New Observables in Quarkonium Production Quarkonium polarisation in (p-A and) nucleus-nucleus collisions from SPS to the LHC A long standing puzzle General remarks on the measurement method A rotation-invariant formalism to measure vector polarizations and parity asymmetries Quarkonium polarization Heavy Ion applications João Seixas (LIP & Physics Dep. IST Lisbon) in collaboration with Pietro Faccioli, Carlos Lourenço, Hermine Wöhri, Valentin Knünz, Ilse Kratschmer New Observables in Quarkonium Production ECT* Trento, 28 Fev-4 Mar 2016

A varied menu for the LHC (and AFTER) Measure polarization = determine average angular momentum composition of the particle, through its decay angular distribution It offers a much closer insight into the quality/topology of the contributing production processes wrt to decay-averaged production cross sections Polarization analyses are particularly important to (for example): understand still unexplained production mechanisms [J/ψ, χc , ψ’, , χb] characterize the spin of newly (eventually) discovered resonances [X(3872), Higgs, Z’, graviton, ...] Understand the properties of dense and hot matter

Task list One assumes that the production of quark-antiquark states can be described using perturbative QCD, as long as we “factor out” long-distance bound-state effects A seemingly inescapable prediction of NRQCD approach is that “high” pT quarkonia come from fragmenting gluons and are fully tranversely polarized However, despite good success in describing cross sections...

Task list One assumes that the production of quark-antiquark states can be described using perturbative QCD, as long as we “factor out” long-distance bound-state effects A seemingly inescapable prediction of NRQCD approach is that “high” pT quarkonia come from fragmenting gluons and are fully tranversely polarized the first comparisons with polarization data were not promising… HX frame J/ψ @1.96 TeV NRQCD factorization Braaten, Kniehl & Lee, PRD62, 094005 (2000) CDF Run II CDF Coll., PRL 99, 132001 (2007) But: Until recently the experimental situation was contradictory and incomplete, as it was emphasized in Eur. Phys. J. C69, 657 (2010)  improve drastically the quality of the experimental information maybe the theory is only valid at asymptotically high pT  extend measurements to pT >> M contributions of intermediate P-wave states have not been fully calculated yet and are still unknown experimentally (remember Ilse’s talk)  measure polarizations of directly produced states, ψ’ and (3S)  measure polarizations of P-wave states, χc and χb, and their feeddown to S states

Task list There are problems actually on the theory side which are becoming quite evident Remember that in NRQCD the factorization hypothesis implies that the cross-section for the inclusive production of a meson H in a A+B collision is 𝜎 𝐴+𝐵→𝐻+𝑋 = 𝑆,𝐿,𝐶 𝒮(𝐴+𝐵→𝑄 𝑄 2𝑆+1 𝐿 𝐽 𝐶 +𝑋)×ℒ( 𝑄 𝑄 2𝑆+1 𝐿 𝐽 𝐶 →𝐻) SDC LDME

Task list There are problems actually on the theory side which are becoming quite evident Remember that in NRQCD the factorization hypothesis implies that the cross-section for the inclusive production of a meson H in a A+B collision is 𝜎 𝐴+𝐵→𝐻+𝑋 = 𝑆,𝐿,𝐶 𝒮(𝐴+𝐵→𝑄 𝑄 2𝑆+1 𝐿 𝐽 𝐶 +𝑋)×ℒ( 𝑄 𝑄 2𝑆+1 𝐿 𝐽 𝐶 →𝐻) SDC LDME

Task list There are problems actually on the theory side which are becoming quite evident Remember that in NRQCD the factorization hypothesis implies that the cross-section for the inclusive production of a meson H in a A+B collision is 𝜎 𝐴+𝐵→𝐻+𝑋 = 𝑆,𝐿,𝐶 𝒮(𝐴+𝐵→𝑄 𝑄 2𝑆+1 𝐿 𝐽 𝐶 +𝑋)×ℒ( 𝑄 𝑄 2𝑆+1 𝐿 𝐽 𝐶 →𝐻) SDC LDME 𝜆 𝜃 = 𝒮 𝑇 + 𝒮 𝐿 𝒮 𝑇 − 𝒮 𝐿

Task list There are problems actually on the theory side which are becoming quite evident Remember that in NRQCD the factorization hypothesis implies that the cross-section for the inclusive production of a meson H in a A+B collision is 𝜎 𝐴+𝐵→𝐻+𝑋 = 𝑆,𝐿,𝐶 𝒮(𝐴+𝐵→𝑄 𝑄 2𝑆+1 𝐿 𝐽 𝐶 +𝑋)×ℒ( 𝑄 𝑄 2𝑆+1 𝐿 𝐽 𝐶 →𝐻) SDC LDME IT IS possible to define kinematic discriminants to distinguish 3 𝑃 𝐽 [8] on a statistical basis from the other terms. One could then identify regions of phase space where the quarkonia would have negative cross sections and decay distributions violating angular momentum conservation!

