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Exclusive π− electroproduction off the neutron in deuterium in the resonance region

Y. Tian et al. (The CLAS Collaboration)
Phys. Rev. C 107, 015201 – Published 5 January 2023
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  • INTRODUCTION
  • EXPERIMENTAL FACILITY
  • DATA ANALYSIS
  • EVENT SELECTION
  • SIMULATION
  • CROSS SECTION EXTRACTION
  • RESULTS AND DISCUSSION
  • LEGENDRE POLYNOMIAL EXPANSION
  • CONCLUSIONS AND OUTLOOK
  • ACKNOWLEDGMENTS
  • APPENDICES
    • References

    Abstract

    New results for the exclusive and quasifree cross sections off neutrons bound in deuterium γvn(p)→pπ−(p) are presented over a wide final state hadron angle range with a kinematic coverage of the invariant mass (W) up to 1.825 GeV and the four-momentum transfer squared (Q2) from 0.4 to 1.0 GeV2. The exclusive structure functions were extracted and their Legendre moments were obtained. Final-state-interaction contributions have been kinematically separated from the extracted quasifree cross sections off bound neutrons solely based on the analysis of the experimental data. These new results will serve as long-awaited input for phenomenological analyses to extract the Q2 evolution of previously unavailable n→N* electroexcitation amplitudes and to improve state-of-the-art models of neutrino scattering off nuclei by augmenting the already available results from free protons.

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    • Received 15 April 2022
    • Revised 26 October 2022
    • Accepted 30 November 2022

    DOI:https://doi.org/10.1103/PhysRevC.107.015201

    ©2023 American Physical Society

    Physics Subject Headings (PhySH)

    1. Research Areas
    Lepton induced nuclear reactionsResonance reactionsStrong interaction
    1. Physical Systems
    BaryonsNeutrons
    Nuclear Physics

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    Vol. 107, Iss. 1 — January 2023

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    • Figure 1
      Figure 1

      The comparison of W distributions for π−p electroproduction events in quasifree kinematics within the entire Q2 range covered by this measurement from 0.4 to 1.0 GeV2, where the kinematic energy K=ps22mn. The black line presents Wf calculated from the measured four-momenta of the final π− and proton. The red line shows Wi calculated by setting nμ=(En,n⃗) with En=(−p⃗s)2+(Moff)2 and Moff according to Eq. (8) achieving best agreement with Wf.

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    • Figure 2
      Figure 2

      Kinematic sketch of the three leading terms in the γv+D→π−+p+p process: (a) impulse approximation, (b) pp rescattering, and (c) π−p rescattering. Diagrams (b) and (c) are the two main sources of final state interactions.

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    • Figure 3
      Figure 3

      Schematics of π− electroproduction off a moving neutron.

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    • Figure 4
      Figure 4

      Three-dimensional view of the CLAS detector cut along the beamline [8], with EC–electromagnetic calorimeter, TOF–scintillation counter, CC–Cherenkov counter, three regions R1–R3 of drift chambers, and the torus magnet.

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    • Figure 5
      Figure 5

      A schematic diagram of the “e1e” target [50] indicating the target window positions.

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    • Figure 6
      Figure 6

      Measured electron vertex (Ze) distributions for full target events (black) and scaled empty target events (red).

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    • Figure 7
      Figure 7

      θCC versus CC segment number histogram in sector 2, where μ, μ+3σ, and μ−4σ are marked as black stars and fit by second degree polynomial functions shown by the curves.

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    • Figure 8
      Figure 8

      Nphe histograms of the left and right PMTs in the tenth CC segment of sector 2 plotted separately and fit by the Poisson function in Eq. (11) shown by the red curve.

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    • Figure 9
      Figure 9

      Etotal/p versus p distribution, where the black lines show the upper and lower Etotal/p cut limits. The events outside the cut limits correspond to minimum ionizing particles and background.

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    • Figure 10
      Figure 10

      (a) Typical negative pion ΔT versus p histogram for sector 1 with upper and lower ΔT cut limits. The bands above π− upper ΔT cut limit correspond to negative muons and electrons, separately. (b) Proton ΔT versus p histogram for sector 1 with upper and lower ΔT cut limits. The band above proton upper cut limit corresponds to π+.

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    • Figure 11
      Figure 11

      The fitted mean values of the measured proton spectator missing mass squared μMs2 versus detector sector without any kinematic corrections (black squares), with only electron momentum corrections (red triangles), and with both electron momentum and proton energy loss corrections (blue dots). The black line represents the squared proton rest mass ≈0.88 GeV2.

