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CERN-THESIS-2012-153 26/07/2012 - CERN Document Server

CERN-THESIS-2012-153 26/07/2012 - CERN Document Server

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Luminosity measurement<br />

Accurate determination of the luminosity is an essential ingredient for many different measurements per-<br />

formed by the LHC experiments. The luminosity of a pp collider can be expressed in terms of the rate of<br />

inelastic collisions, Rinel, and the pp inelastic cross-section, σinel:<br />

which can be rewritten as:<br />

L = Rinel<br />

σinel<br />

L = µnbfrev<br />

σinel<br />

with frev and nb previously defined for Equation 3.1, and µ is the average number of inelastic interactions<br />

per BC. Thus, by measuring the ratio µ/σinel, the instantaneous luminosity can be determined. In order to<br />

asses and control systematic uncertainties in the measurement of the luminosity, not only several detectors<br />

are used, but also multiple algorithms or counting techniques. Each algorithm having different acceptance,<br />

response to pile-up and beam-induce backgrounds.<br />

From Equation 3.3 it follows:<br />

L = µnbfrev<br />

σinel<br />

= µvisnbfrev<br />

εσinel<br />

(3.2)<br />

(3.3)<br />

= µvisnbfrev<br />

, (3.4)<br />

σvis<br />

where ε is the event-selection efficiency for one inelastic pp collision, and µvis ≡ εµ is the average number of<br />

visible inelastic interactions per BC (minimum number of pp collisions per BC passing the event selection).<br />

The visible cross section σvis ≡ εσinel is the calibration constant relating the experimentally observable<br />

quatity µvis to the luminosity L. It is then possible to obtain the absolute luminosity calibration, from mea-<br />

sured accelerator parameters, both for online monitoring and for offline analysis. The delivered luminosity<br />

can be written as:<br />

L = nbfrevn1n2<br />

2πΣxΣy<br />

where n1 and n2 are the numbers of particles in the two colliding bunches and Σx and Σy characterize the<br />

widths of the horizontal and vertical beam profiles. The widths of the beam profile are measured using van der<br />

Meer (vdM) scans [71]. In this technique, the observed event rate is recorded while scanning the two beams<br />

across each other (first horizontally, then vertically), yielding two bell-shaped curves, with the maximum<br />

rate at zero separation, from which one extracts the values of Σx and Σy. Combining with an external<br />

36<br />

(3.5)

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