Definition of observables In Quantum Mechanics the study of angular momentum requires a quantization axis (aka “z-axis”) Many possible (known) choices: Gottfried-Jackson (GJ) Collins-Soper (CS) Helicity (HX) Perpendicular Helicity (PX)

CS  HX for mid rap. / high pT Frames and parameters z Collins-Soper axis (CS): ≈ dir. of colliding partons Helicity axis (HX): dir. of quarkonium momentum quarkonium rest frame θ ℓ + production plane x φ y λθ = +1 λφ = λθφ = 0 Jz = ± 1 λθ = +1 : “transverse” (= photon-like) pol. λθ = –1 λφ = λθφ = 0 Jz = 0 λθ = 1 : “longitudinal” pol. In general 8 parameters, for parity conserving and symmetric detectors, 3 z z′ CS  HX for mid rap. / high pT CS HX 90º x x′ y y′

The azimuthal anisotropy is not a detail Case 2: natural longitudinal polarization, observation frame  to the natural one Case 1: natural transverse polarization z z Jx = 0 x Jz = ± 1 x λθ = +1 λφ = 0 λθ = +1 λφ =  1 y y Two very different physical cases Indistinguishable if λφ is not measured (integration over φ)

Frame-independent polarization The shape of the distribution is obviously frame-invariant. → it can be characterized by a frame-independent parameter, e.g. Note: 𝝀 =𝟏 means Lam-Tung relation z λθ = –1 λφ = 0 λθ = +1 λφ = 0 λθ = –1/3 λφ = –1/3 λθ = +1/5 λφ = +1/5 λθ = +1 λφ = –1 λθ = –1/3 λφ = +1/3 P. Faccioli, C. Lourenço, J.S., PRL 105, 061601; PRD 82, 096002; PRD 83, 056008

Positivity constraints for dilepton distributions P. Faccioli, C.Lourenço, J.S., PRL 105, 061601 (2010); PRD 83, 056008 (2011) General and frame-independent constraints on the anisotropy parameters of vector particle decays λφ Jy V = 0 Jx V = ±V ~ λ = +1 Jz V = 0 Jz V = ±V ~ λ = –1 Jy V = ±V Jx V = 0 λθ λθφ λθφ physical domain λθ λφ

Positivity constraints for dilepton distributions P. Faccioli, C.Lourenço, J.S., PRL 105, 061601 (2010); PRD 83, 056008 (2011) General and frame-independent constraints on the anisotropy parameters of vector particle decays F = 𝟏+ 𝝀 𝟑+ 𝝀 physical domain

What polarization axis? 1) helicity conservation (at the production vertex) → J =1 states produced in fermion-antifermion annihilations (q-q or e+e–) at Born level have transverse polarization along the relative direction of the colliding fermions (Collins-Soper axis) 1 . 5 Drell-Yan Drell-Yan is a paradigmatic case but not the only one 1 . (2S+3S) Remember: DY for Y is a background to deal with λθ . 5 z(HX) . E866 (p-Cu) Collins-Soper frame high pT 90° - . 5 z(CS) 1 2 pT [GeV/c] c 2) g ( ) NRQCD → at very large pT , quarkonium produced from the fragmentation of an on-shell gluon, inheriting its natural spin alignment c g J/ψ NRQCD g g λθ CDF → large, transverse polarization along the QQ (=gluon) momentum (helicity axis) pT [GeV/c]

Some remarks on methodology Measurements are challenging A typical collider experiment imposes pT cuts on the single muons; this creates zero-acceptance domains in decay distributions from “low” masses: helicity Collins-Soper φHX φCS Toy MC with pT(μ) > 3 GeV/c (both muons) Reconstructed unpolarized (1S) pT() > 10 GeV/c, |y()| < 1 cosθHX cosθCS This spurious “polarization” must be accurately taken into account. Large holes strongly reduce the precision in the extracted parameters

