Gerasimov-Drell-Hearn Research Articles

Artificial dynamical effects in quantum field theory

In Newtonian mechanics, inertial pseudoforces - or fictitious forces - appear in systems studied in non-Galilean reference frames; e.g., a centrifugal force seems to arise if the dynamics is analyzed in a rotating reference frame. The equivalent of Galilean invariance for relativistic kinematics is Poincar\'e invariance; analogous artificial effects may arise in relativistic quantum field theory (QFT) if a system is studied in a framework violating Poincar\'e invariance. We highlight how such issues complicate the traditional canonical quantization of QFTs and can lead to a subjective description of natural phenomena. In fact, if the system involves the strong interaction, obtaining objective results can become an intractable problem using canonical quantization because the pseudoforces are essentially nonperturbative. In contrast, the treatment of the same problem using light-front (LF) quantization is free of spurious pseudoeffects because Poincar\'e invariance is manifest; thus the treatment of strong interaction problems becomes simpler. These statements are illustrated using several examples: the Gerasimov-Drell-Hearn (GDH) relation, a fundamental feature of QFT; the absence of any measurable impact of Lorentz contraction in high-energy collisions; and the fictitious character of vacuum fluctuation contributions to the cosmological constant.

Single-pion contribution to the Gerasimov-Drell-Hearn sum rule and related integrals

Phenomenological amplitudes obtained in partial-wave analyses (PWA) of single-pion photoproduction are used to evaluate the contribution of this process to the Gerasimov-Drell-Hearn (GDH), Baldin, and Gell-Mann--Goldberger--Thirring (GGT) sum rules, by integrating up to $2\phantom{\rule{4pt}{0ex}}\mathrm{GeV}$ in photon energy. Our study confirms that the single-pion contribution to all these sum rules converges even before the highest considered photon energy, but the levels of saturation are very different in the three cases. Single-pion production almost saturates the GDH sum rule for the proton, while a large fraction is missing in the neutron case. The Baldin integrals for the proton and the neutron are both saturated to about four fifths of the predicted total strength. For the GGT sum rule, the wide variability in predictions precludes any definitive statement.

Doubly-polarised pion photoproduction on the nucleon at MAMI

The A2 Collaboration at MAMI (Mainz) carried out new measurements of the helicity dependence of the total inclusive photo-absorption cross section and of the partial cross sections for several reaction channels on the proton and on the neutron in the photon energy region 200 He targets. Hadronic reaction products were detected by the large acceptance Crystal Ball-TAPS spectrometer, complemented by plastic scintillators and vertex detectors for charged particle tracking and identification.These new, high-quality doubly-polarised pion-photoproduction data sets provide a valuable input to the study of the nucleon structure and excitation spectrum by significantly constraining the electromagnetic multipole evaluation performed by the different available partial wave analysis models. Furthermore, the helicity dependent observables provide the main ingredient for the verification of the well-known Gerasimov-Drell-Hearn (GDH) sum rule, which relates the helicity-dependent photoasborption process to the main static nucleon properties (mass, charge, spin).

Evaluation of the forward Compton scattering off protons. II. Spin-dependent amplitude and observables

The forward Compton scattering off the proton is determined by substituting the empirical total photoabsorption cross sections into dispersive sum rules. In addition to the spin-independent amplitude evaluated previously [Phys. Rev. D 92, 074031 (2015)], we obtain the spin-dependent amplitude over a broad energy range. The two amplitudes contain all the information about this process, and we, hence, can reconstruct the nonvanishing observables of the proton Compton scattering in the forward kinematics. The results are compared with predictions of chiral perturbation theory where available. The low-energy expansion of the spin-dependent Compton scattering amplitude yields the Gerasimov-Drell-Hearn (GDH) sum rule and relations for the forward spin polarizabilities (FSPs) of the proton. Our evaluation provides an empirical verification of the GDH sum rule for the proton, and yields empirical values of the proton FSPs. For the GDH integral, we obtain $204.5(21.4)$ $\mu$b, in agreement with the sum rule prediction: $204.784481(4)$ $\mu$b. For the FSPs, we obtain: $\gamma_0=-92.9(10.5) \times 10^{-6}$ fm$^4$, and $\bar{\gamma_0}=48.4(8.2) \times 10^{-6}$ fm$^6$, improving on the accuracy of previous evaluations.

