Analysis of neutrino event generators for KM3NeT/ORCA Bachelorarbeit
vorgelegt von Patrick Heuer
Erlangen Centre for Astroparticle Physics Physikalisches Institut 4 Friedrich-Alexander-Universität Erlangen-Nürnberg
1. Gutachter: Dr. Thomas Eberl 2. Gutachter: Prof. Dr. Gisela Anton
Tag der Abgabe: 09. 07. 2018 Contents
1. Introduction 3
2. Neutrino detection5 2.1. Neutrino physics ...... 5 2.1.1. Elementary particles and fundamental forces ...... 5 2.1.2. Neutrino oscillation ...... 6 2.1.3. Neutrino-nucleus interactions ...... 7 2.1.4. Cross-sections ...... 9 2.2. Detection principles ...... 10 2.2.1. Cherenkov light ...... 11 2.2.2. Neutrino telescopes ...... 11 2.2.3. KM3NeT/ORCA ...... 12
3. Neutrino simulation 14 3.1. gSeaGen ...... 14 3.2. GiBUU ...... 15 3.2.1. Job card ...... 15 3.2.2. Output file ...... 16 3.2.3. Cross-sections ...... 17 3.3. Comparison ...... 17 3.3.1. yb-distributions ...... 19 3.3.2. yb-φν,µ distributions ...... 20 3.3.3. Mean yb ...... 22 3.3.4. Scatter type ratio ...... 23 3.3.5. Particle multiplicities ...... 26 3.3.6. Mean particle production ...... 26 3.3.7. Mean pion production ...... 26 3.4. Differences in GiBUU by changing the use of PYTHIA ...... 28 3.4.1. Cross-sections ...... 29 3.4.2. yb-distributions ...... 30 3.4.3. Mean yb ...... 30
1 2 Contents
3.4.4. Scatter type ratio ...... 32 3.4.5. Particle-production ...... 32
4. Summary and conclusion 34
List of Figures 36
List of Tables 39
Bibliography 40
A. example job card 43
B. yb distributions 45
C. yb-φν,µ distributions 53
D. Particle production 55
E. New PYTHIA settings 59 1 Introduction
The detection of neutrinos is a challenge in experimental physics dating back to 1930, when Wolfgang Pauli postulated them. From there, it took over 20 years to finally prove the existence of the elusive particle in the Cowan?Reines neutrino experiment.[1] To learn about the properties of the neutrino, one has to detect the particles produced in interactions with matter. Once believed to be massless in the Standard Model of particle physics, we know today that neutrinos have a rest mass. This results in an effect called neutrino oscillation, where a neutrino changes its flavour during propagation. This is firmly established by a number of experiments measuring the corresponding squared mass differences and mixing angles occurring in the theory of neutrino oscillation.[2–7] One of the remaining questions is the hierarchy of the mass eigenstates or more 2 precisely the sign of the larger of the two mass-squared differences ∆m23. One approach to learn about the phenomenon of neutrino oscillations, is the detection of neutrinos created in air-showers, induced by cosmic rays in the atmosphere, after propagating through the Earth. This approach is pursued by KM3NeT/ORCA, a future multi-megaton underwater Cherenkov detector.[8, 9] To understand the measurements of ORCA and generally all neutrino telescopes, we rely on the use of simulations of the interaction of neutrinos, in the detector material. In the first step in such simulations, a so-called event generator is employed, simulating the first interaction and the final state particles of the reaction. Over the last decade it has become evident that the standard approach used in neutrino simulations, namely the Relativistic Fermi Gas Model (RFGM), conspicuously fails to account for the complexity of nuclear dynamics and the variety of reaction mechanisms contributing to the detected signals.[10] The currently used event generator in the KM3NeT collaboration is gSeaGen, a home-brew generator based on GENIE, which relies on the RFGM. An improvement of these simulations could be achieved using the new generator GiBUU. GiBUU was written over the last decades and is aiming to provide a unified theoretical transport framework in the MeV and GeV energy regimes for a wide array of reaction types like hadron-, photon-, electron-, neutrino- and heavy-ion-induced reactions on nuclei.[11] The goal of this thesis is to understand the usage of GiBUU for KM3NeT/ORCA and compare its output to the one of gSeaGen. To do this it will first introduce the physical principles involved in neutrino detection, following with an introduction of the two generators and a comparison of the
3 4 1. Introduction respective output. It will end with an evaluation, summarizing the found contradictions between the generators and search for explanations of these. 2 Neutrino detection
Neutrinos are electrically neutral, extremely light particles with spin 1/2 that only have weak and gravitational interaction. They were postulated in 1930 by Wolfgang Pauli as a remedy to conserve energy in the beta decay. First assumed to be massless, neutrinos have the ability to change their flavour, in a process called neutrino oscillation. This behaviour can only be explained if neutrinos have mass. To better understand this phenomenon and to determine the mass hierarchy of neutrino masses, neutrino telescopes, like the future KM3NeT/ORCA, measure atmospheric neutrinos in the few-GeV range.
2.1. Neutrino physics
Covering all physical principles involved in neutrino physics is beyond the scope of this thesis. A short summary of relevant principles will be given with a focus on those most relevant for the thesis.
2.1.1. Elementary particles and fundamental forces
Elementary particles are particles that have no known constituents. These particles and their fundamental interactions are explained in the Standard Model of particle physics. The current elementary particles are grouped into three classes: quarks, leptons and gauge bosons. There are six known quarks: up, down, charm, strange, top and bottom. They are the only particles to carry a fractional electric charge and are the constituents of hadrons, held together by the strong force. These are grouped into baryons (three quarks) and mesons (two quarks). The most commonly known baryons are protons, consisting of two up and one down-quark and neutrons, consisting of two down and one up-quark. Mesons are unstable products of particle interactions involving quarks. The lightest meson is the pion (π) consisting of a quark-anti-quark pair. Leptons can be categorized into two groups, electrically charged (with a charge of -1e, where e is the elementary charge) and electrical-neutral leptons. The best-known charged lepton is the electron (e−), whereas muons (µ−) and taus (τ −) can be described as heavier versions of the e−. Every charged lepton has a corresponding neutral lepton, the neutrino (νe, νµ, ντ ). The correspondence of the
5 6 2. Neutrino detection
Family Name Charge (e) Interaction Quark up 3/2 em, strong, weak, gravitation down -1/2 em, strong, weak, gravitation charm 3/2 em, strong, weak, gravitation strange -1/2 em, strong, weak, gravitation top 3/2 em, strong, weak, gravitation bottom -1/2 em, strong, weak, gravitation Lepton e− 1 em, weak, gravitation νe 0 weak, gravitation µ− 1 em, weak, gravitation νµ 0 weak, gravitation τ − 1 em, weak, gravitation ντ 0 weak, gravitation Family Name Charge (e) Force carrier of Gauge boson γ 0 em gluon 0 strong W ± ±1 weak Z0 0 weak
Table 2.1.: Elementary particles and the force carriers of the fundamental forces.
neutrino to one of the charged lepton is called flavour. Each of these particles interact only via certain fundamental forces. There are four known fundamental forces: the electromagnetic (em) force, the strong force, the weak force and the gravitational force. While the electromagnetic and the gravitational force act on infinite scales the strong and the weak force only act on subatomic levels. All these forces interact via the exchange of gauge bosons. Every force is mediated via another one of these bosons. The boson mediating the electromagnetic force is the photon (γ), the ones mediating the weak force are the Z0, W + and W −, the ones mediating the strong force are gluons and the one mediating the gravitational force, called graviton, is, to this day, still hypothetical. An overview of the different particles, their charge and their interactions can be found in Table 2.1. Every particle has one corresponding anti-particle with same mass but opposite charge. For example, the anti-particle of the e− is the positron e+, with same mass but a positive charge. For further reading about the Standard Model of particle physics see [12] and [13].
