NEUTRINO MASS AND THE LHC
Ray Volkas
School of Physics
The University of Melbourne
@RVolkas
CoEPP Workshop, Cairns, July 2013
1. Neutrino oscillations and mass
2. Experimental discovery of neutrino
oscillations
3. The see-saw mechanisms
4. Radiative neutrino mass generation
5. Final remarks
1. NEUTRINO OSCILLATIONS AND MASS
The neutrino flavour or interaction eigenstates are not
Hamiltonian eigenstates in general:
  e   U e1 U e 2 U e3  1 
  
 


U
U
U



1

2

3
  
 2 
   U


     1 U 2 U 3  3 
unitary mixing matrix
mass estates
m 1, m 2, m 3
  e   cos 
 
     sin 
Two flavour case
for clarity:
sin    1 
 
cos   2 
Say at t=0 a e is produced by some weak interaction process:
| t  0 | e   cos  |1   sin  | 2 
After time evolution:
| t   cos  exp(iE1t ) |1   sin  exp(iE2t ) | 2  | e 
(  c  1)
Suppose they are ultrarelativistic 3-momentum eigenstates:
Ei 
mi2
p m  p
2p
2
2
i
Probability that the state is  is:
2 ö
æ
2
2 Dm t
P(n e ® n m ) = 1- át | t = 0ñ = sin 2q sin ç
÷
è 4p ø
æ
ö
2
2
2
2 L km
» sin 2q sin ç1.27Dm eV
÷
E GeV ø
è
2
Amplitude set by
mixing angle
Oscillation length set by
Dm2/E=(m22-m12)/E
For solar neutrinos, this formula is invalidated by the “matter effect”
-- a refractive index effect for neutrinos.
2. EXPERIMENTAL DISCOVERY OF NEUTRINO
OSCILLATIONS
Solar neutrinos
pp 
Boron 
Beryllium 
Sudbury Neutrino Observatory (SNO) proves flavour conversion:
Courtesy of SNO Collaboration
SNO was a heavy water detector.
It was sensitive to e’s through charge-exchange
deuteron dissociation:
diagrams courtesy of SNO collaboration
But, through Z-boson exchange, it was also sensitive to the
TOTAL neutrino flux e +  + :
Diagrams courtesy of SNO Collaboration
Terrestrial confirmation from KAMLAND
Integrated flux of anti-e from Japanese (and Korean!) reactors
Diagrams courtesy of KAMLAND collab.
13. N eut r i no m i xi
Survival Probability
1
0.8
0.6
0.4
0.2
3-n best-fit oscillation
Data - BG - Geo ne
2-n best-fit oscillation
0
20
30
40
50
60
70
L0/En (km/MeV)
e
80
90
100
110
Atmospheric neutrinos
Atmospheric neutrinos
Cosmic rays hit upper
atmosphere, produce
pions and kaons.
They decay to give
neutrinos.
   
