This Letter presents a measurement of the inelastic proton-proton cross section using 60  μb^{-1} of pp collisions at a center-of-mass energy sqrt[s] of 13 TeV with the ATLAS detector at the LHC. Inelastic interactions are selected using rings of plastic scintillators in the forward region (2.07 10^{-6}, where M_{X} is the larger invariant mass of the two hadronic systems separated by the largest rapidity gap in the event. In this ξ range the scintillators are highly efficient. For diffractive events this corresponds to cases where at least one proton dissociates to a system with M_{X}>13  GeV. The measured cross section is compared with a range of theoretical predictions. When extrapolated to the full phase space, a cross section of 78.1±2.9  mb is measured, consistent with the inelastic cross section increasing with center-of-mass energy.

/pdf/measurement-of-the-inelastic-proton-proton-cross-section-at-1ikm1g9xjg.pdf

Measurement of the inelastic proton-proton cross section at √s=13 TeV with the ATLAS detector at the LHC

The dependence of the rate of proton-proton interactions on the centre-of-mass collision energy, root s, is of fundamental importance for both hadron collider physics and particle astrophysics. The ...

/pdf/measurement-of-the-inelastic-proton-proton-cross-section-at-3wxq4dgg5q.pdf

Measurement of the inelastic proton–proton cross-section at √ s =7 TeV with the ATLAS detector

Universality of ultra-relativistic gravitational scattering

Colliding high-energy hadrons either produce new particles or scatter elastically with their quantum numbers conserved and no other particles produced. We consider the latter case here. Although inelastic processes dominate at high energies, elastic scattering contributes considerably (18–25%) to the total cross section. Its share first decreases and then increases at higher energies. Small-angle scattering prevails at all energies. Some characteristic features can be seen that provide information on the geometrical structure of the colliding particles and the relevant dynamical mechanisms. The steep Gaussian peak at small angles is followed by the exponential (Orear) regime with some shoulders and dips, and then by a power-law decrease. Results from various theoretical approaches are compared with experimental data. Phenomenological models claiming to describe this process are reviewed. The unitarity condition predicts an exponential fall for the differential cross section with an additional substructure to occur exactly between the low momentum transfer diffraction cone and a power-law, hard parton scattering regime under high momentum transfer. Data on the interference of the Coulomb and nuclear parts of amplitudes at extremely small angles provide the value of the real part of the forward scattering amplitude. The real part of the elastic scattering amplitude and the contribution of inelastic processes to the imaginary part of this amplitude (the so-called overlap function) are also discussed. Problems related to the scaling behavior of the differential cross section are considered. The power-law regime at highest momentum transfer is briefly described.

/pdf/elastic-scattering-of-hadrons-2e0f4qz7fu.pdf

Elastic scattering of hadrons

The integrated luminosity, a key figure of merit for any particle-physics collider, is closely linked to the peak luminosity and to the beam lifetime. The instantaneous peak luminosity of a collider is constrained by a number of boundary conditions, such as the available beam current, the maximum beam-beam tune shift with acceptable beam stability and reasonable luminosity lifetime (i.e., the empirical ``beam-beam limit''), or the event pileup in the physics detectors. The beam lifetime at high-luminosity hadron colliders is largely determined by particle burn off in the collisions. In future highest-energy circular colliders synchrotron radiation provides a natural damping mechanism, which can be exploited for maximizing the integrated luminosity. In this article, we derive analytical expressions describing the optimized integrated luminosity, the corresponding optimum store length, and the time evolution of relevant beam parameters, without or with radiation damping, while respecting a fixed maximum value for the total beam-beam tune shift or for the event pileup in the detector. Our results are illustrated by examples for the proton-proton luminosity of the existing Large Hadron Collider (LHC) at its design parameters, of the High-Luminosity Large Hadron Collider (HL-LHC), and of the Future Circular Collider (FCC-hh).

/pdf/optimizing-integrated-luminosity-of-future-hadron-colliders-5gcpp0ej9h.pdf

Optimizing integrated luminosity of future hadron colliders

The energy dependence of the total hadronic cross section at high energies is investigated with focus on the recent experimental result by the Total Elastic and Diffractive Cross-section Measurement Collabora- tion at 7 TeV and the Froissart-Martin bound. On the basis of a class of analytical parametrization with the exponent γ in the leading logarithm contribution as a free parameter, different variants of fits to pp and ¯ pp total cross-section data above 5 GeV are developed. Two ensembles are considered, the first comprising data up to 1.8 TeV and the second also including the data collected at 7 TeV. We show that in all fit variants applied to the first ensemble, the exponent is statis- tically consistent with γ = 2. Applied to the second ensemble, however, the same variants yield γ values above 2, a result already obtained in two other analysis, by Amaldi et al. and by the UA4/2 Collaboration. As recently discussed by Azimov, this faster-than-squared- logarithm rise does not necessarily violate unitarity. Our results suggest that the energy dependence of the hadronic total cross section at high energies still consti- tutes an open problem.

Total Hadronic Cross-Section Data and the Froissart–Martin Bound

Forward amplitude analyses constitute an important approach in the investigation of the energy dependence of the total hadronic cross-section σtot and the ρ parameter. The standard picture indicates for σtot a leading log-squared dependence at the highest c.m. energies, in accordance with the Froissart–Lukaszuk–Martin bound and as predicted by the COMPETE Collaboration in 2002. Beyond this log-squared (L2) leading dependence, other amplitude analyses have considered a log-raised-to-gamma form (Lγ), with γ as a real free fit parameter. In this case, analytic connections with ρ can be obtained either through dispersion relations (derivative forms), or asymptotic uniqueness (Phragmen–Lindeloff theorems). In this work, we present a detailed discussion on the similarities and mainly the differences between the Derivative Dispersion Relation (DDR) and Asymptotic Uniqueness (AU) approaches and results, with focus on the Lγ and L2 leading terms. We also develop new Regge–Gribov fits with updated dataset on σtot a...

