Chiral 2π2\pi-exchange NN-potentials: Two-loop contributions

We calculate in heavy baryon chiral perturbation theory the local NN-potentials generated by the two-pion exchange diagrams at two-loop order. We give explicit expressions for the mass-spectra (or imaginary parts) of the corresponding isoscalar and isovector central, spin-spin and tensor NN-amplitudes. We find from two-loop two-pion exchange a sizeable isoscalar central repulsion which amounts to $62.3$MeV at $r=1.0$fm. There is a similarly strong isovector central attraction which however originates mainly from the third order low energy constants $\bar d_j$ entering the chiral $\pi N$-scattering amplitude. We also evaluate the one-loop $2\pi$-exchange diagram with two second order chiral $\pi \pi NN$-vertices proportional to the low energy constants $c_{1,2,3,4}$ as well as the first relativistic 1/M-correction to the $2\pi$-exchange diagrams with one such vertex. The diagrammatic results presented here are relevant components of the chiral NN-potential at next-to-next-to-next-to-leading order.Comment: 6 pages, 2 figure

Induced pseudoscalar form factor of the nucleon at two-loop order in chiral perturbation theory

We calculate the imaginary part of the induced pseudoscalar form factor of the nucleon $G_P(t)$ in the framework of two-loop heavy baryon chiral perturbation theory. The effect of the calculated three-pion continuum on the pseudoscalar constant $g_P = (m_\mu/2M) G_P(t=-0.877m_\mu^2)$ measurable in ordinary muon capture $\mu^-p\to \nu_\mu n$ turns out to be negligibly small. Possible contributions from counterterms at two-loop order are numerically smaller than the uncertainty of the dominant pion-pole term proportional to the pion-nucleon coupling constant $g_{\pi N}= 13.2\pm 0.2$. We conclude that a sufficiently accurate representation of the induced pseudoscalar form factor of the nucleon at low momentum transfers $t$ is given by the sum of the pion-pole term and the Adler-Dothan-Wolfenstein term: $G_P(t) = 4g_{\pi N} M f_\pi/ (m_\pi^2 -t)- 2g_A M^2 /3$, with $= (0.44 \pm 0.02)$ fm$^2$ the axial mean square radius of the nucleon.Comment: 6 pages, 2 figures, accepted for publication in Physical Review

Determination of the chiral coupling constants c3 and c4 in new pp and np partial-wave analyses

As a first result of two new partial-wave analyses, one of the pp and another one of the np scattering data below 500 MeV, we report a study of the long-range chiral two-pion exchange interaction which contains the chiral coupling constants c1, c3, and c4. By using as input a theoretical value for c1 we are able to determine in pp as well as in np scattering accurate values for c3 and c4. The values determined from the pp data and independently from the np data are in very good agreement, indicating the correctness of the chiral two-pion exchange interaction. The weighted averages are c3 = -4.78(10) / GeV and c4 = 3.96(22) / GeV, where the errors are statistical. The value of c3 is best determined from the pp data and that of c4 from the np data.Comment: 9 pages, 1 figure. Accepted for publication in Phys. Rev.

Chiral corrections to kaon-nucleon scattering lengths

We calculate the threshold T-matrices of kaon-nucleon and antikaon-nucleon scattering to one loop order in SU(3) heavy baryon chiral perturbation theory. To that order the complex-valued isospin-1 $\bar KN$ threshold T-matrix can be successfully predicted from the isospin-0 and 1 $KN$ threshold T-matrices. As expected perturbation theory fails to explain the isospin-0 $\bar KN$ threshold T-matrix which is completely dominated by the nearby subthreshold $\Lambda^*(1405)$-resonance. Cancelations of large terms of second and third chiral order are observed as they seem to be typical for SU(3) baryon chiral perturbation theory calculations. We also give the kaon and eta loop corrections to the $\pi N$ scattering lengths and we investigate $\pi\Lambda$ scattering to one-loop order. The second order s-wave low-energy constants are all of natural size and do not exceed 1 GeV$^{-1}$ in magnitude.Comment: 8 pages, 2 figures, published in Phys. Rev. C64, 045204 (2001), corrections of numerical prefactors in Eqs.(10,11,12

