CERN ISR Research Articles

Some remarks on Coulombic effects in pp and p¯p scattering and the determination of ρ

We point out a very simple method for calculating the mixed Coulomb-nuclear corrections to the pp and p¯p scattering amplitudes that has been missed in the extensive past work on this problem. The method expresses the correction in terms of a rapidly convergent integral involving the inverse Fourier-Bessel transform of the nuclear amplitude and a known factor containing the Coulomb phase shift with form-factor corrections. The transform can be calculated analytically for the exponential-type model nuclear amplitudes commonly used in fits to the high-energy data at small momentum transfers, and gives very accurate results for the corrections. We examine the possible effects of the Martin zero in the real part of the nuclear amplitude, and the accuracy of the Bethe-West-Yennie phase approximation for the Coulomb-nuclear corrections. We then apply the method to a redetermination of the ratio ρ of the real to the imaginary parts of the forward scattering amplitude in fits to high-energy Intersecting Storage Rings data previously analyzed using the approximate West-Yennie version of the correction. The only significant changes relative the accuracy of those fits are at 52.8 GeV. Our method is applicable more generally, and can be used also at lower energies and for proton-nucleus scattering. Published by the American Physical Society 2024

Results on elastic cross sections in proton–proton collisions at [formula omitted] GeV with the STAR detector at RHIC

We report results on an elastic cross section measurement in proton–proton collisions at a center-of-mass energy 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≤−t≤0.67 GeV2. This is the only measurement of the proton-proton elastic cross section in this t range for collision energies above the Intersecting Storage Rings (ISR) and below the Large Hadron Collider (LHC) colliders. 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). This is the first measurement below the LHC energies for which the non-constant behavior B(t) is observed. The t dependence of B is also 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 dσ/dt agrees well with the results obtained at s=540 GeV for proton–antiproton collisions by the UA4 experiment. We also determine that the integrated elastic cross section within the STAR t-range is σelfid=462.1±0.9(stat.)±1.1(syst.)±11.6(scale)μb.

Fresh look at experimental evidence for odderon exchange

Theory suggests that in high-energy elastic hadron+hadron scattering, t-channel exchange of a family of colourless crossing-odd states – the odderon – may generate differences between pp¯ and pp cross-sections in the neighbourhood of the diffractive minimum. Using a mathematical approach based on interpolation via continued fractions enhanced by statistical sampling, we develop robust comparisons between pp¯ elastic differential cross-sections measured at √s=1.96 TeV by the D0 Collaboration at the Tevatron and function-form-unbiased extrapolations to this energy of kindred pp measurements at √s/TeV=2.76,7,8,13 by the TOTEM Collaboration at the LHC and a combination of these data with earlier cross-section measurements at √s/GeV=23.5,30.7,44.7,52.8,62.5 made at the intersecting storage rings. Focusing on a domain that straddles the diffractive minimum in the pp¯ and pp cross-sections, we find that these two cross-sections differ at the (2.2−2.6)σ level; hence, supply evidence with this level of significance for the existence of the odderon. If combined with evidence obtained through different experiment-theory comparisons, whose significance is reported to lie in the range (3.4−4.6)σ, one arrives at a (4.0−5.2)σ signal for the odderon.

Deuteron–deuteron elastic scattering with three-nucleon force effect in complete Glauber multiple scattering theory

In the framework of Glauber multiple scattering theory including the three-nucleon force, we can well describe the experimental measurements of deuteron–deuteron elastic scattering differential cross-section at momenta [Formula: see text], [Formula: see text], [Formula: see text] and [Formula: see text] GeV/c and center of mass energies [Formula: see text] and [Formula: see text] GeV. Due to relatively small radius of three-nucleon force it has no effect in the forward direction where [Formula: see text] (GeV/c)2 at any energy. The two-nucleon force is enough to describe the data where the single scattering terms are dominant. At medium energy, the effect of three-nucleon force is clear for [Formula: see text] (GeV/c)2. At the same time, for intersecting storage rings (ISR) energies, the three-nucleon force effect is clearly observed at the minimum of the differential cross-section and for the other values of [Formula: see text] (GeV/c)2 is, in general, small.

