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.
Diffractive scattering of $\gamma~* p \to X + N$, where $N$ is either a proton or a nucleonic system with $M_N<4$GeV has been measured in deep inelastic scattering (DIS) at HERA. The cross section was determined by a novel method as a function of the $\gamma~* p$ c.m. energy $W$ between 60 and 245GeV and of the mass $M_X$ of the system $X$ up to 15GeV at average $Q~2$ values of 14 and 31GeV$~2$. The diffractive cross section $d\sigma~{diff} /dM_X$ is, within errors, found to rise linearly with $W$. Parameterizing the $W$ dependence by the form $d\sigma~{diff}/dM_X \propto (W~2)~{(2\overline{\mbox{$\alpha_{_{I\hspace{-0.2em}P}}$}} -2)}$ the DIS data yield for the pomeron trajectory $\overline{\mbox{$\alpha_{_{I\hspace{-0.2em}P}}$}} = 1.23 \pm 0.02(stat) \pm 0.04 (syst)$ averaged over $t$ in the measured kinematic range assuming the longitudinal photon contribution to be zero. This value for the pomeron trajectory is substantially larger than $\overline{\mbox{$\alpha_{_{I\hspace{-0.2em}P}}$}}$ extracted from soft interactions. The value of $\overline{\mbox{$\alpha_{_{I\hspace{-0.2em}P}}$}}$ measured in this analysis suggests that a substantial part of the diffractive DIS cross section originates from processes which can be described by perturbative QCD. From the measured diffractive cross sections the diffractive structure function of the proton $F~{D(3)}_2(\beta,Q~2, \mbox{$x_{_{I\hspace{-0.2em}P}}$})$ has been determined, where $\beta$ is the momentum fraction of the struck quark in the pomeron. The form $F~{D(3)}_2 = constant \cdot (1/ \mbox{$x_{_{I\hspace{-0.2em}P}}$})~a$ gives a good fit to the data in all $\beta$ and $Q~2$ intervals with $a = 1.46 \pm 0.04 (stat) \pm
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Diffractive dissociation of quasi-real photons at a photon-proton centre of mass energy of W 200 GeV is studied with the ZEUS detector at HERA. The process under consideration is gamma p -> X N, where X is the diffractively dissociated photon system of mass M_X and N is either a proton or a nucleonic system with mass M_N < 2GeV. The cross section for this process in the interval 3 < M_X < 24 GeV relative to the total photoproduction cross section was measured to be sigma~partial_D / sigma_tot = 6.2 +- 0.2(stat) +- 1.4(syst)%. After extrapolating this result to the mass interval of m_phi~2 < M_X~2 < 0.05 W~2 and correcting it for proton dissociation, the fraction of the total cross section attributed to single diffractive photon dissociation, gamma p -> X p, is found to be sigma_SD / sigma_tot = 13.3 +- 0.5(stat) +- 3.6(syst)%. The mass spectrum of the dissociated photon system in the interval 8 < M_X < 24 GeV can be described by the triple pomeron (PPP) diagram with an effective pomeron intercept of alpha_P(0) = 1.12 +- 0.04(stat) +- 0.08(syst). The cross section for photon dissociation in the range 3 < M_X < 8 GeV is significantly higher than that expected from the triple pomeron amplitude describing the region 8 < M_X < 24 GeV. Assuming that this discrepancy is due to a pomeron-pomeron-reggeon (PPR) term, its contribution to the diffractive cross section in the interval 3 < M_X < 24 GeV is estimated to be f_PPR = 26 +- 3(stat) +- 12(syst)%.
Fraction of the total photoproduction cross section attributed to the photon dissociation.
The fraction of the total photoproduction cross section due to single dif fractive photon dissociation, in the mass range M_phi**2 < M_DD < X >**2 < 0.05 *W**2.
Identification of the diffractive processes was performed on the basis of the shape of reconstructed hadronic mass spectrum. No rapidity-gap was required.
