$\bf p$-$\bf p$ minimum-bias dijets and nonjet quadrupole in relation to conjectured collectivity (flows) in high-energy nuclear collisions

Recent observations of ridge-like structure in $p$-$p$ and $p$-$A$ angular correlations at the RHIC and LHC have been interpreted to imply collective motion in smaller collision systems. It is argued that if correlation structures accepted as manifestations of flow in $A$-$A$ collisions appear in smaller systems collectivity (flow) must extend to the smaller systems. But the argument could be reversed to conclude that such structures appearing in $A$-$A$ collisions may not imply hydrodynamic flow. I present spectrum, correlation and fluctuation data from RHIC $p$-$p$ and Au-Au collisions and $p$-$p$, $p$-Pb and Pb-Pb results from the LHC described accurately by a two-component (soft+dijet) model of hadron production. I also present evidence for a significant $p$-$p$ nonjet (NJ) quadrupole ($v_2$) component with $n_{ch}$ systematics directly related to $A$-$A$ NJ quadrupole systematics. The combination suggests that soft, dijet and NJ quadrupole components are distinct phenomena in all cases, inconsistent with hadron production from a common bulk medium exhibiting collective motion (flow).


Introduction
Certain analysis techniques applied to LHC data for smaller collision systems have lead to claims for collectivity (ows) even in p-p collisions at higher energies. The original ow concept has been extended to a universal property of all high-energy nuclear collisions, not just a subset corresponding to the highest particle and energy densities. That conceptual trend is ironic in that accumulating evidence from alternative analysis techniques argues against any hydrodynamic phenomenon in high-energy collisions, a conclusion buttressed by the observation that certain phenomena associated with ows in central A-A collisions also appear in p-p collisions with negligible particle and energy densities. Given the limitation on article length I summarize here only a few results most relevant to recent LHC claims.
2 p-p 2D angular correlations vs n ch the three-component model  densityρ s = n s /∆η within acceptance ∆η = 2. Those results are consistent with previous studies of minimum-bias (MB) p-p collisions [2,3]. In terms of correlated hadron-pair number (e.g. n ch A soft ) the soft (projectile dissociation) pair number scales ∝ρ s , the dijet pair number scales ∝ρ 2 s and the NJ-quadrupole pair number scales ∝ρ 3 s . Since multiplicity n ch = n s + n h varies ten-fold the range of dijet production is 100-fold and the NJ quadrupole varies 1000-fold for this data sample. The dijet trend conrms results from a p t spectrum analysis leading to a two-component model (TCM) where the hard-component (dijet) hadron yield n h is related to the soft-component (projectile-dissociation) yield n s as n h ≈ 0.01n 2 s within ∆η = 1 [4]. The dijet trend for spectra and 2D angular correlations is consistent with recent LHC measurements of ensemble-mean p t [5] and p t uctuations [6] vs n ch where p-p collisions at LHC energies are found to be dominated by dijet production described accurately by the same TCM (see Sec. 4). Dijet correlation trends in Au-Au collisions at the RHIC are consistent with spectrum hard components [7,8] and with QCD (via event-wise reconstructed jets) [9].
The new third model element for p-p collisions (NJ quadrupole) is found to be very signicant for larger multiplicities. Evidence from Au-Au collisions suggests that the NJ quadrupole component in A-A collisions is carried by a small fraction of total hadrons (<5%) [10]. 3 The CMS ridge nonjet quadrupole vs minimum-bias dijets One argument for collectivity (ows) in small collision systems proceeds from identication of a same-side (SS) ridge in 2D angular correlations from 7 TeV p-p collisions with certain cuts applied [11]. Note that several ridges have been identied in RHIC and LHC data including a soft ridge [12] and a ridge associated with trigger-associated combinatoric jet analysis [13] (both probably jet-related). Evidence from 2D angular correlations as in Sec. 2 suggests that the CMS ridge is associated with the NJ quadrupole component [14].   shows the appearance of a SS ridge when a p t cut is applied to CMS highmultiplicity data, the primary evidence for claims of a novel ridge phenomenon interpreted by some to signal ow in p-p collisions. In Ref. [14] dijet and NJ quadrupole trends for 62 and 200 GeV Au-Au collisions were extrapolated rst to N -N collisions and then to 7 TeV. The prediction shown in panel (d) agrees quantitatively with the CMS result in panel (c). One motivation for the p-p correlation study in Sec. 2 was to conrm the extrapolation to N -N collisions in Ref. [14] and that has been achieved. It is notable that as the SS curvature changes sign from positive to negative the negative AS curvature doubles for the same conditions, conrming the role of the NJ quadrupole with its two maxima at 0 and π. 4 p t uctuations at the RHIC and LHC minimum-bias dijets conventional variance-based uctuation measure B as C = B/n ch (n ch − 1), with conditional variance dierence B ≡ (P t − n chpt ) 2 −n ch σ 2 pt (the second term is a central-limit reference). s . The second term is the contribution from MB dijet production that dominates p t uctuations. Corresponding results for other collision energies inferred from known ensemblemeanp t systematics [5] indicate that B (and p t uctuations) are strongly energy dependent as expected for dijets [6]. The ALICE choice of p t uctuation measure (a ratio of ratios) has as one consequence the near cancellation of the dominant dijet contribution, suggesting as a consequence that small collision systems may be substantially thermalized with no signicant correlation structure and that event-wise temperature as a state variable may be relevant.  The hard-component trend ∝ ν is a signature for dijet production that appears to dominate p t uctuations up to central collisions. Figure 4 (d) shows STAR 200 GeV Au-Au uctuation data in the same format (obtained almost ten years ago) that exhibit the same trend [15,16]. The ve-fold increase in overall amplitude from RHIC to LHC is expected from the energy dependence of dijet production. The STAR study derived the underlying p t 2D angular correlations corresponding to measured p t uctuations (via inversion of uctuation scale dependence), and the dominant jet-related correlation structure is undeniable. 5 The nonjet quadrupole ow or nonow?  data for identied hadrons demonstrate that the NJ quadrupole corresponds to an expanding cylindrical shell with xed source boost for all collisions systems [18,19]. The combination of results in Fig. 5 plus other evidence against a hydrodynamic mechanism argues against a ow interpretation for the NJ quadrupole in any high-energy collision system [20]. The possibility emerges that the NJ quadrupole represents an alternative (nonow) QCD mechanism [21].

