M. Weaver, SLAC, CA 94025, USA
W. Kozanecki, CEA/Saclay, F91191 Gif-sur-Yvette, France
B. Viaud, Université de Montréal, Montréal, Québec, Canada
Abstract
We present a novel approach to characterize the
colliding-beam phase space at the interaction point of
the energy-asymmetric PEP-II B-Factory. The method
exploits the fact that the transverse-boost distribution
of e+ e– → μ+ μ– events reconstructed in the BABAR
detector reflects that of the colliding electrons and
positrons. The mean boost direction, when combined
with the measured orientation of the luminous
ellipsoid, determines the e+-e– crossing angles. The
average angular spread of the transverse boost vector
provides an accurate measure of the angular
divergence of the incoming high-energy beam,
confirming the presence of a sizeable dynamic-β
effect. The longitudinal and transverse dependence of
the boost angular spread also allow to extract from the
continuously monitored distributions detailed
information about the emittances and IP β-functions of
both beams during high-luminosity operation.
Introduction
Boost Angles Measurement Technique
• PEP-II collides 9.0 GeV electrons upon 3.1 GeV
positrons.
• The high resolution BABAR particle tracking
detector records e+ e– → μ+ μ– event tracks.
• The boost vector angles {xB’,yB’} can be
reconstructed from the μ± tracks.
• The e± trajectories, and therefore IP parameters,
are

p
reflected in the boost vector angles.
Boost

p  yB
• μ± tracks acquire only a small curvature in the
solenoidal detector field
• μ± momentum is poorly measured
• μ± trajectory is measured precisely
• Measure the boost angles using the vector ^n normal to
the μ+ μ– decay plane.

p
e
n
f (  ) 
yB  f  y  f  y
ˆ
p
ˆ
p

ˆ
p



n

l
y
n
z

y



nˆ 
e
y
ˆ
p
f
U
x

tan ln   x cosfn  y sinfn  l
2
2
2
2
2
 l   x cos fn   y sin fn
E(  )
E  E
n
• Observables are luminosity-weighted
yB
yB 
 L
 L
 L  yB  yB
2
 y 
B
 L

2
- Introduces z-dependent correlations
Dynamic β Observation
Crossing Angle Measurement
• Mean x’B is an E-weighted sum of beam x’ angles
xB  f  x  f  x
• Mean x’L is a size-weighted sum of beam x’ angles
x  x2   x  x2 
 
xL
1  x2   1  x2 
• Measurements are performed in collision
• Dynamic effects (beam-beam) are clearly visible
• X-size of luminous region is proportional to βx*’s
• Size of boost x’ (RMS) is inversely related to βx*’s
Boost z-Dependence
• Fit for zw,β, ε-, ε+


2  
1

 
 f 2    f 2     z  z w 
2 

2 

        
yB
 z  zw 


1 
 
  
waist
Amplitude2
Peak indicates
waist location
Time of x-tune
change towards
½-integer
• Their difference is a measure of the x’ crossing angle
2
2 




1
x
x 
   f  f  
xB  xL
x  x


2
2
2
 x  x 


 
Asymptotic
Limit2
x-size
decrease
 x  x
y
yB ( y , z ) 
 
 1.03 x  x
 2
2
 z  z w      2




     


    2
  yy 
 z  z w 
    


Optimum found during
crossing angle experiment
z = -1
z = +1
x-divergence
increase
IP Parameter Results
○ mean collision point
● βy waist location
○ dy’/dy(z) + σy’(z) fits
● σy’(z) fits only
A vertical β-function waist location
(common for both beams) is fit to
the measurements. The
longitudinal collision location can
be seen to sometimes deviate.
A common βy-function IP value is
fit to either the σy’(z) measurement
or both the σy’(z) and dy’/dy (z)
measurements. A systematic shift
is seen which might be explained
by a more complete consideration
of x-y coupling.
○ dy’/dy(z) + σy’(z) fits
● σy’(z) fits only
○ dy’/dy(z) + σy’(z) fits
● σy’(z) fits only
Individual vertical emittances for the
electron beam (HER) and positron
beam (LER) are also fit to the data.
The combined fit to the σy’(z) and
dy’/dy (z) measurements has
considerably better statistical
precision for the determination of the
positron beam emittance. Initial
investigations also point towards the
presence of x-y coupling as the source
of the observed systematic shift. An
understanding of this systematic
would allow a precise determination
of the vertical emittances.