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.
The proton-proton elastic differential cross section ${\rm d}\sigma/{\rm d}t$ has been measured by the TOTEM experiment at $\sqrt{s}=2.76$ TeV energy with $\beta^{*}=11$ m beam optics. The Roman Pots were inserted to 13 times the transverse beam size from the beam, which allowed to measure the differential cross-section of elastic scattering in a range of the squared four-momentum transfer ($|t|$) from $0.36$ GeV$^{2}$ to $0.74$ GeV$^{2}$. The differential cross-section can be described with an exponential in the $|t|$-range between $0.36$ GeV$^{2}$ and $0.54$ GeV$^{2}$, followed by a diffractive minimum (dip) at $|t_{\rm dip}| = 0.61 \pm 0.03$ GeV$^{2}$ and a subsequent maximum (bump). The ratio of the ${\rm d}\sigma/{\rm d}t$ at the bump and at the dip is $1.7\pm 0.2$. When compared to the $\rm p\bar{p}$ measurement of the D0 experiment at $\sqrt s = 1.96$ TeV, a significant difference can be observed. Under the condition that the effects due to the energy difference between TOTEM and D0 can be neglected, the result provides evidence for a colourless 3-gluon bound state exchange in the $t$-channel of the proton-proton elastic scattering.
Differential cross-section.
Differential cross-section.
The TOTEM collaboration has measured the elastic proton-proton differential cross section ${\rm d}\sigma/{\rm d}t$ at $\sqrt{s}=13$ TeV LHC energy using dedicated $\beta^{*}=90$ m beam optics. The Roman Pot detectors were inserted to 10$\sigma$ distance from the LHC beam, which allowed the measurement of the range $[0.04$ GeV$^{2};4 $GeV$^{2}] $ in four-momentum transfer squared $|t|$. The efficient data acquisition allowed to collect about 10$^{9}$ elastic events to precisely measure the differential cross-section including the diffractive minimum (dip), the subsequent maximum (bump) and the large-$|t|$ tail. The average nuclear slope has been found to be $B=(20.40 \pm 0.002^{\rm stat} \pm 0.01^{\rm syst})~$GeV$^{-2}$ in the $|t|$-range $0.04~$GeV$^{2}$ to $0.2~$GeV$^{2}$. The dip position is $|t_{\rm dip}|=(0.47 \pm 0.004^{\rm stat} \pm 0.01^{\rm syst})~$GeV$^{2}$. The differential cross section ratio at the bump vs. at the dip $R=1.77\pm0.01^{\rm stat}$ has been measured with high precision. The series of TOTEM elastic pp measurements show that the dip is a permanent feature of the pp differential cross-section at the TeV scale.
Differential cross-section.
The TOTEM experiment at the LHC has performed the first measurement at $\sqrt{s} = 13$ TeV of the $\rho$ parameter, the real to imaginary ratio of the nuclear elastic scattering amplitude at $t=0$, obtaining the following results: $\rho = 0.09 \pm 0.01$ and $\rho = 0.10 \pm 0.01$, depending on different physics assumptions and mathematical modelling. The unprecedented precision of the $\rho$ measurement, combined with the TOTEM total cross-section measurements in an energy range larger than 10 TeV (from 2.76 to 13 TeV), has implied the exclusion of all the models classified and published by COMPETE. The $\rho$ results obtained by TOTEM are compatible with the predictions, from alternative theoretical models both in the Regge-like framework and in the QCD framework, of a colourless 3-gluon bound state exchange in the $t$-channel of the proton-proton elastic scattering. On the contrary, if shown that the 3-gluon bound state $t$-channel exchange is not of importance for the description of elastic scattering, the $\rho$ value determined by TOTEM would represent a first evidence of a slowing down of the total cross-section growth at higher energies. The very low-$|t|$ reach allowed also to determine the absolute normalisation using the Coulomb amplitude for the first time at the LHC and obtain a new total proton-proton cross-section measurement $\sigma_{tot} = 110.3 \pm 3.5$ mb, completely independent from the previous TOTEM determination. Combining the two TOTEM results yields $\sigma_{tot} = 110.5 \pm 2.4$ mb.
Differential cross-section.
The TOTEM experiment at the CERN LHC has measured elastic proton-proton scattering at the centre-of-mass energy $\sqrt{s}$ = 8 TeV and four-momentum transfers squared, |t|, from 6 x $10^{-4}$ GeV$^2$ to 0.2 GeV$^2$. Near the lower end of the |t|-interval the differential cross-section is sensitive to the interference between the hadronic and the electromagnetic scattering amplitudes. This article presents the elastic cross-section measurement and the constraints it imposes on the functional forms of the modulus and phase of the hadronic elastic amplitude. The data exclude the traditional Simplified West and Yennie interference formula that requires a constant phase and a purely exponential modulus of the hadronic amplitude. For parametrisations of the hadronic modulus with second- or third-order polynomials in the exponent, the data are compatible with hadronic phase functions giving either central or peripheral behaviour in the impact parameter picture of elastic scattering. In both cases, the $\rho$-parameter is found to be 0.12 $\pm$ 0.03. The results for the total hadronic cross-section are $\sigma_{tot}$ = (102.9 $\pm$ 2.3) mb and (103.0 $\pm$ 2.3) mb for central and peripheral phase formulations, respectively. Both are consistent with previous TOTEM measurements.
Differential cross-section.
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