arXiv subjects
Publications and source records attributed to S. Scherer.
The theoretical and experimental status of the isovector axial-vector current form factors G_A(q^2) and G_P(q^2) of the nucleon is reviewed. We also describe a new calculation of these form factors in manifestly Lorentz-invariant chiral perturbation theory (ChPT) with the inclusion of axial-vector mesons as explicit degrees of freedom.
Using the examples of pion-nucleon scattering and the nucleon mass we analyze the convergence of perturbative series in the framework of baryon chiral perturbation theory. For both cases we sum up sets of an infinite number of diagrams by solving equations exactly and compare the solutions with the perturbative contributions.
The magnetic dipole moment of the $Δ(1232)$ is calculated in the framework of manifestly Lorentz-invariant baryon chiral perturbation theory in combination with the extended on-mass-shell renormalization scheme. As in the case of the nucleon, at leading order both isoscalar and isovector anomalous magnetic moments are given in terms of two low-energy constants. In contrast to the nucleon case, at next-to-leading order the isoscalar anomalous magnetic moment receives a (real) loop contribution. Moreover, due to the unstable nature of the $Δ(1232)$, at next-to-leading order the isovector anomalous magnetic moment not only receives a real but also an imaginary loop contribution.
We analyze the constraint structure of a spin-3/2 particle interacting with a pseudoscalar. Requiring the self consistency of the considered effective field theory imposes restrictions on the possible interaction terms. In the present case we derive two constraints among the three lowest-order $πΔ$ interaction terms. From these constraints we find that the total Lagrangian is invariant under the so-called point transformation. On the other hand, demanding the invariance under the point transformation alone is less stringent and produces only classes of relations among the coupling constants.
We introduce a new formulation of baryon chiral perturbation theory which improves the ultraviolet behavior of propagators and can be interpreted as a smooth cutoff regularization scheme. It is equivalent to the standard approach, preserves all symmetries and therefore satisfies the Ward identities. Our formulation is equally well defined in the vacuum, one- and few-nucleon sectors of the theory. The equations (Bethe-Salpeter, Lippmann-Schwinger, etc.) for the scattering amplitudes of the few-nucleon sector are free of divergences in the new approach. Unlike the usual cutoff regularization, our 'cutoffs' are parameters of the Lagrangian and do not have to be removed.
We discuss the reaction $π^- e^- \to π^- e^- π^{0}$ with the purpose of obtaining information on the $γπ\to ππ$ anomalous amplitude ${\cal F}_{3π}$. We compare a full calculation at ${\cal O}(p^6)$ in chiral perturbation theory and various phenomenological predictions with the existing data of Amendolia {\em et al}. By integrating our theory results using Monte Carlo techniques we obtain $σ= 2.05 $ nb at ${\cal O}(p^6)$ and $σ= 2.17 $ nb after including the dominant electromagnetic correction. Both results are in good agreement with the experimental cross section of $σ= (2.11 \pm 0.47)$ nb. On the basis of the ChPT results one would extract from the the experimental cross section as amplitudes ${\cal F}_{3π}^{(0)\rm extr} = (9.9 \pm 1.1)$ GeV$^{-3}$ and ${\cal F}_{3π}^{(0)\rm extr} = (9.6 \pm 1.1)$ GeV$^{-3}$, respectively, which have to be compared with the low-energy theorem ${\cal F}_{3π}=e/(4π^2 F_π^3)=9.72 {GeV}^{-3}$. We emphasize the need for new data to allow for a comparison of experimental and theoretical distributions and to obtain ${\cal F}_{3π}$ with smaller uncertainty.
Quantum electrodynamics for $ρ$ mesons is considered. It is shown that, at tree level, the value of the gyromagnetic ratio of the $ρ^+$ is fixed to 2 in a self-consistent effective quantum field theory. Further, the mixing parameter of the photon and the neutral vector meson is equal to the ratio of electromagnetic and strong couplings, leading to the mass difference $M_{ρ^0}-M_{ρ^\pm}\sim 1 {\rm MeV}$ at tree order.
Baryon chiral perturbation theory with explicit $Δ(1232)$ degrees of freedom is considered. Using the extended on-mass-shell renormalization scheme, a manifestly Lorentz-invariant effective field theory with a systematic power counting is obtained. As applications we discuss the mass of the nucleon, the pion-nucleon sigma term, and the pole of the $Δ$ propagator.
