In a special run of the LHC with $\beta^\star = 2.5~$km, proton-proton elastic-scattering events were recorded at $\sqrt{s} = 13~$TeV with an integrated luminosity of $340~\mu \textrm{b}^{-1}$ using the ALFA subdetector of ATLAS in 2016. The elastic cross section was measured differentially in the Mandelstam $t$ variable in the range from $-t = 2.5 \cdot 10^{-4}~$GeV$^{2}$ to $-t = 0.46~$GeV$^{2}$ using 6.9 million elastic-scattering candidates. This paper presents measurements of the total cross section $\sigma_{\textrm{tot}}$, parameters of the nuclear slope, and the $\rho$-parameter defined as the ratio of the real part to the imaginary part of the elastic-scattering amplitude in the limit $t \rightarrow 0$. These parameters are determined from a fit to the differential elastic cross section using the optical theorem and different parameterizations of the $t$-dependence. The results for $\sigma_{\textrm{tot}}$ and $\rho$ are \begin{equation*} \sigma_{\textrm{tot}}(pp\rightarrow X) = \mbox{104.7} \pm 1.1 \; \mbox{mb} , \; \; \; \rho = \mbox{0.098} \pm 0.011 . \end{equation*} The uncertainty in $\sigma_{\textrm{tot}}$ is dominated by the luminosity measurement, and in $\rho$ by imperfect knowledge of the detector alignment and by modelling of the nuclear amplitude.
The measured total cross section. The systematic uncertainty includes experimental and theoretical uncerainties.
The measured total cross section. The systematic uncertainty includes experimental and theoretical uncerainties.
The rho-parameter, i.e. the ratio of the real to imaginary part of the elastic scattering amplitude extrapolated to t=0. The systematic uncertainty includes experimental and theoretical uncerainties.
The properties of the diffractive peak observed in the mass spectra of systems recoiling against observed high-momentum protons emerging from pp collisions at the CERN ISR have been investigated. The cross sections in this peak have been found to have a steep t dependence which flattens out as | t | increases. The high mass side of the peak varies approximately as 1/ M 2 (where M is the missing mass of the recoiling system) and scales well in terms of the variable M 2 / s . The position of the maximum has been observed to move to lower values of M 2 / s as the kinematic boundary of this variable decreases with increasing s . The measured cross sections, integrated up to M 2 / s =0.05, rise by (15±5)% over the s range 549 to 1464 GeV 2 .
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We measured d σ d t(90° cm ) for ↑+ p ↑→ p + p from 1.75 to 5.5 GeV/ c , using the Argonne zero-gradient synchrotron 70% polarized proton beam and a 70% polarized proton target. We found that the spin-spin correlation parameter. A nn , equals 60% at low energy, then drops sharply to about 10% near 3.5 GeV/ c , and remains constant up to 5.5 GeV/ c .
ANALYZING POWER. QUOTED ERRORS DUE TO 4.3 PCT POINT TO POINT RELATIVE ERROR.
THE SPIN-SPIN CORRELATION PARAMETER CNN IS NOW DENOTED BY ANN ACCORDING TO THE NEW ANN ARBOR CONVENTION.
The elastic cross section for proton proton scattering at 11.75 GeV/ c was measured at the Argonne ZGS using a 50% polarized target. In the range p ⊥ 2 =0.6 → 2.2 (GeV/ c ) 2 we obtained precise measurements of d σ d t(ij) for the ⇈ ⇊, and ⇅ initial spin states perpendicular to the scattering plane. We confirmed that the asymmetry parameter, A , decreases with energy in the diffraction peak, but is approximately energy-independent at large p ⊥ 2 . We found that the spin correlation parameter c nn acquires rather dramatic structure, and at large p ⊥ 2 seems to grow with energy.
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The elastic cross section for proton proton scattering at 6 GeV c was measured using a 70% polarized beam and a 75% polarized target at the Argonne ZGS. In the range P ⊥ 2 = 0.5 → 2.0( GeV c ) 2 we obtained small error measurements for the ↑↑, ↓↓ and ↑↓ initial spin states perpendicular to the scattering plane. At P ⊥ 2 = 0.5 we also measured the recoil spin and found that the 5 different cross sections were very unequal.
