Differential cross section measurements for $\gamma n\to {\pi }^{-}p$ above the first nucleon resonance region

The quasifree $\gamma d\to {\pi }^{-}p\left(p\right)$ differential cross section has been measured with CLAS at photon beam energies $E_{\gamma }$ from 0.445 to 2.510 GeV (corresponding to $W$ from 1.311 to 2.366 GeV) for pion center-of-mass angles $cos{\theta }_{\pi }^{c.m.}$ from $-0.72$ to 0.92. A correction for final state interactions has been applied to these data to extract the $\gamma n\to {\pi }^{-}p$ differential cross sections. These cross sections are quoted in 8428 $(E_{\gamma },cos{\theta }_{\pi }^{c.m.})$ bins, a factor of nearly 3 increase in the world statistics for this channel in this kinematic range. These new data help to constrain coupled-channel analysis fits used to disentangle the spectrum of $N^{*}$ resonances and extract their properties. Selected photon decay amplitudes $N^{*}\to \gamma n$ at the resonance poles are determined for the first time and are reported here.

Figure 1

Cutaway view of the CLAS detector [11] illustrating the torus magnet, three regions of drift chambers (R1–R3), Cherenkov counters (CC), time-of-flight scintillators (TOF), and electromagnetic calorimeters (EC). The CLAS detector is roughly 10 m in diameter.

Figure 2

$\mathrm{\Delta }\beta$ vs momentum for proton (a) and ${\pi }^{-}$ (b) candidates. $\mathrm{\Delta }\beta$ is centered at zero for the protons and ${\pi }^{-}$'s, and the neighboring bands are from other particle types, such as ${\pi }^{+}$'s, or from choosing the wrong beam bunch.

Figure 3

The vertex $z$ of the reconstructed tracks in $\gamma d\to {\pi }^{-}p\left(p\right)$. Tracks with $z>5$ cm were cut, removing backgrounds from the aluminum end cap of the target assembly at $z=7$ cm.

Figure 4

(a) The $\gamma d\to {\pi }^{-}p\left(p\right)$ missing momentum and (b) the same missing momentum vs $cos\theta$ of the missing momentum in the laboratory frame. The low-momentum, quasifree protons followed the Fermi motion distribution and were relatively uniformly distributed in $cos\theta$. The high-momentum tail of rescattered protons was removed by the 200-MeV/$c$ cut on the missing momentum [indicated by the red vertical line in (a)].

Figure 5

The proton reconstruction efficiency ratio defined by Eq. (1) as a function of laboratory polar angle. In (a), sector $\varphi$ is the azimuthal angle relative to the center of the CLAS sector. Both plots are summed over all CLAS sectors. The magenta lines indicate the cuts used to reject data that were not accurately modeled by the simulation.

Figure 6

The proton (a) and ${\pi }^{-}$ (b) triggering efficiencies in CLAS sector 2 in terms of momentum $p$ vs laboratory polar angle $\theta$. The proton triggering was efficient in general, but the ${\pi }^{-}$ efficiency was affected over portions of the acceptance due to low-gain TOF PMTs.

Figure 7

Sample fit of the missing-proton peak in the missing mass off of $\gamma d\to {\pi }^{-}p$. The signals were fit to a double-Gaussian function over a linear background. The blue line shape represents the double-Gaussian fit function, the magenta line shape represents the linear fit function, and the black line shape represents the total fit function.

Figure 8

A comparison of the reconstructed $\gamma d\to {\pi }^{-}p\left(p\right)$ yields between the experimental data (black) and the simulation (red) as a function of the pion c.m. angle $cos{\theta }_{\pi }^{c.m.}$ in two selected beam energy bins for the 2.655-GeV data. The simulated yields have been scaled such that their integral matches that of the experimental data.

Figure 9

The CLAS acceptance in selected energy bins as a function of the pion c.m. angle $cos{\theta }_{\pi }^{c.m.}$. The dips in the acceptance are primarily due to triggering inefficiencies and problematic areas of the drift chambers.

Figure 10

Selected cross section data for $\gamma n\to {\pi }^{-}p$ vs $cos{\theta }_{\pi }^{c.m.}$ below $E_{\gamma }=1.05$ GeV: CLAS g13 (black open circles), SLAC [23] (blue open triangles), DESY [24] (violet open squares), MAMI-B [25] (cyan open down triangles), and Frascati [26] (pink open stars); ${\pi }^{-}p\to \gamma n$ data: BNL [27] (green open diamonds), LBL [28] (orange closed diamonds), and LAMPF [29] (gray closed circles); fits: SAID MA27 (blue solid lines), SAID PR15 [30] (red dot-dashed lines), BG2014-02 [4] (green dashed lines), and MAID2007 [31] (violet dotted lines). The $y$ axes are log scale. Only angle-dependent uncertainties are shown for all data. The total normalization uncertainties for the CLAS g13 data are about 3.4%.