2.1.2. Neutrino oscillation
In the last decade a number of experiments were conducted that showed neutrinos change their flavour over time. This can be explained with neutrino oscillations, resulting from the flavour eigenstates (νe, νµ and ντ ) being linear combinations of the mass eigenstates (ν1, ν2 and ν3). If we only consider the 2.1. Neutrino physics 7
eigenstates νµ, ντ , ν2 and ν3 the linear combinations would be
νµ = ν2 cos θ23 + ν3 sin θ23
ντ = −ν2 sin θ23 + ν3 cos θ23
with θ23 the so-called mixing angle. If the eigenstates are evolved in time, one can show the probability of a νµ staying in its flavour is
2 ! 2 2 1.27∆m23L P (νµ → νµ) = 1 − sin (2θ23) sin , Eν
2 2 2 with m23 = m3 − m2 the difference in the squared masses, L the distance the neutrino travelled and Eν the energy of the neutrino.[14] In the 3-ν framework the mixing between the states is given in the Pontecorvo-Maki-Nakagawa-Sakata (PMNS) matrix U:
−iδ 1 0 0 c13 0 e s13 c12 s12 0 U = 0 c23 s23 × 0 1 0 × −s12 c12 0 iδ 0 −s23 c23 −e s13 0 c13 0 0 1
with δ, the complex CP phase, cij = cos θij and sij = sin θij. Contradictory to the Standard Model of particle physics, the existence of neutrino oscillations imply a non-zeo neutrino rest mass. The neutrino mass hierarchy (NHM), meaning the ordering of the mass 2 eigenstates, is not yet determined. There are two possibilities, depending on the sign of ∆m31: the normal hierarchy (m1 < m2 < m3) and the inverted hierarchy (m3 < m1 < m2). "From a theoretical point of view, the determination of the NMH is of fundamental importance to constrain the models that seek to explain the origin of mass in the leptonic sector and the differences in the mass spectrum of charged quarks and leptons. More practically, it has also become a primary experimental goal because the NMH can have a strong impact on the potential performances of next generation experiments with respect to the determination of other unknown parameters such as the CP phase δ (related to the presence of CP-violating processes in the leptonic sector), the absolute value of the neutrino masses, and their Dirac or Majorana nature (as probed in neutrinoless double beta decay experiments, or 0νββ). From the astrophysical point of view, the NMH impacts e.g. neutrino flavour conversion in supernovae. Finally, the NMH also affects the precise determination of the PMNS-matrix parameters."[8]
2.1.3. Neutrino-nucleus interactions
Neutrinos only interact via the weak force. As such we can not detect them directly, but merely the products of their interactions with matter. One of the sources of neutrinos reaching the earth are interactions of cosmic rays with nuclei in the atmosphere. In these mainly πs are produced. The 8 2. Neutrino detection
CC NC − QE νl + p → l + n ν + N → ν + N + ν¯l + n → l + p Neutrino and nucleon remain unchanged but The neutrino changes to its corresponding lep- energy is transferred ton and the nucleon changes its type RES νl + N → l + R ν + N → ν + R The neutrino changes to its corresponding lep- The neutrino remains unchanged and the nu- ton and the nucleon enters an excited state cleon enters an excited state 0 DIS νl + q → l + q ν + q → ν + q The neutrino interacts directly with a quark in The neutrino interacts directly with a quark in the nucleon, resulting in a possible break-up the nucleon, resulting in a possible break-up of the nucleon of the nucleon
Table 2.2.: Overview of the different interaction processes of neutrinos with nucleons. νl is a neutrino with flavour l, l is a charged lepton, N is a unspecified nucleus, R is an excited state of the target, q is a quark and q0 denotes a changed quark.
decay of these and the secondary decays are given by
− − π → µ +ν ¯µ + + π → µ + νµ π0 → 2γ − − µ → e +ν ¯µ + νe + + µ → e + νµ +ν ¯e. These neutrinos are capable of interacting further and will produce measurable particles. We differentiate between two main interactions of neutrinos with nucleons, named charged current (CC) and neutral current (NC). While in a CC interaction a W ± is exchanged, in NC interactions a Z0 is exchanged. As a result, CC interactions change the neutrino to a corresponding charged lepton and NC interactions only change the energy of the neutrino. Each of these interactions can be categorized into one of three processes: Quasi-elastic-scattering (QE), Resonance-scattering (RES) and deep-inelastic-scattering (DIS). For an overview of the different processes see Table 2.2.
Quasi-elastic-scattering
The simplest case of neutrino-nucleus interaction is QE. In case of a CC-interaction, the neutrino interacts with a nucleon of the target via the exchange of a W ±. To conserve the charge the nucleon has to change its charge. As a result only the following two processes can happen:
− νl + p → l + n + ν¯l + n → l + p For NC-interactions the neutrino exchanges a Z0 with the nucleon and thus simply transfers energy. QE-CC events are important for experimental neutrino physics. Because of the simple kinematics 2.1. Neutrino physics 9
Symbol q content decays to ∆++ uuu p + π+ ∆+ uud p + π0 n + π+ ∆0 udd p + π− n + π0 ∆− ddd n + π−
Table 2.3.: ∆-baryons and their decay.
involved one can derive an equation for the energy of the incoming neutrino (Eν) using the energy of the outgoing lepton (El) and the scattering angle between in and outgoing lepton φν,l :
2 ml El − 2MN Eν = q 2 2 1 − El − cos φν,l El − ml
So to reconstruct the neutrino energy one has to measure the outgoing lepton and the nucleon.[15]
Resonance-scattering
At higher energies, the neutrino can transfer enough energy to excite the nucleon into a resonant baryonic state. These states further decay into a nucleon sending out secondary particles like πs. The interaction is denoted as:
νl + N → l + R (CC) ν + N → ν + R (NC).
The most prominent of these excited states are the ∆-baryons. There are four of these baryons consisting of any possible combinations of three up and down-quarks. They all rapidly decay via the strong interaction into one nucleon and a π of fitting charge as shown in Table 2.3.[16, 17]
Deep-inelastic-scattering
At high energies, the neutrino interacts with a single quark in the nucleon, shattering the nucleon, which results in the production of mesons. DIS was first used to probe the inside of hadrons to prove that nucleons consist of sub particles.[18]
2.1.4. Cross-sections
Every process described in subsection 2.1.3 occurs with a certain probability depending on the energy of the neutrino. In particle physics these probabilities are expressed with cross-sections. The unit of cross-sections is barn=10−28m2, although in practice smaller units are common. 10 2. Neutrino detection
As seen in Figure 2.1 the energy regime <1 GeV is dominated by QE, RES dominating the range from 1 GeV to 5 GeV (10 GeV for ν¯) and DIS dominating the regime above it. At 100 GeV, DIS is the only relevant process. The difference in the cross-sections for ν and ν¯ can be explained with the helicity of neutrinos. This describes the handedness, meaning the relation between the spin and the momentum vector of the particle. A particle is left-handed if its spin is anti-parallel to its momentum and is right-handed if they are parallel. The weak force only couples to left-handed fermions and right-handed anti-fermions. This was shown by measuring the distribution of electrons emitted from a polarized sample of radioactive 60Co atoms.[19] As same-handed fermions interact stronger via the weak force neutrinos (left-handed) have a larger cross-section on quarks (also left-handed) than anti-neutrinos (right-handed). [20, 21] As shown in [22], the cross-sections for ν + q and ν¯ + q for (anti-)neutrino-nucleon scattering are given by dσ G2 sˆ ν,q = F (2.1) dyb π 2 dσν,q¯ GF sˆ 2 = (1 − yb) , (2.2) dyb π where dσν,q , respectively dσν,q¯ , is the differential cross-section of (anti-)neutrino-quark scattering, √dyb dy 2 2g2 2 GF = W/8mW is the Fermi-constant of the weak interaction, with gW the coupling constant of weak 2 interaction and mW the mass of the W -boson, sˆ = (2E) is the νµ − d centre-of-mass energy and yb is the Bjorken-y, also-called inelasticity, that describes the energy that is transferred to the hadronic shower divided by the neutrino energy. It is defined as
Eν − El yb = , Eν with Eν the energy of the incoming neutrino and El the energy of the outgoing lepton. It is a dimensionless quantity with values between 0 and 1.