Spectral functions of isoscalar scalar and isovector electromagnetic form factors of the nucleon at two-loop order

We calculate the imaginary parts of the isoscalar scalar and isovector electromagnetic form factors of the nucleon up to two-loop order in chiral perturbation theory. Particular attention is paid on the correct behavior of Im $\sigma_N(t)$ and Im $G_{E,M}^V(t)$ at the two-pion threshold $t_0=4 m_\pi^2$ in connection with the non-relativistic 1/M-expansion. We recover the well-known strong enhancement near threshold originating from the nearby anomalous singularity at $t_c = 4m_\pi^2-m_\pi^4/M^2 = 3.98 m_\pi^2$. In the case of the scalar spectral function Im $\sigma_N(t)$ one finds a significant improvement in comparison to the lowest order one-loop result. Higher order $\pi\pi$-rescattering effects are however still necessary to close a remaining 20%-gap to the empirical scalar spectral function. The isovector electric and magnetic spectral functions Im $G_{E,M}^V(t)$ get additionally enhanced near threshold by the two-pion-loop contributions. After supplementing their two-loop results by a phenomenological $\rho$-meson exchange term one can reproduce the empirical isovector electric and magnetic spectral functions fairly well.Comment: 10 pages, 6 figures, submitted to Physical Review

Baryon polarization in low-energy unpolarized meson-baryon scattering

We compute the polarization of the final-state baryon, in its rest frame, in low-energy meson--baryon scattering with unpolarized initial state, in Unitarized BChPT. Free parameters are determined by fitting total and differential cross-section data (and spin-asymmetry or polarization data if available) for $pK^-$, $pK^+$ and $p\pi^+$ scattering. We also compare our results with those of leading-order BChPT

Vector meson production and nucleon resonance analysis in a coupled-channel approach for energies m_N < sqrt(s) < 2 GeV I: pion-induced results and hadronic parameters

We present a nucleon resonance analysis by simultaneously considering all pion- and photon-induced experimental data on the final states gamma N, pi N, 2 pi N, eta N, K Lambda, K Sigma, and omega N for energies from the nucleon mass up to sqrt(s) = 2 GeV. In this analysis we find strong evidence for the resonances P_{31}(1750), P_{13}(1900), P_{33}(1920), and D_{13}(1950). The omega N production mechanism is dominated by large P_{11}(1710) and P_{13}(1900) contributions. In this first part, we present the results of the pion-induced reactions and the extracted resonance and background properties with emphasis on the difference between global and purely hadronic fits.Comment: 54 pages, 26 figures, discussion extended, typos corrected, references updated, to appear in Phys. Rev.

Radio emission and jets from microquasars

To some extent, all Galactic binary systems hosting a compact object are potential `microquasars', so much as all galactic nuclei may have been quasars, once upon a time. The necessary ingredients for a compact object of stellar mass to qualify as a microquasar seem to be: accretion, rotation and magnetic field. The presence of a black hole may help, but is not strictly required, since neutron star X-ray binaries and dwarf novae can be powerful jet sources as well. The above issues are broadly discussed throughout this Chapter, with a a rather trivial question in mind: why do we care? In other words: are jets a negligible phenomenon in terms of accretion power, or do they contribute significantly to dissipating gravitational potential energy? How do they influence their surroundings? The latter point is especially relevant in a broader context, as there is mounting evidence that outflows powered by super-massive black holes in external galaxies may play a crucial role in regulating the evolution of cosmic structures. Microquasars can also be thought of as a form of quasars for the impatient: what makes them appealing, despite their low number statistics with respect to quasars, are the fast variability time-scales. In the first approximation, the physics of the jet-accretion coupling in the innermost regions should be set by the mass/size of the accretor: stellar mass objects vary on 10^5-10^8 times shorter time-scales, making it possible to study variable accretion modes and related ejection phenomena over average Ph.D. time-scales. [Abridged]Comment: 28 pages, 13 figures, To appear in Belloni, T. (ed.): The Jet Paradigm - From Microquasars to Quasars, Lect. Notes Phys. 794 (2009