Gerasimov-Drell-Hearn Sum Rule Research Articles

A gamma ray detector with lead-scintillator tiles and WLS fiber readout for the experiment at SPring-8 to study the GDH sum rule

A prototype gamma ray detector for the detection of π 0 in the proposed experiment at SPring-8 to study the Gerasimov–Drell–Hearn (GDH) sum rule (GDH experiment) has been built and tested. The detector is fabricated with lead-scintillator tiles and wave length shifter fiber readout. This detector will be placed inside the bore of the superconducting magnet which supplies the polarized target with a 2.5 T magnetic field. High-detection efficiency (above 85%) for the gamma rays is the most important requirement for this detector to be employed in the proposed experiment. It has been tested with minimum ionizing particles, electrons and gamma rays. The results of the tests in comparison with some Monte Carlo simulations are presented. The evaluated efficiency for gamma rays ranging in energy above 50 MeV is higher than 90%.

The Gerasimov-Drell-Hearn Sum Rule and the Spin Structure of the Proton

We present an overview of the present theoretical status of the Gerasimov-Drell-Hearn (GDH) sum rule. It is emphasized the importance of near threshold s-wave photoproduction contributions to the sum rule. We also discuss the experimental verification of the sum rule, with particular emphasis on the recent experiment at the Mainz Microtron (MAMI). The spin polarizabilities and the generalized GDH sum rule, which are of interest to issues related to the spin of the proton as measured at high energies, are discussed.

Threshold contribution to the Gerasimov–Drell–Hearn sum rule in 3He

Measurements of the cross section, vector and tensor analyzing powers, and gamma-ray polarization in the radiative capture reactions D(p,γ)3He and p(d,γ)3He at cm. energies in the range 0–53 keV allow the determination of the reduced matrix elements (RMEs) relevant for these transitions. The RMEs provide values of the doublet and quartet Ml cross sections, as well as the asymptotic D-to-S state ratio. These quantities are in good agreement with theoretical predictions. The RMEs can also be used to compute the value of the integral which determines the Gerasimov-Drell-Hearn sum rule for 3He in the energy region of our experiment. The results are compared with the predictions of an ab initio microscopic three-body model calculation. The theoretical predictions for the value of this integral based on a ”nucleons-only” assumption are an order-of-magnitude smaller than experiment. The discrepancy is reduced to about a factor of two when meson-exchange currents are taken into account.

Generalized Drell–Hearn–Gerasimov sum rule

Generalized Drell–Hearn–Gerasimov sum rule

Q2-Dependence of the Bjorken Sum Rule in the Resonance Region

Q2-evolution of the Bjorken sum rule in the resonance region is studied. The roles of the Roper resonance N*(1440) estimated by the constituent quark model and by the hybrid model are stressed. Moreover, the Q2- dependence of the Gerasimov–Drell-Hearn sum rule contributed by the resonances is also discussed.

Nucleon spin structure functions in the resonance region with constituent quark models

Q 2 -evolution of the nucleon spin structure functions g 1 , g 2 and the generalized Gerasimov–Drell–Hearn sum rule in the small- Q 2 region are investigated by considering the resonance contributions based on nonrelativistic constituent quark model and on relativistic four-dimensional harmonic oscillator model, respectively. Results of the two models are compared and the relativistic effects are discussed. Moreover, influences of the longitudinal transitions of the resonances on the sum rules of the nucleon spin structure functions are addressed.

A compact solid-state detector for small angle particle tracking

MIcrostrip Detector Array System (MIDAS) is a compact silicon-tracking telescope for charged particles emitted at small angles in intermediate energy photonuclear reactions. It was realized to increase the angular acceptance of the DAPHNE detector and used in an experimental program to check the Gerasimov–Drell–Hearn sum rule at the Mainz electron microtron (MAMI). MIDAS provides a trigger for charged hadrons, p/π ± identification and particle tracking in the region 7°< ϑ<16°. In this paper we present the main characteristics of MIDAS and its measured performances.

Gravitons and the Drell–Hearn–Gerasimov sum rule

One-loop diagrams containing a graviton provide a finite contribution to the anomalous magnetic moment a ℓ of a lepton, whether or not the graviton propagates in n large extra compact dimensions. In the present work, the tree graph photoproduction of a graviton, integrated up to an arbitrary cutoff, is shown to violate the Drell–Hearn–Gerasimov sum rule for a ℓ 2. The possibility of resurrecting the sum rule from high energy contributions originating in string excitations is discussed in a qualitative manner, and various problems associated with such a program are pointed out.

Parameterisation of [ σ1/2− σ3/2] for Q2≥0 and non-resonance contribution to the GDH sum rule

A description of the virtual photon absorption cross section difference σ 1/2−σ 3/2 for the proton and neutron is obtained with a parameterisation based on a Regge type approach. The parametrisation is obtained from global fits to the cross section data derived from the spin asymmetries measured in deep inelastic scattering of longitudinally polarised leptons from polarised 1H, 3He and 2H targets in the range 0.3 GeV 2< Q 2<70 GeV 2 and 4 GeV 2< W 2<300 GeV 2. The fits give a reliable description of the data and provide predictions for the photo-production through a smooth Q 2-transition. The contribution above the resonance region to the Gerasimov–Drell–Hearn sum rule for real and virtual photons has been evaluated. For the real photons this contribution accounts for a large fraction of the discrepancy between the sum rule expectations and the single pion photo-production analysis estimates.

