NEUTRINO MASS AND THE LHC
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NEUTRINO MASS AND THE LHC
Ray VolkasSchool of Physics
The University of Melbourne
CoEPP Workshop, Cairns, July 2013
@RVolkas
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1. Neutrino oscillations and mass2. Experimental discovery of neutrino
oscillations3. The see-saw mechanisms4. Radiative neutrino mass generation5. Final remarks
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The neutrino flavour or interaction eigenstates are not Hamiltonian eigenstates in general:
1 2 3 1
1 2 3 2
1 2 3 3
e e e eU U UU U UU U U
unitary mixing matrixmass estatesm1, m2, m3
1. NEUTRINO OSCILLATIONS AND MASS
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Two flavour casefor clarity:
1
2
cos sinsin cos
e
Say at t=0 a e is produced by some weak interaction process:
1 2| 0 | cos | sin |et
After time evolution:
1 1 2 2| cos exp( ) | sin exp( ) | | et iE t iE t
( 1)c
Suppose they are ultrarelativistic 3-momentum eigenstates:2
2 2
2i
i im
E p m pp
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Probability that the state is is:
Amplitude set bymixing angle Oscillation length set by
Dm2/E=(m22-m1
2)/E
For solar neutrinos, this formula is invalidated by the “matter effect”-- a refractive index effect for neutrinos.
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2. EXPERIMENTAL DISCOVERY OF NEUTRINO OSCILLATIONS
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Solar neutrinos
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pp
Boron Beryllium
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Sudbury Neutrino Observatory (SNO) proves flavour conversion:
Courtesy of SNO Collaboration
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diagrams courtesy of SNO collaboration
SNO was a heavy water detector.
It was sensitive to e’s through charge-exchange deuteron dissociation:
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But, through Z-boson exchange, it was also sensitive to the TOTAL neutrino flux e + + :
Diagrams courtesy of SNO Collaboration
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Terrestrial confirmation from KAMLAND
Integrated flux of anti-e from Japanese (and Korean!) reactors
Diagrams courtesy of KAMLAND collab.
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Atmospheric neutrinosAtmospheric neutrinos
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Cosmic rays hit upperatmosphere, producepions and kaons.
They decay to giveneutrinos.
ee
Provided muons decayin time, you get 2:1 ratioof to e type neutrinos.
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Super-K results
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Terrestrial confirmation: K2K
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Terrestrial confirmation: MINOS
Long baseline experiment from Fermilab to the Soudan mine in northern Minnesota
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neutrinos antineutrinos
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MINOS has also provided strong evidence that ’s oscillate into ’s
Neutral current measurement
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Reactor anti-νe disappearance and θ13
Daya Bay collaborationAlso: Reno, Double-CHOOZ, T2K, MINOS
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Fogli et al: PRD86 (2012) 013012
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3. THE SEE-SAW MECHANISMS
Minimal standard model:
No RH neutrinos means zero neutrino masses
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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
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Type 1 see-saw:
RH Majorana massDirac mass
Neutrino massmatrix:
For M >> m: 3 small evalues of magnitude mν=m2/M 3 large evalues of order M
see-sawMajoranaestates: Notoriously hard to test because N is
mostly sterile to SM gauge interactionsand also expected to be very massive
Minkowski; Gell-Mann, Ramond, Slansky; Yanagida; Mohapatra and Senjanovic
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Type 2 see-saw: Add Higgs triplet instead of RH neutrinos:
Why small <Δ>?
<H> induces linearterm in Δ
positive
Weak and EM interactions:more testable
Magg; Wetterich; Schechter; Valle; Lazarides; Shafi; Mohapatra; Senjanovic; Cheng; Li.
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Mass limits on charge-2scalar. Depends on BRassumption.
Eur.Phys.J. C72 (2012) 2244
Barberio, Hamano, Rodd
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Type 3 see-saw:Foot, Lew, He, Joshi
ATLAS-CONF-2013-19
Barberio, Hamano, Ong
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Seesaw Models - a common thread:
Dimension-5 Weinberg effectiveoperator (1/M)LLHH (shorthand).
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4. RADIATIVE NEUTRINO MASS GENERATION
Start with the Weinberg operator and “open it up” – derive it in the low-energy 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.
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d f operator(s) scale from mν (TeV)
model(s)? comments
7 4 107 Z (1980,d) pure-leptonic,1-loop, ruled out
105,8 BJ (2012,d) BL (2001,b)
2012 = 2-loop2001 = 1-loop
107,9 BL (2001,b) 1-loopvector leptoquarks
104 BJ (2010,d) 2-loop
9 4 106 BL (2001,b) 1-loop
107
102
105 purely leptonic
106
107 BL (2001,b) 1-loop
d=detailed, b=briefB=Babu J=Julio L=Leung Z=Zee
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d f operator(s) scale from mν (TeV)
model(s)? comments
9 6 103 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 modelsone 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 dGJ (2008,b) at least 3-loop
40 at least 3-loop
A=Angel dGJ=deGouvêa+Jenkins
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Zee-Babu model
Effective op Opening it up 2-loop nu massdiagram
Doubly-chargedscalar k
The previously shown ATLAS bounds on doubly-charged scalars couplingto RH charged leptons apply to this model as well.
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Angelic O11 model
ΔL=2 term
(Angel, Cai, Rodd, Schmidt, RV, nearly finished!)
leptoquark scalar colour octet fermion
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Neutrino mass and mixing angles can be fittedwith 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.
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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.