Drell Hearn Sum Rule Research Articles

Partial wave analysis for KΣ photoproduction on the nucleon valid from threshold up to W = 2.8 GeV

We have simultaneously analyzed the available kaon photoproduction data for the , , , and channels by using an isobar model constructed from the Feynman diagrammatic approach for the background terms and multipoles formulation for the resonance terms. The unknown coupling constants in the background terms as well as the helicity amplitudes and the kaon branching ratios of the resonance terms were extracted by fitting the calculated observables to nearly 8000 data points from the latest experimental measurements, including the recent and data from MAMI A2 collaboration. During the fitting process we used the data listed in the Review of Particle Properties of Particle Data Group as a guidance for the resonance properties. Since in the previous study the kaon branching ratio of the N(1710)P11 state was found to be relatively large and, as a consequence, a sizable spike appeared in the K+Σ− cross section near the threshold, in the present work we propose two isobar models, i.e. with and without this state. We have found that both models can nicely fit the data. Extensive comparisons between the result of model calculation and experimental data are presented in this paper. To investigate the role of each resonance in the present work the significance of each resonance is calculated and discussed. The present work indicates that the N(1895)S11 and Δ(1900)S31 as the important resonances in the KΣ photoproduction. We also present two examples of application of the presented isobar models, i.e. investigation of the nucleon resonance N(1535)S11 coupling to the KΣ channels and the contribution of KΣ channels to the Gerasimov–Drell–Hearn sum rule.

Moments of the spin structure functions [formula omitted] and [formula omitted] for [formula omitted

The spin structure functions g 1 for the proton and the deuteron have been measured over a wide kinematic range in x and Q 2 using 1.6 and 5.7 GeV longitudinally polarized electrons incident upon polarized NH 3 and ND 3 targets at Jefferson Lab. Scattered electrons were detected in the CEBAF Large Acceptance Spectrometer, for 0.05 < Q 2 < 5 GeV 2 and W < 3 GeV . The first moments of g 1 for the proton and deuteron are presented – both have a negative slope at low Q 2 , as predicted by the extended Gerasimov–Drell–Hearn sum rule. The first extraction of the generalized forward spin polarizability of the proton γ 0 p is also reported. This quantity shows strong Q 2 dependence at low Q 2 . Our analysis of the Q 2 evolution of the first moment of g 1 shows agreement in leading order with Heavy Baryon Chiral Perturbation Theory. However, a significant discrepancy is observed between the γ 0 p data and Chiral Perturbation calculations for γ 0 p , even at the lowest Q 2 .

A derivative of the Gerasimov–Drell–Hearn sum rule

We derive a sum rule which establishes a linear relation between a particle's anomalous magnetic moment and a quantity connected to the photoabsorption cross section. This quantity cannot be measured directly. However, it can be computed within a given theory. As an example, we demonstrate validity of the sum rule in QED at tree level—the renowned Schwinger's correction to the anomalous magnetic moment is readily reproduced. In the case of the strong interactions, we also consider the calculation of the nucleon magnetic moment within chiral theories.

The generalized Gerasimov–Drell–Hearn sum rule for deuteron electrodisintegration

The generalized Gerasimov–Drell–Hearn sum rule IGDHγ∗d(Q2) for deuteron electrodisintegration d(e,e′)np as function of the squared four-momentum transfer Q2 is evaluated by explicit integration. The calculation is based on a conventional nonrelativistic framework using a realistic NN-potential and including contributions from meson exchange currents, isobar configurations and leading order relativistic terms. Good convergence is achieved. The prominent feature is a deep negative minimum, Iγ∗dGDH=−9.5 mb, at low Q2≈0.2 fm−2 which is almost exclusively driven by the nucleon isovector anomalous magnetic moment contribution to the magnetic dipole transition to the 1S0-state. Above Q2=20 fm−2 the integral IGDHγ∗(Q2) approaches zero rapidly.

Effective densities and polarizations of the targets for the GDH-experiments at MAMI and ELSA

An experimental program has been started at MAMI and ELSA to measure the integrand of the Gerasimov–Drell–Hearn sum rule (GDH) in a photon energy range starting from the pion threshold up to 2.9 GeV . A polarized target has been built, which is based on the frozen spin technique. Since the value of the nucleon polarization and the areal density of the target contribute directly to the result of the GDH-integral both quantities have to be determined with high accuracy.

Effect of double-polarization data in fits to single-pion photoproduction

We investigate the influence of new Jefferson Lab polarization-transfer ${(C}_{{x}^{\ensuremath{'}}}$ and ${C}_{{z}^{\ensuremath{'}}})$ and recoil polarization ${(P}_{y})$ measurements in multipole fits to the single-pion photoproduction database. Results are compared to those found with the addition of a double-polarization quantity associated with the Gerasimov--Drell-Hearn sum rule.

Novel analysis of chiral loop effects in the generalized Gerasimov–Drell–Hearn sum rule

We study the chiral loop corrections to the generalized Gerasimov–Drell–Hearn sum rule of the nucleon for finite photon virtuality in the framework of a Lorentz-invariant formulation of baryon chiral perturbation theory. We perform a complete one-loop calculation and obtain significant differences to previously found results based on the heavy baryon approach for the proton and neutron spin-dependent forward Compton amplitudes.

The Drell–Hearn sum rule at order α3

The Drell–Hearn–Gerasimov–Iddings (DHGI) sum rule for electrons is evaluated at order α 3 and shown to agree with the Schwinger contribution to the anomalous magnetic moment.

