Treatment Of Final State Interactions Research Articles

Failure of Breit-Wigner and success of dispersive descriptions of the τ− → K−ηντ decays

The τ− → K−ηντ decays have been studied using Chiral Perturbation Theory extended by including resonances as active fields. We have found that the treatment of final state interactions is crucial to provide a good description of the data. The Breit-Wigner approximation does not resum them and neglects the real part of the corresponding chiral loop functions, which violates analyticity and leads to a failure in the confrontation with the data. On the contrary, its resummation by means of an Omnes-like exponentiation of through a dispersive representation provides a successful explanation of the measurements. These results illustrate the fact that Breit-Wigner parametrizations of hadronic data, although simple and easy to handle, lack a link with the underlying strong interaction theory and should be avoided.As a result of our analysis we determine the properties of the K* (1410) resonance with a precision competitive to its traditional extraction using τ− → (Kπ)-ντ decays, albeit the much limited statistics accumulated for the τ- → K-ηντ channel. We also predict the soon discovery of the τ- → K-η'ντ decays.

Role of the isovector nucleon-nucleus interaction potential in nonmesonic hypernuclear decay

We develop a theoretical finite nucleus framework for the evaluation of the coincidence number of pairs ${N}_{\mathit{nN}}$ and the asymmetry parameter ${a}_{\ensuremath{\Lambda}}$ in nonmesonic hypernuclear decay $\ensuremath{\Lambda}N\ensuremath{\rightarrow}\mathit{nN}$, and introduce the effect of final-state interactions. The primary nonmesonic weak hyperon-nucleon decay process is described through the independent-particle shell model. We work within the $2p1h$ subspace of final states, assuming a simple approach for finite nuclei based on the eikonal approximation. An optical potential including the nucleon-nucleus isoscalar and isovector interactions is introduced to take into account the minimum nuclear-medium effects. The calculated values for ${}_{\ensuremath{\Lambda}}^{5}\mathrm{He}$ and ${}_{\ensuremath{\Lambda}}^{12}\mathrm{C}$ show that our treatment of final-state interactions, even those considered as restricted to a subspace of states, brings the independent-particle model results closer to the experimental data.

Hadrons in Medium — Theory Confronts Experiment

In this talk we briefly summarize our theoretical understanding of in-medium selfenergies of hadrons. With the special case of the ω meson we demonstrate that earlier calculations that predicted a significant lowering of the m ass in medium are based on an incorrect treatment of the model Lagrangian; more consistent calculations lead to a significant broadening, but hardly any mass shift. We stress that the experimental reconstruction of hadron spectral functions from measured decay products always requires knowledge of the decay branching ratios which may also be strongly mass-dependent. It also requires a quantitatively reliable treatment of final state interactions which has to be part of any reliable theory.

Two-body electrodisintegration ofHe3at high momentum transfer

The $^3$He$(e,e^\prime p)$$d$ reaction is studied using an accurate three-nucleon bound state wave function, a model for the electromagnetic current operator including one- and two-body terms, and the Glauber approximation for the treatment of final state interactions. In contrast to earlier studies, the profile operator in the Glauber expansion is derived from a nucleon-nucleon scattering amplitude, which retains its full spin and isospin dependence and is consistent with phase-shift analyses of two-nucleon scattering data. The amplitude is boosted from the center-of-mass frame, where parameterizations for it are available, to the frame where rescattering occurs. Exact Monte Carlo methods are used to evaluate the relevant matrix elements of the electromagnetic current operator. The predicted cross section is found to be in quantitative agreement with the experimental data for values of the missing momentum $p_{\rm m}$ in the range (0--700) MeV/c, but underestimates the data at $p_{\rm m} \simeq 1$ GeV/c by about a factor of two. However, the longitudinal-transverse asymmetry, measured up to $p_{\rm m} \simeq$ 600 MeV/c, is well reproduced by theory. A critical comparison is carried out between the results obtained in the present work and those of earlier studies.

Polarization Transfer inH4e(e→,e′p→)H3: Is the RatioGEp/GMpModified in the Nuclear Medium?

Polarization observables in the (4)He(e-->,e'p-->)(3)H reaction are calculated using accurate three- and four-nucleon bound-state wave functions, a realistic model for the nuclear electromagnetic current operator, and a treatment of final-state interactions with an optical potential. In contrast to earlier studies, no significant discrepancies are found between theory and experiment both for the ratio of transverse to longitudinal polarization transfers and for the induced polarization, when free-nucleon electromagnetic form factors are used in the current operator. The present results challenge the current interpretation of the experimental data in terms of medium-modified form factors.

Polarization transfer in the 4He(e-->,e'p-->)3H reaction up to Q2=2.6 (GeV/c)2.

We have measured the proton recoil polarization in the 4He(e-->,e(')p-->)4H reaction at Q(2)=0.5, 1.0, 1.6, and 2.6 (GeV/c)(2). The measured ratio of polarization transfer coefficients differs from a fully relativistic calculation, favoring the inclusion of a medium modification of the proton form factors predicted by a quark-meson coupling model. In addition, the measured induced polarizations agree reasonably well with the fully relativistic calculation indicating that the treatment of final-state interactions is under control.

