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Contribution of Coherent Neutral-Pion Photoproduction Channel to the Gerasimov-Drell-Hearn Sum Rule for the Deuteron
Abstract
The helicity dependence of the γ→d→ π0d reaction channel is studied for incident photon energies from threshold up to the Δ(1232)-resonance using an enhanced elementary pion photoproduction operator and a realistic high-precision potential for the deuteron wave function. The doubly polarized total cross sections for parallel and antiparallel helicity states are predicted. Then the contribution to the deuteron spin asymmetry is calculated. In addition, the contribution to the Gerasimov-Drell-Hearn (GDH) integral is evaluated by explicit integration up to a photon lab-energy of 350 MeV. The sensitivity of the results to the elementary pion photoproduction amplitude and the potential model used for the deuteron wave function is also investigated. Considerable dependence of the results on both the elementary amplitude and the deuteron wave function is found. We expect that these results may be useful to interpret the recent measurements from A2 and GDH@MAMI Collaborations.
... So far, many studies have been carried out dealing with the reaction γd → π 0 d in the photon energy region from π-threshold up to 1 GeV in order to obtain information on π 0 -photoproduction off free neutrons [15][16][17][18][19][20][21][22][23][24][25][26][27][28][29][30][31][32][33]. In spite of all these great theoretical efforts, a good description of the experimental data has not been yet found [3,4,6,7]. ...
... In the present work, we set Ω = 1, because we do not consider any polarization analysis of the final deuteron. The scattering M m d λm d -matrix is given by isolating the azimuthal dependence as follows [17,22]: ...
... As mentioned in Refs. [22,34], the beamtarget double polarization E-asymmetry is an excellent observable to test any weakness in the underlying elementary pion photoproduction model. Figure 13 shows that the helicity E-asymmetry is sensitive to the choice of the elementary γN → πN amplitude at incident photon lab-energies close to threshold. ...
We discuss possible uncertainties in theoretical predictions for γd → π 0 d observables near threshold due to the use of different elementary γN → πN amplitudes using an approach which is based on time-ordered perturbation theory. Results are presented for unpolarized cross sections and all possible spin asymmetries of differential and total cross sections. Our results indicate that the estimations of the uncertainty on the γd → π 0 d observables show important sensitivity to the modeling of the elementary γN → πN operator. A comparison to presently available experimental data is given. The results presented here are of particular interest for the evaluation of the systematic uncertainties caused by the use of different elementary operators in the analyses of γd → π 0 d measurements to extract information on the free neutron amplitude from deuteron data.
... In many cases the deviation among results obtained using different operators is very large. The coherent pion photoproduction on the deuteron has been investigated in [3] with special emphasize on the doubly polarized cross sections. The contribution of d d 0 to the Gerasimov-Drell-Hearn (GDH) integral has been explicitly evaluated in said work. ...
... Considerable dependence of the results on the elementary amplitude and the deuteron wave function has been found. In the present paper we extend the work in the preceding paper [3] by predicting unpolarized total and differential cross sections and extend the photon labenergy range up to 1 GeV. ...
... The ultimate goal of the present paper is, therefore, to extend the model, recently presented in [3], to make theoretical predictions for the process d d 0 in the energy range from threshold up to 1 GeV. For the elementary N N 0 amplitude, an enhanced elementary pion photoproduction operator taken from [2] is used. ...
According to the complexity of credit guarantee products risk, a corresponding risk evaluation system is established here. And uncertain linguistic information is adopted to describe the attribute weight and attribute value of evaluation indicators, and thus a multi-attribute group decision-making model of uncertain linguistic information concerning credit guarantee products risks is established. ULWM and ULHA operators are respectively used in this paper to collect evaluation values of synthesized attribute and overall attribute values of groups. And thus the comprehensive evaluation information of alternatives will be obtained. Then, possibility formula is used to construct a possibility matrix based on which we can decide how to arrange the decision-making schemes. At last, through case analysis, the feasibility and efficiency of evaluation of credit guarantee products risks are demonstrated here.