Q2-dependence of the Gerasimov-Drell-Hearn sum rule

We test the Gerasimov-Drell-Hearn (GDH) sum rule numerically by calculating the total photon absorption cross sections σ 1 2 and σ 3 2 on the nucleon via photon excitation of baryon resonances in the constituent quark model. A total of seventeen, low-lying, non-strange baryon resonances are included in this calculation. The transverse and longitudinal interference cross section, σ 1 2 TL , is found to play an important role in the study of the Q 2 variation of the sum rule. The results show that the GDH sum rule is saturated by these resonances at a confidence level of 94%. In particular, the P 33(1232) dominates at small Q 2. The GDH integral has a strong Q 2-dependence below Q 2 = 1.0 GeV 2 and changes its sign around Q 2 = 0.3 GeV 2. It becomes weakly Q 2-dependent for Q 2 > 1.0 GeV 2 because of the quick decline of the resonance contributions.

The Drell–Hearn–Gerasimov Sum-Rule in QCD

Photoproduction spin sum-rules offer a new window on the spin structure of the nucleon that complements the information we can learn from polarized deep inelastic scattering experiments. We review the theory and present status of the Drell–Hearn–Gerasimov sum-rule in QCD, emphasizing the possible relation between the present "discrepancy" in this sum-rule and the nucleon's strangeness magnetic moment. In the case of an elementary electron or photon target (say at the NLC) the Drell–Hearn–Gerasimov sum-rule provides a test for physics beyond the minimal Standard Model.

The Drell-Hearn-Gerasimov sum rule

The Drell-Hearn-Gerasimov (DHG) sum rule relates the helicity structure of the photoabsorption cross section to the anomalous magnetic moment of the nucleon. It is based on Lorentz and gauge invariance, crossing symmetry, causality and unitarity. A generalized DHG sum rule my be derived for virtual photons. At low momentum transfer this generalized sum rule is saturated by the resonance region, at high momentum transfer it may be expressed by the parton spin distributions measured in deep inelastic scattering. The longitudinal-transverse interference determines the Cottingham sum rule, which is related to the elastic and magnetic form factors over the whole range of momentum tranfer.

Incompatibility of multipole predictions for the nucleon spin-polarizability and Drell-Hearn-Gerasimov sum rules.

Energy-weighted integrals of the difference in helicity-dependent photoreaction cross sections (${\mathrm{\ensuremath{\sigma}}}_{1/2}$-${\mathrm{\ensuremath{\sigma}}}_{3/2}$) provide information on the nucleon's spin-dependent polarizability (\ensuremath{\gamma}), and on the spin-dependent part of the asymptotic forward Compton amplitude through the Drell-Hearn-Gerasimov (DHG) sum rule. Estimates from current \ensuremath{\pi}-photoproduction multipole analyses, particularly for the proton-neutron difference, are in good agreement with relativistic-one-loop chiral calculations for \ensuremath{\gamma} but predict large deviations from the DHG sum rule. Either (a) both the two-loop corrections to the spin-polarizability are large and the existing multipoles are wrong, or (b) modifications to the Drell-Hearn-Gerasimov sum rule are required to fully describe the isospin structure of the nucleon.

What can we learn from the recent measurements of the spin-dependent structure function g1(x)?

In this paper, we argue that the effects of the Drell-Hearn-Gerasimov (DHG) sum rule should be included to extract the sum rule of polarized neutrons from the recent Spin Muon Collaboration measurement of the spin-dependent structure function [ital g][sub 1]([ital x]) of the deuteron, since the measurement was obtained at fairly low [ital Q][sup 2]. The value [Gamma][equivalent to][integral][sub 0][sup 1][ital g][sub 1]([ital x])[ital dx] could be modified significantly at [ital Q][sup 2] around 2--4 GeV[sup 2] by the high twist effects connected with the DHG sum rule. More accurate data for the spin-dependent structure function in the resonance region are needed to obtain reliable information on [Gamma] for the polarized protons and neutrons.

Polarized structure function of the nucleon in the resonance region.

In this paper, we show how the Drell-Hearn-Gerasimov (DHG) sum rule in the real photon limit can be generalized to electroproduction, and related to the sum rules in deep inelastic scattering. A general ${\mathit{Q}}^{2}$ dependence for the polarized function is discussed, particularly in the resonance region. The resonance ${\mathit{P}}_{33}$(1232) plays a very important role in the resonance region; in particular, it saturates the DHG sum rule for neutrons in the SU(6)\ensuremath{\bigotimes}O(3) basis. We show that the information from the polarized structure function in the low-${\mathit{Q}}^{2}$ region where the baryon resonances play a dominant role provides a very important probe of the spin-flavor structure of the nucleon.

Electromagnetic interactions of weakly-bound composite systems

Relativistic definitions of c.m. and internal dynamical variables are obtained for a weakly bound, Lorentz invariant system containing an arbitrary number of particles. The method used is a generalization of the one developed by Osborn for the case of two-body systems. Once defined, the variables are used in a study of the interaction of composite systems with an external electromagnetic field. It is found that one obtains additional relativistic corrections to those usually included in such calculations. These corrections can be classified as being either spin dependent or spin independent. The importance of the former has previously been established. The importance of the latter is established here. Finally, it is shown that the Drell-Hearn Gerasimov sum rule can now be validated for an arbitrary, weakly-bound N-body system.