The CMS collaboration at the LHC has reported a remarkable and unexpected
phenomenon in very high-multiplicity high energy proton-proton collisions: a
positive correlation between two particles produced at similar azimuthal
angles, spanning a large range in rapidity. We suggest that this "ridge"-like
correlation may be a reflection of the rare events generated by the collision
of aligned flux tubes connecting the valence quarks in the wave functions of
the colliding protons. The "spray" of particles resulting from the approximate
line source produced in such inelastic collisions then gives rise to events
with a strong correlation between particles produced over a large range of both
positive and negative rapidity. We suggest an additional variable that is
sensitive to such a line source which is related to a commonly used measure,
ellipticity.Comment: Updated figure. Version to be published in Physics Letters 

/SLAC

Bjorken, James D.

Brodsky, Stanley J.

Goldhaber, Alfred Scharff

Physics Letters B

English

arXiv

UNT (University of North Texas) Digital Library

SLAC-PUB-15352Possible multiparticle ridge-like correlationsin very high multiplicity proton-proton collisionsJames D. Bjorken,1 Stanley J. Brodsky,1 and Alfred Scharff Goldhaber1, 21SLAC National Accelerator Laboratory,Stanford University, Stanford, California 94309, USA2C.N. Yang Institute for Theoretical Physics,State University of New York, Stony Brook, NY 11794-3840, USAAbstractThe CMS collaboration at the LHC has reported a remarkable and unexpected phenomenonin very high-multiplicity high energy proton-proton collisions: a positive correlation between twoparticles produced at similar azimuthal angles, spanning a large range in rapidity. We suggestthat this “ridge”-like correlation may be a reflection of the rare events generated by the collision ofaligned flux tubes connecting the valence quarks in the wave functions of the colliding protons. The“spray” of particles resulting from the approximate line source produced in such inelastic collisionsthen gives rise to events with a strong correlation between particles produced over a large range ofboth positive and negative rapidity. We suggest an additional variable that is sensitive to such aline source which is related to a commonly used measure, ellipticity.PACS numbers: 11.15.Bt, 12.20.DsPublished in arXiv:1308.1435v2.Work supported in part by US Department of Energy under contract DE-AC02-76SF00515.I. INTRODUCTIONAn unexpected finding by the CMS collaboration at the Large Hadron Collider (LHC) isa same-side “ridge” in two-particle correlations produced in very high-multiplicity proton-proton collisions. To be precise, plots of the two-body correlation in relative azimuthal angleδφ, integrated over relative pseudo-rapidity δη at a fixed range of transverse momentum p⊥,exhibit a tendency to peak at δφ ' 0 [1, 2].Two immediate qualifications are in order: First, there is a much higher ridge near δφ ∼ π.Secondly, for small pseudo-rapidity difference there is a large peak in the correlation functionnear δφ = 0. Both of these effects have plausible explanations. The away-side ridge reflectsthe conservation of transverse momentum: If one particle appears with positive transversemomentum along the x axis, say, then there must be a particle or particles with negativetransverse momentum to balance it. The peak at small δφ for small δη reflects the presenceof a jet and/or a resonance which decays to more than one particle near a given η and φ.The same-side ridge found by CMS in events with more than 110 particles is statisticallysignificant, but it is not an overwhelming effect. It comes against a background of graduallyincreasing correlation with increasing δφ. Thus an alternative interpretation could be that,instead of a ridge, the dynamically important phenomenon is actually a dip at a particularsmall, but nonzero, value of δφ. A number of authors have made comments and suggestedexplanations for the same-side ridge, including [3]-[19] .As the authors of the experimental paper have noted, the ridge recalls a similar, moreconspicuous, effect seen in nucleus-nucleus collisions. A plausible explanation for the nucleareffect is that when two identical nuclei collide at intermediate impact parameter, the regionof overlap between the two has an approximately elliptical shape in the plane transverse tothe collision axis. Simple hydrodynamics then implies that the expansion along the shortaxis of the overlap ellipse will be more vigorous than the expansion in the long direction, withequal correlations for δφ ≈ 0 and δφ ≈ π. This effect is amplified by looking at multiparticlecorrelations which emphasize the second moment of the azimuthal distribution.Our purpose here is to suggest that a similar ridge effect, albeit with a quite differentphysical mechanism, may be at work in the high multiplicity pp collisions. If we think ofa proton as three quarks bound by color forces, then a plausible