Neutrino mass is established but its origin is still unknown. The Large Hadron Collider (LHC) may play a crucial role in unraveling the mystery by probing new physics at the TeV scale. LHC could discover the seesaw mechanism responsible for neutrino mass through the detection of new particles like heavy neutrinos. Low-energy neutrino experiments provide complementary information that can be linked to LHC results through precision measurements of neutrino properties. Together, low and high-energy experiments offer an opportunity to understand the origin of neutrino mass.

1. Neutrino mass and the LHC
Miha Nemevšek
ICTP, Trieste
with Maiezza, Melfo, Nesti, Senjanović, Tello, Vissani and Zhang
Balkan Workshop 2011, Donji Milanovac

2. LHC a neutrino machine?
Neutrino mass is an experimentally
established fact for BSM physics.
Might as well be @ TeV (hierarchy)
A phenomenological hint may already be here

3. Neutrino mass and BSM
Facts Questions
2
∆mS,A & θA,S,13 Mass scale & hierarchy
At least two massive light CP phases
neutrinos Dirac or Majorana
LHC may play a crucial role
Low-high energy interplay becomes important
The theory of neutrino mass?

4. Origin of mν
Standard Model νL only, mν = 0
h h y2v2
Effective theory OW =y ⇒ mν =
Λ Λ
High scale TeV
Typical in GUTs Theory: GUT remnant
Indirect, LHC of little use Phenomenological
Neutrino mass and the LHC

5. UV completions of OW
Renormalizable theory = seesaw scenarios
Fermionic singlet Bosonic triplet Fermionic triplet
I II III
h h
h h h h
∆
ν S ν ν T0 ν
ν ν
Type I+III
Triplet predicted at TeV by a minimal SU(5) with 24F
Neutrino mass matrix through decays
Bajc, Senjanović ’06
Oscillations-collider connection Bajc, MN, Senjanović ’07

6. UV completions of OW
Fermionic singlet Bosonic triplet Fermionic triplet
I II III
h h
h h h h
∆
ν S ν ν T0 ν
ν ν
Type I+II
Predicted by a minimal LR symmetric theory
Singlet is gauged, type I required by anomalies
Triplet breaks the LR symmetry - type II
May need to be light →

7. Left-Right symmetry
νL νR
, WL ↔ , WR
eL eR
Parity restoration at high scales Pati, Salam ’74
Mohapatra, Pati ’75
Spontaneously broken Mohapatra, Senjanović ’75
Minkowski ’77
Origin of the seesaw mechanism Senjanović ’79
Senjanović, Mohapatra ’80

8. Minimal LR Model
SU (2)L × SU (2)R × U (1)B−L
LR symmetric Higgs sector, parity invariant L
Φ(2, 2, 0), ∆L (3, 1, 2), ∆R (1, 3, 2)
First stage @ TeV Second stage @ 100 GeV
0 0 v1 0
∆R = Φ =
vR 0 0 v2 eiα
∆L ≡ vL = 0 vL = λ v 2 /vR
Breaks SU (2)R and Lepton number
MW ∝ v ≡ 2 2
v1 + v2 , mD ∝ v
MWR = g vR , mN = y vR

9. Mass spectra
˜ ˜
LY = L (YΦ Φ + YΦ Φ) R + T
L Y∆L ∆L L + T
R Y∆R ∆R R + h.c.
Dirac terms Majorana terms
MD = v1 YΦ + v2 e ˜
YΦ , MνR
−iα
= vR Y∆R
M = iα ˜
v2 e YΦ + v1 YΦ MνL T
= vL Y∆L − MD MνR MD
−1
C: YΦ = YΦ T , Y∆L,R = Y∆R,L ∗
Mass eigenstate basis
† ∗ † ∗ †
M =U Lm U R, MνL = UνL mν UνL , MνR = UνR mN UνR
∗
C:U L = UR

