Strongly intensive variables and long-range correlations in the model with a lattice in the transverse plane

S. N. Belokurova ; V. V. Vechernin

Teoretičeskaâ i matematičeskaâ fizika, Tome 200 (2019) no. 2, pp. 195-214

Résumé

In the framework of the quark–gluon string fusion model on the transverse lattice, we study a strongly intensive variable characterizing correlations between the number of particles produced in hadronic interactions in two observation windows separated by a rapidity interval. We show that in the case of independent identical strings, this variable is indeed strongly intensive. It depends only on string characteristics and is independent of trivial so-called volume fluctuations in the string number resulting, in particular, from inevitable impact parameter fluctuations. With string fusion effects causing the production of string clusters with new properties taken into account, this variable turns out to be equal to the weighted average of its values for different string clusters. The weighting coefficients depend on the collision conditions, and the variable loses its strongly intensive character. In the framework of this model in a realistic case with a nonuniform string distribution in the transverse plane, we find explicit analytic formulas for the asymptotic coefficients of long-range correlations between different quantities including an intensive one, the average transverse momentum. We analyze the properties of the obtained correlation coefficients, the studied strongly intensive variable, and also the possibilities of its experimental observation.

Détail

Keywords: hadronic interaction, high energy, quark–gluon string, strongly intensive variable, correlation
Mots-clés : multiparticle production, fluctuation, transverse momentum.

Bibliographie

[1] A. Capella, U. Sukhatme, C.-I. Tan, J. T. Thanh Van, “Jets in small-$p_\mathrm{T}$ hadronic collisions, universality of quark fragmentation, and rising rapidity plateaus”, Phys. Lett. B, 81:1 (1979), 68–74 | DOI

[2] A. B. Kaidalov, “The quark-gluon structure of the pomeron and the rise of inclusive spectra at high energies”, Phys. Lett. B, 116:6 (1982), 459–463 | DOI

[3] F. Bissey, A. I. Signal, D. B. Leinweber, “Comparison of gluon flux-tube distributions for quark-diquark and quark-antiquark hadrons”, Phys. Rev. D, 80:11 (2009), 114506, 6 pp., arXiv: 0910.0958 | DOI

[4] P. Cea, L. Cosmai, F. Cuteri, A. Papa, “Flux tubes in the QCD vacuum”, Phys. Rev. D, 95:11 (2017), 114511, 9 pp., arXiv: 1702.06437 | DOI

[5] G. 't Hooft, “A planar diagram theory for strong interactions”, Nucl. Phys. B, 72:3 (1974), 461–473 | DOI

[6] G. Veneziano, “Some aspects of a unified approach to gauge, dual and Gribov theories”, Nucl. Phys. B, 117:2 (1976), 519–545 | DOI

[7] A. Capella, U. Sukhatme, C.-I. Tan, J. T. Thanh Van, “Dual parton model”, Phys. Rep., 236:4–5 (1994), 225–329 | DOI

[8] K. Werner, “Strings, pomerons and the VENUS model of hadronic interactions at ultrarelativistic energies”, Phys. Rep., 232:2–5 (1993), 87–299 | DOI

[9] E. G. Gurvich, “The quark-antiquark pair production mechanism in a quark jet”, Phys. Lett. B, 87:4 (1979), 386–388 | DOI

[10] A. Casher, H. Neunberg, S. Nussinov, “Chromoelectric-flux-tube model of particle production”, Phys. Rev. D, 20:1 (1979), 179–188 | DOI

[11] M. Gyulassy, A. Iwazaki, “Quark and gluon pair production in $\mathrm{SU}(N)$ covariant constant fields”, Phys. Lett. B, 165:1–3 (1985), 157–161 | DOI

[12] A. Bialas, “Fluctuations of the string tension and transverse mass distribution”, Phys. Lett. B, 466:2–4 (1999), 301–304, arXiv: hep-ph/9909417 | DOI

[13] J. Schwinger, “On gauge invariance and vacuum polarization”, Phys. Rev., 82:5 (1951), 664–679 | DOI

[14] A. I. Nikishov, “Barrier scattering in field theory removal of Klein paradox”, Nucl. Phys. B, 21:2 (1970), 346–358

[15] T. D. Cohen, D. A. McGady, “Schwinger mechanism revisited”, Phys. Rev. D, 78:3 (2008), 036008, 6 pp., arXiv: 0807.1117 | DOI

[16] X. Artru, “Classical string phenomenology. How strings work”, Phys. Rep., 97:2–3 (1983), 147–171 | DOI

[17] V. V. Vechernin, “Space-time picture of string fragmentation and the fusion of colour strings”, Relativistic Nuclear Physics and Quantum Chromodynamics, Proceedings of Baldin ISHEPP XIX, v. 1, JINR, Dubna, 2008, 276–281, arXiv: 0812.0604

