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Register a new userThe Static Baryon Potential
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C. Alexandrou n
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Using state of the art lattice techniques we investigate the static baryon potential. We employ the multi-hit procedure for the time links and a variational approach to determine the ground state with sufficient accuracy that, for distances up to $sim 1.2$ fm, we can distinguish the $Y$- and $Delta$- Ansatze for the baryonic Wilson area law. Our analysis shows that the $Delta$-Ansatz is favoured. This result is also supported by the gauge-invariant nucleon wave function which we measure for the first time.
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A qualitative discussion on the range of the potentials as they result from the phenomenological meson-exchange picture and from lattice simulations by the HAL QCD Collaboration is presented. For the former pion- and/or $eta$-meson exchange are considered together with the scalar-isoscalar component of correlated $pipi /K bar K$ exchange. It is observed that the intuitive expectation for the behavior of the baryon-baryon potentials for large separations, associated with the exchange of one and/or two pions, does not always match with the potentials extracted from the lattice simulations. Only in cases where pion exchange provides the longest ranged contribution, like in the $Xi N$ system, a reasonable qualitative agreement between the phenomenological and the lattice QCD potentials is found for baryon-baryon separations of $r gtrsim 1$ fm. For the $Omega N$ and $OmegaOmega$ interactions where isospin conservation rules out one-pion exchange a large mismatch is observed, with the potentials by the HAL QCD Collaboration being much longer ranged and much stronger at large distances as compared to the phenomenological expectation. This casts some doubts on the applicability of using these potentials in few- or many-body systems.
We perform path integral for a quark (antiquark) in the presence of an arbitrary space-dependent static color potential A^a_0(x)(=-int dx E^a(x)) with arbitrary color index a=1,2,...8 in SU(3) and obtain an exact non-perturbative expression for the generating functional. We show that such a path integration is possible even if one can not solve the Dirac equation in the presence of arbitrary space-dependent potential. It may be possible to further explore this path integral technique to study non-perturbative bound state formation.
We report an analysis of the octet baryon masses using the covariant baryon chiral perturbation theory up to next-to-next-to-next-to-leading order with and without the virtual decuplet contributions. Particular attention is paid to the finite-volume corrections and the finite lattice spacing effects on the baryon masses. A reasonable description of all the publicly available $n_f=2+1$ lattice QCD data is achieved.Utilyzing the Feynman-Hellmann theorem, we determine the nucleon sigma terms as $sigma_{pi N}=55(1)(4)$ MeV and $sigma_{sN}=27(27)(4)$ MeV.
We report on a recent study of the ground-state octet baryon masses and sigma terms in covariant baryon chiral perturbation theory with the extended-on-mass-shell scheme up to next-to-next-to-next-to-leading order. To take into account lattice QCD artifacts, the finite-volume corrections and finite lattice spacing discretization effects are carefully examined. We performed a simultaneous fit of all the $n_f = 2+1$ lattice octet baryon masses and found that the various lattice simulations are consistent with each other. Although the finite lattice spacing discretization effects up to $mathcal{O}(a^2)$ can be safely ignored, but the finite volume corrections cannot even for configurations with $M_phi L>4$. As an application, we predicted the octet baryon sigma terms using the Feynman-Hellmann theorem. In particular, the pion- and strangeness-nucleon sigma terms are found to be $sigma_{pi N} = 55(1)(4)$ MeV and $sigma_{sN} = 27(27)(4)$ MeV, respectively.
We study the scattering of a pseudoscalar meson off one ground state octet baryon in covariant baryon chiral perturbation theory (BChPT) up to the next-to-next-to-leading order. The inherent power counting breaking terms are removed within extended-on-mass-shell scheme. We perform the first combined study of the pion-nucleon and kaon-nucleon scattering data in covariant BChPT and show that it can provide a reasonable description of the experimental data. In addition, we find that it is possible to fit the experimental baryon masses and the pion-nucleon and kaon-nucleon scattering data simultaneously at this order, thus providing a consistent check on covariant BChPT. We compare the scattering lengths of all the pertinent channels with available experimental data and those of other approaches. In addition, we have studied the leading order contributions of the virtual decuplet and found that they can improve the description of the $pi N$ phase shifts near the $Delta(1232)$ peak, while they have negligible effects on the description of the $K N$ phase shifts.
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