School of Physics and Astronomy

Queen Mary University of London

Neutrino Oscillation Detection at

the T2K Experiment

Sean Cooper (120206797)

1 April 2016

Supervisor: Dr Teppei Katori

SPA6913 Physics Review Project

15 Credit Units

Submitted in partial fulfilment of the requirements for the degree of

MSci Physics from Queen Mary University of London

Declaration

I hereby certify that this project report, which is approximately eight thousand

words in length, has been written by me at the School of Physics and Astronomy,

Queen Mary University of London, that all material in this dissertation which is not

my own work has been properly acknowledged, and that it has not been submitted

in any previous application for a degree.

Sean Cooper (120206797)

ii

Abstract

The purpose of the T2K experiment is to precisely determine the θ13 mixing angle. It

is measured by observing νµ → νe oscillations, resulting in sin2 2θ13 = 0.088+0.049−0.039 (for

normal mass hierarchy and fixed oscillation parameters). θ13 is the last of the lepton

sector mixing angles, governing the rates of neutrino mixing, to be determined.

The T2K’s experimental setup is explained, and the theory of neutrino oscillations

reviewed. The proposed Hyper-Kamiokande experiment is also briefly discussed.

iii

Contents

List of Figures vi

List of Tables vii

1 Introduction 1

2 Neutrino Mixing 2

2.1 Theory . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2

2.1.1 Oscillation Probabilities in a Vacuum . . . . . . . . . . . . . . 2

2.1.2 The Two Neutrino Approximation . . . . . . . . . . . . . . . 3

2.1.3 Three Neutrinos in a Vacuum . . . . . . . . . . . . . . . . . . 5

2.1.4 Oscillations in Matter . . . . . . . . . . . . . . . . . . . . . . 7

2.2 Observing Oscillations . . . . . . . . . . . . . . . . . . . . . . . . . . 10

2.2.1 Measuring a Probability . . . . . . . . . . . . . . . . . . . . . 10

2.2.2 Determining the θ13 Mixing Angle . . . . . . . . . . . . . . . . 10

3 The T2K Experiment 12

3.1 Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12

3.2 Beam Production . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13

3.2.1 Proton Acceleration (J-PARC) . . . . . . . . . . . . . . . . . . 13

3.2.2 Primary Beamline . . . . . . . . . . . . . . . . . . . . . . . . . 15

3.2.3 Pion Production . . . . . . . . . . . . . . . . . . . . . . . . . 16

3.2.4 Secondary Beamline . . . . . . . . . . . . . . . . . . . . . . . 18

3.2.5 Beam Performance Monitoring (INGRID) . . . . . . . . . . . 20

3.3 Pre-Oscillation Measurements . . . . . . . . . . . . . . . . . . . . . . 21

3.3.1 ND280 Overview . . . . . . . . . . . . . . . . . . . . . . . . . 21

3.3.2 The UA1 Magnetic Yoke . . . . . . . . . . . . . . . . . . . . . 22

3.3.3 The Pi-Zero Detector (PØD) . . . . . . . . . . . . . . . . . . 22

3.3.4 Time Projection Chambers (TPCs) . . . . . . . . . . . . . . . 24

3.3.5 Fine Grained Detectors (FGDs) . . . . . . . . . . . . . . . . . 25

3.3.6 The Electromagnetic Calorimeter (ECal) . . . . . . . . . . . . 26

iv

3.3.7 The Side Muon Range Detector (SMRD) . . . . . . . . . . . . 27

3.4 Post-Oscillation Measurements . . . . . . . . . . . . . . . . . . . . . . 27

3.4.1 The Super-Kamiokande Far Detector . . . . . . . . . . . . . . 27

3.4.2 νµ and νe Event Reconstruction . . . . . . . . . . . . . . . . . 28

4 The T2K’s θ13 Measurements 31

4.1 Eliminating Unwanted Backgrounds . . . . . . . . . . . . . . . . . . . 31

4.2 The θ13 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31

5 The Hyper-Kamiokande 33

5.1 Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33

5.2 Beam Production . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34

5.3 Pre-Oscillation Measurements . . . . . . . . . . . . . . . . . . . . . . 34

5.4 Post-Oscillation Measurements . . . . . . . . . . . . . . . . . . . . . . 34

6 Conclusion 36

Bibliography 37

v

List of Figures

2.1 The probabilities of measuring a muon neutrino as a different flavour,

over some relatively short range. . . . . . . . . . . . . . . . . . . . . . 4

2.2 The neutral-current interaction νe,µ,τe− → νe,µ,τe

− that applies to all

neutrino and antineutrino flavours. . . . . . . . . . . . . . . . . . . . 7

2.3 The charged-current interactions of νe and νe with the electrons present

in matter. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7

3.1 Passage of the muon neutrino beam from J-PARC to Super-K. [15] . . 12

3.2 A comparison of how off-axis positioning influences muon neutrino

disappearance, and beam profile, 295 km from the source. [16] . . . . . 13

3.3 A rudimentary diagram of a drift tube LINAC. The arrows denote

the particles’ relative velocities. . . . . . . . . . . . . . . . . . . . . . 14

3.4 A schematic showing the primary and secondary beamlines at J-

PARC. [15] . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15

3.5 A side view of the secondary beamline. A close-up of the target

station is also shown. [16] . . . . . . . . . . . . . . . . . . . . . . . . . 18

3.6 A cross section of the magnetic focusing horn containing the graphite

target. [15] . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19

3.7 The predicted neutrino flux at the Super-K for different magnetic

horn currents. [16] . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19

3.8 The INGRID on-axis detector. [21] . . . . . . . . . . . . . . . . . . . . 21

3.9 An exploded cross section of the ND280. [15] . . . . . . . . . . . . . . . 22

3.10 A schematic of the PØD, the beam enters from the left side of the

figure. [22] . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23

3.11 A simplified cut-away drawing of a TPC. [24] . . . . . . . . . . . . . . 25

3.12 An example event inside the ND280’s tracking section. A neutrino

appears to have undergone deep inelastic scattering inside the FGD1.

A product of an interaction outside of the tracking section can be

seen in the top-left. A more typical neutrino event would involve

fewer particle tracks than seen here. [24] . . . . . . . . . . . . . . . . . 26

vi

3.13 A diagram of the Super-Kamiokande. [15] . . . . . . . . . . . . . . . . 28

3.14 A cone of Cherenkov radiation (blue) emitted by a charged particle

(red). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29

3.15 Two example event displays from the Super-K. [15] . . . . . . . . . . . 30

4.1 These plots show the possible values of sin2 2θ13 for all possible values

of δCP . The top plot (a) shows the values assuming normal mass

hierarchy, and the bottom plot (b) assumes an inverted mass hierarchy.

The 68% and 90% confidence regions are clearly shown, along with

several best-fit lines. [14] . . . . . . . . . . . . . . . . . . . . . . . . . . 32

5.1 A schematic view of the proposed Hyper-K detector. [8] . . . . . . . . 33

5.2 A cross section of one of the Hyper-K’s two cylinders. [8] . . . . . . . . 35

List of Tables

3.1 The fraction of neutrino flux sourced from each type of meson. The

left columns show percentages relative to their specific flavour, and

the right columns show percentages relative to the total neutrino flux. [16] 17

4.1 The oscillation parameters used to achieve the plots seen in figure

4.1. [14] . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32

vii

1 Introduction

In 1930, Wolfgang Pauli postulated the existence of a small, neutral particle. This

particle, later dubbed the neutrino, was proposed to explain the missing momenta

seen in beta decay experiments. These neutral leptons became part of the Standard

Model of particle physics, and were assumed to be massless.