10. The Interactions
g
New Gauge: Lcc = √ νL VL † W
¯ / L ¯ † /
+ νR VR W R R
2
T ++
New Scalar: L∆++ = eR Y ∆R eR
g ∗ †
Y = VR mN VR
MWR
∗
Flavor fixed in type II: VR = VL
Remember; two angles, one limit, no phases

11. The Interactions
g
New Gauge: Lcc = √ νL VL † W
¯ / L ¯ † /
+ νR VR W R R
2
T ++
New Scalar: L∆++ = eR Y ∆R eR
g ∗ †
Y = VR mN VR
MWR
Flavor fixed in type II: VR = oL ly!
∗
Vn
xam ple
E
Remember; two angles, one limit, no phases
LHC could eventually measure these

12. Bounds on the LR scale
Theoretical bounds since ’81 Beall et al. ’81...Zhang et al. ’07
A recent detailed study, including CP violation
Maiezza, Nesti, MN, Senjanović ’10
C : MWR > 2.5 TeV P : MWR > 3.2 − 4.2 TeV
Direct searches
Dijets MWR > 1.51 TeV CMS 1107.4771
Light neutrino MWR > 2.27 TeV CMS PAS EXO-11-024
LHC is here! L ≈ 2.5 fb −1

13. Left-Right @ LHC
Most interesting channel: l l j j
Keung, Senjanović ’83
LNV at colliders
p
WR
i
Gauge production: s-channel,
VR iα
p Nα
W nearly on-shell
VR jα j
Clean, no missing energy
WR
j Reconstructs W and N masses
j
Information on the flavor

14. Limits from the LHC
MN, Nesti, Senjanović, Zhang ’11
1000 1.64` 1000
1.64`
800 800
D0: dijets
2
D0: dijets
2
GeV
3
GeV
600 600
4
4 3
MNΜ
MN
400 400
200 200
1
L 33.2pb L 34pb 1
0 0
800 1000 1200 1400 1600 1800 800 1000 1200 1400 1600 1800
March MWR GeV MWR GeV
High N inaccessible due to jets, low N due to isolation
This year: L = 0.1(1) fb −1
: MWR > 1.6(2.2) TeV
Electron and muon channel essentially the same

15. Limits from the LHC
CMS PAS EXO-11-002 MN, Nesti, Senjanović, Zhang ’11
CMS Preliminary CMS Preliminary
MNe [GeV]
MNµ [GeV]
MNe > MWR 240 pb-1 at 7 TeV
1.64` MNµ > MWR 240 pb-1 at 7 TeV
1200
1000
Observed
1200
1000
Observed
1.64`
Expected Expected
800 800
D0: dijets
1000 1000 2
D0: dijets
2
GeV
3
GeV
600 600
4
4 3
800 800
MNΜ
MN
400 400
200
600 600
200
1
L 33.2pb L 34pb 1
Excluded by Tevatron
Excluded by Tevatron
0 0
800 1000 1200 1400 1600 1800
400 400
800 1000 1200 1400 1600 1800
March MWR GeV MWR GeV
200 200
High N inaccessible due to jets, low N due to isolation
0 0
This year: L = 0.1(1) fb 800 1000 1200 1400 1600
−1
: MWR > 1.6(2.2) TeV
800 1000 1200 1400 1600
July MWR [GeV] MWR [GeV]
Electron and muon channel essentially the same

16. Low/high energy interplay
Majorana mass term dominance
∗
MνR = vR Y MνL = vL Y
Implications for masses and mixings
∗ ∗
mN ∝ mν UνR = UνL ⇒ VR = VL
mN 2 2 − mN 1 2 mν2 2 − mν1 2 Hierarchy probe
= ±0.03
mN 3 2 − mN 1 2 mν3 2 − mν1 2 @ LHC
i mN i
mcosm = ∆m2
A , Cosmo-oscillations
|mN3 2 − m2 2 |
N -LHC link