How hadron collider experiments contributed to the development of QCD: from hard-scattering to the perfect liquid

A revolution in elementary particle physics occurred during the period from the ICHEP1968 to the ICHEP1982 with the advent of the parton model from discoveries in Deeply Inelastic electron-proton Scattering at SLAC, neutrino experiments, hard-scattering observed in p$+$p collisions at the CERN ISR, the development of QCD, the discovery of the J/$\Psi$ at BNL and SLAC and the clear observation of high transverse momentum jets at the CERN SPS $\bar{p}+p$ collider. These and other discoveries in this period led to the acceptance of QCD as the theory of the strong interactions. The desire to understand nuclear physics at high density such as in neutron stars led to the application of QCD to this problem and to the prediction of a Quark-Gluon Plasma (QGP) in nuclei at high energy density and temperatures. This eventually led to the construction of the Relativistic Heavy Ion Collider (RHIC) at BNL to observe superdense nuclear matter in the laboratory. This article discusses how experimental methods and results which confirmed QCD at the first hadron collider, the CERN ISR, played an important role in experiments at the first heavy ion collider, RHIC, leading to the discovery of the QGP as a perfect liquid as well as discoveries at RHIC and the LHC which continue to the present day.

Unexpected properties of interaction of high-energy protons**This review is an extended version of a talk at the Scientific Session of the Physical Sciences Division, Russian Academy of Sciences, “On the 100th anniversary of the birth of Vitaly Ginzburg,” held on October 5, 20016 [see Physics-Uspekhi 60 (4) 413 (2017)

Experimental data on proton–proton interactions in high-energy collisions show that the elastic-to-inelastic scattering ratio varies in an unexpected way with the collision energy: the decrease at comparatively low energies is followed by an increase by a factor of over 1.5 (!) in the energy range from 11–60 GeV at the Intersecting Storage Rings (ISR) to 7–13 TeV at the Large Hadron Collider (LHC). Intuitive expectations are that, classically, proton break-up processes continue increasing in number compared to proton survivals. It can be assumed that this surprising effect is due to either the asymptotic freedom property or the collision time being extremely short at such high energies. The unquestionable unitarity principle is combined with the available elastic scattering data to gain new insight into the spatial shape of the interaction region of colliding protons. We discuss how this region evolves at energies currently used and make some predictions on its behavior at still higher energies under different assumptions concerning the relative roles of elastic scattering and inelastic processes. The shape can transform rather drastically if elastic processes keep increasing in proportion. There is an unexpected corollary to this unexpected property. The possible origins of the effect and its relation to strong interaction dynamics are discussed.

James Watson Cronin

James Watson Cronin

Soft edge of hadron scattering and minijet models for the total and inelasticppcross sections at LHC and beyond

We show that the onset and rise of QCD minijets provide the dynamical mechanism behind the appearance of a soft edge in $pp$ collisions around CERN intersecting storage rings (ISR) energies, and thus such a soft edge is built in our minijet model with soft gluon resummation. Here the model is optimized for the LHC at $\sqrt{s}=7$, 8 TeV and predictions made for higher LHC and cosmic ray energies. Further, we provide a phenomenological picture to discuss the breakup of the total cross section into its elastic, uncorrelated, and correlated inelastic pieces in the framework of a one-channel eikonal function.

How do quarks and gluons lose energy in the QGP?

