Holographic models that consider classical vector fields in a 5-d background provide effective descriptions for heavy vector meson spectra. This is true both in vacuum and a thermal medium, such as quark gluon plasma. However, the manner in which these phenomenological models work is unclear. In particular, what is the role of the fifth dimension, and what is the relation between the holographic 5-d background and physical (4-d) heavy mesons? Hadrons, in contrast to leptons, are composite particles with some internal structure that depends on the energy at which they are observed. In this study, a static meson is represented by a heavy quark-antiquark pair with an interaction described by a Nambu Goto string existing in the same 5-d background that provides field solutions leading to masses and decay constants of charmonium states. The resulting interaction potential is linear for large distances, with a string tension consistent with the effective Cornell potential. Introducing temperature $\textit{T}$ in the background, it is found for the $J/\psi$ case that there is a deconfining transition at some critical value of $\textit{T}$. The obtained results indicate that the 5-d background effectively represents the internal structure of the (static) charmonium (quasi) states.

Brazil

Nelson R.F. Braga

Yan F. Ferreira

William S. Cunha

Holography and the internal structure of charmonium * The authors are partially supported by CNPq — Conselho Nacional de Desenvolvimento Científico e Tecnologico, by FAPERJ — Fundação Carlos Chagas Filho de Amparo à Pesquisa do Estado do Rio de Janeiro and by Coordenação de Aperfeiçoamento de Pessoal de Nível Superior — Brasil (CAPES), Finance Code 001

Several fixed-target experiments reported J/ψ and ϒ polarizations, as functions of Feynman x (<math><msub><mrow><mi>x</mi></mrow><mrow><mi>F</mi></mrow></msub></math>) and transverse momentum (<math><msub><mrow><mi>p</mi></mrow><mrow><mi>T</mi></mrow></msub></math>), in three different frames, using different combinations of beam particles, target nuclei, and collision energies. Despite the diverse and heterogeneous picture formed by these measurements, a detailed look allows us to discern qualitative physical patterns that inspire a simple empirical model. This data-driven scenario offers a good quantitative description of the J/ψ and ϒ(1S) polarizations measured in proton- and pion-nucleus collisions, in the <math><msub><mrow><mi>x</mi></mrow><mrow><mi>F</mi></mrow></msub><mo>≲</mo><mn>0.5</mn></math> domain: more than 80 data points (not statistically independent) are well reproduced with only one free parameter. This study sets the context for future low-<math><msub><mrow><mi>p</mi></mrow><mrow><mi>T</mi></mrow></msub></math> quarkonium polarization measurements in proton- and pion-nucleus collisions, such as those to be made by the AMBER experiment, and shows that such measurements provide significant constraints on the poorly-known parton distribution functions of the pion.

Portugal

Pietro Faccioli

Austria

Ilse Krätschmer

CERN

Carlos Lourenço

Low- quarkonium polarization measurements: Challenges and opportunities

Of the J/ψ mesons (inclusively) produced in pp collisions, a big fraction results from B decays, increasing with transverse momentum and exceeding 50% for p T &gt; 20 GeV. These events must be subtracted in measurements of the polarization of prompt J/ψ mesons. While several studies have addressed the ψ(2S) and χ  c  impact on the determination of the polarization of the directly-produced J/ψ mesons, the theoretical and experimental knowledge of the non-prompt polarization is very poor. Furthermore, non-prompt J/ψ polarization measurements can provide interesting information on quarkonium hadroproduction, complementing the studies of prompt production. We review the method of measuring the polarization of non-prompt J/ψ mesons (produced in decays of unreconstructed B mesons and detected in the dilepton channel), in conditions typical of LHC experiments studying J/ψ production. Realistic model-independent scenarios are validated with data from experiments studying e + e  −  → Υ(4S) interactions, converted to the high-momentum regime using B differential cross sections measured at the LHC. The non-prompt J/ψ polarization measurements are seen to remain dependent on the event selection criteria, even after correcting for the dilepton acceptance and efficiencies. This implies that reproducible definitions of all relevant analysis choices must be reported with the polarization result, for rigorous comparisons with other measurements and/or theoretical calculations. We also discuss how the non-prompt J/ψ polarization significantly depends on the relative importance of two complementary B → J/ψ decay topologies, two-body (reasonably dominated by singlet production) and multi-body (including octet contributions), providing, hence, valuable information for studies of the charmonium formation mechanisms.