Final state interaction effects in [formula omitted

Asymmetries in quasi-elastic 3He(e→,e′p) have been measured at a momentum transfer of 0.67 (GeV/c)2 and are compared to a calculation which takes into account relativistic kinematics in the final state and a relativistic one-body current operator. With an exact solution of the Faddeev equation for the 3He-ground state and an approximate treatment of final state interactions in the continuum good agreement is found with the experimental data.

Chiral perturbation theory, dispersion relations and final state interactions in K → ππ

We discuss the recent literature on the treatment of final state interactions in K → ππ. Various approaches are compared and particular emphasis is given to the possibility of combining dispersive methods with lattice input. Recent results on the dependence of various quantities on the quark masses at order p 6 in the chiral expansion are presented and the relevance for the lattice calculations is discussed.

Hard-core final state interaction effects in deep inelastic scattering

Hard-core final state interaction effects in the response function are investigated in the asymptotic limit of momentum transfer q → ∞. The relevant scattering contribution is displayed and a modification of the otherwise expected free response is obtained for Bose and Fermi systems. A comparison with other treatments of final state interactions is made.

Consistent microscopic study of the4He(e, e?d)d reaction

We have studied the4He(e,e′d)d reaction within a consistent microscopic cluster model. Our calculation reproduces theQ2-dependence of the Nikhef data, but overestimates its magnitude. A more detailed treatment of final state interactions seems to be important.

Y scaling and final state interactions in 3He

Two theoretical approaches to y-italic scaling based on different treatments of final state interactions are compared. Experimental data show scaling in both treatments; however, there is strong disagreement between data and the West prediction based on a Faddeev momentum distribution. Partial inclusion of final state interaction by Sick, Day, and McCarthy substantially improves the comparison with data. Dramatic sensitivity to the treatment of final state interaction suggests that existing theoretical analyses are not decisive.

Approximations for the treatment of final state interactions in nuclear knockout form factors

To investigate the role of final state interactions in knockout reactions, we study the transition form factor corresponding to the absorption of a scalar probe in a single particle model description of the nucleus. The numerical aspects of an approximation which treats at the same level initial and final state interactions are discussed. It provides fair agreement with the corresponding exact calculations for momenta of the ejected nucleon larger than 2 fm/sup -1/. Comparisons with various other approximations show that a careful treatment of the final state interaction is necessary to obtain a realistic estimate of the form factor.

Factorization of Deep Inelastic Final State Interactions in Quarkonium Models

We consider the deep inelastic process for a nonrelativistic quark confined by the po­ tential, allowing emissions of mesons for transitions from one level to the others of the quark bound states. We study the mechanisms by which the meson emission process (quark materialization) can be factorized out, and clarify it for some examples of the potential. These mechanisms are useful in understanding the similar problem in relativistic field theories. § I. Introduction Although the free parton model has succeeded in predicting many phenomeno­ logical features of deep inelastic processes, it contains the difficult problem that the basic assumption of the model, that the struck quark is essentially free, seem­ ingly contradicts the quark confinement. It is conventionally asserted that the effect of the final-state interactions by confinements can be factorized out from the whole amplitude and can reduce to the term representing unit probability. However, the previous investigations]) on the simple field theoretical model [ ¢ 3-multiperipheral model] do not lead to the above assertions; every diagram with final state interactions gives the vanishing contribution for Q--.oo. It is also ar­ gued in the covariant parton modeJ2l that softened field theories, producing the transverse momentum cutoff, give vanishing amplitudes for final state interactions. In this paper, we shall discuss the deep inelastic processes in a simple quantum mechanical system where a quark is confined inside the potential [Quarkonium] and the struck quark yet confined as an excited state can fall back into lower levels by meson emissions. We are not going to assert that the model is phenomenologically workable in the analyses of existing data of deep inelastic processes. Our aim is to get, through this simple solvable model, a c1 ue to the proper treatment of final state interactions. In our model, two types of the final state interactions exist: The one is clue to the potential and the other the quark materialization through the emissions of mesons. There have already been many investigations 31 ' 41 on the deep process in the quarkonium model. In all these, however, no consideration was put on the quark materialization. The latter is important in the field theoretical

Electrodisintegration of the Deuteron. II. Final-State Interactions

The effects of interactions between the outgoing nucleons on the cross sections for the inelastic electron-deuteron scattering process $e+d\ensuremath{\rightarrow}e+p+n$ are examined in detail. Results are presented as corrections to the theoretical cross sections which were calculated in a previous paper with a relativistic theory but neglecting final-state interactions. The changes are significant for the determination of the electromagnetic form factors of the neutron from the experimental cross sections. The method of the paper follows the treatment of final-state interactions given by Durand, extended to include the $D$ state of the deuteron and the coupling between final-state partial waves of the same total angular momentum and parity. The resulting expressions for the quasielastic peak cross sections are expected to be valid in the momentum-transfer range $0\ensuremath{\lesssim}{q}^{2}\ensuremath{\lesssim}1.0$ ${(\mathrm{B}\mathrm{e}\mathrm{V}/\mathit{c})}^{2}$. An alternative approach is suggested for the analysis of experiments at larger ${q}^{2}$ using an absorption model of the type which has been applied successfully to high-energy particle reactions.