2 years status report and thesis outline

person.gif A. Salzburger, University of Innsbruck and CERN PH-ATC

persons.gif Supervision:

  • Prof. Dr. Dietmar Kuhn, University of Innsbruck, Austria
  • Dr. Markus Elsing, PH-ATC, CERN

days.gif Start of PhD_StaraWersja program: 1st of July, 2003
days.gif Date: 1st of June, 2005


A high precision W mass measurement with the ATLAS Detector

Introduction

The measurement of the $ W $ mass with a precision of below 25 MeV is a challanging aim for the ATLAS detector. If this precision can be achieved and in combination with results from the CMS experiment an overall precision of better than 15 MeV for the $ W $ mass at the LHC can be expected. A precise knowledge of the $ W $ mass is not only a test of the Standard Model, but is in addition highly sensitive for physic models beyond the standard model (a more detailed description of the fundamental relations can be found in the Appendix of this report).

For the LHC the error on the direct measurment of the $ W $ mass (such as for various other measurements) will be purely dominated by the systematical error as the statistical error vanishes due to the high luminosity and crosssection. In particular, for the measurement of $ M_{W} $, the dominating factor of the systematical error is the knowledge of the lepton mass and energy scale [3,4]. The precision of the overall lepton (muon) mass scale depends mainly on the knowlegde of the material and the magnetic field and its correct treatment in track reconstruction algorithms.

The desired precision of 25 MeV for the $ W $ mass with the ATLAS detector is planed to be achieved by using the leptonic decay channel of the $ W $: $ W \rightarrow l\nu, $ where $ l=e,\mu  $. As the longitudinal momentum of the neutrino can not be measured, the measurement is done using the transverse momentum of lepton and neutrino, which is calculated through a recoil method [2],[3]. Results from CDF and D0 [4] have shown that an unprecise knowlegde of the total lepton energy and momentum scale is the dominating source of uncertainty of the $ W $ mass measurement. The knowledge of the lepton mass scale requires a deep understanding of the material in the ATLAS Inner Detector with a uncertainty of about 1% which is of an order of magnitude better than in any comparable high energy physics experiment so far. In addition the magnetic field map has to be known with a precision of 0.1%. This also requires tracking algorithms to process this detailed input. The methology on how to achieve such a detailed description and its correct treatment including energy loss and multiple scattering effects during track extrapolation will be described in this thesis.

These stringent goals can only be met using a software infrastructure that explicitely allows to reach this performance figures. High granularity and newly developed tracking algorithms and concepts have to be implemented into the the reconstruction software. Achieving this high precision with have direct influence on many other measurements in ATLAS.

Subject of this thesis will be the development of such an infrastructure in collaboration with other members of the ATLAS tracking group. The validation and its application in view of a prospect $ W $ mass measurement will be presented.

Realization

A vital part of most track reconstruction algorithm is the transport or propagation of track parameters and their associated covariances to measurement surfaces in the detector. The correct treatment of energy loss and multiple scattering during this extrapolation process are together with the precise knowledge of the magnetic field crucial for the precision that can be achieved in track reconstruction.

In the context of the general restructuring of the ATLAS reconstruction software a new track extrapolation package has been developed to serve this functionality. The software was designed with high granularity in the various steps of the track extrapolation process. This enables systematic studies of single effects (detail of material description, magnetic field parameterizations, etc.) on the track reconstruction, and to learn how to regulate these effects in the simulation.

The track extrapolation can be in general divided into two different steps:

  • purely mathematical propagation
  • interaction with material during propagation
A correct propagation requires in addition the infrastructure to get the material passed by the track such as the magnetic field access at any stage. For this purpose a complete new software framework has been established, including the development of a fully navigable reconstruction geometry that is characterized through a connective volume geometry. Currently three propagation methods are in use, following a straight line or a helical track model, such as a Runge-Kutta based propagation. The material integration for this propagation methods has been implemented. In addition, a new propagation method that takes material effects in a continous way during the Runge-Kutta based propagation into account has been developed and integrated into the extrapolation scheme. This new propagation method has not been used so far in track reconstruction and will allow a more realistic treatment of the passage of muons through dense material. It will serve as a the main propagation method for combined Inner Detector - Muon System tracking (passage through Calorimeter, material in Muon System). The construction of this reconstruction geometry is closely bound to the common ATLAS detector description GeoModel to avoid duplication of detector description specifications.

In prospect of the upcoming "as-build material description" of the ATLAS Data Challange 3, the material integration has been designed in a modular way, to be adopted and to allow studies of the impact of this more realistice material description on the ATLAS track reconstruction performance.

The intrinsic navigation of the track extrapolation enables a predictive extrapolation within this geometry. By changing the material interaction to be dependend on a random number generation the extrapolation serves as a track creation engine producing Monte Carlo tracks by using the reconstruction geometry. This is crucial for the validation of various tracking algorithms (track fitters, holes on track search, etc.). It also enhances dedicated studies of the effect of disagreement in the material description between simulation and reconstruction to a level that can not be achieved with full simulation.

In the Combined Testbeam 2004 (CTB2004) the extrapolation package became the new standard for track finding and reconstruction of the Inner Detector. This allowed various studies on real taken data including different particle types and energies, as well as different setups of the magnetic field. This feedback was integrated into the the software validation.

