CERN Proton-Antiproton Collider Overview

• CERN Proton-Antiproton Collider is a historic experimental setup that probes nonperturbative QCD via elastic scattering and crossing-odd (odderon) phenomena.
• It employs advanced model frameworks like the ReBB and Regge models to compare pp and p¯p interactions across a wide energy spectrum.
• The program integrates precision antiproton production techniques and suggests future collider designs, including a 100 TeV proposal with improved performance.

Searching arXiv for the cited CERN proton–antiproton collider and antiproton-target literature. arXiv search query: CERN proton antiproton collider elastic scattering odderon target antiproton 100 TeV CERN’s proton-antiproton program spans elastic $p\bar p$ measurements at the ISR/SPS, fixed-target antiproton production in the Proton Synchrotron/Antiproton Decelerator chain, and later high-energy comparisons with LHC $pp$ data that isolate crossing-odd strong-interaction effects. Within this experimental lineage, proton-antiproton collisions are important not only as a historical collider mode but also as a precision probe of nonperturbative QCD, a driver of demanding target-engineering work for antiproton production, and a continuing reference point for future collider proposals and for precision antiproton cross-section measurements with CERN-reach beams (Szanyi, 28 May 2025, Martin et al., 2016, Oliveros et al., 2017).

1. Elastic-scattering formalism and crossing structure

The high-energy elastic-scattering framework is expressed in terms of the Mandelstam variables

$$s=(p_1+p_2)^2=4E^2,\qquad t=(p_1-p_1')^2=2|\vec p|^2(1-\cos\theta),$$

with the differential elastic cross section

$$\frac{d\sigma_{\rm el}}{dt}(s,t)=\frac{|M_{\rm el}(s,t)|^2}{16\pi s^2},$$

and the optical theorem relation

$$\sigma_{\rm tot}(s)=\frac{\operatorname{Im}M_{\rm el}(s,t=0)}{s}.$$

For collider comparisons, the relevant forward observables are the optical point $a(s)=\left.d\sigma_{\rm el}/dt\right|_{t=0}$, the local slope

$$B(s,t)=\frac{d}{dt}\ln\!\left(\frac{d\sigma_{\rm el}}{dt}\right),$$

its forward limit $B_0(s)$, and the $\rho$ parameter

$$\rho(s,t)=\frac{\Re M_{\rm el}(s,t)}{\Im M_{\rm el}(s,t)},\qquad \rho_0(s)=\lim_{t\to 0}\rho(s,t).$$

The key symmetry principle is crossing. The $pp$0 and $pp$1 amplitudes are two analytic continuations of the same function, with decomposition

$pp$2

In the TeV region, the crossing-even part is associated mainly with the pomeron, while the crossing-odd part is associated with the odderon. In the Regge sense, the odderon is a crossing-odd $pp$3-channel exchange with odd signature, $pp$4, near $pp$5, and quantum numbers

$pp$6

In QCD language, it is interpreted as a color-neutral three-gluon exchange in the $pp$7-channel, that is, an odd-gluon analog of the pomeron. At larger $pp$8, the dissertation also notes three-gluon-exchange behavior with a characteristic power-law falloff and opposite sign in $pp$9 versus $$s=(p_1+p_2)^2=4E^2,\qquad t=(p_1-p_1')^2=2|\vec p|^2(1-\cos\theta),$$0 (Szanyi, 28 May 2025).

2. CERN measurements and the collider energy hierarchy

The experimental record relevant here combines CERN $$s=(p_1+p_2)^2=4E^2,\qquad t=(p_1-p_1')^2=2|\vec p|^2(1-\cos\theta),$$1 measurements from the ISR/SPS era with later Fermilab Tevatron $$s=(p_1+p_2)^2=4E^2,\qquad t=(p_1-p_1')^2=2|\vec p|^2(1-\cos\theta),$$2 data and CERN LHC $$s=(p_1+p_2)^2=4E^2,\qquad t=(p_1-p_1')^2=2|\vec p|^2(1-\cos\theta),$$3 data. The dissertation emphasizes that the TeV-scale comparison of these two reactions is the cleanest way to search for the odderon, because at sufficiently high energy the usual mesonic Regge exchanges are strongly suppressed (Szanyi, 28 May 2025).

