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G. Martinelli

Publications and source records attributed to G. Martinelli.

At least 199 records · Page 11Linked to original sources
arXiv1995

Non-Perturbative Renormalisation of the Lattice $Δs=2$ Four-Fermion Operator

We compute the renormalised four-fermion operator $O^{ΔS=2}$ using a non-perturbative method recently introduced for determining the renormalisation constants of generic lattice composite operators. Because of the presence of the Wilson term, $O^{ΔS=2}$ mixes with operators of different chiralities. A projection method to determine the mixing coefficients is implemented. The numerical results for the renormalisation constants have been obtained from a simulation performed using the SW-Clover quark action, on a $16^3 \times 32$ lattice, at $β=6.0$. We show that the use of the constants determined non-perturbatively improves the chiral behaviour of the lattice kaon matrix element $\<\bar K^0| O^{ΔS=2} | K^0\>_{\latt}$.

hep-lat↗
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

Quenched $B_K$-parameter with the Wilson and Clover actions at $β= 6.0$

We present results for the Kaon $B$ parameter from a sample of $200$ configurations using the Wilson action and $460$ configurations using the Clover action, on a $18^3 \times 64$ lattice at $β=6.0$. A slight improvement of the chiral behaviour of $B_K$ is observed due to the Clover action. We have also compared the results for $B_K$ obtained from two different procedures for the boosting of the coupling constant $g$. We observe a strong dependence of $B_K$ on the prescription adopted for $g$ in the Wilson case, contrary to the results of the Clover case which are almost unaffected by the choice of $g$. Combining some recently obtained non perturbative estimates for the renormalisation constants with our Clover matrix element, we observe a significant improvement in the chiral behaviour of $B_K$.

hep-lat↗
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

Estimates of $ε\prime/ε$

We review the latest calculations of the next-to-leading $\DSone$ effective Hamiltonian, relevant for $K\to ππ$ transitions. Numerical results for the Wilson coefficients are given for different regularization schemes. Predictions of $\epse$, obtained using different approaches to evaluate the relevant hadronic matrix elements, are compared. Given the present value of the top mass, $m_t=(174\pm 17)$ GeV, all the analyses, in spite of the large theoretical uncertainties, indicate that the value of $\epse$ is smaller than $1\times 10^{-3}$.

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↗
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↗
arXiv1995

DEPENDENCE OF THE CURRENT RENORMALISATION CONSTANTS ON THE QUARK MASS

We study the behaviour of the vector and axial current renormalisation constants $Z_V$ and $Z_A$ as a function of the quark mass, $m_q$. We show that sizeable $O(am_q)$ and $O(g_0^2 a m_q)$ systematic effects are present in the Wilson and Clover cases respectively. We find that the prescription of Kronfeld, Lepage and Mackenzie for correcting these artefacts is not always successful.

hep-lat↗
arXiv1995

An Upgraded Analysis of $ε\prime/ε$ at the Next-to-Leading Order

An upgraded analysis of $\ep$, $x_d$ and $\epp/\ep$, using the latest determinations of the relevant experimental and theoretical parameters, is presented. Using the recent determination of the top quark mass, $m_t=(174 \pm 17)$ GeV, our best estimate is $\epp/\ep= 3.1 \pm 2.5 $, which lies in the range given by E731. We describe our determination of $\epp/\ep$ and make a comparison with other similar studies. A detailed discussion of the matching of the full theory to the effective Hamiltonian, written in terms of lattice operators, is also given.

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

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

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

A Lattice Study of the Gluon Propagator in the Landau Gauge

We present the results of two high-statistics studies of the gluon propagator in the Landau gauge, at $β=6.0$, on different lattice volumes. The dependence of the propagator on the momenta is well described by the expression $G(k^2) = \Big[ M^2+Z\cdot k^2(k^2/ Λ^2)^η)\Big]^{-1}$. We obtain a precise determination of $η=0.532(12)$, and verify that $M^2$ does not vanish in the infinite volume limit.

hep-ph↗
arXiv1994

The Gluon Propagator on a Large Volume, at $β=6.0$

We present the results of a high statistics lattice study of the gluon propagator, in the Landau gauge, at $β=6.0$. As suggested by previous studies, we find that, in momentum space, the propagator is well described by the expression $G(k^2)= \Big[ M^2 + Z\cdot k^2(k^2/Λ^2)^η\Big]^{-1} $. By comparing $G(k^2)$ on different volumes, we obtain a precise determination of the exponent $η=0.532(12)$, and verify that $M^2$ does not vanish in the infinite volume limit. The behaviour of $η$ and $M^2$ in the continuum limit is not known, and can only be studied by increasing the value of $β$.

hep-lat↗
arXiv1994

$b \rightarrow s γ$ AND $b \rightarrow s g$: A THEORETICAL REAPPRAISAL

We present upgraded theoretical predictions for inclusive and exclusive radiative decays of {\it B} mesons. Our results include those next-to-leading order corrections that have already been computed. Our best estimates in the Standard Model are $BR(B \rightarrow K^* γ)=(4.3 \pm 0.9^{ +1.4}_{-1.0}) \times 10^{-5}$, $BR(B \rightarrow X_s γ) =(1.9 \pm 0.2\pm 0.5) \times 10^{-4}$, $Γ(B \rightarrow K^* γ)/ Γ(B \rightarrow X_s γ)=0.23 \pm 0.09$ and $BR(B \rightarrow X_s g)= (1.57 \pm 0.15 ^{+0.86}_{-0.59} \pm 0.23) \times 10^{-3}$. We also consider limits found with two-Higgs-doublet models.

hep-ph↗
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↗