17. 0ν2β and cosmology
1.01 Majorana mass implies
0ν2β Vissani ’99
0.1
0.1
inverted
Gerda, Cuore, Majorana,...
|mee| in eV
0.01
0.01 Review by Rodejohann ’11
normal
ν
Claim of observation
10−3
0.001
|mν |
ee
0.4 eV
10−4 −4
10 4 4 Klapdor-Kleingrothaus ’06, ’09
10
10 0.001
0.001 0.01
0.01 0.1
0.1 1
1
lightest neutrino mass in eV

18. 0ν2β and cosmology
1.01 Cosmological bounds
mν < 0.17 eV
0.1
0.1
inverted
Seljak et al. ’06
|mee| in eV
WMAP alone
0.01
0.01
normal
ν
mν < 0.44 eV
10−3
0.001 Hannestad et al. ’10
10−4 −4
10 4 4
If confirmed, a hint for NP
10
10 0.001
0.001 0.01
0.01 0.1
0.1 1
1
Vissani ’02
lightest neutrino mass in eV

19. New Diagrams for 0ν2β
Mohapatra, Senjanović ’81
n p n p n p
WR
W WR
VR eα e e
e (YL )ee (YR )ee
WR
Nα
VR eα
e
vL
∆L
∆L
e
vR
∆R
∆R
e
W WR
WR
n p n p n p
∝ 1/mN ∝ mν ∝ mN
Large? Tiny Subdominant?
In agreement with cosmology?

20. 0ν2β : the new contribution
e
LR mixings small e e
e
;N ´L;R
sin ξ < MW /MWR < 10 −3
c
WL;R WL;R WL;R WL;R
mD 0 A A A A A A
ZX Z`1 X Z`2 X ZX Z`1 X Z`2 X
4
2 2 1 2 mN j MW µ c
HNP = GF VR ej + 4 JRµ JR eR eR
mN j m2∆ MWR
Type II: VR = VL
∗
∆L suppressed: mν /m∆ 1
LFV: mN /m∆R < 1
The gauge contribution is dominant

21. 0ν2β : the total contribution
LHC accessible regime ee 2
|mν+N | ≡
lightest mN in GeV
ee 2 ee 2
1.
1.0
1 10 100 400 500 |mν | + |mN |
0.5 Interference small
normal
inverted
|mee | in eV
0.1 Reversed role of
0.05 hierarchies
ν +N
0.01 No tension with
0.005 MWR = 3.5 TeV cosmology
largest mN = 0.5 TeV
10−3
0.001 −4
A light mN < MWR
10 4
10 0.001
0.001 0.01
0.01 0.1 1
lightest neutrino mass in eV
No cancellations

22. LHC and 0ν2β
Suppose NP is a must for 0ν2β ; θ13 0 α = 2(ϕ2 − ϕ1 )
ee 2 2 iα 2 2
|Mν+N | = |mν1 cos θ12 + mν2 e sin θ12 | +
4 2
2 MW 1 2 1 iα 2
p 4 cos θ12 + e sin θ12
MWR mN 1 mN 2

23. LHC and 0ν2β
Suppose NP is a must for 0ν2β ; θ13 0 α = 2(ϕ2 − ϕ1 )
1000
1000 1000
1000
Normal Hierarchy Normal Hierarchy
500 MWR = 3.5TeV, α = 0
500 500 MWR = 3.5TeV, α = π
500
ee ee
|Mν+N | |Mν+N |
200
200 200
200
mN1 in GeV
mN1 in GeV
0.05 ee 2 2 0.05
iα 2 2
|Mν+N | = |mν1 cos θ12 + m e
100
100 100 ν2
100 sin θ12 | +
0.1 0.1
50
50
4 50
50 2
0.2
2 MW 1 2 1 0.2iα 2
20
20
p0.4 4 cos θ12 + 20 0.4 sin θ12
20
e
MWR mN 1 mN 2
10
10 0.6 10
10 0.6
1.0 1.0
55 5
5
10−4
0.0001 0.001
0.001 0.01
0.01 0.1
0.1 1
1 10−4
0.0001 0.001
0.001 0.01
0.01 0.1
0.1 1
1
lightest neutrino mass in eV lightest neutrino mass in eV
jj : mN 50 GeV v : mN
/ 20 GeV
LHC: j : mN 20 GeV /
E : mN 3 − 7 GeV

