Ridge Production in High-Multiplicity Hadronic Ultra-Peripheral Proton-Proton Collisions
Stanley J. Brodsky, Stanislaw D. Glazek, Alfred S. Goldhaber, Robert W. Brown
RRidge Production in High-Multiplicity Hadronic Ultra-PeripheralProton-Proton Collisions
Stanley J. Brodsky
SLAC National Accelerator Laboratory, Stanford University
Stanislaw D. Glazek
Faculty of Physics, University of Warsaw
Alfred S. Goldhaber
C. N. Yang Institute for Theoretical Physics, Stony Brook University
Robert W. Brown
Case Western Reserve University
Abstract
An unexpected result at the RHIC and the LHC is the observation that high-multiplicity hadronic events in heavy-ion and proton-proton collisions are dis-tributed as two “ridges", approximately flat in rapidity and opposite in az-imuthal angle. We propose that the origin of these events is due to the inelasticcollisions of aligned gluonic flux tubes that underly the color confinement ofthe quarks in each proton. We predict that high-multiplicity hadronic ridgeswill also be produced in the high energy photon-photon collisions accessibleat the LHC in ultra-peripheral proton-proton collisions or at a high energyelectron-positron collider. We also note the orientation of the flux tubes be-tween the q ¯ q of each high energy photon will be correlated with the planeof the scattered proton or lepton. Thus hadron production and ridge forma-tion can be controlled in a novel way at the LHC by observing the azimuthalcorrelations of the scattering planes of the ultra-peripheral protons with the ori-entation of the produced ridges. Photon-photon collisions can thus illuminatethe fundamental physics underlying the ridge effect and the physics of colorconfinement in QCD. Keywords
QCD, hadron production; two-photon collisions; ultra-peripheral collisions;ridge production; LHC. Introduction
One of the striking features of proton-proton collisions at RHIC [1, 2] and the LHC [3–5] is the obser-vation that high multiplicity events are distributed as “ridges" which are approximately flat in rapidity.Two ridges appear, with opposite azimuthal angles, simultaneously reflecting collective multiple particleflow and transverse momentum conservation. This statement follows from the analyses in the quotedreferences, although it does not appear there explicitly.Experimental results from PHENIX [1, 2] are illustrated in Fig. 1. Since ridges appear in proton-proton collisions [6] as well as heavy ion collisions, this phenomenon evidently does not require theformation of a quark-gluon plasma. In addition, the high-multiplicity events show an unexpectedly highstrangeness content [5].In a previous publication with J. D. Bjorken, we suggested [7] that the “ridge” correlations reflectthe rare events generated by the collision of aligned flux tubes that connect the quark to the diquark inthe wave function of the colliding protons. The “spray” of particles resulting from the approximate linesource produced in such inelastic collisions then gives rise to events with strong correlations over a largerange of both positive and negative rapidity. a r X i v : . [ h e p - ph ] O c t idge phenomena observed in both p-p and Au-Au collisions p + p ! X, p s = 200 GeV Au + Au ! X, p s = 200 GeV Fig. 1:
Ridge formation in proton-proton and nucleus-nucleus collisions
Ultra-peripheral proton-proton and heavy ion collisions (UPC) would allow the study of multi-TeV photon-photon interactions at the LHC [8, 9]. Possible photon-photon studies include light-by-light scattering [10], top-pair production via γγ → t ¯ t processes, electroweak tests such as W − pairproduction in γγ → W + W − events [11], QCD studies, such as hard inclusive and exclusive hadronicreactions, and measurements sensitive to the photon structure function [12–14]. In this report we showthat the photon-photon collisions provided by ultra-peripheral proton-proton collisions at the LHC canilluminate the physical QCD mechanisms which underly high mutiplicity hadronic events and ridgeformation, including the role of color confinement and gluonic string formation.In ultra-peripheral proton-proton collisions, each of the virtual photons can