In a paper first published in 1957, Bruno Pontecorvo postulated the idea of

neutrino mixing. [1] This mixing was proposed as a parallel to Kaon mixing, a process

in which charge-parity violation is observed. This theory of neutrino oscillations

allows neutrinos to change their leptonic charge, being observed as one flavour

at one time, and another flavour at a later time. The theory arises when the

weakly interacting neutrinos are rewritten as superpositions of mass eigenstates.

This requires that massive neutrino states exist, something which ran counter to

the Standard Model.

In the late 1960’s, the Homestake Experiment measured the neutrino flux coming

from the Sun. [2] These experiments measured a deficit in the number of electron

neutrinos they had expected, sparking what became known as the “Solar Neutrino

Problem”. Later experiments confirmed that this solar neutrino deficit was a direct

result of neutrino oscillation.

Neutrino oscillation probabilities are governed by parameters called mixing angles.

The purpose of the T2K experiment is to precisely measure θ13, the last unknown

lepton sector mixing angle. [3] This is done by looking for the appearance of electron

neutrinos in a muon neutrino beam.

1

2 Neutrino Mixing

2.1 Theory

2.1.1 Oscillation Probabilities in a Vacuum

Let us consider the weakly interacting neutrinos of the Standard Model: νe, νµ

and ντ . Each of these neutrinos, along with its charged counterpart, forms one of

three generations: electronic, muonic or tauonic. As such, each family is attributed

a distinct lepton number. Under weak interactions these three lepton numbers

are conserved independently, however neutrino oscillation offers the possibility of

forgoing this conservation law. Instead it considers the probability of a neutrino, of

some definite flavour, to be later measured as a different flavour altogether.

In the following equations, the Dirac notation |ν〉 will represent the quantum

mechanical state of a neutrino. Since this state exists over some vector space, we

can decompose it into a linear combination of the basis elements spanning that

space. As such, we will construct a basis from the mass eigenstates of the flavourful

neutrinos: [4]

|νl〉 =∑i

U∗li |νi〉 (2.1)

Here, l = e, µ, τ labels our definite flavour neutrinos, and i = 1, 2, 3 labels the

definite mass eigenstates from which they are comprised. The key observation, is

that we can write each of our three Standard model neutrinos as a superposition

of the same mass eigenbasis. The coefficients relating the flavourful neutrinos to

their mass eigenstates are said to be elements of a unitary matrix, U , known as the

Pontecorvo-Maki-Nakagawa-Sakata mixing matrix.1 However, whilst U determines

the fraction of each eigenstate present at some instantaneous time, the ratios of these

eigenstates at a later time are not necessarily constant. In natural units, c = ~ = 1,

1Some extensions of the Standard Model, such as the seesaw mechanism, do not preclude thepossibility of a non-unitary mixing matrix. However, for the purposes of this report the writerwill only consider unitary mixing matrices.

2

the time evolved mass eigenstates can be expressed as:

|νi(t)〉 = e−iHt |νi〉 (2.2)

When applied to the eigenstate |νi〉, the Hamiltonian, H, yields the corresponding

energy eigenvalue Ei. Upper bounds on the neutrino masses have been calculated,

with them expected to be of the order of 1 eV/c2 or lower. [5] Since these masses are

very small, and lowest currently detectable neutrinos are orders of magnitude more

energetic, we can employ an ultrarelativistic approximation:

Ei =√p2 +m2

i (2.3)

Here, p denotes the neutrino’s momentum and mi labels the mass of each eigenstate.

Since p >> mi we shall consider the Taylor series of Ei about mi = 0. Discarding

terms of order m4i or higher we find:

Ei ' p+m2i

2p≈ E +

m2i

2E(2.4)

By combining this result with (2.2), we can write the time evolved mass eigenstate

in terms of mi and the neutrino’s total energy E:

|νi(t)〉 = e−iELe−im2iL/2E |νi〉 (2.5)

Since these neutrinos are ultrarelativistic, and we are in natural units, the parameter

t has been replaced by the distance travelled L. Finally, consider the probability

that, at some time t, a neutrino known to initially known to be of flavour l is

measured as flavour l′:

Pl→l′ = ‖〈νl′|νl(t)〉‖2 =

∥∥∥∥∥∑i

Ul′iU∗lie−im2

iL/2E

∥∥∥∥∥2

(2.6)

Thus we have derived the oscillation probability, of some flavourful neutrino, in

terms of the eigenstate masses and the mixing matrix.

2.1.2 The Two Neutrino Approximation

The equations in 2.1.1 were found without reference to the number of neutrinos that

exist. Back in 1957, when Bruno Pontecorvo first postulated the idea of neutrino

oscillation, there were only two known neutrino flavours. Today’s Standard Model of

3

course includes three neutrinos, however a two flavour approximation often proves

a reasonably accurate one. For example, Figure 2.1 sees that an initially muon

neutrino is much more likely to be detected as either a muon-type or tau-type

neutrino than it is to be detected as an electron neutrino. Atmospheric neutrinos

created by cosmic rays entering our atmosphere are predominantly muonic. Whilst

the suppression of electron neutrinos seen in this plot is only valid over a relatively

short range, it is valid over the distance that the atmospheric neutrinos travel. In

this case, a two neutrino approximation that ignores electron neutrinos altogether

can be a reliable one.

0 1000 2000 3000 40000.0

0.2

0.4

0.6

0.8

1.0

Relative Distance, L�E Hkm�GeVL

Dete

cti

on

Probabil

ity

Time Evolution of an Initially Muon Neutrino

Νe

ΝΜ

ΝΤ

Figure 2.1: The probabilities of measuring a muon neutrino as a different flavour, over somerelatively short range.

Since in this approximation we only have two neutrino flavours, it is sufficient to

consider just two mass eigenstates. As such, the neutrino mixing matrix is a 2x2

unitary matrix. One key feature of unitary matrices is that they preserve norms,

thus we can conveniently consider our matrix to take the form of a rotation operator:

U =

[cos θ sin θ

− sin θ cos θ

](2.7)

Now the 2x2 mixing matrix is a function of just one parameter, θ, the mixing angle.

By substituting the elements from this matrix into (2.6) we arrive at the probability

of our flavour l neutrino oscillating to the second flavour l′:

Pl→l′ =∥∥∥sin θ cos θ

[e−im

21L/2E − e−im2

2L/2E]∥∥∥2

(2.8)

4

With some manipulation this equation can be reduced to the more simplified form:

Pl→l′ = sin2 2θ sin2

(∆m2L

4E

)(2.9)

Here, the new parameter ∆m2 ≡ m22 −m2

1 is known as the squared mass difference.

One can observe that θ determines the maximum probability amplitudes, and ∆m2

the period of oscillations. It is also trivial to notice that maximal mixing would

occur with sin2 2θ = 1, i.e. θ = π/4.

Let us now return to the atmospheric neutrino example. If we were to only

consider muon and tau neutrinos, then in the case of maximal mixing our flavour

states could be written as:

|νµ〉 =1√2

(|ν1〉+ |ν2〉)

|ντ 〉 =−1√

2(|ν1〉 − |ν2〉)

(2.10)

Experimental measurements of the atmospheric mixing angle have found sin2 2θ >

0.92. [6] As such, the use of a maximal mixing two neutrino approximation is sufficient

for many calculations.

2.1.3 Three Neutrinos in a Vacuum

The Standard Model of particle physics contains three generations of neutrino;

naturally then the most precise formalism of neutrino mixing is one which describes

all three of these flavours. Consequently, a 3x3 mixing matrix is required. In 2.1.2

a 2x2 mixing matrix was conveniently expressed as a rotation about the angle θ.

