Measurements of the Generalized Electric and Magnetic Polarizabilities of the Proton at LowQ2Using the Virtual-Compton-Scattering Reaction

Abstract

The mean square polarizability radii of the proton have been measured for the first time in a virtualCompton-scattering experiment performed at the MIT-Bates out-of-plane scattering facility. Response functions and polarizabilities obtained from a dispersion analysis of the data at Q 2 0:057 GeV 2 =c 2 are in agreement with Op 3 heavy baryon chiral perturbation theory. The data support the dominance of mesonic effects in the polarizabilities. DOI: 10.1103/PhysRevLett.97.212001 PACS numbers: 13.60.Fz, 13.40.Gp, 14.20.Dh The electromagnetic polarizabilities of the nucleon provide a vital testing ground for theories of low-energy QCD and nucleon structure, and are of compelling experimental and theoretical interest [1]. In the case of atomic polarizabilities the electric polarizability is approximately equal to the atomic volume. By contrast, the electric polarizability of the nucleon is approximately 10 4 times smaller than the nucleon volume, demonstrating in a qualitative fashion the extreme stiffness of the nucleon relative to the atom. Although the electric and magnetic polarizabilities of the proton and are known with reasonable accuracy [2] from real Compton scattering (RCS), much less is known about the polarizability distributions inside the nucleon. To measure these distributions it is necessary to use the virtual-Compton-scattering (VCS) reaction [3], where the incident photon is virtual. At low Q 2 it is expected [4] that Q 2 should decrease with increasing Q 2 with a characteristic length scale given by the pion range. The first VCS experiments at Mainz [5] at Q 2 0:33 GeV 2 =c 2 and later at Jefferson Lab (JLab) [6] at Q 2 0:92 and 1:76 GeV 2 =c 2 established that Q 2 is falling off, but with a form inconsistent with a simple dipole shape [6]. By contrast, because of the destructive interference between paramagnetism and diamagnetism which is necessary to generate a small , Q 2 is predicted [4] to be relatively flat as a function of Q 2 with a 20% peaking near Q 2 0:1 GeV 2 =c 2 caused by a paramagnetic pion-loop contribution that increases with Q 2 . This Letter reports on a VCS experiment on the proton performed at the out-ofplane scattering facility at the MIT-Bates linear accelerator at Q 2 0:057 GeV 2 =c 2 . Data taken at this low Q 2 can provide a test of chiral perturbation theory (ChPT), and are sensitive to the mean square electric and magnetic polarizability radii. At this low value of Q 2 ChPT also predicts increased sensitivity to the polarizabilities Q 2 and Q 2 relative to the Mainz kinematics [4]. The relationship between VCS cross sections and the polarizabilities is most easily seen in the low-energy expansion (LEX) of the unpolarized VCS cross section [3],where q (q 0 ) is the incident (final) photon three-momenta in the photon-nucleon c.m. frame, " is the photon polarization, () is the c.m. polar (azimuthal) angle for the outgoing photon, and is a phase space factor. d 5 BHBorn is the cross section for the Bethe-Heitler Born amplitudes only, i.e., no nucleon structure, and is e...

Virtual Compton scattering and nucleon generalized polarizabilities

“…14. The first one is the MIT-Bates LEX point for P LT , lying at a large negative value. It is well understood in terms of a bias in the LEX fit [77,78], due to the competition of the lowest-order and higher-order GP terms of the low-energy expansion 18 . The DR fit in this experiment is obviously better behaved than the LEX fit, and gives a [34] appeared as very successful in describing the VCS observables, due to its good agreement with the measurements from the MAMI-I and MIT-Bates experiments.…”

“…The exclusive reaction is then identified using the missing mass squared of the undetected photon. Complementary information can be found in previous reviews [4][5][6][7][8][9]; details on apparatus and physics analyses can be found in the Thesis works [55][56][57][60][61][62][63][64][65][66][67][68][69][70][71][72][73] and the experimental publications [7,11,[74][75][76][77][78][79][80][81][82][83].…”

“…This experiment was also the first one to show that GP extractions both below and above the pion production threshold, using respectively the LEX and DR formalisms, gave consistent results. The MIT-Bates experiment [77,78] exploited out-of-plane kinematics more specifically, and made measurements at the smallest Q 2 so far (0.057 GeV 2 ), enabling the first estimation of the mean-square radius of the electric GP (see Sect. 4.6).…”

“…The effect of such systematic errors is thus greatly reduced by adopting this renormalization procedure. Every VCS experiment having low-q ′ cm data utilized them to test the absolute normalization of the cross section, and to renormalize it if needed [7,[74][75][76][77][78]83]. By this method, the overall normalization uncertainty was reduced to, e.g., ± 1% in the MAMI-I experiment [57,74] and in the MAMI-VI experiment [83].…”

“…Such a work was presented in Ref. [78], based on the two experimental data points: RCS and the MIT-Bates measurement at Q 2 = 0.057 GeV 2 . With the addition of the MAMI-VI measurements at Q 2 = 0.1 GeV 2 and the new RCS values of Ref.…”