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V. Bernard

Publications and source records attributed to V. Bernard.

54 records · Page 3Linked to original sources
arXiv1996

The reaction $πN \to ππN$ at threshold in chiral perturbation theory

In the framework of heavy baryon chiral perturbation theory, we give thIn the framework of heavy baryon chiral perturbation theory, we give the chiral expansion for the $πN \to ππN$ threshold amplitudes $D_1$ and $D_2$ to quadratic order in the pion mass. The theoretical results agree within one standard deviation with the empirical values. We also derive a relation between the two threshold amplitudes of the reaction $πN \to ππN$ and the $ππ$ S--wave scattering lengths, $a_0^0$ and $a_0^2$, respectively, to order ${\cal O}(M_π^2)$. We show that there are uncertainties mostly related to resonance excitation which make an accurate determination of the $ππ$ scattering length $a_0^0$ from the $ππN$ threshold amplitudes at present very difficult. The situation is different in the $ππ$ isospin two final state. Here, the chiral series converges and one finds $a_0^2 = -0.031 \pm 0.007$ consistent with the one--loop chiral perturbation theory prediction.

hep-ph↗
arXiv1996

Improved description of threshold pion electroproduction in chiral perturbation theory

We investigate neutral pion electroproduction off protons in the framework of heavy baryon chiral perturbation theory. The chiral expansion of the S--wave multipoles $E_{0+}$ and $L_{0+}$ is carried out to three orders. There appear several undetermined low--energy constants. Three are taken from a recent study of the new TAPS threshold $π^0$ photoproduction data, one is fixed from the proton Dirac form factor and the novel S--wave constants appearing at orders $q^4$ and $q^5$ are determined from a best fit (constrained by resonance exchange) to the recent NIKHEF and MAMI data at photon momentum transfer squared $k^2 = -0.1 \, \, {\rm GeV}^2$. The inclusion of a particular set of dimension five operators is forced upon the fit by a soft--pion theorem which severely constrains the momentum dependence of the longitudinal S--wave multipole $L_{0+}$ at order $q^4$. We give predictions for lower photon virtualities for the various multipoles and differential cross sections. Further improvements are briefly touched upon.

hep-ph↗
arXiv1995

Chiral symmetry and the reaction $γp \to π^0 p$

We analyze the new threshold data for neutral pion photoproduction off protons in the framework of heavy baryon chiral perturbation theory. We show that large loop corrections are needed to understand the S--wave multipole $E_{0+}$ and that all pertinent low--energy constants can be understood within the framework of resonance exchange saturation. Previous inconsistencies in the description of this reaction in the threshold region are resolved.

hep-ph↗
arXiv1995

Pion Observables in the Extended NJL Model with Vector and Axial-Vector Mesons

The momentum-space bosonization method of a Nambu and Jona-Lasinio type model with vector and axial-vector mesons is applied to $ππ$ scattering. Unlike the case in earlier published papers, we obtain the $ππ$ scattering amplitude using the linear and nonlinear realizations of chiral symmetry and fully taking into account the momentum dependence of meson vertices. We show the full physical equivalence between these two approaches. The chiral expansion procedure in this model is discussed in detail. Chiral expansions of the quark mass, pion mass and constant $f_π$ are obtained. The low-energy $ππ$ phase shifts are compared to the available data. We also study the scalar form factor of the pion.

hep-ph↗
arXiv1995

Chiral Prediction for the $πN$ Scattering Length $a^-$ to Order ${\cal O}(M_π^4)$

We evaluate the S-wave pion--nucleon scattering length $a^-$ in the framework of heavy baryon chiral perturbation theory up--to--and--including terms of order $M_π^4$. We show that the order $M_π^4$ piece of the isovector amplitude at threshold, $T^-_{\rm thr}$, vanishes exactly. We predict for the isovector scattering length, $0.088 \, M_{π^+}^{-1} \le a^- \le 0.096 \, M_{π^+}^{-1}$.

hep-ph↗
arXiv1995

On the Interpretation of $πN \to ππN$ Data near Threshold

Near threshold pion production experiments have been recently carried out and used to extract S--wave $ππ$ scattering lengths. We emphasize here that at present these processes are related only at the tree level (and its first correction) in chiral perturbation theory. Higher order corrections (including loops) must be evaluated before rigorous claims concerning S--wave $ππ$ scattering lengths can be made.

hep-ph↗
arXiv1994

Novel Pion Electroproduction Low-Energy Theorems

We present novel low--energy theorems for the P--wave multipoles $2M_{1+} + M_{1-}$, $M_{1+} -M_{1-}$, $E_{1+}$ and $L_{1\pm}$ for neutral pion electroproduction off protons. These should be very useful for the analysis of existing or future threshold data.