On the polarization of the non-prompt contribution to inclusive J/ψ production in pp collisions

While the prompt $$\mathrm{J}/\psi $$ <math><mrow><mi>J</mi><mo>/</mo><mi>ψ</mi></mrow></math>  cross section and polarization have been measured with good precision as a function of transverse momentum, $$p_\mathrm{T}$$ <math><msub><mi>p</mi><mi>T</mi></msub></math> , those of the directly produced $$\mathrm{J}/\psi $$ <math><mrow><mi>J</mi><mo>/</mo><mi>ψ</mi></mrow></math>  are practically unknown, given that the cross sections and polarizations of the $$\chi _{{c}1} $$ <math><msub><mi>χ</mi><mrow><mi>c</mi><mn>1</mn></mrow></msub></math>  and $$\chi _{{c}2} $$ <math><msub><mi>χ</mi><mrow><mi>c</mi><mn>2</mn></mrow></msub></math>  mesons, large indirect contributors to $$\mathrm{J}/\psi $$ <math><mrow><mi>J</mi><mo>/</mo><mi>ψ</mi></mrow></math>  production, are only known with rather poor accuracy. The lack of precise measurements of the $$\chi _{{c}J} $$ <math><msub><mi>χ</mi><mrow><mi>cJ</mi></mrow></msub></math>  polarizations induces large uncertainties in the level of their feed-down contributions to the prompt $$\mathrm{J}/\psi $$ <math><mrow><mi>J</mi><mo>/</mo><mi>ψ</mi></mrow></math>  yield, because of the polarization-dependent acceptance corrections. The experimental panorama of charmonium production can be significantly improved through a consistent and model-independent global analysis of existing measurements of $$\mathrm{J}/\psi $$ <math><mrow><mi>J</mi><mo>/</mo><mi>ψ</mi></mrow></math> , $$\psi \mathrm{(2S)}$$ <math><mrow><mi>ψ</mi><mrow><mo>(</mo><mn>2</mn><mi>S</mi><mo>)</mo></mrow></mrow></math>  and $$\chi _{c}$$ <math><msub><mi>χ</mi><mi>c</mi></msub></math>  cross sections and polarizations, faithfully respecting all the correlations and uncertainties. In particular, it is seen that the $$\chi _{{c}J} $$ <math><msub><mi>χ</mi><mrow><mi>cJ</mi></mrow></msub></math>  polarizations and feed-down fractions to $$\mathrm{J}/\psi $$ <math><mrow><mi>J</mi><mo>/</mo><mi>ψ</mi></mrow></math>  production have a negligible dependence on the $$\mathrm{J}/\psi $$ <math><mrow><mi>J</mi><mo>/</mo><mi>ψ</mi></mrow></math>  $$p_\mathrm{T}$$ <math><msub><mi>p</mi><mi>T</mi></msub></math> , with average values $$\lambda _\vartheta ^{\chi _{{c}1}} = 0.55 \pm 0.23$$ <math><mrow><msubsup><mi>λ</mi><mi>ϑ</mi><msub><mi>χ</mi><mrow><mi>c</mi><mn>1</mn></mrow></msub></msubsup><mo>=</mo><mn>0.55</mn><mo>±</mo><mn>0.23</mn></mrow></math> , $$\lambda _\vartheta ^{\chi _{{c}2}} = -0.39 \pm 0.22$$ <math><mrow><msubsup><mi>λ</mi><mi>ϑ</mi><msub><mi>χ</mi><mrow><mi>c</mi><mn>2</mn></mrow></msub></msubsup><mo>=</mo><mo>-</mo><mn>0.39</mn><mo>±</mo><mn>0.22</mn></mrow></math> , $$R^{\chi _{{c}1}} = (18.8 \pm 1.4)\%$$ <math><mrow><msup><mi>R</mi><msub><mi>χ</mi><mrow><mi>c</mi><mn>1</mn></mrow></msub></msup><mo>=</mo><mrow><mo>(</mo><mn>18.8</mn><mo>±</mo><mn>1.4</mn><mo>)</mo></mrow><mo>%</mo></mrow></math>  and $$R^{\chi _{{c}2}} = (6.5 \pm 0.5)\%$$ <math><mrow><msup><mi>R</mi><msub><mi>χ</mi><mrow><mi>c</mi><mn>2</mn></mrow></msub></msup><mo>=</mo><mrow><mo>(</mo><mn>6.5</mn><mo>±</mo><mn>0.5</mn><mo>)</mo></mrow><mo>%</mo></mrow></math> . The analysis also shows that $$(67.2 \pm 1.9)$$ <math><mrow><mo>(</mo><mn>67.2</mn><mo>±</mo><mn>1.9</mn><mo>)</mo></mrow></math> % of the prompt $$\mathrm{J}/\psi $$ <math><mrow><mi>J</mi><mo>/</mo><mi>ψ</mi></mrow></math>  yield is due to directly-produced mesons, of polarization constrained to remarkably small values, $$\lambda _\vartheta ^{\mathrm{J}/\psi } = 0.04 \pm 0.06$$ <math><mrow><msubsup><mi>λ</mi><mi>ϑ</mi><mrow><mi>J</mi><mo>/</mo><mi>ψ</mi></mrow></msubsup><mo>=</mo><mn>0.04</mn><mo>±</mo><mn>0.06</mn></mrow></math> .

