The Drell-Yan process in which a lepton pair is produced in hadron-hadron collisions is one of the most extensively studied reactions. The precision measurements of dilepton angular coefficients at various energies were presented over the past years. However, the values of angular coefficients strongly depend on the choice of a reference frame. That is why an adequate comparison between observables measured in different coordinate systems and between theory and experiment requires the development of a frame invariant formalism. Therefore, an interesting research avenue is a search for frame-independent combinations of angular coefficients. Such parameters would provide a powerful tool for the data analysis, can reveal systematic biases that were not taken into account and overall are expected to be better observables.
The search of rotational invariants was an actively discussed topic for the past ten years. Several special invariants for $SO(2)$ rotations around fixed coordinate axes were proposed [1-4]. In addition, significant progress was achieved in [5], where the number of $SO(3)$ rotational invariants for the most general form of the dilepton angular distribution were counted and a recipe for their derivation was developed.
Our present work is focused on the dilepton angular distributions in vector decays. We suggest a method which is a generalization of the procedure first proposed in [6]. The key idea of the approach is to express the hadronic tensor (initial state density matrix) corresponding to the process in terms of the coefficients of the final state angular distribution and then explore the invariants of the obtained matrix. This formalism allowed us to derive five independent $SO(3)$ rotational invariants and constrain their values using the positivity of the hadronic tensor. Moreover, the set of invariants that we propose seem to be more convenient for use since the expressions we obtained are more compact compared to the results from [5]. In addition, in our analysis we reduced the maximum power of the angular coefficients entering the invarinats by one (from the fifth power to the forth).
References
[1] P. Faccioli, C. Lourenço, and J. Seixas, Physical review letters 105, 061601 (2010).
[2] P. Faccioli, C. Lourenco, J. Seixas, and H. K. Wöhri, Physical Review D 82, 096002 (2010).
[3] S. Palestini, Physical Review D 83, 031503 (2011).
[4] P. Faccioli, C. Lourenço, J. Seixas, and H. K. Wöhri, Physical Review D 83, 056008 (2011).
[5] Y.-Q. Ma, J.-W. Qiu, and H. Zhang, arXiv preprint arXiv:1703.04752 (2017).
[6] O. Teryaev, Nuclear Physics. B, Proceedings Supplements 214, 118 (2011).