Abstract
Using the helicity formalism, we calculate the combined angular distribution function of the two photons (γ1 and γ2) and electron (e −) in the cascade process \(\overline{p}p\to {}^3{D_3}\to {}^3{P_2}+{\gamma_1}\to \left( {\psi +{\gamma_2}} \right)+{\gamma_1}\to \left( {{e^{+}}+{e^{-}}} \right)+{\gamma_2}+{\gamma_1}\),when \(\overline{p}\) and p are unpolarized. We also derive six different partially integrated angular distribution functions which give the angular distributions of one or two particles in the final state. Once the angular distributions are measured, our expressions will enable one to determine the relative magnitudes as well as the cosines of the relative phases of all the angular-momentum helicity amplitudes in the radiative decay processes 3 D 3 → 3 P 2 + γ1 and 3 P 2 → ψ + γ2.
Similar content being viewed by others
References
T. Barnes, S. Godfrey and E. Swanson, Higher charmonia, Phys. Rev. D 72 (2005) 054026 [hep-ph/0505002] [INSPIRE].
E.J. Eichten, K. Lane and C. Quigg, New states above charm threshold, Phys. Rev. D 73 (2006) 014014 [Erratum ibid. D 73 (2006) 079903] [hep-ph/0511179] [INSPIRE].
E. Eichten, S. Godfrey, H. Mahlke and J.L. Rosner, Quarkonia and their transitions, Rev. Mod. Phys. 80 (2008) 1161 [hep-ph/0701208] [INSPIRE].
T. Fernández-Caramés, A. Valcarce and J. Vijande, Charmonium spectroscopy above thresholds, Phys. Rev. Lett. 103 (2009) 222001 [arXiv:1001.4506] [INSPIRE].
T. Barnes and S. Godfrey, Charmonium options for the X(3872), Phys. Rev. D 69 (2004) 054008 [hep-ph/0311162] [INSPIRE].
E.J. Eichten, K. Lane and C. Quigg, Charmonium levels near threshold and the narrow state X(3872) → π+π− J/ψ, Phys. Rev. D 69 (2004) 094019 [hep-ph/0401210] [INSPIRE].
D. Bettoni, The PANDA experiment at FAIR, eConf C 070805 (2007) 39 [arXiv:0710.5664] [INSPIRE].
PANDA collaboration, M. Lutz et al., Physics Performance Report for PANDA: Strong Interaction Studies with Antiprotons, arXiv:0903.3905 [INSPIRE].
M. Jacob and G. Wick, On the general theory of collisions for particles with spin, Annals Phys. 7 (1959) 404 [INSPIRE].
A.D. Martin and T.D. Spearman, Elementary Particle Theory, North-Holland Publishing Company, Amsterdam The Netherlands (1970), pg. 129 and 204.
A.W.K. Mok and K.J. Sebastian, Polarized angular distributions in the decays of the 3D 2 state of charmonium produced in unpolarized proton-antiproton annihilation, Eur. Phys. J. C 67 (2010) 125 [INSPIRE].
A.W.K. Mok and K.J. Sebastian, Polarized angular distributions in the decays of the ψ′ charmonium state directly produced in unpolarized proton-antiproton collisions, Eur. Phys. J. C 56 (2008) 189 [INSPIRE].
A.W.K. Mok and M.-F. Chow, Polarized angular distributions in the decays of the singlet D 2 state of charmonium originating from pp collisions, Eur. Phys. J. C 71 (2011) 1792 [INSPIRE].
A.W.K. Mok and K.J. Sebastian, Angular distributions in the decays of the triplet D 2 state of charmonium directly produced in polarized proton-antiproton collisions, Eur. Phys. J. C 63 (2009) 101 [INSPIRE].
W.A.K. Mok and K.J. Sebastian, Angular distributions in the decays of the ψ′ charmonium state directly produced in polarized proton anti-proton collisions, Nuovo Cim. A 110 (1997) 429 [INSPIRE].
F. Karl, S. Meshkov and J.L. Rosner, Symmetries, angular distributions in ψ′ → γχ → γγψ and the interpretation of the χ(3400 − 355−) levels, Phys. Rev. D13 (1976) 1203 [INSPIRE].
K.J. Sebastian and X.G. Zhang, Radiative transitions of the D states of charmonium in potential models, Phys. Rev. D 55 (1997) 225 :10.1103/PhysRevD.55.225 [INSPIRE].
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Mok, A.W.K., Wong, CP. & Sit, WY. Angular distribution functions in the decays of the 3 D 3 state of charmonium originating from unpolarized \(\overline{p}p\) collisions. J. High Energ. Phys. 2012, 83 (2012). https://doi.org/10.1007/JHEP10(2012)083
Received:
Revised:
Accepted:
Published:
DOI: https://doi.org/10.1007/JHEP10(2012)083