A higher order PMNS matrix requires more parameters, nonetheless it can still be

written in terms of rotation operators. In this case, three distinct rotations are

needed: [7]

R12 =

c12 s12 0

−s12 c12 0

0 0 1

R13 =

c13 0 s13e−iδCP

0 1 0

−s13eiδCP 0 c13

R23 =

1 0 0

0 c23 s23

0 −s23 c23

(2.11)

Here, cij ≡ cos θij and sij ≡ sin θij. We see that three mixing angles, θ12, θ13, and

θ23, are required, as well as the phase angle δCP . This phase, δCP , parametrises

the contribution due to charge-parity violation. If there is no CP violation then we

would observe δCP = 0, with all δCP 6= 0 corresponding to at least some CP violation

5

in the lepton sector. Current experiments are unable to directly measure δCP ,

however proposed projects such as the Hyper-Kamiokande hope to determine this

CP phase. [8] A large δCP could explain the universe’s matter/antimatter asymmetry.

The rotations (2.11) can then be combined to give the PMNS matrix:

U = R12R13R23 =

c12c13 s12c13 s13e−iδCP

−s12c23 − c12s23s13eiδCP c12c23 − s12s23s13e

iδCP s23c13

s12s23 − c12c23s13eiδCP −c12s23 − s12c23s13e

iδCP c23c13

(2.12)

It is encouraging that this matrix appears to be the leptonic analogue of the Cabibbo-

Kobayashi-Maskawa quark mixing matrix. However, we must consider the possibility

that neutrinos are Majorana particles. If this is indeed the case, the PMNS matrix

will differ from the CKM matrix by including two additional parameters. These

parameters, α1 and α2, are the Majorana phases, which can be applied to the mixing

matrix as so: [9]

U ′ = U

eiα1/2 0 0

0 eiα2/2 0

0 0 1

(2.13)

Whilst these Majorana phases would have an effect on some processes, including

neutrinoless double beta decay, they do not make any contribution to neutrino

oscillation. As such, when considering neutrino mixing there is no advantage to

using the corrected matrix, U ′, over the previously derived one. At present it is still

unknown whether neutrinos behave as Majorana particles or not. If they are found

to be Majorana particles then the neutrino be would identical to its antimatter

counterpart.

In 2.1.2 the oscillation probability was written in terms of the squared mass

difference ∆m2. By further simplifying (2.6) the probabilities become:

Pl→l′ = δll′ − 4∑i>j

Re[U∗liUl′iUljU∗l′j] sin2

(∆m2

ijL

4E

)

+ 2∑i>j

Im[U∗liUl′iUljU∗l′j] sin

(∆m2

ijL

4E

) (2.14)

Here, ∆m2ij ≡ m2

i −m2j . By comparing this to the mixing matrix found in (2.12),

we see that all Im[U∗liUl′iUljU∗l′j] = 0 if there is no CP violation (i.e. δCP = 0). This

equation can be expanded in terms of the mixing angles, in a similar manner to

(2.8), however the result is somewhat unwieldy.

6

2.1.4 Oscillations in Matter

Thus far we have considered the process of neutrino oscillation in vacua. Let us

not forget, however, that oscillation is not the only process that neutrinos undergo;

they are free to weakly interact with other particles. The way these matter effects

modify neutrino oscillations was first considered by Lincoln Wolfenstein in 1978. [10]

The formalisation of the propagation of neutrinos through matter is now known as

the Mikheyev-Smirnov-Wolfenstein effect.

Z0

e−

νe,µ,τ

e−

νe,µ,τ

Figure 2.2: The neutral-current interaction νe,µ,τe− → νe,µ,τe

− that applies to all neutrino andantineutrino flavours.

When considering matter’s effect on neutrino oscillation, we are primarily interested

in the processes which preserve our neutrinos – i.e., scattering processes, particularly

those that result in coherent forward scattering. Figure 2.2 depicts the neutral-

current interaction neutrinos undergo in matter, occurring with electrons and nucleons

alike. Importantly, this process is the same for all flavours of neutrino and antineutrino.

This causes a phenomenon analogous to the optical refraction of light.

W±

νe

e−

e−

νe

(a) νee− → νee

−

W−

e−

νe

νe

e−

(b) νee− → νee

−

Figure 2.3: The charged-current interactions of νe and νe with the electrons present in matter.

Besides neutral-current interactions, neutrinos will also undergo charged-current

7

interactions when passing through matter. The leptons of which stable matter is

comprised are predominantly electrons. As such, we need only consider the charged-

current processes in which neutrinos exchange W bosons with electrons. Figures 2.3a

and 2.3b depict the relevant interactions. Crucially, these processes only scatter

electron neutrinos (and electron antineutrinos). The unequal numbers of particles

and antiparticles in ordinary matter can cause a matter-induced CPT violation. [11]

Experiments searching for CP violation intrinsic to the oscillation process will have

to account for these “fake” violations.

We can introduce these weak interactions into our neutrino mixing model by

considering them as a potential acting on our flavourful neutrinos. This allows us to

write the system’s Hamiltonian, H = H0 + V , with V being a potential perturbing

our vacuum Hamiltonian H0. [12]

The potential V can be thought of as a combination of a neutral-current potential

and a charged-current potential. As such, this potential acting on some flavour l

neutrino is Vl = δleVcc + Vnc with the Kronecker delta denoting that only electronic

neutrinos feel the charged-current contribution. Since our neutral-current contribution

effects all neutrino flavours equally, it merely introduces a phase shift to our system,

and is of no physical importance. [10] We can therefore ignore these contributions,

simplifying our potential to one that only acts on the electron neutrino:2 [13]

Ve =√

2GFne (2.15)

Here, GF is the Fermi coupling constant, and ne is the electron density of the

medium.

It can be shown, using an ultrarelativistic approximation similar to (2.4), that H0

written in terms of the mixing matrix is: [12]

H0 =1

2EUM2

diagU† (2.16)

With M2diag ≡ diag(m2

1,m22,m

23). For simplicity, we will now consider the two

neutrino approximation seen in 2.1.2. In this approximation H0 simplifies to:

H0 =∆m2

4E

[− cos 2θ sin 2θ

sin 2θ cos 2θ

](2.17)

With this vacuum Hamiltonian now established we can write the Hamiltonian in

2The potential acting on an electron antineutrino is negative instead of positive. It is of the samemagnitude as the potential seen in (2.15).

8

matter:

H =∆m2

4E

[− cos 2θ sin 2θ

sin 2θ cos 2θ

]+

[Ve 0

0 0

](2.18)

We are free to add any multiple of the identity to the Hamiltonian without changing

its physical meaning. Hence:

H =∆m2

4E

[− cos 2θ sin 2θ

sin 2θ cos 2θ

]+

[Ve/2 0

0 −Ve/2

](2.19)

In this form it is difficult to gain any intuitive sense of what difference this matter

potential has made to the neutrino mixing. However, in the case where the matter

density is constant, we can restructure this Hamiltonian as:

H =∆m2

m

4E

[− cos 2θm sin 2θm

sin 2θm cos 2θm

](2.20)

This is reminiscent of the vacuum Hamiltonian except with two new parameters:

∆m2m, the effective squared mass difference, and θm, the effective mixing angle in

matter. With H cast in a form analogous to (2.17), the oscillation probability is

clearly:

Pl→l′ = sin2 2θm sin2

(∆m2

mL

4E

)(2.21)

By equating (2.19) and (2.20) we are able to determine these matter parameters in

terms of the vacuum parameters: [12]

sin2 2θm =1

Rsin2 2θ and ∆m2

m =√R ∆m2 (2.22)

Where R is the resonance factor :

R ≡(

cos 2θ − 2VeE

∆m2

)2

+ sin2 2θ (2.23)

In a vacuum the electron density is zero. In this limit Ve → 0, therefore R→ 1 and

the vacuum equations are recovered. Interestingly, maximal mixing occurs in cases

where 2VeE/∆m2 = cos 2θ, resulting in sin2 2θm = 1. [13] This resonant condition

maximises the oscillation amplitudes, even in cases where vacuum mixing would be

very small.