The multiple use of the new track extrapolation in the ATLAS reconstruction and physics analysis software can be shown by the big number of client algorithms that have incorporated this package:

  • Different track fitters have been implemented on top of the extrapolation package and can be used for track fitting, re-fitting independently of sub-detector technology. These fittes will also be used in the commissioning phase of the ATLAS detector with cosmics runs.
  • The extrapolation from Inner Detector and Muon System tracks to the Calorimeter and the matching with Calorimeter clusters takes use of the extrapolation package and is widely used in the e/gamma reconstruction in ATLAS.
  • The vertex reconstruction for displaced vertices uses the correct transport of trackparameters and their associated covariances to the vertex canditate.
  • The holes-on-track search uses both, the navigation and the extrapolation from the new package.
  • parts of the ATLAS alignment software uses the new trak fitters for refittend and therefor directly depend on the new extrapolation
  • combined track fitting with tracks from the stand alone muon reconstruction has been done
This has a major impact on the overall physics performance of the ATLAS detector and the precision of various future measurements. First results using the new extrapolation in both track reconstruction and physics analysis have been presented in various talks at the ATLAS physics workshop in Rome 2005 [5].

Future prospectives

The forthcoming work can be divided into four different realms:

  • Development of an ESD based analysis chain to incorporate the results of the mentioned studies into the $ W $ mass measurement. A cooperation with a group in Copenhagen working on a general ESD based analysis chain for the $ W $ mass measurement has already started. The systematic study of a correct treatment of material and magnetic field in the Inner Detector to determine the lepton mass scale will be granted with a special focus in this thesis.

  • The extrapolation package is integrated in various currently developed track fitting/filtering algorithms, such as the Determinsitic Annealing Filter and the Gaussian Sum Filter. Studies on the performance of these algorithms will be started.

  • The validation of the entire track extrapolation has started more than a year ago by using data from the CTB2004, this validation process will be expanded by implementing a reconstruction geometry for the CTB2004 setup. Using taken data from the Testbeam, first tests of the extrapolation with material interactions on real data can be done. The results of these studies will be used as a feedback to the general ATLAS setup. The validation of the extrapolation package in the ATLAS detector setup has started already.

  • The Monte Carlo simulation will allow start systematic studies on the dependence of the quality of track reconstruction on the precision of the reconstruction geometry material description, the magnetic field map, detector efficiencies, etc. A validation package for track fitters in the new tracking realm has been set up including this dedicated purpose.



________________________________________________

Andreas Salzburger, University of Innsbruck & CERN/PH-ATC


Contract Extension

We agree for 6 months extension of the contract as an unpaid associate member of personnel.




________________________________________________

Prof. Dietmar Kuhn, University of Innsbruck




_________________________________________________

Dr. Markus Elsing, CERN/PH-ATC





Apendix

Theoretical Motivation

(following the nominclature of [1])

The Standard Model (SM) has, when ommiting the fermion masses, the Higgs boson mass and the mixing angles, three free parameters. The most common expression of this set is:

  • the QED fine structure constant $ \alpha $,
  • the Fermi constant $ G_{F} $, and
  • the $ Z $ boson mass
Given these inputs, the weak mixing parameter $ \sin^2 \theta_W $ and the $ W $ boson mass, $ M_{W} $ can be calculated, when the values of the top quark mass $ m_t $ and the higgs boson mass $ M_{H} $ are known. In contrary, $ M_{H} $ can be constrained by $ \sin^2 \theta $ and $ M_{W} $.

Using the on-shell parameterization, the relation between the $ Z $ and $ W $ boson mass is fixed in all orders of pertubation theory to the renormalized weak mixing angle $ \theta_{W} $ to

$ \sin^2 \theta_{W} = 1 - \frac{M_{Z}^2}{M_{W}^2} $.
The expression of $ \sin^2 \theta_{W} $ via the formerly described set of free SM parameters $ M_{Z}, G_{F} $, and $ \alpha $ carries then a correction factor $ (1-\Delta r) $ to be
$ \sin^2 \theta_{W} = \frac{1}{2} \cdot (1 - \sqrt{1-\frac{4\pi\alpha}{\sqrt{2}G_{F}M_{Z}^2} \cdot \frac{1}{1-\Delta r} })  $ ,

where $ \Detla r = \Delta \alpha - \cot^2 \theta_{W} \Delta \rho + \Delta r_{rem}$ contains the weak corrections: $ \Delta \alpha $ occurs due to the running of $ \alpha $, $ \Delta \rho $ describes the vacuum polarization contribution to the $ W $ and $ Z $ propagators, whereas the remaining part $ \Delta r_{rem} $ contains the vertex corrections and the effects due to the Higgs boson mass appearing as a logarithmic term $ \tilde = \ln(\frac{M_H^{2}}{M_{Z}^2}}) $.

As $ \alpha $ (measured of the anomalous magnetic moment of the electron), $ G_F $ (determined formt he muon lifetime formula), and both $ M_{Z} $ and $ \sin^2 \theta_{W} $ (measured at LEP) are known to a very high precision, the mass of the $ W $ has sensitivity for the Higgs boson mass and vice versa.

References

  • [1] Particle Data Group, Review of Particle Physics, Volume 592, ISSN-0370-2693 (2004)
  • [2] ATLAS Collaboration, ATLAS Detector and Physics Performance TDR, Part II, LHCC/99-15 (1999)
  • [3] Gianotti, F., Measurement of the W mass with the LHC, ATL_COM_PHYS-99-063 (1999)
  • [4] Amidei, D. et al, Future electroweak physics at the Fermilab Tevatron, FERMILAB-PUB-96/082 (1996)
  • [5] Agenda of ATLAS physics workshop, http://agenda.cern.ch/fullAgenda.php?ida=a044738

-- AndreasSalzburger - 13 May 2005


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