We report on the measurement of the Central Exclusive Production of charged particle pairs $h^{+}h^{-}$ ($h = \pi, K, p$) with the STAR detector at RHIC in proton-proton collisions at $\sqrt{s} = 200$ GeV. The charged particle pairs produced in the reaction $pp\to p^\prime+h^{+}h^{-}+p^\prime$ are reconstructed from the tracks in the central detector, while the forward-scattered protons are measured in the Roman Pot system. Differential cross sections are measured in the fiducial region, which roughly corresponds to the square of the four-momentum transfers at the proton vertices in the range $0.04~\mbox{GeV}^2 < -t_1 , -t_2 < 0.2~\mbox{GeV}^2$, invariant masses of the charged particle pairs up to a few GeV and pseudorapidities of the centrally-produced hadrons in the range $|\eta|<0.7$. The measured cross sections are compared to phenomenological predictions based on the Double Pomeron Exchange (DPE) model. Structures observed in the mass spectra of $\pi^{+}\pi^{-}$ and $K^{+}K^{-}$ pairs are consistent with the DPE model, while angular distributions of pions suggest a dominant spin-0 contribution to $\pi^{+}\pi^{-}$ production. The fiducial $\pi^+\pi^-$ cross section is extrapolated to the Lorentz-invariant region, which allows decomposition of the invariant mass spectrum into continuum and resonant contributions. The extrapolated cross section is well described by the continuum production and at least three resonances, the $f_0(980)$, $f_2(1270)$ and $f_0(1500)$, with a possible small contribution from the $f_0(1370)$. Fits to the extrapolated differential cross section as a function of $t_1$ and $t_2$ enable extraction of the exponential slope parameters in several bins of the invariant mass of $\pi^+\pi^-$ pairs. These parameters are sensitive to the size of the interaction region.
Differential fiducial cross section for CEP of $\pi^+\pi^-$ pairs as a function of the invariant mass of the pair. Systematic uncertainties assigned to data points are strongly correlated between bins and should be treated as allowed collective variation of all data points. There are two components of the total systematic uncertainty. The systematic uncertainty related to the experimental tools and analysis method is labeled "syst. (experimental)". The systematic uncertainty related to the integrated luminosity (fully correlated between all data points) is labeled "syst. (luminosity)". Fiducial region definition: * central state $\pi^+$, $\pi^-$ - $p_{\mathrm{T}} > 0.2~\mathrm{GeV}$ - $|\eta| < 0.7$ * intact forward-scattered beam protons $p'$ - $p_x > -0.2~\mathrm{GeV}$ - $0.2~\mathrm{GeV} < |p_{y}| < 0.4~\mathrm{GeV}$ - $(p_x+0.3~\mathrm{GeV})^2 + p_y^2 < 0.25~\mathrm{GeV}^2$
Differential fiducial cross section for CEP of $K^+K^-$ pairs as a function of the invariant mass of the pair. Systematic uncertainties assigned to data points are strongly correlated between bins and should be treated as allowed collective variation of all data points. There are two components of the total systematic uncertainty. The systematic uncertainty related to the experimental tools and analysis method is labeled "syst. (experimental)". The systematic uncertainty related to the integrated luminosity (fully correlated between all data points) is labeled "syst. (luminosity)". Fiducial region definition: * central state $K^+$, $K^-$ - $p_{\mathrm{T}} > 0.3~\mathrm{GeV}$ - $min(p_{\mathrm{T}}(K^+), p_{\mathrm{T}}(K^-)) < 0.7~\mathrm{GeV}$ - $|\eta| < 0.7$ * intact forward-scattered beam protons $p'$ - $p_x > -0.2~\mathrm{GeV}$ - $0.2~\mathrm{GeV} < |p_{y}| < 0.4~\mathrm{GeV}$ - $(p_x+0.3~\mathrm{GeV})^2 + p_y^2 < 0.25~\mathrm{GeV}^2$
Differential fiducial cross section for CEP of $p\bar{p}$ pairs as a function of the invariant mass of the pair. Systematic uncertainties assigned to data points are strongly correlated between bins and should be treated as allowed collective variation of all data points. There are two components of the total systematic uncertainty. The systematic uncertainty related to the experimental tools and analysis method is labeled "syst. (experimental)". The systematic uncertainty related to the integrated luminosity (fully correlated between all data points) is labeled "syst. (luminosity)". Fiducial region definition: * central state $p$, $\bar{p}$ - $p_{\mathrm{T}} > 0.4~\mathrm{GeV}$ - $min(p_{\mathrm{T}}(p), p_{\mathrm{T}}(\bar{p})) < 1.1~\mathrm{GeV}$ - $|\eta| < 0.7$ * intact forward-scattered beam protons $p'$ - $p_x > -0.2~\mathrm{GeV}$ - $0.2~\mathrm{GeV} < |p_{y}| < 0.4~\mathrm{GeV}$ - $(p_x+0.3~\mathrm{GeV})^2 + p_y^2 < 0.25~\mathrm{GeV}^2$
We report a high precision measurement of the transverse single spin asymmetry $A_N$ at the center of mass energy $\sqrt{s}=200$ GeV in elastic proton-proton scattering by the STAR experiment at RHIC. The $A_N$ was measured in the four-momentum transfer squared $t$ range $0.003 \leqslant |t| \leqslant 0.035$ $\GeVcSq$, the region of a significant interference between the electromagnetic and hadronic scattering amplitudes. The measured values of $A_N$ and its $t$-dependence are consistent with a vanishing hadronic spin-flip amplitude, thus providing strong constraints on the ratio of the single spin-flip to the non-flip amplitudes. Since the hadronic amplitude is dominated by the Pomeron amplitude at this $\sqrt{s}$, we conclude that this measurement addresses the question about the presence of a hadronic spin flip due to the Pomeron exchange in polarized proton-proton elastic scattering.
