1.Preliminaries 2.Digressing to spin-dependent sum rules 3.QED and Atoms 4.CQM and Nucleons Visualizing and quantifying quark correlations in the radiative excitations of the nucleon resonances S.B. Gerasimov Bogoliubov Laboratory of Theoretical Physics, JINR, Dubna EMIN-18, October 11, 2018 S.B. Gerasimov Visualizing and quantifying quark correlations in the radiative excitations
1.Preliminaries 2.Digressing to spin-dependent sum rules 3.QED and Atoms 4.CQM and Nucleons Table of contents 1.Preliminaries 2.Digressing to spin-dependent sum rules 3.QED and Atoms 4.CQM and Nucleons S.B. Gerasimov Visualizing and quantifying quark correlations in the radiative excitations
1.Preliminaries 2.Digressing to spin-dependent sum rules 3.QED and Atoms 4.CQM and Nucleons Preliminaries Prologue: Non-relativistic dipole sum rules for atomic and nuclear photoeffect. � ∞ d ω ω n σ E 1 ( ω ) σ n ( E 1) = thr Examples: n = − 2 → Kramers-Heisenberg sum rule (SR) for static electric-dipole polarizability of a given quantum system; n = − 1 → the bremsstrahlung-weighted SR, dependent of charged-”parton” correlation in a given system; n = 0 → the famous Thomas-Reiche-Kuhn SR, known as a precusor of not less as Quantum Mechanics itself. S.B. Gerasimov Visualizing and quantifying quark correlations in the radiative excitations
1.Preliminaries 2.Digressing to spin-dependent sum rules 3.QED and Atoms 4.CQM and Nucleons Digressing to spin-dependent sum rules The a.m.m. sum rules express a model-independent correspondence between static properties of a particle (or bound system of particles) and integrals over the photo-absorption spectrum. For particles with the spin S = 1 / 2 the sum rule for the anomalous magnetic moment κ reads � ∞ 2 π 2 ακ 2 d ν = ν ( σ p ( ν ) − σ a ( ν )) m 2 thr S.B. Gerasimov Visualizing and quantifying quark correlations in the radiative excitations
1.Preliminaries 2.Digressing to spin-dependent sum rules 3.QED and Atoms 4.CQM and Nucleons Digressing to spin-dependent sum rules The validity of the SR was checked in the lowest order of QED (SG, somewhere in the interval 1960-1963,unpubl.), S.G. and J.Moulin, Tests of Sum Rules for Photon Total Cross Sections in Quantum Electrodynamics and Mesodynamics // Nucl.Phys.B.1975.V.98.P.349. taking the Schwinger’s κ = α 2 π successful analytic and partially computer check of SR was done by Dicus and Vega (2000). Later on, for the physical reasons, we shall replace κ 2 entering different sum rules just by its integral expression in the GDH sum rule. S.B. Gerasimov Visualizing and quantifying quark correlations in the radiative excitations
1.Preliminaries 2.Digressing to spin-dependent sum rules 3.QED and Atoms 4.CQM and Nucleons QED and Atoms In what follows we will consider relativistic dipole moment fluctuation sum rules in the ”valence-parton” approximation, that is neglecting virtual particle-antiparticle configurations in the ground state of the considered systems or diffractively produced in the final states of photo-absorption reactions. S.B. Gerasimov Visualizing and quantifying quark correlations in the radiative excitations
1.Preliminaries 2.Digressing to spin-dependent sum rules 3.QED and Atoms 4.CQM and Nucleons QED and Atoms � ∞ 3 < D 2 > − κ 2 4 π 2 α [1 d ν 4 m 2 ] = ν σ tot ( ν ) thr or, using � ∞ 2 π 2 ακ 2 d ν = ν ( σ p ( ν ) − σ a ( ν )) m 2 thr we get another form to be used later � ∞ 4 π 2 α [1 d ν 3 < D 2 > ] = ν ( σ p ( ν ) thr S.B. Gerasimov Visualizing and quantifying quark correlations in the radiative excitations
1.Preliminaries 2.Digressing to spin-dependent sum rules 3.QED and Atoms 4.CQM and Nucleons QED and Atoms We apply derived sum rule to the system of the highly ionized atom Pb 81+ , thoroughly considered about half-century ago by J.S Levinger and co-workers:Phys.Rev.(1956-1957). Using the form of the sum rule with our included term κ atom ≃ µ el . , we reduced deviation between left- and right-hand sides of the sum rule to one-half percent. Numerically: � ∞ 4 π 2 α 1 3 < D 2 > [937 . 2 b ] − 4 π 2 α ( κ d ν 2 M ) 2 [67 . 9 b ] = ν σ tot ( ν )[874 b ] thr S.B. Gerasimov Visualizing and quantifying quark correlations in the radiative excitations
