157 research outputs found
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 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 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 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 , which expresses the static neutrino
potential created by a neutron medium of density .Comment: Latex file (Revtex), 9 pages, 1 figure, one reference change
Testing Landau gauge OPE on the Lattice with a Condensate
Using the operator product expansion we show that the 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 .
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: 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
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 , i.e. negligible with respect to the neutron mass density.Comment: Latex file (Revtex), 34 pages, 8 postscripted figure
Asymptotic scaling of the gluon propagtor on the lattice
We pursue the study of the high energy behaviour of the gluon propagator on
the lattice in the Landau gauge in the flavorless case (n_f=0). It was shown in
a precedin g paper that the gluon propagator did not reach three-loop
asymptotic scaling at an energy scale as high as 5 GeV.
Our present high statistics analysis includes also a simulation at
( fm), which allows to reach GeV.
Special care has been devoted to the finite lattice-spacing artifacts as well
as to the finite volume effects, the latter being acute at where
the volume is bounded by technical limits. Our main conclusion is a strong
evidence that the gluon propagator has reached three-loop asymptotic scaling,
at ranging from 5.6 GeV to 9.5 GeV. We buttress up this conclusion on
several demanding criteria of asymptoticity, including scheme independence. Our
fit in the 5.6 GeV to 9.5 GeV window yields MeV, in good agreement with our previous result,
MeV, obtained from the three gluon
vertex, but it is significantly above the Schr\"odinger functional method
estimate : MeV. The latter difference is not understood.
Confirming our previous paper, we show that a fourth loop is necessary to fit
the whole () GeV energy window.Comment: latex-file, 19 pgs., 6 fig
Testing QCD factorisation and charming penguins in charmless
We try a global fit of the experimental branching ratios and CP-asymmetries
of the charmless 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 , 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.
First lattice QCD estimate of the g_{D^* D pi} coupling
We present the results of the first lattice QCD study of the strong coupling
g_{D^* D pi}. From our simulations in the quenched approximation, we obtain
g_{D^* D pi} = 18.8 +/- 2.3^{+1.1}_{-2.0} and hat(g)_c = 0.67 +/-
0.08^{+0.04}_{-0.06}. Whereas previous theoretical studies gave different
predictions, our result favours a large value for hat(g)_c. It agrees very well
with the recent experimental value by CLEO. hat(g) varies very little with the
heavy mass and we find in the infinite mass limit hat(g)_infinity = 0.69(18).Comment: 24 pages, 7 figures; references added, corrected typos, Comments
added about the continuum limi
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 ÎČ=6.4 on a 243Ă60 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 BâÏlÎœl)=|Vub|2(12±8)1012sâ1 and Î(BâÏlÎœl)=|Vub|2(13±12)1012sâ1, which can be used to give upper bounds on the rates
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