1. Effect of Coupling on Boost Measurements  y’B (z) - angular spread of boost vector  yy’B (z) – angle position correlation  xy’B (z) – y-angle x-position correlation Measures of  y,  * y Measure of coupling?

2. Using MIA results of Apr 21 ’06  2 H 0.36nm,  2 L 1.13nm,  * H 11.0mm,  * L 9.5mm colliding electrons colliding positrons measurable

3. Which w parameters are significant? “waist shift”

4. Angle-position correlation colliding electrons colliding positrons measurable

5. Which w parameters are significant? “waist shift”

6.  y’ (z) Fit Only  y’ (z) + dy’/dy Fit Common  *, z w Unable to describe this shape without separate values for waists and  *s

7.  y’ (z) + dy’/dy Fit Differing  *, z w

8. Inputs:  2 H 0.36nm,  2 L 1.13nm,  * H 11.0mm,  * L 9.5mm Without coupling  * y (mm)  H (nm)  L (nm) z w (mm)  y’ B 9.90.360.80.20  y’ B +  y’ B /  y common  *,z w 10.120.4050.580.11  y’ B +  y’ B /  y differing  *,z w 10.78 / 9.40.390.810.20 / -0.01 With coupling  y’ B 17.81.1970.16-3.22  y’ B +  y’ B /  y common  *,z w 15.00.811.8-3.32  y’ B +  y’ B /  y differing  *,z w 13.0 / 15.60.672.25-6.6 / 0.8

9. Using MIA results of Apr 21 ’06 Replacing  2 H 3.0nm,  2 L 5.9nm,  * H 11.0mm,  * L 9.5mm measurable

10. Inputs:  2 H 3.0nm,  2 L 5.9nm,  * H 11.0mm,  * L 9.5mm Without coupling  * y (mm)  H (nm)  L (nm) z w (mm)  y’ B 10.02.86.00.2  y’ B +  y’ B /  y common  *,z w 10.63.3 0.21  y’ B +  y’ B /  y differing  *,z w 11.0 / 9.53.06.00.26 / -0.08 With coupling  y’ B 11.23.46.7-0.34  y’ B +  y’ B /  y differing  *,z w 11.73.84.2-0.51  y’ B +  y’ B /  y common  *,z w 11.9 / 10.83.38.1-0.9 / 0.3

11. dy’ B /dx = measurement of coupling? y’ (mrad) x (cm) Example from data Expectation using MIA results dy’/dx z (cm) 0.36nm, 1.13nm 3.0nm, 5.9nm

12.  y’ B /  x [rad/m] Measurements over Run5

13. Which w parameters are significant? (Doesn’t depend much upon  2 )

14. What about the other x-y combination? This effect is getting too small to see.

15. Summary Coupling may have a significant effect on  * and  measurements, particularly when  2 is small. Should be able to measure some coupling with boost-position correlation dy’ B /dx