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.

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.

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.

Source Theory Discussion of Deep Inelastic Scattering with Polarized Particles

A general phenomenological framework is provided for the discussion of the inelastic scattering of polarized electrons (muons) on polarized nucleons, when regarded as the absorption of polarized virtual photons. The relevant cross sections compare parallel and antiparallel orientations of the photon helicity and nucleon spin, and also deal with linear combinations of longitudinal and transverse polarization. The polarization asymmetry for transverse polarization, P, assumes a scaling form in the deep inelastic scattering region, and should go to zero as omega(-1) for large omega. The latter behavior is connected, through the use of the improved scaling variable omega(s), with the high energy real photon situation. A sum rule is exhibited which implies that P must change sign in the deep inelastic region. This sum rule also yields the known Drell-Hearn sum rule for real photon Compton scattering, when combined with another, new, sum rule for the anomalous magnetic moment. The latter is verified in the context of pure electrodynamics to the lowest order in alpha. Finally, it is conjectured that P specifically changes from negative to positive values as omega varies from 1 to infinity.

Magnetic Dipole and Electric Quadrupole Moments of theW±Meson

It is shown that the magnetic dipole and the electric quadrupole moments of the W± meson must be equal to em and −em2, respectively, if we demand either that the Drell-Hearn sum rule is satisfied up to order α2 or that the helicity of W± is conserved in the scattering from an arbitrary electromagnetic field at high energies and at small but finite scattering angles.

Drell-Hearn Sum Rule from Light-Cone Current Commutators

The Drell-Hearn sum rule for the nucleon anomalous magnetic moment is derived by using the light-cone commutator for the + components of the current. The ${q}^{2}=0$ limits of several other sum rules are also derived from the ++ commutator. These other sum rules have been previously derived but only by using a more model-dependent commutator.

The Drell-Hearn sum rule and the lepton magnetic moment in the Weinberg model of weak and electromagnetic interactions

We verify that the fourth-order Compton amplitude for the scattering of a photon off a charged lepton is finite in Weinberg's model of weak and electro-magnetic interactions, and obeys the Drell-Hearn sum rule. We also compute the second-order weak corrections to the anomalous magnetic moment of a charged lepton in the same model. For the case of the muon, we find the bounds: + 0.2 × 10 −8 ⩽ K ⩽ + 0.56 × 10 −8 .

Drell-Hearn Sum Rule from Equal-Time Commutators

It is shown that the Drell-Hearn sum rule can be obtained from the equal-time commutator $[{D}^{+}(t),{D}^{\ensuremath{-}}(t)]=0, \mathrm{where} {D}^{\ifmmode\pm\else\textpm\fi{}}(t)=\ensuremath{\int}{d}^{3}x\frac{{x}_{1}\ifmmode\pm\else\textpm\fi{}i{x}_{2}}{\sqrt{2}}\ensuremath{\rho}(x),$ $\ensuremath{\rho}(x)$ being the electric charge density.

Exponentiation and sum rules

The eikonal approximation is applied to the scattering of a fast particle of arbitrary spin in a slowly varying external electromagnetic field. It is found that“exponentiation“ occurs only for the gyromagnetic ratio g = 2, when transitions to excited states are ignored. However, when transitions to excited states are included, exponentiation always occurs, provided that the anomalous magnetic moment obeys a generalized version of the Drell-Hearn sum rule.

Compton Scattering Sum Rules and Their Saturation

Theoretical features of the many fixed-momentum-transfer dispersive sum rules which can be written for the 26 possible generalized nucleon Compton scattering amplitudes (retarded products of vector currents) are surveyed, and the sum rules are put to experimental test. Theoretical attention is focused on the occurrence of right-signature fixed poles in the angular momentum plane, such as the $j=1$ fixed poles whose couplings are related to electromagnetic form factors by current algebra. Unitarity is used to estimate the sum-rule integrands in terms of data for the photoproduction processes $\ensuremath{\gamma}N\ensuremath{\rightarrow}\ensuremath{\pi}N$ and $\ensuremath{\gamma}N\ensuremath{\rightarrow}\ensuremath{\pi}\ensuremath{\Delta}$. Limitations of the data require that the sum rules be cut off at photon lab energy ${E}_{\mathrm{lab}}=1.12$ GeV. The main results are as follows: (a) Reasonable evidence is presented that two-time-component current-algebra sum rules involving the electric and magnetic isovector form factors ${{G}_{E}}^{V}(t)$ and ${{G}_{M}}^{V}(t)$ are correct for small spacelike $\ensuremath{-}t$. If they are also to be correct for $\ensuremath{-}t\ensuremath{\gtrsim}\ensuremath{-}0.6 {(\frac{\mathrm{GeV}}{c})}^{2}$, then the $\ensuremath{\rho}$ Regge pole must choose nonsense at $\ensuremath{\alpha}=0$, and the associated wrong-signature fixed pole there must be multiplicative. A time-space current-algebra sum rule probably fails. (b) The separate isotopic components of the Drell-Hearn sum rule are investigated. Those with $I=0$ exchange in the $t$ channel seem very successful, whereas the $I=1$ exchange sum rule clearly fails. The failure indicates an important contribution of a hitherto unsuspected ${J}^{P}({I}^{G})={1}^{+}({1}^{\ensuremath{-}})$ fixed pole. (c) Detailed results on wrong-signature antialgebra sum rules, on Regge-pole sum rules (FESR's), and on sum rules testing conspiracy are presented.