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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?
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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
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Which w parameters are significant? “waist shift”
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Angle-position correlation colliding electrons colliding positrons measurable
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Which w parameters are significant? “waist shift”
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y’ (z) Fit Only y’ (z) + dy’/dy Fit Common *, z w Unable to describe this shape without separate values for waists and *s
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y’ (z) + dy’/dy Fit Differing *, z w
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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
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Using MIA results of Apr 21 ’06 Replacing 2 H 3.0nm, 2 L 5.9nm, * H 11.0mm, * L 9.5mm measurable
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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
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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
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y’ B / x [rad/m] Measurements over Run5
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Which w parameters are significant? (Doesn’t depend much upon 2 )
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What about the other x-y combination? This effect is getting too small to see.
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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
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