[18] S. Ferreres-Solé, T. Sjöstrand, “The space-time structure of hadronization in the Lund model”, Eur. Phys. J. C, 78:11 (2018), 983, 23 pp., arXiv: 1808.04619 | DOI

[19] A. Capella, A. Krzywicki, “Unitarity corrections to short range order: long range rapidity correlations”, Phys. Rev. D, 18:1 (1978), 4120–4133

[20] V. Vechernin, “Forward-backward correlations between multiplicities in windows separated in azimuth and rapidity”, Nucl. Phys. A, 939 (2015), 21–45, arXiv: 1210.7588 | DOI

[21] C. Pruneau, S. Gavin, S. Voloshin, “Methods for the study of particle production fluctuations”, Phys. Rev. C, 66:4 (2002), 044904, 12 pp., arXiv: nucl-ex/0204011 | DOI

[22] V. N. Gribov, “Redzhionnaya diagrammnaya tekhnika”, ZhETF, 53:2 (1967), 654–672

[23] M. I. Gorenstein, M. Gazdzicki, “Strongly intensive quantities”, Phys. Rev. C, 84:1 (2011), 014904, 5 pp., arXiv: 1101.4865 | DOI

[24] E. V. Andronov, “Vliyanie mekhanizma sliyaniya kvark-glyuonnykh strun na dalnie bystrotnye korrelyatsii i fluktuatsii”, TMF, 185:1 (2015), 28–36 | DOI | DOI | MR

[25] V. V. Vechernin, “Korrelyatsiya mezhdu poperechnymi impulsami v modeli so sliyaniem strun”, TMF, 184:3 (2015), 437–448 | DOI | DOI | MR

[26] V. V. Vechernin, “Asimptotika koeffitsientov korrelyatsii poperechnykh impulsov v modeli so sliyaniem strun”, TMF, 190:2 (2017), 293–311 | DOI | DOI | MR

[27] T. S. Biro, H. B. Nielsen, J. Knoll, “Colour rope model for extreme relativistic heavy ion collisions”, Nucl. Phys. B, 245 (1984), 449–468 | DOI | MR

[28] M. A. Braun, C. Pajares, “A probabilistic model of interacting strings”, Nucl. Phys. B, 390:2 (1993), 542–558 | DOI

[29] V. V. Vechernin, R. S. Kolevatov, “Diskretnyi podkhod k opisaniyu dalnykh korrelyatsii mnozhestvennosti i $p_t$ v modeli sliyaniya strun”, Vestn. S.-Peterb. un-ta. Ser. 4. Fizika. Khimiya, 4 (2004), 11–27, arXiv: hep-ph/0305136

[30] M. A. Braun, R. S. Kolevatov, C. Pajares, V. V. Vechernin, “Correlations between multiplicities and average transverse momentum in the percolating color strings approach”, Eur. Phys. J. C, 32:4 (2004), 535–546, arXiv: hep-ph/0307056 | DOI

[31] M. A. Braun, C. Pajares, “Elliptic flow from colour strings”, Eur. Phys. J. C, 71:2 (2011), 1558–1570, arXiv: 1008.0245 | DOI

[32] M. A. Braun, C. Pajares, V. V. Vechernin, “Anisotropic flows from colour strings: Monte Carlo simulations”, Nucl. Phys. A, 906 (2013), 14–27, arXiv: 1204.5829 | DOI

[33] M. A. Braun, C. Pajares, V. V. Vechernin, “Ridge from strings”, Eur. Phys. J. A, 51 (2015), 44, 11 pp., arXiv: 1407.4590 | DOI

[34] V. V. Vechernin, “Short- and long-range rapidity correlations in the model with a lattice in transverse plane”, EPJ Web Conf., 191 (2018), 04011, 8 pp. | DOI

[35] A. Titov, V. Vechernin, “Net charge fluctuations in AA collisions in a simple string-inspired model”, PoS(Baldin ISHEPP XXI), 173 (2013), 047, 11 pp.

[36] B. Alessandro, F. Antinori, J. A. Belikov et al. [ALICE Collab.], “ALICE: Physics performance report, volume II”, J. Phys. G, 32:10 (2006), 1295–2040 | DOI

[37] J. Adam, D. Adamova, M. M. Aggarwal et al. [ALICE Collab.], “Forward-backward multiplicity correlations in pp collisions at $\sqrt{s}= 0.9$, 2.76 and 7\;TeV”, JHEP, 05 (2015), 097, 28 pp., arXiv: 1502.00230 | DOI

[38] A. Bialas, W. Czyz, “Conversion of color field into $q\bar q$ matter in the central region of high-energy heavy ion collisions”, Nucl. Phys. B, 267:1 (1986), 242–252 | DOI

[39] V. V. Vechernin, R. S. Kolevatov, “O korrelyatsiyakh mnozhestvennosti i pt v stolknoveniyakh ultrarelyativistskikh ionov”, YaF, 70:10 (2007), 1846–1857 | DOI