Testing CP and Time Reversal Symmetries with Decays

Abstract

In this letter, an overview is given for interesting tests of both CP and Time Reversal symmetries with the beauty baryon Λ b . Extensive use of the helicity formalism and HQET is done for all calculations. Then, emphasis is put on sophisticated methods like analysis of resonance polarizations and particular angle distributions which can exhibit a clear signal of TR violation. PHYSICAL MOTIVATIONSModern Particle Physics is well described by gauge field theories which are built on fundamental principles, the most important ones being Lorentz Invariance, Unitarity and Hermiticity. An immediate consequence of these principles is the famous CPT theorem which stipulates that any physical system and its CPT-conjugate one have identical physical laws. On another side, CPT theorem supposes that, if CP symmetry is violated, Time Reversal (TR) is no longer a good symmetry and this mathematical feature represents only an indirect violation of TR symmetry. However some experiments performed recently at CERN and Fermilab have shown a clear signal of direct TR violation in the K 0K 0 system. Our aim is to demonstrate that search for direct TR violation can be performed at the LHC energies by studying the cascade decays of Λ b → ΛV, Λ → pπ, V → x + x − , x being a lepton or a pion. Our main tool is constructing Triple Product Correlations (TPC) defined by the following relations Cascade decaysThe initial laboratory frame to which Λ b polarization is referred is defined like: e 1 = p 1 /p 1 , e 3 = p1× p b | p1× p b | , e 2 = e 3 × e 1 where p 1 and p b are respectively the incident proton momentum and the produced Λ b one. Λ b being transversally polarized, its polarization value is given by P Λ b = S Λ b · e 3 . Let M i be the Λ b spin projection along e 3 axis and, λ 1 and λ 2 are respectively the helicity values of Λ and V . Conservation of total angular momentum leads to four possible values for the pair (λ 1 , λ 2 ) = (1/2, 0), (1/2, 1), (−1/2, −1), (−1/2, 0) 1

B, D and K decays

“…An additional application of the Λ b baryon that has been considered is testing CP and T symmetries using the decay modes Λ b → ΛV , where V = J /ψ, ρ 0 , ω. This is discussed in [856].…”

Time-reversal asymmetries and angular distributions in Λb → ΛV

“…In two or three-body decays, T-odd observables can be constructed in the spin correlations among the particles [1][2][3][4][5][6][7][8][9][10]. Since the particle spins could not be directly measured in the current high energy physics experiments, we have to extract their effects through the angular distributions in the cascade decays [11][12][13][14][15][16][17][18][19][20][21][22][23][24].…”

Results from LHCb in charmless $b$-baryon decay

“…Triple products asymmetries can also be computed in the Λ 0 b → Λ φ decay due to the spin structure of the decay. These have been performed following the formalism in [7]. Four triple products are possible, corresponding to cos Φ n Λ ,φ and sin Φ n Λ ,φ , where Φ n Λ ,φ is the azimuthal angle of the resonance decay planes with normal vector n Λ ,φ .…”