Exclusive vector-toponium photoproduction in hadronic collisions

An exploratory study of the exclusive production of a vector - toponium $ψ_t$ state by photon - hadron interactions is performed considering proton - proton and proton - nucleus collisions at the Large Hadron Collider (LHC) and Future Circular Collider (FCC) energies. The scattering amplitude is calculated using the $k_T$ - factorization formalism assuming that the vector - toponium state can be described by a Gaussian light-cone wave function and considering different models for the unintegrated gluon distribution. Predictions for the rapidity distributions and total cross - sections are presented. Our results indicate that the experimental measurement of this final state will be very difficult for the expected integrated luminosities at the LHC and FCC.

💡 Research Summary

This paper presents the first exploratory theoretical study of the exclusive photoproduction of the vector-toponium state (ψ_t, a bound state of top and anti-top quarks) in proton-proton (pp) and proton-lead (pPb) collisions at the energies of the Large Hadron Collider (LHC) and the Future Circular Collider (FCC).

Motivated by the recent observation of the scalar toponium (η_t) and the experimental success in studying exclusive photoproduction of lighter quarkonia like J/ψ, the authors investigate an alternative production mechanism for the ψ_t, as its direct production via gluon-gluon fusion is forbidden by the Landau-Yang theorem. The process involves one incident hadron emitting a quasi-real photon, which then interacts with the other hadron to produce the ψ_t exclusively, leaving the hadrons intact and typically resulting in a rapidity gap.

The theoretical framework employs the Equivalent Photon Approximation (EPA) to factorize the total cross-section into the photon flux from the hadrons and the photon-hadron interaction cross-section. For the latter, the scattering amplitude is calculated using the k_T-factorization formalism. This approach explicitly factorizes the amplitude into two non-perturbative inputs: the unintegrated gluon distribution (UGD) of the target hadron and the light-cone wave function of the ψ_t.

To assess theoretical uncertainties, two distinct models for the proton UGD are considered: one based on the CCFM evolution equation and another (HERA I+II) obtained from a fit to HERA data using DGLAP evolution plus parton branching. For the ψ_t wave function, a Gaussian ansatz is adopted. Its parameters are determined by normalizing the wave function and by using the theoretically calculated value for the leptonic decay width Γ(ψ_t → e+e-), which is derived from the radial wave function at the origin, R_S(0), obtained by solving the non-relativistic Schrödinger equation.

Key predictions are presented for rapidity distributions and total cross-sections:

1. Photon-Proton Scattering: The exclusive γp → ψ_t p cross-section rises with the center-of-mass energy W. The CCFM UGD predicts larger cross-sections than the HERA I+II model. In the kinematic range accessible to potential future electron-proton colliders like the LHeC or FCC-eh, cross-sections on the order of a few attobarns (ab, 10^-36 cm²) are predicted.
2. Rapidity Distributions in Hadronic Collisions: For pp collisions, the distributions are symmetric and become broader and larger in magnitude with increasing collision energy. In pPb collisions, the distributions are asymmetric due to the differing photon fluxes (Z²-enhanced from the lead) and photon-hadron cross-sections (much smaller for a lead target than for a proton target).
3. Total Cross-Sections: The predicted integrated cross-sections are extremely small. For pp collisions at LHC (14 TeV), they range from ~0.87 ab (HERA I+II) to ~6.79 ab (CCFM). At FCC (100 TeV), they increase to ~16.55-83.40 ab. Cross-sections for pPb collisions are larger by roughly one (LHC) to two (FCC) orders of magnitude compared to pp, but the absolute values remain minute.

The paper concludes that the experimental measurement of this process will be exceedingly difficult at both the LHC and FCC, given the predicted tiny cross-sections and the small expected branching fraction of ψ_t into dileptons (on the order of 10^-5), which is the typical detection channel. Even with the high integrated luminosities anticipated for the High-Luminosity LHC (HL-LHC) and future colliders, the number of observable events would be severely suppressed. The study serves as a quantitative reality check on the challenges of observing heavy quarkonium states like the ψ_t and suggests that while forward proton detectors might in principle be able to tag such exclusive events due to the high mass of the ψ_t, achieving sufficient statistics remains a formidable hurdle. The authors note the potential for dedicated studies at future electron-hadron colliders and mention ongoing investigations into alternative detection strategies.