arXiv subjects
Publications and source records attributed to F. Myhrer.
We develop a toy model of pion production in nucleon-nucleon collisions that reproduces some of the features of the chiral Lagrangian calculations. We calculate the production amplitude and examine some common approximations.
A modified linear sigma model that allows for $g_A = 1.26$ by addition of vector and pseudovector $πN$ coupling terms was discussed by Bjorken and Nauenberg and by Lee. In this extended linear sigma model the elastic $π$N scattering amplitudes satisfy the relevant chiral low-energy theorems, such as the Weinberg-Tomozawa relation for the isovector scattering length and in some cases Adler's "consistency condition". The agreement of the isospin symmetric $πN$ scattering length with experiment is substantially improved in this extended sigma model as compared with the original one. We show that the nucleon sigma term ($Σ_N$) in the linear- and the extended sigma models with three different kinds of chiral symmetry breaking terms are identical. Within the tree approximation the formal operator expression for the $Σ_N$ term and the value extracted from the $πN$ scattering matrix coincide. Large values of $Σ_N$ are easily obtained without any $s\bar s$ content of the nucleon. Using chiral rotations the Lagrangian of this extended sigma model reproduces the lowest-order $πN$ chiral perturbation theory Lagrangian.
We discuss the results of a systematic calculation of the next-to-next-to-leading order amplitude for the pp -> ppπ^0 S-wave production at the threshold in heavy-baryon chiral perturbation theory. We find six new diagrams, two of which can be viewed as vertex corrections, of 15 - 20 %, to the pion-exchange graph, whereas the rest are much larger, one exceeding 900 %. We discuss the reasons for this enhancement, as well as the steps necessary to be taken before the final comparison with experiment.
The observed scaling laws for large angle exclusive hadronic reactions are successfully accounted for by the short-distance QCD quark interchange processes. We focus on three hadronic reactions which shows evidence for a slight oscillatory deviation from the expected scaling behaviour. Possible explanations for these oscillations and connections to spin observables will be mentioned. Better data from excisting facilities (or a possible future KEK proton accelerator, JHP) can clarify the theoretical situation.
We present a systematic analysis of next-to-next-to-leading-order diagrams that contribute to the $pp \to ppπ^0$ production at threshold. Analytic expressions are given for the effective transition operators, and the relative importance of various types of diagrams is discussed. The vertex-correction-type graphs are found to give only small corrections to lower order graphs in conformity with expectations. By contrast, we find very large contributions from the two-pion graphs which can be interpreted as a part of effective $σ$-meson exchange diagrams. The recoil correction to the pion rescattering diagram also turns out to be large.
Chiral symmetry serves as a guiding principle in low-energy hadron dynamics. An effective lagrangian, which explicitly breaks chiral symmetry via a small mass term, allows for a systematic method of calculating higher order corrections to tree-level results. This is applied to radiative muon capture on hydrogen, %to extract the weak pseudoscalar form factor, and to proton-proton $π^0$ production near threshold. Both processes pose theoretical challenges in light of recent experimental results.
The first measurement of the radiative muon capture (RMC) rate on a proton was recently carried out at TRIUMF. The TRIUMF group analyzed the RMC rate in terms of the theoretical formula of Beder and Fearing, and found the surprising result that the pseudoscalar coupling g_P is 1.5 times the value expected from PCAC. To assess the reliability of the theoretical framework used by the TRIUMF group to relate the RMC rate to the pseudoscalar form factor, we calculate the RMC rate in chiral perturbation theory, which provides a systematic framework to describe all the vertices involved in RMC, fulfilling gauge-invariance and chiral-symmetry requirements in a transparent manner. As a first step we present a chiral perturbation calculation at tree level which includes sub-leading order terms.
A chiral-perturbative consideration of the near-threshold pp -> pp pi0 reaction indicates that the pion-rescattering term has a substantial energy and momentum dependence. The existing calculations that incorporate this dependence give pion rescattering contributions significantly larger than those of the conventional treatment, and this enhanced rescattering term interferes destructively with the one-body impulse term, leading to theoretical cross sections that are much smaller than the observed values. However, since the existing calculations are based on coordinate-space representation, they involve a number of simplifying assumptions about the energy-momentum flow in the rescattering diagram, even though the delicate interplay between the one-body and two-body terms makes it desirable to avoid these kinematical assumptions. We carry out here a momentum-space calculation that retains the energy-momentum dependence of the vertices as predicted by chiral perturbation theory. Our improved treatment increases the rescattering amplitude by a factor of 3 over the value obtained in the r-space calculations. The pp -> pp pi0 transition amplitude, which is now dominated by the rescattering term, leads to the cross section much larger than what was reported in the approximate r-space calculations. Thus, the extremely small cross sections obtained in the previous chiral perturbative treatments of this reaction should be considered as an accidental consequence of the approximations employed rather than a general feature.
