EJEMPLOS LITERARIOS DE LAS RELACIONES ENTRE LA

4.18.1 Calorimeter Jets

The calorimeter jets, or reconstructed jets29 _{(see Sec. 4.19.), are obtained by applying}

the jet clustering algorithm to the calorimeter signals. Calorimeter signals are defined by grouping the calorimeter cells to obtain a granularity best suited to the scale of hadronic showers.

A considerable problem in the construction of calorimetric jets is noise. In essence the output signal of a calorimeter cell, in the absence of any energy deposition, has a continuous component superimposed to electronic noise. The continuum component is subtracted from the signal. A symmetric noise remains. Typical size of noise fluctuations fake a signal of few hundred MeV.

The most common clusterization consists in assembling calorimeters cells into towers in (η, φ) space. CMS builds towers of dimension (∆η×∆φ) = 0.087×0.087 (the granularity of the hadronic section) in the central region, gradually increasing in the end-cap and forward region, for a total of 4167 towers. The noise suppression algorithm consists in building the towers using only those cells whose signals is higher than a predefine energy threshold, whose value depends on the cell position in the calorimeters, i.e. on the pseudorapidity and on the longitudinal position (where longitudinal refers to the direction pointing to the interaction region). Various threshold schemes have been considered, and the most used so far in the analyses uses 0.7 GeV and 0.85 GeV thresholds for the Hadronic calorimeter barrel and outer section respectively. In this scheme the noise contribution for a ∆R= 0.5 cone jet is equal to 1.4 GeV with a negligible loss of signal.

In ATLAS 6400 towers are built with a fixed dimension of (∆η_×∆φ) = 0.1_×0.1, corre- sponding to the granularity of the central hadronic section. There is no noise suppression applied by the tower builder algorithm.

A second and more evolved clusterization scheme has been developed to obtain a good noise suppression while avoiding large biases in the energy measurement. This scheme consists of building three-dimensional clusters associating neighboring cells which belong to any calorimeter section[1], with three minimum cell thresholds: If a cell has energy higher thanTseed, it starts a cluster, and all cells confining with it and having transverse

energy higher than Tneigh are added to it. Finally, all contour cells (i.e. cells confining

with any of the cells included with the two steps above) with transverse energy greater

29_{Although it has to be reminded that jets can be formed from other inputs, e.g., the Particle Flow objects} (until very recent times, the slightly confusing term “Energy Flow” was instead used in the literature).

thanTcontare added to the cluster. The defaults threshold values, applied to the absolute

cell energy, are Tseed = 4σnoise, Tneigh = 2σnoise,Tcont = 0σnoise. The last condition

means that all contour cells are added to the cluster.

The resulting clusters may contain one or more local maxima. Eventually, the local maxima are interpreted as contributions from multiple particles and a splitting procedure is applied to separate superimposed or connected clusters. A large reduction of noise is obtained if three-dimensional clusters are used instead of the towers.

4.18.2 Calibration

The goal of jet calibration is to correct for various effects that degrade the measurement of the jet energy in the calorimeter. These effects may be divided in two classes: detec- tor driven effects (noise, non-compensation, cracks, dead-material, magnetic field effects, pile-up) and physics driven effects (underlying event, showering effects, clustering). Many different strategies may be chosen to implement the jet calibration and to check its per- formance and systematics. In the next subsections the baseline strategies for the two experiments are discussed.

Figure 4.36: CMS Jet linearity after applying calibration (left) as a function of the particle jet pseudo-rapidity and in various particle jet energy ranges. Jet energy resolution resolution (right) as a function of particle jet energy in three ranges of pseudo-rapidity. Jets have been reconstructed with the IC algorithm with ∆R = 0.5 [7].

4.18.3 Calibration to the Particle Jet

The degradation of the jet measurement performance caused by the detector effects may be corrected by applying weights that calibrate the reconstructed jet to the particle jet. The idea to separate detector and physics effect corrections is based on the fact that these two classes of effects have different correlation to the jet kinematics.

In order to obtain the calibration parameters, both ATLAS and CMS use QCD di-jet events generated with PYTHIA [3] and simulated with the full detector descriptions. Calorimeter and particle jets are matched on the base of their distance in the (η, φ) space. In CMS the pseudo-rapidity range|η_|<4.8 is divided into 16 regions. For each region the mean ratio of reconstructed jet transverse energy (E_Tcalo) to particle jet transverse energy (E_Tptcl), Rjet = ETcalo/ETptcl, as a function of E

ptcl

T , is approximated by a set

of functions [15]. Thus, let us stress that E_Tcalo is the jet ET obtained by applying the

jet finding algorithm to the calorimeter energy deposition, which in turn is obtained by grouping valorimeter cells and applying the noise reduction procedure (as outlined in sec. 4.18.1) to the output of the full simulation, with the magnetic field included. With

