High-energy strong interactions: from `hard to `soft

We discuss the qualitative features of the recent data on multiparticle production observed at the LHC. The tolerable agreement with Monte Carlos based on LO DGLAP evolution indicates that there is no qualitative difference between hard' and soft’ interactions; and that a perturbative QCD approach may be extended into the soft domain. However, in order to describe the data, these Monte Carlos need an additional infrared cutoff k_min with a value k_min ~ 2-3 GeV which is not small, and which increases with collider energy. Here we explain the physical origin of the large k_min. Using an alternative model which matches the soft' high-energy hadron interactions smoothly on to perturbative QCD at small x, we demonstrate that this effective cutoff k_min is actually due to the strong absorption of low k_t partons. The model embodies the main features of the BFKL approach, including the diffusion in transverse momenta, lnk_t, and an intercept consistent with resummed next-to-leading log corrections. Moreover, the model uses a two-channel eikonal framework, and includes the contributions from the multi-Pomeron exchange diagrams, both non-enhanced and enhanced. The values of a small number of physically-motivated parameters are chosen to reproduce the available total, elastic and proton dissociation cross section (pre-LHC) data. Predictions are made for the LHC, and the relevance to ultra-high-energy cosmic rays is briefly discussed. The low x inclusive integrated gluon PDF, and the diffractive gluon PDF, are calculated in this framework, using the parameters which describe the high-energy pp and p\bar{p} soft’ data. Comparison with the PDFs obtained from the global parton analyses of deep inelastic and related `hard’ scattering data, and from diffractive deep inelastic data looks encouraging.

💡 Research Summary

The paper addresses a puzzling feature of LHC multiparticle production data: while leading‑order (LO) DGLAP‑based Monte‑Carlo generators (e.g. PYTHIA, HERWIG) can reproduce many inclusive observables, they require an infrared cutoff k_min that grows with the centre‑of‑mass energy, reaching values of about 2–3 GeV at √s = 7 TeV. Such a large, energy‑dependent cutoff is not expected in a naïve perturbative picture and suggests that low‑k_T partons are being strongly suppressed.

The authors propose that this suppression originates from absorptive effects at low transverse momentum, which can be understood within a QCD‑based Pomeron framework that incorporates both BFKL dynamics and multi‑Pomeron exchanges. They construct a model that smoothly interpolates between the traditional “soft” Regge description of high‑energy hadron scattering and the perturbative QCD (pQCD) description valid at small‑x and relatively large k_T. The key ingredients are:

1. BFKL‑like evolution with diffusion in ln k_T, an intercept Δ≈0.3 (consistent with NLL‑resummed BFKL), and a small trajectory slope α′≈0, reflecting the dominance of high‑k_T configurations inside the bare Pomeron.

2. Two‑channel eikonal formalism that accounts for elastic rescattering (eikonal diagrams) and for enhanced multi‑Pomeron interactions where additional Pomerons couple to intermediate partons.

3. Enhanced diagrams (e.g. triple‑Pomeron) that generate an absorptive cross section σ_abs∝1/k_T², thereby damping the growth of the parton density at low k_T. Two hypotheses for the multi‑Pomeron vertices are examined: (a) a generic exponential suppression exp(‑λΩ) for each intermediate parton, and (b) a critical regime with a specific relation between the triple‑Pomeron coupling g_3P and the intercept Δ.

By fitting a small set of physically motivated parameters to pre‑LHC total, elastic and single‑proton‑dissociation data, the model reproduces the LHC measurements of charged‑particle multiplicities, p_T spectra, and the observed increase of the mean transverse momentum ⟨p_T⟩ with energy. The effective infrared cutoff emerges dynamically from the enhanced absorption, rather than being an ad‑hoc parameter.

The framework also allows the calculation of low‑x inclusive gluon PDFs and diffractive gluon PDFs using the same parameters that describe soft pp and p p̄ data. Comparisons with global PDF fits (e.g. CT, MMHT) and with diffractive PDFs extracted from HERA show encouraging agreement, indicating that the same underlying QCD Pomeron governs both soft and hard processes.

Finally, the authors discuss implications for ultra‑high‑energy cosmic‑ray interactions. The energy‑dependent suppression of low‑k_T partons modifies the development of extensive air showers, suggesting that current hadronic interaction models used in cosmic‑ray physics could be improved by incorporating the dynamical k_min mechanism derived here.

In summary, the paper provides a unified QCD description that bridges the gap between hard (perturbative) and soft (non‑perturbative) high‑energy interactions, explains the origin of the large, energy‑dependent infrared cutoff required by Monte‑Carlo generators, and offers predictions for both collider and cosmic‑ray phenomenology.