Nuclear Instruments and Methods in Physics Research A 731 (2013) 194–197

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Nuclear Instruments and Methods inPhysics Research A

0168-90http://d

n CorrTel.: +41

E-m

journal homepage: www.elsevier.com/locate/nima

Impact of pixel size and shape on physics analyses

Christoph Nägeli a,b,n, Roland Horisberger a

a Paul Scherrer Institute, 5232 Villigen, Switzerlandb ETH Zürich, Schafmattstrasse 20, 8093 Zürich, Switzerland

a r t i c l e i n f o

Available online 15 May 2013

Keywords:Pixel detectorImpact parameter resolutionPixel resolutionBs-μþμ−

02/$ - see front matter & 2013 Elsevier B.V. Ax.doi.org/10.1016/j.nima.2013.05.021

esponding author at: Paul Scherrer Institute79 230 07 08.

ail address: christoph.naegeli@psi.ch (C. Näge

a b s t r a c t

The choice of the pixel shape and size in the r�ϕ and z-directions results in different position resolutions,that in turn, influence the impact parameter resolution. A study based on a Monte Carlo simulation ispresented to quantify the effect of the impact parameter resolution on the search for new physics usingthe rare decay B0

s-μþμ− . The presented study illustrates the performance of this search for differentresolution scenarios. For an optimal result, it is found that the transversal and longitudinal impactparameter resolution must be balanced.

& 2013 Elsevier B.V. All rights reserved.

1. Introduction

The two general purpose experiments at the LHC [1], ATLASand CMS, have chosen different pixel geometries for their detec-tors. CMS has chosen to use a more square pixel, with size of 100�150 μm2 [2], while ATLAS has chosen to use a more rectangularpixel with size of 50� 400 μm2 [3].

Studies of pixel detectors usually report the hit resolutiontogether with the impact parameter resolution. For events withhundreds of tracks, it is crucial to know whether two tracksactually come from the same vertex. This is because the signalfor long lived particles is reconstructed by fitting pairs of tracks toa common detached vertex. The more precise the impact para-meter, the more combinatorial background can be rejected. On theother hand, physics analyses already start with reconstructedtracks, incorporating the impact parameter and its resolution ina non-transparent way. In general, these analyses do not considerhypothetical detector resolutions and do not estimate what wouldbe gained if the resolution was changed. This leaves a gap as thefinal goal is not the impact parameter resolution but rather thephysics result.

The aim of this study is to investigate the effect of the pixel sizeand shape on the outcome of a hypothetical search for B0

s-μþμ�.

2. B0s-μþμ�

ATLAS, CMS and LHCb are looking for the rare decay B0s-μþμ�

[4–6]. This decay has a clear signal topology, two muons

ll rights reserved.

, 5232 Villigen, Switzerland.

li).

originating from the same vertex displaced from the collisionvertex. This channel is sensitive to new physics as it is heavilysuppressed in the standard model due to an effective flavorchanging neutral current and helicity suppression. The branchingfraction can change due to new couplings and new particlesentering the loops in the Feynman diagrams [7].

If one assumes a perfect detector resolution of the pixeldetector, the signal and the background can be separated com-pletely. Hence, this search provides an excellent candidate for sucha study.

3. Tracking

A track can be described by five parameters, a reference point,and the direction of the track. In the special case of a constantmagnetic field, these variables can be defined as follows [8]:

�

d0, transversal impact parameter. � dz , longitudinal impact parameter. � ϕ, azimuthal angle of track momentum. � θ, polar angle of track momentum. � pT , magnitude of momentum in plane perpendicular to beam

axis describing curvature of helix.

The direction of the track is specified using the variables ϕ, θ, andpT while the reference point is described by the impact parametersd0 and dz . The ability to decide whether two tracks meet in three-dimensional space is given by the resolution of the two impactparameters and these are determined mostly by the pixel detector.

The resolution of the detector itself ðspixÞ is given by the size ofthe pixel cells and the charge sharing between the pixels assumingthe charge produced by a ionizing particle can be measured with asufficient degree of accuracy. To measure the charge and trigger

s→μμ)

0.02

0.03

0.04×10-3

C. Nägeli, R. Horisberger / Nuclear Instruments and Methods in Physics Research A 731 (2013) 194–197 195

the pixel, the size of the readout electronics is limited by the sizeof the pixel. Therefore smaller pixels suggest a less complexreadout for a given technology choice.