An experiment on the radiative pi^+ meson photoproduction from the proton (gamma p->gamma pi^+ n) was carried out at the Mainz Microtron MAMI in the kinematic region 537 MeV <E_{gamma}<817 MeV, 140^o<theta_{gamma-gamma'}^cm<180^o. The pi^+ meson polarizabilities have been determined from a comparison of the data with the predictions of two different theoretical models, the first one being based on an effective pole model with pseudoscalar coupling while the second one is based on diagrams describing both resonant and nonresonant contributions. The validity of the models has been verified by comparing the predictions with the present experimental data in the kinematic region where the pion polarizability contribution is negligible (s_1<5 mu^2) and where the difference between the predictions of the two models does not exceed 3%. In the region, where the pion polarizability contribution is substantial (5<s_1/mu^2<15, -12<t/mu^2<-2), the difference (alpha-beta)_{pi^+} of the electric (alpha) and the magnetic (beta) polarizabilities has been determined. As a result we find: (alpha-beta)_{pi^+}=(11.6\pm 1.5_{stat}\pm 3.0_{syst}\pm 0.5_{mod})x10^-4fm^3. This result is at variance with recent calculations in the framework of chiral perturbation theory.
We discuss the masses of the ground state baryon octet and the nucleon sigma terms in the framework of manifestly Lorentz-invariant baryon chiral perturbation theory. In order to obtain a consistent power counting for renormalized diagrams the extended on-mass-shell renormalization scheme is applied.
It is shown that both the universal coupling of the rho-meson and the Kawarabayashi-Suzuki-Riadzuddin-Fayyazuddin expression for the magnitude of its coupling constant follow from the requirement that chiral perturbation theory of pions, nucleons, and rho-mesons is a consistent effective field theory. The prerequisite of the derivation is that all ultraviolet divergences can be absorbed in the redefinition of fields and the available parameters of the most general effective Lagrangian.
It is argued that Weinberg's approach to the nucleon-nucleon (NN) interaction problem within effective field theory provides a consistent power counting for renormalized diagrams. Within this scheme the NN potential is organized as an expansion in terms of small quantities like small external momenta and the pion mass (divided by the characteristic large scale of the effective theory). Physical observables to any given order in these small quantities are calculated from the solutions of the Lippmann-Schwinger (or Schr\" odinger) equation.
We briefly outline the so-called extended on-mass-shell renormalization scheme for manifestly Lorentz-invariant baryon chiral perturbation theory which provides a simple and consistent power counting for renormalized diagrams. We comment on the role of chiral symmetry in the renormalization program and discuss as applications the mass and the electromagnetic form factors of the nucleon.
Using a toy model Lagrangian we demonstrate the application of both infrared and extended on-mass-shell renormalization schemes to multiloop diagrams by considering as an example a two-loop self-energy diagram. We show that in both cases the renormalized diagrams satisfy a straightforward power counting.
We discuss a renormalization scheme for relativistic baryon chiral perturbation theory which provides a simple and consistent power counting for renormalized diagrams. The method involves finite subtractions of dimensionally regularized diagrams beyond the standard $\bar{\rm MS}$ scheme of chiral perturbation theory to remove contributions violating the power counting. This is achieved by a suitable renormalization of the parameters of the most general effective Lagrangian. In addition to simplicity our method has the benefit that it can be easily applied to multiloop diagrams. As an application we discuss the mass and the scalar form factor of the nucleon and compare the results with the expressions of the infrared regularization of Becher and Leutwyler.
We formulate the infrared regularization of Becher and Leutwyler in a form analogous to our recently proposed extended on-mass-shell renormalization. In our formulation, IR regularization can be applied straightforwardly to multi-loop diagrams with an arbitrary number of particles with arbitrary masses.
We consider a renormalization scheme for relativistic baryon chiral perturbation theory which provides a simple and consistent power counting for renormalized diagrams. As an application we discuss the chiral expansion of the nucleon mass.
It is demonstrated that using a suitable renormalization condition one obtains a consistent power counting in manifestly Lorentz-invariant baryon chiral perturbation theory including vector mesons as explicit degrees of freedom.