Neutrino masses : beyond d=5 tree-level operators Florian Bonnet - - PowerPoint PPT Presentation
Neutrino masses : beyond d=5 tree-level operators Florian Bonnet Wrzburg University based on arXiv:0907 .3143, JHEP 10 (2009) 076 and arXiv:1205.5140 to appear in JHEP In collaboration with Daniel Hernandez, Martin Hirsch, Toshi Ota and
1
What’ s ? Invisibles12, Firenze, July 2012
Würzburg University
In collaboration with Daniel Hernandez, Martin Hirsch, Toshi Ota and Walter Winter
F . Bonnet July 2012 - GGI
based on arXiv:0907 .3143, JHEP 10 (2009) 076 and arXiv:1205.5140 to appear in JHEP
ν
Seesaw Mechanism
Identifying NP ∼ constraining new parameters
2 F . Bonnet
Leff = LSM + δLd=5 + δLd=6 + . . .
Lowest order: unique d=5 operator
Weinberg operator Neutrino masses
Recent review
Standard Model (SM) does not explain masses
ν
Call for New Physics (NP) > EW
Model independent approach : effective theories
H L L H
July 2012 - GGI
Seesaw Mechanism
Identifying NP ∼ constraining new parameters
3 F . Bonnet
H L L H
July 2012 - GGI
Seesaw Mechanism
Identifying NP ∼ constraining new parameters
4 F . Bonnet
NR ΣR ∆ YN YΣ Y∆ µ∆
Type I Type II Type III
Y T
N
Y T
Σ
Minkowski 1977 Yanagida 1979 Gell-Mann et al. 1979 Mohapatra, Senjanovic 1980 Magg, Wetterich 1980, Schechter, Valle 1980, Wetterich 1980, Cheng, Li 1980, Lazarides, Shafi, Wetterich 1981 Mohapatra, Senjanovic 1981, Foot, Lew, He and Joshi 1989
H L L H H L L H H L L H
July 2012 - GGI
Seesaw Mechanism
Identifying NP ∼ constraining new parameters
5 F . Bonnet
NR ΣR ∆ YN YΣ Y∆ µ∆
Type I Type II Type III
Y T
N
Y T
Σ
Y T
Σ
v2 MΣ YΣ Y T
N
v2 MN YN Y∆µ∆ v2 M 2
∆
mν ∝
Problem :
mν < eV ⇒ ⇢ Y ∼ O(1), M ∼ GUT Y ∼ 10−5, M ∼ TeV
No LHC access small couplings
mν ∝ mν ∝
H L L H H L L H H L L H
July 2012 - GGI
Way out
Identifying NP ∼ constraining new parameters
6 F . Bonnet
Goals : New Physics @ TeV large couplings (LFV) Means : need of additional source of suppression Radiative generation of neutrino masses d>5 operator Small lepton number violating contributions
mν ∝ v2 Λ × ✓ 1 16⇡2 ◆n × ✏LNV × ⇣ v Λ ⌘d−5
July 2012 - GGI
Small lepton number violation contributions
Inverse/Linear Seesaw
Identifying NP ∼ constraining new parameters
8 F . Bonnet
Type II : natural
∆ Y∆ µ∆ Y∆µ∆ v2 M 2
∆
LFV
mν
Y †
∆Y∆
H L L H
July 2012 - GGI
Inverse/Linear Seesaw
Identifying NP ∼ constraining new parameters
8 F . Bonnet
Type II : natural
∆ Y∆ µ∆ Y∆µ∆ v2 M 2
∆
Type I/III : extra fermion
N1 N1 N2 YN Y T
N
µ ν N1 N2 ν N1 N2 YN Y T
N
Λ Λ µ
−Y T
N
µ Λ2 YNv2
LFV
mν
Y †
∆Y∆
LFV
mν
Y †
NYN
Mohapatra, Valle 1986
H L L H H L L H Inverse Seesaw
July 2012 - GGI
Inverse/Linear Seesaw
Identifying NP ∼ constraining new parameters
8 F . Bonnet
Type II : natural
∆ Y∆ µ∆
Type I/III : extra fermion
N1 N2 Y 0
N
Y T
N
ε ν N1 N2 ν N1 N2 YN εY 0
N
Y T
N
Λ εY 0
N T
Λ
ε ✓ Y 0
N T v2
Λ YN + Y T
N
v2 Λ Y 0
N
◆
LFV
