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

Measureof coupling?

eeB ppp

Using MIA results of Apr 21 ’06 2

H 0.36nm, 2L 1.13nm, *H 11.0mm, *L 9.5mm

collidingelectrons

collidingpositrons

mea

sura

ble

Which w parameters are significant?

“waist shift”

Angle-position correlation

collidingelectrons

collidingpositrons

mea

sura

ble

Which w parameters are significant?

“waist shift”

y’(z) Fit Only y’(z) + dy’/dy FitCommon *, zw

Unable to describe this shapewithout separate values for

waists and *s

y’(z) + dy’/dy FitDiffering *, zw

Inputs: 2H 0.36nm, 2

L 1.13nm, *H 11.0mm, *L 9.5mm

Without coupling

*y (mm) H (nm) L (nm) zw (mm)

y’B 9.9 0.36 0.8 0.20

y’B+y’B/y

common *,zw

10.12 0.405 0.58 0.11

y’B+y’B/y

differing *,zw

10.78 / 9.4 0.39 0.81 0.20 / -0.01

With coupling

y’B 17.8 1.197 0.16 -3.22

y’B+y’B/y

common *,zw

15.0 0.81 1.8 -3.32

y’B+y’B/y

differing *,zw

13.0 / 15.6 0.67 2.25 -6.6 / 0.8

Using MIA results of Apr 21 ’06Replacing 2

H 3.0nm, 2L 5.9nm, *H 11.0mm, *L 9.5mmm

easu

rab

le

mea

sura

ble

Inputs: 2H 3.0nm, 2

L 5.9nm, *H 11.0mm, *L 9.5mm

Without coupling

*y (mm) H (nm) L (nm) zw (mm)

y’B 10.0 2.8 6.0 0.2

y’B+y’B/y

common *,zw

10.6 3.3 3.3 0.21

y’B+y’B/y

differing *,zw

11.0 / 9.5 3.0 6.0 0.26 / -0.08

With coupling

y’B 11.2 3.4 6.7 -0.34

y’B+y’B/y

differing *,zw

11.7 3.8 4.2 -0.51

y’B+y’B/y

common *,zw

11.9 / 10.8 3.3 8.1 -0.9 / 0.3

dy’B/dx = measurement of coupling?

y’ (

mra

d)

x (cm)

Example from data

Expectation using MIA results

dy’

/dx

z (cm)

0.36nm, 1.13nm 3.0nm, 5.9nm

y’ B

/x

[ra

d/m

]Measurements over Run5

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

What about the other x-y combination?

This effect is getting too small to see.

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