Contribution of Coherent and Incoherent π-Photoproduction Channels to the Spin Asymmetry and the GDH Sum Rule for the Deuteron

An explicit evaluation of the deuteron spin asymmetry and the associated Gerasimov–Drell–Hearn (GDH) integral for coherent and incoherent π-photoproduction channels with inclusion of rescattering effects is presented. The helicity-dependent total inclusive photoabsorption cross section on the deuteron and the helicity-dependent semiexclusive channels γd → π±NN and γd → π0X (X = pn or d) are explicitly evaluated up to 1.5 GeV. Our model calculations indicate that convergence of the GDH integral is reached for π0-production, while it is not completely reached for π±-production. For the sum of γd → πNN and γd → π0d contributions to the finite GDH integral by explicit integration up to 1.5 GeV, a value of 249.73 μb is obtained. The extracted results are compared with available experimental data from MAMI and ELSA. We find that our predictions fairly well reproduce the data in the π±NN case, while fail to predict the measured shape of the π0X channel.

Measurement of the doubly-polarized [formula omitted] reaction at 16.5 MeV and its implications for the GDH sum rule

We report new measurements of the double-polarized photodisintegration of 3He at an incident photon energy of 16.5 MeV, carried out at the High Intensity γ-ray Source (HIγS) facility located at Triangle Universities Nuclear Laboratory (TUNL). The spin-dependent double-differential cross sections and the contribution from the three-body channel to the Gerasimov–Drell–Hearn (GDH) integrand were extracted and compared with the state-of-the-art three-body calculations. The calculations, which include the Coulomb interaction and are in good agreement with the results of previous measurements at 12.8 and 14.7 MeV, deviate from the new cross section results at 16.5 MeV. The GDH integrand was found to be about one standard deviation larger than the maximum value predicted by the theories.

Helicity-dependent reaction γd → π0d near the η-threshold and its contribution to the E-asymmetry and the GDH sum rule for the deuteron

The helicity-dependent coherent π0-photoproduction in the reaction γd → π0d near the η-threshold is investigated. The calculations are performed within an approach which includes the reaction amplitudes of the impulse approximation (IA), two-step process with intermediate πN- and ηN-rescattering, and the higher order terms in the multiple scattering series for the intermediate ηNN interaction. The contribution of γd → π0d to the deuteron spin asymmetry is calculated and its contribution to the Gerasimov–Drell–Hearn (GDH) integral is explicitly evaluated by integration up to a photon energy of 900 MeV. In addition, the helicity E-asymmetry is calculated. The results revealed that the doubly polarized differential cross-sections and the helicity E-asymmetry are sensitive to the interference of rescattering effects, specially at photon energies 600–800 MeV and extreme backward pion angles. The sensitivity of the obtained results for the GDH integral to the choice of NN potential model governing the deuteron wave function is discussed. We find that the deviation among results obtained for the deuteron GDH integral using different deuteron wave functions is quite large.

Helicity Dependence and Contribution to the Spin Asymmetry and the GDH Sum Rule of the \(\vec{\gamma }\vec{d} \to \pi ^{0}d\) Reaction Near the η-Threshold

The helicity dependence of the \(\vec{\gamma }\vec{d} \to \pi ^{0}d\) reaction is studied for incident photon lab-energies near the η-threshold at backward center-of-mass pion angles. The influence of first-order rescattering with intermediate production of both π- and η-mesons on the doubly polarized differential and total cross sections for parallel and antiparallel helicity states is investigated. Then the contribution of \(\vec{\gamma }\vec{d} \to \pi ^{0}d\) to the deuteron spin asymmetry of the total cross section is calculated and its contribution to the Gerasimov–Drell–Hearn (GDH) integral for the deuteron is explicitly evaluated by integration up to a photon lab-energy of 900 MeV. Moreover, the double polarization E-asymmetry is predicted. Although the first-order rescattering effect is found to be negligible in the doubly polarized total photo-absorption cross sections and the deuteron GDH integral, it reached on average about 40% in the doubly polarized differential cross sections and the helic...

Contributions of γd → πNN + π0 d channels to the spin asymmetry and the Gerasimov-Drell-Hearn integral for the deuteron

Contributions from the semi-exclusive channels γd → π±NN + π0d and γd → π0X (X=pn or d) to the deuteron spin asymmetry and the Gerasimov-Drell-Hearn (GDH) integral are explicitly evaluated using an enhanced elementary pion photoproduction operator and a realistic, high-precision potential model for the deuteron wave function. The sensitivity of the results to the elementary pion photoproduction operator is also investigated and considerable dependence is found. Results for the deuteron GDH integral are compared with the measurements from A2 and GDH@MAMI Collaborations.