couple to a virtual q ¯ q pair. The quark and antiquark are connected by a flux tube, reflecting color-confining QCD interactions,as illustrated in Fig. 2. One can identify the flux tubes with the string-like network of gluonic interactionswhich confine color. Such gluonic flux tubes were originally postulated by Isgur and Paton in ref. [15].The high-energy inelastic collisions of the two flux tubes when they are maximally aligned will then leadto high-multiplicity hadronic events distributed across the rapidity plateau. Moreover, one expects theplanes of the ridges to be correlated with the planes of the flux tubes. Thus in a γ − γ UPC collision, thetwo overlapping flux tubes can collide and interact (by multi-gluon exchange) to produce the final-statehadrons. The final-state interactions put the system on-shell so that four-momentum is conserved. Thisis illustrated in Fig. 3.Photon-photon collisions with aligned flux tubes can also be studied at a high energy electron-ion collider (EIC) or in photon-proton collisions at the proposed LHeC collider, as well as with UPCproton-proton collisions at the LHC.We come now to an interesting puzzle about the process of forming two coordinated ridges in pp collisions, where both protons suffer momentum transfer along the same axis.2 idge creation in Ultra-Peripheral pp scattering p p p p ⇤ ⇤ x, ~k ? x, ~k ? q ¯ q pp ! ⇤ ⇤ p p ! X p p Planes of quark anti-quark and produced ridges aligned with planes of proton scattering M q ¯ q = k ? + m q x (1 x ) Off-shell in P - and invariant mass Hadrons produced from the collisions of flux tubes
Fig. 2:
Hadron production from aligned flux tubes in UPC collisions ⇤ ⇤ Hadrons produced from Collisions of Flux-Tubes ⇤ ⇤ ! hadrons Fig. 3:
Hadron formation from the collision of flux tubes in two-photon reactions pp scattering an extremely interesting experiment.A light-front wavefunction (LFWF) of a hadron ψ H ( x i , (cid:126)k ⊥ i , λ i ) = < n | ψ H > for an n -partonFock state is the hadronic eigensolution | ψ H > of the QCD light-front Hamiltonian H LF | ψ > = M H | ψ > projected on the free parton basis. Here x i = k + i /P + = ( k + k ) / ( P + P ) is the boost-invariantLF momentum fraction of constituent i , with (cid:80) ni =1 x i = 1 . The squares of the LFWFs integrated overtransverse momentum underly the hadronic structure functions, and the overlaps of the LFWFs generatethe hadronic form factors. A light-front wavefunction is defined at a fixed LF time τ = t + z ; it thus canbe arbitrarily off-shell in P − and in invariant mass M = P + P − − P ⊥ = (cid:80) i ( k ⊥ + m x ) i . For example,the pointlike-coupling of a photon in perturbative QED to an intermediate lepton pair (cid:96) + (cid:96) − has the form ψ γ → (cid:96) ¯ (cid:96) ∝ √ α (cid:126)(cid:15) · (cid:126)k ⊥ M , where (cid:82) d k ⊥ dx | ψ | ∼ α . One can study analogous double-lepton-pair formation inUPC collisions pp → p (cid:48) p (cid:48) + [ (cid:96) + (cid:96) − ] + [ (cid:96) + (cid:96) − ] as a check on the basic formalism. For related calculations,see ref. [16]. The coupling of the photon to quark pairs in QCD has both soft and hard contributions.The same couplings contribute to the structure and evolution of the photon structure function [12–14].We have found that it can be useful to analyze high energy collisions in the “Fool’s ISR" frame,where the two incident projectiles both have positive P + = P + P z and nonzero transverse momenta ± (cid:126)r ⊥ . The CM energy squared s = ( p A + p B ) = 4 r ⊥ is then carried by the nonzero transverse momenta.For an example, see ref. [17]. This frame choice simplifies factorization analyses for pQCD in the frontform since it allows a single light-cone gauge A + = 0 for both projectiles. Origin of Flux Tubes in UPC and γγ collisions We will assume that QCD color confinement creates a gluonic string between the q and the ¯ q of thephoton. This can be motivated using AdS/QCD, together with LF holography. This formalism has beensuccessful in predicting virtually the entire hadronic spectrum, as well as dynamics such as hadron formfactors, and structure functions at an initial