Facility and experiment	Reaction	Energy
CERN ISR	$$s=(p_1+p_2)^2=4E^2,\qquad t=(p_1-p_1')^2=2|\vec p|^2(1-\cos\theta),$$4; qualitative dip-region comparison with $$s=(p_1+p_2)^2=4E^2,\qquad t=(p_1-p_1')^2=2|\vec p|^2(1-\cos\theta),$$5-like behavior	$$s=(p_1+p_2)^2=4E^2,\qquad t=(p_1-p_1')^2=2|\vec p|^2(1-\cos\theta),$$6 GeV
CERN SPS/UA4	elastic $$s=(p_1+p_2)^2=4E^2,\qquad t=(p_1-p_1')^2=2|\vec p|^2(1-\cos\theta),$$7	$$s=(p_1+p_2)^2=4E^2,\qquad t=(p_1-p_1')^2=2|\vec p|^2(1-\cos\theta),$$8 GeV
FNAL Tevatron E710 and D0	elastic $$s=(p_1+p_2)^2=4E^2,\qquad t=(p_1-p_1')^2=2|\vec p|^2(1-\cos\theta),$$9	$$\frac{d\sigma_{\rm el}}{dt}(s,t)=\frac{|M_{\rm el}(s,t)|^2}{16\pi s^2},$$0 TeV
CERN LHC/TOTEM	elastic $$\frac{d\sigma_{\rm el}}{dt}(s,t)=\frac{|M_{\rm el}(s,t)|^2}{16\pi s^2},$$1	$$\frac{d\sigma_{\rm el}}{dt}(s,t)=\frac{|M_{\rm el}(s,t)|^2}{16\pi s^2},$$2 TeV

The ISR result at $$\frac{d\sigma_{\rm el}}{dt}(s,t)=\frac{|M_{\rm el}(s,t)|^2}{16\pi s^2},$$3 GeV already showed a qualitative difference between $$\frac{d\sigma_{\rm el}}{dt}(s,t)=\frac{|M_{\rm el}(s,t)|^2}{16\pi s^2},$$4 and $$\frac{d\sigma_{\rm el}}{dt}(s,t)=\frac{|M_{\rm el}(s,t)|^2}{16\pi s^2},$$5-like behavior in the dip region, but mesonic exchanges were still relevant there. The SPS/UA4 measurements extended elastic $$\frac{d\sigma_{\rm el}}{dt}(s,t)=\frac{|M_{\rm el}(s,t)|^2}{16\pi s^2},$$6 scattering to $$\frac{d\sigma_{\rm el}}{dt}(s,t)=\frac{|M_{\rm el}(s,t)|^2}{16\pi s^2},$$7, $$\frac{d\sigma_{\rm el}}{dt}(s,t)=\frac{|M_{\rm el}(s,t)|^2}{16\pi s^2},$$8, and $$\frac{d\sigma_{\rm el}}{dt}(s,t)=\frac{|M_{\rm el}(s,t)|^2}{16\pi s^2},$$9 GeV. The decisive high-energy $$\sigma_{\rm tot}(s)=\frac{\operatorname{Im}M_{\rm el}(s,t=0)}{s}.$$0 reference was later provided by D0 at $$\sigma_{\rm tot}(s)=\frac{\operatorname{Im}M_{\rm el}(s,t=0)}{s}.$$1 TeV, while TOTEM supplied high-precision $$\sigma_{\rm tot}(s)=\frac{\operatorname{Im}M_{\rm el}(s,t=0)}{s}.$$2 measurements at $$\sigma_{\rm tot}(s)=\frac{\operatorname{Im}M_{\rm el}(s,t=0)}{s}.$$3, $$\sigma_{\rm tot}(s)=\frac{\operatorname{Im}M_{\rm el}(s,t=0)}{s}.$$4, $$\sigma_{\rm tot}(s)=\frac{\operatorname{Im}M_{\rm el}(s,t=0)}{s}.$$5, and $$\sigma_{\rm tot}(s)=\frac{\operatorname{Im}M_{\rm el}(s,t=0)}{s}.$$6 TeV. The historical significance of the earlier CERN $$\sigma_{\rm tot}(s)=\frac{\operatorname{Im}M_{\rm el}(s,t=0)}{s}.$$7 programs lies in providing the initial phenomenological pattern; the later significance lies in enabling a TeV-scale comparison against LHC data (Szanyi, 28 May 2025).

