3,354,607 research outputs found
B, Bs -> K form factors: an update of light-cone sum rule results
We present an improved QCD light-cone sum rule (LCSR) calculation of the B ->
K and Bs -> K form factors, by including SU(3)-symmetry breaking corrections.
We use recently updated K-meson distribution amplitudes which incorporate the
complete SU(3)-breaking structure. By applying the method of the direct
integration in the complex plane, which is presented in a detail, the
analytical extraction of the imaginary parts of LCSR hard-scattering amplitudes
becomes unnecessary and therefore the complexity of the calculation is greatly
reduced. The values obtained for the relevant B_{(s)} -> K form factors are as
follows: f^+_{BK}(0)= 0.36^{+0.05}_{-0.04}, f^+_{B_sK}(0)= 0.30^{+0.04}_{-0.03}
and f^T_{BK}(0)= 0.38\pm 0.05, f^T_{B_sK}(0)= 0.30\pm 0.05. By comparing with
the B -> pi form factors extracted recently by the same method, we find the
following SU(3) violation among the B -> light form factors:
f^+_{BK}(0)/f^+_{B\pi}(0) = 1.38^{+0.11}_{-0.10}, f^+_{B_sK}(0)/f^+_{B\pi}(0) =
1.15^{+0.17}_{-0.09}, f^T_{BK}(0)/f^T_{B\pi}(0) = 1.49^{+0.18}_{-0.06} and
f^T_{B_sK}(0)/f^T_{B\pi}(0) = 1.17^{+0.15}_{-0.11}.Comment: 14 pages, 9 figures, some figures and discussions added; version to
appear in PR
Rogers functions and fluctuation theory
Extending earlier work by Rogers, Wiener-Hopf factorisation is studied for a
class of functions closely related to Nevanlinna-Pick functions and complete
Bernstein functions. The name 'Rogers functions' is proposed for this class.
Under mild additional condition, for a Rogers function f, the Wiener--Hopf
factors of f(z)+q, as well as their ratios, are proved to be complete Bernstein
functions in both z and q. This result has a natural interpretation in
fluctuation theory of L\'evy processes: for a L\'evy process X_t with
completely monotone jumps, under mild additional condition, the Laplace
exponents kappa(q;z), kappa*(q;z) of ladder processes are complete Bernstein
functions of both z and q. Integral representation for these Wiener--Hopf
factors is studied, and a semi-explicit expression for the space-only Laplace
transform of the supremum and the infimum of X_t follows.Comment: 70 pages, 2 figure
Topology and Factorization of Polynomials
For any polynomial , we describe a
-vector space of solutions of a linear system of equations
coming from some algebraic partial differential equations such that the
dimension of is the number of irreducible factors of . Moreover, the
knowledge of gives a complete factorization of the polynomial by
taking gcd's. This generalizes previous results by Ruppert and Gao in the case
.Comment: Accepted in Mathematica Scandinavica. 8 page
Archimedean theory and -factors for the Asai Rankin-Selberg integrals
In this paper, we partially complete the local Rankin-Selberg theory of Asai
-functions and -factors as introduced by Flicker and Kable. In
particular, we establish the relevant local functional equation at Archimedean
places and prove the equality between Rankin-Selberg's and Langlands-Shahidi's
-factors at every place. Our proofs work uniformly for any
characteristic zero local field and use as only input the global functional
equation and a globalization result for a dense subset of tempered
representations that we infer from work of Finis-Lapid-M\"uller. These results
are used in another paper by the author to establish an explicit Plancherel
decomposition for , a
quadratic extension of local fields, with applications to the Ichino-Ikeda and
formal degree conjecture for unitary groups
Lifting classes for the fixed point theory of -valued maps
The theory of lifting classes and the Reidemeister number of single-valued
maps of a finite polyhedron is extended to -valued maps by replacing
liftings to universal covering spaces by liftings with codomain an orbit
configuration space, a structure recently introduced by Xicot\'encatl. The
liftings of an -valued map split into self-maps of the universal
covering space of that we call lift-factors. An equivalence relation is
defined on the lift-factors of and the number of equivalence classes is the
Reidemeister number of . The fixed point classes of are the projections
of the fixed point sets of the lift-factors and are the same as those of
Schirmer. An equivalence relation is defined on the fundamental group of
such that the number of equivalence classes equals the Reidemeister number. We
prove that if is a manifold of dimension at least three, then algebraically
the orbit configuration space approach is the same as one utilizing the
universal covering space. The Jiang subgroup is extended to -valued maps as
a subgroup of the group of covering transformations of the orbit configuration
space and used to find conditions under which the Nielsen number of an
-valued map equals its Reidemeister number. If an -valued map splits into
single-valued maps, then its -valued Reidemeister number is the sum of
their Reidemeister numbers.Comment: near complete rewrite from previous versio
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