mν
Y †
NYN
Y∆µ∆ v2 M 2
∆
LFV
mν
Y †
∆Y∆
Akhmedov et al. 1995
H L L H H L L H Linear Seesaw
July 2012 - GGI
d>5 operators
d>5 operator
Identifying NP ∼ constraining new parameters
10 F . Bonnet
concept :
Od=5 = LLHH Od=7 = (LLHH)(H†H) Od=9 = (LLHH)(H†H)2
problem :
∝ 1 16π2 1 ΛNP (LLHH)
ΛNP > 3 TeV
if H H H H H H L L L L
arXiv:0907 .3143, JHEP 10 (2009) 076
July 2012 - GGI
∝ 1 Λ3
NP
(LLHH)(H†H)
d>5 operator
Identifying NP ∼ constraining new parameters
11 F . Bonnet
concept :
Od=5 = LLHH Od=7 = (LLHH)(H†H) Od=9 = (LLHH)(H†H)2
solution : genuine d=D operator as LO with all d<D forbidden new U(1) or discrete symmetry Pb : H†H singlet -> need new fields
On+5 ∼ (LLHH)Sn
Chen, de Gouvea, Dobrescu 2006 Gogoladze, Okada, Shafi, 2008
July 2012 - GGI
d>5 operator
Identifying NP ∼ constraining new parameters
11 F . Bonnet
concept :
Od=5 = LLHH Od=7 = (LLHH)(H†H) Od=9 = (LLHH)(H†H)2
solution : genuine d=D operator as LO with all d<D forbidden new U(1) or discrete symmetry Pb : H†H singlet -> need new fields
On+5 ∼ (LLHH)Sn O2n+5 ∼ (LLHuHu)(HuHd)n
simplest possibility : d=7 with
(LLHuHu)(HuHd) Z5
Chen, de Gouvea, Dobrescu 2006 Gogoladze, Okada, Shafi, 2008
July 2012 - GGI
d>5 operator
Identifying NP ∼ constraining new parameters
12 F . Bonnet
decomposition : finding all possible heavy fields (mediators) for tree-level realizations of
L
Lorentz: S (scalar), V (vector), R/L (fermion) Hypercharge SU(2)
(LLHuHu)(HuHd)
July 2012 - GGI
d>5 operator
Identifying NP ∼ constraining new parameters
12 F . Bonnet
Type I (fermion singlet) Type II (scalar triplet) Type III (fermion triplet)
1R/L 3R/L 3S
−1 July 2012 - GGI
Identifying NP ∼ constraining new parameters
14 F . Bonnet
L L
Hu Hu Hu Hd φ
d>5 operator : first example
NR NR N 0
L
N 0
L
Λ Λ κ µ
Yν Yν N, N 0 ∼ 1F φ ∼ 1S
July 2012 - GGI
Identifying NP ∼ constraining new parameters
14 F . Bonnet
L L
Hu Hu Hu Hd φ
d>5 operator : first example
NR NR N 0
L
N 0
L
Λ Λ κ µ
Masses @TeV ->
Yν ∼ 10−4 Yν Yν mν = v3
uvd
2 Y T
ν (Λ−1)T κµ
M 2
φ
Λ−1 Yν N, N 0 ∼ 1F φ ∼ 1S
July 2012 - GGI
Identifying NP ∼ constraining new parameters
14 F . Bonnet
L L
Hu Hu Hu Hd φ
d>5 operator : first example
NR NR N 0
L
N 0
L
Λ Λ κ µ
mν = v3
uvd
2 Y T
ν (Λ−1)T κµ
M 2
φ
Λ−1 Yν Yν Yν
Y T
ν hH0 ui
YνhH0
ui
Λ Λ µLNV Y T
ν hH0 ui
YνhH0
ui
Λ Λ 2κ µ
M 2
φ hH0
uH0 di
Mφ → ∞
N, N 0 ∼ 1F φ ∼ 1S
July 2012 - GGI
Identifying NP ∼ constraining new parameters
14 F . Bonnet
L L
Hu Hu Hu Hd NR N 0
L
Φ
d>5 operator : second example
Y T
ν hH0 ui ζhH0
dihH0 ui2
M 2
Φ
Y 0
ν T
YνhH0
ui
Λ
ζhH0
dihH0 ui2
M 2
Φ
Y 0
ν
Λ
Y T
ν hH0 ui
εLNV Y 0
ν T
YνhH0
ui
Λ εLNV Y 0
ν
Λ
MΦ → ∞
mν = ζv3
uvd
4M 4
Φ
⇣ Y T
ν Λ1Y 0 ν + Y 0 ν T Λ1Yν
⌘
Λ ζ Yν Y 0
ν
N, N 0 ∼ 1F Φ ∼ 2S
+1/2 July 2012 - GGI
Identifying NP ∼ constraining new parameters
15 F . Bonnet
d>5 operator :
µLNV εLNV
1F
0 /3F
1F
0 /3F
1F
0 /3F
1F
0 /3F
July 2012 - GGI
