共查询到20条相似文献,搜索用时 31 毫秒
1.
G. Wanders 《The European Physical Journal C - Particles and Fields》2000,17(2):323-336
The Roy equations determine the S- and P-wave phase shifts on a low energy interval. They allow the derivation of threshold parameters from experimental data. We examine
the solutions of these equations that are in the neighborhood of a given solution by means of a linearization procedure. An
updated survey of known results on the dimension of the manifold of solutions is presented. The solution is unique for a low
energy interval with upper end at 800 MeV. We determine its response to small variations of the input: S-wave scattering lengths
and absorptive parts above 800 MeV. We confirm the existence of a universal curve of solutions in the plane of the S-wave
scattering lengths and provide a control of the decrease of the influence of the input absorptive parts with increasing energy.
A general result on the suppression of unphysical singularities at the upper end of the low energy interval is established
and its practical implications are discussed.
Received: 9 May 2000 / Published online: 31 August 2000 相似文献
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S. Descotes N.H. Fuchs L. Girlanda J. Stern 《The European Physical Journal C - Particles and Fields》2002,24(3):469-483
The recently published E865 data on charged decays and phases are reanalyzed to extract values of the two S-wave scattering lengths, of the subthreshold parameters and , of the low-energy constants and as well as of the main two-flavour order parameters: and in the limit taken at the physical value of the strange quark mass. Our analysis is exclusively based on direct experimental information
on phases below 800 MeV and on the new solutions of the Roy equations by Ananthanarayan et al. The result is compared with the
theoretical prediction relating 2a
0
0-5a
0
2 and the scalar radius of the pion, which was obtained in two-loop Chiral Perturbation Theory. A discrepancy at the 1- level is found and commented upon.
Received: 11 December 2001 / Revised version: 28 March 2002 / Published online: 7 June 2002 相似文献
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Tobias Isken Bastian Kubis Sebastian P. Schneider Peter Stoffer 《The European Physical Journal C - Particles and Fields》2017,77(7):489
We present a dispersive analysis of the decay amplitude for \(\eta '\rightarrow \eta \pi \pi \) that is based on the fundamental principles of analyticity and unitarity. In this framework, final-state interactions are fully taken into account. Our dispersive representation relies only on input for the \({\pi \pi }\) and \({\pi }\eta \) scattering phase shifts. Isospin symmetry allows us to describe both the charged and neutral decay channel in terms of the same function. The dispersion relation contains subtraction constants that cannot be fixed by unitarity. We determine these parameters by a fit to Dalitz-plot data from the VES and BES-III experiments. We study the prediction of a low-energy theorem and compare the dispersive fit to variants of chiral perturbation theory. 相似文献
6.
We propose a Coulomb-like kernel for the relativistic two-fermion Bethe-Salpeter equation, to be used as the lowest-order approximation in systematic perturbative calculation of bound-state energy levels in QED. The kernel is symmetric in the two fermions and for the exchange of in and out momenta. The resulting equation is exactly soluble, unlike previously considered unperturbed kernels. We give explicitly the Green function and eigen-functions. We also discuss the problem of the behaviour of the wave functions at zero relative coordinate in connection with the contribution to energy levels from the one-photon annihilation channel in QED. 相似文献
7.
G. V. Efimov 《Few-Body Systems》2007,41(3-4):157-184
The Bethe-Salpeter (BS) equation in the ladder approximation is studied within a fermion theory: two fermion fields (constituents) with mass m interacting via an exchange of a scalar field with mass μ. The BS equation can be written in the form of an integral equation in the configuration Euclidean x-space with the symmetric kernel K for which Tr K 2 = ∞ due to the singular character of the fermion propagator. This kernel is represented in the form K = K 0 + K I . The operator K 0 with Tr K 0 2 = ∞ is of the “fall at the center” potential type and describes a continuous spectrum only. Besides the presence of this operator leads to a restriction on the value of the coupling constant. The kernel K I with Tr K I 2 < ∞ is responsible for bound fermion-fermion states. Our approach is that the eigenvalue problem of the equation $\Lambda\Psi = g^2(K_0 + K_I)\Psi \qquad {\rm with}\qquad \Lambda = 1The Bethe-Salpeter (BS) equation in the ladder approximation is studied within a fermion theory: two fermion fields (constituents)
with mass m interacting via an exchange of a scalar field with mass μ. The BS equation can be written in the form of an integral equation
in the configuration Euclidean x-space with the symmetric kernel K for which Tr K
2 = ∞ due to the singular character of the fermion propagator. This kernel is represented in the form K = K
0 + K
I
. The operator K
0 with Tr K
0
2 = ∞ is of the “fall at the center” potential type and describes a continuous spectrum only. Besides the presence of this
operator leads to a restriction on the value of the coupling constant. The kernel K
I
with Tr K
I
2 < ∞ is responsible for bound fermion-fermion states.