description of the bindinginvolves color flux ‘strings’ or tubes connecting to each quark, and to each other, like the2bisectors of a triangle with the quarks at the vertices (“Y” diagrams). The idea of such fluxtubes goes back at least to the work of Isgur and Paton [20]. Planar networks of stronglyinteracting gluons connecting valence quarks are also natural in the higher Fock states ofthe light-front wave functions of the proton as discussed by Mueller [21]. Such saturatingconfigurations can lead to BFKL phenomena, color-glass models [22], and they could evenprovide the color-confining potential of valence quarks as seen in the AdS/QCD soft-wallmodel [23] using light-front holography [24–26] . We also note that ‘H ′-diagrams (e.g., twovertical gluons, interacting via horizontal rungs, connecting a heavy quark and antiquark)which enter the heavy-quark potential [27] have a similar origin.II. CONSEQUENCES OF THE COLLISIONS OF ORIENTED QCD FLUX TUBESA linear configuration of the proton has two valence quarks near one end of a gluonflux tube and a third valence quark at the other end. We assume that the flux tube has atransverse size no larger than a few tenths of a Fermi [28]. The probability of finding sucha linear configuration is arguably quite considerable, especially given the phenomenologicalsuccess of quark-diquark models in spectroscopy and other QCD applications. We guessthe odds of having such a linear configuration as 20%, with an uncertainty either way of afactor two or so. For the collisions of interest, we need the projection of the tube onto the“impact-plane”, and well over half of the linear configurations should survive this projection.We are interested in the head-on collision of two such configurations. The overlap wouldbe significant as long as the impact parameter between the flux tubes were less than thewidth of either flux tube. Just as with the elliptical overlap between two nuclei, this shapewould tend to produce larger momenta in the transverse direction perpendicular to the linesthan in the direction parallel to the lines. The cost in aligning them azimuthally is a factor10 or 20, just from simple geometrical considerations. The impact parameter must of coursebe small, with a transverse size of order of 0.2 fermi. Along the string direction we can loosenthis demand to, say, 0.5 fermi. This gives a cross-section of about 1 mb. After the penaltyfactors which we have enumerated are included, the estimated cross-section for the collisionof aligned flux tubes is reduced to a value in the neighborhood of 1 microbarn. This is quitesimilar to the cross section for events with a trigger of more than 110 charged-particle tracksused in the CMS experimental ‘ridge’ analysis [1].3An illustration of the collision of oriented flux tubes – i.e., high-density gluonic strings –is given in fig. 1.u duduuu duduu Quark-GluonPlasma8-20138825A7EmittedHadronsHigh PTHighest dNdd dq(a) (b) (c)FIG. 1: (a) Collisions of oriented flux tubes (high-density gluonic strings ) acting between a quarkand diquark configuration in each proton projectile in pp inelastic collisions. The tubes are shownprojected onto the impact plane, which is perpendicular to the velocities of the two protons. Asdrawn, the tubes would miss each other, giving negligible contribution to the ridge signal. (b) Whenthe flux tubes overlap, the plasma produced by the collisions of the line sources moves horizontally,and is subject to two-dimensional hydrodynamic expansion, whereas the hadronic density movingvertically is subject to the usual three-dimensional expansion. (c) Most of the energy density in thetransverse direction is emitted as hadrons adjacent to the leading edge of the (transverse) pulse.When such a high multiplicity event occurs, almost all of the center-of-mass energy isexpected to be expended in particle production; relatively little should be radiated down thebeam directions. We estimate roughly that dET/dη in the central region of rapidity couldbe of order 10 − 20 GeV for these events: The transverse dimensions of the overlappingflux tubes correspond to 1 − 2 GeV of momentum. If one has independent emissions forevery piece of the flux tube of length equal to the transverse dimension, then it is reasonable4that the resulting total transverse energy per unit rapidity would be an order of magnitudehigher. While some of this transverse energy can be expected to be in visible minijets, it isquite possible that at least some subset of these events are relatively jet-free. We come tothis conclusion by assuming that jets should come from overlap of ‘occupied pixels’ in thecolliding flux tubes, where the pixels have dimensions about an order of magnitude smallerthan the width of a flux tube. To obtain the assumed total energy one finds only a minorityof the pixels are occupied, and thus the frequency of mini-jet formation may be low.Looking down the beam direction, the generator of particle production in the flux-tubecollisions