To get the total cross-section one has to simply integrate Equation 2.1 and Equation 2.2 over yb and gets G2 sˆ σ = F ν,q π G2 sˆ and σ = F . ν,q¯ 3π The ratio of those two is given as σ 1 ν,q¯ = σν,q 3 showing that the same-handed particles ν and q have a higher cross-section than the opposite-handed ν¯ and q.
2.2. Detection principles
The only possibility to detect neutrinos is by detecting the particles resulting from interactions of neutrinos with matter. In the following there will be a short introduction of the techniques involved 2.2. Detection principles 11
Figure 2.1.: Total CC cross-sections for neutrinos (left) and anti-neutrinos (right) per nucleon for an isoscalar target[21].
in neutrino detection with the future KM3NeT/ORCA.
2.2.1. Cherenkov light
As neutrino telescopes measure light, one important effect in neutrino detection is the Cherenkov effect. It describes that charged particles, travelling through a medium at a velocity higher than the speed of light in the medium emit light. While the speed of light c is an absolute constant for light travelling through the vacuum, it has 0 a reduced value in a medium. This reduced speed of light is denoted as c = c/n(λ), with n(λ) the wavelength dependent refractive index of the material and λ the wavelength of the light. Because of this it is possible for a particle to surpass the speed of light in a medium. A charged particle with velocity v > c0 will emit Cherenkov light under an angle 1 cos θ = c βn
with β = v/c. The total number of Cherenkov photons released per unit path length dl is given by d2N 2πα 1 ! = 1 − , (2.3) dldλ λ2 n(λ)2β2 where α is the fine-structure constant.
0 For example, for λ = 550 nm, nW ater = 1.33[23], resulting in a speed of light in water of cW ater ≈ 0.75c, ◦ Equation 2.3 would yield about 200 Cherenkov photons per cm under an angle of θc ≈ 43 .[9, 14]
2.2.2. Neutrino telescopes
Because of their nature, neutrinos only generate a small number of detectable events, that we can measure on Earth. As a result neutrino detectors need to cover a big area to detect sufficient amounts 12 2. Neutrino detection
of events. Neutrino detectors are situated underground (Super-Kamiokande and Borexino), in ice (IceCube) or underwater (ANTARES, KM3NeT, Baikal and NESTOR Project) therefore using the denser surroundings as detector material, in which secondary particles will generate light via the Cherenkov effect. They detect the light generated by charged particles originating from neutrino interactions. To suppress atmospheric muons, neutrino telescopes need to be situated at a depth of more than a kilometre. Neutrino telescopes consist of an array of photomultiplier tubes(PMTs). PMTs are sensitive light detectors that amplify a current, induced by incoming light and generate a measurable signal.[14]
2.2.3. KM3NeT/ORCA
KM3NeT is a future research infrastructure consisting of a network of deep-sea neutrino telescopes in the Mediterranean Sea. All PMTs used in the telescopes will be housed in so-called digital optical modules (DOM). Each DOM hosts 31 PMTs and their associated readout electronics in a transparent glass sphere. Figure 2.2a shows a DOM for KM3NeT. The DOMs will be attached to a detection string. KM3NeT will consist of three so-called blocks each uniting 115 detection strings with different density depending on the block. One of the three blocks will be referred to as ORCA: Oscillation Research with Cosmics in the Abyss. It will be deployed at a depth of 2450 m, about 40 km offshore from Toulon and used for precise measurements of atmospheric neutrino oscillations. ORCA will be much denser than the other blocks. Each string will have a length of about 200 m resulting in 9 m vertical distance of the DOMs. Each string will have about 20 m horizontal distance to one-another. The layout of the ORCA detector can be seen in Figure 2.2b. The denser composition of ORCA will allow it to detect atmospheric neutrinos in the few-GeV range.[8] 2.2. Detection principles 13
(a)
(b)
Figure 2.2.: Photograph of a completed DOM(left) and the layout of the ORCA detector depicting the 115 (+5 contingency) Detection Units, cables and connection devices of the full array(right)[8]. 3 Neutrino simulation
The simulation of neutrinos interacting with the detector material and the propagation of the final state particles through the material is a crucial aspect of understanding the measurements of neutrino telescopes. The standard approach in neutrino simulation is to employ an event generator which calculates the first interaction of the neutrino with the detector material and all final states particles. These generated events will be fed to a simulation propagating all the resulting particles through the medium of the detector, taking size, geometry and other features of the detector into account. As the events of the neutrino generator will contain systematic and statistic errors, that will aggravate in the following steps of the complete simulation, it is essential to employ state-of-the-art event generators. In the following, two neutrino event generators, gSeaGen and GiBUU, will be presented and compared. In the comparison, differences in the output of the two generators are shown. As this thesis focuses on the use for ORCA all simulations were done for hydrogen and oxygen in the low energy regime (<5 GeV). While the data from GiBUU was produced as part of the work on this thesis, the data from gSeaGen was taken from past simulations of the KM3NeT collaboration. All data was processed using python 3.6.2 including the numpy (http://www.numpy.org/), pandas (http://pandas.pydata.org/) and km3pipe (https://github.com/tamasgal/km3pipe) packages.
3.1. gSeaGen
The gSeaGen code is a GENIE based application to generate neutrino-induced events in an underwater neutrino detector.[24] GENIE itself is a ROOT based Neutrino MC Generator[25] which incorporates the dominant scattering mechanisms from several MeV to several hundred GeV and are appropriate for any neutrino flavour and target type.[26] It uses the Relativistic Fermi Gas Model (RFGM) of Bodek and Ritchie[27] for all processes. For the calculation of secondary particles resulting from the de-excitation of the nucleus it uses the Andreopoulos?Gallagher?Kehayias?Yang (AGKY) model.[28] gSeaGen utilises the calculations provided by GENIE to provide a generator for neutrino telescopes. It depends only on the so-called "can", which defines size and medium of the detector. It describes
14 3.2. GiBUU 15
Figure 3.1.: Illustration of the detector can[24]. the detector horizon, meaning the volume sensitive to light. This exceeds the instrumented volume by three light absorption lengths. A schematic of the can is shown in Figure 3.1. Within this volume the code will generate neutrinos with a power-law energy spectrum and with a random direction according to a flat distribution in the solid angle. gSeaGen is tested and verified for experimental cross-sections.[25]
3.2. GiBUU
The Giessen Boltzmann-Uehling-Uhlenbeck project (short GiBUU) provides a unified theory and transport framework for elementary reactions on nuclei and heavy-ion collisions in the MeV and GeV regime. Because it incorporates a full dynamical description and delivers the final state of an event, it can be used as an event generator.[29] The calculations in GiBUU are modelled with the Boltzmann-Uehling-Uhlenbeck-equation (BUU-equation). It describes the space-time evolution of a many-particle system under the influence of mean field potentials and a collision term. It can be more precisely described as the time evolution of the Wigner transform of the real-time Green’s function which is a generalization of the classical phase-space density.[11, 30]
3.2.1. Job card
As GiBUU is built to model a wide array of particle interactions one must configure it to a certain set-up. For this, GiBUU utilizes so-called job cards. A job card is a plain text document which needs to have the ".job" data format. Every job card consists of several namelists, which address specific modules in GiBUU. Namelists are marked with a & in the job card. Every namelist consists of several switches that can be set to specific values. Most switches have a reasonable default value which will be used if no value is given. For an index of every namelist and their switches see [31]. An example job card for muon-neutrino interactions with hydrogen at 5 GeV can be found in Appendix A. Every job card used in this thesis can be derived from the example job card. For further 16 3. Neutrino simulation
16 Figure 3.2.: Example data output of GiBUU for an interaction of a νµ with Eν = 3 GeV and 8 O(top) and a 3D-plot of all final state particles(bottom). The length of all vectors was normed to 5 to enhance visibility.
information on installing an running GiBUU just follow the steps in the ’Using GiBUU’ section on [29].
