We report results on an elastic cross section measurement in proton-proton collisions at a center-of-mass energy $\sqrt{s}=510$ GeV, obtained with the Roman Pot setup of the STAR experiment at the Relativistic Heavy Ion Collider (RHIC). The elastic differential cross section is measured in the four-momentum transfer squared range $0.23 \leq -t \leq 0.67$ GeV$^2$. We find that a constant slope $B$ does not fit the data in the aforementioned $t$ range, and we obtain a much better fit using a second-order polynomial for $B(t)$. The $t$ dependence of $B$ is determined using six subintervals of $t$ in the STAR measured $t$ range, and is in good agreement with the phenomenological models. The measured elastic differential cross section $\mathrm{d}\sigma/\mathrm{dt}$ agrees well with the results obtained at $\sqrt{s} = 546$ GeV for proton--antiproton collisions by the UA4 experiment. We also determine that the integrated elastic cross section within the STAR $t$-range is $\sigma^\mathrm{fid}_\mathrm{el} = 462.1 \pm 0.9 (\mathrm{stat.}) \pm 1.1 (\mathrm {syst.}) \pm 11.6 (\mathrm {scale})$~$\mu\mathrm{b}$.
Top panel: The $pp$ elastic differential cross section $d\sigma/dt$ fitted with an exponential $A e^{-B(t)|t|}$. Bottom panel: Residuals (Data - Fit)/Error. Uncertainties on the data points are smaller than the symbol size. The vertical scale uncertainty of 2.5% is not included in in the full error.
Results of the exponential function $A e^{-B(t)|t|}$ fit to the elastic differential cross section data as well as the integrated fiducial cross section are listed. Also listed are the corresponding values of the statistical and systematic uncertainties. The scale (luminosity and trigger efficiency) uncertainty of 2.5% applicable to the fit parameter $A$ and fiducial cross section $\sigma^\mathrm{fid}_\mathrm{el}$ is not included in the full error.
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 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 nuclear slope parameter B from a fit of the form exp(-Bt-Ct^2-Dt^3). The systematic uncertainty includes experimental and theoretical uncerainties.
A precise measurement of the analyzing power $A_N$ in proton-proton elastic scattering in the region of 4-momentum transfer squared $0.001 < |t| < 0.032 ({\rm GeV}/c)^2$ has been performed using a polarized atomic hydrogen gas jet target and the 100 GeV/$c$ RHIC proton beam. The interference of the electromagnetic spin-flip amplitude with a hadronic spin-nonflip amplitude is predicted to generate a significant $A_N$ of 4--5%, peaking at $-t \simeq 0.003 ({\rm GeV}/c)^2$. This kinematic region is known as the Coulomb Nuclear Interference region. A possible hadronic spin-flip amplitude modifies this otherwise calculable prediction. Our data are well described by the CNI prediction with the electromagnetic spin-flip alone and do not support the presence of a large hadronic spin-flip amplitude.
Analysing power as a function of momentum transfer T. The first DSYS error is the systematic error, the second is the normalization error on the target polarization.
At the Cooler Synchrotron COSY/J\ulich spin correlation parameters in elastic proton-proton (pp) scattering have been measured with a 2.11 GeV polarized proton beam and a polarized hydrogen atomic beam target. We report results for A$_{NN}$, A$_{SS}$, and A_${SL}$ for c.m. scattering angles between 30$^o$ and 90$^o$. Our data on A$_{SS}$ -- the first measurement of this observable above 800 MeV -- clearly disagrees with predictions of available of pp scattering phase shift solutions while A$_{NN}$ and A_${SL}$ are reproduced reasonably well. We show that in the direct reconstruction of the scattering amplitudes from the body of available pp elastic scattering data at 2.1 GeV the number of possible solutions is considerably reduced.
Spin correlation parameters.
Excitation functions AN(pp,Θc.m.) of the analyzing power in pp→ elastic scattering have been measured with a polarized atomic hydrogen target for projectile momenta pp between 1000 and 3300 MeV/ c. The experiment was performed for scattering angles 30°≤Θc.m.≤90° using the recirculating beam of the proton storage ring COSY during acceleration. The resulting excitation functions and angular distributions of high internal consistency have significant impact on the recent phase shift solution SAID SP99, in particular, on the spin triplet phase shifts between 1000 and 1800 MeV, and demonstrate the limited predictive power of single-energy phase shift solutions at these energies.
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Excitation functions of proton-proton elastic scattering cross sections have been measured in narrow steps for projectile momenta pp (energies Tp) from 1100 to 3300MeV/c (500 to 2500 MeV) in the angular range 35°≤Θc.m.≤90° with a detector providing ΔΘc.m.≈1.4° resolution. Measurements have been performed continuously during projectile acceleration in the cooler synchrotron COSY with an internal CH2 fiber target, taking particular care to monitor luminosity as a function of Tp. The advantages of this experimental technique are demonstrated, and the excitation functions obtained are compared to existing cross section data. No evidence for narrow structures was found.
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Accelerating polarized protons to 22 GeV/c at the Brookhaven Alternating Gradient Synchro- tron required both extensive hardware modifications and a difficult commissioning process. We had to overcome 45 strong depolarizing resonances to maintain polarization up to 22 GeV/c in this strong-focusing synchrotron. At 18.5 GeV/c we measured the analyzing power A and the spin-spin correlation parameter Ann in large- P⊥2 proton-proton elastic scattering, using the polarized proton beam and a polarized proton target. We also obtained a high-precision measurement of A at P⊥2=0.3 (GeV/c)2 at 13.3 GeV/c. At 18.5 GeV/c we found that Ann=(-2±16)% at P⊥2=4.7 (GeV/c)2, where it was about 60% near 12 GeV at the Argonne Zero Gradient Synchrotron. This sharp change suggests that spin-spin forces may have a strong and unexpected energy dependence at high P⊥2.
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2.2 GeV point taken from Brown et al., PR D31(85) 3017.
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We measured the analyzing power A and the spin-spin correlation parameter Ann in medium-P⊥2 proton-proton elastic scattering, using a polarized-proton target and the 18.5-GeV/c Brookhaven Alternating-Gradient Synchrotron polarized-proton beam. We found sharp dips in both A and Ann, which occur at different P⊥2 values. The unexpected sharp structure in the spin-spin force occurs near P⊥2=2.3 (GeV/c)2 where the elastic cross section has no apparent structure.
Errors contain both statistics and systematics.
We measured the analyzing power A and the spin-spin correlation parameter Ann, in large-P⊥2 proton-proton elastic scattering, using a polarized-proton target and the polarized-proton beam at the Brookhaven Alternating-Gradient Synchrotron. We also used our polarimeter to measure A at small P⊥2 at 13 GeV with good precision and found some deviation from the expected 1Plab behavior. At 18.5 GeV/c we found Ann=(−2±16)% at P⊥2=4.7 (GeV/c)2. Comparison with lower-energy data from the Argonne Zero-Gradient Synchrotron shows a sharp and surprising energy dependence for Ann at large P⊥2.
POL is error weighted average of polarized beam and target measurements.
POL is error-weighted average of polarized beam and target measurements.
POL is error-weighted average of polarized beam and target measurement.
The spin analyzing power A in 28-GeV/c proton-proton elastic scattering was measured at P⊥2=6.5 (GeV/c)2 using a polarized proton target and a high-intensity unpolarized proton beam at the Brookhaven National Laboratory Alternating Gradient Synchrotron. The result of (24±8)% confirms that the analyzing power is large and rising in the large-P⊥2 region.
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