is an approximate line source, more extreme in azimuthal asymmetry than thealmond-shaped source region typical of intermediate-impact-parameter heavy-ion collisions.Therefore, one should expect that this special class of events has even stronger “ellipticity”effects than in the nuclear case. In particular, a broader transverse momentum distributionis to be expected in the azimuthal direction normal to the flux tubes. Furthermore, thisproperty is expected to be “boost invariant”: If one were to compare the produced-particledistribution for such an event at zero rapidity at the LHC with what would be seen at zerorapidity for a hypothetical asymmetric collider—say 350 TeV against 35 GeV—the resultwould be expected to be very similar because the geometry of the relevant active collision areais essentially the same. Therefore the azimuthal asymmetries seen in the positive-rapidityhalf of the detector should be strongly correlated with those seen in the negative-rapidityhalf of the detector. This feature is the basic correlation structure of all “ridge” phenomena.This discussion suggests a flexible search strategy for uncovering not only this phe-nomenon, but also related effects associated with the nontrivial impact-plane geometry.For example, one might begin by restricting attention to the properties of events in thepositive-rapidity half of the detector. After a choice of judicious, creative cuts and/or eventscans, one will hopefully have a sample of candidate events exhibiting “ridge” effects. Foreach such event, one then looks at the data from the other half of the detector. If the “ridge”effects we have proposed are genuine, they should be largely reproduced in the other half ofthe event. In other words, the correlations should be seen along virtually the entire rapidityplateau.In addition to the general strategy described above, we can suggest a more specific test.The key point is that a multi-particle correlation should give a much more conspicuous signalthan the two-particle correlation used so far in the experimental analysis, but of course only5in that small fraction of the events where the prerequisite conditions of coincidence of narrowstrings in the projectile and target are in fact obtained. To be specific, we suggest looking atthe following vector ~V , computing its magnitude for each event. If the number of events withlarge magnitude are greater than expected from chance, one would have powerful evidencefor the proposed colliding flux tube mechanism. Define~V =N∑i=1[cos 2φix̂+ sin 2φiŷ] , (1)and obtain the distribution of ~V 2. If the particles were distributed randomly in φ, then theexpectation value of ~V 2 would be N , where N is the number of particles in the event inthe given region of transverse momentum. The probability of getting a value N2 may beestimated by introducing quadrants in the variable 2φ: Assume each vector can take onlythe values ±x̂ or ±ŷ, with each having a probability 1/4. Suppose the first vector is +x̂.Then the chance that the remainder would all be in the same direction would be (1/4)N−1.For N = 5, this would yield a probability 1/256. If, among events in which the ridge wasseen, with more than 110 particles per event, and 5 particles separated from each other byabout one unit in δη in an interval of p⊥ between 1 and 2 GeV/c, as many as 2% of theevents should show ~V 2 ≈ 25, that could be evidence for the kind of correlation we suggest.This exercise is equivalent to asking the probability – assuming complete randomness in φ –that all 5 particles are in either of two opposite octants of φ. If they were more collimatedthan that, the probability would be even smaller.Counting all particles in each event in the specified range of transverse momentum, re-gardless of rapidity separation, should give a reliable measure of the correlation. Technically,~V 2 is just the square of the usual ellipticity variable. An advantage of squaring is that max-imal ellipticity events are easy to pick out. Also, it is easier to think about such a scalarvariable rather than a vector variable.At this point let us take a step back to gain perspective on what could cause such phe-nomena. Obviously projectile and target must overlap in impact parameter to some extent.Dynamics, in the form of the conservation of momentum or of the attraction of outgoingparticles to each other, can – as earlier discussed – produce certain correlations, such asthe away-side ridge and the clustering of particles with small relative velocity. However,the dynamics cannot explain the long-range (in rapidity) near-side correlations. For thisone needs geometry in the transverse plane. We have given a specific example of such a6geometry, the presence of parallel overlapping strings with a substantial projection onto thetransverse plane. Clearly the overlap mentioned for lower-energy nucleus-nucleus collisionsalso is an example, even though it involves a very different mechanism.III. CONCLUSIONSWe have