542 research outputs found
A Parametrization for
We discuss various models and Chiral Perturbation Theory results for the
form factors and . We check in how much a simple
parametrization with a few parameters can be used to extract information from
experiment.Comment: 19 pages, 14 figure
On the two-loop contributions to the pion mass
We derive a simplified representation for the pion mass to two loops in
three-flavour chiral perturbation theory. For this purpose, we first determine
the reduced expressions for the tensorial two-loop 2-point sunset integrals
arising in chiral perturbation theory calculations. Making use of those
relations, we obtain the expression for the pion mass in terms of the minimal
set of master integrals. On the basis of known results for these, we arrive at
an explicit analytic representation, up to the contribution from K-K-eta
intermediate states where a closed-form expression for the corresponding sunset
integral is missing. However, the expansion of this function for a small pion
mass leads to a simple representation which yields a very accurate
approximation of this contribution. Finally, we also give a discussion of the
numerical implications of our results.Comment: Typos corrected and minor changes in Table 2. Published version. 19
pages, 1 figure, 2 table
Error estimates for pi-pi scattering threshold parameters in Chiral Perturbation Theory to two loops
Using the analysis of ChPT to two loops, we perform an error analysis of the
threshold and low energy parameters, based on the uncertainties for the one
loop low energy parameters and the resonance saturation mechanism. Different
sets of one loop low energy constants have been considered.Thus, the predictive
power of the effective field theory is quantified on the basis of the present
experimental uncertainties.Comment: 12 pages, 2 tables, 3 figures. Numerics upgraded to v2 of ref.(8).
New reference added. Typos corrected. New figure for SU(3) parameters
include
Anomalies and WZW-term of two-flavour QCD
The U(2)_R x U(2)_L symmetry of QCD with two massless flavours is subject to
anomalies which affect correlation functions involving the singlet currents
A^0_\mu or V^0_\mu. These are relevant for pion-photon interactions, because -
for two flavours - the electromagnetic current contains a singlet piece. We
give the effective Lagrangian required for the corresponding low energy
analysis to next-to-leading order, without invoking an expansion in the mass of
the strange quark. In particular, the Wess-Zumino-Witten term that accounts for
the two-flavour anomalies within the effective theory is written down in closed
form.Comment: 17 pages, 1 figur
Resumming QCD vacuum fluctuations in three-flavour Chiral Perturbation Theory
Due to its light mass of order Lambda_QCD, the strange quark can play a
special role in Chiral Symmetry Breaking (ChSB): differences in the pattern of
ChSB in the limits N_f=2 (m_u,m_d->0, m_s physical) and N_f=3 (m_u,m_d,m_s->0)
may arise due to vacuum fluctuations of s-bar s pairs, related to the violation
of the Zweig rule in the scalar sector and encoded in particular in the O(p^4)
low-energy constants L_4 and L_6. In case of large fluctuations, we show that
the customary treatment of SU(3)xSU(3) chiral expansions generate instabilities
upsetting their convergence. We develop a systematic program to cure these
instabilities by resumming nonperturbatively vacuum fluctuations of s-bar s
pairs, in order to extract information about ChSB from experimental
observations even in the presence of large fluctuations. We advocate a Bayesian
framework for treating the uncertainties due to the higher orders. As an
application, we present a three-flavour analysis of the low-energy pi-pi
scattering and show that the recent experimental data imply a lower bound on
the quark mass ratio 2m_s/(m_u+m_d) > 14 at 95 % confidence level. We outline
how additional information may be incorporated to further constrain the pattern
of ChSB in the N_f=3 chiral limit.Comment: 58 pages, 8 figure
Non-Perturbative Study of the Light Pseudoscalar Masses in Chiral Dynamics
We perform a non-perturbative chiral study of the masses of the lightest
pseudoscalar mesons. In the calculation of the self-energies we employ the
S-wave meson-meson amplitudes taken from Unitary Chiral Perturbation Theory
(UCHPT) that include the lightest nonet of scalar resonances. Values for the
bare masses of pions and kaons are obtained, as well as an estimate of the mass
of the \eta_8. The former are found to dominate the physical pseudoscalar
masses. We then match to the self-energies from Chiral Perturbation Theory
(CHPT) to O(p^4), and a robust relation between several O(p^4) CHPT
counterterms is obtained. We also resum higher orders from our calculated
self-energies. By taking into account values determined from previous chiral
phenomenological studies of m_s/\hat{m} and 3L_7+L^r_8, we determine a tighter
region of favoured values for the O(p^4) CHPT counterterms 2L^r_6-L^r_4 and
2L^r_8-L^r_5. This determination perfectly overlaps with the recent
determinations to O(p^6) in CHPT. We warn about a likely reduction in the value