9

2.2 Observing Oscillations

2.2.1 Measuring a Probability

At first, a probability can seem like a very abstract quantity to measure. Let’s

consider a simple example in which a fair coin is flipped. If the coin is flipped just

a few times the results appear unpredictable. However, if the coin is flipped many

times we would see that it lands heads up approximately 50% of the time. By using

a large sample size the probability becomes an easily predicted statistical effect.

Let’s now consider a neutrino beam that is generated as just one flavour, l.

At some later time the beam hits a target, allowing us to measure its flavour

composition. If many neutrinos are measured, the probability of a neutrino having

oscillated to flavour l′ is:

Pl→l′ =Number of l′ detected

Total number of neutrinos(2.24)

However, neutrinos do not interact very abundantly with matter. This means

detecting a large sample size is difficult, and so the random nature of the oscillations

introduces uncertainty in the calculated probabilities.

2.2.2 Determining the θ13 Mixing Angle

The T2K experiment looks for the appearance of electron neutrinos in a muon

neutrino beam. This rate of appearance is then used to infer the νµ → νe oscillation

probability, from which the θ13 mixing angle can be determined. The full equation

for this oscillation probability, including the terms describing matter effects, is given

by: [14]

Pνµ→νe =1

(A− 1)2sin2 2θ13 sin2 θ23 sin2[(A− 1)∆]

− α

A(1− A)cos θ13 sin 2θ12 sin 2θ23 sin 2θ13 sin δCP sin ∆ sinA∆ sin[(1− A)∆]

+α

A(1− A)cos θ13 sin 2θ12 sin 2θ23 sin 2θ13 cos δCP cos ∆ sinA∆ sin[(1− A)∆]

+α2

A2cos2 θ23 sin2 2θ12 sin2A∆

(2.25)

10

Here: α =∆m2

21

∆m232� 1, ∆ =

∆m232L

4E, and A = 2

√2GFne

E∆m2

32. This equation is difficult

to interpret, however over the L/E range covered by the T2K it can be simplified

to: [14]

Pνµ→νe ≈ sin2 2θ13 sin2 θ23 sin2 ∆m232L

4E(2.26)

We see that the rate of νe appearance in the beam can be used to calculate θ13

providing that we know the parameters: θ23, ∆m232, L, and E.

Using this method to calculate θ13 requires the squared mass difference ∆m232.

This means that the experimental value of θ13 is different depending on whether the

neutrino mass hierarchy is normal or inverted. The neutrino mass hierarchy refers

the orderings of the mass eigenstate masses. In the normal hierarchy m21 < m2

2 < m23,

whereas in the inverted hierarchy m23 < m2

1 < m22. It is still unknown whether the

mass hierarchy is normal or inverted, so the sign of ∆m232 could be positive or

negative. This means that different values of θ13 will be calculated depending on

which hierarchy is assumed.

11

3 The T2K Experiment

3.1 Overview

The T2K experiment looks for neutrino oscillation in a beam of muon neutrinos

produced at the J-PARC facility in Tokai, Japan. The premise is that by measuring

the beam twice, shortly after production and then again at the Super-Kamiokande

observatory, the neutrinos can be characterised both before and after oscillation.1

The difference in these two measurements then allows for the muon neutrinos’

oscillation probabilities to be calculated.

Since neutrinos seldom interact with matter, the beam conveniently passes through

the Earth’s crust with no need of a pipe to contain it. Figure 3.1 shows the beam’s

path from J-PARC to the Super-K. Clearly we can divide the experiment into three

sections:

• The J-PARC facility where the beam is produced.

• The near detector (ND280), 280 m from the source. This is where the pre-

oscillation measurements are made.

• The far detector (Super-K), 295 km from the source. It is here that the post-

oscillation measurements are made.

Figure 3.1: Passage of the muon neutrino beam from J-PARC to Super-K. [15]

1The Super-K is based near the Kamioka section of Hida City, hence the experiment’s namesake:“Tokai-to-Kamioka”.

12

The T2K’s primary goal is to precisely determine the θ13 mixing angle, which

governs the rate of νµ → νe oscillations. However, as seen in figure 2.1, the

appearance of electron neutrinos is very scarce over these ranges. To maximise these

oscillations, the detectors are positioned off-axis from the beam’s centre. Figure 3.2

shows that setting the detector 2.5◦ off-axis results in a narrow-band of energies

centred around 0.6 GeV. This setup is clearly optimal, maximising the conversion

of muon neutrinos to other flavours.

Figure 3.2: A comparison of how off-axis positioning influences muon neutrino disappearance, andbeam profile, 295 km from the source. [16]

3.2 Beam Production

3.2.1 Proton Acceleration (J-PARC)

The production of the T2K’s neutrino beam begins with the acceleration of protons.

These protons then collide with a target, producing a shower of pions and kaons.

The muon neutrinos are then generated during the decay of these mesons.

The beam initially consists of hydrogen anions produced by a negative ion source.

These H− ions are then accelerated up to 400 MeV by a 330 m long linear accelerator

(LINAC).2 [17] The majority of the H− acceleration takes place in between the

2Unless otherwise stated, the energy values given from here on are kinetic energies.

13

accelerator’s drift tubes. As illustrated by figure 3.3, there are electric fields of

alternating polarity in each drift tube. A radio frequency driven voltage is used to

generate these electric fields. As each particle exits a tube, the oscillating voltage

flips the electric fields. This means that the H− ions always see a positive electric

field in front of them and a negative one behind them. As such, the particles are

only ever accelerated and not decelerated. This method requires the ions to spend

the same amount of time in each drift tube. Consequently, as the beam speeds up

the tubes must increase in length. Due to this constraint, LINACs are not ideal for

accelerating particles to high energies.

Figure 3.3: A rudimentary diagram of a drift tube LINAC. The arrows denote the particles’ relativevelocities.

After exiting the LINAC, the beam is injected into a rapid-cycling synchrotron

(RCS). As they are injected, the H− ions pass through a charge-stripping foil. This

foil removes the unwanted electrons, leaving just a proton beam behind. The beam’s

path into the RCS is guided by a magnetic field. As such, any unstripped particles

will follow a different trajectory and not make it into the synchrotron. Not only

does stripping the beam leave us with the desired protons, but it also means that

the same voltage used to accelerate the beam towards the foil will accelerate it away.

Synchrotrons overcome the size constraint of LINACs by directing their beam along

a closed path. As the electric fields accelerate the protons, the magnetic field used to

guide them must increase. Since the magnetic field is time-dependant, the protons

are sent through in bunches instead of as a continuum. Just two of these bunches

are accelerated by the RCS per cycle. [3]

The RCS accelerates the beam up to 3 GeV. Approximately 5% of the proton

bunches are directed into the main ring (MR) synchrotron, the remainder are supplied

to the Material and Life Science Facility to be used in other experiments. [3] The

MR has two extraction points: one used for hadron beamline experiments, and the

other to produce the T2K’s neutrino beamline. The proton bunches headed to the

neutrino beamline circle the MR just once before extraction. The MR accelerates

these protons up to 30 GeV, however it has the capacity to increase this energy to

14

50 GeV in the future. [3]

3.2.2 Primary Beamline

After the accelerated proton bunches leave the MR they form what is known as the

primary beamline. As seen in figure 3.4, the primary beamline can be split into three

sections: the preparation section, the arc section, and the final focusing section. The

primary beamline is where any fine tunings, and final adjustments, are made to the

beam before it hits the target.