Summary
The two-component (soft + hard) model (TCM) provides a remarkably accurate description of hadron production over a broad range of collision systems p-p and p-A or d-A vs n ch and A-A vs centrality measure ν at RHIC and LHC collision energies. The dijet (hard) component of the TCM is quantitatively consistent with spectrum hard components and with data from event-wise reconstructed jets. Evidence from p t spectra, ensemble-mean p t , p t uctuations and 2D angular correlations shows that minimum-bias (MB) dijets dominate high-energy collisions. However, alternative spectrum, uctuation and correlation measures can act to suppress evidence for large dijet contributions, for instance in the form of statistical ratios of ratios that cancel the hard components of TCM trends or spectrum ratios (e.g. R AA ) that suppress spectrum hard components at smaller p t where they achieve their maximum values. dense bulk medium, support instead an expanding thin cylindrical shell with source boost independent of collision centrality for those few hadrons carrying the NJ quadrupole.
The CMS ridge, seen as a novel phenomenon suggesting collectivity (ow) in small collision systems at LHC energies, is simply explained as an interplay of the NJ quadrupole with the away-side dijet peak that controls the same-side net azimuth curvature. The LHC phenomenon can be predicted quantitatively from quadrupole and dijet trends observed already in RHIC collisions. One could argue that appearance of an NJ quadrupole component in p-p collisions does support a ow interpretation there, as recently claimed. But the opposite is more likely: the appearance of a quadrupole component in small systems where the particle density is negligible argues against a hydro interpretation, instead is consistent with mounting evidence against a hydrodynamic description in any high-energy collision system.
The unanticipated abundance of resolved low-energy (MB) jets or minijets in more-central Au-Au collisions at the RHIC became apparent in STAR angular-correlation data more than ten years ago, already casting doubt on claims for local thermalization in such collisions and therefore for a owing bulk medium or QGP. Evidence against thermalization and hydrodynamic ows has mounted steadily since then. Statistical and correlation measures and spectrum-analysis techniques that reveal the persistent large dijet contribution and evidence against ows have been developed and published throughout that period. It is remarkable how little inuence those results have had on the larger community over the ensuing ten years.