Study of the Inclusive Reactionγp→π−+(Anything)with Polarized Photons at 2.8, 4.7, and 9.3 GeV

Abstract

We study the inclusive spectra of ${\pi }^{-}$ mesons from the events obtained in three exposures of the SLAC 82-in. hydrogen bubble chamber to a nearly monochromatic polarized photon beam of mean energies 2.8, 4.7, and 9.3 GeV. The data are presented in terms of transverse momentum $p_{\perp }$ and three suggested choices for the other independent variable, i.e., the longitudinal momentum $p_{\parallel }$ in the laboratory system, the rapidity variable $y=\frac{1}{2}\ln \left[\frac{(E+p_{\parallel })}{(E-p_{\parallel })}\right]$, and the variable suggested by Feynman $x=\frac{p_{\parallel }^{*}}{p_{max}^{*}}$ in the c.m. system. The $4\pi$ geometry of the bubble chamber allows us to cover the entire kinematically allowed range of these variables. We show that exact limiting fragmentation does not occur at our energies, but the data are compatible with an approach to a limiting distribution as $A+B{s}^{\frac{-1\mathrm{}}{2}}$. The qualitative features of the structure function $f(x,p_{\perp }^{}{}_{}{}^2)$ in terms of Feynman's $x$ variable are similar at the three energies. Quantitatively, we find 5-10% differences between the 4.7- and 9.3-GeV data near $x=0\mathrm{}$. We find $f(x,p_{\perp }^{}{}_{}{}^2)$ is not factorizable into independent functions of $x$ and $p_{\perp }^{}{}_{}{}^2$. For our data the mean ${\pi }^{-}$ multiplicity is described well by $〈n^{-}〉=c^{-}\ln s+d^{-}$, where $c^{-}=0.44\mathrm{}\pm 0.04$ and $d^{-}=0.07\mathrm{}\pm 0.08$. Following the procedure suggested by Bali et al., we calculate $c^{-}$ from our experimentally observed 9.3-GeV structure function at $x=0\mathrm{}$ and find $c^{-}=0.44\mathrm{}\pm 0.02$ in agreement with the value obtained directly. We find a correlation between the azimuth of the ${\pi }^{-}$ and the photon polarization plane only for $x>\mathrm{}0.3\mathrm{}$ when elastic ${\rho }^0$ photo-production is excluded. Lastly, we note that the distribution of

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