Figure 3.4: A schematic showing the primary and secondary beamlines at J-PARC. [15]

During the preparation section the extracted proton beam is tuned by 11 normal

conducting magnets. [3] Of these magnets there are 4 steering magnets, 2 dipole

magnets, and 5 quadrupole magnets. The steering and dipole magnets are used to

guide the beam as it travels from the extraction point to the arc section. Quadrupole

magnets create a field that is at it’s minimum at the beam’s centre, but increases

rapidly with radial distance. For this reason, the quadrupole magnets are used to

focus the beam.

As the proton beam travels through the arc section it is bent through a total angle

of 80.7◦, resulting in a 104 m radius of curvature. [3] This bending aims the beam in

the direction of Kamioka (westwards across Japan). Superconducting magnets are

15

used to bend the beam through this dramatic angle.

The final focusing section marks the last segment of the primary beamline, after

which the protons will hit the graphite target. 10 normal conducting magnets are

used: 4 steering magnets, 2 dipole magnets, and 4 quadrupole magnets. These

magnets focus and guide the beam onto the target, which is just 2.6 cm in diameter. [3]

Focusing the beam is required to maximise the number of interactions with the

target. The magnets in this section are also used to angle the beam downwards

3.637◦ with respect to the horizontal. [3]

The proton bunches are monitored throughout the primary beamline. These

readings allow the beam’s tuning to be optimised, and therefore minimise the beam

loss. Various properties of the beam are measured including: beam intensity and

beam position. Since the monitors are numerous, it is possible to reconstruct each

bunch’s beam profile at many stages though the primary beamline.

3.2.3 Pion Production

The 30 GeV protons from the primary beamline bombard a stationary graphite

target producing a variety of hadrons. The target is 2.6 cm in diameter and 91.4 cm

long, which corresponds to approximately 1.9 interaction lengths. [3] As the beam

hits the target a large amount of energy is deposited, this results in an almost

instantaneous increase in temperature. [18] Graphite was chosen as a target material

since its melting point is relatively high. It is also stable, which makes it an easy

substance to work with. Whilst a higher density might allow for more interactions,

substances denser than graphite are unlikely to withstand the heat load. [19]

When the incident protons interact with the target nucleons hadrons are produced.

These produced hadrons, the large majority of which are pions or other mesons,

then either decay or undergo secondary interactions with the target. The lack of

knowledge about what hadrons are produced here is the largest source of uncertainty

on the T2K’s initial neutrino flux measurements. [20] The NA61/SHINE experiment

at the CERN SPS replicates the proton-graphite interactions that take place in the

neutrino beamline, cataloguing the hadrons produced by these collisions. It is hoped

that NA61/SHINE can help reduce the total systematic uncertainty on the neutrino

flux to less than 5%. [20]

The NA61/SHINE collides 31 GeV protons with two different targets. In one

experiment, a thin 2 cm target is used. [20] Here, the secondary hadrons produced

from the primary proton-nucleon interactions are measured. These secondary hadrons

account for approximately 60% of the T2K neutrino flux. [20] The remaining 40%

16

comes from the decay of tertiary hadrons produced in successive interactions. This

is measured in the second experiment, which utilises a replica of the T2K target.

The data from NA61/SHINE is then used to build and improve Monte Carlo

simulations of the T2K neutrino beamline. Table 3.1 shows Monte Carlo data of the

predicted neutrino flux from the different hadron decays. The data shows that whilst

small, the νe production is measurable. Any of this νe flux should be accounted for

to minimise errors in the T2K’s results.

Flux of each neutrino flavour (%) Flux of all neutrino flavours (%)Parent νµ νµ νe νe νµ νµ νe νe

Secondaryπ± 60.0 41.8 31.9 2.8 55.6 2.5 0.4 0.0K± 4.0 4.3 26.9 11.3 3.7 0.3 0.3 0.0K0L 0.1 0.9 7.6 49.0 0.1 0.1 0.1 0.1

Tertiaryπ± 34.4 50.0 20.4 6.6 31.9 3.0 0.2 0.0K± 1.4 2.6 10.0 8.8 1.3 0.2 0.1 0.0K0L 0.0 0.4 3.2 21.3 0.0 0.1 0.0 0.0

Table 3.1: The fraction of neutrino flux sourced from each type of meson. The left columns showpercentages relative to their specific flavour, and the right columns show percentagesrelative to the total neutrino flux. [16]

The majority of the muon neutrino beam is sourced from pion decays, with some

fraction from kaons. Leptons produced during these decays may then also decay,

producing neutrinos of various flavours. The π+ meson’s primary decay mode is

π+ → µ+νµ. In the Standard Model, the neutrinos produced in these π+ decays must

always be left-handed. For helicity to be conserved the emitted antilepton should

also be left-handed. In the limit where the electron’s mass is negligible, we see that

an emitted positron must be right-handed. This would defy helicity conservation.

Of course the electron is not massless, however it is much less massive than the

muon. This means that electronic decay mode is helicity suppressed, with the π+

meson much more likely to decay to a muon neutrino. The antimuon produced from

this process may later go on to decay as so: µ+ → e+νµνe.

17

3.2.4 Secondary Beamline

The secondary beamline defines the final section of the neutrino beamline at J-

PARC. It follows the proton-target interaction products as they decay into the final

neutrino beam. This secondary beamline is comprised of three parts: the target

station, the decay volume, and the beam dump. Figure 3.5 shows a cross section of

the beamline, detailing each of these three sections.

Figure 3.5: A side view of the secondary beamline. A close-up of the target station is also shown. [16]

The secondary beamline is water cooled and filled with helium gas. Helium

gas reduces the production of nitrogen oxides and radioactive materials; it also

serves to reduce the number of pions that are absorbed before they decay. [18] The

target station’s beam window separates this gas filled environment from the primary

beamline’s near vacuum. It is made from a helium-cooled titanium-alloy, and is

0.3 mm thick. [3] This allows the high energy protons to pass through, but prevents

the gas from escaping.

Once the protons enter the target station they travel through a 1.7 m long graphite

baffle. The proton beam passes through a 3 mm diameter hole in this baffle. [3] Its

purpose is to remove any off-course protons, preventing them from damaging any of

the first magnetic horn’s components. After exiting the baffle the beam is measured

by an optical transistor radiation monitor (OTR). This OTR has a thin titanium-

alloy foil angled at 45◦ to the proton beam. [3] As the beam passes through the foil

a narrow cone of visible light is produced. This transition radiation can then be

measured to attain a two-dimensional profile of the beam. The OTR has an eight-

position carousel that allows the foil to be switched for different beam energies.

After passing through the OTR, the beam hits the target (as described in 3.2.3).

18

There are three magnetic focusing horns in the target station. These magnetic

horns generate toroidal magnetic fields that allow the positive mesons to be focused

independently of the negative ones. This selective focusing keeps π+ mesons on-axis,

but removes π− mesons, increasing the νµ to νµ ratio. Neutral particles, such as

π0 mesons, cannot be focused. Instead Monte Carlo simulations must be used to

estimate their trajectories.

