Single spin asymmetry utilising relative luminosity

Single spin asymmetry making use of relative luminosity

I also calculate the asymmetry via an alternative method, making use of Tai Sakuma's relative luminosity work. The left-right asymmetry is defined as

Equation 1

where N_L is the particle yield to the left of the polarised beam. The decomposition of the up/down yields into contributions from the four different beam polarisation permutations is the same as given in the cross-asymmetry section (equations 2 and 3). Here, the yields must be scaled by the appropriate relative luminosity, giving the following relations:

Contributions to blue beam counts, scaled for luminosity

Equation 2

Contributions to yellow beam counts, scaled for luminosity

Equation 3

The relative luminosities R4, R5 and R6 are the ratios of luminosity for, respectively, up-up, up-down and down-up bunches to that for down-down bunches. I record the particle yields for each polarisation permutation (i.e. spin bits) on a run-by-run basis, scale each by the appropriate relative luminosity for that run, then combine yields from all the runs in a given fill to give fill-by-fill yields. These are then used to calculate a fill-by-fill raw asymmetry, which is scaled by the beam polarisation. The figures below show the resultant fill-by-fill asymmetry for each beam and particle species, summed over all p_T. The fits are again satisfactory, and give asymmetries consistent with zero within errors, as expected.

$K^{0}_{S} blue beam asymmetry using relative luminosity$

Figure 1a: Blue beam asymmetry for K⁰_S

$K^{0}_{S} yellow beam asymmetry using relative luminosity$

Figure 1b: Yellow beam asymmetry for K⁰_S

Lambda blue beam asymmetry using relative luminosity

Figure 2a: Blue beam asymmetry for Λ

Lambda yellow beam asymmetry using relative luminosity

Figure 2b: Yellow beam asymmetry for Λ