Download Experimental_Neutrino_Physics

Susan Cartwright
University of Sheffield
 Dirac and Majorana masses
 The mixing matrix and neutrino oscillations
Massive neutrinos in the
Standard Model
 In the original Standard Model, neutrinos are two-
component spinors with mass exactly zero
 disproved by existence of neutrino oscillations—see later
 There are two ways to add a neutrino mass term to the
SM Lagrangian
 Dirac:  mD  L R  R L 

exactly like other fermion masses



 Majorana:  12 mL  L  L    L   L  12 mR  R  R    R   R
 where νc = Cν̄T = Cγ0ν*
 different chiral states need not have same mass in this case
 neutrino and “antineutrino” same particle, different chirality
M
c
c
M
c
c

Seesaw mechanism
 General mass term has both Dirac and Majorana
components:


c
M



m
mD 
c
L
L
1

Lmass   2  L  R M    h.c., where M  
M

m
m
 R
 D
R 
 If M  mRM  mD  mLM   , we can diagonalise
matrix to get eigenstates
mD
mD
c
c
c
N   R  R 
 L  L ,    L  L 
 R  Rc
M
M
with masses
naturally
mD2
small mass
mN  M; m   
M
for LH state








Neutrino oscillations
 If neutrinos have mass, then they can be described in
terms of mass eigenstates as well as weak (flavour)
eigenstates
 no reason why these should align (and they don’t), so we
have a 3×3 unitary mixing matrix (the PMNS matrix) U:
    Um  m
m
 mass eigenstates propagate according to
 m (t )  e
i Emt pmL 
 m (0)  e
2
i (Mm
2E ) L
 m (0)
if c = 1 and v ≈ c (and hence L ≈ t)
 therefore even if |ν(0)⟩ is a pure flavour state, |ν(L)⟩ is not
Neutrino oscillations
 Probability of observing neutrinos of flavour ℓ' at
distance L (in vacuo) from a beam of initial flavour ℓ:
P     ; L       (0)   Um
2
i (Mm
/ 2E )L *
e
U
m
 For two-flavour case we have
giving
 cos 
U 
  sin
sin 

cos  
2
m
therefore key
variable for
experiments
is L/E
2 


M
L
2
2

 (where M2  M22  M12 )
P     ; L   sin 2 sin 

4
E


can’t measure absolute masses
Matter effects
 νe interact with electrons via W
exchange; νμ, ντ do not
 This leads to an increased effective
mass for a νe-dominated state in
dense matter
 as ν propagates out through
decreasing density, effective mass
drops, eventually crossing another
eigenvalue
 resulting resonant conversion can
greatly enhance oscillation
 critical for solar neutrinos, significant
for long baseline terrestrial too
 MSW effect—sees sign of ΔM2
Theory Summary
 Non-zero neutrino masses imply
 neutrino oscillation (change of effective flavour)

hence, non-conservation of lepton family number


this is experimentally established
also, if 3×3 mixing, non-conservation of CP


imaginary phase δ in PMNS matrix
not established yet
 if non-zero Majorana mass, ν = ν̄

hence, non-conservation of global lepton number

not established
 Experimental tasks
 determine oscillation parameters (Δm2, θ, δ)
 measure neutrino masses
 Principles of oscillation measurements
 Solar neutrinos, θ12
 Atmospheric neutrinos, θ23
 New measurements of θ13
Principles of oscillation
measurements
 Relevant physical properties are Δm2ij and θij
 Experiment parameters are L, E and initial flavour e, μ
 but physical parameter is L/E, so result is conversion
probability P(L/E), giving contour on Δm2 – sin2 2θ plane
 Two distinct experimental techniques
 disappearance experiments look for reduction in flux of
original flavour

only possibility for very low-energy neutrinos (reactor ν̄e, solar νe)
 appearance experiments look for converted flavour

e.g. νe events from a νμ beam
The PMNS matrix
0
0  c13
1


U   0 c23 s23  0
0  s
  s e i
c

23
23 
13
atmospheric
neutrinos
νμ ↔ ντ
0 s13e i  c12

1
0   s12

0
c13  0
reactor & accel.
neutrinos
νμ ↔ νe
s12
c12
0
solar
neutrinos
νe ↔ νX
need all three mixing angles to be non-zero
for CP violation to be possible
0

