Υ ( nS ) polarizations versus particle multiplicity in pp collisions at √ s = 7 TeV

Article history: Received 9 March 2016 Received in revised form 5 July 2016 Accepted 26 July 2016 Available online 2 August 2016 Editor: M. Doser


Introduction
Studies of heavy-quarkonium production contribute to an improved understanding of hadron formation within the context of quantum chromodynamics (QCD) [1]. Quarkonium production is expected to proceed in two steps [2]. First, a heavy quarkantiquark pair, QQ, is produced, with angular momentum L and spin S. Then this "pre-resonance" binds into the measured quarkonium state through a nonperturbative evolution that may change L and/or S. The short-distance QQ production cross sections are functions of the QQ momentum and are calculated in perturbative QCD [3][4][5][6], while the probabilities that QQ pairs of different quantum properties form the observed quarkonium state are parametrized by momentum-independent long-distance matrix elements (LDMEs). Since they are expected to scale with powers of the heavy-quark velocity squared, v 2 , in the nonrelativistic limit (v 2 1) most LDMEs are negligible and S-wave vector quarkonia should be dominantly formed from QQ pairs produced as coloursinglet, 3 S [1] 1 , or as one of the 1 S [8] 0 , 3 S [8] 1 and 3 P [8] J colour-octet states. While the colour-singlet LDME can be calculated with potential models, the others, reflecting the complexity of the evolution of a coloured QCD system into a formed hadron, are determined through phenomenological analyses of quarkonium production data [3][4][5][6][7]. Polarization data play a central role in these E-mail address: cms-publication-committee-chair@cern.ch. analyses [7], which are performed in the zero-momentum frame of the quarkonium state (and, approximately, of the QQ pair) and can directly reveal the quantum properties of the QQ, relying in most cases only on basic angular-momentum analysis. For example, 1 S [8] 0 QQ states evolve into unpolarized 3 S 1 quarkonia, while 3 S [8] 1 states, with quantum numbers identical to those of a gluon, lead to transversely polarized 3 S 1 quarkonia.
The factorization hypothesis of nonrelativistic QCD implicitly assumes that the LDMEs are universal constants, independent of the short-distance process that created the QQ: the same LDMEs should be extracted from proton-(anti)proton and e + e − data, for example. However, cross section and polarization measurements at high transverse momentum, p T , are currently limited to pp collisions, so that the LDME universality hypothesis remains a nontrivial assumption requiring direct experimental investigation. Since the nonperturbative quarkonium formation process involves interactions with the QCD medium surrounding the QQ state, allowing it to neutralize its net colour through emission or absorption of soft gluons, it is important to verify if the polarizations (directly related to the LDMEs) depend on the complexity of the hadronic environment created by the collision. Probing if the polarizations are affected by an increase in the multiplicity of particles produced in pp collisions, the topic of the present analysis, is a first step in such a study, to be followed by analogous investigations using proton-nucleus and nucleus-nucleus data collected at different collision centralities. Such studies are crucial for a reliable interpretation of the quarkonium suppression patterns seen in high-energy nuclear collisions (see Ref. [8] and references therein) and of their relation to signatures of quark-gluon plasma formation [9][10][11]. While changes in integrated yields or in p T and rapidity, y, distributions can be caused by effects such as modified parton densities in the nucleus or parton energy loss, the observation of changes in quarkonium polarization would be a direct signal of a modification in the bound-state formation mechanism.
This Letter reports how the polarizations of the ϒ(1S), ϒ(2S), and ϒ(3S) mesons produced in pp collisions at a centre-of-mass energy of 7 TeV change as a function of charged particle multiplicity, N ch . It complements two observations made for pp and pPb collisions [12]: the ϒ(nS) cross sections, normalised by their N ch -integrated values, increase with N ch ; the ϒ(2S) and ϒ(3S) cross sections, normalised by the ϒ(1S) value, decrease with N ch .
The measurements are performed using a dimuon data sample collected in 2011 by the CMS experiment at the CERN LHC, corresponding to an integrated luminosity of 4.9 fb −1 , and follow the analysis method used in the N ch -integrated measurement [13].
The dimuon mass distribution is used to separate the ϒ(nS) signals from each other and from muon pairs due to other processes, such as decays of heavy flavour mesons. The ϒ(nS) polarizations are characterized through three parameters, λ = (λ ϑ , λ ϕ , λ ϑϕ ), reflecting the anisotropy of the angular distribution of the decay muons [14], where ϑ and ϕ are the polar and azimuthal angles, respectively, of the μ + . These λ parameters, as well as the frame-invariant pa- [15], are measured in the centreof-mass helicity frame (HX), where the z axis coincides with the direction of the ϒ momentum. The y axis of the polarization frame is reversed between positive and negative rapidity, a definition that avoids the cancellation of λ ϑϕ when integrating events over a symmetrical range in rapidity. This is explained in Ref.
[16], which provides a pedagogical introduction to quarkonium polarization physics. As in the previous CMS quarkonium polarization measurements [13,17], the analysis is exclusively based on measured data: the 3-momentum vectors of the two muons (containing the spin alignment information of the decaying ϒ(nS) mesons) and the muon detection efficiencies.