3.2.2. Output file
After submitting a job card to GiBUU, it will produce a number of output files with the file ’FinalEvents.dat’ being of most interest. In it, every simulated event with every produced particle, in its final state, is written out. It includes the following variables: Run describes the number of the run, the number of runs can be specified in the corresponding namelist of the job card (see Appendix A). Event particles produced in the same event share a event number. ID every particle produced in an interaction is labelled with an ID. GiBUU uses its own particle numbering scheme described on their homepage. [32]. The scheme does not distinguish between particles that only vary in charge. Charge describes the charge of the outgoing particle in units of e. perweight is the abbreviation for perturbative weight and is needed to calculate cross-sections as described in [33]. xpos-zpos describes the position in fm in 3D space of the particle in its final state with the point of 3.3. Comparison 17
origin in the point of the first interaction. E-zmom describes the 4-vector of the produced particle in GeV. history describes the origin and generation of the particle. It is calculated by history = 1.000.000 ∗ generation + 1.000 ∗ id2 + id1. All particles with history 0 are generated in the first interaction. The particle with history and perweight 0 is the target of the neutrino. productionID describes the type of the first interaction of the event. Quasi-elastic-scattering is numbered with 1, ∆-excitations and higher resonances are numbered with 2-33 and deep- inelastic-scatering is numbered with 34. enu gives the energy of the incoming neutrino in GeV.
In Figure 3.2 we see an example event of such an output file for the interaction of a νµ with Eν = 3 16 GeV and 8 O and a visualisation of the example event. With the output file we can reconstruct the interaction. We see a DIS-event (productionID=34) between the neutrino and a neutron (ID=1, charge=0, perweight=0). At the first interaction also a proton (ID=1, charge=1, history=0) was involved. The target was destroyed resulting in one proton (history=1105001) and two π0 (ID=101, charge=0, history=1105001). The process involved a ω-meson (ID=105 as seen in the history of the other particles) that already decayed in the final state.
3.2.3. Cross-sections
GiBUU was tested and verified for experimental cross sections.[30, 34] As a cross-check it was attempted to plot the cross-sections in GiBUU for oxygen and compare them to the ones found in subsection 2.1.4. The total cross-section and the cross-section for every scattering process are written into the file "neutrino_absorption_cross_section_ALL.dat" by GiBUU. As seen in Figure 3.3 the calculated cross-sections of GiBUU follow the same trend as the ones of Formaggio and Zeller[21] but are lower for all energies.
3.3. Comparison
As outlined in section 3.1 and section 3.2 the two generators follow different approaches in simulating neutrino interactions. While GiBUU models the full space-time evolution of the phase space densities of all relevant particle species during a nuclear reaction within a consistent treatment of the initial vertex and the final-state processes, gSeaGen considers initial-state and final-state interactions independently, using the RFGM for the initial state and a cascade model for the final-state interactions. Also GiBUU does not rely on tuning specific input to describe a specific reaction channel or parametrization to fit experimental data. To compare the output of the programs, a variety of variables, that are relevant for the reconstruction of neutrino events, were derived from the produced data and plotted. As all plots are derived for specific energies and gSeaGen produces neutrinos in an energy spectrum, it was necessary to filter the output of gSeaGen. To get sufficient data every event with Eν = x ± 0.1 GeV, with x being the filtered energy, was selected. 18 3. Neutrino simulation
16 Figure 3.3.: Comparison of the GiBUU calculated cross sections for 8 O (left) and the total cross- sections of neutrino interactions for isosclar targets[21](right) with νµ(top) and ν¯µ(bottom). 3.3. Comparison 19
16 Figure 3.4.: yb-distribution of CC-events, divided by process, of νµ(top) and ν¯µ(bottom) on 8 O with GiBUU(left) at Eν = 3 GeV and gSeaGen(right) at Eν = 3 ± 0.1 GeV, all plots are normed to the maximum being 1.
3.3.1. yb-distributions
The reaction inelasticity yb (explained in Equation 2.1.4) is an important parameter for the recon- struction of events. It describes the energy transferred into the hadronic shower. For GiBUU, yb was derived from the energy of the outgoing lepton, while gSeaGen writes it directly into the output. For the comparison of the yb distribution several simulations with energies from 1 to 5 GeV were performed, with the 3 GeV ones being used as examples. All plots were normed by dividing every bin height by the largest bin size, thus yielding a maximum of 1 in all plots.
For oxygen, seen in Figure 3.4, the produced yb of the two generators contradict each other especially for ν¯µ.
For νµ we see a uniform like distribution in GiBUU with a decline from 0.9 to 1. In gSeaGen we see a local minimum at around 0.1 and a decline towards high yb. If we take a look at the different processes we see a similar peak for QE events but a stronger decline of the QE portion in gSeaGen. The RES part is much more dominant in GiBUU and shows a lesser decline than in gSeaGen. The DIS part in GiBUU starts at higher yb than in gSeaGen and is generally lower.
If we look at the distributions for ν¯µ we see a much stronger contradiction between the two generators. While the yb-distribution in GiBUU is very similar to the one for νµ, gSeaGen shows a stronger decline 20 3. Neutrino simulation
towards high yb. We can also see the local minimum at around 0.1 in gSeaGen that is not present in GiBUU and the behaviour of the process parts is similar but lower for gSeaGen. The strong decline in gSeaGen results in a lower mean yb (< yb >). Commencing with the simulation for hydrogen in Figure 3.5 we can find similar contradictions. Note that the QE process for CC-events is not possible for hydrogen as it is basically one proton and the only possible process is + ν¯µ + p = µ + n.
In GiBUU, we see again a uniform-like distribution for νµ with a rise from 0 to 0.2, resulting from the absence of QE events, while gSeaGen strongly declines toward 1. Again the DIS part starts at higher yb in GiBUU and the RES part is more populated for higher yb.
For ν¯µ we see a peak in QE events in both GiBUU and gSeaGen but it is much more prominent in gSeaGen. Again the DIS starts at higher yb and we see a higher population of RES events in GiBUU, while most events in gSeaGen are QE events. Again the strong decline in gSeaGen results in a lower < yb >.
Note that the plots for GiBUU for νµ and ν¯µ for oxygen and hydrogen are very similar (for hydrogen there are no QE events for neutrinos but the shape of RES and DIS is similar in both plots) we see huge differences between νµ and ν¯µ in gSeaGen for both targets.
The < yb > and the ratio of the several scatter types are further investigated in subsection 3.3.3 and subsection 3.3.4. For yb-distributions at different energies see Appendix B.