3. Dip-bump phenomenology and the odderon signal

The crucial observables are the elastic differential cross sections $$\sigma_{\rm tot}(s)=\frac{\operatorname{Im}M_{\rm el}(s,t=0)}{s}.$$8, especially in the diffractive minimum or dip-bump region. In $$\sigma_{\rm tot}(s)=\frac{\operatorname{Im}M_{\rm el}(s,t=0)}{s}.$$9 scattering at TeV energies, a prominent dip-bump structure is seen; in $a(s)=\left.d\sigma_{\rm el}/dt\right|_{t=0}$0 scattering, that dip is largely filled in, appearing as a shoulder rather than a deep minimum. The dissertation treats this as the clearest qualitative signature of a $a(s)=\left.d\sigma_{\rm el}/dt\right|_{t=0}$1-odd exchange. It also discusses the forward observables $a(s)=\left.d\sigma_{\rm el}/dt\right|_{t=0}$2, $a(s)=\left.d\sigma_{\rm el}/dt\right|_{t=0}$3, $a(s)=\left.d\sigma_{\rm el}/dt\right|_{t=0}$4, $a(s)=\left.d\sigma_{\rm el}/dt\right|_{t=0}$5, and $a(s)=\left.d\sigma_{\rm el}/dt\right|_{t=0}$6, since differences in $a(s)=\left.d\sigma_{\rm el}/dt\right|_{t=0}$7 and $a(s)=\left.d\sigma_{\rm el}/dt\right|_{t=0}$8 at the LHC were also interpreted as possible odderon effects (Szanyi, 28 May 2025).

A common misconception is that the central issue is simply whether hadronic cross sections rise with energy. The stated key physics question is instead whether crossing-odd effects survive at high energy. The answer reported in the dissertation is yes: the $a(s)=\left.d\sigma_{\rm el}/dt\right|_{t=0}$9 versus $$B(s,t)=\frac{d}{dt}\ln\!\left(\frac{d\sigma_{\rm el}}{dt}\right),$$0 difference is consistent with a nonzero odderon.

The reported significance levels are method-dependent and reflect an evolving analysis chain. In preliminary ReBB and Regge analyses, the difference between $$B(s,t)=\frac{d}{dt}\ln\!\left(\frac{d\sigma_{\rm el}}{dt}\right),$$1 and $$B(s,t)=\frac{d}{dt}\ln\!\left(\frac{d\sigma_{\rm el}}{dt}\right),$$2 differential cross sections at $$B(s,t)=\frac{d}{dt}\ln\!\left(\frac{d\sigma_{\rm el}}{dt}\right),$$3 TeV gave odderon signals around $$B(s,t)=\frac{d}{dt}\ln\!\left(\frac{d\sigma_{\rm el}}{dt}\right),$$4 to $$B(s,t)=\frac{d}{dt}\ln\!\left(\frac{d\sigma_{\rm el}}{dt}\right),$$5. A model-independent $$B(s,t)=\frac{d}{dt}\ln\!\left(\frac{d\sigma_{\rm el}}{dt}\right),$$6-scaling analysis yielded a $$B(s,t)=\frac{d}{dt}\ln\!\left(\frac{d\sigma_{\rm el}}{dt}\right),$$7 odderon observation by comparing TOTEM $$B(s,t)=\frac{d}{dt}\ln\!\left(\frac{d\sigma_{\rm el}}{dt}\right),$$8 at $$B(s,t)=\frac{d}{dt}\ln\!\left(\frac{d\sigma_{\rm el}}{dt}\right),$$9 TeV with D0 $B_0(s)$0 at $B_0(s)$1 TeV. In the final ReBB analysis, combining results at $B_0(s)$2, $B_0(s)$3, $B_0(s)$4, and $B_0(s)$5 TeV, the odderon signal exceeds $B_0(s)$6 (Szanyi, 28 May 2025).

The historical point is correspondingly narrow and technically specific: proton-antiproton scattering at TeV energies is indispensable when the goal is to isolate the crossing-odd component of the elastic amplitude. This suggests that the collider legacy of CERN $B_0(s)$7 running is not exhausted by its original measurements; it persists through the analytic leverage those measurements provide when combined with later $B_0(s)$8 data.

4. Model frameworks used in $B_0(s)$9 and $\rho$0 comparison

The main phenomenological framework is the Real-extended Bialas–Bzdak model, based on Glauber multiple scattering in impact-parameter space. Its elastic amplitude is written as

$\rho$1

where the opacity $\rho$2 generates the elastic amplitude. The original BB model was purely imaginary. The ReBB model introduces a real part through an imaginary component of the opacity,

$\rho$3

so that the single parameter $\rho$4 controls the real part and is crucial for odderon-sensitive effects (Szanyi, 28 May 2025).

