On the recurrence set of planar Markov Random Walks

In this paper, we investigate the properties of recurrent planar Markov random walks. More precisely, we study the set of recurrent points with the use of local limit theorems. The Nagaev-Guivarc'h spectral method provides several examples for which these local limit theorems are satisfied as soon as the (standard or non-standard) central limit theorem holds

Ghost-gluon coupling, power corrections and ΛMS‾\Lambda_{\overline {\rm MS}} from twisted-mass lattice QCD at Nf=2

We present results concerning the non-perturbative evaluation of the ghost-gluon running QCD coupling constant from $N_f=2$ twisted-mass lattice calculations. A novel method for calibrating the lattice spacing, independent of the string tension and hadron spectrum is presented with results in agreement with previous estimates. The value of $\Lambda_{\overline{MS}}$ is computed from the running of the QCD coupling only after extrapolating to zero dynamical quark mass and after removing a non-perturbative OPE contribution that is assumed to be dominated by the dimension-two \VEV{A^2} gluon condensate. The effect due to the dynamical quark mass in the determination of \Lams is discussed.Comment: 33 pages, 6 fig

Addendum to Finite-size effects on multibody neutrino exchange

The interaction energy of the neutrons due to massless neutrino exchange in a neutron star has recently been proved, using an effective theory, to be extremely small and infrared-safe. Our comment here is of conceptual order: two approaches to compute the total interaction energy density have recently been proposed. Here, we study the connection between these two approaches. From CP invariance, we argue that the resulting interaction energy has to be even in the parameter $b=-G_F n_n /\sqrt{2}$, which expresses the static neutrino potential created by a neutron medium of density $n_n$.Comment: Latex file (Revtex), 9 pages, 1 figure, one reference change

Testing Landau gauge OPE on the Lattice with a <A2><A^2> Condensate

Using the operator product expansion we show that the $O(1/p^2)$ correction to the perturbative expressions for the gluon propagator and the strong coupling constant resulting from lattice simulations in the Landau gauge are due to a non-vanishing vacuum expectation value of the operator $A^\mu A_\mu$. This is done using the recently published Wilson coefficients of the identity operator computed to third order, and the subdominant Wilson coefficient computed in this paper to the leading logarithm. As a test of the applicability of OPE we compare the $$ estimated from the gluon propagator and the one from the coupling constant in the flavourless case. Both agree within the statistical uncertainty: $\sqrt{} \simeq 1.64(15)$ GeV. Simultaneously we fit \Lams = 233(28) MeV in perfect agreement with previous lattice estimates. When the leading coefficients are only expanded to two loops, the two estimates of the condensate differ drastically. As a consequence we insist that OPE can be applied in predicting physical quantities only if the Wilson coefficients are computed to a high enough perturbative order.Comment: 15 pages, LaTex file with 5 figure

Testing QCD factorisation and charming penguins in charmless B→PV{\boldsymbol{B\to PV}}

We try a global fit of the experimental branching ratios and CP-asymmetries of the charmless $B\to PV$ decays according to QCD factorisation. We find it impossible to reach a satisfactory agreement, the confidence level (CL) of the best fit is smaller than .1 %. The main reason for this failure is the difficulty to accomodate several large experimental branching ratios of the strange channels. Furthermore, experiment was not able to exclude a large direct CP asymmetry in $\bar {B^0}\to\rho^+ \pi^-$, which is predicted very small by QCD factorisation. Trying a fit with QCD factorisation complemented by a charming-penguin inspired model we reach a best fit which is not excluded by experiment (CL of about 8 %) but is not fully convincing. These negative results must be tempered by the remark that some of the experimental data used are recent and might still evolve significantly.Comment: 21 pages, 4 figures; several typos corrected, added one footnote and two references, comments added about PQCD. To appear in Phys.Rev.

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 243×60 lattice, using the Wilson action in the quenched approximation. We obtain f+K(0)=0.65±0.18, V(0)=0.95±0.34, A1(0)=0.63±0.14 and A2(0)=0.45±0.33. We also obtain A1(q2max)=0.62±0.09, V(0)/A1(0)=1.5±0.28 and A2(0)/A1(0)=0.7±0.4. The results for f+K(0), V(0) and A1(0) are consistent with the experimental data and with previous lattice determinations with larger lattice spacings. In the case of A2(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 A2/A1 increases with the heavy quark mass. We also get very rough estimates for the partial decay widths B→πlνl)=|Vub|2(12±8)1012s−1 and Γ(B→ρlνl)=|Vub|2(13±12)1012s−1, which can be used to give upper bounds on the rates