A high-quality double-polarization data set for the helicity dependence of the total and differential cross-sections for both gammap --> Npi channels in the Delta region has been obtained in the framework of the GDH experiment. The experiment, performed at the Mainz microtron MAMI, used a 4pi detection system, a circularly polarized photon beam, and a longitudinally polarized frozen-spin target. These data are included in the database to perform a multipole analysis to determine the properties of the Delta(1232)-resonance. For the resonant Delta(1232) multipoles we find a very good agreement with previous analyses, while the nonresonant ones show significant deviations.
The helicity dependence of the -vectord-vectorpp,-vectord-vector{sup +}nn, and -vectord-vector°np reaction channels is studied for incident photon energies from threshold up to the (1232) resonance with inclusion of leading 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 ° 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.
In view of practical nuclear structure calculations the Paris N-N potential is parametrized in a simple analytical form. This parametrization consists of a regularized discrete superposition of Yukawa-type terms. Results for phase shifts and deuteron parameters are presented as well as nuclear matter binding energy obtained with this potential.
Angular distributions of the cross section and linear analyzing powers have been measured for the d(γ , n)p reaction at the High Intensity γ -ray Source with linearly polarized beams of 14 and 16 MeV. The outgoing neutrons were detected using the Blowfish detector array, consisting of 88 liquid scintillator detectors with large solid angle coverage. The amplitudes of the reduced transition matrix elements were extracted by means of fits to the data and good agreement was found with a recent potential model calculation of the splittings of the triplet p-wave amplitudes. The extracted amplitudes are used to reconstruct the Gerasimov-Drell-Hearn sum rule integrand for the deuteron and are compared to theory.
We present an extraction of the E2/M1 ratio of the Δ(1232) from experimental data applying an effective Lagrangian model. We compare the result obtained with different nucleonic
models and we reconcile the experimental results with the lattice QCD calculations.
To determine nonspherical angular-momentum amplitudes in hadrons at long ranges (low Q2), data were taken for the p(¯e, e'p)π0 reaction in the Δ region at Q
2 = 0.060 (GeV/c)2 utilizing the magnetic spectrometers of the A1 Collaboration at MAMI. The results for the dominant transition magnetic dipole
amplitude and the quadrupole to dipole ratios at W = 1232 MeV are
M1+3/2=(40.33 ±0.63stat+syst ±0.61model)(10-3/mp+)\ensuremath M_{1+}^{3/2}=(40.33 \pm 0.63_{\rm stat+syst} \pm 0.61_{\rm model})(10^{-3}/m_{\pi^+})
, Re(
E1+3/2/M1+3/2)=(-2.28 ±0.29stat+syst ±0.20model\ensuremath E_{1+}^{3/2}/M_{1+}^{3/2})=(-2.28 \pm 0.29_{\rm stat+syst} \pm 0.20_{\rm model}
)%, and Re(
S1+3/2/M1+3/2) = (-4.81 ±0.27stat+syst ±0.26modelS_{1+}^{3/2}/M_{1+}^{3/2})\ensuremath =(-4.81 \pm 0.27_{\rm stat+syst} \pm 0.26_{\rm model}
)%. These disagree with predictions of constituent quark models but are in reasonable agreement with lattice calculations
with nonlinear (chiral) pion mass extrapolations, with chiral effective field theory, and with dynamical models with pion
cloud effects. These results confirm the dominance, and general Q2 variation, of the pionic contribution at large distances.
We analyze the γp→ηp process from threshold up to 1.2 GeV, employing an effective Lagrangian approach that allows for a mixing of eta couplings of pseudoscalar and pseudovector nature. The mixing ratio of the couplings may serve as a quantitative estimation of the SUL(3)×SUR(3) extended chiral symmetry violation in this energy regime. The data analyzed (differential cross sections and asymmetries) show a preference for the pseudoscalar coupling—91% of pseudoscalar coupling component for the best fit. We stress that a more conclusive answer to this question requires a more complete electromagnetic multipole database than the presently available one.
For the first time we checked the fundamental Gerasimov-Drell-Hearn (GDH) sum rule for the proton experimentally in the photon energy range from 0.2-2.9 GeV with the tagged photon facilities at MAMI (Mainz) and ELSA (Bonn). New data of the doubly polarized total cross section difference are presented in the energy range from 1.6 to 2.9 GeV. The contribution to the GDH integral from 0.2-2.9 GeV yields [254+/-5(stat)+/-12(syst)] microb with negative contributions in the Regge regime at photon energies above 2.1 GeV. This trend supports the validity of the GDH sum rule.
