111,674 research outputs found
An exact solution for the KPZ equation with flat initial conditions
We provide the first exact calculation of the height distribution at
arbitrary time of the continuum KPZ growth equation in one dimension with
flat initial conditions. We use the mapping onto a directed polymer (DP) with
one end fixed, one free, and the Bethe Ansatz for the replicated attractive
boson model. We obtain the generating function of the moments of the DP
partition sum as a Fredholm Pfaffian. Our formula, valid for all times,
exhibits convergence of the free energy (i.e. KPZ height) distribution to the
GOE Tracy Widom distribution at large time.Comment: 4 pages, no figur
Bound on the curvature of the Isgur-Wise function of the baryon semileptonic decay Lambda_b -> Lambda_c + l + nu
In the heavy quark limit of QCD, using the Operator Product Expansion, the
formalism of Falk for hadrons or arbitrary spin, and the non-forward amplitude,
as proposed by Uraltsev, we formulate sum rules involving the Isgur-Wise
function of the baryon transition , where the light cloud has for both
initial and final baryons. We recover the lower bound for the slope
obtained by Isgur et al., and we
generalize it by demonstrating that the IW function is an
alternate series in powers of , i.e. . Moreover, exploiting systematically the sum rules, we get an improved
lower bound for the curvature in terms of the slope, . This
bound constrains the shape of the Isgur-Wise function and it will be compelling
in the analysis of future precise data on the differential rate of the baryon
semileptonic decay , that
has a large measured branching ratio, of about 5%.Comment: 16 page
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