395 research outputs found
pi-pi and pi-K scatterings in three-flavour resummed chiral perturbation theory
The (light but not-so-light) strange quark may play a special role in the
low-energy dynamics of QCD. The presence of strange quark pairs in the sea may
have a significant impact of the pattern of chiral symmetry breaking : in
particular large differences can occur between the chiral limits of two and
three massless flavours (i.e., whether m_s is kept at its physical value or
sent to zero). This may induce problems of convergence in three-flavour chiral
expansions. To cope with such difficulties, we introduce a new framework,
called Resummed Chiral Perturbation Theory. We exploit it to analyse pi-pi and
pi-K scatterings and match them with dispersive results in a frequentist
framework. Constraints on three-flavour chiral order parameters are derived.Comment: Proceedings of the EPS-HEP 2007 Conference, Manchester (UK). 3 pages,
1 figur
The role of strange sea quarks in chiral extrapolations on the lattice
Since the strange quark has a light mass of order Lambda_QCD, fluctuations of
sea s-s bar pairs may play a special role in the low-energy dynamics of QCD by
inducing significantly different patterns of chiral symmetry breaking in the
chiral limits N_f=2 (m_u=m_d=0, m_s physical) and N_f=3 (m_u=m_d=m_s=0). This
effect of vacuum fluctuations of s-s bar pairs is related to the violation of
the Zweig rule in the scalar sector, described through the two O(p^4)
low-energy constants L_4 and L_6 of the three-flavour strong chiral lagrangian.
In the case of significant vacuum fluctuations, three-flavour chiral expansions
might exhibit a numerical competition between leading- and
next-to-leading-order terms according to the chiral counting, and chiral
extrapolations should be handled with a special care. We investigate the impact
of the fluctuations of s-s bar pairs on chiral extrapolations in the case of
lattice simulations with three dynamical flavours in the isospin limit.
Information on the size of the vacuum fluctuations can be obtained from the
dependence of the masses and decay constants of pions and kaons on the light
quark masses. Even in the case of large fluctuations, corrections due to the
finite size of spatial dimensions can be kept under control for large enough
boxes (L around 2.5 fm).Comment: 31 pages, 9 figures. A few comments added and typos correcte
A note on renormalon models for the determination of alpha_s(M_tau)
The tau hadronic width provides a determination of the strong coupling
constant alpha_s at low energies, since it can be related to a weighted
integral of the Adler function in the complex energy plane. Using Operator
Product Expansion, one sees that the sensitivity to alpha_s comes from the
perturbative contribution, which can be obtained by integrating the
perturbative expansion of the Adler function. Two different prescriptions
proposed to perform this integral, called Fixed-Order Perturbation Theory and
Contour-Improved Perturbation Theory (FOPT and CIPT), yield different results
for the strong coupling constant. Recently, models for the Adler function based
on renormalon calculus have been proposed to determine which of the two methods
is the most accurate, by comparing the resulting asymptotic series with the
true value of the integral. We discuss the assumptions of such ansatz and the
determination of their free parameters. We show that variations of this
renormalon ansatz can yield opposite conclusions concerning the comparison of
CIPT versus FOPT, and that such models are not constrained enough to provide a
definite answer on this issue or to be exploited for a high-precision
determination of alpha_s(m_tau^2).Comment: 28 pages, 5 figure
Renormalization of B-meson distribution amplitudes
We summarize a recent calculation of the evolution kernels of the
two-particle B-meson distribution amplitudes and taking into
account three-particle contributions. In addition to a few phenomenological
comments, we give as a new result the evolution kernel of the combination of
three-particle distribution amplitudes and confirm constraints
on and derived from the light-quark equation of motion.Comment: 7 pages, 2 figures. Contribution to the proceedings of the Int.
Workshop on Effective Field Theories: from the pion to the upsilon. Feb.
2009. Valencia, Spai
Low-energy pi-pi and pi-K scatterings revisited in three-flavour resummed chiral perturbation theory
Chiral symmetry breaking may exhibit significantly different patterns in two chiral limits: N_f=2 massless flavours (m_u=m_d=0, m_s physical) and N_f=3 massless flavours (m_u=m_d=0=m_s=0). Such a difference may arise due to vacuum fluctuations of s-bar{s} pairs related to the violation of the Zweig rule in the scalar sector, and could yield a numerical competition between contributions counted as leading order and next-to-leading in the chiral expansions of observables. We recall and extend Resummed Chiral Perturbation Theory (ReChPT), a framework that we introduced previously to deal with such instabilities: it requires a more careful definition of the relevant observables and their one-loop chiral expansions. We analyse the amplitudes for low-energy pi-pi and pi-K scatterings within ReChPT, which we match in subthreshold regions with dispersive representations obtained from the solutions Roy and Roy-Steiner equations. Using a frequentist approach, we constrain the quark mass ratio as well as the quark condensate and the pseudoscalar decay constant in the N_f=3 chiral limit. The results favour significant contributions of vacuum fluctuations suppressing the N_f=3 quark condensate compared to its N_f=2 counterpart
Three-particle contributions to the renormalisation of B-meson light-cone distribution amplitudes
We study light-cone distribution amplitudes of heavy-light systems, such as a
B-meson. By an explicit computation, we determine how two-parton distribution
amplitudes mix with three-parton ones at one loop: \phi_+ is shown to mix only
into itself, whereas \phi_- mixes with the difference of three-parton
distribution amplitudes \Psi_A-\Psi_V. We determine the corresponding anomalous
dimension and we check the gauge independence of our result by considering a
general covariant gauge. Finally, we comment on some implications of our result
for phenomenological models of these distribution amplitudes.Comment: 21 pages, 5 figures, some comments and 2 references added, except for
typesetting matches version published in JHE
pi K scattering inputs to ChPT
Experimental information on low energy scattering would shed light on
the poorly known OZI suppressed sector of ChPT. I describe recent work aimed at
generating such information based on available experimental data by setting up
and then solving with appropriate boundary conditions a non linear system of
equations of the Roy and Steiner type. First results of this analysis are
presented.Comment: Talk given at QCD'03 conference, 2-9 July 2003, Montpellie
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