Longitudinal-transverse Interference Research Articles

Measurement of the cross section for hard exclusive π0 muoproduction on the proton

We report on a measurement of hard exclusive π0 muoproduction on the proton by COMPASS using 160GeV/c polarised μ+ and μ− beams of the CERN SPS impinging on a liquid hydrogen target. From the average of the measured μ+ and μ− cross sections, the virtual-photon proton cross section is determined as a function of the squared four-momentum transfer between initial and final proton in the range 0.08(GeV/c)2<|t|<0.64(GeV/c)2. The average kinematics of the measurement are 〈Q2〉=2.0(GeV/c)2, 〈ν〉=12.8GeV, 〈xBj〉=0.093 and 〈−t〉=0.256(GeV/c)2. Fitting the azimuthal dependence reveals a combined contribution by transversely and longitudinally polarised photons of (8.2±0.9stat−1.2+1.2|sys)nb/(GeV/c)2, as well as transverse-transverse and longitudinal-transverse interference contributions of (−6.1±1.3stat−0.7+0.7|sys)nb/(GeV/c)2 and (1.5±0.5stat−0.2+0.3|sys)nb/(GeV/c)2, respectively. Our results provide important input for modelling Generalised Parton Distributions. In the context of the phenomenological Goloskokov-Kroll model, the statistically significant transverse-transverse interference contribution constitutes clear experimental evidence for the chiral-odd GPD E‾T.

Study of the proton deformation using the Out-Of-Plane Spectrometers

Nucleon deformation can be studied through electro-excitation to the first nucleon resonance, the Δ+(1232), and quantified through the quadrupole amplitudes in the γ*Ν --&gt; Δ transition. A search for these small amplitudes has been the fo­ cus of a series of measurements undertaken at Bates-MIT. A first set of in-plane data show evidence for strong resonant and non-resonant ("background") ampli­ tudes in the longitudinal-transverse interference, which is sensitive to leading order to quadrupole contributions. Using beams of polarized electrons and the technique of out-of-plane detection, a second data set was collected on the two hadronic decay channels. It contains the first measurement of the fifth structure function on the nucléon, which provides an important theoretical constraint on the "background" amplitudes. Planned future measurements will focus on refining the resonance- background decomposition which is absolutely necessary before conclusions on the issue of nucléon deformation can be drawn.

Measurement of the beam spin asymmetry of [formula omitted] in the deep-inelastic regime with CLAS

The beam spin asymmetry of the exclusive pseudoscalar channel e→p→e′p′η was measured for the first time in the deep-inelastic regime (W>2 GeV/c2 and Q2>1 GeV2/c2) using a longitudinally polarized 5.78 GeV electron beam at Jefferson Lab with the CEBAF Large Acceptance Spectrometer. The data were accumulated in 144 four-dimensional bins of Q2, xB, −t and ϕ over a wide kinematic range, where ϕ is the azimuthal angle between the lepton and hadron scattering planes, The measured azimuthal dependence with large amplitudes of the sin⁡ϕ moments is a clear indication of a substantial contribution to the polarized cross-section from transversely polarized virtual photons. In the framework of generalized parton distributions (GPDs) this contribution is expressed via longitudinal-transverse interference between chiral-even and chiral-odd GPDs. The experimental results are compared to the existing theoretical models demonstrating the sensitivity to the product of chiral-odd and chiral-even GPDs and provide new constraints to the existing GPD parameterizations.