CMS detector and data analysis
The CMS apparatus is based on a superconducting solenoid of 6 m internal diameter, providing a 3.8 T field. Within the solenoid volume are a silicon pixel and strip tracker, a lead tungstate crystal electromagnetic calorimeter, and a brass and scintillator hadron calorimeter. Muons are measured with drift tubes, cathode strip chambers, and resistive-plate chambers. The main detectors used in this analysis are the silicon tracker and the muon system, which enable the measurement of muon momenta over the pseudorapidity range |η| < 2.4. A more detailed description of the CMS detector, together with a definition of the coordinate system used and the relevant kinematic variables, can be found in Ref. [18]. The events were collected using a two-level trigger system. The first level uses custom hardware processors to select events with two muons. The high-level trigger, adding information from the silicon tracker, selects opposite-sign muon pairs of invariant mass 8.5 < M < 11.5 GeV, |y| < 1.25 and p T > 5 or 7 GeV (depending on the instantaneous luminosity); the dimuon vertex fit χ 2 probability must exceed 0.5% and the two muons must have a distance of closest approach smaller than 5 mm. Although the trigger logic does not reject events on the basis of the p T of the single muons, at mid-rapidity the bending induced by the magnetic field prevents muons of p T smaller than ∼3 GeV from reaching the muon stations.
The offline analysis selects muon tracks with hits in more than ten tracker layers, at least two of which are in the pixel layers, and matched with segments in the muon system. They must have a good track fit quality, point to the interaction region, and match the muon objects that triggered the event. The selected muons are required to satisfy |η| < 1.6 and to have p T above 4.5, 3.5, and 3 GeV for |η| < 1.2, 1.2 < |η| < 1.4, and 1.4 < |η| < 1.6, respectively, to ensure reliable detection and trigger efficiencies. The combinatorial background from uncorrelated muons is suppressed by requiring a dimuon vertex fit χ 2 probability larger than 1% and by rejecting events where the distance between the dimuon vertex and the primary vertex is larger than twice its resolution. In events with multiple reconstructed primary vertices (pileup), the one nearest to the point of closest approach between the trajectory of the dimuon and the beam line is selected. The N ch variable is computed by counting "high purity" [19] charged tracks, excluding the two muons, of |η| < 2.4, p T > 500 MeV, and p T measured with better than 10% relative accuracy. Acceptance and reconstruction efficiencies are not corrected for. Each track is assigned a weight reflecting the likelihood that it belongs to the primary vertex [19]; tracks consistent with the vertex have a weight close to unity. The migration of events from one N ch bin to the next, caused by inadvertently counting spurious tracks produced in near-by pileup vertices, is kept negligible by rejecting events with more than 16 vertices. Fig. 1 shows the N ch distribution of the events selected in this analysis.
The dimuon mass distribution, shown in Fig