1.Preliminaries 2.Digressing to spin-dependent sum rules 3.QED and Atoms 4.CQM and Nucleons QED and Atoms The sum rule for the free electron in the α 2 -approximation was checked analytically in the work by E.A. Kuraev, L.N.Lipatov and N.P.Merenkov (1973). S.B. Gerasimov Visualizing and quantifying quark correlations in the radiative excitations
1.Preliminaries 2.Digressing to spin-dependent sum rules 3.QED and Atoms 4.CQM and Nucleons CQM and Nucleons In what follows we shall use the representation of the quark structure parameters in the transverse plane to get ”visualizable” picture of the valent quark correlations using experimentally measurable parameters of the resonance nucleon photo-excitation reactions. S.B. Gerasimov Visualizing and quantifying quark correlations in the radiative excitations
1.Preliminaries 2.Digressing to spin-dependent sum rules 3.QED and Atoms 4.CQM and Nucleons CQM and Nucleons Following formally to the p z → ∞ techniques derivation of the Cabibbo-Radicati or GDH sum rule we can obtain the relation � d ν 4 π 2 α (1 D 2 > − ( κ N 3 < � ) 2 ) = ν σ res tot ( ν ) , 2 m N We use the definitions 3 � ˆ Q q ( j ) � x ) d 3 x = � D = � x ˆ ρ ( � d j , j =1 3 � 2 ˆ Q q ( j ) � r 2 x 2 ˆ x ) d 3 x = � 1 = � ρ ( � d j j =1 S.B. Gerasimov Visualizing and quantifying quark correlations in the radiative excitations
1.Preliminaries 2.Digressing to spin-dependent sum rules 3.QED and Atoms 4.CQM and Nucleons CQM and Nucleons The defined operators Q q ( j ) and � d j are the electric charges and configuration variables of point-like interacting quarks in the infinite-momentum frame of the bound system. Finally, we relate the electric dipole moment operator correlators, sucessively for the proton, the neutron and the pure ”isovector-nucleon” part equal for both nucleons and the isovector part of the mean-squared radii operators, which all are sandwiched by the nucleon state vectors in the ”infinite - momentum frame”, with experimentally measurable data on the resonance parts of the photoabsorption cross sections on the proton and neutron presently known below ∼ 2 GeV. S.B. Gerasimov Visualizing and quantifying quark correlations in the radiative excitations
1.Preliminaries 2.Digressing to spin-dependent sum rules 3.QED and Atoms 4.CQM and Nucleons CQM and Nucleons The listed operator mean values are parametrized as follows R V = 1 1 > N ) = α − 1 2( < r 2 1 > P − < r 2 2 β J P = 1 D 2 > P = 8 27 α + 1 27 β + 8 27 γ − 8 3 < ˆ 27 δ J N = 1 D 2 > N = 2 27 α + 4 27 β + 2 27 γ − 8 3 < ˆ 27 δ J V = 1 D 2 > V = 2 3 α + 1 3 β + 2 3 γ − 4 3 < ˆ 3 δ S.B. Gerasimov Visualizing and quantifying quark correlations in the radiative excitations
1.Preliminaries 2.Digressing to spin-dependent sum rules 3.QED and Atoms 4.CQM and Nucleons CQM and Nucleons 2 > = < � 2 > = α , < � 2 > = β , < � where < � d 1 · � d 1 d 2 d 3 d 2 > = γ , < � d 1 · � d 3 > = < � d 2 · � d 3 > = δ indices ”1” and ”2” refer to the like quarks (i.e. to the u ( d )- and ”3” to the odd quark. S.B. Gerasimov Visualizing and quantifying quark correlations in the radiative excitations
1.Preliminaries 2.Digressing to spin-dependent sum rules 3.QED and Atoms 4.CQM and Nucleons CQM and Nucleons Important retreat: Are the full symmetry conditions: α = β and γ = δ acceptable? With these suggested hypotheses one obtains J P + 3 J N = J V ,then J P ( N ) = ( A S ± A V ) 2 , J V = A 2 V and solving equation for A V through A S , or vice-verse, one obtains the complex values which we suggest to consider unacceptable, as well as the hypothesis on full symmetry over all quark coordinates. S.B. Gerasimov Visualizing and quantifying quark correlations in the radiative excitations
1.Preliminaries 2.Digressing to spin-dependent sum rules 3.QED and Atoms 4.CQM and Nucleons CQM and Nucleons Evaluation of the relativistic electric dipole moment fluctuation and the iso-vector charge radius sum rules for the nucleon was carried out with the available compilation of the resonance pion-photoproduction data on the proton and neutron A P ( N ) and A P ( N ) and all integrals over photoexcited nucleon 1 / 2 3 / 2 resonances were taken in the narrow resonance approximation, when 4 π m n | A res 3 / 2(1 / 2) | 2 J res p ( a ) ≃ , m 2 res − m 2 n where m n ( res ) is the nucleon (or resonance)mass. S.B. Gerasimov Visualizing and quantifying quark correlations in the radiative excitations
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