e e 
Provided muons decay
in time, you get 2:1 ratio
of  to e type neutrinos.
Super-K results
Terrestrial confirmation: K2K
Terrestrial confirmation: MINOS
Long baseline experiment from Fermilab to the
Soudan mine in northern Minnesota
neutrinos
antineutrinos
MINOS has also provided strong evidence that
’s oscillate into ’s
Neutral current measurement
n2 (1.267∆ m 231 L / E )
Reactor anti-νe disappearance and θ13
θ12 sin2 (1.267∆ m 221 L / E ) ,
026
eV , sin 2θ12 = 0.861+− 0.
0.022 ,
5
eV 2 [53]. T he uncert ainty
le effect and t hus was not
2
Entries / 0.25MeV
2
T he observed ν e spect rum in t he far hall was compared t o a predict ion based on t he near hall measurement s αM a + βM b in Fig. 24. T he dist ort ion of t he
spect ra is consist ent wit h t hat expect ed due t o oscillat ions at t he best -fit θ13 obt ained from t he rat e-based
analysis.
Far Hall
2000
5s
1000
3s
1s
0.05
0.1
sin 22q13
500
0.15
EH3
1
Near Halls (weighted)
1500
1.2 1.4 1.6 1.8
2
Weighted Baseline [km]
easured versus expect ed
or, assuming no oscillais t he uncorrelat ed unD, including st at ist ical,
background-relat ed unpect ed signal has been
est -fit normalizat ion pa-
Far / Near (weighted)
70
60
50
40
30
20
10
0
0
0
0
5
10
No Oscillation
Best Fit
1.2
1
0.8
0
5
10
Prompt Energy (MeV)
Fig. 24. Top: M easured prompt energy spect rum of t he far hall (sum of t hree A Ds) comDaya Bay collaboration
pared wit h t he no-oscillat ion predict ionAlso:
basedReno, Double-CHOOZ, T2K, MINOS
on t he measurement s of t he t wo near halls.
Spect ra were background subt ract ed. Uncer-
Fogli et al: PRD86 (2012) 013012
3. THE SEE-SAW MECHANISMS
Minimal standard model:
No RH neutrinos means zero neutrino masses
Dirac neutrinos:
simply add
like all the other fermions
Possible, but (1) no explanation for why
(2) RH neutrino Majorana mass terms are
gauge invariant and thus can be in the
Lagrangian
Minkowski; Gell-Mann, Ramond, Slansky; Yanagida; Mohapatra and Senjanovic
Type 1 see-saw:
Dirac mass
RH Majorana mass
Neutrino mass
matrix:
For M >> m: 3 small evalues of magnitude mν=m2/M
3 large evalues of order M
see-saw
Majorana
estates:
Notoriously hard to test because N is
mostly sterile to SM gauge interactions
and also expected to be very massive
Magg; Wetterich; Schechter; Valle; Lazarides; Shafi; Mohapatra; Senjanovic; Cheng; Li.
Type 2 see-saw:
Add Higgs triplet instead of RH neutrinos:
Why small <Δ>?
positive
<H> induces linear
term in Δ
Weak and EM interactions:
more testable
Mass limits on charge-2
scalar. Depends on BR
assumption.
Eur.Phys.J. C72 (2012) 2244
Barberio, Hamano, Rodd
Foot, Lew, He, Joshi
SEESAW NEUTRINO MASSES INDUCED BY A TRIPLET OF LEPTONS - INSPIRE- HEP
2/ 07/ 13 11:45 AM
Citation history:
Type 3 see-saw:
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Page 2 of 2
ATLAS-CONF-2013-19
Barberio, Hamano, Ong
Seesaw Models - a common thread:
Dimension-5 Weinberg effective
operator (1/M)LLHH (shorthand).
4. RADIATIVE NEUTRINO MASS GENERATION
Start with the Weinberg operator and “open it up” – derive it in the lowenergy limit of a renormalisable model – in all possible minimal ways.
You will then systematically construct the three see-saw models.
This procedure can be used for higher mass-dimension ΔL=2 effective
operators.
In principle, one can construct all possible minimal* models of Majorana
neutrinos.
All d>5 operators [except those of the form LLHH(H Hbar)n] produce neutrino
mass only at loop-level. For success need 1-loop, 2-loop and maybe 3-loop
scenarios.
* Have to define “minimal” – there are always assumptions.
d=detailed, b=brief
B=Babu J=Julio L=Leung Z=Zee
d
f
7
4
9
4
operator(s)
scale from mν
(TeV)
model(s)?
comments
107
Z (1980,d)
pure-leptonic,1loop, ruled out
105,8
BJ (2012,d) BL
(2001,b)
2012 = 2-loop
2001 = 1-loop
107,9
BL (2001,b)
1-loop
vector leptoquarks
104
BJ (2010,d)
2-loop
106
BL (2001,b)
1-loop
107
102
105
purely leptonic
106
107
BL (2001,b)
1-loop
A=Angel
d
f
9
6
dGJ=deGouvêa+Jenkins
operator(s)
scale from mν
(TeV)
model(s)?
comments
103
BZ (1988,d)
2-loop, purely leptonic
104
BL (2001,b)
two 2-loop models
30, 104
BL (2001,b)
A (2011,d)
three 2-loop models
one 2-loop model
104,7
BL (2001,b)
2-loop
104
103,6
103
at least 3-loop
2
at least 3-loop
2
at least 3-loop
2
at least 3-loop
1
40
dGJ (2008,b)
at least 3-loop
at least 3-loop
Doubly-charged
scalar k
Zee-Babu model
c
e
ec
h
ec
L
k
L
L
L
h
ec
L
L
L
L
ec
L
Effective op
Opening it up
L
L
H
O9
ec
H
2-loop nu mass
diagram
The previously shown ATLAS bounds on doubly-charged scalars coupling
to RH charged leptons apply to this model as well.
L
Angelic O11 model
(Angel, Cai, Rodd, Schmidt, RV, nearly finished!)
leptoquark scalar
colour octet fermion
ΔL=2 term
Neutrino mass and mixing angles can be fitted
with mf, mϕ ~ TeV and couplings 0.01-0.1.
Need two generations of ϕ to get rank-2
neutrino mass matrix.
Flavour violation bounds can be satisfied.
5. FINAL REMARKS
• Neutrinos have mass. We don’t know Dirac
or Majorana, or the mechanism.
• Conspicuously light: different mechanism?
• The answer “probably” lies beyond the LHC,
but at the very least we should understand
what the LHC excludes.