Neutron decay from the giant resonance via theB10(e,e'n) reaction

The cross sections and angular correlations for neutron decay into various states in the residual nucleus following the $^{10}\mathrm{B}$($e,{e}^{'}n$) reaction have been measured over the excitation energy range of 18--33 MeV at an effective momentum transfer of 0.56 fm${}^{\ensuremath{-}1}$. In the giant resonance, neutron emission leads to the population of two higher excited states in addition to the ground-state transition: 6.97 MeV $7/{2}^{\ensuremath{-}}({n}_{5}$) and 11.70 MeV $7/{2}^{\ensuremath{-}}+12.06$ MeV $3/{2}^{\ensuremath{-}}({n}_{6,7}$). This is the first observation of the neutron population of these states. The angular correlations for ${n}_{0}$ show a strong forward-backward asymmetry, which suggests interference from a transition with the opposite parity to $E1$. The angular correlations for ${n}_{5}$ and ${n}_{6,7}$ have a peak shift of about ${50}^{\ifmmode^\circ\else\textdegree\fi{}}$ at lower excitation energy and recover above about 24 and 25 MeV for ${n}_{5}$ and ${n}_{6,7}$, respectively. Their patterns are considerably different from that for ${n}_{0}$. The angular correlations for each transition were fitted with a Legendre polynomial. The longitudinal-transverse interference coefficient ${C}_{2}/{A}_{0}$ is negligible for all populations. For ${n}_{0}$ decay, all Legendre coefficients ${b}_{i}$ are positive, but ${b}_{2}$ and ${b}_{3}$ for the ${n}_{5}$ and ${n}_{6,7}$ decays are negative at lower excitation energy, and the latter causes a shift of the forward peak. The negative values may come from the signs of the phase differences of $\mathrm{cos}{\ensuremath{\delta}}_{21}$ and $\mathrm{cos}{\ensuremath{\delta}}_{20}$. The $^{10}\mathrm{B}$($e,{e}^{'}n$) cross section measured up to ${E}_{x}~32$ MeV agrees well with that of $^{10}\mathrm{B}$($\ensuremath{\gamma},n$), except for a peak at 23 MeV of the giant resonance. In comparison with shell-model calculations, the partial cross section for ${n}_{0}$ is sizable up to higher excitation energy, and predicted large partial cross sections populating the 6.97 MeV $7/{2}^{\ensuremath{-}}$ and 11.70 MeV $7/{2}^{\ensuremath{-}}+12.06$ MeV $3/{2}^{\ensuremath{-}}$ states in the giant resonance were not observed.

Pion-less effective field theory on low-energy deuteron electrodisintegration

In view of its relation to Big Bang nucleosynthesis and a reported discrepancy between nuclear models and data taken at S-DALINAC, electro-induced deuteron breakup {sup 2}H(e,e{sup '}p)n is studied at momentum transfer q<100 MeV and close to threshold in the low-energy nuclear effective field theory without dynamical pions, EFT({pi} /). The result at next-to-next-to-leading order (N{sup 2}LO) for electric dipole currents and at next-to-leading order (NLO) for magnetic ones converges order-by-order better than quantitatively predicted and contains no free parameter. It is at this order determined by simple, well-known observables. Decomposing the triple differential cross section into the longitudinal-plus-transverse (L+T), transverse-transverse (TT), and longitudinal-transverse interference (LT) terms, we find excellent agreement with a potential-model calculation by Arenhoevel and co-workers, based on the Bonn potential. Theory and data also agree well on {sigma}{sub L+T}. There is however no space on the theory side for the discrepancy of up to 30%(3{sigma}) between theory and experiment in {sigma}{sub LT}. From universality of EFT({pi} /), we conclude that no theoretical approach with the correct deuteron asymptotic wave function can explain the data. Undetermined short-distance contributions that could affect {sigma}{sub LT} enter only at high orders (i.e., at the few-percent level). We notice some issuesmore » with the kinematics and normalization of the data reported.« less

Measurement ofep→epπ0beam spin asymmetries above the resonance region

The beam spin asymmetry (BSA) in the exclusive reaction ep->ep pi0 was measured with the CEBAF 5.77 GeV polarized electron beam and Large Acceptance Spectrometer(CLAS). The xB, Q2, t and phi dependences of the pi0 BSA are presented in the deep inelastic regime. The asymmetries are fitted with a sin(phi) function and their amplitudes are extracted. Overall, they are of the order of 0.04 - 0.11 and roughly independent of t. This is the signature of a non-zero longitudinal-transverse interference. The implications concerning the applicability of a formalism based on generalized parton distributions, as well as the extension of a Regge formalism at high photon virtualities, are discussed.

Use of W-boson longitudinal–transverse interference in top quark spin-correlation functions: II

This continuation of the derivation of general beam-referenced stage-two spin-correlation functions is for the analysis of top-antitop pair-production at the Tevatron and at the Large Hadron Collider. Both the gluon-production and the quark-production contributions are included for the charged-lepton-plus-jets reaction p p or p bar{p} --> t bar{t} --> (W^+ b)(W^- bar{b}) --> (l^{+} nu b)(W^- bar{b}). There is a simple 4-angle beam-referenced spin-correlation function for determination of the relative sign of, or for measurement of a possible non-trivial phase between the two dominant helicity amplitudes for t --> W^{+} b decay. There is an analogous function and tests for bar{t} --> W^{-} bar{b} decay. This signature requires use of the (t bar{t}) c.m.-energy of the hadronically decaying W-boson, or the kinematically equivalent cosine of the polar-angle of W-boson emission in the anti-top (top) decay frame. Spinors and their outer-products are constructed so that the helicity-amplitude phase convention of Jacob & Wick can be used throughout for the fixing of the signs associated with this large W-boson longitudinal-transverse interference effect.