Figure 3.6: A cross section of the magnetic focusing horn containing the graphite target. [15]

Figure 3.7: The predicted neutrino flux at the Super-K for different magnetic horn currents. [16]

Figure 3.6 shows a cross section of the first magnetic horn, with the graphite target

contained within it. The graphite target, light green in the image, is fitted inside

the horn. The target must be fitted internally to ensure that all of the hadrons are

focused, regardless where along the target they are produced. The three magnetic

focusing horns are essential for a well-directed neutrino beam. A focused, on-axis,

secondary beamline corresponds to a narrow neutrino beam. This can be seen in

19

figure 3.7, where the neutrino flux at the Super-K is compared with and without

the magnetic horns activated.

After the interaction products leave the target station they travel through the

decay volume. As the name suggests, this is where the majority of the mesons

decay and the neutrinos are produced. Any particles that do not decay during

this 96 m long decay volume will reach the beam dump. The beam dump’s core

is made of 75 tons of graphite, and is contained within a helium vessel. The iron

plates surrounding this vessel add an additional 2.4 m of thickness. Any hadrons,

or tertiary muons below 5 GeV/c, that reach this point will be stopped. [3]

Only muons above 5 GeV/c can pass through the beam dump, and into the muon

monitor.3 [3] The majority of these muons would have been produced during the π+

decays. This means that data from the muon monitor can be used to characterise

the neutrinos also produced during these decays. As previously seen in table 3.1,

this corresponds to the majority of the neutrinos in the T2K’s beam. As such, the

muon monitor is able to measure the neutrino beam’s direction to a precision better

than 0.25 mrad, and its intensity to better than 3%. [3] Due to this experiment’s

long baseline, high precision measurements are important to accurately calculate

the neutrino flux. A second detector, just downstream from the muon monitor,

measures the flux and momentum distribution of the remaining muons. [3]

3.2.5 Beam Performance Monitoring (INGRID)

The Interactive Neutrino GRID (INGRID) is an on-axis neutrino detector 280 m

downstream from the proton beam’s target. [21] INGRID is comprised of 16 identical

modules, their arrangement can be seen in figure 3.8. The centre of INGRID’s cross

sits directly inline with the direction of the primary proton beamline. [3] This 0◦ point

is the only part of the detector covered by two modules. INGRID’s main purpose is

to monitor the neutrino beam direction to a precision better than 1 mrad. [21] This

is achieved by comparing the number of neutrino events observed in each module,

providing a measurement of the beam’s centre.

Each of INGRID’s modules consists of nine iron target plates and 11 tracking

scintillator planes, arranged in alternating layers. [21] The iron plates serve as an

interaction medium for the incident neutrinos. Any charged particles produced

should then be detected in the scintillating planes downstream of the interaction.

Since the neutrinos are not directly detectable, their interaction products will begin

midway through the module. Particles detected at the start of the module are

3The majority of the particles detected by the muon monitor are actually antimuons.

20

disregarded, as it is not possible to tell whether they were sourced from a neutrino

interaction. The modules are surrounded by veto scintillator planes. These veto

planes identify particles entering from the side of the module, allowing them to be

disregarded.

In addition to INGRID’s standard modules, there is unique proton module located

at the cross’s centre. The purpose of this module is to determine through which

channel the neutrinos have interacted. It uses scintillating bars to track the protons,

pions, and muons, produced during neutrino interactions [21]

Figure 3.8: The INGRID on-axis detector. [21]

3.3 Pre-Oscillation Measurements

3.3.1 ND280 Overview

The ND280 takes measurements of the neutrino beam, 280 m from its source. This

detector’s goal is to take pre-oscillation observations of the beam, at the same off-

axis angle as the Super-K. The beam’s flavour composition, energy spectrum, and

interaction rates are measured. [3] Figure 3.9 shows a breakdown of the ND280’s

components. These components are actually a selection of different subdetectors,

all surrounded by the UA1 Magnetic Yoke. The ND280’s core consists of the Pi-

Zero Detector, followed by a series of TPCs and FGDs. These central detectors

are surrounded by a series of Electromagnetic Calorimeters. There is also a Side

Muon Range Detector located inside of the UA1’s yoke. Despite housing all of these

21

detectors, the internal volume enclosed by the UA1 magnet is only 7.0 m x 3.5 m x

3.6 m. [3]

Figure 3.9: An exploded cross section of the ND280. [15]

3.3.2 The UA1 Magnetic Yoke

The UA1 magnet consists of 16 C-shaped flux return yokes, eight of which can

be seen in figure 3.9. [3] The remaining eight sit directly opposite them, forming a

ring covering the four sides parallel to the beam’s direction. The UA1 magnet was

repurposed for this experiment after its previous usage during the UA1 and NOMAD

experiments at CERN. It generates a horizontally orientated dipole field with a

field strength of 0.2 T. [3] This magnetic field allows the detectors to distinguish

between the positive and negatively charge particles generated during the neutrino

interactions. It also allows the momenta of these particles to be easily determined.

3.3.3 The Pi-Zero Detector (PØD)

The first ND280’s subdetector that the beam encounters is the PØD. The PØD’s

primary goal is to measure the neutral current process νµ+N → νµ+N+π0+X on a

water (H2O) target. [22] These single π0 producing neutral current interactions form a

significant background in the νe events observed at the Super-K. [23] In the Super-K,

electron neutrinos undergo charged current quasi-elastic (CCQE) interactions. High

22

energy electrons generated by these interactions will then trigger electromagnetic

showers. The aforementioned π0 mesons decay into two photons, each of which

can also cause an electromagnetic shower. Generally, the Super-K can identify

these photon sourced showers since they come in pairs, whereas the CCQE induced

showers are sourced from single particles. However, if only one of the photon showers

is observed, the signal becomes indistinguishable from an electron sourced one. This

means that νµ neutral current events can be falsely observed as νe events. The

number of false νe events due to this background can be estimated by using the

PØD’s measurements of the neutral current process’s cross section.

Figure 3.10: A schematic of the PØD, the beam enters from the left side of the figure. [22]

The PØD contains a total of 40 scintillator modules, or “PØDules”, which are

assembled into four super-PØDules. [22] These super-PØDules can be seen in figure

3.10. The Upstream Ecal and Central ECal super-PØDules consist of seven PØDules

alternating with seven steel-clad lead sheets. [22] Any electromagnetic showers that

occur here will be contained by these lead sheets. These ECal super-PØDules allow

any signals caused by interactions before or after the water target to be rejected.

Instead of a lead containment sheet, the Water Target super-PØDules have a brass

23

sheet and water bladder between each scintillating PØDule. Each of these Water

Target super-PØDules contains 13 scintillating PØDules. The PØD contains over

1900 kg of water for the π0 producing interactions to occur within, emulating the

water filled Super-K. [3]

Each PØDule is a plane formed from 260 scintillating bars. [22] Each plane consists

of one layer of horizontal bars and one layer of vertical bars. [3] A wavelength-shifting

fibre is threaded through each bar. A scintillator fluoresces when ionising radiation

passes through it. Luminescent materials in the scintillator are excited by the

incoming particle. This excitation energy is then re-emitted in the form of photons.

An optical fibre then guides this light to a photodetector at the edge of the PØDule.

These fibres have been doped with a wavelength shifter. This wavelength shifter

absorbs any photons that are too energetic and re-emits multiple lower energy ones.

Each bar is given a reflective coating to increase the probability that emitted light

hits an optical fibre. The PØD’s scintillating bars provide sufficient segmentation

to reconstruct both charged particle tracks and electromagnetic showers. [3]

3.3.4 Time Projection Chambers (TPCs)

Just downstream of the PØD is the tracking section of the ND280. This tracking

section consists of three TPCs and two FGDs. The FGDs are positioned either side

of the middle TPC, as seen in figure 3.9. The TPCs perform three key functions: [3]

• The excellent three-dimensional tracking provided by the TPCs allows the

number of incident charged particles, and their orientations, to be determined.