An explicit evaluation of the spin asymmetry of the deuteron and the associated Gerasimov-Drell-Hearn sum rule is presented which includes photodisintegration, and single and double pion and eta production as well. Photodisintegration is treated with a realistic retarded potential and a corresponding meson exchange current. For single pion and eta production the elementary operator from MAID is employed, whereas for double pion production, an effective Lagrangian approach is used. A large cancellation between the disintegration and the meson production channels yields for the explicit GDH integral a value of 27.31 microb to be compared to the sum rule value 0.65 microb.
The magnetic dipole (M1), the electric quadrupole (E2), and the Coulomb quadrupole (C2) amplitudes for gammaN-->Delta are calculated in quenched lattice QCD. Using a new method, which combines an optimal choice of interpolating fields for the Delta and an overconstrained analysis, we obtain statistically accurate results for the dipole form factor and for the ratios R(EM)=E2/M1 and R(SM)=C2/M1, up to momentum transfer squared 1.5 GeV2. We show for the first time, using lattice QCD, that both R(EM) and R(SM) are nonzero and negative, in qualitative agreement with experiment and indicating the presence of deformation in the N/Delta system.
Helicity-dependent total photoabsorption cross sections on the deuteron have been measured for the first time at ELSA (Bonn) in the photon energy range from 815 to 1825 MeV. Circularly polarized tagged photons impinging on a longitudinally polarized LiD target have been used together with a highly efficient 4pi detector system. The data around 1 GeV are not compatible with predictions from existing multipole analyses. From the measured energy range an experimental contribution to the GDH integral on the neutron of [33.9 +/- 5.5(stat) +/- 4.5(syst)] microb is extracted.
A measurement of the helicity dependence of the total inclusive photoabsorption cross section on the deuteron was carried out at MAMI (Mainz) in the energy range 200 < E-gamma < 800 MeV. The experiment used a 4 pi detection system, a circularly polarized tagged photon beam and a frozen-spin target which provided longitudinally polarized deuterons. The contribution to the Gerasimov-Drell-Hearn sum rule for the deuteron determined from the data is 407 +/- 20(stat)+/- 24(syst) mu b for 200 < E-gamma < 800 MeV.
A partial-wave analysis of single-pion photoproduction data has been completed. This study extends from threshold to 2 GeV in the laboratory photon energy, focusing mainly on the influence of new measurements and model-dependence in the choice of parameterization employed above the two-pion threshold. Results are used to evaluate sum rules and estimate resonance photo-decay amplitudes. These are compared to values obtained in the MAID analysis.
We investigate the importance of crossing symmetry in effective field models and the effects of phenomenological nucleon resonance widths on the paradigmatic case of pion photoproduction. We use reaction models containing four star resonances up to 1.8 Gev ((1232), N(1440), N(1520), N(1535), (1620), N(1650), (1700), and N(1720)) with different prescriptions for crossed terms and widths, to fit the latest world database on pion photoproduction. We compare results from selected multipoles and fits. The is highly dependent on the fulfillment of crossing symmetry and the inclusion of u channels.
The problem of extracting information on new and known N
∗ resonances by fitting isobar models to photonuclear
data is addressed. A new fitting strategy, incorporating a genetic
algorithm, is outlined. As an example, the method is applied to a
typical tree-level analysis of published p( γ, K+)
Λ data. It is shown that, within the limitations of this
tree-level analysis, a resonance in addition to the known set is
required to obtain a reasonable fit. An additional P11
resonance, with a mass of about 1.9 GeV, gives the best agreement with
the published data, but additional S11 or D13
resonances cannot be ruled out. Our genetic algorithm method predicts
that photon beam asymmetry and double polarization p( γ,
K+) Λ measurements should provide the most sensitive
information with respect to missing resonances.
Recent results are presented for quasifree pion photoproduction off the deuteron in the energy region from threshold up to the Δ(1232)‐resonance with inclusion of all leading
πNN
effects. Final‐state interaction effects are investigated and their role in polarized and unpolarized observables are found to be significant. The sensitivity of results to the elementary
N(γ,π)N
operator is discussed and considerable dependence is found. We expect that these results may be useful to interpret the recent measurements from LEGS, A2 and GDH Collaborations.
DOI:https://doi.org/10.1103/PhysRevLett.16.908
It is shown that a measurement of the analyzing power obtained with linearly polarized 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 (gamma0) near photodisintegration threshold. An analysis of data for the d(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 -603±43mub between the photodisintegration threshold and 6 MeV. This result is the first confirmation of the large contribution of the 1S0(M1) transition predicted for the deuteron near photodisintegration threshold. In addition, a sum rule value of 3.75±0.18 fm4 for gamma0 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.
The E2/M1 ratio (EMR) of the δ(1232) is extracted from the world data in pion photoproduction by means of an effective Lagrangian approach (ELA). This quantity has been derived within a crossing symmetric, gauge invariant, and chiral symmetric Lagrangian model which also contains a consistent modern treatment of the δ(1232) resonance. The bare s-channel δ(1232) contribution is well isolated and final state interactions (FSI) are effectively taken into account fulfilling Watson's theorem. The obtained EMR value, EMR =(-1.30{+-}0.52)%, is in good agreement with the latest lattice QCD calculations [Phys. Rev. Lett. 94, 021601 (2005)] and disagrees with results of current quark model calculations.
We report new high-precision measurements of p(γ-->,γ),
p(γ-->,π0) and p(γ-->,π+)
cross section and beam asymmetry angular distributions for photon beam
energies in the range from 213 MeV to 333 MeV. The cross sections for
all three channels are locked together with a small common systematic
scale uncertainty of 2%. A large overdetermination of kinematic
parameters was used to achieve the first complete separation of the
Compton scattering and π0-production channels. This has
also allowed all detector efficiencies for the p(γ-->,γ)
and p(γ-->,π0) channels to be measured directly
from the data itself without resorting to simulations. The new Compton
results are approximately 30% higher than previous Bonn data near the
peak of the Δ resonance, resolving a long-standing unitarity
puzzle. However, our p(γ-->,π0) and
p(γ-->,π+) cross sections are also about 10%
higher than both earlier Bonn data and recent Mainz measurements, while
our p(γ-->,π+) cross sections are in good
agreement with results from Tokyo. Our polarization asymmetry data are
of the highest precision yet available and have considerable impact upon
multipole analyses. These new data have been combined with other
polarization ratios in a simultaneous analysis of both Compton
scattering and π production, with Compton scattering providing two
new constraints on the photopion amplitude. This analysis has improved
the accuracy in the E2/M1 mixing ratio for the N-->Δ
transition, EMR=-[3.07+/-0.26(stat+syst)+/-0.24(model)](%), and the
corresponding N-->Δ transverse helicity amplitudes,
A1/2=-[135.7+/-1.3(stat+syst)+/-3.7(model)](10-3
GeV-1/2) and
A3/2=-[266.9+/-1.6(stat+syst)+/-7.8(model)](10-3
GeV-1/2). From these we deduce an oblate spectroscopic
deformation for the Δ+. The same simultaneous analysis
has been used to extract the proton dipole polarizabilities,
α¯-β¯=+[10.39+/-1.77(stat+syst)+1.02-1.87(model)](10-4
fm3) in agreement with previous low energy measurements, and
α¯+β¯=+[13.25+/-0.86(stat+syst)+0.23-0.58(model)](10-4
fm3) in agreement with recent evaluations of the Baldin sum
rule. Our simultaneous analysis has also provided the first
determination of the proton spin polarizabilities,
γπ=-[27.23+/-2.27(stat+syst)+2.24-2.10(model)](10-4
fm4),
γ0=-[1.55+/-0.15(stat+syst)+0.03-0.03(model)](10-4
fm4),
γ13=+[3.94+/-0.53(stat+syst)+0.20-0.18(model)](10-4
fm4), and
γ14=-[2.20+/-0.27(stat+syst)+0.05-0.09(model)](10-4
fm4). The extracted value of the backward spin
polarizability, γπ, is considerably different from
other analyses and this has been instrumental in bringing the value of
α¯-β¯ extracted from high energy data into
agreement with low energy experiments.