Germany

Thomas Madlener

From prompt to direct $$\mathrm{J}/\psi $$ <math><mrow><mi>J</mi><mo>/</mo><mi>ψ</mi></mrow></math>  production: new insights on the $$\chi _{{c}1} $$ <math><msub><mi>χ</mi><mrow><mi>c</mi><mn>1</mn></mrow></msub></math>  and $$\chi _{{c}2} $$ <math><msub><mi>χ</mi><mrow><mi>c</mi><mn>2</mn></mrow></msub></math>  polarizations and feed-down contributions from a global-fit analysis of mid-rapidity LHC data

The observation of unpolarized quarkonium production in high energy pp collisions, at mid rapidity, implies a significant violation of the non-relativistic QCD (NRQCD) velocity scaling rules. A precise experimental confirmation of this picture could definitely rule out the current formulation of the factorization expansion. This conclusion relies on current perturbative determinations of the short-distance kinematic factors and may be reverted if improved calculations would modify, in a very specific way, their transverse momentum dependences. That solution would result, however, in a full degeneracy in the presently assumed basis of $$^{2S+1}L_J$$ <math><mrow><msup><mrow></mrow><mrow><mn>2</mn><mi>S</mi><mo>+</mo><mn>1</mn></mrow></msup><msub><mi>L</mi><mi>J</mi></msub></mrow></math>  Fock states. Therefore, whatever the outcome, improved polarization measurements will challenge and improve our fundamental understanding of quarkonium production.

NRQCD colour-octet expansion vs. LHC quarkonium production: signs of a hierarchy puzzle?

Measurements made at the LHC have shown that the production of the $$\mathrm{J}/\psi $$ <math><mrow><mi>J</mi><mo>/</mo><mi>ψ</mi></mrow></math> , $$\psi \mathrm{(2S)}$$ <math><mrow><mi>ψ</mi><mrow><mo>(</mo><mn>2</mn><mi>S</mi><mo>)</mo></mrow></mrow></math> , $$\varUpsilon \mathrm{(1S)}$$ <math><mrow><mi>Υ</mi><mrow><mo>(</mo><mn>1</mn><mi>S</mi><mo>)</mo></mrow></mrow></math>  and $$\varUpsilon \mathrm{(2S)}$$ <math><mrow><mi>Υ</mi><mrow><mo>(</mo><mn>2</mn><mi>S</mi><mo>)</mo></mrow></mrow></math>  quarkonia is suppressed in Pb–Pb collisions, with respect to the extrapolation of the pp production yields. The $$\psi \mathrm{(2S)}$$ <math><mrow><mi>ψ</mi><mrow><mo>(</mo><mn>2</mn><mi>S</mi><mo>)</mo></mrow></mrow></math>  and $$\varUpsilon \mathrm{(2S)}$$ <math><mrow><mi>Υ</mi><mrow><mo>(</mo><mn>2</mn><mi>S</mi><mo>)</mo></mrow></mrow></math>  states are more strongly suppressed than the ground states and the level of the suppression changes with the centrality of the collision. We show that the measured patterns can be reproduced by a simple model, where all quarkonia are treated in a unified way, starting from the recent realisation that, in pp collisions, the probability of quarkonium formation has a universal dependence on the binding-energy of the bound state. The hot-medium suppression effect is parametrized by a penalty factor in the binding energy, identical for all (S- and P-wave) charmonium and bottomonium states, including those that indirectly contribute to the measured results through feed-down decays. This single parameter, computed through a global fit of all available suppression patterns, fully determines the hierarchy of nuclear effects, for all states and centrality bins. The resulting faithful description of the data provides convincing evidence in favour of the conjecture of sequential quarkonium suppression induced by QGP formation.