Our approach is that the eigenvalue problem of the equation
can be rewritten in the form
The kernel of the last equation is finite for g
2 < g
c
2 and the variational procedure of calculations of eigenvalues and eigenfunctions can be applied.
The quantum pseudoscalar and scalar mesodynamics is considered. The binding energy of the state 1+ (deuteron) as a function of the coupling constant is calculated in the framework of the procedure formulated above. It is
shown that this bound state is absent in the pseudoscalar mesodynamics and does exist in the scalar mesodynamics. A comparison
with the non-relativistic Schr?dinger picture is made.
Correspondence: G. V. Efimov, Bogoliubov Laboratory of Theoretical Physics, Joint Institute for Nuclear Research, 141980 Dubna,
Russia 相似文献
9.
David A. Owen 《Foundations of Physics》1997,27(1):57-66
We develop here the general treatment of the Bethe—Salpeter equation for the bound state of two spin-l particles interacting through an electromagnetic interaction. The treatment here, which can be generalized to strong interactions,
combines the two-component approach utilized previously by the author in conjunction with spontaneous symmetry breaking. This
is done by using a Lagrangian having SU(2)×U(1) symmetry (without fermions) and then choosing the ′t Hooft gauge. In this way, a renormalizable theory for the interaction
of two spin-l particles via an electromagnetic interaction is ensured. 相似文献
10.
The Bethe-Salpeter equation for a fermion-antifermion system, coupled by photons, is considered in the Feynman gauge. The kernel is that resulting from exchange of a single photon. The usual reduction of the sixteen B-S spinor amplitudes in terms of tensors leads to 16 coupled integro-differential equations. By straightforward application of charge conjugation-, parity-, and Lorentz-invariance, the system of coupled equations is reduced to ones involving no more than eight and as few as three scalar structure functions for the various parity, charge conjugation, and total angular momentum states. The results hold for arbitrary coupling strength. As a check of the equations obtained, a perturbation theory is carried out for the Coulomb interaction. It leads to effective potentials in agreement with those obtained previously to order mα4 for positronium. 相似文献
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M. J. Zieliński P. Moskal A. Kupść 《The European Physical Journal A - Hadrons and Nuclei》2011,47(8):1-6
Isospin violating hadronic decays of the $ \eta$ and $ \eta{^\prime}$ mesons into 3 $ \pi$ mesons are driven by a term in the QCD Lagrangian proportional to the mass difference of the d and u quarks. The source giving large yield of the mesons for such decay studies are pp interactions close to the respective kinematical thresholds. The most important physics background for $ \eta$ , $ \eta{^\prime}$ $ \rightarrow$ $ \pi$ $ \pi$ $ \pi$ is coming from direct three-pion production reactions. In case of the $ \eta$ meson the background for the decays is relatively low ( $ \approx$ 10% . The purpose of this article is to provide an estimate of the direct pion production background for the $ \eta{^\prime}$ $ \rightarrow$ 3 $ \pi$ decays. Using the inclusive data from the COSY-11 experiment we have extracted the differential cross-section for the pp $ \rightarrow$ pp -multipion production reactions with the invariant mass of the pions equal to the $ \eta{^\prime}$ meson mass and estimated an upper limit for the signal to background ratio for studies of the $ \eta{^\prime}$ $ \rightarrow$ $ \pi^{+}_{}$ $ \pi^{-}_{}$ $ \pi^{0}_{}$ decay. 相似文献
14.