RHIC introduced the method of hard scattering of partons as an in-situ probe of the the medium produced in A+A collisions. A suppression, RAA ≈ 0.2 relative to binaryscaling, was discovered for π0 production in the range 5 < pT < 20 GeV/c in central Au+Au collisions at = 200 GeV, and surprisingly also for single-electrons from the decay of heavy quarks. Both these results have been confirmed in Pb+Pb collisions at the LHC at = 2.76 TeV. Interestingly, in this pT range the LHC results for pions nearly overlap the RHIC results. Thus, due to the flatter spectrum, the energy loss in the medium at LHC in this pT range must be ~ 40% larger than at RHIC. Unique at the LHC are the beautiful measurements of the fractional transverse momentum imbalance of di-jets in Pb+Pb collisions. At the Utrecht meeting in 2011, I corrected for the fractional imbalance of di-jets with the same cuts in p-p collisions and showed that the relative fractional jet imbalance in Pb+Pb/p-p is ≈ 15% for jets with 120 ≤ ≤ 360 GeV/c. CMS later confirmed this much smaller imbalance compared to the same quantity derived from two-particle correlations of di-jet fragments at RHIC corresponding to jet ≈ 10 - 20 GeV/c, which appear to show a much larger fractional jet imbalance ≈ 45% in this lower range. The variation of apparent energy loss in the medium as a function of both pT and is striking and presents a challenge to both theory and experiment for improved understanding. There are many other such unresolved issues, for instance, the absence of evidence for a effect, due to momentum transferred to the medium by outgoing partons, which would widen the away-side di-jet and di-hadron correlations in a similar fashion as the kT-effect. Another issue well known from experiments at the CERN ISR, SpS and SpS collider is that parton-parton hard-collisions make negligible contribution to multiplicity or transverse energy production in p-p collisions-soft particles, with pT ≤ 2 GeV/c, predominate. Thus an apparent hard scattering component for A+A multiplicity distributions based on a popular formula, dNAAch/dη = [(1 - x) ⟨Npart⟩ dNppch/dη/2 + x ⟨Ncoll⟩dNppch/dη], seems to be an unphysical way to understand the deviation from Npart scaling. Based on recent p-p and d+A measurements, a more physical way is presented along with several other stimulating results and ideas from recent d+Au (p+Pb) measurements.

Study of Double Pomeron Exchange with the SFM detector at the CERN ISR

Selected results from the study of Double Pomeron Exchange with the Split Field Magnet detector at the CERN Intersecting Storage Rings are presented. This concerns various general features of central pionic systems as well as the spectroscopy in the π+π- channel, emphasizing the production properties of the f2(1270) meson. This summary refers to a series of publications over a time span of 17 years based on the work of the CCHK1,2 and ABCDHW3–7 collaborations at the CERN ISR.

Double pomeron exchange at the CERN Intersecting Storage Rings and $Sp\bar{p}S$ Collider

The CERN Intersecting Storage Rings, with [Formula: see text] from 22 GeV to 63 GeV and [Formula: see text], allowed the first observations of p + p → p + X + p with two leading protons (xF &gt; 0.95) or two rapidity gaps Δy &gt; 3. Studies of the central hadronic system (X) were made to search for glueballs, finding f0 and f2 resonances, and to advance our understanding of hadronic diffraction. I review the experiments, not including those at the Split Field Magnet (SFM) facility covered elsewhere in this volume. Some double pomeron exchange studies at the CERN [Formula: see text] Collider are also covered.

ELASTIC SCATTERING OF PROTONS FROM $\sqrt{s} = 23.5~{\rm GeV}$ to 7 TeV FROM A GENERALIZED BIALAS–BZDAK MODEL

The Bialas–Bzdak model of elastic proton–proton scattering is generalized to the case when the real part of the parton–parton level forward scattering amplitude is nonvanishing. Such a generalization enables the model to describe well the dip region of the differential cross-section of elastic scattering at the intersecting storage rings (ISR) energies, and improves significantly the ability of the model to describe also the recent TOTEM data at [Formula: see text] LHC energy. Within this framework, both the increase of the total cross-section, as well as the decrease of the location of the dip with increasing colliding energies, is related to the increase of the quark–diquark distance and to the increase of the "fragility" of the protons with increasing energies. In addition, we present and test the validity of two new phenomenological relations: one of them relates the total p+p cross-section to an effective, model-independent proton radius, while the other relates the position of the dip in the differential elastic cross-section to the measured value of the total cross-section.

On the understanding of the pressure bump

The interpretation of the ion-induced pressure bump observed in CERN's Intersecting Storage Ring (ISR) is re-examined. An improved formulation is proposed by combining the time-variation of the number of molecules on the chamber wall with the pressure change. Assuming proper conditions on the molecules contributing to the ion-desorption, the pressure bump can be described with a consistent manner. Unlike a generally accepted view, the pressure is not in stationary conditions during the pressure bump. Usual criterion on the occurrence of the pressure bump is still valid. However, the pressure bump must be understood as a dynamic phenomenon.

