Polarization observables in e+e− annihilation to a baryon-antibaryon pair

Abstract

Using the helicity formalism of Jacob and Wick we derive spin density matrices of baryon antibaryon pairs produced in e + e − annihilation. We consider the production of pairs with spins 1/2 + 1/2, 1/2 + 3/2 (+c.c.) and 3/2 + 3/2. We provide modular expressions to include chains of weak hadronic two-body decays of the produced hyperons. The expressions are suitable for the analysis of high statistics data from J/ψ and ψ(2S) decays at e + e − colliders, by fits to the fully differential angular distributions of the measured particles. We illustrate the method by examples, such as the inclusive measurement of the e + e − → ψ(2S) → Ω −Ω+ process where one decay chain Ω − → ΛK − followed by Λ → pπ − is considered. Finally we show that the inclusive angular distributions can be used to test spin assignment of the produced baryons.

Measurement of the weak mixing angle at a Super Charm-Tau factory with data-driven monitoring of the average electron beam polarization

“…Further application of the helicity formalism to the baryon-antibaryon pairs produced in collisions of unpolarized electron-positron beams is elaborated in ref. [11].…”

CP symmetry tests in the cascade-anticascade decay of charmonium

“…Due to the parity conservation only two transitions are independent and the C µν matrix can be parameterized by: α ψ -baryon angular distribution parameter, −1 ≤ α ψ ≤ 1, and ∆Φrelative phase between the two transitions. The elements of the C µν matrix are functions of the scattering angle θ of the B baryon [18]:…”

“…It is enough to know how each base spin matrix transforms under a decay process. One can therefore represent the weak decay by a decay matrix a D µµ which transforms the base matrices [18]:…”

“…The explicit form of the a D µν is given in Ref. [18], where a two angle helicity rotation matrix convention is used. If the polarization of the baryon B B is not measured the decay is described by the a D µ0 elements of the decay matrix and only the α D parameter is involved.…”

Novel aspects of baryon-antibaryon production in e+ e- annihilations

“…The final state baryons can have both ±1/2 helicities. Due to parity conservation out of the four possible helicity transitions only two are independent: A 1/2,1/2 = A −1/2,−1/2 =: h 1 and A 1/2,−1/2 = A −1/2,1/2 =: h 2 [13]. Therefore e + e − → B 1B2 process at fixed c.m.…”