In the paper’s interpretation, all geometric parameters of the proton, $\rho$5, $\rho$6, and $\rho$7, are compatible with the same energy dependence in $\rho$8 and $\rho$9, while the opacity parameter $$\rho(s,t)=\frac{\Re M_{\rm el}(s,t)}{\Im M_{\rm el}(s,t)},\qquad \rho_0(s)=\lim_{t\to 0}\rho(s,t).$$0 behaves differently in the two channels. That difference is the model’s imprint of the odderon. This is a constrained claim: it does not attribute the channel difference to a gross change in proton geometry, but to the parameter governing the real part of the amplitude.

The complementary Regge-based picture writes the elastic amplitudes as pomeron $$\rho(s,t)=\frac{\Re M_{\rm el}(s,t)}{\Im M_{\rm el}(s,t)},\qquad \rho_0(s)=\lim_{t\to 0}\rho(s,t).$$1 odderon contributions. In the dipole Regge model, the trajectories are parameterized as

$$\rho(s,t)=\frac{\Re M_{\rm el}(s,t)}{\Im M_{\rm el}(s,t)},\qquad \rho_0(s)=\lim_{t\to 0}\rho(s,t).$$2

and

$$\rho(s,t)=\frac{\Re M_{\rm el}(s,t)}{\Im M_{\rm el}(s,t)},\qquad \rho_0(s)=\lim_{t\to 0}\rho(s,t).$$3

This model was used to extrapolate between energies and compare the D0 $$\rho(s,t)=\frac{\Re M_{\rm el}(s,t)}{\Im M_{\rm el}(s,t)},\qquad \rho_0(s)=\lim_{t\to 0}\rho(s,t).$$4 data at $$\rho(s,t)=\frac{\Re M_{\rm el}(s,t)}{\Im M_{\rm el}(s,t)},\qquad \rho_0(s)=\lim_{t\to 0}\rho(s,t).$$5 TeV with TOTEM $$\rho(s,t)=\frac{\Re M_{\rm el}(s,t)}{\Im M_{\rm el}(s,t)},\qquad \rho_0(s)=\lim_{t\to 0}\rho(s,t).$$6 data at $$\rho(s,t)=\frac{\Re M_{\rm el}(s,t)}{\Im M_{\rm el}(s,t)},\qquad \rho_0(s)=\lim_{t\to 0}\rho(s,t).$$7 TeV. The coexistence of ReBB and Regge analyses matters because the odderon claim is not tied to a single fitting ansatz; the qualitative $$\rho(s,t)=\frac{\Re M_{\rm el}(s,t)}{\Im M_{\rm el}(s,t)},\qquad \rho_0(s)=\lim_{t\to 0}\rho(s,t).$$8/$$\rho(s,t)=\frac{\Re M_{\rm el}(s,t)}{\Im M_{\rm el}(s,t)},\qquad \rho_0(s)=\lim_{t\to 0}\rho(s,t).$$9 shape difference is common to both approaches (Szanyi, 28 May 2025).

5. Antiproton production infrastructure: the CERN AD target

The fixed-target infrastructure that supplies antiprotons is centered on the AD-Target system, the main particle-production element of the CERN Antiproton Decelerator. In this chain, a beam from the CERN Proton Synchrotron hits a fixed target, producing secondary particles including antiprotons, which are then collected and transported into the AD complex for antimatter experiments. The current configuration dates from the late 1980s and consists of a $pp$00 mm diameter, $pp$01 mm long iridium rod as the core, embedded in a $pp$02 mm diameter graphite matrix, all inside a water-cooled Ti-6Al-4V body (Martin et al., 2016).

The PS antiproton-production pulse used in the study comprises $pp$03 protons, $pp$04 proton bunches, bunch spacing of $pp$05, bunch length of $pp$06, total pulse intensity of $pp$07, and total pulse duration of about $pp$08. The energy deposited in the target core is approximately $pp$09 per pulse. Because this is deposited in only about $pp$10 in the hydrocode-coupling description, the effective power is $pp$11, with mean power density $pp$12. The resulting transient loading includes a temperature rise above $pp$13, pressure waves of several GPa, and strain rates well above $pp$14 (Martin et al., 2016).

The computational workflow is FLUKA plus ANSYS AUTODYN®. FLUKA computes the spatial energy deposition from the proton beam and the particle cascade; the deposition map is passed into AUTODYN through a user subroutine; AUTODYN solves the coupled conservation equations for mass, momentum, and energy in a Lagrangian frame. The FLUKA-to-AUTODYN coupling is one-way, justified on the grounds that the density change during the pulse is only about $pp$15, since the material does not melt. Although the real target core is iridium, the calculations use pure tungsten because the necessary dynamic material data are more available. The modeling stack uses a Mie–Grüneisen equation of state, a Johnson–Cook strength model, and a minimum hydrostatic pressure failure criterion with tungsten spall strength $pp$16 (Martin et al., 2016).