Extraction of the polarization parameters
The two-dimensional angular distribution, in cos ϑ and ϕ, of the background corresponding to a given ϒ(nS) state is evaluated as a weighted average of the distributions measured in the two mass sidebands, the weights reflecting (linearly) the dif-  bin is then defined as a product over the remaining (signal-like) events i, where E represents the event probability distribution as a function of the muon momenta p 1,2 in event i. This analysis method does not use model-dependent (cos ϑ, ϕ) acceptance maps; each event is attributed a probability reflecting the full event kinematics (not only cos ϑ and ϕ) and the values of the polarization parameters, where ( p 1 , p 2 ) is the measured detection efficiency. The normalization factor N ( λ) is calculated by integrating W · over cos ϑ and ϕ uniformly, using (p T , |y|, M) distributions determined from the background-subtracted data. To account for the statistical fluctuations related to its random nature, the background subtraction procedure is repeated 50 times. Fig. 3 compares the cos ϑ and ϕ distributions measured for ϒ(2S) signal events of 15 < p T < 35 GeV and 10 < N ch < 20 with curves representing the "best fit". For illustration, curves reflecting extreme polarization scenarios are also shown: fully transverse (λ ϑ = +1) and fully longitudinal (λ ϑ = −1) in the cos ϑ panel, and λ ϕ = ±0.5 in the ϕ panel (|λ ϕ | must be smaller than 0.5 if Each of the systematic uncertainties on the polarization parameters caused by the analysis framework and the detection efficiencies is individually evaluated through 50 statistically independent pseudo-experiments. For each effect, the systematic uncertainty is the difference between the injected and resulting parameters. The robustness of the framework to measure the signal polarization is validated for several signal and background polarization scenarios. The impact of residual biases that could be caused by uncertainties on the muon or dimuon efficiencies is evaluated by extracting the polarization parameters after applying corresponding variations to the input efficiencies. The background model uncertainty is evaluated by modifying the relative weights of the low-and high-mass sidebands when building the background distributions. A broad range of hypotheses is considered, including the assumption that the background under the ϒ(1S) (ϒ(3S)) peak resembles exclusively the low-mass (high-mass) sideband, or assuming that it is reproduced by an equal mixture of the two sideband distributions. Several systematic uncertainties have similar levels, except in the highest N ch bins and the lowest p T range, where the background model uncertainty dominates, especially for the ϒ(2S) and ϒ(3S) states. For the ϒ(1S) state and in the HX frame, the N ch -dependent systematic uncertainties are ∼0.1 for λ ϑ and ∼0.03-0.05 for λ ϕ and λ ϑϕ , slightly increasing with N ch . The corresponding ϒ(2S) and ϒ(3S) values are slightly larger: ∼0.2 for λ ϑ , ∼0.04 for λ ϕ , and ∼0.05-0.08 for λ ϑϕ . The statistical uncertainties are negligible for the ϒ(1S) state and become dominant for the ϒ(2S) and ϒ(3S) states, as N ch increases.

Results
The final PPD of the polarization parameters is an envelope of the PPDs corresponding to all hypotheses considered in the evaluation of the systematic uncertainties. In each analysis bin, the central values and 68.3% confidence level (CL) uncertainties of each polarization parameter are evaluated from the corresponding one-dimensional marginal posterior, calculated by numerical integration. In the HX frame, the λ parameters are measured with negligible correlations, as illustrated by Fig. 4, which shows the two-dimensional marginals of the PPD in the λ ϕ vs. λ ϑ and λ ϑϕ vs. λ ϕ planes, for a representative analysis bin. Fig. 5 shows the λ ϑ , λ ϕ , λ ϑϕ , and λ values measured in the HX frame for the three ϒ(nS) states, in both p T ranges. The corresponding numerical results are tabulated in the supplemental material. The λ values have also been measured in the Collins-Soper frame (CS) [22], whose z axis is the average of the two beam directions in the ϒ rest frame, and in the perpendicular helicity frame

Summary
The polarizations of the ϒ(1S), ϒ(2S), and ϒ(3S) mesons produced in pp collisions at √ s = 7 TeV have been determined as functions of the charged particle multiplicity of the event in two ϒ(nS) p T ranges. The measurements do not show significant variations as a function of N ch , even though the large ϒ(2S) and ϒ(3S) uncertainties preclude definite statements in these cases.
This study opens the way for analogous measurements extending to the charmonium family, particularly interesting for the ψ (2S), which is unaffected by feed-down decays and, therefore, provides a more direct probe of LDME universality. Equivalent analyses should also be performed in pPb and PbPb event samples, in view of evaluating how quark-antiquark bound-state formation is influenced by the surrounding medium, which is an essential input for the interpretation of quarkonium suppression patterns in nuclear collisions.

Acknowledgements
We congratulate our colleagues in the CERN accelerator departments for the excellent performance of the LHC and thank the technical and administrative staffs at CERN and at other CMS institutes for their contributions to the success of the CMS effort. In addition, we gratefully acknowledge the computing centres and personnel of the Worldwide LHC Computing Grid for delivering so effectively the computing infrastructure essential to our analyses.