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    • Figure 12
      Figure 12

      (a) ϕe versus θe distribution of electrons for sector 4 within the 1.12<|p⃗e|<1.2 GeV momentum interval. The blue lines show the fiducial cut boundaries for electrons. (b) ϕe distributions for the selected θe bin [29∘<θe<30∘ shown as the vertical shaded band in (a)] for the same momentum bin. The green area in the center indicates the selected fiducial range.

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    • Figure 13
      Figure 13

      Typical ϕ versus θ distributions for π− (a) and protons (b) in sector 1 within the same momentum interval 0.6<|p⃗|<0.8 GeV.

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    • Figure 14
      Figure 14

      Typical θ versus p histograms of π− in sector 2 are compared for experiment (a) and simulation reconstructed (b) data. The paired black lines show the corresponding removed low efficiency region defined from experiment data.

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    • Figure 15
      Figure 15

      Ms2 distribution with the cut region represented by the red lines showing the exclusive event selection process.

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    • Figure 16
      Figure 16

      Experimental momentum resolution Δp_s, which is described by the difference between the simulation thrown and reconstructed momenta.

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    • Figure 17
      Figure 17

      The black histogram represents the missing momentum distribution (|p⃗s|) of the unmeasured proton from experimental data. Based on the CD-Bonn potential [55], the scaled Monte Carlo simulated (thrown) proton momentum distribution is shown by the red histogram and the detector-reconstructed Monte Carlo distribution by the blue histogram. (b) Zoomed in version of (a) to show this comparison at small more clearly. The red vertical line indicates the 200MeV missing momentum cut position.

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    • Figure 18
      Figure 18

      The missing momentum distributions of the “spectator” proton |p⃗s| of experimental data (black histogram) and simulation (blue histogram) where the “green” and “red” filled areas represent the integral of the blue distribution from 0 to 200MeV and above 200MeV, respectively.

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    • Figure 19
      Figure 19

      Experimental W distribution of quasifree exclusive event yields in comparison to various maid models.

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    • Figure 20
      Figure 20

      Typical of acceptance correction factors as a function of ϕπ−c.m. for W= 1.2125 GeV and Q2= 0.5 GeV2, and cosθπ−c.m.= 0.1.

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    • Figure 21
      Figure 21

      Ms2 distributions for the measured (black histogram) and simulated γvn(p)→pπ−(p) (blue histogram) data, as well as the simulated γvp→pπ−π+ events (magenta histogram). The Ms2 cut region is shown by the vertical lines.

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    • Figure 22
      Figure 22

      The final-state-interaction contribution factor RFSI determined from experiment data which account for the FSI in deuteron target as a function of θπc.m. for individual Wf bins in 0.025 GeV increments in the range of 1.1375<W<1.3375 GeV for 0.4<Q2<0.6 GeV2. The gray shaded regions represent the corresponding systematic uncertainties.

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    • Figure 23
      Figure 23

      The final-state-interaction contribution factor RFSI determined from experiment data which account for the FSI in deuteron target as a function of θπc.m. for individual Wf bins in 0.025 GeV increments in the range of 1.1375<W<1.3375 GeV for 0.6<Q2<0.8 GeV2. The gray shaded regions represent the corresponding systematic uncertainties.

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    • Figure 24
      Figure 24

      The final-state-interaction contribution factor RFSI determined from experiment data which account for the FSI in deuteron target as a function of θπc.m. for individual Wf bins in 0.025 GeV increments in the range of 1.1375<W<1.3375 GeV for 0.8<Q2<1.0 GeV2. The gray shaded regions represent the corresponding systematic uncertainties.

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    • Figure 25
      Figure 25

      Fully exclusive (black points) and quasifree (green squares) cross sections in μb/sr for W= 1.2125 GeV and Q2= 0.5 GeV2. The ϕπc.m.-dependent cross sections are shown in each cosθπc.m. bin and the color-matched dashed lines represent the fits to the cross sections by the function a+bcos2ϕπc.m.+ccosϕπc.m.. The magenta and blue solid lines show the said [63, 64] and maid2000 [57] model predictions, respectively. The gray bars at the bottom of each subplot quantify the systematic uncertainties of each cross section point and the statistical uncertainties are typically smaller than the data point markers.

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    • Figure 26
      Figure 26

      Full exclusive (black points) and quasifree (green squares) cross sections in μb/sr are presented for W = 1.5125 GeV and Q2 = 0.5 GeV2. The ϕπc.m.-dependent cross sections are shown in each cosθπc.m. bin and the color-matched dashed lines represent the fits to the cross sections by the function a+bcos2ϕπc.m.+ccosϕπc.m.. The magenta and blue solid lines show the said [63, 64] and maid2000 [57] model predictions, respectively. The magenta points show the previous available world data [44, 45, 46]. The gray bars at the bottom of each subplot quantify the systematic uncertainties of each cross section point and the statistical uncertainties are typically smaller than the data point markers.

