Centroid Centerline Boundary Three-Row Scan - Detector Physics: Timing and Spatial Reconstruction Step by Step

This centroid scan uses two weighted hits to see whether a reconstructed position stays before a fiducial center line. Left-heavy weights place the centroid at 5/4 meters, equal weights land at 3/2 meters on the boundary, and right-heavy weights move it to 7/4 meters past the line. Real centroid cuts depend on calibration, sensor pitch, charge sharing, noise, alignment, finite resolution, and uncertainty.

Weighted hits move the centroid through a fiducial center line. Exact arithmetic here means exact results for the stated model inputs; measured inputs still carry uncertainty and significant-figure limits.

highlighted = computed this step

Left-heavy weights stay before the center line

Weights 3 and 1 place the centroid at 5/4 meters.

m=x_{\max}\mathbin{-}x_c=3/2\mathbin{-}5/4=1/4,\quad\text{pass}

Equal weights land on the center line

Weights 1 and 1 place the centroid at 3/2 meters.

m=x_{\max}\mathbin{-}x_c=3/2\mathbin{-}3/2=0,\quad\text{pass}

Right-heavy weights cross the center line

Weights 1 and 3 place the centroid at 7/4 meters.

m=x_{\max}\mathbin{-}x_c=3/2\mathbin{-}7/4=-1/4,\quad\text{fail}