Use of W-boson longitudinal-transverse interferencein top quark spin-correlation functions

Most of this paper consists of the derivation of general beam-referenced stage-two spin-correlation functions for the analysis of top-antitop pair production at the Tevatron, at the Large Hadron Collider, and/or at an International Linear Collider. However, for the charged-lepton plus jets reaction $q \bar{q} \rightarrow t \bar{t} \rightarrow (W^ + b) (W^- \bar{b} ) \rightarrow (l^{ + } \nu b ) (W^- \bar{b} )$ , there is a simple three-angle spin-correlation function for the determination of the relative sign of or for the measurement of a possible non-trivial phase between the two dominant λb=-1/2 helicity amplitudes for the t → W+b decay mode. For the CP-conjugate case, there is an analogous function and tests for $\bar{t} \rightarrow W^{-} \bar{b}$ decay. These results make use of W-boson longitudinal-transverse interference.

Survey of [formula omitted] asymmetries in semi-exclusive electron scattering on 4He and 12C

Single spin azimuthal asymmetries A L T ′ were measured at Jefferson Lab using 2.2 and 4.4 GeV longitudinally polarised electrons incident on 4He and 12C targets in the CLAS detector. A L T ′ is related to the imaginary part of the longitudinal-transverse interference and in quasifree nucleon knockout it provides an unambiguous signature for final state interactions (FSI). Experimental values of A L T ′ were found to be below 5%, typically | A L T ′ | ⩽ 3 % for data with good statistical precision. Optical model in eikonal approximation (OMEA) and relativistic multiple-scattering Glauber approximation (RMSGA) calculations are shown to be consistent with the measured asymmetries.

Meson retardation in deuteron electrodisintegration

The effect of meson retardation in NN-interaction and exchange currents on deuteron electrodisintegration is studied in a coupled channel approach including NN-, NΔ-, and πd-channels. It is shown that the influence of retardation depends on the energy regime: whereas below π-threshold calculations with static and retarded operators yield almost identical results, they differ significantly in the Δ-region. Especially, the longitudinal and the longitudinal-transverse interference structure functions are strongly affected.

Deuteron Breakup in theH2(e,e′p)Reaction at Low Momentum Transfer and Close to Threshold

Deuteron breakup has been studied in a 2H(e,e' p) coincidence experiment at low momentum transfer and for energies close to threshold. The longitudinal-plus-transverse ( L+T) and longitudinal-transverse ( LT) interference cross sections are deduced. Nonrelativistic calculations based on the Bonn potential and including leading order relativistic contributions, meson exchange currents, and isobar configurations describe the ( L+T) data well. Surprisingly, large deviations of 30% to 45% are observed for the LT contribution.

Relativistic eikonal approximation in high-energyA(e,e′p)reactions

A fully relativistic model for the description of exclusive (e,e'p) reactions off nuclear targets at high energies and momentum transfers is outlined. It is based on the eikonal approximation for the ejectile scattering wave function and a relativistic mean-field approximation to the Walecka model. Results for ^{12}C(e,e'p) and ^{16}O(e,e'p) differential cross sections and separated structure functions are presented for four-momenta in the range 0.8 \leq Q^{2} \leq 20 (GeV/c)^{2}. The regions of applicability of the eikonal approximation are studied and observed to be confined to proton knockout in a relatively small cone about the momentum transfer. A simple criterium defining the boundaries of this cone is determined. The Q^2 dependence of the effect of off-shell ambiguities on the different (e,e'p) structure functions is addressed. At sufficiently high values of Q^2 their impact on the cross sections is illustrated to become practically negligible. It is pointed out that for the whole range of Q^2 values studied here, the bulk of the relativistic effects arising from the coupling between the lower components in the wave functions, is manifesting itself in the longitudinal-transverse interference term.

Precise pion electroproduction in thep(e, e? ?+)n reaction at W=1125 MeV

The reactione+p →> e+π ++n at c.m. energyW=1125MeV and momentum transfer Q2=0.117GeV2/c2 has been measured. The transverse and longitudinal structure functions have been separated by varying the polarization of the virtual photon (Rosenbluth plot) with a 3 to 4% error. In addition the longitudinal-transverse interference term has been determined measuring the right-left asymmetry with an accuracy of 3%. The experimental data are compared to model calculations, and the sensitivity of the results to the axial and pion formfactors is discussed.

Measurement of the longitudinal, transverse, and longitudinal-transverse structure functions in the 2H(e,e'p)n reaction.