Leading components in forward elastic hadron scattering: Derivative dispersion relations and asymptotic uniqueness

A forward amplitude analysis on $pp$ and $\bar{p}p$ elastic scattering above 5 GeV is presented. The dataset includes the recent high-precision TOTEM measurements of the $pp$ total and elastic (integrated) cross-sections at 7 TeV and 8 TeV. Following previous works, the leading high-energy contribution for the total cross-section ($\sigma_{tot}$) is parametrized as $\ln^{\gamma}(s/s_h)$, where $\gamma$ and $s_h$ are free \textit{real} fit parameters. Singly-subtracted derivative dispersion relations are used to connect $\sigma_{tot}$ and the rho parameter ($\rho$) in an analytical way. Different fit procedures are considered, including individual fits to $\sigma_{tot}$ data, global fits to $\sigma_{tot}$ and $\rho$ data, constrained and unconstrained data reductions. The results favor a rise of the $\sigma_{tot}$ faster than the log-squared bound by Froissart and Martin at the LHC energy region. The parametrization for $\sigma_{tot}$ is extended to fit the elastic cross-section ($\sigma_{el}$) data with satisfactory results. The analysis indicates an asymptotic ratio $\sigma_{el}/\sigma_{tot}$ consistent with 1/3 (as already obtained in a previous work). A critical discussion on the correlation, practical role and physical implications of the parameters $\gamma$ and $s_h$ is presented. The discussion confronts the 2002 prediction of $\sigma_{tot}$ by the COMPETE Collaboration and the recent result by the Particle Data Group (2012 edition of the Review of Particle Physics). Some conjectures on possible implications of a fast rise of the proton-proton total cross-section at the highest energies are also presented.

An updated analysis on the rise of the hadronic total cross-section at the LHC energy region

pp elastic scattering above 5 GeV is presented. The dataset includes the recent high-precision TOTEM measurements of the pp total and elastic (integrated) cross-sections at 7 TeV and 8 TeV. Following previous works, the leading high-energy contribution for the total cross-section (�tot) is parametrized as ln(s/sh), where and sh are free real fit parameters. Singly-subtracted derivative dispersion relations are used to connecttot and the rho parameter (�) in an analytical way. Different fit procedures are considered, including individual fits totot data, global fits totot anddata, constrained and unconstrained data reductions. The results favor a rise of thetot faster than the log-squared bound by Froissart and Martin at the LHC energy region. The parametrization fortot is extended to fit the elastic cross-section (�el) data with satisfactory results. The analysis indicates an asymptotic ratioel/�tot consistent with 1/3 (as already obtained in a previous work). A critical discussion on the correlation, practical role and physical implications of the parameters and sh is presented. The discussion confronts the 2002 prediction oftot by the COMPETE Collaboration and the recent result by the Particle Data Group (2012 edition of the Review of Particle Physics). Some conjectures on possible implications of a fast rise of the proton-proton total cross-section at the highest energies are also presented.

An Updated Analysis on the Rise of the Hadronic Total Cross-Section at the Lhc Energy Region

Forward amplitude analyses constitute an important approach in the investigation of the energy dependence of the total hadronic cross-section $\sigma_{tot}$ and the $\rho$ parameter. The standard picture indicates for $\sigma_{tot}$ a leading log-squared dependence at the highest c.m. energies, in accordance with the Froissart-Lukaszuk-Martin bound. Beyond this log-squared (L2) leading dependence, other amplitude analyses have considered a log-raised-to-gamma form (L$\gamma$), with $\gamma$ as a real free fit parameter. In this case, analytic connections with $\rho$ can be obtained either through dispersion relations (derivative forms), or asymptotic uniqueness (Phragmen-Lindeloff theorems). In this work we present a detailed discussion on the similarities and mainly the differences between the Derivative Dispersion Relation (DDR) and Asymptotic Uniqueness (AU) approaches and results, with focus on the L$\gamma$ and L2 leading terms. We also develop new Regge-Gribov fits with updated dataset on $\sigma_{tot}$ and $\rho$ from $pp$ and $\bar{p}p$ scattering, in the region 5 GeV-8 TeV. The recent tension between the TOTEM and ATLAS results at 7 TeV and mainly 8 TeV is considered in the data reductions. Our main conclusions are: (1) all fit results present agreement with the experimental data analyzed and the goodness-of-fit is slightly better in case of the DDR approach; (2) by considering only the TOTEM data at the LHC region, the fits with L$\gamma$ indicate $\gamma\sim 2.0\pm 0.2$ (AU) and $\gamma\sim 2.3\pm 0.1$ (DDR); (3) by including the ATLAS data the fits provide $\gamma\sim 1.9\pm 0.1$ (AU) and $\gamma\sim 2.2\pm 0.2$ (DDR); (4) in the formal and practical contexts, the DDR approach is more adequate for the energy interval investigated than the AU approach. A review on the analytic results for $\sigma_{tot}$ and $\rho$ from the Regge-Gribov, DDR and AU approaches is presented.

M. J. Menon

Papers

Total Hadronic Cross-Section Data and the Froissart–Martin Bound

Leading components in forward elastic hadron scattering: Derivative dispersion relations and asymptotic uniqueness

An updated analysis on the rise of the hadronic total cross-section at the LHC energy region

An Updated Analysis on the Rise of the Hadronic Total Cross-Section at the Lhc Energy Region

Leading components in forward elastic hadron scattering: Derivative dispersion relations and asymptotic uniqueness