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    • Figure 27
      Figure 27

      Full exclusive (black points) and quasifree (green squares) cross sections in μb/sr are presented for W = 1.6625 GeV and Q2 = 0.5 GeV2. The ϕπc.m.-dependent cross sections are shown in each cosθπc.m. bin (the bins with reasonable statistics are shown) and the color-matched dashed lines represent the fits to the cross sections by the function a+bcos2ϕπc.m.+ccosϕπc.m.. The magenta and blue solid lines show the said [63, 64] and maid2000 [57] model predictions, respectively. The magenta points show the previous available world data [44, 45, 46]. The gray bars at the bottom of each subplot quantify the systematic uncertainties of each cross section point and the statistical uncertainties are typically smaller than the data point markers.

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    • Figure 28
      Figure 28

      Example of the W-dependent σT+εσL, σTT, and σLT structure functions at cosθπc.m.=−0.3 and Q2= 0.5 GeV2 that were extracted from the fully exclusive (black points) and quasifree (green squares) cross sections. For W> 1.35 GeV, the rightmost y-axis scale is used. The data are compared with the maid2000 [57] (magenta line) and maid2007 [56] (blue line) models. The gray bars represent the corresponding systematic uncertainties. The origin of the large gray bars is described in Sec. 7c.

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    • Figure 29
      Figure 29

      Examples of the W-dependent σT+εσL structure function at Q2= 0.5 GeV2 for various cosθπc.m. that were extracted from the fully exclusive (black points) and quasifree (green squares) cross sections up to W< 1.35 GeV and compared with the model-independent interpolation of all available CLAS π+n electroproduction cross section results (magenta points). The gray bars at the bottom represent the corresponding systematic uncertainties of the fully exclusive data (black points). The origin of the large gray bars is described in Sec. 7c.

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    • Figure 30
      Figure 30

      Example of the cosθπc.m.-dependent structure functions σT+εσL (top row), σTT (middle row), and σLT (bottom row) for W= 1.2125 GeV at Q2= 0.5 GeV2 (left column), Q2= 0.7 GeV2 (middle column), and Q2= 0.9 GeV2 (right column) that were extracted for the exclusive (black points) and quasifree (green squares) cross sections and compared with the predictions of the said SM08 (red line), maid2000 (magenta line), and maid2007 (blue line) models. The solid gray bars represent the corresponding systematic uncertainties of the data. The Legendre polynomial expansions were fitted to the corresponding structure function data for π−p orbital momenta up to lmax=1 (black dashed lines) and lmax=2 (black solid lines).

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    • Figure 31
      Figure 31

      The W-dependent Legendre moments Ai of σT+εσL in Eq. (31) up to lmax= 2 at Q2= 0.5 GeV2 that are extracted from the exclusive (black points) and quasifree (green squares) cross sections. For W> 1.35 GeV, the rightmost y-axis scale is used. The data are compared with the maid2007 [56] and maid2000 [57] models. The solid lines represent the full model calculations. The dashed lines correspond to the maid2007 model with specific resonant helicity amplitudes turned off [e.g., noP33 indicates turning off the Δ(1232)3/2+ contributions]. The gray bars represent the corresponding systematic uncertainties of the data.

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    • Figure 32
      Figure 32

      The W-dependent Legendre moments Bi of σTT in Eq. (32) up to lmax= 2 at Q2= 0.5 GeV2 that are extracted from the exclusive (black points) and quasifree (green squares) cross sections. For W> 1.35 GeV, the rightmost y-axis scale is used. The data are compared with the maid2007 [56] and maid2000 [57] models. The solid lines represent the full model calculations. The dashed lines correspond to the maid2007 model with specified resonant helicity amplitudes turned off [e.g., noP33 indicates turning off the Δ(1232)3/2+ contributions]. The gray bars represent the corresponding systematic uncertainties of the data.

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    • Figure 33
      Figure 33

      The W-dependent Legendre moments Ci of σLT in Eq. (33) up to lmax= 2 at Q2= 0.5 GeV2 that are extracted from the exclusive (black points) and quasifree (green squares) cross sections. For W> 1.35 GeV, the rightmost y-axis scale is used. The data are compared with the maid2007 [56] and maid2000 [57] models. The solid lines represent the full model calculations. The dashed lines correspond to the maid2007 model with specified resonant helicity amplitudes turned off [e.g., noP33 indicates turning off the Δ(1232)3/2+ contributions]. The gray bars represent the corresponding systematic uncertainties of the data.

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