arXiv subjects
Publications and source records attributed to Johan Bijnens.
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, $m_π^2$, $m_K^2$ and $m_η^2$, and the decay constants, $F_π$, $F_K$ and $F_η$. We present some numerical results after a simple resonance estimate of some of the new ${\cal O}(p^6)$ constants.
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.
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.
We discuss the matching between long-distance and short-distance at next-to-leading in $1/N_c$ 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 $O(p^2)$ 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 $Q_6$ operator in the chiral limit. We update our earlier results on the $B_K$ parameter as well.
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.
We calculate the leading quark mass corrections of order $m_q\log(m_q)$, $m_q$ and $m_q^{3/2}$ to the vector meson decay constants within Heavy Vector Meson Chiral Perturbation Theory. We discuss the issue of electromagnetic gauge invariance and the heavy mass expansion. Reasonably good fits to the observed decay constants are obtained.
We properly define off-shell $K\toπ$ transition amplitudes and use them to extract information for on-shell $K\toππ$ amplitudes within Chiral Perturbation Theory. At order $p^2$ in the chiral expansion all three parameters of weak interaction can be determined. At order $p^4$ we are able to fix eleven additional constants out of thirteen contributing to off-shell $K\toπ$ transitions, which leaves four undetermined constants in the on-shell $K\toππ$ amplitudes. All ${\cal O}(p^4)$ contributions have been exactly derived with $m_π^2\ne 0$. We finally discuss the weak mass term issue and find contributions to on-shell $ΔS=\pm 1$ Kaon decays, in particular to transitions like $K_L \to γγ$, $K_L \to μ^+ μ^-$ and $K_S \to π^0 γγ$ at the lowest non-zero order.
Various topics in and around Goldstone Boson Production and Decay in CHPT are discussed, in particular I describe some of the progress in $p^6$ Chiral Perturbation Theory Calculations, the progress in calculating hadronic contributions to the muon anomalous magnetic moment, here comparing the two latest results of the light-by-light in some detail. I also present some progress in various $η$ and $K$ decays and their relevance for CHPT.
The unknown constants in Chiral Perturbation Theory needed for an all orders analysis of the polarizabilities and electromagnetic corrections to the masses of the pseudo-Goldstone bosons are estimated at leading order in $1/N_c$. We organize the calculation in an $1/N_c$-expansion and separate long- and short-distance physics contributions by introducing an Euclidean cut-off. The long-distance part is evaluated using the ENJL model and the short-distance part using perturbative QCD and factorization. We obtain very good matching between both. We then include these estimates in a full Chiral Perturbation Theory calculation to order $e^2$ $p^2$ for the masses and $p^6$ for the polarizabilities. For the electromagnetic corrections to the masses, we confirm a large violation of Dashen's theorem getting a more precise value for this violation. We make comparison with earlier related work. Some phenomenological consequences are discussed too.
We evaluate the long distance weak contribution to the neutron and proton electric dipole moments using an effective Lagrangian framework. We estimate the coefficients needed by a factorization hypothesis and additional assumptions on $γ_5$ terms in the baryon lagrangian. We obtain $|d_e^n|\approx 5\times 10^{-32}$ e$\cdot$cm and $|d_e^p|\approx 4\times 10^{-32}$ e$\cdot$cm. The former estimate is similar to the quark model estimates done previously.
We calculate the hadronic light-by-light contributions to the muon $g-2$. We use both $1/N_c$ and chiral counting to organize the calculation. Then we calculate the leading and next-to-leading order in the $1/N_c$ expansion low energy contributions using the Extended Nambu--Jona-Lasinio model as hadronic model. We do that to all orders in the external momenta and quark masses expansion. Although the hadronic light-by-light contributions to muon $g-2$ are not saturated by these low energy contributions we estimate them conservatively. A detailed analysis of the different hadronic light-by-light contributions to muon $g-2$ is done. The dominant contribution is the twice anomalous pseudoscalar exchange diagram. The final result we get is $a_μ^{\rm light-by-light}= (-9.2\pm3.2 ) \cdot 10^{-10}$. This is between two and three times the expected experimental uncertainty at the forthcoming BNL muon $g-2$ experiment.
