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Register a new userElectromagnetic polarizabilities and the excited states of the nucleon
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Authors
Martin Schumacher
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The electromagnetic polarizabilities of the nucleon are shown to be essentially composed of the nonresonant $alpha_p(E_{0+})=+3.2$, $alpha_n(E_{0+})=+4.1$,the $t$-channel $alpha^t_{p,n}=-beta^t_{p,n}=+7.6$ and the resonant $beta_{p,n}(P_{33}(1232))=+8.3$ contributions (in units of $10^{-4}$fm$^3$. The remaining deviations from the experimental data $Deltaalpha_p=1.2pm 0.6$, $Deltabeta_p=1.2mp 0.6$, Deltaalpha_n=0.8pm 1.7$ and $Deltabeta_n=2.0mp 1.8$ are contributed by a larger number of resonant and nonresonant processes with cancellations between the contributions. This result confirms that dominant contributions to the electric and magnetic polarizabilities may be represented in terms of two-photon couplings to the $sigma$-meson having the predicted mass $m_sigma=666$ MeV and two-photon width $Gamma_{gammagamma}=2.6$ keV.
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The energies of the excited states of the Nucleon, $Delta$ and $Omega$ are computed in lattice QCD, using two light quarks and one strange quark on anisotropic lattices. The calculation is performed at three values of the light quark mass, corresponding to pion masses $m_{pi}$ = 392(4), 438(3) and 521(3) MeV. We employ the variational method with a large basis of interpolating operators enabling six energies in each irreducible representation of the lattice to be distinguished clearly. We compare our calculation with the low-lying experimental spectrum, with which we find reasonable agreement in the pattern of states. The need to include operators that couple to the expected multi-hadron states in the spectrum is clearly identified.
We review recent developments in the theoretical investigation of the nucleon polarizabilities. We first report on the static polarizabilities as measured in real Compton scattering, comparing and interpreting the results from various theoretical approaches. In a second step, we extend the discussion to the generalized polarizabilities which can be accessed in virtual Compton scattering, showing how the information encoded in these quantities can provide a spatial interpretation of the induced polarization densities in the nucleon.
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