DETAILED ANALYSIS OF p+p ELASTIC SCATTERING DATA IN THE QUARK–DIQUARK MODEL OF BIALAS AND BZDAK FROM $\sqrt{s} = 23.5~{\rm GeV}$ TO 7 TeV

Final results of a detailed analysis of p+p elastic scattering data are presented, utilizing the quark–diquark model of protons in a form proposed by Bialas and Bzdak. The differential cross-section of elastic proton–proton collisions is analyzed in a detailed and systematic manner at small momentum transfers, starting from the energy range of CERN ISR at [Formula: see text], including also recent TOTEM data at the present LHC energies at [Formula: see text]. These studies confirm the picture that the size of proton increases systematically with increasing energies, while the size of the constituent quarks and diquarks remains approximately independent of (or only increases slightly with) the colliding energy. The detailed analysis indicates correlations between model parameters and also indicates an increasing role of shadowing at LHC energies. Within the investigated class of models, a simple and model-independent phenomenological relation was discovered that connects the total p+p scattering cross-section to the effective quark, diquark size and their average separation. Our best fits indicate that the relative error of this phenomenological relation is 10–15% in the considered energy range.

The CERN intersecting storage rings (ISR)

The CERN Intersecting Storage Rings (ISR) was the first facility ever built providing colliding hadron beams. It mainly operated with protons with beam energies of 15 to 31 GeV. The ISR was conceived in the years 1960 to 1964 and was approved in 1965. It came into operation at the beginning of 1971 and was decommissioned as a collider in 1983. A number of accelerator technologies have been either much improved or developed at the ISR which subsequently have become enabling technologies for a number of hadron storage rings and large colliders. Prominent examples of such technologies are ultra-high vacuum technology, beam diagnostics based on Schottky signals and stochastic cooling. The experiences obtained with the ISR were later exploited at the proton-antiproton facility in the CERN SPS, the Tevatron at Fermilab, the RHIC at Brookhaven and, finally, by the LHC at CERN.

Pp→ppK+K−reaction at high energies

We evaluate differential distributions for the four-body $p p \to p p K^{+} K^{-}$ reaction at high energies which constitutes an irreducible background to three-body processes $p p \to p p M$, where $M=\phi$, $f_{2}(1275)$, $f_{0}(1500)$, $f_{2}'(1525)$, $\chi_{c0}$. We consider central diffractive contribution mediated by Pomeron and Reggeon exchanges as well as completely new mechanism of emission of kaons from the proton lines. We include absorption effects due to proton-proton interaction and kaon-kaon rescattering. We compare our results with measured cross sections for the CERN ISR experiment. We make predictions for future experiments at RHIC, Tevatron and LHC. Differential distributions in invariant two-kaon mass, kaon rapidities and transverse momenta of kaons are presented. Two-dimensional distribution in $(y_{K^+}, y_{K^-})$ is particularly interesting. The higher the incident energy, the higher preference for the same-hemisphere emission of kaons. We find that the kaons from the new mechanism of emission directly from proton lines are produced rather forward and backward but the corresponding cross section is rather small. The processes considered here constitute a sizeable contribution to the total proton-proton cross section as well as to kaon inclusive cross section. We consider a measurement of exclusive production of scalar $\chi_{c0}$ meson in the proton-proton collisions via $\chi_{c0} \to K^{+}K^{-}$ decay. The corresponding amplitude for exclusive central diffractive $\chi_{c0}$ meson production is calculated within the $k_{t}$-factorization approach. The influence of kinematical cuts on the signal-to-background ratio is discussed.

Exclusive Central Meson Production in Proton Antiproton Collisions at the Tevatron

It has been known since the days of the Intersecting Storage Rings, ISR, at CERN, that one can have pp interactions with more than one pomeron, ℙ, exchanged, known as double pomeron exchange. Exclusive hadronic systems, produced by double pomeron exchange, DℙE, have the potential of opening a rich new window on hadron spectroscopy and the diffraction mechanism. We have studied events of the type p + → p + X + where X is a hadron pair (mostly π + π − ) at √s = 900 GeV and 1960 GeV in the Collider Detector at Fermilab (CDF). The hadron pair is central, y ≈ 0, and between two rapidity gaps Δy ≈ 4. The dominant process is double pomeron exchange, DℙE, with restrictions on the quantum numbers of X: Q = S = 0, C = +1, J = 0 or 2. The mass spectra, with about 300K candidate events assumed to be π + π − , shows strong resonant structures attributed to f 0 and f 2 states. We give the ratio of cross sections at √s = 900 GeV and 1960 GeV, and compare with Regge expectations.

