Setup of a Drift Tube Muon Tracker and Calibration of Muon ...

More documents

Recommendations

Info

eigenstates |ν i 〉:|ν α 〉 = ∑ iU ∗ αi |ν i〉, (2.1)where U is the unitary leptonic mixing matrix, often called the Maki-Nakagawa-Sakata or Pontecorvo-Maki-Nakagawa-Sakata Matrix after the physicists who firstintroduced the idea of neutrino mixing in the late 1950s and early 1960s [21–23].If the neutrino mass eigenstates are different from each other, quantum mechanicsleads to the possibility of flavor changes for neutrinos traveling in vacuum or matter.A neutrino only interacts through the weak force, thus it is always created as a weakor flavor eigenstate. For the evolution of the neutrino, the superposition of its masseigenstates has to be considered. If the neutrino then interacts with matter againthe flavor eigenstate determines the type of reaction. The probability of a changeof flavor α into β for a neutrino withe energy E ν traveling a distance L in vacuumcan be calculated by:〈 ∣ ∣ 〉∣ ∣∣∣P να→ν β=∣ ν β e −i m2 i ∣∣∣ ∣∣∣22Eν L ν α ,where m i is the mass of the eigenstate |ν i 〉. While there are three known flavoreigenstates of the neutrino, the number of different mass eigenstates can in principleexceed this number (leading to the possibility of sterile neutrinos). In the case ofjust three mass eigenstates, the mixing matrix can be parametrized as a 3×3 matrixwith three mixing angles θ ij and one phase δ. In the case of neutrinos being theirown anti particles, two additional Majorana phases α 1 and α 2 have to be includedin the mixing matrix. The mixing matrix U can thus be parametrized as follows:⎛⎞ ⎛1 0 0 cos θ 13 0 sin θ 13 e −iδ ⎞U = ⎝0 cos θ 23 sin θ 23⎠ × ⎝ 0 1 0 ⎠0 − sin θ 23 cos θ 23 − sin θ 13 e iδ 0 cos θ 13⎛⎞ ⎛cos θ 12 sinθ 12 0 e iα ⎞1/20 0× ⎝− sin θ 12 cos θ 12 0⎠ × ⎝ 0 e iα 2/20⎠ .0 0 1 0 0 1The mixing angles θ 23 [24–28] and θ 12 [29–31] have been measured by various experiments.For the remaining mixing angle θ 13 , an upper limit only could be determinedso far [32]. The complex phase δ can be responsible for CP violation in the leptonsector. Using the notation above implies that CP violation in the lepton sector willonly have an effect in neutrino oscillations when θ 13 is non vanishing. An overviewof the oscillation parameters determined so far is presented in Tab. 2.1.In most cases, it is sufficient to consider the oscillation of only two neutrinoflavors. This simplification can be done because two of the squared mass splittingsare quite different from each other. In the case of two flavor oscillations, the mixingmatrix simplifies to:U =( ) cos θ sin θ, (2.2)− sin θ cos θ8
Table 2.1: Neutrino oscillation parameters determined by recent oscillation experiments.Values taken from the Lepton Particle Listings in [33].Oscillation ∆m 2 [eV 2 ] sin 2 (2θ)21 (sol) 7.59 +0.19−0.21 × 10−5 0.87 ± 0.0332 (atm) (2.43 ± 0.13) × 10 −3 > 0.9231 - < 0.15with just one mixing angle θ. Defining the squared mass splitting ∆m 2 = m 2 1 − m2 2 ,the oscillation probability can then be expressed as:( 1.27∆mP να→ν β= sin 2 (2θ)sin 2 2 )L, (2.3)E νwhere E ν is given in GeV and L in km.2.2.2 Oscillations in Matter - MSW EffectThe oscillation formalism described above describes the flavor change of neutrinostraveling in vacuum. The presence of matter influences this effect through coherentforward scattering of the neutrinos by the particles along their way. The influenceof matter to neutrino oscillations was first suggested by L. Wolfenstein in 1977 [34].There are two possibilities for scattering of neutrinos: the first is through theexchange of a Z 0 boson with an ambient electron, proton or neutron and the secondthrough a CC interaction between a ν e and an electron by exchange of a W boson.It is noteworthy that the latter process is only possible for electron type neutrinosin ordinary matter whereas the NC channel is open to all neutrino types alike. TheCC channel leads to an extra interaction potential energy V