Renormalization of Velocity-Changing Dimension-Five Operators in the Heavy-Quark Effective Theory

We study the renormalization of operators of the type ${\bar h_{v'}} \Gamma G^{\mu\nu} h_v$ in the heavy-quark effective theory (HQET). We construct the combinations of such operators that are renormalized multiplicatively, and calculate their velocity-dependent anomalous dimensions at the one-loop order. We then show that the virial theorem of the HQET is not renormalized, and that in the limit of equal velocities the anomalous dimension of the chromo-electric operator vanishes to all orders in perturbation theory. This implies an exact relation between renormalization constants, which may help in a future calculation of the two-loop anomalous dimension of the chromo-magnetic operator.Comment: 9 pages, 1 figur

Comment on "On the TST_S-Anomaly in Betaine Calcium Chloride Dihydrate"

Recently, Hlinka and Ishibashi [J. Phys. Soc. Jpn. 67, 495 (1998)] discussed the $T_S$-anomaly in betaine calcium chloride dihydrate (BCCD) in a Landau-type approach. We comment on the shortcomings of this approach and discuss the $T_S$-anomaly in the framework of a microscopical pseudo spin model based on a realistic description of BCCD in terms of symmetry-adapted local modes.Comment: 2 pages, RevTex, submitted to J. Phys. Soc. Jp

Higher-order estimates of the chromomagnetic moment of a heavy quark

The leading beta_0^(n-1) alpha_s^n terms in the Wilson coefficient and anomalous dimension of the chromomagnetic operator in the heavy-quark effective Lagrangian are summed to all orders of perturbation theory. The perturbation series for the anomalous dimension is well behaved, while that for the Wilson coefficient exhibits a divergent behaviour already in low orders, caused by a nearby infrared renormalon singularity. The resulting ambiguity is commensurate with terms of order 1/m^2 in the effective Lagrangian, whose corresponding ultraviolet renormalons are identified. An excellent approximation for the scheme-invariant Wilson coefficient at next-to-next-to-leading order in renormalization-group improved perturbation theory is obtained.Comment: 16 pages, 3 figures embedde

Note on Tests of the Factorization Hypothesis and the Determination of Meson Decay Constants

We discuss various tests of the factorization hypothesis making use of the close relationship between semi-leptonic and factorized nonleptonic decay amplitudes. It is pointed out that factorization leads to truely model-independent predictions for the ratio of nonleptonic to semi-leptonic decay rates, if in the nonleptonic decay a spin one meson of arbitrary mass or a pion take the place of the lepton pair. Where the decay constants of those mesons are known, these predictions represent ideal tests of the factorization hypothesis. In other cases they may be used to extract the decay constants. Currently available data on the decays $\bar B^0 \to D^+\pi^-,\, D^{*+}\pi^-,\, D^+\varrho^-,\, D^{*+}\varrho^-$ are shown to be in excellent agreement with the factorization results. A weighted average of the four independent values for the QCD coefficient $a_1$ extracted from the data gives $a_1=1.15\pm 0.06$ suggesting that it may be equal to the Wilson coefficient $c_1(\mu)$ evaluated at the scale $\mu = m_b$.Comment: (9 pages, ReVTeX, no figures), HD-THEP-92-3

Violations of Local Duality in the Heavy Quark Sector

We examine the origin of possible failures of the quark-hadron local duality. In particular, we consider a correlator of two currents comprising heavy quark operators, and compare the evaluation by the Operator Product Expansion with the result obtained inserting an infinite set of hadronic states, in the N_c to infinity limit. Whereas the smeared spectral functions agree with each other, their local behaviour is different. The difference manifests itself in the form of a term O(Lambda/epsilon) (epsilon being the residual energy) that is not present in the expansion in powers of Lambda/epsilon predicted by the OPE.Comment: Latex, 14 pages, 1 figur

Non-perturbative Effects in B→Xsl+l−B\to X_sl^+l^-

The rare decay $B\to X_sl^+l^-$ provides excellent prospects for precision tests of Standard Model flavour dynamics. The process can be computed in perturbation theory with small uncertainty. However, in order to ensure a reliable theoretical prediction, also potentially important effects from non-perturbative QCD have to be controlled with sufficient accuracy. The present article summarizes recent developments related to this topic.Comment: Invited Talk presented at the QCD Euroconference 98, Montpellier, 2-8 July 1998, 7 pages, 1 figur

Two-loop hybrid renormalization of local dimension-4 heavy-light operators

The renormalization of local dimension-4 operators containing a heavy and a light quark field at scales below the heavy-quark mass is discussed, using the formalism of the heavy-quark effective theory. The anomalous dimensions of these operators and their mixing are calculated to two-loop order. Some phenomenological applications are briefly discussed.Comment: 11 pages, 2 figure

A High-Statistics Lattice Calculation of λ1\lambda_1 and λ2\lambda_2 in the BB meson

We present a high-statistics lattice calculation of the kinetic energy $-\lambda_1/2 m_b$ of the heavy quark inside the $B$-meson and of the chromo-magnetic term $\lambda_2$, 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 $\beta=6.0$, 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 $-\lambda_1=\langle B \vert \bar h (i\vec{D})^{2} h \vert B \rangle /(2 M_B )=-(0.09 \pm 0.14)$~GeV$^2$, which is interesting for phenomenological applications. We also find $\lambda_2= 0.07 \pm 0.01$ GeV$^2$, corresponding to $M^2_{B^*}-M^2_B= 4 \lambda_2= 0.280 \pm 0.060$ GeV$^2$, which is about one half of the experimental value. The origin of the discrepancy with the experimental number needs to be clarified.Comment: 26 pages, latex, 5 figure

Long-range two-body final-state interactions and direct CP asymmetry in {B}^{+}\to{\pi}^{+} {K}^{0} decay

We present a calculation of the direct CP asymmetry, $A_{CP}^{dir}$, for the process $B^+ \to \pi^+ K^0$ including the effects of long-range inelastic final-state interactions (FSI). We admit three channels in our calculation: $B^+ \to (\pi^+ K^0), (\eta K^+)$, and $(D_s^+ \bar{D}^0)$. The strong scattering is described in terms of Pomeron and Regge exchanges. We find that the direct CP asymmetry is enhanced by a factor of $\sim 3$ as a result of FSI, but remains well short of the claims of (10 - 20)% in recent literature. A critical assessment of papers claiming large CP asymmetries is also presented.Comment: 21 pages, latex, no figures. Added the charge-exchange channel {B}^{+}\to {\pi}^{0} {K}^{+}. Expanded the discussion section. To be published in Phys. Rev.