalar B-meson. In order to cancel the ambiguities due to the ultraviolet renormalons present in the operator matrix elements, this calculation has required the non-perturbative subtraction of the power divergences present in the Lagrangian operator $\energy$ and in the kinetic energy operator $\kkinetic$. The non-perturbative renormalization of the relevant operators has been implemented by imposing suitable renormalization conditions on quark matrix elements in the Landau gauge.

hep-lat↗
arXiv1994

A General Method for Non-Perturbative Renormalization of Lattice Operators

We propose a non-perturbative method for computing the renormalization constants of generic composite operators. This method is intended to reduce some systematic errors, which are present when one tries to obtain physical predictions from the matrix elements of lattice operators. We also present the results of a calculation of the renormalization constants of several two-fermion operators, obtained, with our method, by numerical simulation of $QCD$, on a $16^3 \times 32$ lattice, at $β=6.0$. The results of this simulation are encouraging, and further applications to four-fermion operators and to the heavy quark effective theory are proposed.

hep-lat↗
arXiv1994

Computing the Slope of the Isgur-Wise Function

We propose a method for evaluating the slope (and higher derivatives) of the Isgur-Wise function at the zero recoil point using lattice simulations. These derivatives are required for the extrapolation of the experimental data for $B\rightarrow D^*l\barν$ decays to the zero recoil point, from which the $V_{cb}$ element of the CKM-matrix can be determined.

hep-lat↗
arXiv1993

Non-Perturbative Renormalisation of Composite Operators

It is shown that the renormalisation constants of two quark operators can be accurately determined (to a precision of a few per-cent using 18 gluon configurations) using Chiral Ward identities. A method for computing renormalisation constants of generic composite operators without the use of lattice perturbation theory is proposed.

hep-lat↗
arXiv1993

Lattice Phenomenology

A review of the status of lattice simulations in particle physics phenomenology is presented. Recent computations of leptonic decay constants of light and heavy mesons, and of the Isgur-Wise function relevant for semi-leptonic decays of $B$-mesons, are discussed in some detail. Calculations of other quantities are briefly outlined. The systematic errors inherent in lattice simulations, and procedures to reduce and control them, are described.

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↗