2D Michel Reconstruction in MicroBooNE Kathryn Sutton∗ Columbia University, Nevis Labs, Irvington, New York y 8/6/2015 Abstract This paper describes an algorithm that can be applied to cosmic data in MicroBooNE to identify and cluster Michel electron showers and reconstruct their energy using only 2D reconstruction information. It takes into account charge and position information from the collection plane only. An accurate recon- struction of the Michel energy spectrum will be useful as a calibration method in the early stages of data collection. 1 Introduction 1.1 The Standard Model of Particle Physics The Standard Model aims to describe the elemen- tary particles responsible for all of the visible matter in the universe and its fundamental forces. Under the Standard Model there are twelve elementary particles 1 with spin 2 known as fermions, each with a corre- sponding anti-particle. These fermions fall into two main categories: quarks (up, down, charm, strange, top, bottom) and leptons (electron, electron neutrino, muon, muon neutrino, tau, tau neutrino), each of which is further divided into three generations (see Fig. 1). There are also the force carriers; gluons, W ± and Z0, and photons, which mediate the strong, weak, and electromagnetic forces respectively. 2 1 Quarks carry fractional charges (+ 3 or - 3 ) and are grouped according to flavor. They are bound Figure 1: The Standard Model of Particle Physics [1]. together to form hadrons. Hadrons can be further Increasing generations of fermions (reading from left described as baryons, composed of three quarks, and to right) correspond to increasing masses. ∗Electronic Address: [email protected] yPermanent Address: Gallatin School of Individualized Study, New York University, New York, New York 1 mesons, composed of a quark and an anti-quark. Neutrons and protons are both examples of baryons while a pion is an example of a meson, and all of these particles are hadrons. Because quarks only exist in bound states they are only observable indirectly. Leptons have only integer charges (−1 or 0); an electron has charge −1 while neutrinos are taken to have zero charge and mass [3]. In the Standard Model the recently discovered Higgs boson is responsible for giving masses to these Figure 2: [2] Probability of an electron neutrino oscil- fundamental particles, however gravity is still not lation as a function of distance per energy. The black well accounted for. The Standard Model also does curve shows the probability of observing an electron not explain why neutrinos have very small but non- neutrino, red a tau neutrino, and blue a muon neu- zero masses. Despite some residual unresolved ques- trino. Here it is clear that at short distances the prob- tions from the Standard Model it has proven to be ability of observing an electron neutrino remains close a robust model of the elementary particles and their to 1, but at certain greater distances the probabilities behaviors in both experimental and theoretical inves- of observing a muon or tau neutrino dominate. tigations. 0 1 1.2 Neutrino Oscillations 1 0 0 C = @ 0 cos θ23 sin θ23 A (4) Neutrinos are created and annihilated as three fla- 0 − sin θ23 cos θ23 vor eigenstates, νe,νµ, and ντ , but propagate through Where θij is the mixing angle between two mass space according to their mass eigenstates, ν1,ν2, and eigenstates and δCP is the charge-parity violation ν3, with each flavor eigenstate being a certain linear combination of the three mass eigenstates: phase which has yet to be experimentally determined but predicted to be non-zero. If this is the case it X jν i = U jν i would indicate that neutrinos and anti-neutrinos os- α αi i cillate differently, a violation of CP symmetry [3]. i For a given pair of neutrino flavors the probability Where U is the unitary matrix: αi that a neutrino with flavor α will be observed at a 0 1 later time as a neutrino with flavor β is given by (see Ue1 Ue2 Ue3 Fig. 2): Uαi = @ Uµ1 Uµ2 Uµ3 A (1) Uτ1 Uτ2 Uτ3 2 2 X ∗ −imi L=2E 2 Pα!β = jhνβjναij = j UαiUβie j This matrix can be further decomposed into mixing i matrices: such that mi is the mass of a given mass eigenstate, Uαi = [A][B][C] L is the distance traveled, and E is the energy. For such that: two neutrino case this simplifies to: 0 1 cos θ12 sin θ12 0 2 2 2 Pα!