The asymmetry $\varepsilon(\varphi)/(P_B + P_Y)$ for various $t$-intervals.
The measured single spin asymmetry $A_N$ for five $-t$ intervals.
Fitted value of $r_5$.
Results are reported concerning the charged-particle multiplicity distribution obtained in an exposure of the high-resolution hydrogen bubble chamber LEBC to a beam of 800 GeV protons at the Fermilab MPS. This is the first time that such data have been available at this energy. The distribution of the number n ch of charged particles produced in inelastic interactions obeys KNO-scaling. The average multiplicity is 〈 n ch 〉 = 10.26±0.15. For n ch ⩾8 the data can be well fitted to a negative binomial. The difference between the overall experimental multiplicity distribution and that resulting from the latter fit is in agreement with the contribution expected from diffractive processes.
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Deep inelastic scattering and its diffractive component, $ep \to e^{\prime}\gamma^* p \to e^{\prime}XN$, have been studied at HERA with the ZEUS detector using an integrated luminosity of 52.4 pb$^{-1}$. The $M_X$ method has been used to extract the diffractive contribution. A wide range in the centre-of-mass energy $W$ (37 -- 245 GeV), photon virtuality $Q^2$ (20 -- 450 GeV$^2$) and mass $M_X$ (0.28 -- 35 GeV) is covered. The diffractive cross section for $2 < M_X < 15$ GeV rises strongly with $W$, the rise becoming steeper as $Q^2$ increases. The data are also presented in terms of the diffractive structure function, $F^{\rm D(3)}_2$, of the proton. For fixed $Q^2$ and fixed $M_X$, $\xpom F^{\rm D(3)}_2$ shows a strong rise as $\xpom \to 0$, where $\xpom$ is the fraction of the proton momentum carried by the Pomeron. For Bjorken-$x < 1 \cdot 10^{-3}$, $\xpom F^{\rm D(3)}_2$ shows positive $\log Q^2$ scaling violations, while for $x \ge 5 \cdot 10^{-3}$ negative scaling violations are observed. The diffractive structure function is compatible with being leading twist. The data show that Regge factorisation is broken.
Cross section for diffractive scattering GAMMA* P --> DD X where M(DD) < 2.3 GeV and M(X) = 1.2 GeV for Q**2 = 25 GeV**2.
Cross section for diffractive scattering GAMMA* P --> DD X where M(DD) < 2.3 GeV and M(X) = 1.2 GeV for Q**2 = 35 GeV**2.
Cross section for diffractive scattering GAMMA* P --> DD X where M(DD) < 2.3 GeV and M(X) = 1.2 GeV for Q**2 = 45 GeV**2.
Diffractive photoproduction of D*+/-(2010) mesons was measured with the ZEUS detector at the ep collider HERA, using an integrated luminosity of 78.6 pb^{-1}. The D* mesons were reconstructed in the kinematic range: transverse momentum p_T(D*) > 1.9 GeV and pseudorapidity |eta(D*)| < 1.6, using the decay D*+ -> D0 pi+_s followed by D0 -> K- pi+ (+c.c.). Diffractive events were identified by a large gap in pseudorapidity between the produced hadronic state and the outgoing proton. Cross sections are reported for photon-proton centre-of-mass energies in the range 130 < W < 300 GeV and for photon virtualities Q^2 < 1 GeV^2, in two ranges of the Pomeron fractional momentum x_pom < 0.035 and x_pom < 0.01. The relative contribution of diffractive events to the inclusive D*+/-(2010) photoproduction cross section is about 6%. The data are in agreement with perturbative QCD calculations based on various parameterisations of diffractive parton distribution functions. The results are consistent with diffractive QCD factorisation.