24. LHC and 0ν2β
Suppose NP is a must for 0ν2β ; θ13 0 α = 2(ϕ2 − ϕ1 )
1000
1000
1000
1000 1000
1000 Inverted Hierarchy
1000
1000
Normal Hierarchy
Inverted Hierarchy Normal Hierarchy
500 MWR = 3.5TeV, α = 0
500
500
500
3.5TeV, α = 0 500 MWR = 3.5TeV, α = π
500 MWR = 3.5TeV, α = π
500
500
ee
|Mν+N |
ee ee
|Mν+N | |Mν+N |
200
200
200 0.05 200
200
200
200
mN1 in GeV
200
mN in GeV
mN1 in GeV
mN11 in GeV
0.05 ee 2 2 0.05
iα 2 2
|M
100
100
100 0.1
ν+N | = |mν1 cos θ12 + m e 100
100
100
100 |M ee
ν2 ν+N | sin θ12 | +
0.1 0.1
50
50
50 0.2 4 50
50
50
50 0.05 2
0.2
2 M W 1 2 1 2 0.2iα
0.1
20
20
p
0.4 4 cos θ12 + 20 0.4 sin θ12
20
20
20
e
20 0.4
0.6 M WR mN 1 mN2 0.2
10
10 0.6 10
10
10
10 0.6
10 1.0 0.4
1.0 1.0
0.6
55 5
55
50.0001
10−4
0.0001 0.001
0.001
0.001 0.01
0.01
0.01
0.01 0.1
0.1
0.1
0.1 11
11 10−4
10−4
0.0001 0.001
0.001
0.001
0.001 0.01
0.01
0.01
0.01 0.1
0.1
0.1
0.1 1
1
1
1
lightest neutrino mass in eV
neutrino mass in eV lightest neutrino mass in eV
lightest neutrino mass in eV
jj : mN 50 GeV v : mN
/ 20 GeV
LHC: j : mN 20 GeV /
E : mN 3 − 7 GeV

25. Lepton Flavor Violation
Cirigliano et al ’04
LFV rates computable: type II (or LHC) Raidal, Santamaria ’97
µ Y∆µe e
T
→3 tree ∆++
L,R
VL mN /m∆ VL
e Y∆ ∗
ee e
γ
†
→ γ loop ∆++ ∆++ VL mN /m∆ VL
µ Y∆µi c Y∆ ∗ e
i ie
µL Y∆ Y∆ ∗ eL
L (νL )
∆++ (∆+ ) ∆++ (∆+ )
†
µN− eN log VL mN /m∆ VL
L L L L
γ, ZL , ZR
N N

26. Combined LFV constraints
Muonic and tau channels Tello, MN, Senjanović, Vissani ’10
Varying PMNS constrains mN /m∆ < 1
5.0 5.0
5.
absolute bound from LFV 5. absolute bound from LFV
1.0
1. 1.0
1.
mN/m∆
mN/m∆
0.5
0.5 0.5
0.5
0.1
0.1 0.1
0.1
0.05 always allowed by LFV
0.05 0.05 always allowed by LFV
0.05
MWR = 3.5TeV MWR = 3.5TeV
0.01 4 Inverted Hierarchy 0.01 4 Normal Hierarchy
0.01 0.01
10−4
10 0.001
0.001 0.01
0.01 0.1
0.1 1
1
10−4
10 0.001
0.001 0.01
0.01 0.1
0.1 1
1
lightest neutrino mass in eV lightest neutrino mass in eV

27. Triplet searches
2001 2003 2003 2004 2004 2005 2006 2008 2008 2011 2011 2011
350
313
300
250
200 LHC
150 156
m
146 141 144
150 136
118.4 114
98.5 97.3 100
100
Delphi CDF CDF CDF H1 D0 CDFII D0 CMS CMS
Opal L3
50 ΤΤ ΜΜ e&Μ 0 eΜ ΜΜ eΤ ΜΤ April July
0
2001 2003 2003 2004 2004 2005 2006 2008 2008 2011 2011 2011