3.3.2. yb-φν,µ distributions
The scattering angle φν,µ describes the angle between the direction of the incoming neutrino and the T outgoing muon. It can be calculated from the momenta ~p = (px, py, pz) of the outgoing lepton and the incoming neutrino: ~pν ◦ ~pµ cos φν,µ = (3.1) |~pν| · |~pµ| If the direction of the neutrino is defined as one of the axes (e.g. the z-axis) the calculation in Equation 3.1 can be simplified to: pµz cos φν,µ = . |~pµ|
In Figure 3.6 we see 2D histograms of yb and φν,µ for νµ interacting with oxygen, normalized to the integral of the bins being one. Note that python will not just integrate over the height of the bin but over the height times the size of the bin. These distributions are of interest because they tell us which yb has higher probabilities under certain angles.
We can see that the angle increases with yb. If we compare the output of GiBUU and gSeaGen we see that the substructure, visible in gSeaGen, in the low yb and low φν,µ region, is not present in GiBUU. This results from the former described local minimum in the yb-distributions in gSeaGen. Because of this, we have a much lower probability of events with low yb and φν,µ in the blue area of the substructure in gSeaGen. The outer shape of the distributions is similar but gSeaGen tends to scatter at the edges. GiBUU also has a higher population towards the lower edges of the axes. We 3.3. Comparison 21
1 Figure 3.5.: yb-distribution of CC-events, divided by process, of νµ(top) and ν¯µ(bottom) on 1H with GiBUU(left) at Eν = 3 GeV and gSeaGen(right) at Eν = 3 ± 0.1 GeV, all plots are normed to the maximum being 1. 22 3. Neutrino simulation
16 Figure 3.6.: yb-φ distributions for νµ on 8 O with GiBUU(left) at Eν = 3 GeV and gSeaGen(right) at Eν = 3 ± 0.1 GeV.
16 Figure 3.7.:< yb> distribution for νµ on 8 O with GiBUU(left) and gSeaGen(right). also see a more defined core of the distribution, meaning that in gSeaGen the probability decreases stronger towards the edges of the distribution than in GiBUU.
For yb-φν,µ distributions at other energies see Appendix C.
3.3.3. Mean yb
As seen in the yb-distributions GiBUU and gSeaGen do not agree on the mean < yb >. It was calculated by adding the yb of every event and dividing it by the number of events. The resulting values were then plotted over the energy of the incoming neutrino.
If we look at the plot for oxygen in Figure 3.7, we see a strong difference in the behaviour of νµ and ν¯µ. While the data for νµ and ν¯µ are nearly the same for GiBUU, with ν¯µ being a little lower, we see a strong difference between the two in gSeaGen. For νµ GiBUU shows a strong growth towards higher energies, where gSeaGen shows a slow growth. For ν¯µ, the behaviour strongly differs. While it follows νµ in GiBUU, it shows a decline to lower values in gSeaGen. As such GiBUU shows a stronger energy dependence of the resulting yb. 3.3. Comparison 23
1 Figure 3.8.:< yb> distribution Eν for νµ on 1H with GiBUU(left) and gSeaGen(right).
Another contradiction can be seen in the plot for hydrogen in Figure 3.8. Here we see that GiBUU and gSeaGen show a similar behaviour with a declining < yb > for νµ and a grow in ν¯µ but strongly deviate in values. While GiBUU and gSeaGen agree in the starting point at Eν = 1 GeV for νµ gSeaGen shows a stronger decline towards higher energy. For ν¯µ GiBUU has a higher starting point and grows more rapidly. Here gSeaGen shows a stronger energy dependence of yb for νµ but for ν¯ν it is stronger for GiBUU.
3.3.4. Scatter type ratio
We saw in the yb distributions, that the ratio of the process types differ between the two generators. To quantify this, the ratio of each scatter type to another was plotted over Eν. To get the ratio every event of a certain process type was counted and the resulting total was divided by the number of all events in the simulation.
We see for oxygen in Figure 3.9 that for νµ DIS is not present for 1 GeV in GiBUU while it starts at 0.1 in gSeaGen. It also grows slower in GiBUU and we see DIS being the dominant process between 4 and 5 GeV in GiBUU while taking over in gSeaGen between 2 and 3 GeV. For RES we have a higher ratio over all energies in GiBUU and a similar behaviour, but with a stronger decline towards higher energies in gSeaGen. The QE part follows the same progression in both generators but declines stronger in GiBUU. For hydrogen the plot can be found in Figure 3.10. We can see that the QE events in GiBUU stay at zero while there are QE events in gSeaGen for 4 and 5 GeV. This can also be seen in the yb distributions for these energies in Figure 3.11 which is a general contradiction to the physics involved in this process. As described earlier a QE process can not occur for a CC interaction between νµ and p. Furthermore, we can see that DIS does not occur for 1 GeV in GiBUU while being at around 0.1 in gSeaGen. We can also see that DIS events start to dominate the events at higher energies in GiBUU than in gSeaGen. For ν¯µ the QE part in GiBUU is generally lower than in gSeaGen but decline in a similar manner. The RES part is higher over the whole energy range and shows a stronger grow to 2 GeV and a stronger decline afterwards. The DIS part, again, starts at 0 in GiBUU but shows a stronger grow after 2 GeV. 24 3. Neutrino simulation
16 Figure 3.9.: Process type ratio over Eν of νµ(top) and ν¯µ(bottom) on 8 O with GiBUU(left) and gSeaGen(right). 3.3. Comparison 25
1 Figure 3.10.: Process type ratio over Eν of νµ(top) and ν¯µ(bottom) on 1H with GiBUU(left) and gSeaGen(right).
1 Figure 3.11.: yb-distributions in gSeaGen on 1H for Eν = 4±0.1 GeV(left) and Eν = 5±0.1 GeV(right), showing QE events that can not occur in a CC reaction between νµ and a proton. 26 3. Neutrino simulation
3.3.5. Particle multiplicities
Another interesting quantity is the number and kind of the particles produced in an event. To study this, the particles per event were counted and divided by the number of events. Protons and neutrons were ignored in the calculations as they are not produced in the interaction. The result can be seen in Figure 3.12.
− + 0 − For νµ the two generators seem to agree for the most produced particles being µ , π , π , π and K+. Note that gSeaGen has γ before π0 which do not appear in the final state of GiBUU. This could be the result of the decay of π0 that already happened in gSeaGen. For the following particles we see strong contradictions, with different K being produced in GiBUU and K− being a lot rarer in GiBUU. We also see Λ and Σ appearing in GiBUU while gSeaGen produces e± and µ+. The missing of particles like Λ and Σ in gSeaGen could also result from the decay of such particles in gSeaGen. It must be said that the contradictions at very low appearances (<10−4) could result from statistical uncertainties as the occurrence of these particles has a magnitude of 10.
+ − 0 + For ν¯µ we see a hierarchy of µ , π , π and π . Again no γs appear in the final state output of GiBUU. After that we have a mixture of mesons while gSeaGen produces mainly K and e−. For particle productions at different energies see Appendix D. We also see that gSeaGen produces more particles which is further investigated in subsection 3.3.6 and subsection 3.3.7.
3.3.6. Mean particle production
To get the mean number of produced particles all produced particles were counted and divided by the number of events, again ignoring protons and neutrons. In Figure 3.13 we see the mean number of produced particles for energies between 1 and 5 GeV on oxygen.
For νµ GiBUU shows a lower number of produced particles for all energies. The plot in Figure 3.13 shows that γs are missing in GiBUU and they have a mean number of around 0.4 per event for Eν = 3 GeV. As π0 decays into 2γs this could explain this difference.
For ν¯µ we see a similar difference. GiBUU produces less particles than gSeaGen over the whole energy range. But gSeaGen has a lower gradient than GiBUU for νµ resulting in a lower difference between the two generators for higher energies. Again we rougly have the same amount of γs in gSeaGen for 3 GeV that are missing in GiBUU.
Note that the curves for GiBUU are very similar for νµ and ν¯µ while gSeaGen shows a difference between particles and anti-particles.