Figure 4.37: ATLAS jet linearity (left) and resolution (right) after applying calibration as a function of the particle jet energy and in various pseudo-rapidity ranges (|η|<0.7 (black circles), 0.7 < _|η_| < 1.5 (red squares), 1.5 <_|η_|< 2.5 (green triangles), 2.5 < _|η_| < 3.2 (blue triangles)). Jets have been reconstructed with the ∆R = 0.7 cone algorithm. E_Tptcl (where ptcl stands for “particles”) we denote the transverse energy obtained by applying the jet finding algorithm to the particles generated by the Monte Carlo. The values ofRjet obtained are then used to correct the transverse jet energy. Since Rjet is a

function ofE_Tptcl, which is unknown in real data, an iterative procedure is used to obtain for each calorimeter jet energy the best estimate of the calibration parameter [7]. The linearity and the resolution obtained by applying this calibration to a statistical independent sample of QCD di-jet events are shown in Figure 4.36. The maximum deviation from linearity for theET range [20 GeV - 4 TeV] is∼5%. The energy resolution in the region|η|<1.4 is :

σ(ET) ET = p 1.25 ET(GeV) ⊕ 5.6 ET(GeV) ⊕ 0.03 (4.98) .

In ATLAS the calibrated jet energy is obtained by applying the weights (wi) to the cell

energies (Ecell) that compose the jets:

Ecalib=X

i

wiEi (4.99)

The weights, which depend on the position and energy density of the cells, are extracted by minimizing a χ2 defined as : χ2 =X j Ecalib j E_jptcl −1 !2 (4.100) where the index j runs on the ensemble of jets of all the events. The dependence of the weight wi on the cell energy density is parameterized with a polynomial. The basic idea

behind this kind of calibration, which exploits the shower shapes, is that hadronic showers are diffuse while electromagnetic ones are dense. Thereforewiis typically larger than 1 for

low cell energy densities and is around 1 for high cell energy densities. This is a consequence of the fact that the ATLAS calorimeter (as the CMS one) is non–compensating (i.e. it

has different efficiency in the measurement of the electromagnetic and hadronic part of the shower), and thus the calorimeter response to hadrons is non–linear with the energy. To understand the lower (and non–linear) response of non–compensating calorimeters to hadrons, consider the following three facts:

• Part of the shower produced by hadrons in the calorimeter is electromagnetic. This

is because of the decay of π0 produced in the shower.

• In non–compensating calorimeters, the efficiency of the measurement of the electro-

magnetic and hadronic part of the shower are different (e/h ₆= 1). This is mainly because part of the hadronic energy is lost in nuclear reactions to break the nuclei.

• The electromagnetic fraction,i.e. the fraction of the shower energy carried by pho-

tons, depends on the energy of the impinging hadron. This can be understood with the following, simplified model [16]. Suppose a charged pion is impinging on the calorimeter: on the first hadronic interaction, mainly charged and neutral pions will be produced. On average, 1/3 of the energy will be carried by neutral pions. On the second stage, the fraction of the energy carried byπ0_{will bef}

em = 1/3+2/3·1/3. On

then–th stage,fem= 1−(1−1/3)n, wheren, the maximum number of interactions,

is energy dependent.

This three facts together make the calorimeter response to hadrons non–linear. Fur- thermore, since the fraction of produced neutral pions undergoes large fluctuation, non- compensation also induces a worse resolution in the jet energy measurement.

The linearity and resolution, as a function of the particle jet energy, obtained on a sample of QCD di-jet events for various pseudo-rapidity regions are shown on figure 4.37. The maximum deviation from linearity is within 2% in the jet energy range [40 GeV - 2 TeV] and the resolution in the pseudo-rapidity region|η|<0.7 is equal to :

σ(E) E = 0.67 p E(GeV) ⊕ 4.3 E(GeV) ⊕0.02 (4.101)

The jet linearity, as estimated using a sample of events with different parton composition and topology, generated by HERWIG [17], is also well within_±2%.

4.18.4 Parton-level calibration

Calibration to the parton jet can be implemented as a second step in addition to particle jet calibration or as a single step which corrects for both detector and physics effect. ATLAS is presently considering the first strategy, while CMS has implemented both [18]. The definition of the parton jet energy is somehow artificial, since partons cannot be defined as isolated objects (not even in the short time scales of the hard interactions). Furthermore, as previously, discussed, the association of a primary parton to a jet is unavoidably dependent upon the Monte Carlo one is using. It has been however widely used by previous experiments [19]. It is fair to say that, with this method one can use the kinematics of the reconstructed partons to look for mass peaks; however, the method cannot yield an accurate mass measurement.

