Abstract
It has been proposed recently (Phys. Rev. Lett. 115 (2015) 022001) that the charmoniumlike state named X(3915) and suggested to be a 0++ scalar, is just the helicity-0 realisation of the 2++ tensor state χ c2(3930). This scenario would call for a helicity-0 dominance, which were at odds with the properties of a conventional tensor charmonium, but might be compatible with some exotic structure of the χ c2(3930). In this paper, we investigate, if such a scenario is compatible with the assumption that the χ c2(3930) is a \( {D}^{\ast }{\overline{D}}^{\ast } \) molecular state — a spin partner of the X(3872) treated as a shallow bound state. We demonstrate that for a tensor molecule the helicity-0 component vanishes for vanishing binding energy and accordingly for a shallow bound state a helicity-2 dominance would be natural. However, for the χ c2(3930), residing about 100 MeV below the \( {D}^{\ast }{\overline{D}}^{\ast } \) threshold, there is no a priori reason for a helicity-2 dominance and thus the proposal formulated in the above mentioned reference might indeed point at a molecular structure of the tensor state. Nevertheless, we find that the experimental data currently available favour a dominant contribution of the helicity-2 amplitude also in this scenario, if spin symmetry arguments are employed to relate properties of the molecular state to those of the X(3872). We also discuss what research is necessary to further constrain the analysis.
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References
N. Brambilla et al., Heavy quarkonium: progress, puzzles and opportunities, Eur. Phys. J. C 71 (2011) 1534 [arXiv:1010.5827] [INSPIRE].
N. Brambilla et al., QCD and Strongly Coupled Gauge Theories: Challenges and Perspectives, Eur. Phys. J. C 74 (2014) 2981 [arXiv:1404.3723] [INSPIRE].
Belle-II collaboration, T. Abe et al., Belle II Technical Design Report, arXiv:1011.0352 [INSPIRE].
A.G. Drutskoy, F.-K. Guo, F.J. Llanes-Estrada, A.V. Nefediev and J.M. Torres-Rincon, Hadron physics potential of future high-luminosity B-factories at the Y(5S) and above, Eur. Phys. J. A 49 (2013) 7 [arXiv:1210.6623] [INSPIRE].
D.M. Asner et al., Physics at BES-III, Int. J. Mod. Phys. A 24 (2009) S1 [arXiv:0809.1869] [INSPIRE].
PANDA collaboration, M.F.M. Lutz et al., Physics Performance Report for PANDA: Strong Interaction Studies with Antiprotons, arXiv:0903.3905 [INSPIRE].
Belle collaboration, S. Uehara et al., Observation of a charmonium-like enhancement in the γγ → ωJ/ψ process, Phys. Rev. Lett. 104 (2010) 092001 [arXiv:0912.4451] [INSPIRE].
BaBar collaboration, J.P. Lees et al., Study of X(3915) → J/ψω in two-photon collisions, Phys. Rev. D 86 (2012) 072002 [arXiv:1207.2651] [INSPIRE].
X. Liu, Z.-G. Luo and Z.-F. Sun, X(3915) and X(4350) as new members in P-wave charmonium family, Phys. Rev. Lett. 104 (2010) 122001 [arXiv:0911.3694] [INSPIRE].
Particle Data Group collaboration, C. Patrignani et al., Review of Particle Physics, Chin. Phys. C 40 (2016) 100001 [INSPIRE].
F.-K. Guo and U.-G. Meißner, Where is the χ c0(2P)?, Phys. Rev. D 86 (2012) 091501 [arXiv:1208.1134] [INSPIRE].
S.L. Olsen, Is the X(3915) the χ c0(2P)?, Phys. Rev. D 91 (2015) 057501 [arXiv:1410.6534] [INSPIRE].
X. Li and M.B. Voloshin, X(3915) as a \( {D}_s{\overline{D}}_s \) bound state, Phys. Rev. D 91 (2015) 114014 [arXiv:1503.04431] [INSPIRE].
Z.-Y. Zhou, Z. Xiao and H.-Q. Zhou, Could the X(3915) and the X(3930) Be the Same Tensor State?, Phys. Rev. Lett. 115 (2015) 022001 [arXiv:1501.00879] [INSPIRE].
