- Open Access
Soft and semihard components of multiplicity distributions in the -factorization approach
Phys. Rev. D 112, 094045 – Published 24 November, 2025
DOI: https://doi.org/10.1103/wcld-3j5q
Abstract
Particle production in hadronic collisions can be studied in the low-momentum (soft) and high-momentum (hard) transfer regimes. While the latter can be well understood within perturbative QCD, the former contains nonperturbative effects which cannot be calculated from first principles. There is also an intermediate regime called semihard, in which the momentum transfer runs typically from 1 to 10 GeV. As the hadron-hadron collision energy increases, we expect to see a relative growth of the number of semihard events. It has been conjectured that this growth would be the cause of some changes observed in the multiplicity distributions measured in proton-proton collisions. In this paper we revisit the separation between soft and semihard events using the formalism of factorization. The separation is implemented through the introduction of a scale that is the cutoff in the transverse momentum of the produced gluon and allows us to compute the average number of particles produced in each regime. These numbers are used as input in the double negative binomial fit of data, from which we can extract correlations between the fraction of semihard events and the violation of Koba-Nielsen-Olsen scaling.
Physics Subject Headings (PhySH)
Article Text
References (43)
- J. F. Grosse-Oetringhaus and K. Reygers, Charged-particle multiplicity in proton-proton collisions, J. Phys. G 37, 083001 (2010).
- Y. L. Dokshitzer and B. R. Webber, Hadron multiplicity fluctuations in perturbative QCD, J. High Energy Phys. 08 (2025) 168.
- F. Gelis, E. Iancu, J. Jalilian-Marian, and R. Venugopalan, The color glass condensate, Annu. Rev. Nucl. Part. Sci. 60, 463 (2010).
- T. Sjostrand, S. Mrenna, and P. Z. Skands, pythia 6.4 physics and manual, J. High Energy Phys. 05 (2006) 026.
- C. Bierlich, S. Chakraborty, G. Gustafson, and L. Lönnblad, Setting the string shoving picture in a new frame, J. High Energy Phys. 03 (2020) 270.
- K. Aamodt et al. (ALICE Collaboration), Charged-particle multiplicity measurement in proton-proton collisions at and 2.36 TeV with ALICE at LHC, Eur. Phys. J. C 68, 89 (2010).
- J. Adam et al. (ALICE Collaboration), Charged-particle multiplicities in proton–proton collisions at to 8 TeV, Eur. Phys. J. C 77, 33 (2017).
- G. N. Fowler, F. S. Navarra, M. Plumer, A. Vourdas, R. M. Weiner, and G. Wilk, Interacting gluon model for hadron-nucleus and nucleus-nucleus collisions in the central rapidity region, Phys. Rev. C 40, 1219 (1989).
- G. N. Fowler, E. M. Friedlander, R. M. Weiner, and G. Wilk, Possible manifestation of quark-gluon plasma in multiplicity distributions from high-energy reactions, Phys. Rev. Lett. 57, 2119 (1986); 57, 3124(E) (1986).
- A. Giovannini and R. Ugoccioni, Possible scenarios for soft and semihard components structure in central hadron hadron collisions in the TeV region, Phys. Rev. D 59, 094020 (1999); 69, 059903(E) (2004).
- P. Ghosh, Negative binomial multiplicity distribution in proton-proton collisions in limited pseudorapidity intervals at LHC up to and the clan model, Phys. Rev. D 85, 054017 (2012).
- I. Zborovský, Three-component multiplicity distribution, oscillation of combinants and properties of clans in pp collisions at the LHC, Eur. Phys. J. C 78, 816 (2018).
- A. Giovannini and R. Ugoccioni, Clan structure analysis and QCD parton showers in multiparticle dynamics: An intriguing dialog between theory and experiment, Int. J. Mod. Phys. A 20, 3897 (2005).
- Z. Koba, H. B. Nielsen, and P. Olesen, Scaling of multiplicity distributions in high-energy hadron collisions, Nucl. Phys. B40, 317 (1972).
- S. Acharya et al. (ALICE Collaboration), Multiplicity dependence of charged-particle production in pp, p-Pb, Xe-Xe and Pb-Pb collisions at the LHC, Phys. Lett. B 845, 138110 (2023).
- S. Acharya et al. (ALICE Collaboration), Pseudorapidity densities of charged particles with transverse momentum thresholds in pp collisions at and 13 TeV, Phys. Rev. D 108, 072008 (2023).
- L. V. Gribov, E. .M. Levin, and M. .G. Ryskin, Large—E(t) processes as a main source of hadrons at very high-energies, Phys. Lett. 121B, 65 (1983).
- Y. V. Kovchegov and E. Levin, Quantum Chromodynamics at High Energy (Oxford University Press, New York, 2013), Vol. 33.