In this work we provide a dispersive analysis of \(\pi \pi \rightarrow K{\bar{K}}\) scattering. For this purpose we present a set of partial-wave hyperbolic dispersion relations using a family of hyperbolas that maximizes the applicability range of the hyperbolic dispersive representation, which we have extended up to 1.47 GeV. We then use these equations first to test simple fits to different and often conflicting data sets, also showing that some of these data and some popular parameterizations of these waves fail to satisfy the dispersive analysis. Our main result is obtained after imposing these new relations as constraints on the data fits. We thus provide simple and precise parameterizations for the S, P and D waves that describe the experimental data from \(K{{\bar{K}}}\) threshold up to 2 GeV, while being consistent with crossing symmetric partial-wave dispersion relations up to their maximum applicability range of 1.47 GeV. For the S-wave we have found that two solutions describing two conflicting data sets are possible. The dispersion relations also provide a representation for S, P and D waves in the pseudo-physical region. 相似文献
15.
A high-quality double-polarization data set for the helicity dependence of the total and differential cross-sections for both
channels in the
region has been obtained in the framework of the GDH experiment. The experiment, performed at the Mainz microtron MAMI, used a 4
detection system, a circularly polarized photon beam, and a longitudinally polarized frozen-spin target. These data are included in the database to perform a multipole analysis to determine the properties of the
-resonance. For the resonant
(1232) multipoles we find a very good agreement with previous analyses, while the nonresonant ones show significant deviations.Received: 11 July 2003, Revised: 16 January 2004, Published online: 17 August 2004PACS:
13.60.Le Meson production - 14.20.Gk Baryon resonances with S = 0 - 25.20.Lj Photoproduction reactions 相似文献
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S. Descotes-Genon B. Moussallam 《The European Physical Journal C - Particles and Fields》2014,74(7):1-22
We consider the evaluation of the \(\eta \pi \) isospin-violating vector and scalar form factors relying on a systematic application of analyticity and unitarity, combined with chiral expansion results. It is argued that the usual analyticity properties do hold (i.e. no anomalous thresholds are present) in spite of the instability of the \(\eta \) meson in QCD. Unitarity relates the vector form factor to the \(\eta \pi \rightarrow \pi \pi \) amplitude: we exploit progress in formulating and solving the Khuri–Treiman equations for \(\eta \rightarrow 3\pi \) and in experimental measurements of the Dalitz plot parameters to evaluate the shape of the \(\rho \) -meson peak. Observing this peak in the energy distribution of the \(\tau \rightarrow \eta \pi \nu \) decay would be a background-free signature of a second-class amplitude. The scalar form factor is also estimated from a phase dispersive representation using a plausible model for the \(\eta \pi \) elastic scattering \(S\) -wave phase shift and a sum rule constraint in the inelastic region. We indicate how a possibly exotic nature of the \(a_0(980)\) scalar meson manifests itself in a dispersive approach. A remark is finally made on a second-class amplitude in the \(\tau \rightarrow \pi \pi \nu \) decay. 相似文献
18.
We describe the spectra and decays of
and
atoms within a non-relativistic effective field theory. The evaluations of the energy shifts and widths are performed at next-to-leading order in isospin symmetry breaking. We provide general formulae for all S-states, and discuss the states with angular momentum one in some detail. The prediction for the lifetime of the
atom in its ground state yields
s.Received: 9 May 2004, Published online: 23 July 2004 相似文献
19.
M. Böhm 《Nuclear Physics B》1975,91(3):494-508
Current conservation in the form of the Ward identity between the electromagnetic vertex and the propagator implies that the energy dependence of the BS kernel is restricted and that the propagator cannot be chosen independently from the kernel. It is rather determined from the BS kernel in terms of an integral equation. Convolution type, energy-independent kernels are compatible with current conservation. We study the propagator and form factor resulting from smooth kernels. 相似文献