Quarkonium polarization: a “puzzle” 17 Quarkonium polarization: a “puzzle” J/𝜓: Measurements at Tevatron , LHC (ALICE) _ J/ψ, pp √s = 1.96 TeV CDF Run I CDF Run II Only 𝜆 𝜃 measured Only one frame used (HX) |y| < 0.4 CDF II vs CDF I → not known what caused the change |y| < 0.6 Helicity frame PRL 85, 2886 (2000) PRL 99, 132001 (2007) J/ψ, pp √s = 7 TeV 𝜆 𝜃 and 𝜆 𝜙 separately measured Two frames used (HX & CS) |cos 𝜃| & |ϕ| dist. fit imposing 𝜆 to be invariant in the two frames ALICE 2.5 < y < 4, 2 < pT < 8 GeV/c PRL 108, 082001 (2012)

Quarkonium polarization: a “puzzle” 18 Quarkonium polarization: a “puzzle” J/𝜓: HERA-B J/ψ, p-Cu and p-W √s = 41.6 GeV 𝜆 𝜃 , 𝜆 𝜙 and 𝜆 𝜃𝜙 measured by single variable projections Three frames used (HX, GJ & CS) −1.5 < y < 0.8 −0.34 < 𝑥 𝐹 < 0.14 0 < pT < 5.4 GeV/c EPJ C60 517 (2009)

Quarkonium polarization: a “puzzle” 19 Quarkonium polarization: a “puzzle” J/𝜓: Other fixed target experiments 𝜆 𝜃 J/ψ, 252 GeV 𝝅 on W Chicago-Iowa-Princeton Coll (E615). 𝜆 𝜃 , 𝜆 𝜙 and 𝜆 𝜃𝜙 measured Three frame used (GJ, CS, UC) Violates Lam-Tung relation 𝜆 𝜃 𝜆 𝜙 PRL 58, 2523 (1987) 2𝜆 𝜃𝜙 PRD 39, (1989)

Quarkonium polarization: a “puzzle” 𝜰(nS): Measurements at Tevatron (2002-2012) 20 CDF+D (2002) Only 𝜆 𝜃 measured Only one frame used (HX) _ (1S), pp √s = 1.96 TeV CDF (2012) 𝜆 𝜃 , 𝜆 𝜙 and 𝜆 𝜃𝜙 measured 𝜆 checked Two frames used (HX & CS)

Quarkonium polarization: a “puzzle” 21 Quarkonium polarization: a “puzzle” 𝜰(nS): Measurements at LHC (CMS) (nS), pp √s = 7 TeV 𝜆 𝜃 , 𝜆 𝜙 and 𝜆 𝜃𝜙 measured Three frames used (HX, CS, PX) 𝜆 checked Fully multidimensional |y| < 0.6 0.6<|y| < 1.2 10 < 𝑝 𝑇 < 40 GeV/c 252 000 Y(1S), 94 000 Y(2S), and 58 000 Y(3S) Phys. Rev. Lett. 110, 081802 Comparison with CDF results

Quarkonium polarization: a “puzzle” 22 Quarkonium polarization: a “puzzle” 𝜰(nS): Measurements at LHC (CMS) (nS), pp √s = 7 TeV 𝜆 𝜃 , 𝜆 𝜙 and 𝜆 𝜃𝜙 measured Three frames used (HX, CS, PX) 𝜆 checked Fully multidimensional |y| < 0.6 0.6<|y| < 1.2 10 < 𝑝 𝑇 < 40 GeV/c 252 000 Y(1S), 94 000 Y(2S), and 58 000 Y(3S) Phys. Rev. Lett. 110, 081802 Comparison with CDF results

Quarkonium polarization: a “puzzle” 23 Quarkonium polarization: a “puzzle” 𝜰(nS): Measurements at LHC (CMS) (nS), pp √s = 7 TeV 𝜆 𝜃 , 𝜆 𝜙 and 𝜆 𝜃𝜙 measured Three frames used (HX, CS, PX) 𝜆 checked Fully multidimensional Phys. Rev. Lett. 110, 081802

Quarkonium polarization: a “puzzle” 24 Quarkonium polarization: a “puzzle” 𝜰(nS): Mesurements at LHC (CMS) (nS), pp √s = 7 TeV 𝜆 𝜃 , 𝜆 𝜙 and 𝜆 𝜃𝜙 measured Three frames used (HX, CS, PX) 𝜆 checked Fully multidimensional Phys. Rev. Lett. 110, 081802

