Documentation for a systematic uncertainty in the Run 5 charged pion A_{LL} based on non-longitudinal components in the beam polarization vector.

The beam polarization vectors in 2005 were determined by analyzing left-right and up-down asymmetries in the BBC for longitudinal and transverse running. The analysis was performed by Kasia Kowalik and documented here. The observed asymmetries correspond to beam angles of

θ_B = 7.9°
ϕ_B = 74.0°

θ_Y = 17.2°
ϕ_Y = 138.7°

Since the beam polarization vector has non-longitudinal components, a non-zero double-transverse asymmetry A_Σ would contaminate our measured A_LL at some small level.

The 2005 transverse running at STAR was too short to obtain a statistically significant measurement of A_Σ, so I’ve chosen to measure A_Σ using Run 6 transverse data instead. I analyzed runs that passed Murad’s run QA and had relative luminosities for either board 5 or board 6 (documented by Tai Sakuma here). Assuming no phi-dependent A_TT, I obtain the following results:

The systematic uncertainty due to A_Σ is given by the equation (courtesy Steve Vigdor)

Plugging in the polarization vector calculations reported above we have

I use max(δA_{Σ}, |A_{Σ}|) to account for cases where A_{Σ} is statistically consistent with zero. The final p_{T}-dependent systematics from this analysis are then

π+: {1.11, 2.30, 6.86, 6.16} e-4
π-: {1.15, 2.47, 6.35, 6.93} e-4