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 STAR Collaboration reports on the photoproduction of $\pi^+\pi^-$ pairs in gold-gold collisions at a center-of-mass energy of 200 GeV/nucleon-pair. These pion pairs are produced when a nearly-real photon emitted by one ion scatters from the other ion. We fit the $\pi^+\pi^-$ invariant mass spectrum with a combination of $\rho$ and $\omega$ resonances and a direct $\pi^+\pi^-$ continuum. This is the first observation of the $\omega$ in ultra-peripheral collisions, and the first measurement of $\rho-\omega$ interference at energies where photoproduction is dominated by Pomeron exchange. The $\omega$ amplitude is consistent with the measured $\gamma p\rightarrow \omega p$ cross section, a classical Glauber calculation and the $\omega\rightarrow\pi^+\pi^-$ branching ratio. The $\omega$ phase angle is similar to that observed at much lower energies, showing that the $\rho-\omega$ phase difference does not depend significantly on photon energy. The $\rho^0$ differential cross section $d\sigma/dt$ exhibits a clear diffraction pattern, compatible with scattering from a gold nucleus, with 2 minima visible. The positions of the diffractive minima agree better with the predictions of a quantum Glauber calculation that does not include nuclear shadowing than with a calculation that does include shadowing.
The $\pi^+\pi^-$ invariant-mass distribution for all selected $\pi\pi$ candidates with $p_T~<~100~\textrm{MeV}/c$.
The ratio $|B/A|$ of amplitudes of nonresonant $\pi^+\pi^-$ and $\rho^0$ mesons in the present STAR analysis.
The ratio $|B/A|$ of amplitudes of nonresonant $\pi^+\pi^-$ and $\rho^0$ mesons in the previous STAR analysis, Phys. Rev. C 77 034910 (2008).
A measurement of the total $pp$ cross section at the LHC at $\sqrt{s}=8$ TeV is presented. An integrated luminosity of $500$ $\mu$b$^{-1}$ was accumulated in a special run with high-$\beta^{\star}$ beam optics to measure the differential elastic cross section as a function of the Mandelstam momentum transfer variable $t$. The measurement is performed with the ALFA sub-detector of ATLAS. Using a fit to the differential elastic cross section in the $-t$ range from $0.014$ GeV$^2$ to $0.1$ GeV$^2$ to extrapolate $t\rightarrow 0$, the total cross section, $\sigma_{\mathrm{tot}}(pp\rightarrow X)$, is measured via the optical theorem to be: $\sigma_{\mathrm{tot}}(pp\rightarrow X) = {96.07} \; \pm 0.18 \; ({{stat.}}) \pm 0.85 \; ({{exp.}}) \pm 0.31 \; ({extr.}) \; {mb} \;,$ where the first error is statistical, the second accounts for all experimental systematic uncertainties and the last is related to uncertainties in the extrapolation $t\rightarrow 0$. In addition, the slope of the exponential function describing the elastic cross section at small $t$ is determined to be $B = 19.74 \pm 0.05 \; ({{stat.}}) \pm 0.23 \; ({{syst.}}) \; {GeV}^{-2}$.
The measured total cross section, the first systematic error accounts for all experimental uncertainties and the second error for the extrapolation t-->0.
The nuclear slope of the differential eslastic cross section at small |t|, the first systematic error accounts for all experimental uncertainties and the second error for the extrapolation t-->0.
The total elastic cross section and the observed elastic cross section within the fiducial volume.
About 100 000 pictures, with an average of ∼12K + per picture, taken in the 81 cm Saclay deuterium bubble chamber exposed to a separated 3 GeV/c K + beam have been analysed for the reaction K + d→K 0 pp in the 1-prong V 0 and 2-prong V 0 topologies. 214 such events have been found allowing a determination of the differential cross-section. A comparison with the prediction of Rarita and Schwarzschild yields reasonable agreement; in particular a large real part is inferred for the amplitude for the reaction K + n→K 0 p.
The errors are statistical only.
The errors are statistical only. To evaluate the cross section on neutron thE data are divided on (1-FORMFACTOR(C=DEUT). For definition of the formfactor see L. Durand, Phys. Rev. 115 (1959) 1020.