28. Gauge Production
√
∆+ / 2 ∆++
∆= √
∆0 −∆+ / 2
Pair-wise through Z, γ ∗
∗ ∆+ ∆++ ∆0
γ ,Z ∗
γ ,Z Z
∆− ∆−− ∆0
Associated via W
±
∆±± ±
∆±
W W
GeV
∆ ∆0

29. Gauge Production
√
2.00 ∆+ / 2 ∆++ LHC @ 7 TeV
∆= √
1.00
∆0 −∆+ / 2
0.50 Pair-wise through Z, γ ∗
solid=LO
0.20
Z dashed=NLO
Σ pb
0
∗ ∆+ ∆++ ∆
γ ,Z ∗
γ ,Z
0.10
0.05
∆− ∆−−
K-factor =1.3
∆0
0.02 Associated via W
100 120W ± 140
∆±±
160 180 ± ±
200
∆
red = assoc.
W
M TeV
GeV
∆ ∆0 blue=pair.

30. Decay Phase Diagram
m∆ U ∗ mν U † m3 v∆ 2
Γ∆→ ∝ Γ∆→V V ∝ ∆
4
Γ∆→∆ V ∝ ∆m5 /m4
W
v∆ v
a) b) c)
Decays
a) Leptonic ∆→ Tiny v∆
b) Gauge boson ∆→VV Large v∆
c) Cascade ∆→∆V Mass split
D0: pair-production only, CMS degenerate mass

31. Decay Phase Diagram
100.0
50.0 ∗ Cascade 2
Decay
m∆ U mν U † m3 v∆
Γ∆→ ∝ Γ∆→V V ∝ ∆
4
Γ∆→∆ V ∝ ∆m5 /m4
W
v∆ v
a) b) c)
10.0
Decays
M GeV
5.0
a) Leptonic ∆→ Tiny v∆
1.0 Leptonic Decay
b) Gauge boson
0.5 ∆→VV Large v∆
Gauge
c) Cascade ∆→∆V Mass split
Boson Decay
D0: pair-production only, 6
10 10 10 8 10 CMS degenerate mass
10 4 0.01 1
v GeV

32. Mass splits
The general potential
2 † 2 † T ∗
V =− mH H H + m∆ Tr∆ ∆ + (µH iσ2 ∆ H + h.c.)+
† 2 † c2 † 2
λ1 (H H) + λ2 (Tr∆ ∆) + λ3 Tr(∆ ∆) +
† † † †
α H H Tr∆ ∆ + β H ∆∆ H
Splits components by v 2; there is a sum rule
2 2 2 2 2
m∆ + − m∆++ m∆ 0
− m∆ + β v /4
c
mS mA = m∆ 0
v2
Only two mass scales govern the spectrum up to O
v∆ 2

33. Electroweak Precision Tests
EWPT calculated for the first time Melfo, MN, Nesti, Senjanović, Zhang ’11
Oblique parameters suffice (Yukawa small by LFV)
m 200 GeV
100 T parameter
80
T positive definite, controlled by
60
mass splits
GeV
40
68
20 95
Heavy Higgs=negative T
m
99
Bottom-line
m
0
20
O(10 GeV) splits allowed
40
100 200 300 400 500 600 Cascade region opens up...
mh GeV

34. Type II Roadmap
Melfo, MN, Nesti, Senjanović, Zhang ’11
100
100 Sum Rule
Sum Rule
β<3
c
Direct search
Direct search
50
50 LHC 980 pb 11
LHC 980 pb
CMS data
GeV
GeV
v 10 66 GeV
v 10 GeV
EWPT
0
0 CMS-PAS-
mh 300GeV
m
m
HIG-11-007
LE
m
LEP
m
50
50 EWPT
Light Higgs
P
mh 130GeV
Sum Rule &
Sum Rule &
100
100 Z width
Z width mh = 130 GeV
c
0
0 100
100 200
200 300
300 400
400 500
500 600
600 700
700
mm GeV
GeV