3.3.7. Mean pion production
As pions will produce light in the detector (π0 → 2γ, π+ + n → π0 + p, π± producing µ± which can produce Cherenkov light) the produced pions are also an interesting quantity. All pions, distinguished by their charge, were counted and divided by the number of events. In Figure 3.14 we see these numbers plotted over Eν. + For νµ we see that, for 1GeV, the number of π is lower in GiBUU. For the other π they agree. All 3.3. Comparison 27
16 Figure 3.12.: Particle production of the interaction of νµ(top) and ν¯µ(bottom) with 8 O with GiBUU(left) at Eν = 3 GeV and gSeaGen(right) at Eν = 3 ± 0.1 GeV.
16 Figure 3.13.: Mean number of particles produced from νµ(left) and ν¯µ(right) on 8 O over the energy. 28 3. Neutrino simulation
16 Figure 3.14.: Mean number of produced pions for νµ(top) and ν¯µ(bottom) on 8 O over the energy with GiBUU(left) and gSeaGen(right).
curves have a similar shape but gSeaGen is a bit steeper resulting in higher production of all π at higher energies.
− For ν¯µ at 1 GeV GiBUU and gSeaGen produce a similar amount of π but GiBUU produces more of the other π. Here we see a steeper progression of GiBUU, resulting in a higher number of all π than in gSeaGen. It also can be seen that the two plots of GiBUU are very similar (with switched π+ and π−) while gSeaGen differs between νµ and ν¯µ.
3.4. Differences in GiBUU by changing the use of PYTHIA
For the final state of DIS events, GiBUU utilises PYTHIA.[35] As such it is possible to change the settings of PYTHIA using the &pythia namelist. Following the recommendations, from correspondence with the GiBUU team, the value PARP(91) of the namelist was changed to 0.44. This can be done by simply adding &pythia PARP(91)=0.44 3.4. Differences in GiBUU by changing the use of PYTHIA 29
16 Figure 3.15.: Calculated cross-sections for 8 O in GiBUU with default settings(left) and with changed PYTHIA settings(right) for νµ(top) and ν¯µ(bottom)
/ to the job card found in Appendix A. The PARP(91) variable describes the width of Gaus- k2 2 sian primordial k⊥-distribution inside hadrons, i.e. exp (− ⊥/σ ) k⊥dk⊥ with σ=PARP(91) and 2 2 < k⊥ >=PARP(91) .[36] The default value of the variable is 2 and needs to be lowered for lower energies. This is a GiBUU-standard but not yet implemented as being the default setting. It is planned to set 0.44 as the new default value in future versions of GiBUU. Following this all simulations done in section 3.3 were redone using the new job card, resulting in some interesting changes in the output.
3.4.1. Cross-sections
In Figure 3.15 the cross sections calculated by GiBUU for default settings and with the adjusted PYTHIA settings are compared. As one could expect, the main difference between the settings is a change in the DIS cross-section which results in a changed total cross-section. For both νµ and ν¯µ we se a stronger grow of the DIS cross section towards higher energies. This results in a higher total cross section towards higher energies. 30 3. Neutrino simulation
Figure 3.16.: yb distributions of GiBUU with default settings(left) and with changed PYTHIA set- 16 tings(right) for νµ(top) and ν¯µ(bottom) with Eν = 3 GeV on 8 O.
3.4.2. yb-distributions
For oxygen in Figure 3.16 we see a change in the amount of RES and DIS events, while QE seems unchanged. While there are less RES events the number of DIS amounts rises. Interestingly the increase of DIS seems to be equivalent to the loss of RES, resulting in a similar sum of the distributions and the same (or nearly the same for ν¯µ) < yb >. This holds true for both νµ and ν¯µ. For hydrogen in Figure E.1 we see the exact same behaviour.
3.4.3. Mean yb
We saw that the value of < yb > did not change significantly for the new PYTHIA setting. As seen in Figure 3.17 this behaviour is true for the whole energy range with the values with the new settings being a little higher to higher energies for νµ and ν¯µ.
For hydrogen in Figure 3.18 we see that νµ starts higher in the old settings but ends lower. For ν¯µ we see no change. 3.4. Differences in GiBUU by changing the use of PYTHIA 31
16 Figure 3.17.:
1 Figure 3.18.:
16 Figure 3.19.: Process type ratio over Eν of νµ(top) and ν¯µ(bottom) on 8 O of GiBUU with default settings(left) and with changed PYTHIA settings(right).
3.4.4. Scatter type ratio
The ratio of scattering types shows the same behaviour like the yb distributions in subsection 3.4.2. In Figure 3.19 we see an increase in DIS with a decline in RES and an unchanged amount of QE. This holds true for νµ and ν¯µ and also for hydrogen found in Figure E.2.
3.4.5. Particle-production
For particle production in Figure 3.20 we see more or less the same distribution, with only slight changes in the least produced particles for νµ and ν¯µ. 3.4. Differences in GiBUU by changing the use of PYTHIA 33
16 Figure 3.20.: Particle production of the interaction of νµ(top) and ν¯µ(bottom) with 8 O of GiBUU with default settings(left) and with changed PYTHIA settings(right) with Eν = 3 GeV. 4 Summary and conclusion
In the following the differences between the two neutrino generators, GiBUU and gSeaGen, will be summarized and an attempt will be made to explain said differences. After that, an outlook will be given on how to continue and improve the investigations on GiBUU for the use in KM3NeT/ORCA One difference between the two generators is the handling of anti-neutrinos. While the produced data shows strong similarities in GiBUU, we see strong differences between νµ and ν¯µ in gSeaGen. It seems that for the calculations in GiBUU, it makes no difference whether a neutrino or an anti- neutrino interacts with the target. As the weak force couples stronger to same-handed fermions than to opposite-handed fermions, we expect to see a difference in the output for νµ and ν¯µ. As both generators are verified for experimental cross-sections, the similarity, of νµ and ν¯µ in GiBUU, shouldn’t be a result of cross-section calculations. Even though, the cross sections of Formaggio and Zeller[21], the cross-sections of GiBUU showed lower results for ν¯µ than for νµ. If the GiBUU code proves to be more accurate it would mean that the distinction of νµ and ν¯µ in the measurements would be more difficult.
Next to the similarity, respectively dissimilarity, of νµ and ν¯µ in GiBUU and gSeaGen, we also see a general disagreement between the two generators. For νµ we see different distributions of the interaction inelasticity yb, resulting in different yb − φν,µ-distributions, a different mean yb in the energy range from 1 to 5 GeV, a different ratio of the occurrence of the different scattering types and different numbers of produced particles and pions. All these differences are stronger for ν¯µ, because of the described similarity of the simulation of particles and anti-particles in GiBUU.
As the yb-distributions produced by GiBUU are nearly uniformly distributed, it would mean that every amount of energy transfer has the same probability, meaning the energy of the hadronic shower - in the studied energy range - could origin from every incoming neutrino energy, only limited by the energy of the neutrino. If the yb-distributions of gSeaGen are accurate the measured yb could be more easily matched to specific neutrino energies as specific energy transfers have a higher probability for specific energies.
As they are connected we see similar differences in the yb-φν,µ-distributions. Because the distributions in GiBUU are more evenly distributed it is harder to match certain measurements to certain Eν.
The mean yb for oxygen shows some of the strongest contradictions between the two generators. For oxygen it shows on the one hand the similarity of νµ and ν¯µ in GiBUU, on the other hand a stronger
34 35
energy dependence of yb in GiBUU. For hydrogen we see a similar progress in both generators but different energy dependencies.
