Lifetime of (π+π−)(\pi^+\pi^-) Atom: Analysis of the Role of Strong Interactions

The expression for the $(\pi^+\pi^-)$ atom lifetime is derived within the Bethe-Salpeter approach. First-order perturbative corrections due to the contribution of strong interactions are taken into account. It is demonstrated that the atom lifetime can be expressed in terms of the solutions of the Coulombic problem (the wave function of the $1S$ state at the origin $\Psi_1(0)$, the binding energy of the $S$-state $E_1$), the difference of the $S$-wave $\pi\pi$ scattering lengths and the energy shift $\Delta E_1$ of the level due to the strong interactions: $1/(\tau_{1})\sim (a^0_0-a^2_0)^2 |\Psi_1(0)|^2 (1-(9\Delta E_1)/(8E_1))$Comment: 8 pages, LaTeX-fil

Chiral Prediction for the πN\pi N Scattering Length a−a^- to Order O(Mπ4){\cal O}(M_\pi^4)

We evaluate the S-wave pion--nucleon scattering length $a^-$ in the framework of heavy baryon chiral perturbation theory up--to--and--including terms of order $M_\pi^4$. We show that the order $M_\pi^4$ piece of the isovector amplitude at threshold, $T^-_{\rm thr}$, vanishes exactly. We predict for the isovector scattering length, $0.088 \, M_{\pi^+}^{-1} \le a^- \le 0.096 \, M_{\pi^+}^{-1}$.Comment: 5 pp, LaTeX file, 2 figures (appended as separate compressed tar file, amin.uu

Aspects of chiral pion-nucleon physics

The next-to-leading order chiral pion-nucleon Lagrangian contains seven finite low-energy constants. Two can be fixed from the nucleon anomalous magnetic moments and another one from the quark mass contribution to the neutron-proton mass splitting. We find a set of nine observables, which to one loop order do only depend on the remaining four dimension two couplings. These are then determined from a best fit. We also show that their values can be understood in terms of resonance exchange related to $\Delta$ excitation as well as vector and scalar meson exchange. In particular, we discuss the role of the fictitious scalar-isoscalar meson. We also investigate the chiral expansion of the two P-wave scattering volumes $P_1^-$ and $P_2^+$ as well as the isovector S-wave effective range parameter $b^-$. The one-loop calculation is in good agreement with the data. The difference $P_1^- - P_2^+$ signals chiral loop effects in the $\pi N$ P-waves. The calculated D- and F-wave threshold parameters compare well with the empirical values.Comment: 19 pp, LaTeX, enlarged and revised version, title changed, minor corrections in section 4, more detailed discussion in section 5, additional results in sec. 6 and the appendix, accepted for publication in Nucl. Phys.

Breit type equation for mesonic atoms

The finite size effects and relativistic corrections in pionic and kaonic hydrogen are evaluated by generalizing the Breit equation for a spin-0 - spin-1/2 amplitude with the inclusion of the hadron electromagnetic form factors. The agreement of the relativistic corrections to the energies of the mesonic atoms with other methods used to evaluate them is not exact, but reasonably good. The precision values of the energy shifts due to the strong interaction, extracted from data, are however subject to the hadronic form factor uncertainties.Comment: 11 pages Late

Chiral Dynamics of Deeply Bound Pionic Atoms

We present and discuss a systematic calculation, based on two-loop chiral perturbation theory, of the pion-nuclear s-wave optical potential. A proper treatment of the explicit energy dependence of the off-shell pion self-energy together with (electromagnetic) gauge invariance of the Klein-Gordon equation turns out to be crucial. Accurate data for the binding energies and widths of the 1s and 2p levels in pionic ^{205}Pb and ^{207}Pb are well reproduced, and the notorious "missing repulsion" in the pion-nuclear s-wave optical potential is accounted for. The connection with the in-medium change of the pion decay constant is clarified.Comment: preprint ECT*-02-16, 4 pages, 3 figure

Chiral corrections to the isovector double scattering term for the pion-deuteron scattering length

The empirical value of the real part of the pion-deuteron scattering length can be well understood in terms of the dominant isovector $\pi N$-double scattering contribution. We calculate in chiral perturbation theory all one-pion loop corrections to this double scattering term which in the case of $\pi N$-scattering close the gap between the current-algebra prediction and the empirical value of the isovector threshold T-matrix $T_{\pi N}^-$. In addition to closing this gap there is in the $\pi d$-system a loop-induced off-shell correction for the exchanged virtual pion. Its coordinate space representation reveals that it is equivalent to $2\pi$-exchange in the deuteron. We evaluate the chirally corrected double scattering term and the off-shell contribution with various realistic deuteron wave functions. We find that the off-shell correction contributes at most -8% and that the isovector double scattering term explains at least 90% of the empirical value of the real part of the $\pi d$-scattering length.Comment: 4 pages, 2 figures, to be published in The Physical Review

Renormalization of the isovector πN\pi N amplitude in pionic atoms

The extraction of the isovector s-wave pi N amplitude from pionic atoms is studied with special emphasis on uncertainties and their dependence on the assumptions made regarding the neutron density distributions in nuclei and on the size of the data base used . Only `global' analyses of pionic-atom data reveal a discrepancy between the extracted isovector s-wave pi N amplitude b_1=-0.108\pm0.007 m_\pi^{-1} and its free pi N counterpart b_1^{free}=-0.0885^{+0.0010}_{-0.0021} m_\pi ^{-1}, where the uncertainty in the neutron densities is included in the error analysis. The role of `deeply bound' pionic atom states is discussed and the reason for failure of these states to provide new information is explained.Comment: 17 pages, 4 figures, slightly extended, accepted by NP

Precise strength of th piNN coupling constant

We report here a preliminary value for the piNN coupling constant deduced from the GMO sumrule for forward piN scattering. As in our previous determination from np backward differential scattering cross sections we give a critical discussion of the analysis with careful attention not only to the statistical, but also to the systematic uncertainties. Our preliminary evaluation gives $g^2_c$(GMO) = 13.99(24).Comment: 4 pages, 1 figure, contribution to INPC/98, to be published in Conference Proceedings, Nuclear Physics A (Conference Proceedings

X-ray emission during the muonic cascade in hydrogen

We report our investigations of X rays emitted during the muonic cascade in hydrogen employing charge coupled devices as X-ray detectors. The density dependence of the relative X-ray yields for the muonic hydrogen lines (K_alpha, K_beta, K_gamma) has been measured at densities between 0.00115 and 0.97 of liquid hydrogen density. In this density region collisional processes dominate the cascade down to low energy levels. A comparison with recent calculations is given in order to demonstrate the influence of Coulomb deexcitation.Comment: 5 pages, Tex, 4 figures, submitted to Physical Review Letter