Probing the X(4350) in \(\gamma \gamma \) interactions at the LHC
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Abstract
The production of X(4350) in the \(\gamma \gamma \) interactions that occur in proton–proton, proton–nucleus and nucleus–nucleus collisions at the CERN Large Hadron Collider (LHC) is investigated and predictions for the kinematical ranges probed by the ALICE and LHCb Collaborations are presented. We focus on the \(\gamma \gamma \rightarrow \phi J/\Psi \) process, which have been measured by the Belle Collaboration, and present parameter free predictions for the total cross sections at the LHC energies. Our results demonstrate that the experimental study of this process is, in principle, feasible and can be used to confirm or not the existence of the X(4350) state. Finally, for completeness, we present predictions for the production of the X(3915) state in the \(\gamma \gamma \rightarrow \omega J/\Psi \) process and show that this exotic state can also be probed in \(\gamma \gamma \) interactions at the LHC.
Total cross sections for \(X(4350)[J^P] \rightarrow \phi J/\psi \) production for different center-of-mass energies considering the full LHC rapidity range as well as the rapidity ranges covered by the ALICE and LHCb detectors
Collision | Resonance | LHC | LHCb | ALICE |
---|---|---|---|---|
Full rapidity range | \(2< Y < 4.5\) | \(-1< Y < 1\) | ||
pp (\(\sqrt{s} = \)13 TeV) | X(4350), \(0^{++}\) | (11.88 – 29.50) fb | (2.47 – 6.13) fb | (2.67 – 6.64) fb |
X(4350), \(2^{++}\) | (12.13 – 33.09) fb | (2.52 – 6.88) fb | (2.73 – 7.45) fb | |
pPb (\(\sqrt{s} = \)8.1 TeV) | X(4350), \(0^{++}\) | (36.98 – 91.84) pb | (10.20 – 25.30) pb | (10.10 – 25.00) pb |
X(4350), \(2^{++}\) | (37.76 – 102.99) pb | (10.30 – 28.30) pb | (10.30 – 28.00) pb | |
PbPb (\(\sqrt{s} = \)5.02 TeV) | X(4350), \(0^{++}\) | (93.40 – 231.98) nb | (14.60 – 36.20) nb | (34.60 – 85.90) nb |
X(4350), \(2^{++}\) | (95.38 – 260.14) nb | (14.90 – 40.60) nb | (35.30 – 96.30) nb |
Total cross sections for \(X(3915)[J^P] \rightarrow \omega J/\psi \) production for different center-of-mass energies considering the full LHC rapidity range as well as the rapidity ranges covered by the ALICE and LHCb detectors
Collision | Resonance | LHC | LHCb | ALICE |
---|---|---|---|---|
Full rapidity range | \(2< Y < 4.5\) | \(-1< Y < 1\) | ||
pp (\(\sqrt{s} = \)13 TeV) | X(3915), \(0^{++}\) | (177.89 – 336.24) fb | (36.80 – 69.60) fb | (39.40 – 74.50) fb |
X(3915), \(2^{++}\) | (265.80 – 492.74) fb | (55.00 – 102.00) fb | (58.90 – 109.30) fb | |
pPb (\(\sqrt{s} = \)8.1 TeV) | X(3915), \(0^{++}\) | (561.84 – 1061.98) pb | (150. 00 – 290.00) pb | (150.00 – 280.00) pb |
X(3915), \(2^{++}\) | (839.52 – 1556.28) pb | (230.00 – 420.00) pb | (220.00 – 420.00) pb | |
PbPb (\(\sqrt{s} = \)5.02 TeV) | X(3915), \(0^{++}\) | (1453.61 – 2747.60) nb | (230.00 – 440.00) nb | (520.00 – 990.00) nb |
X(3915), \(2^{++}\) | (2172.03 – 4026.47) nb | (350.00 – 650.00) nb | (790.00 – 1460.00) nb |
The analysis performed above can be directly extended for other exotic meson candidates. In particular, we can also provide predictions for the X(3915) production. A candidate for such state was observed in \(\gamma \gamma \) collisions by the Belle [34] and BaBar [35] Collaborations in the \(\gamma \gamma \rightarrow \omega J/\Psi \) process. Belle Collaboration obtained that [34] \(\Gamma _{X(3915) \rightarrow \gamma \gamma } \times \mathcal{{B}}(X(3915) \rightarrow \omega J/\Psi ) = [61 {\pm 17} \, \text{(stat) } \pm 8 \, \text{(syst) }]\) eV for \(J^P = 0^+\), or \(\Gamma _{X(3915) \rightarrow \gamma \gamma } \times \mathcal{{B}}(X(3915) \rightarrow \omega J/\Psi ) = [18 {\pm 5} \, \text{(stat) } \pm 2 \, \text{(syst) }]\) eV for \(J^P = 2^+\). Using these values as input in our calculations we can estimate the total cross sections for \(X(3915)[J^P] \rightarrow \omega J/\psi \) production in pp / pPb / PbPb collisions at the LHC energies. The predictions are presented in Table 2. In comparison to the results for the X(4350), the cross sections for the \(X(3915)[J^P] \rightarrow \omega J/\psi \) production are one order of magnitude larger.
Two important comments are in order here. First, the analysis of the final states considered in this paper can be limited by the need of a precise reconstruction of the meson masses, which is currently limited at the LHC. Second, the \(J/\Psi \) meson is usually observed through its decays into dileptons, with a branching fraction of the order of \(10 \%\). However, such decay mode is very small for the \(\phi \) and \( \omega \) mesons. Consequently, the study of the \(\phi J/\Psi \) and \(\omega J/\Psi \) only will be feasible if the hadronic decay modes, as e.g. \(\phi \rightarrow K^+ K^-\) and \(\omega \rightarrow \pi ^+ \pi ^- \pi ^0\), were effectively reconstructed. If these shortcomings are surpassed, our results indicate that the analysis of the X(4350) and X(3915) exotic mesons will be, in principle, feasible at the LHC considering the photon induced interactions that occur in hadronic collisions at large impact parameter.
Finally, let’s summarize our main results and conclusions. Over the last years the existence of exotic hadrons has been established and a large number of candidate have been proposed. In particular, the exotic X(4350) and X(3915) mesons have been observed in \(\gamma \gamma \) processes by the Belle Collaboration considering the production of the \(\phi J/\Psi \) and \(\omega J/\Psi \) final states, respectively. However, such states have not be observed at the LHC in the analysis of \(B^+\) decays. Consequently, these states still awaits confirmation. In this study we have proposed the search of these resonances in the \(\gamma \gamma \) interactions present in pp / pPb / PbPb collisions at the LHC. This is a clean process where the particles of the initial state are intact at the final state and can be detected at the forward direction as featured by the presence of two rapidity gaps between the projectiles and the produced resonance, which is assumed to decay in a pair of vector mesons. Our results indicate that the experimental analysis of this process is, in principle, feasible at the LHC and that its study is ideal to confirm (or not) the existence and properties from these resonances.
Notes
Acknowledgements
One of the authors (VPG) is partially supported by the Brazil - U.S. Professorship given jointly by the Sociedade Brasileira de Física (SBF) and the American Physical Society (APS). This work was partially financed by the Brazilian funding agencies CNPq, CAPES, FAPERGS and INCT-FNA (process number 464898/2014-5).
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