Interplay of the Chiral and Large N_c Limits in pi N Scattering

Light-quark hadronic physics admits two useful systematic expansions, the chiral and 1/N_c expansions. Their respective limits do not commute, making such cases where both expansions may be considered to be especially interesting. We first study pi N scattering lengths, showing that (as expected for such soft-pion quantities) the chiral expansion converges more rapidly than the 1/N_c expansion, although the latter nevertheless continues to hold. We also study the Adler-Weisberger and Goldberger-Miyazawa-Oehme sum rules of pi N scattering, finding that both fail if the large N_c limit is taken prior to the chiral limit.Comment: 10 pages, ReVTe

Residual interaction effects on deeply bound pionic states in Sn and Pb isotopes

We have studied the residual interaction effects theoretically on the deeply bound pionic states in Pb and Sn isotopes. We need to evaluate the residual interaction effects carefully in order to deduce the nuclear medium effects for pion properties, which are believed to provide valuable information on nuclear chiral dynamics. The s- and p-wave $\pi-N$ interactions are used for the pion-nucleon residual interactions. We show that the complex energy shifts are around [(10-20)+i(2-7)]keV for 1s states in Sn, which should be taken into account in the analyses of the high precision data of deeply bound pionic $1s$ states in Sn isotopes.Comment: REVTEX4, 6 pages, 5 tables, Submitted to Phys. Rev. C, Some explanations are added in Version

Quasinormal distributions and expansion at the mode

The Gram-Charlier series of type A is discussed in terms of deviants which are related to moments in a way similar to the way Hermite polynomials are related to the powers. Distribution functions are also expressed in terms of the mode and moments (cumulants or deviants), which are useful expansions when the distributions are approximately normal. It is shown that such expansions as well as the Gram-Charlier series are valid asymptotically for discrete distributions defined on the semiinfinite interval [0, ∞].Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/45129/1/10955_2005_Article_BF01010217.pd

Relativistic O(q4)O(q^4) two-pion exchange nucleon-nucleon potential: configuration space

We have recently performed a relativistic $O(q^4)$ chiral expansion of the two-pion exchange $NN$ potential, and here we explore its configuration space content. Interactions are determined by three families of diagrams, two of which involve just $g_A$ and $f_{\pi}$, whereas the third one depends on empirical coefficients fixed by subthreshold $\pi N$ data. In this sense, the calculation has no adjusted parameters and gives rise to predictions, which are tested against phenomenological potentials. The dynamical structure of the eight leading non-relativistic components of the interaction is investigated and, in most cases, found to be clearly dominated by a well defined class of diagrams. In particular, the central isovector and spin-orbit, spin-spin, and tensor isoscalar terms are almost completely fixed by just $g_A$ and $f_{\pi}$. The convergence of the chiral series in powers of the ratio (pion mass/nucleon mass) is studied as a function of the internucleon distance and, for $r>$ 1 fm, found to be adequate for most components of the potential. An important exception is the dominant central isoscalar term, where the convergence is evident only for $r>$ 2.5 fm. Finally, we compare the spatial behavior of the functions that enter the relativistic and heavy baryon formulations of the interaction and find that, in the region of physical interest, they differ by about 5%.Comment: 27 pages, 33 figure

Elastic scattering of low energy pions by nuclei and the in-medium isovector pi N amplitude

Measurements of elastic scattering of 21.5 MeV pi+ and pi- by Si, Ca, Ni and Zr were made using a single arm magnetic spectrometer. Absolute calibration was made by parallel measurements of Coulomb scattering of muons. Parameters of a pion-nucleus optical potential were obtained from fits to all eight angular distributions put together. The `anomalous' s-wave repulsion known from pionic atoms is clearly observed and could be removed by introducing a chiral-motivated density dependence of the isovector scattering amplitude, which also greatly improved the fits to the data. The empirical energy dependence of the isoscalar amplitude also improves the fits to the data but, contrary to what is found with pionic atoms, on its own is incapable of removing the anomaly.Comment: 20 pages, 5 figures, 5 tables. V2 added details on uncertainties,extended discussion. To appear in PR

Precision spectroscopy of pionic 1s states of Sn nuclei and evidence for partial restoration of chiral symmetry in the nuclear medium

Deeply bound 1s states of $\pi^-$ in $^{115,119,123}$Sn were preferentially observed using the Sn($d$,$^3$He) pion-transfer reaction under the recoil-free condition. The 1s binding energies and widths were precisely determined, and were used to deduce the isovector parameter of the s-wave pion-nucleus potential to be $b_1 =-0.115\pm 0.007 ~m_{\pi}^{-1}$. The observed enhancement of $|b_1|$ over the free $\pi N$ value ($b_1^{\rm free}/b_1 = 0.78 \pm 0.05$) indicates a reduction of the chiral order parameter, $f^{*}_{\pi} (\rho)^2/f_{\pi}^2 \approx 0.64$, at the normal nuclear density, $\rho = \rho_0$.Comment: 4 pages including 3 postscript figures, RevTeX 4 with multirow.sty, submitted to Physical Review Letter

Cyclooxygenase-2 overexpression correlates with tumour recurrence, especially haematogenous metastasis, of colorectal cancer

Epidemiological studies have demonstrated that nonsteroidal anti-inflammatory drugs (NSAIDs), known to inhibit cyclooxygenase (COX), reduce the risk of colorectal cancer. COX is a key enzyme in prostaglandin biosynthesis, and two isoforms of COX, COX-1 and COX-2, have been identified. Recently COX-2 has been reported to frequently overexpress in colorectal neoplasms and to play a role in colorectal tumorigenesis and tumour progression. In this study, using immunohistochemistry, we examined COX-2 expression in advanced human colorectal cancer and its correlation with clinicopathological features. COX-2 expression was observed mainly in the cytoplasm of cancer cells in all the specimens examined, but some stromal cells and endothelial cells were also stained. According to the grade of COX-2 expression of the cancer cells, patients were divided into high- and low-COX-2 expression groups. High-COX-2 expression significantly correlated with tumour recurrence, especially haematogenous metastasis. These results suggest that a selective COX-2 inhibitor can be a novel class of therapeutic agents not only for tumorigenesis but also for haematogenous metastasis of cololectal cancer. To our knowledge, this is the first report on the correlation between COX-2 overexpression and recurrence of colorectal cancer. © 2000 Cancer Research Campaig

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

Charge-Independence Breaking in the Two-Pion-Exchange Nucleon-Nucleon Force

Charge-independence breaking due to the pion-mass difference in the (chiral) two-pion-exchange nucleon-nucleon force is investigated. A general argument based on symmetries is presented that relates the charge-symmetric part of that force to the proton-proton case. The static potential linear in that mass difference is worked out as an explicit example by means of Feynman diagrams, and this confirms the general argument.Comment: 10 pages, latex, 1 figure -- epsfig.sty required -- To appear in Phys. Rev.

Equivalence of Nonstatic Two-Pion-Exchange Nucleon-Nucleon Potentials

Off-shell aspects of the one-pion-exchange potential and their relationship to different forms of the nonstatic (subleading-order) chiral two-pion-exchange nucleon-nucleon potential are discussed. Various types of off-shell behavior are categorized and numerous examples are given. Recently derived potentials based on chiral approaches are supplemented by a rather general form of the two-pion-exchange potential derived using old-fashioned methods. The latter is closely related to a general form of one-pion-exchange relativistic corrections and nonstatic two-pion-exchange three-nucleon forces developed long ago.Comment: 16 pages, latex -- Phys. Rev. C (to appear) -- Published versio