Today's Progress 1. Sep. 2005

Study of BLC position

Here, we try to determine the rotation and exact location of BLC with respect to VDCtop, with stopped K^+ data.

The vertex images BEFORE position study is as follows:

The procedure of the BLC position study is:

1. Elimination of position shift. x-shift is detected by the Vca_x distribution. z(y)-shift is detected by the correlation between vertex_z(y) VS Vca_z(y).

2. Elimination of Eular's theta rotation. Theta rotation means the rotation around y axis. The rotation appears in the correlation between Vca_x VS vertex_z.

3. Elimination of Eular's psi+phi rotation. Psi+phi rotation is that around z axis. In the linear approximation of the Eular's rotation matrix, one parameter, phi+psi, can represent the remained rotation after theta inverse-rotation. It appears in the correlation between Vca_x VS vertex_y.

Repeat procedure 1~3 until all correlation vanish.

Elimination of x,y and z shifts of BLC

X shift is most easily detected as the shift of Vca_x distribution.

Z shift is not directly seen. But, it appears as the systematic deviation of the correlation between vertex_z VS Vca_z from Vca_z = 0. Black:nominal, Red:-46mm, Green:+46mm after elimination of x shift by -4.0 mm. z shift is determined to be at around -45 mm.

Alternatively, z shift is also found in the correlation between blcbx VS Vca_z. We can find proper BLC z position removing the correlation. blcbx vs Vca_z before (top) and after (bottom) -42.5 mm z shift are shown below.

Z offset is determined to be -40.5 mm adopting the point gives the minimum chisquare.

Y shift is not directly seen. But, it appears as the systematic deviation of the correlation between vertex_y VS Vca_y from Vca_y = 0 as well as z case. Black:nominal, red:-10mm, blue:+10mm after elimination of x shift by -4.0 mm and z shift by -46 mm. By this procedure, y shift is not detected by mm order.

Alternatively, y shift is also found in the correlation between vdcbx VS Vca_y. We can find proper BLC y position removing the correlation. Figure below::vdcbx vs Vca_y, comparing the correlation before(to) and after(bottom) 10 mm yoffset is intentionally add. The correlation is clearly sensitive to y offset.

Y offset is determined to be +1.7 mm adopting the point gives the minimum chisquare of the constant fitting of the correlation.

Variation DCA distribution with elimination of x,y,z position offset.

After the 1st stage elimination of position error, vertex image has been improved. Now, BLC frame and Al cap are very clearly seen.

Elimination of theta, phi and psi rotations

Theta rotation around y axis is very clearly detected in the correlation between vertex_z and Vca_x. We can eliminate it, applying inverte-rotation to delete the slope of the correlation. Top: Before theta inverse-rotation. Bottom:after theta inverse-rotation by 11.4 mrad.

Psi rotation around z axis is detected in the correlation between vertex_y and Vca_x. We can eliminate it, applying inverte-rotation to delete the slope of the correlation, again. Top: Before psi+phi inverse-rotation. Bottom:after psi inverse-rotation by 5.4 mrad.

Phi rotation around x axis is detected in the correlation between vertex_z and Vca_y. Top: Before phi inverse-rotation. Bottom:after phi inverse-rotation by 14.0 mrad.

theta,psi,phi rotations were determined to be 11.4., 5.4, 14.0 mrad, respectively. The variation of DCA distribution is shown below. Blcak: no rotation. Red: after theta inverse-rotation by 11.4 mrad. Blue: after psi-rotation by 5.4 mrad with the previous theta rotation. magenta: after phi inverse rotation by 14.0 mrad with theta and psi inverse rotation.

Vertex z image after 1st stage elimination of position error and rotation.