• By measuring the momenta of these charged particles, the event rate inside

the ND280 can be found as a function of neutrino energy.

• The amount of ionisation done by these charged particles is recorded. Particles

can then be easily identified by combining this ionisation data with their

measured momenta.

The TPCs do not contain their own target material, instead they measure particles

created elsewhere in the ND280.

Figure 3.11 shows a simplified illustration of a TPC. The inner box is filled with an

Ar : CF4 : i-C4H10 (95 : 3 : 2) gas mixture. [24] As a charged particle passes through

the TPC it will ionise this gas producing electrons. The cathode’s electric field will

cause these electrons to drift towards the micromegas detectors where they are then

observed. Due to argon’s zero electronegativity, it unlikely that a drift electron will

24

be absorbed before it reaches a detector. By combining the pattern of signals in

the detectors with the electron arrival time, a 3D image of the incident particle’s

trajectory and be produced. [3] The space between the inner and outer walls is filled

with CO2 gas. This acts to insulate the inner box from the grounded outer box. [24]

Figure 3.11: A simplified cut-away drawing of a TPC. [24]

Acceleration due to the TPC’s electric field will be in the x-direction, whereas

acceleration due to the ND280’s magnetic field will not. This allows both the charge

and momenta of the incident particles to be calculated. A calibration system uses

the photoelectric effect to produce electrons at known points on the cathode. The

trajectories these photoelectrons can be used calculate and inhomogeneities in the

electric and magnetic fields. [24]

3.3.5 Fine Grained Detectors (FGDs)

The main purpose of the FGDs is to provide target mass for the neutrino beam

to interact with. The first FGD (FGD1) is 86.1% carbon (by mass) and is

comprised solely of scintillating bars. [25] Whilst acting as the FGD1’s target mass,

the scintillators also allow the produced charged particles to be tracked right from

the interaction vertex. 5760 scintillating bars are arranged in alternating horizontal

and vertical planes of 192 bars, providing a total of 1.1 tons of target material. [3]

Figure 3.12 shows an example of an event inside ND280’s tracking section. The

interaction point inside the FGD1 can be clearly seen, with the process’s products

being tracked in each stage of the tracking section.

25

Figure 3.12: An example event inside the ND280’s tracking section. A neutrino appears to haveundergone deep inelastic scattering inside the FGD1. A product of an interactionoutside of the tracking section can be seen in the top-left. A more typical neutrinoevent would involve fewer particle tracks than seen here. [24]

The FGD furthest downstream (FGD2) uses both water and scintillating bars

as its target material. [26] The FGD2’s scintillators can be split into seven pairs of

horizontal and vertical planes. Water targets are placed alternating with these pairs

of planes, for a total of six water targets. Corrugated polycarbonate walls are used

to contain each sheet of water. In total the FGD2 contains 2688 scintillator bars,

and 15 cm thick of water in the beam direction. [3] The FGD2 allows the interaction

rates of neutrinos with water to be observed, which can be used to predict the rates

of processes occurring in the Super-K. [26].

3.3.6 The Electromagnetic Calorimeter (ECal)

The ECal fills the space between the inner detectors (PØD, TPCs, FGDs) and the

UA1 magnet. It’s purpose is to aid these inner detectors in reconstructing events.

The ECal measures the energy, and direction, of photons and charged particles. [3]

As seen in figure 3.9, it consists of three sections: the PØD-ECal, the barrel-ECal,

and the Ds-ECal (Downstream ECal). [27] The PØD-ECal is comprised of six ECal

modules that surround the PØD, two above it, two below it, and one either side.

These modules are attached directly to the UA1 magnet, two top and two bottom

modules are required so that the magnet’s halves can properly separate. The barrel-

ECal is also made up of six modules; these are also attached to the UA1 magnet and

surround the tracker volume in the same manner. The Ds-ECal consists of just one

module, which sits behind the final TPC, orientated to be orthogonal to the beam.

26

Each module consists of layers of scintillating bars, with lead containment sheets

between each layer. In the same manner as the inner detectors’ scintillators, the

layers are assembled with bar orientation alternating at 90◦. [3] Not only does the lead

contain an electromagnetic showers, it also acts as a target target mass and radiator

for each layer. [27] The ECal is constrained by the ND280’s internal dimensions,

consequently the modules are not all the same size. This means the PØD-ECal’s

modules are much thinner than the those in the barrel-ECal, containing fewer

scintillator-lead layers.

3.3.7 The Side Muon Range Detector (SMRD)

The SMRD consists of 440 scintillating modules that fill the 1.7 cm air gaps between

the 4.8 cm thick steel plates that make up the UA1 magnet. [3] It has three purposes:

• To measure the momenta of muons escaping the inner detector at high angles

with respect to the beam direction. [28]

• To identify background generated by neutrino interactions occurring in the

magnetic yoke and the ND280’s surrounding walls. [28]

• To detect any cosmic ray muons that reach the ND280. [3]

3.4 Post-Oscillation Measurements

3.4.1 The Super-Kamiokande Far Detector

The Super-Kamiokande neutrino observatory acts as the T2K’s far detector,

and is located 295 km west of the beam’s source. [3] It provides post-oscillation

measurements of the neutrinos, looking for νe appearance and νµ disappearance in

the beam. The detector cavity, clearly illustrated in figure 3.13, lies 1 km beneath

the peak of Mt. Ikenoyama. [29] This cylindrical cavity is filled with 50 kton of pure

water, which acts as a target material for the neutrino beam to interact with.

The Super-K’s inner walls are covered with a total of 11,129 inward facing

photomultiplier tubes (PMTs). [3] These PMTs make up the inner detector (ID), and

detect any Cherenkov radiation emitted by the interaction products. Surrounding

the ID is an outer detector (OD), comprised of 1,885 outward facing PMTs. [3]

Light-proof plastic sheets are used to optically separate the ID and OD. The outer

side of this separating layer is coated with a reflective material to improve the

light collection capability of the OD’s PMT array. Despite being deep under the

27

Figure 3.13: A diagram of the Super-Kamiokande. [15]

mountain, some cosmic rays still reach the Super-K. The OD allows these rays to

be vetoed, providing almost 100% rejection of this cosmic background. [3]

The Super-K is currently in its fourth running period: SK-IV. Maintenance and

upgrades are done during the downtime between each running period. In November

2001, during the upgrade from SK-I to SK-II, an accident caused about 60% of the

detectors PMTs to be destroyed. [30] This occurred when a single PMT imploded,

causing a shockwave that destroyed adjacent PMTs, creating a chain reaction.

Precautions have since been put in place to prevent such a chain reaction from

reoccurring.

3.4.2 νµ and νe Event Reconstruction

The flavour composition of the oscillated neutrino beam is inferred by counting

the CCQE interactions undergone by muon and electron neutrinos. [3] The charged

leptons produced in these CCQE interactions are of the same flavour as the neutrinos

that caused them. These charged leptons, providing that they are of high enough

energy, will produce a forward-going cone of Cherenkov radiation. When these

Cherenkov photons reach the ID’s PMTs they produce a ring-shaped pattern that

can be used to identify the source particle. [3]

Cherenkov radiation is emitted when a charged particle travels through a medium

faster than the phase velocity of light in that medium. As seen in figure 3.14, the

28

Figure 3.14: A cone of Cherenkov radiation (blue) emitted by a charged particle (red).

emission of this radiation as the particle propagates results in a cone of light. The

emission angle, θ can be calculated as: [31]

cos θ =1

nβ(3.1)

Where n is the refractive index of the medium, and β is the charged particle’s speed

as a fraction of the speed of light. An angle of θ = 0◦ corresponds to no radiation

emission. As such, we see that in water the minimum speed for a particle to produce

Cherenkov radiation is β ≈ 0.74. [31]

As the produced electrons propagate through the Super-K they generate

electromagnetic showers. An electromagnetic shower begins when an electron

decelerates and emits Bremsstrahlung radiation, which then undergoes pair

production to produce an electron-positron pair. These leptons then produce

successive Bremsstrahlung radiation, which then pair produces more leptons. This

cycle continues until either the leptons or the Bremsstrahlung photons no longer

have enough energy to continue the shower. As such, one electron can result in

many charged particles, each of which may produce Cherenkov radiation. This

corresponds to a very “fuzzy”, smeared out, ring pattern detected by the PMTs. [3]

An example of one these electron-type events can be seen in figure 3.15a.