suggested that the ridge-like correlation found by the CMS collaboration [1, 2]in high-multiplicity events in pp collisions at the LHC could be evidence for the collision ofaligned high-intensity flux tubes connecting the valence quarks of the colliding protons. Akey property is the correlation of ridge events between positive and negative rapidity. Furtherstudies clearly are warranted, including an extended analysis of the CMS data based on thesquared correlation vector ~V 2. If one finds evidence for very strongly aligned “ellipticalflow” in pp collisions, where the formation mechanism for the “ellipse” is in our opinion verydifferent from the geometrical overlap mechanism seen in nucleus-nucleus collisions, then theobservation of the “ridge” phenomenon in pp collisions over a large range of rapidity wouldbe a dramatic demonstration of high density effects in QCD.AcknowledgmentsThis research was supported by the Department of Energy contract DE–AC02–76SF00515.[1] V. Khachatryan et al. [CMS Collaboration], “Observation of Long-Range Near-Side An-gular Correlations in Proton-Proton Collisions at the LHC,” JHEP 1009, 091 (2010)[arXiv:1009.4122 [hep-ex]].[2] D. Velicanu [CMS Collaboration], “Ridge correlation structure in high-multiplicity p p colli-sions with CMS,” J. Phys. G G 38, 124051 (2011).[3] S. Alderweireldt and P. Van Mechelen, “Obtaining the CMS Ridge effect with MultipartonInteractions,” arXiv:1203.2048 [hep-ph].[4] B. Arbuzov, “CMS ridge effect at the LHC as a manifestation of bremsstrahlung of gluons offquarks accelerated in a strong color field,” PoS QFTHEP 2011, 024 (2011).7[5] A. Kovner, “Particle production and angular correlations at high energy,” Acta Phys. Polon.B 42, 2717 (2011).[6] K. Dusling and R. Venugopalan, “Azimuthal collimation of long range rapidity correlationsby strong color fields in high multiplicity hadron-hadron collisions,” arXiv:1201.2658 [hep-ph].[7] I. Bautista, J. D. de Deus and C. Pajares, “String percolation and the first LHC data,”arXiv:1112.4994 [hep-ph].[8] C. -Y. Wong, “Momentum Kick Model Description of the Ridge in (Delta-phi)-(Delta eta)Correlation in pp Collisions at 7 TeV,” Phys. Rev. C 84, 024901 (2011) [arXiv:1105.5871[hep-ph]].[9] M. G. Ryskin, A. D. Martin and V. A. Khoze, “Probes of multiparticle production at theLHC,” J. Phys. G G 38, 085006 (2011) [arXiv:1105.4987 [hep-ph]].[10] V. A. Abramovsky and N. V. Radchenko, “Multiplicity Distribution of Secondary Hadronsat LHC Energy and Total Cross Sections of Hadron-Hadron Interactions,” arXiv:0812.2465[hep-ph].[11] E. Levin and A. H. Rezaeian, “The Ridge from the BFKL evolution and beyond,” Phys. Rev.D 84, 034031 (2011) [arXiv:1105.3275 [hep-ph]].[12] H. Bialkowska, “The ridge effect at the LHC: High density in p p,” Acta Phys. Polon. B 42,1359 (2011).[13] S. M. Troshin and N. E. Tyurin, “Correlations in multiparticle production,” arXiv:1108.4584[hep-ph].[14] P. Bozek, Eur. Phys. J. C 71, 1530 (2011) [arXiv:1010.0405 [hep-ph]].[15] A. Dumitru, K. Dusling, F. Gelis, J. Jalilian-Marian, T. Lappi and R. Venugopalan, “TheRidge in proton-proton collisions at the LHC,” Phys. Lett. B 697, 21 (2011) [arXiv:1009.5295[hep-ph]].[16] E. Avsar, C. Flensburg, Y. Hatta, J. -Y. Ollitrault and T. Ueda, “Eccentricity and ellip-tic flow in proton-proton collisions from parton evolution,” Phys. Lett. B 702, 394 (2011)[arXiv:1009.5643 [hep-ph]].[17] I. M. Dremin and A. V. Leonidov, “The Quark-gluon medium,” Phys. Usp. 53, 1123 (2011)[arXiv:1006.4603 [nucl-th]].[18] E. Shuryak, “Comments on the CMS discovery of the ’Ridge’ in High Multiplicity pp collisionsat LHC,” arXiv:1009.4635 [hep-ph].8[19] K. Dusling and R. Venugopalan, “Comparison of the Color Glass Condensate to di-hadroncorrelations in proton-proton and proton-nucleus collisions,” arXiv:1302.7018 [hep-ph]; Phys.Rev. D 87, 094034 (2013).[20] N. Isgur and J. E. Paton, “A Flux Tube Model for Hadrons,” Phys. Lett. B 124, 247 (1983).[21] A. H. Mueller, Nucl. Phys. B 643, 501 (2002) [hep-ph/0206216].[22] L. D. McLerran and R. Venugopalan, Phys. Rev. D 49, 2233 (1994) [hep-ph/9309289].[23] J. Erlich, E. Katz, D. T. Son and M. A. Stephanov, Phys. Rev. Lett. 95, 261602 (2005)[hep-ph/0501128].[24] S. J. Brodsky, G. F. de Teramond and H. G. Dosch, arXiv:1302.4105 [hep-th].[25] G. F. de Teramond and S. J. Brodsky, Phys. Rev. Lett. 94, 201601 (2005) [hep-th/0501022].[26] S. J. Brodsky and G. F. de Teramond, Phys. Rev. Lett. 96, 201601 (2006) [hep-ph/0602252].[27] T. Appelquist, M. Dine and I. J. Muzinich, Phys. Lett. B 69, 231 (1977).[28] R. V. Buniy, J. Cantarella, T. W. Kephart and E. Rawdon, arXiv:1212.1500 [hep-ph].9

Possible Multiparticle Ridge-like Correlations in Very High Multiplicity Proton-proton Collisions

Possible multiparticle ridge-like correlations in very high multiplicity
  proton-proton collisions

Possible multiparticle ridge-like correlations in very high multiplicity proton-proton collisions

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