A model independent spin analysis of fundamental particles using azimuthal asymmetries

Abstract

Exploiting the azimuthal angle dependence of the density matrices we construct observables that directly measure the spin of a heavy unstable particle. A novelty of the approach is that the analysis of the azimuthal angle dependence in a frame other than the usual helicity frame offers an independent cross-check on the extraction of the spin. Moreover, in some instances when the transverse polarisation tensor of highest rank is vanishing, for an accidental or dynamical reason, the standard azimuthal asymmetries vanish and would lead to a measurement with a wrong spin assignment. In a frame such as the one we construct, the correct spin assignment would however still be possible. The method gives direct information about the spin of the particle under consideration and the same event sample can be used to identify the spins of each particle in a decay chain. A drawback of the method is that it is instrumental only when the momenta of the test particle can be reconstructed. However we hope that it might still be of use in situations with only partial reconstruction. We also derive the conditions on the production and decay mechanisms for the spins, and hence the polarisations, to be measured at a collider experiment. As an example for the use of the method we consider the simultaneous reconstruction, at the partonic level, of the spin of both the top and the W in top pair production in e + e − in the semi-leptonic channel.

On polarization parameters of spin-1 particles and anomalous couplings in $$e^+e^-\rightarrow ZZ/Z\gamma $$ e + e - → Z Z / Z γ

“…These parameters are different kinds of polarization. For example, a spin-1/2 fermion has three polarization parameters called longitudinal, transverse, and normal polarizations (see for example [45,46]). Similarly, for a spin-1 particle we have a total of eight such parameters.…”

“…Similarly, for a spin-1 particle we have a total of eight such parameters. Three of them are vectorial like in the spin-1/2 case and the other five are tensorial [46,49] as will be described in Sect. 2 for completeness.…”

Angular distributions as lifetime probes

“…The spin of each particle is unattainable at the LHC, but the angular distributions can be measured. For a review of such methods, see, for example, [19][20][21]. For a chiral theory the angles of the decay products depend on the polarization of the parent particle.…”

On the choice of beam polarization in $$e^+e^-\rightarrow ZZ/Z\gamma $$ e + e - → Z

“…Here we use beam polarizations (longitudinal only) to study anomalous trilinear gauge-boson self couplings in the neutral sector using the complete set of polarization observables of the Z boson [28][29][30] in the process e + e − → Z Z/Z γ . The anomalous couplings among the neutral gauge boson have been studied earlier with unpolarized beams in [31][32][33][34][35][36][37][38][39] as well as with polarized beams in [15][16][17]19,[40][41][42][43][44][45].…”