arXiv subjects
Publications and source records attributed to Ulf-G. Meißner.
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.
In these lectures, the status of baryon chiral perturbation theory is reviewed. Particular emphasis is put on the two--flavor sector and the physics related to electromagnetic probes. I discuss in some detail the structure of the effective Lagrangian at next--to--leading order, the meaning of low--energy theorems in Compton scattering and pion photoproduction and confront the chiral predictions with the existing data. Some remaining problems and challenges are outlined.
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 $γn \to π^0 n$.
I consider some selected topics in chiral perturbation theory (CHPT) as probed at colliders such as DA$Φ$NE. Emphasis is put on processes involving pions in the isospin zero S-wave which require multi-loop calculations. These include the scalar form factor of the pion, two--photon fusion into pion pairs and $K_{\ell 4}$--decays. The physics of the chiral anomaly is briefly touched upon
We summarize the pertinent experimental and theoretical developments in the field of pion photo- and electroproduction in the threshold region. We discuss which experiments and which calculations should be done/performed in the future.
I review recent progress made in the calculation of nucleon properties in the framework of heavy baryon CHPT. Topics include: Compton scattering, $πN$ scattering, the anatomy of a low-energy constant and the induced pseudoscalar form factor.
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 $π^- p \to π^0 π^0 n$.
Using chiral Ward identities of QCD, we derive a relation for the induced pseudoscalar coupling constant which is accurate within a few percent, $g_P = 8.44 \pm 0.16$.
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.
I consider some selected topics in chiral perturbation theory (CHPT). For the meson sector, emphasis is put on processes involving pions in the isospin zero S-wave which require multi-loop calculations. The advantages and shortcomings of heavy baryon CHPT are discussed. Some recent results on the structure of the baryons are also presented.
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.
The momentum-space bosonization method is extended to the case of a Nambu--Jona-Lasinio type model with vector and axial-vector mesons. The method presented gives the possibility of deriving any meson vertex function to all orders in momenta and to the leading order in $1/N_c$. Two-point functions, which describe one-particle transitions to the hadronic vacuum, and meson self-energies are considered. We find new relations which generalize the well-known KSFR relation and both the first and the second Weinberg sum rules. These result from a consistent treatment of higher order terms in the momentum expansion.
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.
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.
We calculate the nucleons' electromagnetic polarizabilities in heavy baryon chiral perturbation theory including all terms to order ${\cal O} (q^4)$. The chiral prediction of the electric polarizabilities for the neutron and the proton are in good agreement with the data. In the case of the magnetic polarizabilities the big positive contribution from the $Δ(1232)$ resonance is largely cancelled by a non--analytic loop contribution of the $\ln M_π$ type. This novel effect helps to understand the rather small empirical value of the nucleons' magnetic polarizability.
I discuss the absorption and dispersion of pions in hot matter. A two-loop calculation in the framework of chiral perturbation theory is presented and its result is compactly written in terms of the two- and three-particle forward $ππ$ scattering amplitudes. At modest temperatures, $T \le 100$ MeV, the change in the pion mass is small and its dispersion law closely resembles the free space one. At these temperatures, all quantities of interest are given to a good degree of accuracy by the first term in the virial expansion which is linear in the density. (BUTP-93/16, uses espcrc1.sty from North-Holland Publishing)
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.
We present an analysis of the octet baryon masses and the $πN$ and $KN$ $σ$--terms in the framework of heavy baryon chiral perturbation theory. At next-to-leading order, ${\cal O}(q^3)$, knowledge of the baryon masses and $σ_{πN}(0)$ allows to determine the three corresponding finite low--energy constants and to predict the the two $KN$ $σ$--terms $σ^{(1,2)}_{KN} (0)$. We also include the spin-3/2 decuplet in the effective theory. The presence of the non--vanishing energy scale due to the octet--decuplet splitting shifts the average octet baryon mass by an infinite amount and leads to infinite renormalizations of the low--energy constants. The first observable effect of the decuplet intermediate states to the baryon masses starts out at order $q^4$. We argue that it is not sufficient to retain only these but no other higher order terms to achieve a consistent description of the three--flavor scalar sector of baryon CHPT. In addition, we critically discuss an SU(2) result which allows to explain the large shift of $σ_{πN}(2M_π^2) - σ_{πN}(0)$ via intermediate $Δ(1232)$ states.