of m_s/\hat{m} by higher loop diagrams and that this is not systematically
accounted for by present lattice extrapolations. We also provide a favoured
interval of values for m_s/\hat{m} and 3L_7+L^r_8.Comment: 26 pages, 9 figures. Original new material is included. Major
rewriting when comparing with lattice QC
Meson-meson Scattering in QCD-like Theories
We discuss meson-meson scattering at next-to-next-to-leading order in the
chiral expansion for QCD-like theories with general degenerate flavours for
the cases with a complex, real and pseudo-real representation. I.e. with global
symmetry and breaking pattern , and . We obtain fully analytical expressions for all
these cases. We discuss the general structure of the amplitude and the
structure of the possible intermediate channels for all three cases. We derive
the expressions for the lowest partial wave scattering length in each channel
and present some representative numerical results. We also show various
relations between the different cases in the limit of large .Comment: 61 page
Pinning down the kaon form factors in K^+ -> mu^+ nu_mu gamma decay
We find that the normal muon polarization in the decay K->mu nu_mu gamma is
very sensitive to the values of the kaon vector F_V and axial-vector F_A form
factors. It is shown that the ongoing KEK-E246 experiment can definitely
determine the signs of the sum of the form factors if their difference is fixed
from other considerations. This method can also verify the form factor values
and signs obtained from the K^+ -> l^+ nu_l e^+ e^- decays. A new experiment
with sensitivity to the normal and transverse muon polarizations of about 10^-4
will provide a unique possibility to determine the F_V and F_A values with a
few percent accuracy.Comment: revtex, 5 pages, 2 figures. Minor corrections made for the journal
version of the pape
Consistency tests of AMPCALCULATOR and chiral amplitudes in SU(3) Chiral Perturbation Theory: A tutorial based approach
Ampcalculator is a Mathematica based program that was made publicly available
some time ago by Unterdorfer and Ecker. It enables the user to compute several
processes at one-loop (upto ) in SU(3) chiral perturbation theory. They
include computing matrix elements and form factors for strong and non-leptonic
weak processes with at most six external states. It was used to compute some
novel processes and was tested against well-known results by the original
authors. Here we present the results of several thorough checks of the package.
Exhaustive checks performed by the original authors are not publicly available,
and hence the present effort. Some new results are obtained from the software
especially in the kaon odd-intrinsic parity non-leptonic decay sector involving
the coupling . Another illustrative set of amplitudes at tree level we
provide is in the context of -decays with several mesons including quark
mass effects, of use to the BELLE experiment. All eight meson-meson scattering
amplitudes have been checked. Kaon-Compton amplitude has been checked and a
minor error in published results has been pointed out. This exercise is a
tutorial based one, wherein several input and output notebooks are also being
made available as ancillary files on the arXiv. Some of the additional
notebooks we provide contain explicit expressions that we have used for
comparison with established results. The purpose is to encourage users to apply
the software to suit their specific needs. An automatic amplitude generator of
this type can provide error-free outputs that could be used as inputs for
further simplification, and used in varied scenarios such as applications of
chiral perturbation theory at finite temperature, density and volume. This can
also be used by students as a learning aid in low-energy hadron dynamics.Comment: 25 pages, plain latex, corresponds to version to appear in EPJA,
additional ancillary files adde
Charged Kaon K \to 3 pi CP Violating Asymmetries at NLO in CHPT
We give the first full next-to-leading order analytical results in Chiral
Perturbation Theory for the charged Kaon K \to 3 pi slope g and decay rates
CP-violating asymmetries. We have included the dominant Final State
Interactions at NLO analytically and discussed the importance of the unknown
counterterms. We find that the uncertainty due to them is reasonable just for
\Delta g_C, i.e. the asymmetry in the K^+ \to pi^+ pi^+ pi^- slope g; we get
\Delta g_C = -(2.4 +- 1.2) 10^{-5}. The rest of the asymmetries are very
sensitive to the unknown counterterms. In particular, the decay rate
asymmetries can change even sign. One can use this large sentivity to get
valuable information on those counterterms and on Im(G_8) coupling --very
important for the CP-violating parameter epsilon'_K-- from the eventual
measurement of these asymmetries. We also provide the one-loop O(e^2 p^2)
electroweak octet contributions for the neutral and charged Kaon K \to 3 pi
decays.Comment: 43+2 pages, 2 figures. Version accepted in JHEP. Small changes in the
final numerics of CP asymmetries due to change in input valu
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