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C. T. Sachrajda

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

At least 109 records · Page 6Linked to original sources
arXiv1998

A Lattice Study of Spectator Effects in Inclusive Decays of B-Mesons

We compute the matrix elements of the operators which contribute to spectator effects in inclusive decays of $B$-mesons. The results agree well with estimates based on the vacuum saturation (factorization) hypothesis. For the ratio of lifetimes of charged and neutral mesons we find $τ(B^-)/τ(B_d)=1.03\pm 0.02\pm 0.03$, where the first error represents the uncertainty in our evaluation of the matrix elements, and the second is an estimate of the uncertainty due to the fact that the Wilson coefficient functions have only been evaluated at tree-level in perturbation theory. This result is in agreement with the experimental measurement. We also discuss the implications of our results for the semileptonic branching ratio and the charm yield.

hep-lat↗
arXiv1998

Flavour Physics

In these four lectures I review the theory and phenomenology of weak decays of quarks, and their rôle in the determination of the parameters of the Standard Model of particle physics, in testing subtle features of the theory and in searching for signatures of new physics. Attempts to understand CP-violation in current and future experiments is discussed.

hep-ph↗
arXiv1997

Theoretical Aspects of Heavy Flavour Physics

I review the status of theoretical aspects of B-decays. The principal difficulty in interpreting the wealth of experimental data is the control of non-perturbative QCD effects, and the talk is focused on attempts to control these effects. Lattice results for the decay constants, B-$\bar B$ mixing and semileptonic form-factors are summarized. The discrepancy of the theoretical predictions and experimental measurements for the ratio of lifetimes $τ(Λ_b)/τ(B_0)$ is discussed, as well as the status of the semileptonic branching ratio of the B-meson. The difficulties in making quantitative predictions for exclusive nonleptonic decays are stressed, and some recent approaches to this problem are outlined.

hep-ph↗
arXiv1997

Heavy Quark Physics From Lattice QCD

We review the application of lattice QCD to the phenomenology of b- and c-quarks. After a short discussion of the lattice techniques used to evaluate hadronic matrix elements and the corresponding systematic uncertainties, we summarise results for leptonic decay constants, B--Bbar mixing, semileptonic and rare radiative decays. A discussion of the determination of heavy quark effective theory parameters is followed by an explanation of the difficulty in applying lattice methods to exclusive nonleptonic decays.

hep-lat↗
arXiv1997

First Lattice Study of Semileptonic Decays of Lambda_b and Xi_b Baryons

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.

hep-lat↗
arXiv1997

Non-perturbative improvement of composite operators with Wilson fermions

We propose a method to improve lattice operators composed of Wilson fermions which allows the removal of all corrections of $O(a)$, including those proportional to the quark mass, leaving only errors of $O(a^2)$. The method exploits the fact that chiral symmetry is restored at short distances. By imposing this requirement on correlation functions of improved lattice operators at short distances, the coefficients which appear in these operators can be determined. The method is an extension of the improvement program of the ALPHA collaboration, which, up to now, has only been applicable in the chiral limit. The extension to quarks with non-zero masses is particularly important for applications in heavy quark physics.

hep-lat↗
arXiv1997

New lattice approaches to the $ΔI=1/2$ rule

Lattice QCD should allow a derivation of the $ΔI=1/2$ rule from first principles, but numerical calculations to date have been plagued by a variety of problems. After a brief review of these problems, we present several new methods for calculating $K\toππ$ amplitudes. These are designed for Wilson fermions, though they can be used also with staggered fermions. They all involve a non-perturbative determination of matching coefficients. We show how problems of operator mixing can be greatly reduced by using point-split hadronic currents, and how CP violating parts of the $K\toππ$ amplitudes can be calculated by introducing a fake top quark. Many of the methods can also be applied to the calculation of two body non-leptonic B-meson decays.

hep-lat↗
arXiv1996

Exclusive Decays of Beauty Hadrons

The principal difficulty in deducing weak interaction properties from experimental measurements of $B$-decays lies in controlling the strong interaction effects. In this talk I review the status of theoretical calculations of the amplitudes for exclusive leptonic and semileptonic decays, in the latter case with special emphasis on the extraction of the $V_{cb}$ and $V_{ub}$ matrix elements.

hep-ph↗
arXiv1996

Spectator Effects in Inclusive Decays of Beauty Hadrons

We present a model-independent study of spectator effects, which are responsible for the lifetime differences between beauty hadrons. These effects can be parametrized in terms of hadronic matrix elements of four four-quark operators. For $B$ mesons, the coefficients of the non-factorizable operators turn out to be much larger than those of the factorizable ones, limiting considerably the usefulness of the vacuum insertion approximation. Non-factorizable contributions to the lifetime ratio $τ(B^-)/τ(B_d)$ could naturally be of order 10--20%, and not even the sign of these contributions can be predicted at present. In the case of the $Λ_b$ baryon, heavy-quark symmetry is used to reduce the number of independent matrix elements from four to two. In order to explain the large deviation from unity in the experimental result for $τ(Λ_b)/τ(B_d)$, it is necessary that these baryon matrix elements be much larger than those estimated in quark models. We have also reexamined the theoretical predictions for the semileptonic branching ratio of $B$ mesons and charm counting, finding that, given the present theoretical and experimental uncertainties, there is no significant discrepancy with experiment.

hep-ph↗
arXiv1996

B Physics on the Lattice: $\overlineΛ$, $λ_{1}$, $\overline{m}_{b}(\overline{m}_{b})$, $λ_2$, $B^{0}-\bar{B}^{0}$ mixing, $\fb$ and all that

