struction
The fourth trigger level does a complete reconstruction and classification of an event. This is realised by software algorithms running on a processor farm. The processing of the event information of the level 4 starts once the central event builder of the data-acquisition system has received the raw event data from all subdetectors. The
pipe-lines are started again, terminating the dead-time of the detector. At this mo- ment the H1 reconstruction software [83] is employed in order to reconstruct clusters and tracks for the event which are then used to reconstruct the full kinematics of an event. The accepted events are classified intoevent classes according to their physics properties (highQ2, highpT etc.). If an event cannot be assigned to any physics class
it is rejected. The accepted events are written to two different data streams, the Pro- duction Output Tapes (POTs) and the Data-Summary-Tape (DST) which are basis for the physics analysis. On the POTs, the complete event information, composed of raw and reconstructed quantities, is stored. A subset of (mainly reconstructed quantities) event information is written to DSTs awaiting further analysis.
Chapter 4
Principles of the CC Cross Section
Measurement
In the previous chapters the theory of the DIS CC interactions has been explained and the H1 detector was introduced with which CC reactions are observed. The aim of this chapter is to describe the principles of the CC cross section measurement. The importance of selection criteria is discussed first, followed by a description of the background sources and the data modelling (“Monte Carlo ” simulations) including the radiative corrections. Finally, the “pseudo charged current” method used to derive important corrections to the Monte Carlo is explained.
4.1
The Total CC Cross Section Measurement
The total cross section σmeas of the CC process measured in counting experiments
such as H1 is defined by the following formula (see equation 3.2):
σmeas = N
data
L (4.1)
whereNdata is the number of observed events andLis the collected luminosity which
is a function of the beam currents and the beam size as has been discussed already (see sections 3.2 and 3.4.5). However, equation 4.1 would be correct only for a perfect detector. In reality, counting the numberNdata of events belonging to the CC process
is not trivial, since the CC events need to be selected using an optimised set of selection criteria (“cuts”) in order to exclude events not generated by the CC process. These cuts inevitably introduce losses, so the efficiency of the cuts is an important issue. In addition, detector effects and contaminating background events need to be taken into account as well as electroweak radiative effects, when the cross section should be compared to theoretical expectations.
Selection of the CC Events and Data Modelling
The CC events are characterised by the neutrino which leaves the H1 detector un- observed, usually leading to a large unbalanced transverse momentum seen in the detector, belonging to the hadronic final state. This momentum is called pT,miss,
since it corresponds to the missing transverse momentum taken by the neutrino. A typical CC event is shown in figure 4.1 where the transverse energy imbalance can be nicely seen. In addition, any ep interaction has to come from the interaction region which means to have a well defined “vertex”. However, many events are collected by the H1 detector containing mainly backgrounds which do not originate from epinter- actions, called non-ep background such as cosmic rays and halo muons. Furthermore, the CC interactions have a relatively small cross section with respect to the other physics processes taken by the H1 detector and therefore constitute only a minority of the collected events.
In order to extract the CC events from the collected sample of all events we have to
Z R
Figure 4.1: The CC event event in the H1 detector shows large deposition of energy in the LAr calorimeter characteristic to CC events. Since the neutrino escapes undetected this energy is unbal- anced.
apply a set ofselection criteria(“cuts”) as will be discussed in detail in chapter 7. The typical selection cuts used in the CC analysis are to require high missing transverse momentum pT,miss and a well defined vertex (see subsection 7.2.4). The selection
criteria are used to reject the contaminating background, but do also reject some real signal CC events and thus introduceinefficiencies which must be properly estimated and taken into account. Due to the selection criteria applied the observed number of data events Ndata in equation 4.1, is reduced to a number of selected events Ndata
sel .