hep-ph↗
arXiv1994

Neutral pion photoproduction off nucleons revisited

We investigate threshold pion photoproduction in the framework of heavy baryon chiral perturbation theory. We give the expansion of the electric dipole amplitude $E_{0+}$ to three orders in $μ$, the ratio of the pion to nucleon mass, and show that it is slowly converging. We argue that this observable is not a good testing ground for the chiral dynamics of QCD. In contrast, we exhibit new and fastly converging low--energy theorems in the P--waves which should be used to constrain the data analysis. We also discuss the importance of polarization observables to accurately pin down certain multipoles and give predictions for the reaction $γn \to π^0 n$.

hep-ph↗
arXiv1994

Threshold Pion Photo- and Electroproduction in Chiral Perturbation Theory

I present some recent results on neutral pion photo- and electroproduction in the threshold region and discuss the low energy theorem for $E_{0+}$ and some novel ones for the $P$-waves. I also study the two-pion production process $γN \to ππN$ from which complementary information can be gained.

hep-ph↗
arXiv1994

The Reaction $πN \to ππN$ at Threshold

We consider the chiral expansion for the reaction $πN \to ππN$ in heavy baryon chiral perturbation theory. To order $M_π$ we derive novel low--energy theorems that compare favorably with recent determinations of the total cross sections for $π^+ p \to π^+ π^+ n$ and $π^- p \to π^0 π^0 n$.

hep-ph↗
arXiv1994

Threshold Two-Pion Photo- and Electroproduction: More neutrals than expected

We present an exploratory study of two pion photo-- and electroproduction off the nucleon in the threshold region. To calculate the pertinent amplitudes, we make use of heavy baryon chiral perturbation theory. We show that due to finite chiral loops the production cross section for final states with two neutral pions is considerably enhanced. The experimental implications are briefly discussed.

nucl-th↗
arXiv1993

Low--Energy Theorems for Weak Pion Production

We derive novel low--energy theorems for single pion production off nucleons through the isovector axial current. We find that the $k^2$-dependence of the multipole $L_{0+}^{(+)}$ at threshold is given by the nucleon scalar form factor, namely $σ(k^2-M_π^2 ) /(3 πM_πF_π)$. The relation to PCAC results for soft pions including electroweak form factors is also clarified.

hep-ph↗
arXiv1993

Aspects of Nucleon Compton Scattering

We consider the spin-averaged nucleon forward Compton scattering amplitude in heavy baryon chiral perturbation theory including all terms to order ${\cal O} (q^4)$. The chiral prediction for the spin-averaged forward Compton scattering amplitude is in good agreement with the data for photon energies $ω\le 110$ MeV. We also evaluate the nucleon electric and magnetic Compton polarizabilities to this order and discuss the uncertainties of the various counter terms entering the chiral expansion of these quantities.

hep-ph↗
arXiv1993

Threshold Pion Electroproduction in Chiral Perturbation Theory

Electroproduction of pions on the nucleon near the threshold is analyzed within the framework of baryon chiral perturbation theory. We give a thorough discussion of the low--energy theorems related to charged and neutral electropionproduction. It is shown how the axial radius of the nucleon can be related to the S--wave multipoles $E_{0+}^{(-)}$ and $L_{0+}^{(-)}$. The chiral perturbation theory calculations of the $γ^\star p \to π^0 p$ reaction are found to be in good agreement with the recent near threshold data. We also discuss the influence of some isospin--breaking effects in this channel. For future experimental tests of the underlying chiral dynamics, extensive predictions of differential cross sections and multipole amplitudes are presented.

hep-ph↗
arXiv1993

Chiral Corrections to the S-Wave Pion-Nucleon Scattering Lengths

We calculate the chiral corrections to Weinberg's prediction for the S--wave $πN$ scattering lengths up--to--and--including order ${\cal O}(M_π^3)$ making use of heavy baryon chiral perturbation theory. For the isospin--odd scattering length $a^-$ these corrections are small and bring the prediction closer to the empirical value. In the case of the isospin--even $a^+$ large cancellations appear so that the ${\cal O}(M_π^3)$ result depends sensitively on certain resonance parameters which enter the calculation of the contact terms present at next--to--leading order.

hep-ph↗
arXiv1993

Strong and Radiative Meson Decays in a Generalized Nambu--Jona-Lasinio Model

We investigate strong and radiative meson decays in a generalized Nambu--Jona-Lasinio model. The one loop order calculation provides a satisfactory agreement with the data for the mesonic spectrum and for radiative decays. Higher order effects for strong decays of $ρ$ and $K^*$ are estimated to be large. We also discuss the role of the flavour mixing determinantal interaction.

hep-ph↗