The fate of quarkonia in heavy-ion collisions at LHC energies: a unified description of the sequential suppression patterns

A global analysis of ATLAS and CMS measurements reveals that, at mid-rapidity, the directly-produced χc1 , χc2 and J/ ψ mesons have differential cross sections of seemingly identical shapes, when presented as a function of the mass-rescaled transverse momentum, pT/M . This identity of kinematic behaviours among S- and P-wave quarkonia is certainly not a natural expectation of non-relativistic QCD (NRQCD), where each quarkonium state is supposed to reflect a specific family of elementary production processes, of significantly different pT -differential cross sections. Remarkably, accurate kinematic cancellations among the various NRQCD terms (colour singlets and octets) of its factorization expansion can lead to a surprisingly good description of the data. This peculiar tuning of the NRQCD mixtures leads to a clear prediction regarding the χc1 and χc2 polarizations, the only observables not yet measured: they should be almost maximally different from one another, and from the J/ ψ polarization, a striking exception in the global panorama of quarkonium production. Measurements of the difference between the χc1 , χc2 and J/ ψ polarizations, complementing the observed identity of momentum dependences, represent a decisive probe of NRQCD.

Mariana Araújo

João Seixas

Valentin Knünz

From identical S- and P-wave pT spectra to maximally distinct polarizations: probing NRQCD with χ states

Dimensional analysis reveals general kinematic scaling rules for the momentum, mass, and energy dependence of Drell–Yan and quarkonium cross sections. Their application to mid-rapidity LHC data provides strong experimental evidence supporting the validity of the factorization ansatz, a cornerstone of non-relativistic QCD, still lacking theoretical demonstration. Moreover, data-driven patterns emerge for the factorizable long-distance bound-state formation effects, including a remarkable correlation between the S-wave quarkonium cross sections and their binding energies. Assuming that this scaling can be extended to the P-wave case, we obtain precise predictions for the not yet measured feed-down fractions, thereby providing a complete picture of the charmonium and bottomonium feed-down structure. This is crucial information for quantitative interpretations of quarkonium production data, including studies of the suppression patterns measured in nucleus-nucleus collisions.

Universal kinematic scaling as a probe of factorized long-distance effects in high-energy quarkonium production

The LHC quarkonium production data reveal a startling observation: the J/ψ , ψ(2S) , χc1 , χc2 and ϒ(nS) pT -differential cross sections in the central rapidity region are compatible with one universal momentum scaling pattern. Considering also the absence of strong polarizations of directly and indirectly produced S-wave mesons, we conclude that there is currently no evidence of a dependence of the partonic production mechanisms on the quantum numbers and mass of the final state. The experimental observations supporting this universal production scenario are remarkably significant, as shown by a new analysis approach, unbiased by specific theoretical calculations of partonic cross sections, which are only considered a posteriori, in comparisons with the data-driven results.

Quarkonium production at the LHC: A data-driven analysis of remarkably simple experimental patterns

Polarization measurements are usually considered as the most difficult challenge for the QCD description of quarkonium production. In fact, global data fits for the determination of the non-perturbative parameters of bound-state formation traditionally exclude polarization observables and use them as a posteriori verifications of the predictions, with perplexing results. With a change of perspective, we move polarization data to the centre of the study, advocating that they actually provide the strongest fundamental indications about the production mechanisms, even before we explicitly consider perturbative calculations.