β,α6=β = sin (2θ) sin (1:27∆m L=E) A = @ − sin θ12 cos θ12 0 A (2) 0 0 1 Because of this ∆m2 term, only the difference between the masses of any two mass states can 0 −iδCP 1 cos θ13 0 e sin θ13 be observed experimentally. Also, because of the 2 2 B = @ 0 1 0 A (3) sin (1:27∆m L=E) term current observations are in- −iδCP 2 e sin θ13 0 cos θ13 sensitive to whether ∆m is positive or negative, 2 Figure 5: Diagram of the MicroBooNE detector. The Figure 3: [4] The two possible neutrino mass hierar- lower right corner shows the three wire planes. The chies, referred to as normal(left) and inverted(right). box in the center shows the liquid argon volume with Because the masses are only know relative to each the wire planes and PMTs on the right edge [5]. other it is currently unclear which version correctly describes their absolute ranking. tions (see Fig. 7) , ionizing the argon atoms and generating a trail of electrons (see Fig. 6). The which leads to an uncertainty in the mass hierarchy information about the position and timing of these [4] (see Fig. 3). interactions is available thanks to the two primary components of the time projection chamber: the pho- 1.3 MicroBooNE tomultiplier tubes (PMTs) and the three wire planes. When ionization occurs in the liquid argon, the MicroBooNE is a liquid argon time projection cham- resulting electrons drift towards the wire recording ber (LArTPC) neutrino oscillation experiment lo- planes at a speed of 1.6 cm/ms thanks to a 500V/cm cated at the Fermi National Accelerator Laboratory electric field generated by a negatively charged cath- (FNAL). It is installed colinear with Booster beam ode plate on the opposite side. The three wire planes line, downstream of the beryllium target at a dis- are each offset by 60 degrees from each other, and tance of 469m (see Fig. 4). With a total volume of each has wires spaced a distance of 3 mm apart. As approximately 170 tons of liquid argon and a 2.4 x the electrons drift past the negatively charged U and 2.4 x 2.4 m3 drift region, it is the largest liquid argon V planes they produce a signal via induction are at- neutrino experiment operating in the U.S. tracted towards the Y plane that collects the elec- Neutrinos in the detector interact with the liquid trons. 36 PMTs are installed behind the wire planes argon via both neutral and charged current interac- to detect the light emitted from liquid argon scintil- lation, each of which is covered by a light shifter to increase the wavelength of the 128nm light to around 430nm. Position and charge information from the wire planes can be used in conjunction with timing information from the PMTs to reconstruct a 3D event in the detector [7] (see Fig. 5). Some of the primary research goals for the Mi- croBooNE experiment are to study neutrino cross- sections in liquid argon and to probe the region of low energy neutrino events seen in excess in MiniBooNE Figure 4: The location of the MicroBooNE experi- [6] at greater resolution than prior experiments (see ment along the booster beam at FNAL. Fig. 8). MicroBooNE will have double the sensi- 3 Figure 6: Example of neutrino event tracks in liquid argon taken in the ArgoNeuT experiment. Regions Figure 8: The signal seen in the MiniBooNE exper- in red indicated a higher charge deposition [9]. iment in the low energy region (200-475 MeV) could not be accounted for by current models [15]. is conserved, one neutrino must be muon-type neu- trino, the other an electron-type anti-neutrino. For charge conservation, the electron must have the same charge as the muon. This decay mode is also called a Michel decay after French physicist Louis Michel and a Michel electron is emitted isotropically from a decay probability given by: Figure 7: [8] Neutrino Scattering Feynman diagrams. In the case of neutral current the neutrino "bounces off” of another particle (shown in the left diagram), dP 1 2 (x; ρ, η) = x2(3(1 − x) + ρ(4x − 3)+ exchanging a neutral Z boson. In a charged current dx N 3 interaction the neutrino interacts via an exhange of 2 me 1 − x 1 me a W boson (shown in the center and right diagrams 3η + f(x) + O 2 ) (5) Emax x 2 E [3]. max Where N is a normalization factor, x = Ee Emax tivity to electron neutrinos than what was observed is the reduced energy that ranges from Ee to 1, Emax with MiniBooNE as well as the ability to differentiate Ee is the energy of the Michel electron, me is its + − me between e and γ ! e + e events. At present the mass, Emax = 2 is the endpoint of the spectrum, MicroBooNE experiment is approaching the data col- f(x) is the term accounting for first order radiative lection period that, barring further delays, will begin corrections assuming local V-A (weak) interaction, later this year.