arXiv subjects

Martin Schumacher

Publications and source records attributed to Martin Schumacher.

28 records · Page 2Linked to original sources

arXiv2009

Polarizabilities of the nucleon and spin dependent photo-absorption

The polarizabilities $α$ (electric), $β$ (magnetic) and $γ_π$ (backward spin) of the nucleon are investigated in terms of degrees of freedom of the nucleon using recent results for the CGLN amplitudes and resonance couplings $A_{1/2}$ and $A_{3/2}$. The photon excitation strengths of the excited states are given in terms of partial integrated photoabsorption cross sections and resonant contributions of the Gerasimov-Drell-Hearn (GDH) sum rule. As a test of the present predictions, cross section differences $(σ_{3/2}-σ_{1/2})$ of the excited states are compared with data recently measured at MAMI (Mainz) and ELSA (Bonn), In order to explain differences between proton and neutron, radiative widths of the excited states are compared with nonrelativistic and relativistic predictions based on the SU(6) harmonic oscillator (HO) quark model, A complete list of partial contributions from the s-channel and the $t$-channel are given for the polarizabilities.

hep-ph↗

arXiv2008

Note on the magnetic moment of the nucleon

The Goldberger-Treiman relation $M=2π/\sqrt{3}f^{\rm cl}_π$ where $M$ is the constituent quark mass in the chiral limit (cl) and $f^{\rm cl}_π$ the pion decay constant in the chiral limit predicts constituent quark masses of $m_u=328.8\pm 1.1$ MeV and $m_d=332.3\pm 1.1$ MeV for the up and down quark, respectively, when $f^{\rm cl}_π=89.8\pm 0.3$ MeV is adopted. Treating the constituent quarks as bare Dirac particles the following zero order values $μ^{(0)}}_p=2.850\pm 0.009$ and $μ^{(0)}}_n= -1.889\pm 0.006$ are obtained for the proton and neutron magnetic moments, leading to deviations from the experimental data of 2.0% and 1.3%, respectively. These unavoidable deviations are discussed in terms of contributions to the magnetic moments proposed in previous work.

hep-ph↗

arXiv2008

Scalar mesons and polarizability of the nucleon

It is shown that the scalar mesons $σ$, $f_0(980)$ and $a_0(980)$ as $t$-channel exchanges quantitatively solve the problem of diamagnetism and give an explanation of the large missing part of the electric polarizability $α$ showing up when only the pion cloud is taken into account. The electric polarizability of the proton $α_p$ confirms a two-photon width of the $σ$ meson of $Γ_{σγγ}=(2.58\pm 0.26)$ keV.

hep-ph↗

arXiv2007

Properties of the $π^0$, $η$, $η'$, $σ$, $f_0(980)$ and $a_0(980)$ mesons and their relevance for the polarizabilities of the nucleon

The signs and values of the two-photon couplings $F_{Mγγ}$ of mesons $(M)$ and their couplings $g_{MNN}$ to the nucleon as entering into the $t$-channel parts of the difference of the electromagnetic polarizabilities $(α-β)$ and the backward angle spin polarizabilities $γ_π$ are determined. The excellent agreement achieved with the experimental polarizabilities of the proton makes it possible to make reliable predictions for the neutron. The results obtained are $α_n=13.4\pm 1.0$, $β_n=1.8\mp 1.0$ ($10^{-4}$ fm$^3$), and $γ^{(n)}_π=57.6\pm 1.8$ ($10^{-4}$ fm$^4$). New empirical information on the flavor wave functions of the $f_0(980)$ and the $a_0(980)$ meson is obtained.

hep-ph↗

arXiv2007

Electromagnetic polarizabilities and the excited states of the nucleon

The electromagnetic polarizabilities of the nucleon are shown to be essentially composed of the nonresonant $α_p(E_{0+})=+3.2$, $α_n(E_{0+})=+4.1$,the $t$-channel $α^t_{p,n}=-β^t_{p,n}=+7.6$ and the resonant $β_{p,n}(P_{33}(1232))=+8.3$ contributions (in units of $10^{-4}$fm$^3$. The remaining deviations from the experimental data $Δα_p=1.2\pm 0.6$, $Δβ_p=1.2\mp 0.6$, Δα_n=0.8\pm 1.7$ and $Δβ_n=2.0\mp 1.8$ 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 $σ$-meson having the predicted mass $m_σ=666$ MeV and two-photon width $Γ_{γγ}=2.6$ keV.

