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Possible Effects of Mixing in Weak Decays
mixing at a detectable level requires the presence of new
physics and may lead to some observable effects in weak decays of mesons.
We show that violation induced by mixing can manifest
itself in the decay-rate asymmetry of
vs . A rephasing-invariant
generalization of the Gronau-Wyler approach is made to determine the weak phase
shift in , which is only sensitive to the
underlying new physics in mixing. We also demonstrate the
possible effect of mixing on violation in decay modes of
the type . Finally the
model of four quark families is taken as an example to illustrate how the new
physics affects mixing, mixing and
asymmetries in the relevant decays.Comment: Postscript 10 page
On equal values of power sums of arithmetic progressions
In this paper we consider the Diophantine equation \begin{align*}b^k
+\left(a+b\right)^k &+ \cdots + \left(a\left(x-1\right) + b\right)^k=\\ &=d^l +
\left(c+d\right)^l + \cdots + \left(c\left(y-1\right) + d\right)^l,
\end{align*} where are given integers. We prove that, under some
reasonable assumptions, this equation has only finitely many integer solutions.Comment: This version differs slightly from the published version in its
expositio
B -> D* l nu and B -> D l nu form factors in staggered chiral perturbation theory
We calculate the B -> D and B -> D* form factors at zero recoil in Staggered
Chiral Perturbation Theory. We consider heavy-light mesons in which only the
light (u, d, or s) quark is staggered; current lattice simulations generally
use a highly improved action such as the Fermilab or NRQCD action for the heavy
(b or c) quark. We work to lowest nontrivial order in the heavy quark expansion
and to one-loop in the chiral expansion. We present results for a partially
quenched theory with three sea quarks in which there are no mass degeneracies
(the "1+1+1" theory) and for a partially quenched theory in which the u and d
sea quark masses are equal (the "2+1" theory). We also present results for full
(2+1) QCD, along with a numerical estimate of the size of staggered
discretization errors. Finally, we calculate the finite volume corrections to
the form factors and estimate their numerical size in current lattice
simulations.Comment: 19 pages, 6 figures, references added, expanded discussion in Section
I
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