The impact parameter resolution can be understood frombasically two effects:

UL(B

0.01

(1) Multiple scattering. (2) Intrinsic detector resolution.

σ(d0)/μm0 100 200300σ(d

z )/μm 0100

2003000

Fig. 1. Upper limit as a function of the impact parameter resolution.

The multiple scattering gives a term which can be described by∼A=pT . The factor A mainly depends on the amount of material inthe first layer and the distance of the first layer to the beam axis.The intrinsic detector resolution, on the other hand, yields aconstant term B and is mainly given by the distance of the layersand the pixel resolution.

×10-3

0.03)

4. Setup

Two Monte Carlo simulations have been produced at a center ofmass energy

ffiffi

sp ¼ 8 TeV:

s→μμ

� Signal simulation, each containing one B0

s-μþμ�.

L(B

�

0.02U

Background simulation, minimum bias events containing bquarks and two muons with pT 42:5 GeV.

In both simulations, candidates are created as follows:

0 100 200 300

0.01

�

Combine two muons to form a candidate. σ(dz)/μm �

×10-3

Apply a loose preselection given in Table 1 where d3;truth meansthe Monte Carlo three-dimensional flight length for signalsimulation. For background simulation it is the distance fromthe primary vertex to the point of closest approach of thetwo muons.

�

0 100 200 300

UL(Bs→

μμ)

0.01

0.02

0.03

σ(d0)/μm

Fig. 2. One-dimensional curves along constant resolutions.

Randomize kinematic variables of the candidate according toan assumed resolution scenario.

Only one variable was used to discriminate the signal from back-ground due to the low statistics of the background Monte Carlosimulation. The distance of closest approach (doca) of the twomuons was used as the selection criteria and it was chosen in sucha way that the signal efficiency is εsig ¼ 0:9. In a perfect detector,this variable is enough to completely differentiate the signal fromthe background candidates. The performance of a given resolutionscenario was evaluated computing the expected upper limit (UL)on the branching fraction.

5. Results

5.1. Intrinsic detector resolution

To understand qualitatively the effect of the asymptotic term,the multiple scattering term has been set to zero. An overview canbe seen in Figs. 1 and 2.

For perfect resolution sðd0Þ ¼ sðdzÞ ¼ 0 μm, one can clearly seethe drop in the expected upper limit. Also, the contour lines ofconstant upper limit tend to have an elliptic shape around theperfect detector. For a fixed z impact parameter resolution, there is

Table 1Preselection cuts.

pT ðGeVÞ 42:5jηðμÞj o2:5d3;truth ðμmÞ 425

a corresponding transverse impact parameter resolution whereimprovement in the transverse plane does not further improve theUL. The same is true if one fixes the transverse impact parameterresolution.

The upper limit sensitivity dependence on the pseudo rapidity(η) of the tracks was also studied. Analogously to Fig. 1 plotsshowing η dependence are shown in Fig. 3. It can be seen that forhigh η�region, improvement of sðd0Þ is much more effective inimproving the UL, while for the low η�region, the improvement ofsðdzÞ is more effective. The physical result should depend on theerror ellipse around the track. For high η�tracks, the z-resolutionis measured almost parallel to the track direction, thus the semi-axis of the error ellipse actually is given by sin θ � sðdzÞ. Hence, forthe high η�region, the measurement of this error ellipse isdominated by the uncertainty in the xy-plane. For the lowη�region one can consider the extreme case η¼ 0. For η¼ 0 tracks,the only important quantity for two tracks to meet is the zcoordinate of the tracks.

Fig. 3. η dependence of resolution impact.

Table 2Comparison of the current CMS detector resolution to the estimated one accordingto the CMS TDR for the pixel upgrade. Cut value of the signal selection variabledistance of closest approach. Expected number of background events (in dimuonmass range 5:26om ðμμÞ=GeVo5:46) and the expected upper limit.

Current Upgrade Change (%)

doca 139 μm 75 μm −46Nbkg 6078 3976 −35UL ð3:4þ0:2

−0:2 Þ � 10−5 ð2:8þ0:2−0:2 Þ � 10−5 −18

Table 3Expected results for the simulated CMS resolution [9] and the enlarged pixel model.