An overview over present achievements and future challenges in the field of few-nucleon systems is presented. Special emphasis
is laid on the construction of a unified approach to hadronic and electromagnetic reactions on few-nucleon systems, necessary
for studying the borderline between quark-gluon and effective descriptions.
We present a pion photoproduction model on the free nucleon based on an Effective Lagrangian Approach (ELA) which includes the nucleon resonances (Δ(1232), N(1440), N(1520), N(1535), Δ(1620), N(1650), and Δ(1700)), in addition to Born and vector meson exchange terms. The model incorporates a new theoretical treatment of spin-3/2 resonances, first introduced by Pascalutsa, avoiding pathologies present in previous models. Other main features of the model are chiral symmetry, gauge invariance, and crossing symmetry. We use the model combined with modern optimization techniques to assess the parameters of the nucleon resonances on the basis of world data on electromagnetic multipoles. We present results for electromagnetic multipoles, differential cross-sections, asymmetries, and total cross-sections for all one pion photoproduction processes on free nucleons. We find overall agreement with data from threshold up to 1 GeV in laboratory frame.
A new operator for pion photo- and electroproduction has been developed for nuclear applications at photon equivalent energies up to 1 GeV. The model contains Born terms, vector mesons and nucleon resonances (P33(1232), P11(1440), D13(1520), S11(1535), F15(1680), and D33(1700)). The resonance contributions are included taking into account unitarity to provide the correct phases of the pion photoproduction multipoles. The Q2 dependence of electromagnetic resonance vertices is described with appropriate form factors in the electromagnetic helicity amplitudes. Within this model we have obtained good agreement with the experimental data for pion photo- and electroproduction on the nucleon for both differential cross sections and polarization observables. The model can be used as a starting point to predict and analyze forthcoming data.
This biennial Review summarizes much of particle physics. Using data from previous editions, plus 2633 new measurements from 689 papers, we list, evaluate, and average measured properties of gauge bosons, leptons, quarks, mesons, and baryons. We also summarize searches for hypothetical particles such as Higgs bosons, heavy neutrinos, and supersymmetric particles. All the particle properties and search limits are listed in Summary Tables. We also give numerous tables, figures, formulae, and reviews of topics such as the Standard Model, particle detectors, probability, and statistics. Among the 110 reviews are many that are new or heavily revised including those on CKM quark-mixing matrix, Vud & Vus, Vcb & Vub, top quark, muon anomalous magnetic moment, extra dimensions, particle detectors, cosmic background radiation, dark matter, cosmological parameters, and big bang cosmology.
A booklet is available containing the Summary Tables and abbreviated versions of some of the other sections of this full Review. All tables, listings, and reviews (and errata) are also available on the Particle Data Group website: http://pdg.lbl.gov.
We present a charge-dependent nucleon-nucleon (NN) potential that fits the world proton-proton data below 350 MeV available in the year of 2000 with a chi^2 per datum of 1.01 for 2932 data and the corresponding neutron-proton data with chi^2/datum = 1.02 for 3058 data. This reproduction of the NN data is more accurate than by any phase-shift analysis and any other NN potential. The charge-dependence of the present potential (that has been dubbed `CD-Bonn') is based upon the predictions by the Bonn Full Model for charge-symmetry and charge-independence breaking in all partial waves with J <= 4. The potential is represented in terms of the covariant Feynman amplitudes for one-boson exchange which are nonlocal. Therefore, the off-shell behavior of the CD-Bonn potential differs in a characteristic and well-founded way from commonly used local potentials and leads to larger binding energies in nuclear few- and many-body systems, where underbinding is a persistent problem. Comment: 69 pages (RevTex) including 20 tables and 9 figures (ps files)
We present an optimization scheme that employs a Genetic Algorithm (GA) to determine the properties of low-lying nucleon excitations within a realistic photo-pion production model based upon an effective Lagrangian. We show that with this modern optimization technique it is possible to reliably assess the parameters of the resonances and the associated error bars as well as to identify weaknesses in the models. To illustrate the problems the optimization process may encounter, we provide results obtained for the nucleon resonances (1230) and (1700). The former can be easily isolated and thus has been studied in depth, while the latter is not as well known experimentally.
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