A lot of measurements to do... Measurement of c0(1P), c1(1P) and c2(1P) production cross sections Measurement of b (1P), b(2P) and b(3P) production cross sections; Measurement of the relative production yields of J = 1 and J = 2 b states Measurement of the c1 (1P) and c2(1P) polarizations versus pT and rapidity Measurement of the b (1P) and b (2P) polarizations …

…and a series of questions to answer Is there a simple composition of processes, probably dominated by one single mechanism, that is responsible for the production of all quarkonia? Solid curve is a fit to the J/𝜓 CMS data (pT/M>3) Remaining curves are replicas with normalizations adjusted to the individual datasets P. Faccioli et al, PLB 736(2014) 98 𝑓 𝑝 𝑇 𝑀 = 1+ 1 𝛽−2 . 𝑝 𝑇 𝑀 2 𝛾 −𝛽 𝛽=3.62±0.07 𝛾=1.29±0.32

…and a series of questions to answer Is there a simple composition of processes, probably dominated by one single mechanism, that is responsible for the production of all quarkonia? P. Faccioli et al, PLB 736(2014) 98

…and a series of questions to answer Is this mechanism perturbed in the presence of matter at high density and high temperature?

Pioneering measurements at SPS: NA60 𝜆 𝜃 and 𝜆 𝜑 measured (p-A); HX and CS frames used. http://arxiv.org/abs/0907.5004 http://arxiv.org/abs/0907.3682

A first step in this program at LHC: polarization as a function of multiplicity CMS p-p

A first step in this program: polarization as a function of multiplicity CMS p-p

Summary The new quarkonium polarization measurements have many improvements with respect to previous analyses and shed, when combined with cross-section data, a new light on quarkonium production Will we (finally) manage to solve an old puzzle? General advice: do not throw away physical information! (azimuthal-angle distribution, rapidity dependence, ...) A new method based on rotation-invariant observables gives several advantages in the measurement of decay distributions and in the use of polarization information Quarkonium polarization could be used to probe hot and dense matter. A complete program is under way.

Backup slides

34 A first step in this program: polarization as a function of multiplicity

Quarkonium polarization: a “puzzle” 36 Quarkonium polarization: a “puzzle” (nS): Measurements at LHC (CMS) (nS), pp √s = 7 TeV 𝜆 𝜃 , 𝜆 𝜙 and 𝜆 𝜃𝜙 measured Three frames used (HX, CS, PX) 𝜆 checked Fully multidimensional 252 000 Y(1S), 94 000 Y(2S), and 58 000 Y(3S) Phys. Lett. B 727 (2013) 381

Quarkonium polarization: a “puzzle” 37 Quarkonium polarization: a “puzzle” (nS): Measurements at LHC (CMS) (nS), pp √s = 7 TeV 𝜆 𝜃 , 𝜆 𝜙 and 𝜆 𝜃𝜙 measured Three frames used (HX, CS, PX) 𝜆 checked Fully multidimensional

Quarkonium polarization: a “puzzle” 38 Quarkonium polarization: a “puzzle” (nS): Mesurements at LHC (CMS) (nS), pp √s = 7 TeV 𝜆 𝜃 , 𝜆 𝜙 and 𝜆 𝜃𝜙 measured Three frames used (HX, CS, PX) 𝜆 checked Fully multidimensional

J/ψ polarization as a signal of colour deconfinement? λθ NRQCD pT [GeV/c] ≈ 0.7 ≈ 0.7 λθ HX frame CS frame Starting “pp” scenario: J/ψ significantly polarized (high pT) feeddown from χc states (≈ 30%) smears the polarizations Si Sequential suppression ≈ 30% from χc decays ≈ 70% direct J/ψ + ψ’ decays J/ψ cocktail: Recombination ? e As the χc (and ψ’) mesons get dissolved by the QGP, λθ should change to its direct value

J/ψ polarization as a signal of sequential suppression? P. Faccioli, JS, PRD 85, 074005 (2012) B.L. Ioffe and D.E. Kharzeev PRC 68 (2003) 061902. CMS data: up to 80% of J/ψ’s disappear from pp to Pb-Pb more than 50% ( fraction of J/ψ’s from ψ’ and χc) disappear from peripheral to central collisions ~ > CMS PAS HIN-10-006 sequential suppression gedankenscenario: in central events ψ’ and χc are fully suppressed and all J/ψ’s are direct It may be impossible to test this directly: measuring the χc yield (reconstructing χc radiative decays) in PbPb collisions is prohibitively difficult due to the huge number of photons However, a change of prompt-J/ψ polarization must occur from pp to central Pb-Pb! prompt J/ψ polarization in pp χc-to-J/ψ fractions in pp χc polarizations in pp prompt J/ψ polarization in PbPb Reasonable sequence of measurements: χc suppression in PbPb!