0
1 
Solar neutrinos
 Produced as by-product of hydrogen fusion
 4 1H → 4He + 2e+ + 2νe
 reaction goes by many
paths which produce
neutrinos of different
energies
 initial flavour state νe
as too little energy to
produce μ, τ
 Detected by inverse β
decay, elastic scattering,
or dissociation of 2H
http://www.kip.uni-heidelberg.de/tt_detektoren/neutrinos.php?lang=en
Solar neutrinos: θ12,
2
Δm
12
2
 7.5  105 eV 2 requires L/E ~ 30 km/MeV in
 m12
vacuum
 experimental approaches:
 solar neutrinos: νe → νX disappearance



resonant conversion via MSW effect in solar interior
expected flux calculated from models of solar luminosity
(John Bahcall et al.)
experimental normalisation via NC reactions (SNO)
 reactor neutrinos: ν̄e → ν̅ X disappearance


requires long-baseline experiment owing to small Δm2
expected flux from known reactor power output
Solar neutrinos: θ12,
2
Δm
12
NC: d + νX → p + n + νX
CC: d + νe → p + p + e−
ES: e− + νX → e− + νX
Solar neutrinos: θ12,
 3-flavour analysis of
SNO+KamLAND data
gives
2
21
m12
 7.4100..19
 105 eV 2
030
tan2 12  0.44600..029
018
sin2 13  0.02500..015
(arXiv 1109.0763)
2
Δm
12
Solar neutrinos: new results
 Measurement of 7Be and pep flux by Borexino
 line fluxes, therefore potentially more informative about
energy dependence
 Also no day-night
asymmetry
 excludes low Δm2
region of plane

this exclusion previously
depended on reactor
data (ν̄)
Atmospheric neutrinos: θ23,
2
Δm
23
 Initially studied using neutrinos produced in cosmic-ray
showers
 incident proton or heavier nucleus produces pions which
decay to μ + νμ
 some of the muons then also decay (to e + νe + νμ)

if they all do so then νμ:νe ratio ~ 2
 Also addressed by accelerator-generated neutrino beams
 essentially identical process: collide proton beam from
accelerator with target, collimate produced pions with
magnetic horns, allow to decay in flight

