Abstract
We update our eikonal fit and comprehensive asymptotic fits to high energy data on proton--proton and antiproton--proton scattering for $\sigma_{\rm tot}$, $\sigma_{\rm elas}$, $\sigma_{\rm inel}$, $\rho$, and $B$. The fits include the new TOTEM values of total proton-proton cross section, $\rho$, and $B$ at $W=\sqrt{s}$ = 13 TeV and the Telescope Array value of the total proton-proton cross section at $W=\sqrt{s}$ = 95 TeV, data from the latest measurements of the inelastic cross sections at $W$= 8 TeV (by TOTEM and ATLAS) and 13 TeV (by CMS, ATLAS, and TOTEM). An important new feature of this work is the correction of the data to include the effects of curvature in $\ln{(d\sigma/dt)}$ on the values of $B$, $d\sigma/dt$ at $t=0$, and $\sigma_{\rm tot}$ obtained by extrapolation from the larger values of $t$ where the differential cross section is measured, The effects are significant. The stability of the fits is excellent and the new results agree well with the predictions of earlier fits. This work again confirms the evidence for the proton asymptotically becoming a black disk of gluons.
Highlights
In a recent paper [1], we presented a detailed eikonal fit to the proton -current scattering at data on proton-proton and center-of-mass energies W1⁄4anptipffisffirofrtoonm-In a second paper [2], we gave the results of a comprehensive fit to the data on the total, inelastic, and elastic scattering cross sections, ρ, and B for pp and pp scattering between 6 GeV and 57 TeV using parametrizations of those quantities which reflect the established ln2 s behavior of the cross sections at high energies [3,4]
With the slightly modified eikonal fit described below, we find B 1⁄4 20.26 GeV−2, C1⁄49.18GeV−4, and D 1⁄4 26.53 GeV−6 at 8 TeV compared to the values 20.47 Æ 0.14 GeV−2, 8.8 Æ 1.6 GeV−4, and 20 Æ 6 GeV−6 found by TOTEM [7]
Since most of the data on differential cross sections at lower energies are not precise or extensive enough to support direct experimental determinations of C and D, we will adopt the procedure used in Ref. [13], in which we showed that the inclusion of curvature terms calculated using the earlier eikonal fit improved the fits to experiment at representative energies and, that a simple semianalytic expression gave corrections to B and σtot consistent with the refitted values
Summary
In a recent paper [1], we presented a detailed eikonal fit to the proton -current scattering at data on proton-proton and center-of-mass energies W. These result from the effects of curvature terms in lnðdσ=dtÞ which were not included in earlier experimental analyses but affect the extrapolation of lnðdσ=dtÞ from the often fairly large values of jtj or q2 measured to t 1⁄4 0 to determine B and dσðW; tÞ=dtjt1⁄40 1⁄4 ð1þ ρ2Þσ2tot=16π. [13] to take into account approximately the effects on measurements of B and σtot of the nonlinear “curvature” terms in the square of the invariant momentum transfer q2 1⁄4 jtj in the expansion lnðdσ=dq2Þ 1⁄4 A − Bq2 þ Cq4 − Dq6 þ Á Á Á These effects have been ignored in most experimental analyses, with lnðdσ=dq2Þ assumed to vary strictly linearly with q2 or t, with the experimental values Aexp and Bexp determined by least-squares fits to dσðW; q2Þ=dq over a range of small q2.
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