We calculate within the Extended Nambu--Jona-Lasinio model the leading in $1/N_c$ contribution to $γγ\toπ^0π^0$ to all orders in the external momenta and quark masses. This result is then combined with the known two-loop Chiral Perturbation Theory and compared with the data and other calculations. A technical difficulty in the same calculation beyond order $p^6$ for $η\toπ^0γγ$ is identified and for this decay results up to order $p^6$ are presented.
Using two different methods inspired by duality transformations we present the equivalence between effective Lagrangians for massive vector mesons using a vector field and an antisymmetric tensor field. This completes the list of explicit field transformations between the various effective Lagrangian methods to describe massive vector and axial vector mesons.
Mistake in FORTRAN program corrected. The numerical results and conclusions are changed significantly: We present a calculation of the hadronic light-by-light contributions to the muon $g-2$ in the $1/N_c$ expansion. We have used an Extended NJL model and introduced an explicit cut-off for the high energy region. We have then critically studied the relative size of the high energy contributions. Although we find them large we can give a conservative estimate of the light-by-light contribution to $a_μ$ which is $-(11\pm5) \cdot 10^{-10}$. This is between two and three sigmas the expected experimental uncertainty at the forthcoming BNL experiment.
A short overview of the current state of Chiral Perturbation Theory is given. This includes a description of the basic assumptions, the usefulness of the external field method is emphasized using a simple lowest order example. Then at next-to-leading order the determination of the parameters is discussed. We also present the status of calculations at ${\cal O}(p^6)$. Finally I present the extension into 3 directions: estimates of the free parameters, inclusion of nonleptonic weak and electromagnetic interactions, and inclusion of non-Goldstone fields in the chiral Lagrangian. Invited Talk at the International Workshop on Nuclear \& Particle Physics ``Chiral Dynamics in Hadrons \& Nuclei,'' Feb 6 $\sim$ Feb 10, 1995, Seoul, Korea.
We calculate the $B_K$ parameter within the framework of the $1/N_c$ expansion. We essentially use the technique presented by Bardeen, Buras and Gérard but calculate an off-shell Green function in order to disentangle different contributions. We study this Green function in pure Chiral Perturbation Theory (CHPT) first and afterwards in the $1/N_c$ expansion in the presence of an explicit cut-off to determine $B_K$ and the counterterms appearing in CHPT. The high energy part is done using the renormalization group. For the low-energy contributions we use both CHPT and an Extended Nambu--Jona-Lasinio model. This model has the right properties to match with the high energy QCD behaviour. We then study explicit chiral symmetry breaking effects by calculating with both massless and degenerate quarks together with the real case. A detailed analysis and comparison with the results found within other approaches is done. Consequences for present lattice calculations of this parameter are then obtained. As final result we get $0.60 < \hat B_K < 0.80$. If $m_s=m_d=0$ we get $0.25 < \hat B^χ_K < 0.55$.
We discuss the low-energy analysis of models involving quarks and four-fermion couplings. The relation with QCD and with other models of mesons and meson plus quarks at low energies is discussed. A short description of how the heat-kernel expansion can be used to get regularization independent information, is given. The anomaly within this class of models and a physical prescription to obtain the correct flavour anomaly while keeping as much of the VMD aspects as possible is discussed. The major part is the discussion within this framework of the order $p^4$ action and of two and some three-point functions to all orders in momenta and quark masses. Some results on hadronic matrix elements are given.
The class of phenomenological Lagrangians used for light constituent quarks is discussed. The Nambu-Jona-Lasinio model is then argued to be a good phenomenological choice and the quality of its prediction in the purely hadronic sector including several relations between parameters illustrated. Then we use these models to calculate nonleptonic matrix elements. The $π^+-π^0$ mass difference and the $B_K$ parameter, relevant in $K^0-\overline{K}^0$ mixing, are treated in more detail.