magnets select charge of pion, hence either νμ or ν̄μ beam
Atmospheric and accelerator νs
−1
0
+1
−1
cos(zenith angle)
0
+1
Atmospheric neutrinos: θ23, Δm223
 MINOS combined fit
2
09
m23
 2.3900..10
 103 eV 2
035
sin2 223  0.95700..036
 3-flavour global fit
2
07
m23
 2.4200..11
 103 eV 2
030
sin2 223  0.95100..024
 first time that best fit θ23 ≠ 45°!
Third mixing angle θ13
 Absence of signal in νe shows that
atmospheric mixing is νμ → ντ
 measurements of ντ appearance in
OPERA and Super-K are statistics-limited
but in qualitative agreement with this
 Therefore 3rd mixing angle θ13
involves νe
 can be seen in νe appearance in νμ beam or
ν̅ e disappearance from reactors
 because Δm213 = Δm223 ± Δm212 and Δm212 ≪ Δm223,
νμ disappearance always dominated by θ23
νe appearance:
Off-axis geometry produces
lower-energy, much more
monochromatic beam
T2K beam is 2.5° off-axis—
optimised for oscillation
measurement
T2K analysis
11 events observed
3.22±0.43 expected
3.2σ effect
 Super-Kamiokande measures Cherenkov radiation
from e/μ produced in interaction
 can distinguish the two based on ring morphology
fuzzy electron ring
sharp muon ring
ν̅e disappearance:
 Multiple detectors associated with extended reactor
complex
 ν̅e detected via inverse β decay
in Gd-loaded liquid scintillator
Daya Bay analysis
 Large difference between Δm213 and Δm212 means that
L/E can be “tuned” for θ13
 no ambiguity—simple
2-flavour system
 “near” and “far” detectors
identical to minimise
systematics
 far/near ratio
R = 0.940 ± 0.011 ± 0.004
 5.2σ effect
ν̅e disappearance:
 Detector design and analysis very similar to Daya Bay
 Results very similar too:
 R = 0.920 ± 0.009 ± 0.014
 4.9σ effect
Results for θ13
053
063
sin2 213  0.09400..040
(NH); 0.11600..049
(IH)
 Daya Bay: sin2 2θ13 = 0.092 ± 0.016 ± 0.005
 Reno:
sin2 2θ13 = 0.113 ± 0.013 ± 0.019
 Global fit (Fogli et al. arXiv 1205.5254):
 T2K :
009
sin2 213  0.09400..008
(NH); 0.095  0.009 (IH)
 measurement of Δm2 still best done by
combining solar & atmospheric Δm2
Open questions
 We know the νe-dominated state m1 is lighter than m2
(from MSW effect), but we still don’t
know if m3 > m2 (normal hierarchy)
or vice versa (inverted hierarchy)
 longer baseline experiments, e.g. NOνA,
should be able to sort this out
via matter effects in Earth
 Constraints on phase δ are very weak
 can be constrained by antineutrino
running and/or matter effects
(NOνA again)
Effect on models
 Tri-bimaximal mixing predicts
 Ue1 2 Ue2 2 Ue3 2   2 1 0 

 3 3

2
2
2
1
1
1
 U 1
U 2
U 3    6 3 2 

 1 1 1
2
2
2
 U 1
U 2
U 3   6 3 2 


and hence θ13 = 0, which it clearly isn’t.
 Theorists are of course trying to rescue this with
perturbations of various kinds
 The current hint that θ23 ≠ 45° is also inconsistent with
tri-bimaximal predictions
 Tritium beta-decay
 Neutrinoless double beta decay
 Astrophysical constraints
Neutrino mass: β decay
 Basic principle: observe electron spectrum of β-decay
very close to endpoint
 presence of mc2 term for neutrino will affect this
 unfortunately not by much!!
tritium (3H)
favoured
because of
combination of
low Q-value
(18.57 keV)
and shortish
half-life (12.3 y)
β decay status and prospects
 Best efforts so far by Mainz and Troitsk experiments of
late 90s:
1/2

2 2
m e    Uei mi   2.3 eV
 i 1

 Two experiments in pipeline should do much better
3
 KATRIN—tritium decay experiment with planned
sensitivity ~0.2 eV
 MARE—rhenium-187 experiment, similar reach
 187Re

has very low Q-value but extremely long half-life
MARE uses single-crystal bolometers to get good energy
resolution and measure differential spectrum
 Very hard experiments: don’t expect results for ~5 years
Neutrinoless double-β decay
 Even-even isobars are lighter
than odd-odd (pairing term)
 can be energetically permitted
for nucleus (Z, A) to decay to
(Z±2, A) but not (Z±1, A)
 these decays do happen
through conventional ββ2ν
mode, albeit at very low rate

lifetime ≫ age of universe
 if neutrino is Majorana
particle, can also happen with
no neutrino emission, ββ0ν
Key features
 Violates lepton number by 2 units
 possible relevance to baryogenesis
2
mi
 Sensitive to mee   Uei
 PMNS matrix multiplied by
diag(1, eiα, eiβ) introducing two
additional phases
2
 Rate  0   Gx (Q, Z ) M x (A, Z ) x
x
 for SM, amplitude ∝ mi/q2 where m ~ 0.5 eV and q ~ 108 eV