Figure 11

Selected cross section data for $\gamma n\to {\pi }^{-}p$ vs $cos{\theta }_{\pi }^{c.m.}$ above $E_{\gamma }=1.05$ GeV: CLAS g13 (black open circles), CLAS g10 [8] (red open pluses), SLAC [23] (blue open triangles), and DESY [24] (violet open squares); fits: SAID MA27 (blue solid lines), SAID PR15 [30] (red dot-dashed lines), BG2014-02 [4] (green dashed lines), and MAID2007 [31] (violet dashed lines). The $y$ axes are log scale. Only angle-dependent uncertainties are shown for all data. The total normalization uncertainties for the CLAS g13 data are about 3.4%.

Figure 12

Selected cross section data for $\gamma n\to {\pi }^{-}p$ vs $W$: CLAS g13 (black open circles), CLAS g10 [8] (red open pluses), SLAC [23] (blue open triangles), DESY [24] (violet open squares), MAMI-B [25] (cyan open down-triangles), and Frascati [26] (pink open stars); ${\pi }^{-}p\to \gamma n$ data: BNL [27] (green open diamonds), LBL [28] (orange closed diamonds), and LAMPF [29] (gray closed circles); fits: SAID MA27 (blue solid lines), SAID PR15 [30] (red dot-dashed lines), BG2014-02 [4] (green dashed lines), and MAID2007 [31] (which terminates at $W$ = 2 GeV or $E_{\gamma }=1.65$ GeV) (violet dotted lines). The $y$ axes are log scale. Only angle-dependent uncertainties are shown for all data. The total normalization uncertainties for the CLAS g13 data are about 3.4%.

Figure 13

Feynman diagrams for the leading terms of the $\gamma d\to {\pi }^{-}pp$ amplitude: (a) IA, (b) $pp$-FSI, and (c) $\pi \mathrm{N}$-FSI. The filled black circles represent the FSI vertices. The wavy, dashed, solid, and double lines correspond to the photons, pions, nucleons, and deuterons, respectively.

Figure 14

The FSI correction factor $R(E_{\gamma },{\theta }_{\pi }^{c.m.})$ for selected beam energies vs $cos{\theta }_{\pi }^{c.m.}$, where ${\theta }_{\pi }^{c.m.}$ is the polar angle of the outgoing ${\pi }^{-}$ in the rest frame of the ${\pi }^{-}$ and the fast proton. The fast knocked-out protons $p_1$ with momentum $>200\mathrm{MeV}/c$ were selected, while the slow proton spectators $p_2$ have momentum $<200\mathrm{MeV}/c$. The 2% normalization uncertainties are not shown.

Figure 15

Coefficients of the Legendre polynomials $A_J\left(W\right)$ (blue filled circles) from the fits of the CLAS g13 $\gamma n\to {\pi }^{-}p$ cross section data. The error bars represent the $A_J\left(W\right)$ uncertainties from the fits in which only the statistical uncertainties were used. The $A_J\left(W\right)$ coefficients have been scaled (dashed horizontal lines) by $n\times A_J+m$ to enable easy visualization. The red vertical arrows in the top row of plots indicate the masses of the PDG four-star resonances (Breit-Wigner masses) in this energy range [2]. The upper row of arrows corresponds to $N^{*}$ states with isospin $I=1/2$ and the lower row corresponds to ${\mathrm{\Delta }}^{*}$ states with $I=3/2$.

Figure 16

Comparison of the previous SAID solution PR15 [30] applied to the present g13 data with (blue filled triangles) and without FSI corrections (black open circles), and the new SAID MA27 (red full circles) solution obtained after adding the present g13 data with FSI corrections into the fit (the solid lines connecting the points are included only to guide the eye). Shown are the fit ${\chi }^2$ per data point values averaged within each energy bin $E_{\gamma }$, where the horizontal dashed lines (blue (black) for PR15 and red for MA27) show the overall ${\chi }^2$ per data point values from Table 2.

Figure 17

Neutron multipole $I$ = 1/2 amplitudes [in attometer (am) units] from threshold to $W=2.43$ GeV ($E_{\gamma }=2.7$ GeV). For the amplitudes, the subscript $n$ denotes a neutron target, the subscript $\ell \pm$ gives the value of $j=\ell \pm 1/2$, and the superscript gives the isospin index. The red solid (blue dash-dotted) lines correspond to the new SAID MA27 (old PR15 [30]) solution. The magenta dotted (black dashed) lines give the BG2014-02 [4] (MAID2007 [31], which terminates at $W=2$ GeV) solution. The vertical arrows indicate the Breit-Wigner mass ($W_R$), and the upper and lower horizontal bars show the partial (${\mathrm{\Gamma }}_{\pi N}$) and the full ($\mathrm{\Gamma }$) widths, respectively, of the resonances extracted by the Breit-Wigner fit of the $\pi N$ data associated with the SAID solution SP06 [33]. The red vertical arrows for (a) and (b) indicate the $\eta$ production threshold.

Figure 18

Neutron multipole $I$ = 1/2 amplitudes [in attometer (am) units] from threshold to $W=2.43$ GeV ($E_{\gamma }=2.7$ GeV). The notation of the multipoles is the same as in Fig. 17.

Figure 19

Neutron multipole $I=1/2$ amplitudes [in attometer (am) units] from threshold to $W=2.43$ GeV ($E_{\gamma }=2.7$ GeV). The notation of the multipoles is the same as in Fig. 17.