W for electron neutrinosin matter:V W = + √ 2G F N e , (2.4)with the Fermi coupling constant G F and the number of electrons per unit volumeN e [35]. For anti electron neutrinos, the sign of Eq. 2.4 changes.Analogously, the NC reaction contributes to an extra interaction potential energyV Z . However, affecting all neutrino flavors equally it does not show any effect inmatter enhanced oscillations and is not further regarded here.The interaction potential energy from Eq. 2.4 has to be considered during theevolution of the neutrino. For simplicity, only two flavor ν α → ν β oscillations areconsidered here. It can be shown (see e.g. [35]) that definingand∆m 2 m ≡ ∆m 2 √sin 2 2θ + (cos 2θ − x) 2 , (2.5)sin 2 2θ m ≡sin 2 2θsin 2 2θ + (cos 2θ − x) 2 (2.6)9
Page 1 and 2: Setup of a Drift Tube Muon Trackera
Page 3: AbstractIn this work the setup and
Page 6 and 7: 3.5.5 Pattern Recognition . . . . .
Page 8 and 9: viii
Page 10 and 11: essential for vetoing these events.
Page 13 and 14: Chapter 2NeutrinosThe standard mode
Page 15: However, it did not yet deliver an
Page 19 and 20: this assumption, the Standard Solar
Page 21 and 22: Figure 2.1: Neutrino flux at Earth
Page 23 and 24: asymmetry between neutrino and anti
Page 25 and 26: Figure 2.3: Expected ¯ν e energy
Page 27: Nb neutrino/fission-11010-2Neutrino
Page 30 and 31: 108−dE/dx (MeV g −1 cm 2 )65432
Page 32 and 33: Figure 3.3: Setup of the muon track
Page 34 and 35: zyxModule b.0Module a.0Module b.1Mo
Page 36 and 37: Figure 3.6: Display of the slow con
Page 38 and 39: plastic scintillators. To avoid all
Page 40 and 41: N hitsHitmap Plane 06000h_hitmap0En
Page 42 and 43: Table 3.4: Data structure for calib
Page 44 and 45: TDC SpectrumN/[2 Channels]1000800H_
Page 46 and 47: Table 3.5: List of variables calcul
Page 48 and 49: with ∆⃗q = ⃗q n − ⃗q n−
Page 50 and 51: N [a.u.]∆ α (x)2200020000da0Entr
Page 52 and 53: d[mm]Reco Drift Distances201816H_RE
Page 54 and 55: N [a.u.]Real DataReal data0.06MCh1E
Page 56 and 57: χ 2N [a.u.]Probability103×10hc2p0
Page 58 and 59: N [a.u]Residuals20001800h0Entries 3
Page 60 and 61: Counts/(10 keV × day × 100 tons)1
Page 62 and 63: 4.1.3 Čerenkov LightČerenkov dete
Page 64 and 65: 4.2 The Borexino DetectorThe Borexi
Page 66 and 67:
muons, is reduced by going deep und
Page 68 and 69:
(typically below 50 cm), the locati
Page 70 and 71:
510Counts/(10 keV x day x 100 tons)
Page 72 and 73:
counts/days*4 hitsDay (Red) and Nig
Page 74 and 75:
eeSurvival probability for ν e, P0
Page 76 and 77:
the CMT to the Borexino tracking, t
Page 78 and 79:
P C P DSCINT C SCINT DySCINT BSCINT
Page 80 and 81:
Figure 5.2: The CMT setup on top of
Page 82 and 83:
Angular AcceptanceAngular Acceptanc
Page 84 and 85:
Comparison nhits=3 vs nhits=4N [a.u
Page 86 and 87:
Table 5.3: Overview of all muon run
Page 88 and 89:
N/dayAll Triggers vs Time12000h_tim
Page 90 and 91:
Reco Hits in Scintillatory [mm]1000
Page 92 and 93:
PMTPMTScintillatorPMTPMTFigure 5.16
Page 94 and 95:
the CMT data file and the Borexino
Page 96 and 97:
Zenith Angle CMT and BX-GL Tracks h
Page 98 and 99:
Lateral x Resolution CMT - IDhlatx_
Page 100 and 101:
Distance d between CMT and BX-GL Tr
Page 102 and 103:
Angular difference αN [arbitrary u
Page 104 and 105:
[m]z bxTrack Position in BX x=0 Pla
Page 106 and 107:
N [arbitrary units]∆y all data200
Page 108 and 109:
To determine the Borexino tracking
Page 110 and 111:
Table A.1: Variables that can be se
Page 112 and 113:
espectively. The channel numbers ar
Page 114 and 115:
xyϕϕ ′βx ′µFigure C.2: Rela
Page 116 and 117:
the z-coordinate z op,0 of the firs
Page 118 and 119:
xyEvent: 470, Entry: 470, Time Tue
Page 120 and 121:
[14] Ch. Kraus et al. Final Results
Page 122 and 123:
[49] T. Araki et al. Experimental i
Page 124 and 125:
116
Page 126:
Jan Lenkeit und Björn Wonsak sowie
show all

Setup of a Drift Tube Muon Tracker and Calibration of Muon ...

You also want an ePaper? Increase the reach of your titles

Delete template?

Save as template?