We present a short review of our most recent high statistics lattice determinations in the HQET of the following important parameters in B physics: the B--meson binding energy, $\overlineΛ$ and the kinetic energy of the b quark in the B meson, $λ_1$, which due to the presence of power divergences require a non--perturbative renormalization to be defined; the $\overline{MS}$ running mass of the b quark, $\overline{m}_{b}(\overline{m}_{b})$; the $B^{*}$--$B$ mass splitting, whose value in the HQET is determined by the matrix element of the chromo--magnetic operator between B meson states, $λ_2$; the B parameter of the $B^{0}$--$\bar{B}^{0}$ mixing, $B_{B}$, and the decay constant of the B meson, $f_{B}$. All these quantities have been computed using a sample of $600$ gauge field configurations on a $24^{3}\times 40$ lattice at $β=6.0$. For $\overlineΛ$ and $\overline{m}_{b}(\overline{m}_{b})$, we obtain our estimates by combining results from three independent lattice simulations at $β=6.0$, $6.2$ and $6.4$ on the same volume.

hep-lat↗
arXiv1996

A High-Statistics Lattice Calculation of $λ_1$ and $λ_2$ in the $B$ meson

We present a high-statistics lattice calculation of the kinetic energy $-λ_1/2 m_b$ of the heavy quark inside the $B$-meson and of the chromo-magnetic term $λ_2$, related to the $B^*$--$B$ mass splitting, performed in the HQET. Our results have been obtained from a numerical simulation based on 600 gauge field configurations generated at $β=6.0$, on a lattice volume $24^3 \times 40$ and using, for the meson correlators, the results obtained with the SW-Clover $O(a)$ improved lattice action for the light quarks. For the kinetic energy we found $-λ_1=\langle B \vert \bar h (i\vec{D})^{2} h \vert B \rangle /(2 M_B )=-(0.09 \pm 0.14)$~GeV$^2$, which is interesting for phenomenological applications. We also find $λ_2= 0.07 \pm 0.01$ GeV$^2$, corresponding to $M^2_{B^*}-M^2_B= 4 λ_2= 0.280 \pm 0.060 $ GeV$^2$, which is about one half of the experimental value. The origin of the discrepancy with the experimental number needs to be clarified.

hep-lat↗
arXiv1996

A High Statistics Lattice Calculation of The B-meson Binding Energy

We present a high statistics lattice calculation of the B--meson binding energy $\overlineΛ$ of the heavy--quark inside the pseudoscalar B--meson. Our numerical results have been obtained from several independent numerical simulations at $β=6.0$, $6.2$ and $6.4$, 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 $\overlineΛ=180^{+30}_{-20}$ MeV. For the $\overline{MS}$ running mass, we obtain $\overline{m}_{b}(\overline{m}_{b})=4.15 \pm 0.05 \pm 0.20$ GeV, in reasonable agreement with previous determinations. The systematic error is the truncation of the perturbative series in the matching condition of the relevant operator of the Heavy Quark Effective Theory.

hep-lat↗
arXiv1996

Lattice Simulations and Effective Theories

I present a brief introduction to the lattice formulation of quantum field theory, and discuss the use of lattice simulations for studies in particle physics phenomenology. The computation of $f_B$, the decay constant of the $B$-meson, is used as a case study. I also explain the appearance and cancellation of ``renormalons'' in the evaluation of power corrections (higher-twist corrections) in hard scattering and decay processes.

hep-lat↗
arXiv1996

On The Difficulty of Computing Higher-Twist Corrections

We discuss the evaluation of power corrections to hard scattering and decay processes for which an operator product expansion is applicable. The Wilson coefficient of the leading-twist operator is the difference of two perturbative series, each of which has a renormalon ambiguity of the same order as the power corrections themselves, but which cancel in the difference. We stress the necessity of calculating this coefficient function to sufficiently high orders in perturbation theory so as to make the uncertainty of the same order or smaller than the relevant power corrections. We investigate in some simple examples whether this can be achieved. Our conclusion is that in most of the theoretical calculations which include power corrections, the uncertainties are at least comparable to the power corrections themselves, and that it will be a very difficult task to improve the situation.

hep-ph↗
arXiv1995

Renormalons

The calculation of higher twist (or dimension) corrections to physical quantities using operator product expansions is delicate. If dimensional regularization is used to regulate the ultra-violet divergences then there are ambiguities in the Wilson coefficient functions due to infra-red renormalon singularities. With a hard ultra violet cut-off, such as the inverse lattice spacing $a$, there are no renormalon ambiguities, as a result of cancellations between terms which in finite orders of perturbation theory diverge as inverse powers of $a$, and those which diverge at most logarithmically. In this lecture I review these questions, explaining the steps necessary to obtain predictions for physical quantities from lattice measurements of matrix elements of higher dimensional operators. The ideas are illustrated by considering quantities computed using the heavy quark effective theory beyond leading order in the heavy quark mass.

hep-lat↗
arXiv1995

Non-perturbative renormalization of the $ΔS=2$ operator and the heavy-light axial current

We apply a recently introduced non-perturbative renormalization method to two types of lattice operators: the $ΔS=2$ four fermion operator and the heavy-light static axial current, which are relevant for the physics of $K$ and $B$ mesons respectively. The results of the non-perturbative calculations of the renormalization constants are compared with the corresponding perturbative ones.

hep-lat↗
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↗