MOMENTS OF SPIN STRUCTURE FUNCTIONS: SUM RULES AND POLARIZABILITIES

Nucleon structure study is one of the most important research areas in modern physics and has challenged us for decades. Spin has played an essential role and often brought surprises and puzzles to the investigation of the nucleon structure and the strong interaction. New experimental data on nucleon spin structure at low to intermediate momentum transfers combined with existing high momentum transfer data offer a comprehensive picture in the strong region of the interaction and of the transition region from the strong to the asymptotic-free region. Insight into some aspects of the theory for the strong interaction, Quantum Chromodynamics (QCD), is gained by exploring lower moments of spin structure functions and their corresponding sum rules (i.e., the Bjorken, Burkhardt–Cottingham, Gerasimov–Drell–Hearn (GDH), and the generalized GDH). These moments are expressed in terms of an operator-product expansion using quark and gluon degrees of freedom at moderately large momentum transfers. The higher-twist contributions have been examined through the evolution of these moments as the momentum transfer varies from higher to lower values. Furthermore, QCD-inspired low-energy effective theories, which explicitly include chiral symmetry breaking, are tested at low momentum transfers. The validity of these theories is further examined as the momentum transfer increases to moderate values. It is found that chiral perturbation theory calculations agree reasonably well with the first moment of the spin structure function g1 at low momentum transfer of 0.05–0.1 GeV2 but fail to reproduce some of the higher moments, noticeably, the neutron data in the case of the generalized polarizability δLT. The Burkhardt–Cottingham sum rule has been verified with good accuracy in a wide range of Q2 assuming that no singular behavior of the structure functions is present at very high excitation energies.

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 the 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 photo-absorption 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.

Measurements ofH→D→(γ→,π)and Implications for the Convergence of the Gerasimov-Drell-Hern Integral

We report new measurements of inclusive pi production from frozen-spin HD for polarized photon beams covering the Delta(1232) resonance. These provide data simultaneously on both H and D with nearly complete angular distributions of the spin-difference cross sections entering the Gerasimov-Drell-Hearn (GDH) sum rule. Recent results from Mainz and Bonn exceed the GDH prediction for the proton by 22 microb, suggesting as yet unmeasured high-energy components. Our pi0 data reveal a different angular dependence than assumed in Mainz analyses and integrate to a value that is 18 microb lower, suggesting a more rapid convergence. Our results for deuterium are somewhat lower than published data, considerably more precise, and generally lower than available calculations.

Gerasimov-Drell-Hearn sum rule and the discrepancy between the new CLAS and SAPHIR data

Contribution of the K^+\Lambda channel to the Gerasimov-Drell-Hearn (GDH) sum rule has been calculated by using the models that fit the recent SAPHIR or CLAS differential cross section data. It is shown that the two data sets yield quite different contributions. Contribution of this channel to the forward spin polarizability of the proton has been also calculated. It is also shown that the inclusion of the recent CLAS C_x and C_z data in the fitting data base does not significantly change the result of the present calculation. Results of the fit, however, reveal the role of the S_{11}(1650), P_{11}(1710), P_{13}(1720), and P_{13}(1900) resonances for the description of the C_x and C_z data. A brief discussion on the importance of these resonances is given. Measurements of the polarized total cross section \sigma_{TT'} by the CLAS, LEPS, and MAMI collaborations are expected to verify this finding.

Near-threshold deuteron photodisintegration: An indirect determination of the Gerasimov-Drell-Hearn sum rule and forward spin polarizability (γ0) for the deuteron at low energies

It is shown that a measurement of the analyzing power obtained with linearly polarized \ensuremath{\gamma}-rays and an unpolarized target can provide an indirect determination of two physical quantities. These are the Gerasimov-Drell-Hearn (GDH) sum rule integrand for the deuteron and the sum rule integrand for the forward spin polarizability (${\ensuremath{\gamma}}_{0}$) near photodisintegration threshold. An analysis of data for the $d(\stackrel{\ensuremath{\rightarrow}}{\ensuremath{\gamma}},n)p$ reaction and other experiments is presented. A fit to the world data analyzed in this manner gives a GDH integral value of $\ensuremath{-}603\ifmmode\pm\else\textpm\fi{}43\ensuremath{\mu}$b between the photodisintegration threshold and 6 MeV. This result is the first confirmation of the large contribution of the ${}^{1}{S}_{0}(M1)$ transition predicted for the deuteron near photodisintegration threshold. In addition, a sum rule value of 3.75\ifmmode\pm\else\textpm\fi{}0.18 fm${}^{4}$ for ${\ensuremath{\gamma}}_{0}$ is obtained between photodisintegration threshold and 6 MeV. This is a first indirect confirmation of the leading-order effective field theory prediction for the forward spin-polarizability of the deuteron.

KAON CONTRIBUTIONS TO THE GERASIMOV–DRELL–HEARN INTEGRALS ON THE PROTON

Using KAON-MAID, an operator for kaon photo- and electro-production on the nucleon, we calculate contributions of kaon–hyperon final states to the Gerasimov–Drell–Hearn (GDH) integrals on the proton. We also calculate the corresponding contributions to the forward spin polarizability γ0 of the proton. By extending the operator to the finite Q2 region we then calculate kaon contributions to the generalized GDH integrals, as well as to the longitudinal-transverse polarizability δ0. Our results show relatively small but still sizable contributions.