J/ψ polarization as a signal of sequential suppression? Example scenario: CDF prompt J/ψ Extrapolated* direct J/ψ CSM direct J/ψ prompt-J/ψ polarization in pp: λθ  – 0.15 direct-J/ψ polarization: λθ  – 0.6 helicity frame (assumed to be the same in pp and PbPb) * R(χc1)+R(χc2) = 42 % R(χc2)/R(χc1) = 38 % h(χc1) = 0 h(χc2) = ±2 Use a model as shown before and use the expression to calculate the prompt lambdas from the direct and feeddown lambdas

J/ψ polarization as a signal of sequential suppression? If we measure a change in prompt polarization like this... λθ “prompt” “direct” ... we are observing the disappearance of the χc relative to the J/ψ R(χc) in PbPb R(χc) in pp the polarization should become significantly more longitudinal (in the helicity frame) after the disappearance of the transversely polarized feed-down contribution due to c decays. We are assuming that the ‘‘base’’ polarizations of the directly produced S and P states remain essentially unaffected by the nuclear medium and are, therefore, not distinguishable Simplifying assumptions: direct-J/ψ polarization is the same in pp and PbPb normal nuclear effects affect J/ψ and χc in similar ways χc1 and χc2 are equally suppressed in PbPb

J/ψ polarization as a signal of sequential suppression? When will we be sensitive to an effect like this? pT(μ) > 3 GeV/c, 6.5 < pT < 30 GeV/c, 0 < |y| < 2.4 CMS-like toy MC with prompt-J/ψ polarization as observed in pp (and peripheral PbPb) prompt-J/ψ polarization as observed in central PbPb efficiency-corrected |cosθHX| distribution precise results in pp very soon ~20k evts ~20k evts In this scenario, the χc disappearance is measurable at ~5σ level with ~20k J/ψ’s in central Pb-Pb collisions

J/ψ polarization as a signal of sequential suppression? When will we be sensitive to an effect like this? CMS-like toy MC

J=1 states are intrinsically polarized Single elementary subprocess: There is no combination of a0, a+1 and a-1 such that λθ = λφ = λθφ = 0 The angular distribution is never intrinsically isotropic Only a “fortunate” mixture of subprocesses (or randomization effects) can lead to a cancellation of all three observed anisotropy parameters To measure zero polarization would be (in fact, is) an exceptionally interesting result...

Basic meaning of the frame-invariant quantities Let us suppose that, in the collected events, n different elementary subprocesses yield angular momentum states of the kind (wrt a given quantization axis), each one with probability . The rotational properties of J=1 angular momentum states imply that The quantity is therefore frame-independent. It can be shown to be equal to In other words, there always exists a calculable frame-invariant relation of the form the combinations are independent of the choice of the quantization axis note: F = 𝟏+ 𝝀 𝟑+ 𝝀

Simple derivation of the Lam-Tung relation Another consequence of rotational properties of angular momentum eigenstates: for each state there exists a quantization axis wrt which → dileptons produced in each single elementary subprocess have a distribution of the type wrt its specific “ ” axis. DY: q q * q * * * q* q* q* _ q q _ Due to helicity conservation at the q-q-* (q-q*-*) vertex, along the q-q (q-q*) scattering direction _ If all a’s are real then z* belongs to the xz plane → for each diagram sum independent of spin alignment directions! → Lam-Tung identity

Essence of the LT relation The existence (and frame-independence) of the LT relation is the kinematic consequence of the rotational properties of J = 1 angular momentum eigenstates Its form derives from the dynamical input that all contributing processes produce a transversely polarized (Jz = ±1) state (wrt whatever axis) More generally: Corrections to the Lam-Tung relation (parton-kT, higher-twist effects) should continue to yield invariant relations. In the literature, deviations are often searched in the form But this is not a frame-independent relation. Rather, corrections should be searched in the invariant form For any superposition of processes, concerning any J = 1 particle (even in parity-violating cases: W, Z ), we can always calculate a frame-invariant relation analogous to the LT relation. The Lam-Tung relation corresponds to the special case when all processes produce transversely polarized dileptons with respect to quantization axes belonging to the production plane