This work has been produced during my time at Freiburg University in the division working for the COMPASS collaboration at CERN. Part of their task is to simulate the behaviour of the particles after the collision in the various detectors. The input data is given out by a generator called HepGen and I tested this data against my own calculations using relativistic dynamics. To be able to do so on a large set of data, I wrote a program in C++ that would execute the computing.
The appendix "Muon-Proton Collision Simulation" shows the results of a simulation of the behaviour of the outgoing particles after a proton-muon collision as performed in the COMPASS experiment at CERN. The input data is given out by a generator called HepGen and this data was tested against calculations using relativistic dynamics. To be able to do so on a large set of data, a program in C++ was written that would execute the computing.
Table of Contents
1. Particle info
2. Muon info
3. Transversal momenta
4. The simulations
5. ECAL0 position
Research Objectives and Topics
This work aims to validate simulation data from the HepGen generator regarding muon-proton collisions at the CERN COMPASS experiment by applying principles of relativistic dynamics and conservation laws through custom C++ computational analysis.
- Simulation of particle behavior post-collision in various detectors.
- Kinematic analysis of muon-proton scattering and virtual photon interaction.
- Verification of theoretical energy and momentum conservation against simulation output.
- Visualization of particle data through comprehensive histogram generation.
- Evaluation of detector positioning and energy measurement accuracy.
Excerpt from the Book
4 The simulations
On pages (4), (5) and (6) I tested the data against calculations using Conservation of Energy and Momentum. I combined the equations for the two vertices Pμ = Pγ∗ + Pμ and Pp + Pγ∗ = Pp + Pγ to Pμ + Pp = Pμ + Pp + Pγ (8) This yields the three relevant equations Pμ = Pμ + Pp − (Pp + Pγ) Pp = Pμ + Pp − (Pμ + Pγ) Pγ = Pμ + Pp − (Pp + Pμ ) Again histograms showing the difference between predicted and actual energy and angle are shown. It can be seen that the difference in energy is the exact same histogram for all three scenarios. This is because the formula for this difference is the same for every case: ΔEγ = ΔEμ = ΔEp = Eμ + Ep − (Eγ + Eμ + Ep ) This histogram has a rather interesting feature in form of a plateau from −0.5 MeV to 0.5 MeV with a sharp peak at 0. This is because the generator gives its output only to 6 significant figures. In the very frequent case that either Eγ or Eμ is greater or equal to 100,000 MeV, this value is given with no decimal places, giving an error of ±0.5 MeV. This can be proven by generating a histogram including only those cases where both Eγ and Eμ are below 100,000 MeV. The plateau then disappears (see diagram ”Filtered energydifference”).
Summary of Chapters
1. Particle info: This chapter provides the angular and energetic calculations for the collision products based on momentum three-vectors and relativistic energy relationships.
2. Muon info: This section details the derivation of kinematic variables, specifically momentum transfer Q2 and the Bjorken scaling variable x, used in DIS and SIDIS processes.
3. Transversal momenta: This chapter outlines the calculation method for transversal momenta of outgoing particles using Cartesian momentum components.
4. The simulations: This section presents the verification of simulation data against energy and momentum conservation laws, identifying specific generator-related rounding errors.
5. ECAL0 position: This chapter defines the mathematical approach used to calculate the specific coordinates of gamma photons on the ECAL0 calorimeter.
Keywords
COMPASS experiment, CERN, Muon-proton collision, HepGen, Relativistic dynamics, Conservation of energy, Momentum transfer, DIS, SIDIS, Kinematic variables, Particle simulation, Calorimeter, ECAL0, Bjorken scaling, C++ programming
Frequently Asked Questions
What is the primary focus of this work?
The work focuses on simulating particle collisions within the COMPASS experiment at CERN and validating the generated data against theoretical relativistic dynamics.
What are the core research areas?
The core areas include muon-proton scattering, kinematic variable derivation, energy-momentum conservation, and detector-specific coordinate mapping.
What is the main objective of the simulation analysis?
The objective is to test whether the output data from the HepGen generator aligns with theoretical calculations regarding the behavior of outgoing particles.
Which scientific methodology is employed?
The author employs relativistic dynamics and conservation laws, implemented via a custom-written C++ program to process large datasets and visualize them through histograms.
What topics are covered in the main body?
The main body covers particle angle and energy calculations, kinematic variables like Q2 and Bjorken x, transversal momentum, simulation verification, and calorimeter positioning.
Which keywords best describe this research?
Key terms include CERN COMPASS experiment, muon-proton collision, relativistic dynamics, simulation validation, and kinematic analysis.
Why is there a plateau observed in the energy difference histograms?
The plateau between -0.5 MeV and 0.5 MeV occurs because the generator outputs data with limited significant figures, leading to rounding errors for energy values equal to or exceeding 100,000 MeV.
How did the author prove the cause of the energy error?
The author proved the origin of the rounding error by generating a filtered histogram that only included data cases where both photon and muon energies were below 100,000 MeV, causing the plateau to disappear.
- Arbeit zitieren
- David Brückner (Autor:in), 2012, Examination of Particle Collisions in the COMPASS experiment, München, GRIN Verlag, https://www.grin.com/document/212754