To correct for the losses in the selection one introduces aselection efficiencyE which leads to the following expression for the cross section:
σmeas= N
data sel
4.1 The Total CC Cross Section Measurement 53
The selection cuts are optimised to remove the background contamination, but still some fraction of background may remain in the data sample and therefore has to be removed:
σmeas = N
data sel −Nbg
EL . (4.3)
All of the above mentioned effects and the contamination by background must be modelled somehow in order to determine E and Nbg. Due to the complexity of the selection cuts, analytical expressions of E and Nbg are usually impossible to formu-
late. Thus, the MC simulations have been used for this purpose. Furthermore, MC programs are used for theoretical predictions of particle interactions. In addition, a major part of the background eventsNbg in the final selected sample is estimated with
the help of MC. Any discrepancy between data and simulation must be taken into account as a correction to the MC in order to model the selection procedure as good as possible. Therefore, some efficiencies, such as the trigger efficiencies, were determined from the data themselves and MC has been adjusted properly (see section 7.5).
Finally, the MC corrected for all effects observed in the data represents the real theoretical expectation of the cross section and can be compared to the experimental results. The theoretically predicted number of events is determined from the MC using the same basic cross section formula 4.1 which was used for the data:
NselM C =ELσM C. (4.4)
Having verified that the MC describes the data, taking into account inefficiencies, detector effects and assuming the same luminosity in data and MC one obtains an expression forEL in equation 4.3:
EL= N
M C sel
σM C . (4.5)
Since we do not want to limit the precision of the measurement by the statistical error of the MC events we generate many MC events corresponding to a much larger luminosity than that collected in data. This means that equation 4.5 will be changed accordingly to: EL= N M C sel σM C → NM C sel σM C · Ldata LM C (4.6)
taking care about the proper weighting of the MC via the factor Ldata
LMC to correct for the difference in the luminosity with respect to the data. In the end, implementing the last expression in the cross section formula 4.3 we obtain the measured cross section:
σmeas= N data sel −Nbg NM C sel · LM C Ldata ·σ M C. (4.7)
Electroweak Radiative Corrections
One should note that the experimentally measured cross sectionσmeas in equation 4.7
contains also radiativeCC events. These are for example events with additional pho- tons radiated from the electron before the interaction. Such events cannot easily be distinguished experimentally from those without radiation. Therefore, the MC used to model the CC events in equation 4.6 must include the radiative corrections as well. That means that the MC cross section σM C is also “radiative”. More gener-
ally, the radiative processes arise from the exchange or emission of additional bosons (γ, Z0, W±) and from diagrams containing additional loops (quantum corrections) as will be discussed in section 4.3.
However, the theory prediction of a cross section is usually given at the Born approximation, which means including only the first order processes. Thus, in order to compare the measurement to the theory we must correct the experimental cross section to the Born level [84], taking into account the radiative effects via a correction factor δrad. Then the measured σmeas and the simulated σM C radiative cross section can be expressed as a function of the Born cross section and the radiative corrections:
σmeas=σmeasBorn(1 +δrad) and σM C =σBornM C (1 +δrad). (4.8) Using the measured Born cross section σmeas
Born from equation 4.8:
σBornmeas=σmeas 1
1 +δrad (4.9)
and implementing it in equation 4.7 one gets the “measured” Born cross section:
σBornmeas= N data sel −Nbg NM C sel · LM C Ldata ·σ M C· 1 1 +δrad. (4.10)
If the data are described by MC in every respect then the Born cross section can be obtained from the measured number of events by replacing the σM C
Born defined in the
right equation 4.8 into the measured cross section given in equation 4.10:
σBornmeas= N data sel −Nbg NM C sel · LM C Ldata ·σ M C Born (4.11)
where NselM C is derived from the radiative MC after the selection criteria and other experimental inefficiencies.
Corrections to MC: Efficiencies
In contrast to the MC simulation where many effects are only approximately described, for instance the noise in the LAr trigger, in data all detector effects are there by definition. As an example for the inedaquacy of the MC simulation, the trigger response of certain subdetectors, as for example the LAr timing information “T0”, is