Critical Analysis of Theoretical Estimates for BB to Light Meson Form Factors and the B→ψK(K∗)B \to \psi K(K^{\ast}) Data

We point out that current estimates of form factors fail to explain the non-leptonic decays $B \to \psi K(K^{\ast})$ and that the combination of data on the semi-leptonic decays $D \to K(K^{\ast})\ell \nu$ and on the non-leptonic decays $B \to \psi K(K^{\ast})$ (in particular recent po\-la\-ri\-za\-tion data) severely constrain the form (normalization and $q^2$ dependence) of the heavy-to-light meson form factors, if we assume the factorization hypothesis for the latter. From a simultaneous fit to \bpsi and \dk data we find that strict heavy quark limit scaling laws do not hold when going from $D$ to $B$ and must have large corrections that make softer the dependence on the masses. We find that $A_1(q^2)$ should increase slower with \qq than $A_2, V, f_+$. We propose a simple parametrization of these corrections based on a quark model or on an extension of the \hhs laws to the \hl case, complemented with an approximately constant $A_1(q^2)$. We analyze in the light of these data and theoretical input various theoretical approaches (lattice calculations, QCD sum rules, quark models) and point out the origin of the difficulties encountered by most of these schemes. In particular we check the compatibility of several quark models with the heavy quark scaling relations.Comment: 48 pages, DAPNIA/SPP/94-24, LPTHE-Orsay 94/1

Measuring ∣Vub∣|V_{ub}| with B→Ds+Xu\to D_s^+ X_u transitions

We propose the determination of the CKM matrix element $|V_{ub}|$ by the measurement of the spectrum of $B \to D_s^+ X_u$, dominated by the spectator quark model mechanism $\bar{b} \to D_s^{(*)+} \bar{u}$. The interest of considering $B \to D_s^+X_u$ versus the semileptonic decay is that more than 50 % of the spectrum for $B \to D_s^+ X_u$ occurs above the kinematical limit for $B \to D_s^+ X_c$, while most of the spectrum $B \to l \nu X_u$ occurs below the $B \to l \nu X_c$ one. Furthermore, the measure of the hadronic mass $M_X$ is easier in the presence of an identified $D_s$ than when a $\nu$ has been produced. As a consistency check, we point out that the rate $\bar{b} \to D_s^{(*)+} \bar{c}$ (including QCD corrections that we present elsewhere) is consistent with the measured $BR (B \to D_s^{\pm} X)$. Although the hadronic complications may be more severe in the mode that we propose than in the semileptonic inclusive decay, the end of the spectrum in $B \to l \nu X_u$ is not well understood on theoretical grounds. We argue that, in our case, the excited $D_s^{**}$, decaying into $D K$, do not contribute and, if there is tagging of the $B$ meson, the other mechanisms to produce a $D_s$ of the right sign are presumably small, of $O(10^{-2})$ relative to the spectator amplitude, or can be controlled by kinematical cuts. In the absence of tagging, other hadronic backgrounds deserve careful study. We present a feasability study with the BaBar detector.Comment: 22 pages, LaTe

Finite-size effects on multibody neutrino exchange

The effect of multibody massless neutrino exchanges between neutrons inside a finite-size neutron star is studied. We use an effective Lagrangian, which incorporates the effect of the neutrons on the neutrinos. Following Schwinger, it is shown that the total interaction energy density is computed by comparing the zero point energy of the neutrino sea with and without the star. It has already been shown that in an infinite-size star the total energy due to neutrino exchange vanishes exactly. The opposite claim that massless neutrino exchange would produce a huge energy is due to an improper summation of an infrared-divergent quantity. The same vanishing of the total energy has been proved exactly in the case of a finite star in a one-dimensional toy model. Here we study the three-dimensional case. We first consider the effect of a sharp star border, assumed to be a plane. We find that there is a non- vanishing of the zero point energy density difference between the inside and the outside due to the refraction index at the border and the consequent non-penetrating waves. An analytical and numerical calculation for the case of a spherical star with a sharp border confirms that the preceding border effect is the dominant one. The total result is shown to be infrared-safe, thus confirming that there is no need to assume a neutrino mass. The ultraviolet cut-offs, which correspond in some sense to the matching of the effective theory with the exact one, are discussed. Finally the energy due to long distance neutrino exchange is of the order of $10^{-8} -- 10^{-13} GeV per neutron$, i.e. negligible with respect to the neutron mass density.Comment: Latex file (Revtex), 34 pages, 8 postscripted figure