For all energies and targets and for νµ and ν¯µ alike we see a stronger dominance of deep-inelastic- scattering and lower ratios for resonance-scattering. This could result from the interpretation of events in the program. We also see the occurrence of quasi-elastic events in charged current interactions of νµ and hydrogen, which should not occur at all. This process is suppressed, as a charged current event, with an νµ, can only occur with a nucleon that can gain a positive charge, without entering a resonance state. As the hydrogen nucleus is simply a single proton this is not possible. While the occurrence was low, it means that there could be an error in the code of gSeaGen, respectively GENIE. In the particle multiplicity distributions produced by the two generators we see gamma-ray photons appearing in the final states of gSeaGen, while they were missing in GiBUU. The difference could result from the decaying of π0 and heavier mesons producing γs which does not seem to occur in GiBUU. This also explains the difference in the mean number of produced particles in the two generators. gSeaGen produces more particles for all studied energies. As the decay of π0 produces two γs the total count of particles rises. Resulting from the mean numbers of produced π we can not verify this, as the number of all produced pions in GiBUU is either lower, for νµ, or higher, for ν¯µ, than in gSeaGen. The change of the PYTHIA PARP(91) variable in GiBUU results in higher DIS and lower RES ratios, while other quantities like the shape of the sum of the yb distributions or the mean yb remained unchanged. This brings us closer to the scatter type ratios of gSeaGen but all other contradictions are unchanged. In conclusion we see that there are a lot of contradictions between the two generators. This should be a result of the different approaches followed in GiBUU and gSeaGen. It seems that GiBUU is the more sophisticated approach but it could be that it requires further improvements, before it can be used for KM3NeT/ORCA. Mainly the handling of νµ and ν¯µ is contradicting the expectations and needs to be explained. To make a definite statement of the usability of GiBUU for KM3NeT/ORCA we need to study the output and the code of the two generators in more depth, than it was possible in the scope of this thesis. List of Figures
2.1. Total CC cross-sections for neutrinos (left) and anti-neutrinos (right) per nucleon for an isoscalar target[21]...... 11 2.2. Photograph of a completed DOM(left) and the layout of the ORCA detector depicting the 115 (+5 contingency) Detection Units, cables and connection devices of the full array(right)[8]...... 13
3.1. Illustration of the detector can[24]...... 15
3.2. Example data output of GiBUU for an interaction of a νµ with Eν = 3 GeV and 16 8 O(top) and a 3D-plot of all final state particles(bottom). The length of all vectors was normed to 5 to enhance visibility...... 16 16 3.3. Comparison of the GiBUU calculated cross sections for 8 O (left) and the total cross-sections of neutrino interactions for isosclar targets[21](right) with νµ(top) and ν¯µ(bottom)...... 18 16 3.4. yb-distribution of CC-events, divided by process, of νµ(top) and ν¯µ(bottom) on 8 O with GiBUU(left) at Eν = 3 GeV and gSeaGen(right) at Eν = 3 ± 0.1 GeV, all plots are normed to the maximum being 1...... 19 1 3.5. yb-distribution of CC-events, divided by process, of νµ(top) and ν¯µ(bottom) on 1H with GiBUU(left) at Eν = 3 GeV and gSeaGen(right) at Eν = 3 ± 0.1 GeV, all plots are normed to the maximum being 1...... 21 16 3.6. yb-φ distributions for νµ on 8 O with GiBUU(left) at Eν = 3 GeV and gSeaGen(right) at Eν = 3 ± 0.1 GeV...... 22 16 3.7.
36 List of Figures 37
16 3.12. Particle production of the interaction of νµ(top) and ν¯µ(bottom) with 8 O with GiBUU(left) at Eν = 3 GeV and gSeaGen(right) at Eν = 3 ± 0.1 GeV...... 27 16 3.13. Mean number of particles produced from νµ(left) and ν¯µ(right) on 8 O over the energy. 27 16 3.14. Mean number of produced pions for νµ(top) and ν¯µ(bottom) on 8 O over the energy with GiBUU(left) and gSeaGen(right)...... 28 16 3.15. Calculated cross-sections for 8 O in GiBUU with default settings(left) and with changed PYTHIA settings(right) for νµ(top) and ν¯µ(bottom) ...... 29
3.16. yb distributions of GiBUU with default settings(left) and with changed PYTHIA 16 settings(right) for νµ(top) and ν¯µ(bottom) with Eν = 3 GeV on 8 O...... 30 16 3.17.
16 B.1. yb-distribution of CC-events, divided by process, of νµ(top) and ν¯µ(bottom) on 8 O with GiBUU(left) at Eν = 1 GeV and gSeaGen(right) at Eν = 1 ± 0.1 GeV, all plots were normed to the maximum being 1 ...... 45 16 B.2. yb-distribution of CC-events, divided by process, of νµ(top) and ν¯µ(bottom) on 8 O with GiBUU(left) at Eν = 2 GeV and gSeaGen(right) at Eν = 2 ± 0.1 GeV, all plots were normed to the maximum being 1 ...... 46 16 B.3. yb-distribution of CC-events, divided by process, of νµ(top) and ν¯µ(bottom) on 8 O with GiBUU(left) at Eν = 4 GeV and gSeaGen(right) at Eν = 4 ± 0.1 GeV, all plots were normed to the maximum being 1 ...... 47 16 B.4. yb-distribution of CC-events, divided by process, of νµ(top) and ν¯µ(bottom) on 8 O with GiBUU(left) at Eν = 5 GeV and gSeaGen(right) at Eν = 5 ± 0.1 GeV, all plots were normed to the maximum being 1 ...... 48 1 B.5. yb-distribution of CC-events, divided by process, of νµ(top) and ν¯µ(bottom) on 1H with GiBUU(left) at Eν = 1 GeV and gSeaGen(right) at Eν = 1 ± 0.1 GeV, all plots were normed to the maximum being 1 ...... 49 1 B.6. yb-distribution of CC-events, divided by process, of νµ(top) and ν¯µ(bottom) on 1H with GiBUU(left) at Eν = 2 GeV and gSeaGen(right) at Eν = 2 ± 0.1 GeV, all plots were normed to the maximum being 1 ...... 50 1 B.7. yb-distribution of CC-events, divided by process, of νµ(top) and ν¯µ(bottom) on 1H with GiBUU(left) at Eν = 4 GeV and gSeaGen(right) at Eν = 4 ± 0.1 GeV, all plots were normed to the maximum being 1 ...... 51 1 B.8. yb-distribution of CC-events, divided by process, of νµ(top) and ν¯µ(bottom) on 1H with GiBUU(left) at Eν = 5 GeV and gSeaGen(right) at Eν = 5 ± 0.1 GeV, all plots were normed to the maximum being 1 ...... 52
16 C.1. yb-φ distributions for νµ on 8 O with GiBUU(left) at Eν = 1 GeV and gSeaGen(right) at Eν = 1 ± 0.1 GeV ...... 53 38 List of Figures