A first difference between particle and parton jet is caused by the smearing produced during final state radiation and fragmentation. Both phenomena generate particles which may not be clustered into the particle jet. This results in a fraction of the parton jet energy not attributed to the particle jet. In the case of cone clustering algorithms these losses are indicated as out-of-cone losses. Second, some of the particles generated in the underlying event may fall in the jet region and be attributed to the particle jet although this contribution is not related to the parent parton jet. In this section some possible strategies to correct for these effects are discussed.

A first possibility, exploited by CMS, to obtain the parton jet energy scale is to use simulated events and obtain a calibration constant kptcl =ETptcl/E

parton

T as a function of

the transverse energy of the parton. In figure 4.38 (left) the values ofkptcl are shown for

Figure 4.38: Left: distributions of the mean value of kptcl as a function of transverse

parton energy for QCD di-jets (green square), for quark jets (open triangle) and for gluon jets (open crosses). Right: distributions of calibration coefficient obtained from γ+jets events (open circles) and their true value for generic QCD jet (full green squares) and quark jets (red triangles). Jets are reconstructed with ∆R = 0.5 cone algorithm in the pseudo-rapidity region_|η_|<1.5 [7].

due to the different fragmentation of gluon and quark generated jets is estimated by com- paring thekptcl values obtained in the two cases. If ∆R= 0.5 cone jets are considered the

calibration coefficients differ by 5% forET = 40 GeV [20].

A second possibility to obtain calibration is to exploit kinematic constraints from real data such as the W mass inW → jj decays or the pT balance in events where the jet is

generated back-to-back with a well measured particle, either a Z decaying to leptons or a γ. In this note studies usingγ+jet events are discussed.

ATLAS and CMS plan to use these events in different ways. CMS exploits thepT balance

constraint to obtain the calibration from calorimeter jet to parton jet while ATLAS plans to apply first the calibration to particle jet and than use the pT balance constraint as a

further step to correct to the parton jet energy scale. In the first phase of data taking the primary role of these events will be to help in understanding particle jet level calibration by comparing the data and Monte CarlopT balance distributions.

The selection of events in CMS requires a well isolated photon having aφopening angle with the jet ∆φ >172o [7, 20]. Events containing more than one jet with ET >20 GeV

are rejected. The main background is given by QCD di-jet events where one jet is misiden- tified as a photon. Background is suppressed well below the signal for E_Tγ > 150 GeV. The ratio kjet = pcaloT /p

γ

T is calculated as a function of p γ

T and defines the calibration

coefficients. The complication given by the presence of initial state radiation that spoils the pT balance constraint is partially overcome by defining, for each pγ_T, the calibration

coefficient to correspond to the most probable value of the pcalo_T /pγ_T spectrum. The pre- dicted values for the calibration coefficients and their true values (ktrue = pcaloT /p

parton T )

for quark jets and for jets from QCD background are shown in figure 4.39. At a transverse energy of 100 GeV a difference of about 10% is observed between QCD jets and quark jets. It should be noticed that this difference may be originated both by the different fragmentation spectrum of particles inside the jet and by the different out-of-cone losses. ThepT coverage of this channel after analysis cuts, indicates that, from a purely statistics

evaluation, with 10f b−1 a 1% statistical error is obtained up to a transverse energy of 800 GeV in the central region.

Figure 4.39: Distribution ofpT Balance = (pjet_T −pγ_T)/pγ_T as a function of (pjet_T +pγ_T)/2 obtained by ATLAS on a sample ofγ+jets events. ThepT Balance distribution is shown for calibrated calorimeter jets (full red circles), particle jets (blue triangles) and partons (black squares) [21]. Jet have been reconstructed with ∆R= 0.7 cone algorithm.

withE_Tγ >30 GeV having an opening angle with respect to the highestpT jet in the event

of ∆φ >168o [10, 21]. In order not to introduce a bias in the definition of the calibration coefficient due to the initial state radiation, the binning is done in bins of (pγ_T +pjet_T )/2. The calibration coefficient in each bin, as for CMS, is defined as the most probable value of thepT balance spectrum. Distributions of thepT balance, defined as (p_Tjet−pγ_T)/pγ_T, as

a function of (pjet_T +pγ_T)/2 are shown in figure 4.39. The three curves correspond to thepT

balance obtained using the jet calibrated to the particle jet (as described in the previous section), the particle jet, and the parent parton. The balance obtained from particle jets and from calibrated jets agree within _±2% indicating that the particle level calibration, obtained on QCD di-jet events, may be applied also to different event topologies and dif- ferent mixtures of partons. This result is somehow in disagreement with what is obtained by CMS (figure 4.38) where a large difference between quark and gluon jets is observed. It should be noticed, however, that the different cone size and the different correction for energy inside the cone makes it difficult to better understand the significance of this discrepancy. We also notice that γ+jet at LHC is dominated by quark jets, while the typical QCD jets are gluon jets. The particle level and parton level balance agree within

±1% indicating that underlying event contribution and the out-of-cone losses compensate

each other to this level. Studies are ongoing to disentangle the two effects.