1. Photon conversions

The photons used in this study were the decay photons of the neutral pions. Pions were thrown uniformly in η, φ, and p_T and later re-weighted using a realistic weight function of p_T that reproduced the measured cross section shape. The point of origin was on the beam axis, and had a Gaussian distribution in z, centered at z = 0 with σ = 60 cm.

The full STAR geometries for d+Au 2003 and p+p 2005 periods were used.

Only the photons at 0 < η < 1, 0.1 < detector-η < 0.9, and |z| < 60 cm were selected. This closely simulates the sample of  photons used in the real data.

The following figures show the distribution of radial distances at which photons converted.

2. Conversion probability

Integrating these distributions over the SVT, SSD, and IFC regions (2–20, 20–40, and 40–50 cm, respectively), and dividing by the total integral, I obtained the following conversion probabilities for a photon.

Using the following formula, I calculated the corresponding probabilities for a π⁰ (probability that at least one photon converts):

P_conv(π⁰) = 2*P_conv(γ)*(1 - P_conv(γ)) + P_conv(γ)²

3. Correction for missing material

In Monte Carlo simulations, there is effectively an implicit factor of 1/(1 - P_conv), taking care of the conversions. In this case, we know that the probabilities are wrong by a factor R = 2, 2, and 1.2 for SVT, SSD, and IFC, respectively.
Therefore, the correction factor was calculated using the following formula:

c_loss = (1 - P_conv) / (1 - RP_conv)

The following values were obtained: