Showing papers by "Johan Bijnens published in 1999"

The Mesonic Chiral Lagrangian of Order $p^6$

Abstract: We construct the effective chiral Lagrangian for chiral perturbation theory in the mesonic even-intrinsic-parity sector at order $p^6$. The Lagrangian contains 112 in principle measurable + 3 contact terms for the general case of $n$ light flavours, 90+4 for three and 53+4 for two flavours. The equivalence between equations of motion and field redefinitions to remove spurious terms in the Lagrangians is shown to all orders in the chiral expansion. We also discuss and implement other methods for reducing the number of terms to a minimal set.

The mesonic chiral lagrangean of order p 6

Abstract: We construct the effective chiral lagrangean for chiral perturbation theory in the mesonic even-intrinsic-parity sector at order p6. The lagrangean contains 112 in principle measurable + 3 contact terms for the general case of n light flavours, 90+4 for three and 53+4 for two flavours. The equivalence between equations of motion and field redefinitions to remove spurious terms in the lagrangeans is shown to all orders in the chiral expansion. We also discuss and implement other methods for reducing the number of terms to a minimal set.

The ΔI = 1/2 rule in the chiral limit

Abstract: We discuss the matching between long-distance and short-distance at next-to-leading in 1/Nc and show how the scheme-dependence from the two-loop renormalization group running can be treated. We then use this method to study the three O(p2) terms contributing to non-leptonic kaon decays, namely the usual octet and 27-plet derivative terms as well as the weak mass term using the Extended Nambu--Jona-Lasinio model as the low energy approximation. We also discuss subtleties in the momentum routing in the low energy theory and a problem in separating factorizable and non-factorizable contributions from the Q6 operator in the chiral limit. We update our earlier results on the BK parameter as well.

Scheme Dependence of Weak Matrix Elements in the $1/N_c$ Expansion

Abstract: We show how the scheme- and scale-dependence of the short-distance operator product expansion with four-quark operators can be correctly accounted for in the framework of the $1/N_c$-expansion once the hadronization of two-quark currents has been fixed. We show formulas explicitly in the case of the $B_K$-parameter. We then use them with our earlier estimates of the long-distance effects. We compare Chiral Perturbation Theory at Leading- and Next-to-Leading-Order with the ENJL model results in the chiral limit. Good matching between the long- and short-distance regimes is obtained and our final value for the physical scheme independent $\hat B_K$ is $0.77\pm0.05\pm0.05$.

A Parametrization for $K^+\to \pi^+\pi^- e^+\nu$

Abstract: We discuss various models and Chiral Perturbation Theory results for the $K_{l4}$ form factors $F$ and $G$. We check in how much a simple parametrization with a few parameters can be used to extract information from experiment.

Two-point Functions at Two Loops in Three Flavour Chiral Perturbation Theory

Abstract: The vector and axial-vector two-point functions are calculated to next-to-next-to-leading order in Chiral Perturbation Theory for three light flavours. We also obtain expressions at the same order for the masses, $m_\pi^2$, $m_K^2$ and $m_\eta^2$, and the decay constants, $F_\pi$, $F_K$ and $F_\eta$. We present some numerical results after a simple resonance estimate of some of the new ${\cal O}(p^6)$ constants.

Chiral effective theories

Abstract: These are the proceedings of the workshop on “Chiral Effective Theories” held at the Physikzentrum Bad Honnef of the Deutsche Physikalische Gesellschaft, Bad Honnef, Germany from November 30 to December 4, 1998. The workshop concentrated on Chiral Perturbation Theory in its various settings and its relations with lattice QCD and dispersion theory. Included are a short contribution per talk and a listing of some review papers on the subject.

I : Chiral Perturbation for Kaons II: The $ΔI=1/2$-rule in the Chiral Limit

Abstract: I : Chiral Perturbation Theory is introduced and its applications to semileptonic and nonleptonic kaon decays are discussed. II: The method of large $N_c$ is used to calculate $K\to\pi\pi$ nonleptonic matrix elements, in particular the matching procedure between long and short-distance evolution that takes all scheme dependence correctly into account is discussed. Numerical results reproduce the $\Delta I=1/2$ rule without the introduction of any free parameters.

Low Energy Constants from Kl4 Form-Factors

Abstract: We have calculated the form-factors F and G in K ---> pi pi e nu decays (Kl4) to two-loop order in Chiral Perturbation Theory (ChPT). Combining this together with earlier two-loop calculations an updated set of values for the L's, the ChPT constants at p^4, is obtained. We discuss the uncertainties in the determination and the changes compared to previous estimates.

Progress in $K\to\pi\pi$ Decays

Abstract: Recent work by J.~Prades and myself on $K\to\pi\pi$ is described. The first part describes our method to connect in a systematic fashion the short-distance evolution with long-distance matrix-element calculations taking the scheme dependence of the short-distance evolution into account correctly. In the second part I show the results we obtain for the $\Delta I=1/2$ rule in the chiral limit.