nonperturbative scale, as well as the QCD running coupling α s ( Q ) at all scales [18, 19]. An example of the predicted meson and baryon Regge spectroscopy usingsuperconformal algebra [18] is shown in Fig. 4.The LF wavefunction ψ ¯ q ¯ q ( x, (cid:126)k ⊥ ) is the off-shell amplitude connecting the photon to the q ¯ q atinvariant mass M = k ⊥ + m q x (1 − x ) , where x = k + P + at fixed LF time τ. The q ¯ q color-confining frame-independent potential for light quarks derived from AdS/QCD and light-front holography has the form U ( ζ ) = κ ζ = κ b ⊥ x (1 − x ) in the light-front Hamiltonian [18]. The color-confining potential thatacts between the q ¯ q pair for the virtual photon then leads to Gaussian fall-off for the photon’s LFWF ψ ¯ q ¯ q ( x, (cid:126)k ⊥ ) with increasing invariant mass as well as Gaussian fall-off in transverse coordinate space: ∼ e − κ ζ = e − κ b ⊥ x (1 − x ) as shown in Fig. 5 The same color-confining dynamics implies a string-likeflux tube of gluons appearing between the q and ¯ q . The gluonic flux tube (illustrated as a thick blueline) shown in Fig. 3 represents the network of gluons that connects the quark to the antiquark. In effect,4 ! !!!!! !!!!!!" " " " M ! GeV " L M ! L B ! Ρ , Ω a , f Ρ , Ω a , f $ ! $ % , $ % $ ! , $ ! , $ ! , $ ! $ ! ⇢ superpartner trajectories Dosch, de Teramond, sjb
Fig. 4:
Prediction of meson and baryon Regge spectroscopy from AdS/QCD, light-front holography, and super-conformal algebra. The predictions for the meson and baryon mass spectra have the form M M = 4 κ ( n + L M ) formesons and M B = 4 κ ( n + L B + 1) for baryons; i.e., universal Regge slopes in the principal quantum number n and orbital angular momentum L for both mesons and baryons. The baryons have a quark plus scalar diquark struc-ture with relative orbital angular momentum L B . Superconformal algebra, together with LF holography, predictsthe equality of meson and baryon masses for L M = L B + 1 . the transverse width of the flux tube is characterized by b ⊥ ∝ κ x (1 − x ) , where κ ∼ / GeV is thecharacteristic mass scale of QCD, and x and − x are the LF momentum fractions of the q and the ¯ q .The width of the stringlike flux tube is thus smallest for x ∼ / and largest at x → , ; i.e., at large M q ¯ q . Note that one is looking at the virtual q ¯ q state and its gluonic string at fixed LF time τ . Thelongitudinal spatial coordinate is x − = x − x , which is conjugate to the LF momentum k + = k + k = xP + . Thus the domain x → , and large invariant pair mass corresponds to large x − ; i.e., large spatialseparation between the q and ¯ q . One can identify the rapidity y of a parton with respect to the parent stateas y = log x . The rapidity difference y q − y ¯ q between the quark and antiquark thus grows as log x . Theinelastic collision of two flux tubes when they are maximally aligned will then lead to high-multiplicityhadronic events distributed across the rapidity plateau, where the plane of the primary ridge is aligned inazimuthal angle parallel to the aligned flux tubes.It is thus clear that the maximum number of hadrons will be created when each virtual q ¯ q pair hasmaximum M and the gluonic strings are long and maximally aligned; i.e., the collision of long fluxtubes. The hadrons in such high multiplicity events will be produced nearly uniformly in rapidity andthus appear as ridges. This description of γγ collisions also provides a model for Pomeron exchangebetween the colliding q ¯ q systems. It would be interesting to relate this physical picture to the Pomeronand string-based analyses such as that given in Ref. [20]5 q q p ⇤ ( q ) Characteristics of the quark-antiquark flux tube p ( x, b ? , Q ) / exp [ b ? x (1 x )( + Q )] < b ? > / x (1 x )( + Q ) x1-x < b ? > / x (1 x )( + Q )+ m q massive quarksmassless quarks Planar structure reflects color-confinement potential p’ < b ? > ! 1 if x ! , M = k ? x (1 x ) / b ? x (1 x ) U ( ) = b ? x (1 x ) AdS/QCD + Light-Front Holography de Teramond, Dosch, Lorce, sjb
Fig. 5:
Origin of the gluonic flux-tube based on the color-confining light-front potential derived from AdS/QCDand light-front holography.
