8,359 research outputs found
Frequently hypercyclic semigroups
We study frequent hypercyclicity in the context of strongly continuous
semigroups of operators. More precisely, we give a criterion (sufficient
condition) for a semigroup to be frequently hypercyclic, whose formulation
depends on the Pettis integral. This criterion can be verified in certain cases
in terms of the infinitesimal generator of semigroup. Applications are given
for semigroups generated by Ornstein-Uhlenbeck operators, and especially for
translation semigroups on weighted spaces of -integrable functions, or
continuous functions that, multiplied by the weight, vanish at infinity
Matching Long and Short Distances in Large-Nc QCD
It is shown, with the example of the experimentally known Adler function,
that there is no matching in the intermediate region between the two asymptotic
regimes described by perturbative QCD (for the very short-distances) and by
chiral perturbation theory (for the very long-distances). We then propose to
consider an approximation of large-Nc QCD which consists in restricting the
hadronic spectrum in the channels with J^P quantum numbers 0^-, 1^-, 0^+ and
1^+ to the lightest state and treating the rest of the narrow states as a
perturbative QCD continuum; the onset of this continuum being fixed by
consistency constraints from the operator product expansion. We show how to
construct the low-energy effective Lagrangian which describes this
approximation. The number of free parameters in the resulting effective
Lagrangian can be reduced, in the chiral limit where the light quark masses are
set to zero, to just one mass scale and one dimensionless constant to all
orders in chiral perturbation theory. A comparison of the corresponding
predictions, to O(p^4) in the chiral expansion, with the phenomenologically
known couplings is also made.Comment: 35 pages, 9 figures, LaTeX. Added a couple of reference
An example of resonance saturation at one loop
We argue that the large-Nc expansion of QCD can be used to treat a Lagrangian
of resonances in a perturbative way. As an illustration of this we compute the
L_10 coupling of the Chiral Lagrangian by integrating out resonance fields at
one loop. Given a Lagrangian and a renormalization scheme, this is how in
principle one can answer in a concrete and unambiguous manner questions such as
at what scale resonance saturation takes place.Comment: 9 pages, 5 figures. Enlarged discussion, results unchanged. To be
published in Phys. Rev.
Possible duality violations in tau decay and their impact on the determination of alpha_s
We discuss the issue of duality violations in hadronic tau decay. After
introducing a physically motivated ansatz for duality violations, we estimate
their possible size by fitting this ansatz to the tau experimental data
provided by the ALEPH collaboration. Our conclusion is that these data do not
exclude significant duality violations in tau decay. This may imply an
additional systematic error in the value of alpha_s(m_tau), extracted from tau
decay, as large as \delta alpha_s(m_tau) \sim 0.003-0.010 .Comment: 20 pages, 4 figures. Minor fixes in the Appendi
Duality Violation and the K --> pi pi Electroweak Penguin Operator Matrix Elements from Hadronic Tau Decays
We discuss a preliminary study of the impact of duality violations on
extractions from tau decay data of the D=6 VEVs which determine chiral limit
Standard Model K-->pi pi matrix elements of the electroweak penguin operators.Comment: 4 pages, 5 figures, prepared for the Proceedings of the 11th Particle
and Nuclear Intersections Conference (PANIC 2011), Boston, USA, July 24-29,
201
Long-distance dimension-eight operators in B_K
Besides their appearance at short distances \gtrsim 1/M_W, local
dimension-eight operators also contribute to kaon matrix elements at long
distances of order \gtrsim 1/mu_ope, where mu_ope is the scale controlling the
Operator Product Expansion in pure QCD, without weak interactions. This comes
about in the matching condition between the effective quark Lagrangian and the
Chiral Lagrangian of mesons. Working in dimensional regularization and in a
framework where these effects can be systematically studied, we calculate the
correction from these long-distance dimension-eight operators to the
renormalization group invariant B_K factor of K^0-K^0bar mixing, to
next-to-leading order in the 1/Nc expansion and in the chiral limit. The
correction is controlled by the matrix element <0|\bar s_L \tilde{G}_{mu
nu}gamma^mu d_L|K^0>, is small, and lowers B_K.Comment: 14 pages, LaTeX. Explanatory comments added to match version in
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