Identifying NP ∼ constraining new parameters
15 F . Bonnet
d>5 operator :
µLNV εLNV
d-5
1/ 1/
µLNV εLNV
1F
0 /3F
1F
0 /3F
1F
0 /3F
1F
0 /3F
d=7
July 2012 - GGI
Identifying NP ∼ constraining new parameters
16 F . Bonnet
L L
d>5 operator : Type II
∆ ∆ ∆ ∆ ∆ ∆
Hu Hd Hu Hu
L L
Hu Hu
L L
Hu Hu
L L
Hu Hu Hd Hd Hu Hu Hd
µ∆
Hu
( ) ( )
July 2012 - GGI
Identifying NP ∼ constraining new parameters
17 F . Bonnet
d-5
Mseesaw @TeV Mother @TeV Yukawa large
1/
Mseesaw @TeV Mother > TeV Yukawa large
1/
µLNV εLNV
d-5
Mseesaw @TeV Mother @TeV Yukawa large
1/
Mseesaw @TeV Mother > TeV Yukawa large
1/
µ∆ Y∆
Mseesaw @TeV Mother > TeV Yukawa large
Type I/III Type II
July 2012 - GGI
d>5 operator
Radiative neutrino masses
Identifying NP ∼ constraining new parameters
19 F . Bonnet
concept : H H L L 1 loop only, no self-energy
arXiv:1205.5140, to be published in JHEP
July 2012 - GGI
Identifying NP ∼ constraining new parameters
20 F . Bonnet
Include Dark doublet Ma 2006 Kubo, Ma, Suematsu 2006 Include Zee Model Zee 1980 Partially Studied in Ma 1998
July 2012 - GGI
Identifying NP ∼ constraining new parameters
21 F . Bonnet July 2012 - GGI
∆ ∆ ∆ ∆ ∆ ∆ N/Σ N/Σ
Identifying NP ∼ constraining new parameters
21 F . Bonnet
N/Σ ∆ ∆
July 2012 - GGI
Identifying NP ∼ constraining new parameters
22 F . Bonnet
Loop Seesaw Other problem : Forbid tree-level d=5 solution : It depends ...
N/Σ ∆ ∆
July 2012 - GGI
Identifying NP ∼ constraining new parameters
23 F . Bonnet July 2012 - GGI
Identifying NP ∼ constraining new parameters
23 F . Bonnet July 2012 - GGI
Identifying NP ∼ constraining new parameters
23 F . Bonnet
simple symmetry is enough
Z2
July 2012 - GGI
Identifying NP ∼ constraining new parameters
24 F . Bonnet
loop = singlet
Zn :
loop tree
⇒
solution : No LNV couplings Fermion in loop : Majorana to prevent scalar vev
Z2
July 2012 - GGI
Identifying NP ∼ constraining new parameters
24 F . Bonnet
loop = singlet
Zn :
loop tree
⇒
solution : No LNV couplings Fermion in loop : Majorana to prevent scalar vev
Z2
July 2012 - GGI
Identifying NP ∼ constraining new parameters
25 F . Bonnet
H L H L L L H H
∆
NR/ΣR
Y∆loop N 0
R/Σ0 R
Yν εY 0
ν
Y T
ν
Λ εY 0
ν T
Λ
Type I/III Type II
July 2012 - GGI
εY 0
∆
∼
Identifying NP ∼ constraining new parameters
26 F . Bonnet
# loops
Mseesaw @TeV Mother @TeV Yukawa large Mseesaw @TeV Mother @TeV Yukawa large
Mseesaw @TeV Mother > TeV Yukawa large
1/ 1/
µLNV εLNV
1/ 1/
µ∆ Y∆
Mseesaw @TeV Mother > TeV Yukawa large
# loops Small = suppressed LFV
Y∆
Type I/III Type II
July 2012 - GGI
Identifying NP ∼ constraining new parameters
26 F . Bonnet
# loops
Mseesaw @TeV Mother @TeV Yukawa large Mseesaw @TeV Mother @TeV Yukawa large
Mseesaw @TeV Mother > TeV Yukawa large
1/ 1/
µLNV εLNV
1/ 1/
µ∆ Y∆
Mseesaw @TeV Mother > TeV Yukawa large
# loops Small = suppressed LFV
Y∆
Type I/III Type II
1/εLNV
July 2012 - GGI
Is there a pattern here?