A.I. Alekseev, Two-photon annihilation of positronium in the P-state, Sov. Zh. Eksp. Teor. Fiz. 34 (1958) 1195.
M. Krammer and H. Krasemann, Two Gluon Jets from Y′(10), Phys. Lett. B 73 (1978) 58 [INSPIRE].
Z.P. Li, F.E. Close and T. Barnes, Relativistic effects in gamma gamma decays of P wave positronium and \( q\overline{q} \) systems, Phys. Rev. D 43 (1991) 2161 [INSPIRE].
A.E. Bondar, A. Garmash, A.I. Milstein, R. Mizuk and M.B. Voloshin, Heavy quark spin structure in Z b resonances, Phys. Rev. D 84 (2011) 054010 [arXiv:1105.4473] [INSPIRE].
M.B. Voloshin, Radiative transitions from Y(5S) to molecular bottomonium, Phys. Rev. D 84 (2011) 031502 [arXiv:1105.5829] [INSPIRE].
T. Mehen and J.W. Powell, Heavy Quark Symmetry Predictions for Weakly Bound B-Meson Molecules, Phys. Rev. D 84 (2011) 114013 [arXiv:1109.3479] [INSPIRE].
C. Hidalgo-Duque, J. Nieves, A. Ozpineci and V. Zamiralov, X(3872) and its Partners in the Heavy Quark Limit of QCD, Phys. Lett. B 727 (2013) 432 [arXiv:1305.4487] [INSPIRE].
J. Nieves and M.P. Valderrama, The Heavy Quark Spin Symmetry Partners of the X(3872), Phys. Rev. D 86 (2012) 056004 [arXiv:1204.2790] [INSPIRE].
F.-K. Guo, C. Hidalgo-Duque, J. Nieves and M.P. Valderrama, Consequences of Heavy Quark Symmetries for Hadronic Molecules, Phys. Rev. D 88 (2013) 054007 [arXiv:1303.6608] [INSPIRE].
M. Albaladejo, F.-K. Guo, C. Hidalgo-Duque, J. Nieves and M.P. Valderrama, Decay widths of the spin-2 partners of the X(3872), Eur. Phys. J. C 75 (2015) 547 [arXiv:1504.00861] [INSPIRE].
V. Baru, E. Epelbaum, A.A. Filin, C. Hanhart, U.-G. Meißner and A.V. Nefediev, Heavy-quark spin symmetry partners of the X(3872) revisited, Phys. Lett. B 763 (2016) 20 [arXiv:1605.09649] [INSPIRE].
E. Cincioglu, J. Nieves, A. Ozpineci and A.U. Yilmazer, Quarkonium Contribution to Meson Molecules, Eur. Phys. J. C 76 (2016) 576 [arXiv:1606.03239] [INSPIRE].
F.-K. Guo, C. Hanhart, Y.S. Kalashnikova, U.-G. Meißner and A.V. Nefediev, What can radiative decays of the X(3872) teach us about its nature?, Phys. Lett. B 742 (2015) 394 [arXiv:1410.6712] [INSPIRE].
J. Hu and T. Mehen, Chiral Lagrangian with heavy quark-diquark symmetry, Phys. Rev. D 73 (2006) 054003 [hep-ph/0511321] [INSPIRE].
J.L. Rosner, Angular distributions in J/ψ(ρ 0 , ω) states near threshold, Phys. Rev. D 70 (2004) 094023 [hep-ph/0408334] [INSPIRE].
T. Mehen, Hadronic loops versus factorization in effective field theory calculations of X(3872) → χ cJ π 0, Phys. Rev. D 92 (2015) 034019 [arXiv:1503.02719] [INSPIRE].
F.-K. Guo, C. Hanhart, U.-G. Meißner, Q. Wang and Q. Zhao, Production of the X(3872) in charmonia radiative decays, Phys. Lett. B 725 (2013) 127 [arXiv:1306.3096] [INSPIRE].
L.D. Landau, Small binding energies in Quantum Field Theory, Sov. Zh. Eksp. Teor. Fiz. 39 (1960) 1856.
