39 research outputs found
Chiral logarithms to five loops
We investigate two specific Green functions in the framework of chiral
perturbation theory. We show that, using analyticity and unitarity, their
leading logarithmic singularities can be evaluated in the chiral limit to any
desired order in the chiral expansion, with a modest calculational cost. The
claim is illustrated with an evaluation of the leading logarithm for the scalar
two-point function to five-loop order.Comment: 13 pages, 5 figure
Radiative corrections in K --> 3 pi decays
We investigate radiative corrections to K --> 3 pi decays. In particular, we
extend the non-relativistic framework developed recently to include real and
virtual photons and show that, in a well-defined power counting scheme, the
results reproduce corrections obtained in the relativistic calculation. Real
photons are included exactly, beyond the soft-photon approximation, and we
compare the result with the latter. The singularities generated by pionium near
threshold are investigated, and a region is identified where standard
perturbation theory in the fine structure constant alpha may be applied. We
expect that the formulae provided allow one to extract S-wave pi pi scattering
lengths from the cusp effect in these decays with high precision.Comment: 57 pages, 17 figure
The cusp effect in eta' --> eta pi pi decays
Strong final-state interactions create a pronounced cusp in eta' --> eta pi0
pi0 decays. We adapt and generalize the non-relativistic effective field theory
framework developed for the extraction of pi pi scattering lengths from K --> 3
pi decays to this case. The cusp effect is predicted to have an effect of more
than 8% on the decay spectrum below the pi+ pi- threshold.Comment: 11 pages, 8 figures; comment added, typos corrected, version
published in Eur. Phys. J.
Leading infrared logarithms for sigma-model with fields on arbitrary Riemann manifold
We derive non-linear recursion equation for the leading infrared logarithms
(LL) in four dimensional sigma-model with fields on an arbitrary Riemann
manifold. The derived equation allows one to compute leading infrared
logarithms to essentially unlimited loop order in terms of geometric
characteristics of the Riemann manifold.
We reduce the solution of the SU(oo) principal chiral field in arbitrary
number of dimensions in the LL approximation to the solution of very simple
recursive equation. This result paves a way to the solution of the model in
arbitrary number of dimensions at N-->ooComment: Talk given by MVP at the conference devoted to memory of A.N.
Vasilie
Leading Chiral Logarithms for Pion Form Factors to Arbitrary Number of Loops
We develop the method of calculation of the leading chiral (infrared)
logarithms to an arbitrary loop order for various form factors of
Nambu-Goldstone bosons. The method is illustrated on example of scalar and
vector form factors in massless 4D O(N+1)/O(N) sigma-model. The analytical
properties of the form factors are derived. The leading chiral (infrared)
logarithms are summed up in the large N limit.Comment: 5 page
Dispersive representation of K -> 3 pi amplitudes and cusps
The NA48/2 collaboration has shown clear experimental evidence for a cusp in
the data for K -> pi pi^0 pi^0. This effect can be used to extract information
on the pi-pi scattering lengths. We address this issue using a two-loop
dispersive construction of pi pi -> pi pi and K -> pi pi pi amplitudes in the
presence of isospin breaking.Comment: 4 pages, 1 figure, to appear in Proceedings of the conference QCD 08,
Montpellier, 7-12 July 200
Cusps in K_L --> 3 pi decays
The pion mass difference generates a pronounced cusp in K --> 3 pi decays,
the strength of which is related to the pi pi S-wave scattering lengths. We
apply an effective field theory framework developed earlier to evaluate the
amplitudes for K_L --> 3 pi decays in a systematic manner, where the strictures
imposed by analyticity and unitarity are respected automatically. The
amplitudes for the decay eta --> 3 pi are also given.Comment: 15 pages, 3 figures, uses Elsevier styl
Convergence properties of decays in chiral perturbation theory
Theoretical efforts to describe and explain the decays reach
far back in time. Even today, the convergence of the decay widths and some of
the Dalitz plot parameters seems problematic in low energy QCD. In the
framework of resummed CHPT, we explore the question of compatibility of
experimental data with a reasonable convergence of a carefully defined chiral
series, where NNLO remainders are assumed to be small. By treating the
uncertainties in the higher orders statistically, we numerically generate a
large set of theoretical predictions, which are then confronted with
experimental information. In the case of the decay widths, the experimental
values can be reconstructed for a reasonable range of the free parameters and
thus no tension is observed, in spite of what some of the traditional
calculations suggest. The Dalitz plot parameters and can be described
very well too. When the parameters and are concerned, we find a
mild tension for the whole range of the free parameters, at less than 2
C.L. This can be interpreted in two ways - either some of the higher order
corrections are indeed unexpectedly large or there is a specific configuration
of the remainders, which is, however, not completely improbable. Also, the
distribution of the theoretical uncertainties is found to be significantly
non-gaussian, so the consistency cannot be simply judged by the 1 error
bars.Comment: 57 pages, 5 figure
Electromagnetic corrections in eta --> 3 pi decays
We re-evaluate the electromagnetic corrections to eta --> 3 pi decays at
next-to-leading order in the chiral expansion, arguing that effects of order
e^2(m_u-m_d) disregarded so far are not negligible compared to other
contributions of order e^2 times a light quark mass. Despite the appearance of
the Coulomb pole in eta --> pi+ pi- pi0 and cusps in eta --> 3 pi0, the overall
corrections remain small.Comment: 21 pages, 11 figures; references updated, version published in EPJ