Global view
Identifying NP ∼ constraining new parameters
29 F . Bonnet
d-5
1/ 1/
µLNV εLNV
# loops d-5
1/µ∆
# loops
Type I/III Type II
1/εLNV
July 2012 - GGI
Identifying NP ∼ constraining new parameters
29 F . Bonnet
d-5
1/ 1/
µLNV εLNV
# loops d-5
1/µ∆
# loops
Type I/III Type II
Global view
1/εLNV
July 2012 - GGI
Identifying NP ∼ constraining new parameters
29 F . Bonnet
# loops d-5
1/µ∆
d-5
1/ 1/
µLNV εLNV
# loops
Type I/III Type II
Global view
1/εLNV
July 2012 - GGI
Identifying NP ∼ constraining new parameters
30 F . Bonnet
# loops
1/(L size) 1/(L size)
d-5
Leff = LSM +δL(0)
d=5 + δL(1) d=5 + δL(2) d=5 + . . .
+δL(0)
d=7 + δL(1) d=7 + δL(2) d=7 + . . .
+δL(0)
d=9 + δL(1) d=9 + δL(2) d=9 + . . .
+ . . .
Global view
July 2012 - GGI
Introduction
Identifying NP ∼ constraining new parameters
30 F . Bonnet
# loops
1/(L size) 1/(L size)
d-5
Leff = LSM +δL(0)
d=5 + δL(1) d=5 + δL(2) d=5 + . . .
+δL(0)
d=7 + δL(1) d=7 + δL(2) d=7 + . . .
+δL(0)
d=9 + δL(1) d=9 + δL(2) d=9 + . . .
+ . . .
July 2012 - GGI
Introduction
Identifying NP ∼ constraining new parameters
30 F . Bonnet
# loops
1/(L size) 1/(L size)
d-5
Leff = LSM +δL(0)
d=5 + δL(1) d=5 + δL(2) d=5 + . . .
+δL(0)
d=7 + δL(1) d=7 + δL(2) d=7 + . . .
+δL(0)
d=9 + δL(1) d=9 + δL(2) d=9 + . . .
+ . . .
July 2012 - GGI
Identifying NP ∼ constraining new parameters
32 F . Bonnet
d-5
1/ 1/
µLNV εLNV
# loops d-5
1/ 1/
µ∆ Y∆
# loops
Type I/III Type II
Global view
July 2012 - GGI
Identifying NP ∼ constraining new parameters
33 F . Bonnet
L L
Hu Hu Hu Hd φ
NR NR N 0
L
N 0
L
Hu Hd ϕ ϕ
L L
Hu Hu φ
NR NR N 0
L
N 0
L
Hu Hd S S S Hd Hd
d=9, tree d=9, 2-loop
m(2loop)
ν
Y T
N hH0 di
(εY 0
ν)(1loop)T
YNhH0
di
µ0(tree) Λ (εY 0
ν)(1loop)
ΛT µtree
Global view
July 2012 - GGI
Identifying NP ∼ constraining new parameters
34 F . Bonnet
Inverse/Linear Seesaw = Effective root for d=7 /1-loop generalization of Type I, II, III Seesaws and can discriminate loop Vs tree level
εLNV µLNV
Conclusions
d-5
1/ 1/
µLNV εLNV
# loops d-5
1/µ∆
# loops
1/εLNV
I/III II
July 2012 - GGI
Identifying NP ∼ constraining new parameters
35 F . Bonnet
Y∆ µ∆
= Tree Loop
µLNV εLNV
With
Conjecture
N/Σ ∆
July 2012 - GGI
Identifying NP ∼ constraining new parameters
35 F . Bonnet
Y∆ µ∆
= Tree Loop
µLNV εLNV
With
Global view
July 2012 - GGI
Identifying NP ∼ constraining new parameters
3 F . Bonnet May 24th 2012 - KIT
Back up
d-5
1/ 1/
µLNV εLNV
# loops d-5
1/ 1/
µ∆ Y∆
# loops
Type I/III Type II
Global view
Identifying NP ∼ constraining new parameters # loops d-5
1/ 1/
µ∆ Y∆
d-5
1/ 1/
µLNV εLNV
# loops
Type I/III Type II
Global view
# loops d-5
1/ 1/
µ∆ Y∆
d-5
1/ 1/
µLNV εLNV
# loops
Type I/III Type II
Global view
d-5
1/ 1/
µLNV εLNV
# loops d-5
1/ 1/
µ∆ Y∆
# loops
Type I/III Type II
Global view