Helicity dependence and contribution to the Gerasimov-Drell-Hearn sum rule of theγ→d→→πNNreaction channels in the energy region from threshold up to theΔ(1232)resonance

The helicity dependence of the {gamma}-vectord-vector{yields}{pi}{sup -}pp,{gamma}-vectord-vector{yields}{pi}{sup +}nn, and {gamma}-vectord-vector{yields}{pi}{sup 0}np reaction channels is studied for incident photon energies from threshold up to the {delta}(1232) resonance with inclusion of leading {pi}NN effects. The doubly polarized total and differential cross sections for parallel and antiparallel helicity states are predicted. Then the contribution of various channels to the deuteron spin asymmetry and the double polarization E asymmetry is calculated. In addition, the contribution to the Gerasimov-Drell-Hearn (GDH) integral from separate channels is evaluated by explicit integration up to a photon lab energy of 350 MeV. Sizeable effects from final-state interactions, specially for {pi}{sup 0} production, are found. The sensitivity of the results to the elementary pion photoproduction operator is also investigated. Considerable dependence of the results on the elementary amplitude is found. We expect that these results may be useful to interpret the recent measurements from LEGS-BNL, A2, and GDH-MAMI Collaborations.

The Gerasimov-Drell-Hearn sum rule at MAMI

An extended experimental program to investigate the Gerasimov-Drell-Hearn (GDH) sum rule and related partial reaction cross sections on proton and neutron has been carried out by the GDH collaboration at the electron accelerators MAMI (Mainz) and ELSA (Bonn). The GDH sum rule connects the helicity-dependent photoabsorption cross section with the anomalous magnetic moment of the nucleon. The GDH collaboration has measured the total cross section of circularly polarised photons with longitudinally polarised protons at MAMI and ELSA to check this sum rule experimentally. In addition partial reaction channels like pion, double pion and eta production were determined. This provides new information on the helicity-dependent excitation spectrum of the nucleon. With the help of partial wave analyses it is possible to extract new, complementary information on the broad, overlapping resonances in this energy region. The double polarisation observable E measured in this experiment enhances the smaller multipoles via interference terms. The analysis of our data provides a new possibility to study the photon couplings to the nucleon resonances, especially above the Δ resonance where many properties of the observed states (e.g., coupling constants, branching ratios, helicity amplitudes) are only poorly known. In this paper we present several new results from our measurements on polarised proton and deuteron targets.

Helicity-dependent photoabsorption cross sections on the nucleon

We examine the energy dependence of single-meson photoproduction as it contributes to the Gerasimov-Drell-Hearn (GDH) sum rule. For photon energies above approximately 1 GeV, through the full resonance region, this contribution dominates the proton sum-rule integral. Over the same energy region, our single-pion contribution to the neutron sum rule also qualitatively follows a recent set of GDH data. The predicted neutral-pion contribution to the neutron sum rule is nearly zero above 1 GeV in this result. The SAID and Mainz (MAID) results are very different for a number of observables over this energy region.

Sum rules for magnetic moments and polarizabilities in QED and chiral effective-field theory

We elaborate on a recently proposed extension of the Gerasimov-Drell-Hearn (GDH) sum rule which is achieved by taking derivatives with respect to the anomalous magnetic moment. The new sum rule features a {\it linear} relation between the anomalous magnetic moment and the dispersion integral over a cross-section quantity. We find some analogy of the linearized form of the GDH sum rule with the `sideways dispersion relations'. As an example, we apply the linear sum rule to reproduce the famous Schwinger's correction to the magnetic moment in QED from a tree-level cross-section calculation and outline the procedure for computing the two-loop correction from a one-loop cross-section calculation. The polarizabilities of the electron in QED are considered as well by using the other forward-Compton-scattering sum rules. We also employ the sum rules to study the magnetic moment and polarizabilities of the nucleon in a relativistic chiral EFT framework. In particular we investigate the chiral extrapolation of these quantities.

GDH sum rule in QED and ChPT

The celebrated Gerasimov-Drell-Hearn (GDH) sum rule (SR) relates the anomalous magnetic moment (a.m.m.) of a spin-1/2 particle to a dispersion integral of its polarized total photoabsorption cross-section: e{sup 2}k{sup 2}/2M{sup 2} = 1/{pi} {integral}{sub 0}{sup {infinity}} d{omega} {Delta}{sigma}({omega})/{omega}, where {Delta}{sigma} = {sigma}{sub 3/2} - {sigma}{sub 1/2} (subscript 3/2 or 1/2 refers to whether the photon beam polarization is in parallel or antiparallel to the polarization of the initial nucleon).