From recent charge exchange measurements in the extreme forward direction, an independent and precise determination of the pion nucleon coupling constant is possible. This determination has reopened the debate on the value of this fundamental coupling constant of nuclear physics. Precise measurements of charge exchange observables at forward angles below 900 MeV/c would also give a better understanding of the long range part of the two-pion exchange potential. For example, the confirmation of the coherence of the tensor forces from the pion exchange and the isovector two-pion exchange would be very valuable. With the present data first attempts at an $\NbarN$ partial wave analysis have been made where, as in nucleon nucleon scattering, the antinucleon nucleon high J partial waves are mainly given by one-pion exchange. Finally a recent $\pbarp$ atomic cascade calculation and the fraction of P-state annihilation in gas targets is commented on.
A simple partial wave amplitude analysis of $\overline{p}p \rightarrow K^-K^+$ has been performed for data in the range $p_{\rm lab}$ = 360 -- 1000 MeV/$c$. In this low momentum interval only partial wave amplitudes with $J$ equal to 0, 1 and 2 are needed to obtain a good fit to the experimental data. This maximal $J$ = 2 value is smaller than what is required for the data of the reaction $\overline{p}p \rightarrow π^-π^+$ in the same momentum interval.
The usual theoretical treatments of the near-threshold $pp \rightarrow ppπ^0$ reaction are based on various phenomenological Lagrangians. In this work we examine the relationship between these approaches and a systematic chiral perturbation method. Our chiral perturbation calculation indicates that the pion rescattering term should be significantly enhanced as compared with the traditional phenomenological treatment, and that this term should have substantial energy and momentum dependence. An important consequence of this energy-momentum dependence is that, for a representative threshold kinematics and within the framework of our semiquantitative calculation, the rescattering term interferes destructively with the Born-term in sharp contrast to the constructive interference obtained in the conventional treatment. This destructive interference makes theoretical cross sections for $pp \rightarrow ppπ^0$ much smaller than the experimental values, a feature that suggests the importance of the heavy-meson exchange contributions to explain the experimental data.
A simple partial wave amplitude analysis of $\overline{p}p \rightarrow π^- π^+$ has been performed for data in the range p$_{\sl lab}$ = 360 -- 1000 MeV/c. Remarkably few partial waves are required to fit the data, while the number of required $J$ values barely changes over this energy range. However, the resulting set of partial wave amplitudes is not unique. We discuss possible measurements with polarized beam and target which will severely restrict and help resolve the present analysis ambiguities. New data from the reaction $\overline{p}p \rightarrow π^0 π^0$ alone, are insufficient for that purpose.
We discuss two topics concerning the application of chiral perturbation theory to nuclear physics: (1) the latest developments in the study of possible kaon condensation in dense baryonic systems; (2) nuclear responses to electro-weak probes.
We reevaluate a quark model prediction using the new QCD evolution function calculated to the 3 loop order and conclude that this model compares favorably with the new experimental results.
The results for meson condensation in the literature vary markedly depending on whether one uses chiral perturbation theory or the current-algebra-plus-PCAC approach. To elucidate the origin of this discrepancy, we re-examine the role of the sigma-term in meson condensation. We find that the resolution of the existing discrepancy requires a knowledge of terms in the Lagrangian that are higher order in density than hitherto considered.
The effective kaon mass in dense baryonic matter is calculated based on PCAC, current algebra and the Weinberg smoothness hypothesis. The off-shell behavior of the K-N scattering amplitudes is treated consistently with PCAC, and the effects of the subthreshold K-N resonances are also included. The effective kaon mass is found to depend crucially on the K-N sigma term. Since the current estimates of K-N Sigma term are very uncertain, we discuss various scenarios treating K-N Sigma term as an input parameter; for certain values of K-N Sigma a collective mode of a hyperon-particle-nucleon-hole state appears at high densities, possibly leading to kaon condensation.
An illustrative analysis is presented to show the origin of the energy-independent maximal asymmetry observed for wide ranges of angles in the reactions $\pbarppipi$ and $\pbarpKK$. % The general nature of our simple relation between helicity -flip and -nonflip partial wave amplitudes enforces the notion that % these features of the asymmetry for these two annihilation reactions are likely to persist within the hadronic regime. % At higher energies these features of the asymmetry will probably be modified significantly, signaling the onset of perturbative QCD. % Our study supports the arguments that the final $\KbarK$ state originates from a more central reaction than the $\pipi$ final state.
Arguments are presented for the expected behaviour of $\piNpiN$ scattering and the $\pbarppipi$ reaction at high energy and large scattering angles. % The annihilation reaction has close to maximal asymmetry ($\approx$ 1) for $p_{lab} \siml $ 2.2 GeV/c. % As will be presented for fixed (90$\degree$) angle this large asymmetry will not become zero but will start to oscillate with energy at higher energies and large $Q^2$ when perturbative QCD becomes applicable. This is due to the energy dependence of a QCD phase difference between the independent quark-quark scattering (Landshoff) and short-distance processes at high but not asymptotic energies. % A consequence of the existence the Landshoff process is that even if helicity is conserved at the quark level ($m_{q}$ = 0 MeV), helicity does not have to be conserved on the hadronic level. % We will discuss the implications for spin observables in $pp$ elastic scattering and argue that