small!
 nuclear matrix element M is a major systematic error

theoretical calculations disagree by factors of 2 or more
Relation of ⟨mee⟩ to lightest mν
hep-ph/1206.2560
Most ββ isotopes
are only ~10% of
natural element.
Enrichment is
often needed.
Experimental issues
 Signature: (A, Z) → (A, Z+2) + 2e−, so
 E(e−) = Q/2 —spike at energy endpoint
 p(e1) = −p(e2) —electrons are back to back
 Two experimental approaches
100
% abund
 source = detector
Nd-150
Xe-136
Te-130
Sn-124
Cd-116
Pd-110
0.1
Mo-100

tracker; topological signature
target isotope variable
Zr-96

1
Se-82
 source ≠ detector
10
Ge-76

calorimetric; energy signature
target isotope fixed
Ca-48

232Th
60Co
 not yet quite in range
of interesting limits
10
 Next few years:
improvement of ~ ×10
 EXO-1000, CUORE,
KamLAND-ZEN,
GERDA/MAJORANA
all hoping for
~0.02-0.06 eV
1
0.1
Nd-150
Xe-136
Te-130
Sn-124
Cd-116
Pd-110
Mo-100
Zr-96
Se-82
⟨mee⟩ ~ 0.2-0.6 eV
Ge-76
 Best results probe down to
Ca-48
Experimental results
10
9
8
7
6
5
4
3
2
1
0
<mee> (eV)
Effect on models
 Sensitivity to hierarchy: IH
implies accessible minimum
mass (∝ Δm213)
 within reach of next generation
 Non-observation possible even with Majorana neutrinos
 in NH masses and phases can conspire to cancel effect
 Conversely, ββ0ν decays can be driven by mechanisms
other than Majorana mass (e.g. LR symmetry)
 such mechanisms do imply that the neutrino has a
Majorana mass, but it can be very small
Astrophysical constraints on mν
 Number density of relic neutrinos from early universe
(CνB) is 112 per species per cm3
 these are hot dark matter and will affect structure
formation—hence leave astrophysical signatures
 Sensitive to ∑mν, which is bounded below by
 Δm223 ~ 0.0024 eV2
∑mν (eV)
oscillations
1.4
1.2
1
0.8
0.6
0.4
0.2
0
means ∑mν ≥ 0.05 eV
 bounds are within factor
of 10 and will improve soon
(e.g. Planck)
Limit on ∑mν
Model dependence
 Quoted constraints assume
 flat geometry
 exactly 3 neutrino species with Tν = (4/11)1/3 TCMB
 dark energy is a cosmological constant
 There are correlations between ∑mν and other parameters
WMAP5
W. Rodejohann, hep-ph/1206.2560
Comparing different measures
ββ0ν
KATRIN
ββ0ν
Cosmology
yes
no
yes
no
yes
QD+M
QD+D
QD
N-S C
no
N-S I
low IH/NH/D
m < 0.1 eV/N-S C
NH
yes
(IH/QD)+M
N-S C/I
no
low IH/(QD+D)
NH
D = Dirac; M = Majorana; QD = quasi-degenerate; NH/IH = normal/inverted;
N-S C = non-standard cosmology; N-S I = non-standard interpretation of ββ0ν
Assumes sensitivities of mβ = 0.2 eV, ⟨mee⟩ = 0.02 eV, ∑mν = 0.1 eV
Conclusion: it does help to have multiple approaches.
 Non-standard interpretations of ββ0ν
 Light sterile neutrinos
 Neutrino astrophysics and cosmology
 All 3 neutrino mixing angles are definitely non-zero—
naïve tri-bimaximal mixing ruled out
 Constraints on δ and determination of hierarchy should
be possible with next generation of oscillation
experiments
 Experimental limits on neutrino mass do not currently
compete with cosmological constraints, but next decade
should see complementarity developing
 Physics of massive neutrinos is a rich and interesting field!
Solar neutrinos
Double beta decay
Hot dark matter
Hannestad et al.,
astro-ph/1004.0695
WMAP7 + halo power spectrum
WMAP7 + HPS + H0
Giusarma et al., astro-ph/1102.4774
Sterile neutrinos and axions
can also contribute to hot dark
matter