1
IP Characterization Measuring the Boost Vector
Matt Weaver
PEP Meeting
May 15, 2006
2
Motivation
• Measure parameters contributing to luminosity to quantitatively verify that we’re generating all we can.
• Machine behavior in collision may have surprises that we can benefit from understanding.
3
Boost Trajectory Measurement
e+e-
LH
LLHHxB EE
xExEp
px
''
'Measure collision point {x,y,z}
and trajectories of pair {x’,y’}
z mean, spread, distribution x,y mean, spread, correlation with zx’,y’ mean, spread, correlation with z
correlation with x,y
B
z resolution ~ 60 mx,y resolution ~ 30 mx’,y’ resolution ~ 0.6 mrad
4
Boost Vector Properties
Near the waist (z << *), x and x’ are uncorrelatedx
z *2
*22
'L
LL
H
HHX ff
B
LLHHB xfxfx '''
LH
LHLH EE
Ef
)()( this 9 times
greater than
Expect that X measurements behave like this (z << *X)Boost X’ spread largely reflects HER X’ angular spread
5
Lu
min
ou
s X
-siz
e (
m)
HE
R X
’-sp
read
(m
rad
)
Move to half-integer x-tune
dynamic
dynamic
6
Far from the waist (z >> *), x and x’ are highly correlated
x
z
**
**2'
L
L
H
H
L
L
H
H
X B
zx
x B '
Boost Vector Properties
Bunch lengths are small compared to *X and comparable to *Y,
so we never see these relations fully.
However, the transition must develop on a z-scale of *, so the z-dependence of these msmts must be a measure of *
7
Boost Vector Z-Dependence
LH
LHBB
xx
'
' (luminosity-weighted)
22*22*'
z
zf
z
zfxx
L
L
H
HB
LH
LHBx
xB
2
2'
'
22
222
2
2'
2
2'
2
22
2
222'
LH
LH
L
L
H
H
LH
Bxx
xx
x
xxL
x
xxH
x
LL
x
HHx
ffff
*2*2
H
HHHH
x
xxxx z
*2'
H
HH
x
xxx z
8
Monte Carlo Validation 14mm * 14mm *
10mm * 10mm *
6mm * 6mm *
y’dy’/dy
z (cm)z (cm)
mra
d-c
m
mra
d
~ 1 week data
5 fit parametersY*
y-waist z offsetH
L
2YY’ detector error
Fit 2 is a simple sumof the two 2s
No y’ dy’/dy} covariance terms included
9
Example measurement of angular spread
Non-zero slope is reminiscentof lumi X-size measurements.
Implies X-waist offset.
“Width” is measure of *.“Height” is measure of *.
Value at z-centroid is well-determined.Limit for z>>* not reached.
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Example measurement of collision position-boost angle correlation
“Z >0”“Z <0”
11
Run5 Fit Results*
(m
m)
z (
mm
)
H
(nm
)
L
(nm
)
waistlumi centroid
12
Y
(m
)S
pec
ific
Lu
min
osi
ty
Y derived from combined-fit results shows good anti-correlation with specific luminosity
13
X s
izes
(m
) X
/
XL
“X”
XL
1
2
2.5
Ratio
of b
eam x-s
izes
X derived from Y measurements
14
Fit Results*
(m
m)
wai
st z
(m
m)
H
(nm
)
L
(nm
)
waistlumi centroid
15
Plans
Separately determine HER, LER *Y and y-waist locations
Estimate impact of coupling, dispersion {Y, Y’}
Make a measure of coupling y’B(x), x’B(y)
What to do with x? 3 measurements { X,X’,x’B(x)}, at least 4 parms
Make quantitative comparisons to beam-beam simulationversus bunch current, tune?
16
Extra Slides
17
Boost Trajectory Measurement
e+e-
n
momenta poorly measured trajectories well measured
reconstruct decay plane normal n
z
x
y
n
n
tan = - x’Bcos – y’Bsin≈
x’(or y’)B = EH x’H – EL x’L EH - EL
18
Y-Y’ Correlation in Run5 Data
y (cm)
y’ (
mra
d)
y (cm)
Y distribution
y’ vs y invarious z-bins
y’ vs y invarious z-bins
dy’
/dy
z (cm)
dy’/dyversus z
Shift in mean
Y-mean dependsupon
More work to do here
Less S-shape
19
d
x’H
/ d
z (m
rad
/cm
)Slope of x’ angular spread
Need to know emittances and beta*s to convert into a waist shift
Move to half-integer x-tune
20
X-w
aist
off
set
(cm
)From x-x’ correlation measurement assuming common waist
Move to half-integer x-tune
21
*
(mm
)
wai
st z
(m
m)
H
(nm
)
L
(nm
)
generated value
Monte Carlo Fit Results
combined fity’(z) fit only
22
Toy Monte Carlo Tests *= L*=10mmzH=zL=0
y’dy’/dy
z (cm)z (cm)
mra
d-c
m
mra
d
≤ 1 week data
7 fit parameters*H, *L
y-waist z offsets (H,L)H, L
2YY’ detector error
Correlated detector errorsare not modeled
*= L*=10mmzH=zL=0
*= L*=10mmzH=+4mmzL=-4mm
*= 8.23mmL*=13.72mmzH=zL=0
*= L*=10mmzH=+4mmzL=-4mm
*= 8.23mmL*=13.72mmzH=zL=0
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*H
(mm
)
*L
(mm
)
z H
(mm
)
z L
(mm
)
generated value
Toy Fit Results
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Fit Results*
(m
m)
wai
st z
(m
m)
H
(nm
)
L
(nm
)
25
Y
(m
)S
pec
ific
Lu
min
osi
ty
Y derived from combined-fit results shows good anti-correlation with specific luminosity
26
Y
(m
)
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