35. Type II Roadmap
Melfo, MN, Nesti, Senjanović, Zhang ’11
100 Sum Rule
β<3
c
Direct search
50 LHC 980 pb 1
CMS data
GeV
v 10 6 GeV
EWPT
0 CMS-PAS-
mh 300GeV
m
HIG-11-007
LE
m
50
Heavy Higgs
P
Sum Rule &
100 Z width
mh = 300 GeV
c
0 100 200 300 400 500 600 700
m GeV

36. Conclusions
0ν2β signal may require new physics at TeV
Left-Right symmetry @ LHC a natural example
no tension with cosmology, precision data or LFV
links oscillations, cosmology and the LHC
Exclusions with fairly low luminosity and 7 TeV
LHC may observe LNV and in turn connect it to low
energy rates, both LNV and LFV

37. Thank you.

38. Higgs decay
Heavy Higgs decay: a way to probe α Akeroyd, Moretti ’11
mh > 2m∆ Br(h → W W )
100
2
Γh→∆++ ∆−− ∝ α 1.5
2
Γh→∆+ ∆− ∝ (α + β/2) 1.0
Α
0.5
Higgs Br’s change 10
0.0
++ 150 200 300 500
Easy to search if ∆ Mh GeV
Hidden if ∆0 Melfo, MN, Nesti, Senjanović, Zhang ’11

39. A global picture
MN, Nesti, Senjanović, Zhang ’11
1000 1
L 33.2pb
500 4 1.64`
D0: dijets
3 2
100
GeV
0Ν2
50 Β H
M
jet EM activity
MN
Τ N 1 mm
10 Displaced Vertex
5 ΤN 5 m
CMS Missing Energy
1
1000 1500 2000 2500 3000
MWR GeV

40. Non-minimal case
CKM CKM∗
Minimal case: gL = gR C : VL = VR
Maiezza, Nesti, MN, Senjanović ’10
1.4
1.2 95% CL
gR gL
1.0
0.8
0.6 mN = 500 GeV
1200 1300 1400 1500 1600 1700 1800
MWR GeV

41. And the WR ?
Less important, loop suppressed
no log enhancement
flavor structure always mN < MWR
†
VL mN /MWR VL
Still, future µ N − e N useful
J-PARC and Fermilab
could probe the mediator Cirigliano, Kitano, Okada, Tuzon ’09
even CP phases if LR Bajc, MN, Senjanović ’09

42. Role of θ13
Flavor structure in muon-electron transitions
iα
A(µ → 3e) ∝ −mN1 + exp mN2 sin 2θ12 cos θ23
2 iα 2 2
mN1 cos θ12 + exp mN2 sin θ12 /m∆++
µ → 3e insensitive to θ13
∆m2 13
N ∆m2
A(µ → e) ∝ S
sin 2θ12 cos θ23 + eiδ sin θ13 sin θ23
m2 ++
∆ 2∆m2A
µ − e conversion and µ → eγ depend a lot

43. Role of θ13
Impact of non zero Θ13
0.200
Flavor structure in muon-electron transitions T2K
sin2Θ12 cosΘ23 ei∆ sinΘ13 sinΘ23
0.100 sin2 2Θ13 0.11
iα Minos
→ 3e)
A(µ 0.050 ∝ −mN1 + exp mN2 sin 2θ12 cos θ23
2 iα 2 sin2 2Θ13 20.04
mN1 cos θ12 + exp mN2 sin θ12 /m∆++
0.020
µ → 3e insensitive to θ13
0.010
Θ13 0
∆m2 13
N
0.005 ∆m2
A(µ → e) ∝ S
sin 2θ12 cos θ23 + eiδ sin θ13 sin θ23
m2 ++ 2∆m2
2 mA 2
A
mS 2
∆ 2 4
0.002 sin 2Θ13 8x10
0.001
µ − e conversion and Π → eγ depend a lot
0 µ
2
Π 3Π 2Π
2
∆