RESULTS FROM PHENIX AT RHIC WITH IMPLICATIONS FOR LHC

Results from the PHENIX experiment at the Relativistic Heavy Ion Collider (RHIC) in nucleus–nucleus and proton–proton collisions at c.m. energy [Formula: see text] are presented in the context of the methods of single and two-particle inclusive reactions which were used in the discovery of hard-scattering in p–p collisions at the CERN ISR in the 1970's. These techniques are used at RHIC in A + A collisions because of the huge combinatoric background from the large particle multiplicity. Topics include J/Ψ suppression, jet quenching in the dense medium (sQGP) as observed with π0 at large transverse momentum, thermal photons, collective flow, two-particle correlations, suppression of heavy quarks at large pT and its possible relation to Higgs searches at the LHC. The differences and similarities of the measurements in p–p and A + A collisions are presented. The two discussion sessions which followed the lectures on which this article is based are included at the end.

A fundamental test of the Higgs Yukawa coupling at RHIC in A+A collisions

Searches for the intermediate boson, W±, the heavy quantum of the Weak Interaction, via its semi-leptonic decay, W → e+v, in the 1970's instead discovered unexpectedly large hadron production at high pT, notably π0, which provided a huge background of e± from internal and external conversions. Methods developed at the CERN ISR which led to the discovery of direct-single-e± in 1974, later determined to be from the semi-leptonic decay of charm which had not yet been discovered, were used by PHENIX at RHIC to make precision measurements of heavy quark production in p-p and Au+Au collisions, leading to the puzzle of apparent equal suppression of light and heavy quarks in the QGP. If the Higgs mechanism gives mass to gauge bosons but not to fermions, then a proposal that all 6 quarks are nearly massless in a QGP, which would resolve the puzzle, can not be excluded. This proposal can be tested with future measurements of heavy quark correlations in A+A collisions

Exclusivepp→ppπ+π−reaction: From the threshold to LHC

We evaluate differential distributions for the four-body $pp\ensuremath{\rightarrow}pp{\ensuremath{\pi}}^{+}{\ensuremath{\pi}}^{\ensuremath{-}}$ (and $p\overline{p}\ensuremath{\rightarrow}p\overline{p}{\ensuremath{\pi}}^{+}{\ensuremath{\pi}}^{\ensuremath{-}}$) reaction which constitutes an irreducible background to three-body processes $pp\ensuremath{\rightarrow}ppM$, where $M$ are a broad resonances in the ${\ensuremath{\pi}}^{+}{\ensuremath{\pi}}^{\ensuremath{-}}$ channel, e.g., $M=\ensuremath{\sigma}$, ${\ensuremath{\rho}}^{0}$, ${f}_{0}(980)$, ${f}_{2}(1275)$, ${f}_{0}(1500)$. We include both double-diffractive contribution (both Pomeron and Reggeon exchanges) as well as pion-pion rescattering contribution. The first process dominates at higher energies and small pion-pion invariant masses while the second becomes important at lower energies and higher pion-pion invariant masses. The amplitude(s) is(are) calculated in the Regge approach. We compare our results with measured cross sections for the Intersecting Storage Ring and Fermi National Accelerator Laboratory experiments. We make predictions for future experiments at the anti-Proton ANnihilation at DArmstadt (PANDA), Relativistic Heavy Ion Collider, Tevatron, and LHC energies. Differential distributions in invariant two-pion mass, pion rapidities and transverse momenta of pions are presented. The two-dimensional distribution in $({y}_{{\ensuremath{\pi}}^{+}},{y}_{{\ensuremath{\pi}}^{\ensuremath{-}}})$ is particularly interesting. The higher the incident energy, the higher preference for the same-hemisphere emission of pions. The processes considered constitute a sizeable contribution to the total nucleon-nucleon cross section as well as to pion inclusive cross section.