We have separated the longitudinal ({ital f}{sub 00}), transverse ({ital f}{sub 11}), and longitudinal-transverse interference ({ital f}{sub 01}) structure functions in the {sup 2}H({ital e},{ital e}{prime}{ital p}){ital n} reaction at {ital q}{searrow}{parallel}{approx_equal} 400 MeV/{ital c} and {omega}{approx_equal}110 MeV. A nonrelativistic calculation which includes effects due to final state interactions, meson exchange currents, and isobar configurations agrees with the measured {ital f}{sub 11} and {ital f}{sub 01} but overpredicts {ital f}{sub 00} by 25{percent} (2{sigma}). The data are also compared to the results of previous structure function measurements. {copyright} {ital 1996 The American Physical Society.}

Exclusive electron scattering from deuterium at high momentum transfer.

Cross sections are presented for the reaction H2(e,e′p)n for momentum transfers in the range 1.2≤Q2≤6.8(GeV/c)2 and for missing momenta from 0 to 250 MeV/c. The longitudinal-transverse interference structure function has been separated at Q2=1.2(GeV/c)2. The observables are compared to calculations performed in nonrelativistic and relativistic frameworks. The data are best described by a fully relativistic calculation.Received 4 November 1994DOI:https://doi.org/10.1103/PhysRevLett.74.4775©1995 American Physical Society

Out-of-plane quasielastic scattering from deuterium using polarized electrons.

We have measured the coincidence d(e→,e′p) reaction in quasielastic scattering, detecting the proton in a noncoplanar geometry. The electron helicity asymmetry Ae and the imaginary part of the longitudinal-transverse interference structure function fLT′ have been determined at a four-momentum transfer Q2=3.3 fm−2. The results are compared with theoretical calculations which use realistic potentials for the NN interaction.Received 1 September 1994DOI:https://doi.org/10.1103/PhysRevC.51.3479©1995 American Physical Society

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.

Excitation of giant resonances in the 40Ca(e,e'n)39Ca reaction.

Decay neutrons from the $^{40}\mathrm{Ca}$(e,e'n${)}^{39}$Ca reaction were studied in the giant resonance region. The cross sections and angular distributions, separated for ${\mathit{n}}_{0}$ and ${\mathit{n}}_{1}$ decays, were obtained for excitation energies between 19 and 27 MeV, at the effective momentum transfer of 0.35 ${\mathrm{fm}}^{\mathrm{\ensuremath{-}}1}$. Legendre polynomial coefficients obtained from fitting the data are compared with those from the (e,e'p) reaction. In the energy range 19--21 MeV, the interference coefficients ${\mathit{b}}_{1}$ and ${\mathit{b}}_{3}$ for the ground state transition are in agreement, but the noninterference coefficient ${\mathit{b}}_{2}$ is different. The different behavior of the angular distribution for protons and neutrons may suggest the interference of the decay from a T=0 quadrupole resonance and the T=1 giant dipole resonance. A similar tendency was also seen in comparing with the (e,e'${\mathit{p}}_{1}$) reaction. The Legendre polynomial coefficients for the ${\mathit{n}}_{0}$ decay in the (e,e'n) reaction, transformed to the photon point, agree well with those of the (\ensuremath{\gamma},${\mathit{n}}_{0}$) reaction. The reduced total cross section is consistent between the (e,e'n) and (\ensuremath{\gamma},n) reactions, but the cross section for (e,e'${\mathit{n}}_{0}$) is larger than that of (\ensuremath{\gamma},${\mathit{n}}_{0}$) near the peak of the resonance. The values of the longitudinal-transverse interference term are close to zero in the present region, which is rather small compared with the value near the resonance of the (e,e'p) reaction.

The (e,e′p0) coincidence cross section for 12C at transfer energy of 40 MeV

Abstract The energy spectra and angular distributions of protons from the 12C(e,e′p) coincidence reaction have been measured at azimuthai angles of φp= −45° and −135° out of the scattering plane, at energy transfer of 40 MeV and momentum transfer of 0.35 fm−1 (69 MeV/c). The longitudinal-transverse interference term, as well as the non-interference term of the (e,e'p0) cross section have been obtained, and the transition amplitudes are deduced in the LS coupling basis. The cross sections are compared with an RPA calculation. The photo-reaction cross section derived from the transverse term is in reasonable agreement with previous experimental results.

Longitudinal-transverse interference structure function in the reaction2H(e, e′ p)

The longitudinal-transverse interference structure functionf01 has been measured in deuterium electrodisintegration experiments at various values of the four-momentum transferQ2. Data taken at different laboratories and at roughly the same value ofQ2 are shown to be consistent. When compared to non-relativistic impulse-approximation calculations mostf01 data show an enhancement. A relativistic treatment of the reaction2H(e, e′ p) removes the discrepancy. More definite evidence for relativistic effects in deuterium electrodisintegration can be obtained at higher values of the recoil momentum. The experimental implications for such2H(e, e′ p) experiments are discussed as well.