Measurement of the Z boson cross-section in - Harvard University ...

Chapter 3: Luminosity Measurement at the LHC and in ATLAS 75
3.2.2 Beam size measurement using Van der Meer scans
An accurate method of measuring the transverse beam size is to displace the
beams against each other and monitor the relative luminosity as a function of the
beam separation (Figure 3.4). Known as separation scans or Van der Meer scans,
this method can also be used to minimize the beam separation in order to maximize
instantaneous luminosity.
]
−2
p)
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[Hz (10
2
/ N
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Rate(PV|MBTS_1) / N
12000
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ATLAS preliminary
RMS: 50.0 µ m
Σx:
(47.3 ± 0.2) µ m
0
−300 −200 −100 0 100 200 300
Δ x [ µ m]
]
−2
p)
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[Hz (10
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/ N
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Rate(PV|MBTS_1) / N
12000
10000
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ATLAS preliminary
RMS: 60.6 µ m
Σy:
(56.3 ± 0.3) µ m
0
−300 −200 −100 0 100 200 300
Δ y [ µ m]
Figure 3.4: Variation in the rate of primary vertices seen in the ATLAS inner detector
as the two beams are displaced relative to each other in the horizontal plane (left)
and in the vertical plane (right). The beam size in each direction obtained from the
double Gaussian fit is shown.
The luminosity reduction due to offset beams is given by formula 3.10:
W = exp(− d2
4σ2 ) (3.15)
i
where d is the beam separation along the ith axis, and i = x, y. A fit of the observed
variation in luminosity, as shown in Figure 3.4 [58], to the above expression gives
the beam size. The scans are performed separately in the horizontal and vertical