Total cross section integrated over the given kinematic range.
Ratio of diffractive to inclusive D* cross section.
Differential cross sections for diffractive photoproduction of D*+- mesons as a function of X(NAME=POMERON).
Deep inelastic scattering and its diffractive component, ep -> e'gamma*p ->e'XN, have been studied at HERA with the ZEUS detector using an integrated luminosity of 4.2 pb-1. The measurement covers a wide range in the gamma*p c.m. energy W (37 - 245 GeV), photon virtuality Q2 (2.2 - 80 GeV2) and mass Mx. The diffractive cross section for Mx > 2 GeV rises strongly with W: the rise is steeper with increasing Q2. The latter observation excludes the description of diffractive deep inelastic scattering in terms of the exchange of a single Pomeron. The ratio of diffractive to total cross section is constant as a function of W, in contradiction to the expectation of Regge phenomenology combined with a naive extension of the optical theorem to gamma*p scattering. Above Mx of 8 GeV, the ratio is flat with Q2, indicating a leading-twist behaviour of the diffractive cross section. The data are also presented in terms of the diffractive structure function, F2D(3)(beta,xpom,Q2), of the proton. For fixed beta, the Q2 dependence of xpom F2D(3) changes with xpom in violation of Regge factorisation. For fixed xpom, xpom F2D(3) rises as beta -> 0, the rise accelerating with increasing Q2. These positive scaling violations suggest substantial contributions of perturbative effects in the diffractive DIS cross section.
Cross section for the diffractive scattering process GAMMA* P --> DD X for a diffractive mass of 1.2 GeV and Q**2 = 2.7 GeV**2.
Cross section for the diffractive scattering process GAMMA* P --> DD X for a diffractive mass of 1.2 GeV and Q**2 = 4.0 GeV**2.
Cross section for the diffractive scattering process GAMMA* P --> DD X for a diffractive mass of 1.2 GeV and Q**2 = 6.0 GeV**2.
We report results on the total and elastic cross sections in proton-proton collisions at $\sqrt{s}=200$ GeV obtained with the Roman Pot setup of the STAR experiment at the Relativistic Heavy Ion Collider (RHIC). The elastic differential cross section was measured in the squared four-momentum transfer range $0.045 \leq -t \leq 0.135$ GeV$^2$. The value of the exponential slope parameter $B$ of the elastic differential cross section $d\sigma/dt \sim e^{-Bt}$ in the measured $-t$ range was found to be $B = 14.32 \pm 0.09 (stat.)^{\scriptstyle +0.13}_{\scriptstyle -0.28} (syst.)$ GeV$^{-2}$. The total cross section $\sigma_{tot}$, obtained from extrapolation of the $d\sigma/dt$ to the optical point at $-t = 0$, is $\sigma_{tot} = 54.67 \pm 0.21 (stat.) ^{\scriptstyle +1.28}_{\scriptstyle -1.38} (syst.)$ mb. We also present the values of the elastic cross section $\sigma_{el} = 10.85 \pm 0.03 (stat.) ^{\scriptstyle +0.49}_{\scriptstyle -0.41}(syst.)$ mb, the elastic cross section integrated within the STAR $t$-range $\sigma^{det}_{el} = 4.05 \pm 0.01 (stat.) ^{\scriptstyle+0.18}_{\scriptstyle -0.17}(syst.)$ mb, and the inelastic cross section $\sigma_{inel} = 43.82 \pm 0.21 (stat.) ^{\scriptstyle +1.37}_{\scriptstyle -1.44} (syst.)$ mb. The results are compared with the world data.
The proton-proton elastic differential cross-section $d\sigma_{el}/dt$ in the t-range 0.045<|t|<0.135 $GeV^{2}$ at sqrt(s) = 200 GeV.
The B-slope of the exponential fit A*exp(-B*|t|) to the single differential proton-proton elastic cross-section in the t-range 0.045<|t|<0.135 GeV**2 at sqrt(s) = 200 GeV.
The total, elastic and inelastic cross-sections for proton-proton scattering at sqrt(s)=200 GeV, the elastic cross-section measured in the t-range 0.045<|t|<0.135 GeV^2 and the value of the differential cross-section extrapolated to |t| = 0.
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