16 C.2. yb-φ distributions for νµ on 8 O with GiBUU(left) at Eν = 2 GeV and gSeaGen(right) at Eν = 2 ± 0.1 GeV ...... 53 16 C.3. yb-φ distributions for νµ on 8 O with GiBUU(left) at Eν = 4 GeV and gSeaGen(right) at Eν = 4 ± 0.1 GeV ...... 54 16 C.4. yb-φ distributions for νµ on 8 O with GiBUU(left) at Eν = 5 GeV and gSeaGen(right) at Eν = 5 ± 0.1 GeV ...... 54
16 D.1. Particle production of the interaction of νµ(top) and ν¯µ(bottom) with 8 O with GiBUU(left) at Eν = 1 GeV and gSeaGen(right) at Eν = 1 ± 0.1 GeV ...... 55 16 D.2. Particle production of the interaction of νµ(top) and ν¯µ(bottom) with 8 O with GiBUU(left) at Eν = 2 GeV and gSeaGen(right) at Eν = 2 ± 0.1 GeV ...... 56 16 D.3. Particle production of the interaction of νµ(top) and ν¯µ(bottom) with 8 O with GiBUU(left) at Eν = 4 GeV and gSeaGen(right) at Eν = 4 ± 0.1 GeV ...... 57 16 D.4. Particle production of the interaction of νµ(top) and ν¯µ(bottom) with 8 O with GiBUU(left) at Eν = 5 GeV and gSeaGen(right) at Eν = 5 ± 0.1 GeV ...... 58
E.1. yb distributions of GiBUU with default settings(left) and with changed PYTHIA 1 settings(right) for νµ(top) and ν¯µ(bottom) with Eν = 3 GeV on 1H...... 59 16 E.2. Process type ratio over Eν of νµ(top) and ν¯µ(bottom) on 8 O of GiBUU with default settings(left) and with changed PYTHIA settings(right)...... 60 List of Tables
2.1. Elementary particles and the force carriers of the fundamental forces...... 6 2.2. Overview of the different interaction processes of neutrinos with nucleons...... 8 2.3. ∆-baryons and their decay...... 9
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&neutrino_induced process_ID = 2 ! 2:CC, 3:NC, −2:antiCC , −3:antiNC flavor_ID = 2 ! 1:electron , 2:muon, 3:tau nuXsectionMode = 6 ! 6: dSigmaMC includeDIS = . true . ! enables DIS events include2p2hQE = . f al se . ! enables 2p2hQE events include2p2hDelta = . f al se . ! enables 2p2hDelta events printAbsorptionXS = T /
&target target_Z=1 target_A=1 /
&input numEnsembles = 100000 ! for H: 100000, ! f o r O: 6400 ! decrease it if there are ! problems with memory or ! for heavier nuclei eventtype = 5 ! 5=neutrino ! of a given particle numTimeSteps = 0 ! the distance numTimeSteps∗delta_T ! should significantly ! exceed the radius ! of the target nucleus ! for H this must be 0 ! numTimeSteps=0 gives inclusive !X−s e c t i o n s delta_T = 0.2 ! timestep for hadron propagation localEnsemble = . true . ! sets fullEnsemble = True
43 44 A. example job card
num_runs_SameEnergy = 1 ! increase these if you want to ! increase statistics ! (= number of generated events) LRF_equals_CALC_frame = . true . ! if .false.: ! no offshelltransport ! p o s s i b l e path_to_input = ’/inputpath/buuinput ’ ! needs to be ! changed to actual path /
&nl_SigmaMC enu = 5 !energy of the initial neutrino /
&nl_neutrinoxsection DISmassless = . f al se . /
&neutrinoAnalysis outputEvents = . true ! output list of events and ! all outgoing particles in ! each event to the file ! FinalEvents.dat / B yb distributions
16 Figure B.1.: yb-distribution of CC-events, divided by process, of νµ(top) and ν¯µ(bottom) on 8 O with GiBUU(left) at Eν = 1 GeV and gSeaGen(right) at Eν = 1 ± 0.1 GeV, all plots were normed to the maximum being 1
45 46 B. yb distributions
16 Figure B.2.: yb-distribution of CC-events, divided by process, of νµ(top) and ν¯µ(bottom) on 8 O with GiBUU(left) at Eν = 2 GeV and gSeaGen(right) at Eν = 2 ± 0.1 GeV, all plots were normed to the maximum being 1 47
16 Figure B.3.: yb-distribution of CC-events, divided by process, of νµ(top) and ν¯µ(bottom) on 8 O with GiBUU(left) at Eν = 4 GeV and gSeaGen(right) at Eν = 4 ± 0.1 GeV, all plots were normed to the maximum being 1 48 B. yb distributions
16 Figure B.4.: yb-distribution of CC-events, divided by process, of νµ(top) and ν¯µ(bottom) on 8 O with GiBUU(left) at Eν = 5 GeV and gSeaGen(right) at Eν = 5 ± 0.1 GeV, all plots were normed to the maximum being 1 49
1 Figure B.5.: yb-distribution of CC-events, divided by process, of νµ(top) and ν¯µ(bottom) on 1H with GiBUU(left) at Eν = 1 GeV and gSeaGen(right) at Eν = 1 ± 0.1 GeV, all plots were normed to the maximum being 1 50 B. yb distributions
1 Figure B.6.: yb-distribution of CC-events, divided by process, of νµ(top) and ν¯µ(bottom) on 1H with GiBUU(left) at Eν = 2 GeV and gSeaGen(right) at Eν = 2 ± 0.1 GeV, all plots were normed to the maximum being 1 51
1 Figure B.7.: yb-distribution of CC-events, divided by process, of νµ(top) and ν¯µ(bottom) on 1H with GiBUU(left) at Eν = 4 GeV and gSeaGen(right) at Eν = 4 ± 0.1 GeV, all plots were normed to the maximum being 1 52 B. yb distributions
1 Figure B.8.: yb-distribution of CC-events, divided by process, of νµ(top) and ν¯µ(bottom) on 1H with GiBUU(left) at Eν = 5 GeV and gSeaGen(right) at Eν = 5 ± 0.1 GeV, all plots were normed to the maximum being 1 C yb-φν,µ distributions
16 Figure C.1.: yb-φ distributions for νµ on 8 O with GiBUU(left) at Eν = 1 GeV and gSeaGen(right) at Eν = 1 ± 0.1 GeV
16 Figure C.2.: yb-φ distributions for νµ on 8 O with GiBUU(left) at Eν = 2 GeV and gSeaGen(right) at Eν = 2 ± 0.1 GeV
53 54 C. yb-φν,µ distributions
16 Figure C.3.: yb-φ distributions for νµ on 8 O with GiBUU(left) at Eν = 4 GeV and gSeaGen(right) at Eν = 4 ± 0.1 GeV
16 Figure C.4.: yb-φ distributions for νµ on 8 O with GiBUU(left) at Eν = 5 GeV and gSeaGen(right) at Eν = 5 ± 0.1 GeV D Particle production
16 Figure D.1.: Particle production of the interaction of νµ(top) and ν¯µ(bottom) with 8 O with GiBUU(left) at Eν = 1 GeV and gSeaGen(right) at Eν = 1 ± 0.1 GeV
55 56 D. Particle production
16 Figure D.2.: Particle production of the interaction of νµ(top) and ν¯µ(bottom) with 8 O with GiBUU(left) at Eν = 2 GeV and gSeaGen(right) at Eν = 2 ± 0.1 GeV 57
16 Figure D.3.: Particle production of the interaction of νµ(top) and ν¯µ(bottom) with 8 O with GiBUU(left) at Eν = 4 GeV and gSeaGen(right) at Eν = 4 ± 0.1 GeV 58 D. Particle production
16 Figure D.4.: Particle production of the interaction of νµ(top) and ν¯µ(bottom) with 8 O with GiBUU(left) at Eν = 5 GeV and gSeaGen(right) at Eν = 5 ± 0.1 GeV E New PYTHIA settings
Figure E.1.: yb distributions of GiBUU with default settings(left) and with changed PYTHIA set- 1 tings(right) for νµ(top) and ν¯µ(bottom) with Eν = 3 GeV on 1H. 60 E. New PYTHIA settings
16 Figure E.2.: Process type ratio over Eν of νµ(top) and ν¯µ(bottom) on 8 O of GiBUU with default settings(left) and with changed PYTHIA settings(right). Erklärung
Hiermit bestätige ich, dass ich diese Arbeit selbstständig und nur unter Verwendung der angegebenen Hilfsmittel angefertigt habe.
Erlangen,
Patrick Heuer