- H.-M. Wang, J.-F. Liu, Z.-Y. Hou, and X.-J. Sun, Pseudo-rapidity distributions of charged hadrons in pp and pa collisions at the LHC, Chin. Phys. C 37, 084101 (2013).
- D. Kharzeev, E. Levin, and M. Nardi, Color glass condensate at the LHC: Hadron multiplicities in pp, pa and aa collisions, Nucl. Phys. A747, 609 (2005).
- K. J. Golec-Biernat and M. Wusthoff, Saturation effects in deep inelastic scattering at low and its implications on diffraction, Phys. Rev. D 59, 014017 (1998).
- K. Golec-Biernat and S. Sapeta, Saturation model of DIS: An update, J. High Energy Phys. 03 (2017) 102.
- L. S. Moriggi, G. M. Peccini, and M. V. T. Machado, Investigating the inclusive transverse spectra in high-energy collisions in the context of geometric scaling framework, Phys. Rev. D 102, 034016 (2020).
- C. Henkels, E. G. de Oliveira, R. Pasechnik, and H. Trebien, Coherent photoproduction of light vector mesons off nuclear targets in the dipole picture, Nucl. Phys. A1055, 123018 (2025).
- A. Dumitru, D. E. Kharzeev, E. M. Levin, and Y. Nara, Gluon saturation in collisions at the LHC: KLN model predictions for hadron multiplicities, Phys. Rev. C 85, 044920 (2012).
- F. Carvalho, F. O. Duraes, V. P. Goncalves, and F. S. Navarra, Gluon saturation and the froissart bound: A simple approach, Mod. Phys. Lett. A 23, 2847 (2008).
- X.-P. Duan, L. Chen, G.-L. Ma, C. A. Salgado, and B. Wu, KNO scaling in quark and gluon jets at the LHC, arXiv:2503.24200.
- V. Khachatryan et al. (CMS Collaboration), Transverse momentum and pseudorapidity distributions of charged hadrons in pp collisions at and 2.36 TeV, J. High Energy Phys. 02 (2010) 041.
- V. Khachatryan et al. (CMS Collaboration), Transverse-momentum and pseudorapidity distributions of charged hadrons in collisions at , Phys. Rev. Lett. 105, 022002 (2010).
- A. Giovannini and R. Ugoccioni, Soft and semihard components structure in multiparticle production in high-energy collisions, Nucl. Phys. B, Proc. Suppl. 71, 201 (1999).
- S. Acharya et al. (ALICE Collaboration), Charged-particle multiplicity distributions over a wide pseudorapidity range in proton-proton collisions at , 7, and 8 TeV, Eur. Phys. J. C 77, 852 (2017).
- S. Acharya et al. (ALICE Collaboration), Charged-particle multiplicity distributions over a wide pseudorapidity range in proton-proton collisions at , 7, and 8 TeV, Eur. Phys. J. C 77, 852 (2017).
- V. V. Begun, M. Gazdzicki, and M. I. Gorenstein, Power law in microcanonical ensemble with scaling volume fluctuations, Phys. Rev. C 78, 024904 (2008).
- M. Maćkowiak-Pawłowska and A. Wilczek (NA61/SHINE Collaboration), Multiplicity fluctuations of identified hadrons in interactions at SPS energies, J. Phys. Conf. Ser. 509, 012044 (2014).
- A. Chandra, B. Ali, and S. Ahmad, Centrality dependence of multiplicity fluctuations in ion-ion collisions from the beam energy scan at FAIR, Adv. High Energy Phys. 2019, 3905376 (2019).
- G. R. Germano and F. S. Navarra, Energy dependence of the multiplicity moments at the LHC, Phys. Rev. D 105, 014005 (2022).
- L. S. Moriggi, F. S. Navarra, and M. V. T. Machado, Universality of scaling entropy in charged hadron multiplicity distributions at the LHC, Phys. Rev. D 112, 074019 (2025).
- M. Broilo, D. A. Fagundes, E. G. S. Luna, and M. J. Menon, Proton-proton forward scattering at the LHC, Phys. Lett. B 799, 135047 (2019).
- T. V. Iser and E. G. S. Luna, Semihard interactions at high energies, Acta Phys. Pol. B Proc. Suppl. 18, 1 (2025).
- H. R. Martins-Fontes and F. S. Navarra, Multiplicity distributions and the frontier between soft and hard physics, arXiv:2509.15056.
- V. Khachatryan et al. (CMS Collaboration), Charged particle multiplicities in interactions at , 2.36, and 7 TeV, J. High Energy Phys. 01 (2011) 079.
- A. Giovannini and R. Ugoccioni, Possible scenarios for soft and semihard components structure in central hadron-hadron collisions in the TeV region: Pseudorapidity intervals, Phys. Rev. D 60, 074027 (1999).
- T. Alexopoulos et al., The role of double parton collisions in soft hadron interactions, Phys. Lett. B 435, 453 (1998).