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Register a new userA model for pion-pion scattering in large-N QCD
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Following up on recent work by Caron-Huot et al. we consider a generalization of the old Lovelace-Shapiro model as a toy model for Pi-Pi scattering satisfying (most of) the properties expected to hold in (t Hoofts) large-N limit of massless QCD. In particular, the model has asymptotically linear and parallel Regge trajectories at positive t, a positive leading Regge intercept $alpha_0 < 1$, and an effective bending of the trajectories in the negative-t region producing a fixed branch point at J=0 for $t < t_0 < 0$. Fixed (physical) angle scattering can be tuned to match the power-like (including logarithmic corrections) behavior predicted by perturbative QCD: $A(s,t) ~ s^{-beta} log(s)^{-gamma} F(theta)$. Tree-level unitarity (i.e. positivity of residues for all values of s and J) imposes strong constraints on the allowed region in the alpha_0-beta-gamma parameter space, which nicely includes a physically interesting region around $alpha_0 = 0.5$, $beta = 2$ and $gamma = 3$. The full consistency of the model would require an extension to multi-pion processes, a program we do not undertake in this paper.
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In recent years, high-accuracy data for pionic hydrogen and deuterium have become the primary source of information on the pion-nucleon scattering lengths. Matching the experimental precision requires, in particular, the study of isospin-breaking corrections both in pion-nucleon and pion-deuteron scattering. We review the mechanisms that lead to the cancellation of potentially enhanced virtual-photon corrections in the pion-deuteron system, and discuss the subtleties regarding the definition of the pion-nucleon scattering lengths in the presence of electromagnetic interactions by comparing to nucleon-nucleon scattering. Based on the pi^{+/-} p channels we find for the virtual-photon-subtracted scattering lengths in the isospin basis a^{1/2}=(170.5 +/- 2.0) x 10^{-3} mpi^{-1} and a^{3/2}=(-86.5 +/- 1.8) x 10^{-3} mpi^{-1}.
We present a lattice QCD study of $Npi$ scattering in the positive-parity nucleon channel, where the puzzling Roper resonance $N^*(1440)$ resides in experiment. The study is based on the PACS-CS ensemble of gauge configurations with $N_f=2+1$ Wilson-clover dynamical fermions, $m_pi simeq 156~$MeV and $Lsimeq 2.9~$fm. In addition to a number of $qqq$ interpolating fields, we implement operators for $Npi$ in $p$-wave and $Nsigma$ in $s$-wave. In the center-of-momentum frame we find three eigenstates below 1.65 GeV. They are dominated by $N(0)$, $N(0)pi(0)pi(0)$ (mixed with $N(0)sigma(0)$) and $N(p)pi(-p)$ with $psimeq 2pi/L$, where momenta are given in parentheses. This is the first simulation where the expected multi-hadron states are found in this channel. The experimental $Npi$ phase-shift would -- in the approximation of purely elastic $Npi$ scattering -- imply an additional eigenstate near the Roper mass $m_Rsimeq 1.43~$GeV for our lattice size. We do not observe any such additional eigenstate, which indicates that $Npi$ elastic scattering alone does not render a low-lying Roper. Coupling with other channels, most notably with $Npipi$, seems to be important for generating the Roper resonance, reinforcing the notion that this state could be a dynamically generated resonance. Our results are in line with most of previous lattice studies based just on $qqq$ interpolators, that did not find a Roper eigenstate below $1.65~$GeV. The study of the coupled-channel scattering including a three-particle decay $Npipi$ remains a challenge.
We study the coupled pion-nucleon system (negative parity, isospin 1/2) based on a lattice QCD simulation for nf=2 mass degenerate light quarks. Both, standard 3-quarks baryon operators as well as meson-baryon (4+1)-quark operators are included. This is an exploratory study for just one lattice size and lattice spacing and at a pion mass of 266 MeV. Using the distillation method and variational analysis we determine energy levels of the lowest eigenstates. Comparison with the results of simple 3-quark correlation studies exhibits drastic differences and a new level appears. A clearer picture of the negative parity nucleon spectrum emerges. For the parameters of the simulation we may assume elastic s-wave scattering and can derive values of the phase shift.
We study the contributions from the connected and disconnected contraction diagrams to the pion-kaon scattering amplitude within the framework of SU$(4|1)$ partially-quenched chiral perturbation theory. Combining this with a finite-volume analysis, we demonstrate that a lattice calculation of the easier computable connected correlation functions is able to provide valuable information of the noisier disconnected correlation functions, and may serve as a theory guidance for the future refinement of the corresponding lattice techniques.
We study coherent pion production in neutrino-nucleus scattering in the energy region relevant to neutrino oscillation experiments of current interest. Our approach is based on a combined use of the Sato-Lee model of electroweak pion production on a nucleon and the Delta-hole model of pion-nucleus reactions. Thus we develop a model which describes pion-nucleus scattering and electroweak coherent pion production in a unified manner. Numerical calculations are carried out for the case of the 12C target. All the free parameters in our model are fixed by fitting to both total and elastic differential cross sections for pi-12C scattering. Then we demonstrate the reliability of our approach by confronting our prediction for the coherent pion photo-productions with data. Finally, we calculate total and differential cross sections for neutrino-induced coherent pion production, and some of the results are (will be) compared with the recent (forthcoming) data from K2K, SciBooNE and MiniBooNE. We also study effect of the non-locality of the Delta-propagation in the nucleus, and compare the elementary amplitudes used in different microscopic calculations.
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