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(a) An electron-type event.

(b) A muon-type event.

Figure 3.15: Two example event displays from the Super-K. [15]

The higher mass of the muons makes them more resilient to changes in their

momentum. [3] Hence, they are much less likely to undergo this showering process.

This means that the muon-type events produce much sharper rings of radiation.

Figure 3.15b shows an example event display of one of these muon-type events.

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4 The T2K’s θ13 Measurements

4.1 Eliminating Unwanted Backgrounds

For the Super-K’s results to be useful, the “true” signal needs to be distinguished

from the unwanted background. There are two main sources of background in the

Super-K’s νe signal:

• The beam produced at J-PARC is not solely composed of muon neutrinos, it

also contains a small fraction of electron neutrinos. Over the T2K’s baseline

these electron neutrinos are unlikely to have oscillated, and so will account for

some of the signal detected at the Super-K. Pre-oscillation measurements of

the beam are used to measure this initial νe flux.

• As detailed in 3.3.3, π0 mesons sourced from νµ interactions can be mistaken

for νe events. Simulations can be done to estimate the two-ring patterns that

the π0 decays result in, and predict the percentage of decays that will result

in just one electron-like ring.

The measurements of interaction cross sections made at the ND280 can be used to

create accurate Monte Carlo simulations. These simulations are useful for properly

determining these background signals. The “true” events can then be found by

subtracting the background from the measured signal.

4.2 The θ13 Results

Figure 4.1 shows the T2K’s measurements of sin2 2θ13 from 2012. As previously

described in 2.2.2, the value of θ13 depends on whether the neutrino mass hierarchy

is normal or inverted. The νe appearance at the Super-K corresponds to a best-fit

value of sin2 2θ13 = 0.088+0.049−0.039 for a normal mass hierarchy. [14] This best-fit value

is given to a 68% confidence level, the other oscillation parameters are fixed at the

values specified in table 4.1.

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Parameter Value∆m2

21 7.6×10−5 eV2

|∆m232| 2.4×10−3 eV2

sin2 θ12 0.32sin2 2θ23 1.0δCP 0

ν travel length 295 kmEarth matter density 2.6 g/cm3

Table 4.1: The oscillation parameters used to achieve the plots seen in figure 4.1. [14]

Figure 4.1: These plots show the possible values of sin2 2θ13 for all possible values of δCP . The topplot (a) shows the values assuming normal mass hierarchy, and the bottom plot (b)assumes an inverted mass hierarchy. The 68% and 90% confidence regions are clearlyshown, along with several best-fit lines. [14]

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5 The Hyper-Kamiokande

5.1 Overview

The Hyper-Kamiokande (Hyper-K) is a proposed next generation neutrino experiment.

It would involve the construction of a new water Cherenkov detector, to act as the

far detector in a long baseline experiment similar to the T2K. Its primary goal is to

determine the leptonic CP violation phase, δCP , to better than 19◦. [8] The Hyper-K

will either be positioned 8 km south of the Super-K, or under Mt. Ikenoyama where

the Super-K is located. The J-PARC’s design means that both of these sites are

295 km from the beam’s source, at an off-axis angle of 2.5◦. As such, the Hyper-K

will be able to operate over the same baseline as the T2K experiment has, using

the existing J-PARC facility. Figure 5.1 shows the proposed layout of the Hyper-K

detector.

Figure 5.1: A schematic view of the proposed Hyper-K detector. [8]

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5.2 Beam Production

The Hyper-K experiment will use the J-PARC facility to produce its neutrino beam.

Upgrades will be made to the J-PARC accelerator to increase the primary beamline’s

intensity. In fast extraction mode, the MR currently provides 1.24 × 1014 protons

per pulse to the neutrino beamline. [8] This corresponds to a beam power of 240 kW,

however the planned upgrades will increase this beam power to 750 kW. [32]

5.3 Pre-Oscillation Measurements

There are two possible near detectors that could be used by the Hyper-K experiment:

• The Hyper-K could use the T2K’s near detectors: INGRID and ND280. There

is the possibility of upgrading the ND280’s tracking section to improve its

sensitivity. [8] Since the Hyper-K will be a water filled detector, measurements

of the background generated by the π0 producing interactions will still be

needed. The ND280’s subdetectors, such as the PØD, already measure the

processes required from a Hyper-K near detector.

• One or more intermediate water Cherenkov detectors could be constructed. By

only using a water target, this type of near detector would be able to measure

interaction cross sections on H2O directly. This cannot be achieved by the

ND280, which has to conduct complicated analyses to extract the interactions

made in its water layers. [8]

There is also the potential for both an upgraded ND280, and intermediate water

Cherenkov detectors to be used.

5.4 Post-Oscillation Measurements

The Hyper-K far detector will contain a total of 0.99 million metric tons of water. [8]

This is approximately 20 times more water than in the Super-K. [32] As seen in figure

5.1, the Hyper-K’s water volume will be separated into two cylindrical caverns.

Figure 5.2 shows a cross section of one of these cylinders. In the same fashion as

the Super-K, the Hyper-K’s PMTs can be divided into an ID and an OD. There are

a total of 99,000 inward facing PMTs in the ID, and 25,000 outward facing PMTs

in the OD. [32]

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Figure 5.2: A cross section of one of the Hyper-K’s two cylinders. [8]

Each of the Hyper-K’s cylinders is approximately 250 m long. This poses an issue,

as this is longer than the typical light attenuation length achieved by the Super-K’s

water filtration system. [8] To stop this from impacting the detector’s performance,

each of the cylinders is optically separated into five sections. This means that the

Hyper-K is actually a combination of 10 detector regions, each providing a similar

performance to the Super-K. [8]

Aside from detecting the neutrino beam sourced at J-PARC, the far detector will

also be able to observe:

• Just like the Super-K, the Hyper-K allows the incident neutrino’s orientation

to be observed. This makes it capable of observing any atmospheric neutrinos

that interact inside the detector.

• The Hyper-K will be able to observe neutrinos coming from astronomical

origins, potentially providing measurements that far exceed the current best. [8]

• If they exist, the Hyper-K will be sensitive to the proton decay modes predicted

by Grand Unified Theories.

The Hyper-K’s construction is expected to begin before the end of the decade.

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6 Conclusion

The T2K experiment has successfully measured the θ13 mixing angle. This means

that all of the mixing angles, required to describe the mixing of the three Standard

Model neutrinos, have been determined. With future experiments on their way, the

remaining neutrino oscillation parameters should soon be observed. The Hyper-K,

for example, will determine the CP violating phase, δCP , to better than 19◦. [8] This

phase angle could help to explain one of the biggest mysteries of modern physics:

the universe’s matter-antimatter asymmetry. Future experiments may also allow us

to determine whether the neutrino mass hierarchy is normal or inverted.

Acknowledgements

The author would like to acknowledge the T2K Collaboration for graciously providing

many of the figures used in this document.

36

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