Three dynamic phenomena are identified. First, a dominant high-frequency radial wave with period $pp$17 produces the main destructive compressive-to-tensile response. With plasticity included, the wave reaches about $pp$18 compressive and about $pp$19 tensile in the core center during the first oscillations, exceeding the tungsten spall threshold. Second, end-of-pulse tensile waves arise at the end of each bunch and can constructively interfere with the radial oscillation, making the real pulse length of $pp$20 a wave-interference parameter. Third, a slower longitudinal wave with period $pp$21 is present in the elastic-only analysis but becomes secondary once plasticity is included (Martin et al., 2016).

The principal engineering mitigation studied is high-density cladding. A $pp$22 mm tantalum cladding reduces the maximum tensile pressure by $pp$23 in the target center, and in the failure calculation the Ta-cladded case shows only about $pp$24 fragmented volume, compared with extensive fragmentation in the uncladded tungsten core. The significance for proton-antiproton operations is direct: loss of density, cracking, or fragmentation in the core reduces proton-to-antiproton conversion and therefore lowers antiproton yield, forcing periodic target replacement in a highly activated system (Martin et al., 2016).

6. Prospective collider extensions and precision antiproton measurements

One future-oriented study explores a $pp$25 proton-antiproton collider with luminosity $pp$26, beam energy $pp$27 per beam, and a $pp$28 ring using $pp$29 single-bore NbTi dipoles. The design choice is motivated by the possibility of reaching seven times the LHC beam energy while using only about twice as much NbTi superconductor as the LHC, enabled by the longer circumference. Because a $pp$30 machine uses opposite-charge beams, the same magnet aperture can guide both beams, so only one ring is needed instead of two separate beam pipes (Oliveros et al., 2017).

The physics argument is that many high-mass states have cross sections around $pp$31 times larger in $pp$32 than in $pp$33 collisions, because antiquarks can come directly from an antiproton rather than indirectly from gluon splitting. The paper associates this with lower beam currents for the same rare-event yield, reduced synchrotron-radiation load, and fewer events per bunch crossing. In its parameter table, the synchrotron-radiation power per meter is $pp$34 for the $pp$35 design, compared with $pp$36 for a $pp$37 $pp$38 collider, and the reported events per bunch crossing are $pp$39, compared with $pp$40 for FCC-hh and $pp$41 for the LHC (Oliveros et al., 2017).

The limiting subsystem in that proposal is antiproton production and cooling. Starting from a Fermilab-like source, the design accepts a wider momentum band around $pp$42, splits the beam into $pp$43 momentum channels, provides $pp$44 stochastic-cooling ring sets, follows them with one electron-cooling ring, and proposes recycling antiprotons during runs by joining old and new bunches with synchrotron damping. The proposal also notes that a $pp$45 tunnel at CERN would be very expensive because of the French Jura mountains, and therefore argues that a more realistic CERN option might be the separate $pp$46–$pp$47 FCC tunnel, though that would require $pp$48 magnets rather than the lower-field design favored in the study (Oliveros et al., 2017).

A distinct but related antiproton program concerns precise production cross sections for cosmic-ray antiproton flux predictions. The relevant requirement is that $pp$49 and helium-induced channels be known to better than a few percent in the dominant regions of phase space. The paper’s baseline prescription is $pp$50 precision in the dominant region and $pp$51 elsewhere, with laboratory-frame coverage from proton beam energies $pp$52 to $pp$53 and pseudorapidity $pp$54 from $pp$55 to almost $pp$56, or equivalently $pp$57 from $pp$58 to $pp$59 and $pp$60 from $pp$61 to $pp$62 in the center-of-mass frame. It concludes that the present collection of data is far from these requirements, but that they could, in principle, be reached by fixed-target experiments with beam energies in the reach of CERN accelerators (Donato et al., 2017).

Taken together, these studies indicate that the CERN proton-antiproton enterprise is not exhausted by a single historical collider configuration. Its enduring content lies in three connected domains: $pp$63 elastic scattering as a uniquely clean discriminator of crossing-odd exchange at high energy, antiproton production as a technically extreme target-and-beam problem, and antiproton beams as a still-active design variable in both future colliders and precision hadronic cross-section measurements.