A measurement of the total $pp$ cross section at the LHC at $\sqrt{s}=7$ TeV is presented. In a special run with high-$\beta^{\star}$ beam optics, an integrated luminosity of 80 $\mu$b$^{-1}$ was accumulated in order to measure the differential elastic cross section as a function of the Mandelstam momentum transfer variable $t$. The measurement is performed with the ALFA sub-detector of ATLAS. Using a fit to the differential elastic cross section in the $|t|$ range from 0.01 GeV$^2$ to 0.1 GeV$^2$ to extrapolate to $|t|\rightarrow 0$, the total cross section, $\sigma_{\mathrm{tot}}(pp\rightarrow X)$, is measured via the optical theorem to be: $$\sigma_{\mathrm{tot}}(pp\rightarrow X) = 95.35 \; \pm 0.38 \; ({\mbox{stat.}}) \pm 1.25 \; ({\mbox{exp.}}) \pm 0.37 \; (\mbox{extr.}) \; \mbox{mb},$$ where the first error is statistical, the second accounts for all experimental systematic uncertainties and the last is related to uncertainties in the extrapolation to $|t|\rightarrow 0$. In addition, the slope of the elastic cross section at small $|t|$ is determined to be $B = 19.73 \pm 0.14 \; ({\mbox{stat.}}) \pm 0.26 \; ({\mbox{syst.}}) \; \mbox{GeV}^{-2}$.
The measured total cross section, the first systematic error accounts for all experimental uncertainties and the second error for the extrapolation t-->0.
The nuclear slope of the differential eslastic cross section at small |t|, the first systematic error accounts for all experimental uncertainties and the second error for the extrapolation t-->0.
The Optical Point dsigma/(elastic)/dt(t-->0), the total elastic cross section and the observed elastic cross section within the fiducial volume. The first systematic error accounts for all experimental uncertainties and the second error for the extrapolation t-->0.
Diffractive photoproduction of vector mesons, gamma p --> V Y, where Y is a proton-dissociative system, has been measured in ep interactions with the ZEUS detector at HERA using an integrated luminosity of 25 pb^-1. The differential cross section, ds/dt, is presented for -t<12 GeV^2, where t is the square of the four-momentum transferred to the vector meson. The data span the range in photon-proton centre-of-mass energy, W, from 80 GeV to 120 GeV. The t distributions are well fit by a power law, ds/dt ~ (-t)^{-n}. The slope of the Pomeron trajectory, measured from the W dependence of the rho^0 and phi cross sections in bins of t, is consistent with zero. The ratios ds_(gamma p --> phi Y)/dt to ds_(gamma p --> rho^0 Y)/dt and ds_(gamma p --> J/psi Y)/dt to ds_(gamma p --> rho^0 Y)/dt increase with increasing -t. Decay-angle analyses for rho^0, phi and J/psi mesons have been carried out. For the rho^0 and phi mesons, contributions from single and double helicity flip are observed. The results are compared to expectations of theoretical models.
Differential cross section for RHO0 production. The second DSYS error is due to the modelling of the proton-dissociation process.
Differential cross section for PHI production. The second DSYS error is due to the modelling of the proton-dissociation process.
Differential cross section for J/PSI production. The second DSYS error is due to the modelling of the proton-dissociation process.
The exclusive photoproduction of J/psi mesons, gamma p->J/psi p, has been studied in ep collisions with the ZEUS detector at HERA, in the kinematic range 20<W<290 GeV, where W is the photon-proton centre-of-mass energy. The J/psi mesons were reconstructed in the muon and the electron decay channels using integrated luminosities of 38 pb^-1 and 55 pb^-1, respectively. The helicity structure of J/psi production shows that the hypothesis of s-channel helicity conservation is satisfied at the two standard-deviation level. The total cross section and the differential cross-section dsigma/dt, where t is the squared four-momentum transfer at the proton vertex, are presented as a function of W, for |t|<1.8 GeV^2. The t distribution exhibits an exponential shape with a slope parameter increasing logarithmically with W with a value b=4.15 \pm 0.05 (stat.)^{+0.30}_{-0.18} (syst.) GeV^-2 at W=90 GeV. The effective parameters of the Pomeron trajectory are alphapom(0) = 1.200 \pm 0.009(stat.)^{+0.004}_{-0.010}(syst.) and alphappom= 0.115 \pm 0.018(stat.)^{+0.008}_{-0.015}(syst.) GeV^-2.
The total exclusive J/PSI photoproduction cross section, the differential cross section extrapolated to t=0 and the slope parameter of the exponential t dependence as afunction of W, the photon-proton c.m. energy, for data from J/PSI muon decay.
The total exclusive J/PSI photoproduction cross section as a function of W,the photon-proton c.m. energy, for data from J/PSI electron decays.
The differential cross section extrapolated to t=0 and the slope parameter of the exponential t dependence for exclusive J/PSI photoproduction as a function of W, the photon-proton c.m. energy for data from J/PSI electron decays.