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The polarization of the recoil proton has been measured in both high-energy elastic and inclusive proton-proton scattering at the internal-target area of Fermi National Accelerator Laboratory. The polarization in elastic scattering was measured at a number of center-of-mass energies up to s=19.7 GeV. Indications of negative polarization were seen at the higher center-of-mass energies for t values of -0.6, -0.8, and -1.0 (GeV/c)2. In the inclusive process p+p→p↑+X the polarization was found to be independent of beam energy from 100 to 400 GeV for xF values of -0.7, -0.8, -0.9. The polarization at PT=1.0 GeV/c, xF=−0.7 and xF=−0.8 was less than 2.5%. This is significantly lower than the corresponding measurements reported for Λ0 inclusive polarization.
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The differential elastic p−p scattering cross section was measured at 6 GeV/c at the Argonne Zero Gradient Synchrotron in the range P⊥2=0.60−1.0 (GeV/c)2 using a 65% polarized target and a 75% polarized proton beam of intensity 3 × 109 protons/pulse. The polarization of the recoil proton was simultaneously measured with a well calibrated carbon-target polarimeter. All three polarizations were measured perpendicular to the horizontal scattering plane. Our results indicate that P and T invariance are both obeyed to good precision even at our largest P⊥2. Parity invariance implies that the eight single-flip transversity cross sections are zero, so our data gives the magnitudes of the eight remaining pure spin cross sections where all spins are measured. We find that the four double-flip transversity cross sections are nonzero.
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THE FIVE INDEPENDENT PURE FOUR-SPIN CROSS SECTIONS AS DERIVED FROM THE EIGHT MEASURED THREE-SPIN CROSS SECTIONS ASSUMING P AND T INVARIANCE. THE ABSOLUTE DIFFERENTIAL CROSS SECTION VALUES ASSUME THAT THE SPIN-AVERAGED D(SIG)/DT IS 2.25, 1.17, 0.365 AND 0.167 MB/GEV**2 FOR EACH VALUE OF PT**2 RESPECTIVELY.
WOLFENSTEIN PARAMETERS. POL(NAME=A) IS (N000) OR (0N00), THE ANALYZING POWER AVERAGED OVER TARGET OR BEAM POLARIZATION. POL(NAME=P) IS (00N0), THE POLARIZATION PARAMETER. TIME-REVERSAL INVARIANCE REQUIRES THAT P = A. POL.POL(NAME=CNN) IS (NN00) USING T-INVARIANCE. POL.POL(NAME=DNN) IS (0N0N). POL.POL(NAME=KNN) IS (N00N). POL.POL(NAME=C3N) IS A COMPONENT OF THE TRIPLE SPIN CORRELATION TENSOR. PARITY INVARIANCE REQUIRES THAT C3N = P.
Proton-proton elastic scattering has been measured in the region 4.9<|t|<12.1 GeV2 at a beam momentum of 201 GeV/c. If the form exp(At) is fitted to the data, the exponent A gradually changes from 1.5 to 0.9 GeV−2 over our t range. The data are consistent with the form exp(−6.6p⊥). A comparison with intersecting storage ring results shows that in this kinematical region the slopes are about the same, but dσdt at fixed t is still dropping with energy.
7904 ELASTIC EVENTS.
1030 ELASTIC EVENTS.
We measured dσdt for p↑+p↑→p+p from P⊥2=4.50 to 5.09 (GeV/c)2 at 11.75 GeV/c. We used a 59%-polarized proton beam and a 71%-polarized proton target with both spins oriented perpendicular to the scattering plane. In these large-P⊥2 hard-scattering events, spin effects are very large and the ratio (dσdt)↑↑:(dσdt)↑↓ grows rapidly with increasing P⊥2, reaching a value of 4 at 90° (c.m.). Thus, hard elastic scattering, which is presumably due to the direct scattering of the protons' constituents, may only occur when the two incident protons' spins are parallel.
THE ERRORS INCLUDE STATISTICAL AND SYSTEMATIC ERRORS ADDED IN QUADRATURE. THE PARALLEL/ANTIPARALLEL SPIN CROSS SECTION RATIO IS (1+CNN)/(1-CNN).
Proton-proton elastic scattering at 400 GeV/c has been measured in the region 5.4<−t<14.4 GeV2 with no sign of a second dip or "break." If the data are fitted by exp(At), the slope A decreases from 1.5±0.1 to 0.7±0.2 GeV−2 over the range. At fixed t the 400-GeV/c cross sections are about 0.6 times those at 200 GeV/c in this t range. At fixed θc.m.=15°, dσdt∝s−n where n=9.7±0.3.
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