An important aspect of the UPC events is that the plane of each produced q ¯ q (and thus the ori-entation of the flux tube) is correlated with the scattering plane of the parent proton since the virtualphotons are transversely polarized to the fermion scattering planes. The correlation to first approxima-tion is proportional to cos ∆ φ where ∆ φ = φ − φ . Since the flux tubes are aligned with the protonscattering planes, one can enhance the probability for high multiplicity hadron production by selectingevents where the planes of the scattered UPC protons are parallel. Conversely, one will produce min-inum hadron multiplicity if the scattering planes are orthogonal ∆ φ = φ − φ (cid:39) π/ . The couplingof the highly virtual photons to strange and charm q ¯ q pairs as well as the composition of the flux tubesthemselves can lead to enhanced charm and strange hadron multiplicity. We also note that in additionto the hadrons produced by the collision of the flux tubes, the q ¯ q pairs can also interact with each otherby gluon exchange and produce up to four near-forward quark jets of various flavors and combinations.Such jet patterns [21] could provide additional information on the physics arising from the collisions ofgluonic strings spanned between quarks.One complication which we are currently investigating is whether the collision of the flux tubesitself can affect the orientation of the incoming q ¯ q planes and thus dilute the predicted alignment betweenthe colliding gluonic strings. One expects that the rotation of the q ¯ q plane will be important when the totalmass of the produced hadronic system is comparable to the q ¯ q invariant mass. However, the predictionthat minimal hadron multiplicity will be produced when the scattering planes of the UPC protons areperpendicular would not be affected.One can think of the initial configuration shown in Fig. 2 as similar to the configuration one hasfor initial distributions in pQCD factorization, such as Drell-Yan lepton pair production. The initial con-figuration can however be modified by the collision itself. This is analogous to the initial-state scattering6 Gluonic distribution reflects quark+diquark color structure of the proton
Color confinement potential —> high density gluon field: flux tube | p > = | u C [ ud ] ¯3 C > J=0 p ( J z = +1 / u ( S z = +1 / u ( S z = / L z = 0 L z = AdS/QCD + Light Front Holography: Proton is bound state of a quark + scalar diquark
Equal probability L=0, L=1
Quark chiral symmetryAnomalous moment nonzeroLeading Twist Sivers Effect C ⇥ C = ¯3 C + 6 C ud Fig. 6:
Quark-diquark configuration of baryons predicted by AdS/QCD, light-front holography, and superconfor-mal algebra. One predicts a color flux tube connecting the C quark to the ¯3 C diquark and a second flux tubewithin the spin-zero diquark. in lepton-pair production that produces the Sivers single-spin correlation [22] or the double- -Mulderseffect [23].In the case of the proton, AdS/QCD predicts a color flux tube which combines two quarks into a ¯3 C diquark system, plus a flux tube that connects the remaining C quark to the flux tube of the diquarksystem. See Fig. 6. The configuration of flux tubes in the proton is a special case of the Y configurationdiscussed in ref. [24]. The activation of both the q [ qq ] and [ qq ] flux tubes in a proton-proton collisioncould thus lead to both v and v correlations in the distributions of the final-state hadrons. In contrast,the UPC photon-photon collisions would only lead to a v correlation from the activation of the [ q ¯ q ] fluxtubes. The dependence of the distributions of high multiplicity events on proton structure is discussedin ref. [24]. One could also study the interactions of flux tubes in γp collisions using a single UPCproton at the LHC. See Fig. 7. The oriented flux tube of the photon generated by the single UPC protoncan interact with either of the two flux tubes within the proton quark-diquark LFWF to produce highmultiplicity hadronic events. The hadrons will tend to be distributed with v or v moments dependingon the details of the collision. The produced ridges of hadrons will in this case tend to be oriented withthe scattering plane of the UPC proton. Acknowledgements
Presented by SJB at Photon 2017: The International Conference on the Structure and the Interactionsof the Photon and the International Workshop on Photon-Photon Collisions. CERN, May 22-26, 2017.This research was supported by the U. S. Department of Energy, contract DE–AC02–76SF00515. SLAC-PUB-17106. 7 ⇤ P B P B ⇤ Collisions of Aligned Flux Tubes in photon-photon, photon-proton, and proton-proton Interactions P A P A P A P B ⇤ ⇤ p ! X ⇤ ⇤ ! X P A P A P B pp ! X Fig. 7:
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