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SUMMARY:Rotation-Invariant Observables as Density Matrix Invariants
DTSTART;VALUE=DATE-TIME:20190226T145400Z
DTEND;VALUE=DATE-TIME:20190226T150600Z
DTSTAMP;VALUE=DATE-TIME:20241010T110548Z
UID:indico-contribution-139@mosphys.ru
DESCRIPTION:Speakers: Margarita Gavrilova (BLTP\, JINR)\nThe Drell-Yan pro
cess 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 o
n the choice of a reference frame. That is why an adequate comparison betw
een observables measured in different coordinate systems and between theor
y and experiment requires the development of a frame invariant formalism.
Therefore\, an interesting research avenue is a search for frame-independe
nt combinations of angular coefficients. Such parameters would provide a p
owerful tool for the data analysis\, can reveal systematic biases that wer
e not taken into account and overall are expected to be better observables
.\nThe search of rotational invariants was an actively discussed topic for
the past ten years. Several special invariants for $SO(2)$ rotations arou
nd fixed coordinate axes were proposed [1-4]. In addition\, significant pr
ogress was achieved in [5]\, where the number of $SO(3)$ rotational invari
ants for the most general form of the dilepton angular distribution were c
ounted and a recipe for their derivation was developed.\nOur present work
is focused on the dilepton angular distributions in vector decays. We sugg
est 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 (initi
al state density matrix) corresponding to the process in terms of the coef
ficients of the final state angular distribution and then explore the inva
riants of the obtained matrix. This formalism allowed us to derive five in
dependent $SO(3)$ rotational invariants and constrain their values using t
he positivity of the hadronic tensor. Moreover\, the set of invariants tha
t we propose seem to be more convenient for use since the expressions we o
btained are more compact compared to the results from [5]. In addition\, i
n our analysis we reduced the maximum power of the angular coefficients en
tering the invarinats by one (from the fifth power to the forth).\n\n**Ref
erences**\n\n[1] P. Faccioli\, C. Lourenço\, and J. Seixas\, Physical rev
iew letters 105\, 061601 (2010).\n[2] P. Faccioli\, C. Lourenco\, J. Seixa
s\, and H. K. Wöhri\, Physical Review D 82\, 096002 (2010).\n[3] S. Pales
tini\, Physical Review D 83\, 031503 (2011).\n[4] P. Faccioli\, C. Louren
ço\, J. Seixas\, and H. K. Wöhri\, Physical Review D 83\, 056008 (2011).
\n[5] Y.-Q. Ma\, J.-W. Qiu\, and H. Zhang\, arXiv preprint arXiv:1703.0475
2 (2017).\n[6] O. Teryaev\, Nuclear Physics. B\, Proceedings Supplements 2
14\, 118 (2011).\n\nhttps://rich2018.org/indico/event/2/contributions/139/
LOCATION:HSE Study Center “Voronovo”
URL:https://rich2018.org/indico/event/2/contributions/139/
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