Current Long Change (%)

doca 139 μm 240 μm +73Nbkg 6078 8379 +38UL ð3:4þ0:2

−0:2 Þ � 10−5 3:9þ0:1−0:2 � 10−5 +15

Table 4Expected results for the simulated CMS resolution [9] and enlarged pixel model,both excluding multiple scattering effects.

Current Long Change (%)

doca 66 μm 214 μm +224Nbkg 3676 8179 +125UL ð2:7þ0:2

−0:2 Þ � 10−5 ð3:9þ0:2−0:2 Þ � 10−5 +32

C. Nägeli, R. Horisberger / Nuclear Instruments and Methods in Physics Research A 731 (2013) 194–197196

5.2. CMS like detector

Two resolution scenarios have been studied according to theCMS TDR for the pixel upgrade [9, Section 2.2.2]: the currentresolution and the resolution after the pixel upgrade. The pre-selection was tightened, with respect to Table 1, to pT 43 GeV andjηjo1:4 (CMS barrel region). Table 2 shows the outcome of thetwo analyses.

Furthermore, the effect of enlarging the z pitch of the pixels onthe impact parameter resolution was investigated. This is becausean enlarged pixel z-resolution should mostly affect the intrinsicdetector resolution. The effect was estimated by consideringstraight tracks ðpT-∞Þ. A Monte Carlo study was done as follows:

(1)

Generate random tracks with associated hits in given pixellayers.

(2)

Randomize pixel hits using the assumed resolution. (3) Fit a track and compute the impact parameter.

This was done with two resolution scenarios: a CMS like scenarioand one with the pixel z-resolution enlarged by a factor 3.5. Thecomputed asymptotic z impact parameter resolution agrees rea-sonably well with the one measured by CMS. Furthermore, thisanalysis shows that the z impact parameter resolution is alsoenlarged by the same factor. This motivated the choice to enlargethe asymptotic resolution for the long pixel detector by the samefactor of 3.5.

The p dependent z impact parameter resolution of the longpixel detector was computed as follows:

�

Decompose CMS detector resolution into multiple scatteringpart and asymptotic part (Assume they add quadratically).

�

Enlarge the asymptotic part. � Add them quadratically to get long pixel detector resolution.

The preselection was again tightened to 3 Gev. The results areshown in Table 3 for the full model. In Table 4 only the asymptoticterm is considered. A more realistic estimate would be somethingin between these two cases.

5.3. Conclusions

�

For accurately selecting secondary vertices the resolution of thelongitudinal and transverse impact parameters must bebalanced. An excellent longitudinal resolution together with apoor transversal resolution will not significantly improve the

C. Nägeli, R. Horisberger / Nuclear Instruments and Methods in Physics Research A 731 (2013) 194–197 197

sensitivity as the background rejection would be limited by thepoor transversal resolution and vice versa.

�

Enlarging the z pixel size of a detector like CMS would restrainphysics analyses reach, as it deteriorates the IP resolution.

Acknowledgments

We would like to thank the PSI CMS pixel group for manycomments on this paper.

References

[1] Lyndon Evans, Philip Bryant, Journal of Instrumentation 3 (2008) S08001.[2] CMS Collaboration, Journal of Instrumentation 03 (2008) S08004.[3] ATLAS Collaboration, Journal of Instrumentation 3 (2008) 823.[4] ATLAS Collaboration, Physics Letters B 713 (2012) 387, arXiv:1204.0735 [hep-

ex].[5] CMS Collaboration, Journal of High Energy Physics 2012 (4) (2012) 33.[6] LHCb Collaboration, Physical Review Letters 108 (2012) 231801,

arXiv:1203.4493 [hep-ex].[7] J.R. Ellis, J.S. Lee, A. Pilaftsis, Physical Review D 76 (2007) 115011.[8] P. Billoir, S. Qian, Nuclear Instrumentation and Methods in Physics A 311 (1992)

139.[9] CMS Collaboration, CMS Technical Design Report for the Pixel Detector

Upgrade, CERN-LHCC-2012-016, CMS-TDR-011.