Results and Next Steps

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alignment results because it ignores a lot of parametes which are important to be free during the fit procedure.

The effect is significantly reduced by a combination of minimum bias data with other data samples such as a cosmic data sample. The ratio in 1:5 of minimum bias and cosmic muon tracks reduces the z-rescaling effect up to tens of micrometers which is relatively acceptable for the official alignment. Thus for the final 2015 alignment procedure the combinations with other data samples in a good proportion was used. This method helps to completely eliminate the z-rescaling effect, but definitely further studies in the direction of the z-rescaling issue are very important to see the complete picture and to find the reason for this weak mode.

Summary and Outlook

Inclusive beauty quark production has been measured from dimuon events. For the HERA analysis the data collected by the ZEUS detector in 2003-2007 at the centre-of-mass energy of

√s= 318 GeV with integrated luminosity of 376 pb⁻¹ were used.

The dimuon events in this analysis mainly consist of beauty, charm, heavy quarkonia, BH, and light flavour events. The beauty fraction of the dimuon events was found by comparing unlike- and like-sign dimuon events. The charm fraction was initially determined by using the charm contribution from the similar event topology of a D^∗µ sample. The isolated part of the dimuon invariant mass distribution was used to normalise the heavy quarkonia and BH contributions. The light flavour background was extracted as the difference between the like-sign dimuon samples of the data and the beauty fraction. The assumption that the light flavour background has almost no charge correlation and therefore contains almost equal number of unlike- and like-sign dimuon has been used to extract the unlike-sign light flavour contribution as a reflection of the like-sign dimuon light flavour events with an additional small correction.

The total and differential cross sections in bins of p^µ_T, η^µ,∆R^µµ and ∆φ^µµ were calculated. The additional fit procedure based on secondary vertex information was used to improve the total cross section calculations. The results were compared to, and show good agreement with, the previous analysis and NLO predictions.

As the technical part of this thesis a study of the systematic shifts of the CMS detector parts called weak modes was done. A study of weak modes in the CMS tracker alignment was performed using 2012 data collected by the CMS detector of the LHC. The alignment procedure was applied on top of the 2012 official geometry with the best estimated (true) parameters at that moment. A “misalignment” procedure was applied to the true geometry for the simulation of the three weak modes: “Twist”, “Sagitta” and “Telescope”. A study of explanations and solutions for the resolution of the weak modes in the alignment fit has been performed. A good recovery has been demonstrated for the “Twist” and “Sagitta” weak-modes while the telescope alignment should be investigated further.

A detailed study of the weak mode related to the systematic shifts such as ∆z = c· z in the CMS tracker detector has been done. All performed tests gave additional information about this mode from different points of view. A significant number of tests such as “High level structure” alignment only, alignment with fixed end caps, impact of P_T dependence of the tracks on the alignment procedure, simulation of cosmic data as collision data, introducing TID and TEC end cap disk constraints and other important tests show important results which

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might help to solve the issue. The reason for this weak mode has not been found in this study but the accumulated information might help to find it in the future. One can extract interesting conclusions from the tests which have been performed: the effect may have a dependence on the track p_T, the issue mainly comes from the TEC and TID end caps. Additional TEC and TID constraints solve the problem, but this can not be used in the final alignment results because it ignores a lot of parameters which are important to be free during the fit procedure. The effect is significantly reduced by a combination of minimum bias data with other data samples such as a cosmic data sample.

Detailed explanations about the track helix parametrisations in the ZEUS and CMS exper-iments is presented in Appendix A, B. A transformation of the track parameters from the CMS into the ZEUS format has been developed as presented in Appendix B. In Appendix C, first steps towards a synergy between corresponding ZEUS and CMS analysis concepts have been explored.

The main part of this thesis combines a physics analysis for the ZEUS experiment and technical work at CMS detector. The ZEUS analysis obtained interesting physics results for beauty production, while the technical part naturally complements the physical part and helps to get correct and precise data for future CMS analyses.

Appendix A: Helix parametrization at CMS

General information

A charged particle has a helix trajectory in a solenoidal magnetic field. For the CMS detector the magnetic field is uniform and directed in the positive “x” direction in the global coordinate system. The x-axis is directed horizontally and points to the center of the LHC ring. The y-axis is directed vertically up. The azimuthal angleφ is measured from thex-axis in thex−y plane. The radial coordinate in this plane is r. The polar angle θ is measured from the z-axis in ther−z plane. All angles are given in radians. The transverse momentumP_t, is defined as the momentum projection into the x-y plane, P_t=P ·sinθ.

A helix parametrization can be defined in many different ways. For CMS it is defined by a set of five track parameters: (qoverp, λ, φ, d_xy, d_sz) [123].

• qoverp= _|p|^q : signed inverse of momentum [GeV /c]⁻¹

• λ= (^π₂ −θ) is the polar angle at the given point

• φ is the azimutal angle at the given point

• d_xy is defined as: d_xy =v_y ·cos(φ)−v_x·sin(φ) [cm]

– (vx, vy, vz) is a reference point on the track

– the (0,0,0) point is the center of the coordinate system. This can be the center of the global coordinate system or the beam spot or some other defined point chosen as origin.

– d_xy, in general, is the signed distance from the defined origin to some reference point on the track in thex−y plane. In the case when the reference point is (0,0), dxy is geometrically the distance in thex−y plane between the (vx, vy) and (0,0) points.

The defined origin may be chosen as the beam spot, in this case d_xy is the distance inx−y plane between the beam spot and (vx, vy) points.

• d_sz is defined as: d_sz =v_z·cos(λ)−sin(λ)·(v_x·cos(φ) +v_y·sin(φ)) [cm]

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– s−z plane : the s-axis is not r. It is defined as s=vy ·cos(φ)−vx·sin(φ) for the coordinate (vx, vy). Thes−z plane is defined by the s and z axes, where (vx, vy) is the point of closest approach in the x-y plane.

– dsz: is the signed distance in thes−zplane between the points (0,0,0) and (vx, vy, vz)

• additional variables:

– R : track circle radius – ρ=q·R= q·|p|·sin(θ)

0.0029979·B_z: signed track circle radius – dz = _sin(θ)^dsz is the longitudinal impact parameter

There are only two cases when d_xy and d_sz provide sensible definitions of the distance from the (0,0,0) point to (v_x, v_y, v_z) [123]:

1. If (v_x, v_y, v_z) already is the point which corresponds to the minimum transverse distance of the helix to (0,0,0)

2. If (v_x, v_y, v_z) is close enough to it that the difference between the exact particle trajectory and a straight line is negligible.

This is usually true for tracks with high momentum. The important point is that the parameters d_xy and d_sz are calculated with respect to the relative point (0,0,0).

Because of the magnetic field direction, the helix axis will be parallel to the z-axis. Due to the Lorentz force equation, positively charged particles move in the clockwise direction in the x-y plane [124], while negative charged particles move in the counter clockwise direction. The sign of d_xy is positive when the z-axis is inside of the track helix and negative when z-axis is outside the track helix.

(a) x-y projection (b) s-z projection

Figure 7.15: Projection of the helix trajectory on the x−y plane. A - some reference point on the track trajectory. pca - point of the colsest approach from (0,0,0) to the track circle. φ₁ - azimutal angle to the reference point. φ₂ - azimutal angle to the point of closest approach. φ₃−φ₂=±^π₂ [124].

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