Elastic and proton-dissociative photoproduction of $\rho^0$, $\phi$ and $J/\psi$ vector mesons ($\gamma p\to Vp$, $\gamma p\to VN$, respectively) have been measured in e^+p interactions at HERA up to -t=3 GeV$^2$, where t is the four-momentum transfer squared at the photon-vector meson vertex. The analysis is based on a data sample in which photoproduction reactions were tagged by detection of the scattered positron in a special-purpose calorimeter. This limits the photon virtuality, Q^2, to values less than 0.01 GeV$^2$, and selects a $\gamma p$ average center-of-mass energy of <W> = 94 GeV. Results for the differential cross sections, d$\sigma$/d$t$, for $\rho^0$, $\phi$ and $J/\psi$ mesons are presented and compared to the results of recent QCD calculations. Results are also presented for the t-dependence of the pion-pair invariant-mass distribution in the $\rho^0$ mass region and of the spin-density matrix elements determined from the decay-angle distributions. The Pomeron trajectory has been derived from measurements of the W dependence of the elastic differential cross sections d$\sigma$/d$t$ for both $\rho^0$ and $\phi$ mesons.
Differential cross section for proton-dissociative RHO0 photoproduction.
Differential cross section for elastic RHO0 photoproduction.
The ratio of the elastic to proton-dissociative cross sections for RHO0 photoproduction.
Exclusive production of $\rho^0$ and $J/\psi$ mesons in e^+ p collisions has been studied with the ZEUS detector in the kinematic range $0.25 < Q^2 < 50 GeV^2, 20 < W < 167 GeV$ for the $\rho^0$ data and $2 < Q^2 < 40 GeV^2, 50 < W < 150 GeV$ for the $J/\psi$ data. Cross sections for exclusive $\rho^0$ and $J/\psi$ production have been measured as a function of $Q^2, W$ and $t$. The spin-density matrix elements $r^{04}_{00}, r^1_{1-1}$ and $Re r^{5}_{10}$ have been determined for exclusive $\rho^0$ production as well as $r^{04}_{00}$ and $r^{04}_{1-1}$ for exclusive $J/\psi$ production. The results are discussed in the context of theoretical models invoking soft and hard phenomena.
Exclusive RHO0 electro- and photo- production and cross sections as a function of Q**2 from the BPC data set.
Exclusive RHO0 electro- and photo- production cross section as a function of W from the BPC data set.
Exclusive RHO0 electro- and photo- production cross sections as a function of W from the DIS data set.
Elastic and proton-dissociative rho0 photoproduction (gamma p-->rho0 p,gamma p -->rho0 N,with rho0-->pi+pi-) has been studied in ep interactions at HERA for gamma-p centre-of-mass energies in the range 50<W<100 GeV and for |t|<0.5 GeV2; the results on the p-dissociative reaction are presented for masses of the dissociated proton system in the range MN^2<0.1W^2.For the elastic process,the pi+pi- invariant mass spectrum has been investigated as a function of t. As in fixed target experiments, the rho0 resonance shape is asymmetric;this asymmetry decreases with increasing |t|.The cross section has been studied as a function of W; a fit to the resonant part with the form W^a gives a=0.16\pm0.06(stat.) +0.11-0.15(syst.). The resonant part of the gamma p-->pi+pi- p cross section is 11.2\pm 0.1(stat.)+1.1-1.2 (syst.) mub at <W>=71.7 GeV. The t dependence of the cross section can be described by a function of the type Ae^(-b|t|+ct^2) with b=10.9\pm0.3(stat.)+1.0-0.5(syst.)GeV-2 and c=2.7\pm0.9(stat.)+1.9-1.7(syst.) GeV-4. The t dependence has also been studied as a function of W and a value of the slope of the pomeron trajectory 0.23\pm0.15(stat.)+0.10-0.07(syst.)GeV-2 has been deduced. The rho spin density matrix elements r^04_00,r^04_1-1 and Re[r^04_10] have been measured and found to be consistent with expectations based on SCHC. For p-dissociative pi+pi- photoproduction in the rho0 mass range, the distributions of the two-pion invariant mass, W and the polar and azimuthal angles of the pions in the helicity frame are the same within errors as those for the elastic process. The t distribution has been fitted to an exponential function with a slope parameter 5.8\pm0.3(stat.)\pm0.5(syst.)GeV-2. The ratio of the elastic to p-dissociative rho0 photoproduction cross section is 2.0\pm0.2(stat.)\pm0.7(syst.).
Integrated elastic rho0 photoproduction cross section.
Integrated elastic pi+ pi- photoproduction cross section.
Differential T distribution. Statistical errors only.
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