S. Weinberg, Evidence That the Deuteron Is Not an Elementary Particle, Phys. Rev. 137 (1965) B672 [INSPIRE].
V. Baru, J. Haidenbauer, C. Hanhart, Y. Kalashnikova and A.E. Kudryavtsev, Evidence that the a 0(980) and f 0(980) are not elementary particles, Phys. Lett. B 586 (2004) 53 [hep-ph/0308129] [INSPIRE].
R. Mertig, M. Böhm and A. Denner, Feyn Calc — Computer algebraic calculation of Feynman amplitudes, Comput. Phys. Commun. 64 (1991) 345 [INSPIRE].
V. Shtabovenko, R. Mertig and F. Orellana, New Developments in FeynCalc 9.0, Comput. Phys. Commun. 207 (2016) 432 [arXiv:1601.01167] [INSPIRE].
H.H. Patel, Package-X: A Mathematica package for the analytic calculation of one-loop integrals, Comput. Phys. Commun. 197 (2015) 276 [arXiv:1503.01469] [INSPIRE].
T. Hahn and M. Pérez-Victoria, Automatized one loop calculations in four-dimensions and D-dimensions, Comput. Phys. Commun. 118 (1999) 153 [hep-ph/9807565] [INSPIRE].
Belle collaboration, S. Uehara et al., Observation of a χ ′ c2 candidate in \( \gamma \gamma \to D\overline{D} \) production at BELLE, Phys. Rev. Lett. 96 (2006) 082003 [hep-ex/0512035] [INSPIRE].
BaBar collaboration, P. del Amo Sanchez et al., Evidence for the decay X(3872) → J/ψω, Phys. Rev. D 82 (2010) 011101 [arXiv:1005.5190] [INSPIRE].
Belle collaboration, K. Abe et al., Observation of a near-threshold ωJ/ψ mass enhancement in exclusive B → KωJ/ψ decays, Phys. Rev. Lett. 94 (2005) 182002 [hep-ex/0408126] [INSPIRE].
BaBar collaboration, B. Aubert et al., Observation of Y (3940) → J/ψω in B → J/ψωK at BABAR, Phys. Rev. Lett. 101 (2008) 082001 [arXiv:0711.2047] [INSPIRE].
BESIII collaboration, M. Ablikim et al., Two-photon widths of the χ c0,2 states and helicity analysis for χ c2 → γγ, Phys. Rev. D 85 (2012) 112008 [arXiv:1205.4284] [INSPIRE].
C. Hanhart, Y.S. Kalashnikova, A.E. Kudryavtsev and A.V. Nefediev, Reconciling the X(3872) with the near-threshold enhancement in the \( {D}^0{\overline{D}}^{\ast 0} \) final state, Phys. Rev. D 76 (2007) 034007 [arXiv:0704.0605] [INSPIRE].
X.W. Kang and J.A. Oller, Different pole structures in line shapes of the X(3872), arXiv:1612.08420 [INSPIRE].
E. Braaten and J. Stapleton, Analysis of J/ψπ + π − and \( {D}^0{\overline{D}}^0{\pi}^0 \) Decays of the X(3872), Phys. Rev. D 81 (2010) 014019 [arXiv:0907.3167] [INSPIRE].
I.K. Hammer, C. Hanhart and A.V. Nefediev, Remarks on meson loop effects on quark models, Eur. Phys. J. A 52 (2016) 330 [arXiv:1607.06971] [INSPIRE].
M. Cleven, F.-K. Guo, C. Hanhart, Q. Wang and Q. Zhao, Employing spin symmetry to disentangle different models for the XYZ states, Phys. Rev. D 92 (2015) 014005 [arXiv:1505.01771] [INSPIRE].
A.E. Bondar, R.V. Mizuk and M.B. Voloshin, Bottomonium-like states: Physics case for energy scan above the \( B\overline{B} \) threshold at Belle-II, Mod. Phys. Lett. A 32 (2017) 1750025 [arXiv:1610.01102] [INSPIRE].
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Baru, V., Hanhart, C. & Nefediev, A.V. Can X(3915) be the tensor partner of the X(3872)?. J. High Energ. Phys. 2017, 10 (2017). https://doi.org/10.1007/JHEP06(2017)010
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DOI: https://doi.org/10.1007/JHEP06(2017)010