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Register a new userExtracting the sigma-term from low-energy pion-nucleon scattering
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We present an extraction of the pion-nucleon ($pi N$) scattering lengths from low-energy $pi N$ scattering, by fitting a representation based on Roy-Steiner equations to the low-energy data base. We show that the resulting values confirm the scattering-length determination from pionic atoms, and discuss the stability of the fit results regarding electromagnetic corrections and experimental normalization uncertainties in detail. Our results provide further evidence for a large $pi N$ $sigma$-term, $sigma_{pi N}=58(5)$ MeV, in agreement with, albeit less precise than, the determination from pionic atoms.
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We have reanalyzed the $pi ^{pm} p$ scattering data at low energy in the Coulomb-nuclear interference region as measured by the CHAOS group at TRIUMF with the aim to determine the pion-nucleon $sigma$ term. The resulting value $sigma=(44pm 12)$ MeV, while in agreement with lattice QCD calculations and compatible with other recent analyses, is significantly lower than that from the GWU-TRIUMF analysis of 2002.
The pion-nucleon $sigma$-term can be stringently constrained by the combination of analyticity, unitarity, and crossing symmetry with phenomenological information on the pion-nucleon scattering lengths. Recently, lattice calculations at the physical point have been reported that find lower values by about $3sigma$ with respect to the phenomenological determination. We point out that a lattice measurement of the pion-nucleon scattering lengths could help resolve the situation by testing the values extracted from spectroscopy measurements in pionic atoms.
Fits of the p^4 covariant SU(2) baryon chiral perturbation theory to lattice QCD nucleon mass data from several collaborations for 2 and 2+1 flavors are presented. We consider contributions from explicit Delta(1232) degrees of freedom, finite volume and finite spacing corrections. We emphasize here our Nf=2+1 study. We obtain low-energy constants of natural size that are compatible with the rather linear pion-mass dependence of the nucleon mass observed in lattice QCD. We report a value for the pion-nucleon sigma term of 41(5)(4) MeV for the 2 flavor case and 52(3)(8) MeV for 2+1 flavors.
Based on our analysis of the contributions from the connected and disconnected contraction diagrams to the pion-kaon scattering amplitude, we provide the first determination of the low-energy constant $L_0^r$ in SU$(4|1)$ Partially-Quenched Chiral Perturbation Theory from data of the Extended Twisted Mass Collaboration, $L_0^r = 0.51(26)cdot 10^{-3}$ at $mu=1$ GeV.
During the workshop Compton Scattering off Protons and Light Nuclei: pinning down the nucleon polarisabilities (ECT*, Trento, Italy, 29 July -- 2 August 2013, http://www.ectstar.eu/node/98), recent developments had been reviewed in experimental and theoretical studies of real and virtual Compton scattering, static and generalized dipole scalar and spin polarisabilities of nucleons, as well as related phenomena in physics of muonic atoms. A vivid topic at the workshop was pathways towards the most precise extraction of the static polarisabilities from low-energy Compton cattering---including pertinent theoretical uncertainties. Being asked by our experimental colleagues, we prepared during the workshop a short letter with conclusions of the discussion, emphasising future prospects.
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