hep-ph↗

arXiv2007

Electromagnetic polarizabilities of the nucleon and properties of the $σ$-meson pole contribution

The $t$-channel contribution to the difference of electromagnetic polarizabilities of the nucleon, $(α-β)^t$, can be quantitatively understood in terms of a $σ$-meson pole in the complex $t$-plane of the invariant scattering amplitude $A_1(s,t)$ with properties of the $σ$ meson as given by the quark-level Nambu--Jona-Lasinio model (NJL). Equivalently, this quantity may be understood in terms of a cut in the complex $t$-plane where the properties of the $σ$ meson are taken from the $ππ-> σ-> ππ$, $γγ-> σ-> ππ$ and $N\bar{N} -> σ-> ππ$ reactions. This equivalence may be understood as a sum rule where the properties of the $σ$ meson as predicted by the NJL model are related to the $f_0(600)$ particle observed in the three reactions. In the following we describe details of the derivation of $(α-β)^t$ making use of predictions of the quark-level NJL model for the $σ$-meson mass.

hep-ph↗

arXiv2005

Polarizability of the Nucleon and Compton Scattering

Different approaches to describe Compton scattering and the polarizability of the nucleon have been discussed up to now. We show that the most appropriate ones are provided by non-subtracted dispersion theories of the fixed-$t$ and fixed-$θ$ types, where the properties of these two versions are complementary so that advantage can be taken from both of them. In the frame of fixed-$t$ dispersion theory it was possible to precisely reproduce experimental differential cross sections obtained for the proton in a wide angular range and for energies up to 1 GeV. At energies of the first resonance region and below, precise values for the electromagnetic polarizabilities and spin-polarizabilities have been determined for the proton and the neutron. The data show that diamagnetism is a prominent property of nucleon structure, where the underlying mechanism is a $t$-channel $σ$-meson exchange. A similar mechanism is responsible for the backward spin-polarizability where the relevant meson is the $π^0$. It is a challenge for further research to integrate the $σ$ and $π^0$ intermediate states into a consistent description of the structure of the nucleon.

hep-ph↗

arXiv2005

Compton Scattering by the Nucleon

The status of Compton scattering by the nucleon at energies of the first and second resonance is summarized. In addition to a general test of dispersion theories and a precise determination of polarizabilities, the validities of four fundamental sum rules are explored. {\it Recommended} averages of experimental values for the electromagnetic polarizabilities and spin-polarizabilities of the nucleon are determined: $α_p=12.0\pm 0.6$, $β_p=1.9\mp 0.6$, $α_n= 12.5 \pm 1.7$, $β_n= 2.7 \mp 1.8$ (unit $10^{-4}$fm$^3$), $γ^{(p)}_π= -38.7 \pm 1.8$, $γ^{(n)}_π= 58.6 \pm 4.0$ (unit $10^{-4}$fm$^4$).

nucl-ex↗

arXiv2003

Spin polarizabilities and polarizabilities of the nucleon studied by free and quasi-free Compton scattering at MAMI (Mainz)

In addition to the E2/M1 ratio of the N->$Δ$ transition, the electromagnetic polarizabilities and spin-polarizabilities are important structure constants of the nucleon which serve as sensitive tests of chiral perturbation theory and of models of the nucleon. Recently, these quantities have been investigated experimentally at MAMI (Mainz) by high-precision Compton scattering using hydrogen and deuterium targets, where for the latter the method of quasi-free scattering has been applied.

nucl-ex↗

arXiv2002

Studies on the electromagnetic structure of the nucleon by free and quasi-free Compton scattering at MAMI (Mainz)

Using hydrogen and deuterium targets, Compton scattering by the proton and neutron have been studied at the tagged photon beam of the MAMI (Mainz) accelerator using different experimental setups. The theoretical tools for the analysis of the experimental data have been investigated, as there are the nonsubtracted dispersion theory and the theory of quasi-free reactions on the proton and neutron bound in the deuteron. Experimental Compton scattering data are understood in the first and second resonance region with good precision. Precise electromagnetic polarizabilities and spin polarizabilities for the proton and neutron have been determined.

nucl-ex↗