Michele Redi
GGI, July 2013
Axion-Higgs Unification
1208.6013 with A. Strumia
Wednesday, July 10, 2013
Natural theories must be extremely smart:
SUSY NGB HIGGSµ ∼ 250GeV
mstop ∼ 700GeV
mgluino ∼ 1500GeV
mfermions ∼ 1000GeV
mvectors ∼ 3000GeV
f ∼ 800GeV
Wednesday, July 10, 2013
- Higgs could be tuned anthropically (as c.c.)
Λ � TeV?
- Explains why we have not seen anything
Wednesday, July 10, 2013
102 104 106 108 1010 1012 1014 1016�0.04
�0.02
0.00
0.02
0.04
0.06
0.08
0.10
RGE scale Μ in GeV
Hig
gsqu
artic
coup
ling��
1Σ bands inMt � 173.1 � 0.7 GeVΑs�MZ� � 0.1184 � 0.0007Mh � 125.5� 0.5 GeV
Quartic almost zero at high scale for 125 GeV Higgs
HINTS ?
• Running:
V (h) = m2h2/2 + λh4/4
De Grassi et al. ’12
Wednesday, July 10, 2013
• Strong CP problem:
θ
32π2
�d4x �µνρσ Tr[GµνGρσ] θ < 10−10
Elegant solution with axions
θ → a(x)
f
Axions are Goldstone bosons of a symmetry anomalous under QCD
ma ∼ mπfπf
Wednesday, July 10, 2013
Axions can be dark matter
ρaρDM
≈ θ2i
�f
2− 3× 1011 GeV
�f ≈ 1011 GeV
θi ∼ 1
f > 109 GeV ma < 10−3 eV
Wednesday, July 10, 2013
Axions can be dark matter
ρaρDM
≈ θ2i
�f
2− 3× 1011 GeV
�f ≈ 1011 GeV
θi ∼ 1
• Neutrino masses
1
Λ(LH)2 mν ∝ v2
Λ
• Unification
Λ < MGUT
f > 109 GeV ma < 10−3 eV
Wednesday, July 10, 2013
- Axions + Higgs can be unified
- 125 GeV Higgs can be explained
Λ ≈ 1011 GeV
Wednesday, July 10, 2013
The Higgs doublet could be a NGB.
GSM ∈ H
NGB =G
H
Georgi, Kaplan ‘80s
δm2h ∼ 3λ2
t
4π2m2
ρ
Ex:
GB = (2, 2) Agashe , Contino, Pomarol, ’04
SO(5)
SU(2)L ⊗ SU(2)R
gρ mρ
Wednesday, July 10, 2013
Deviation from SM: O
�v2
f2
�
mW = 80GeV
mρ ∼ 3TeV
0
Typical spectrum:
mh = 125GeV
Higgs is an angle,
0 < h < 2πf TUNING ∝ f2
v2
f = 0.5− 1TeV
Small Tuning f < TeV
Wednesday, July 10, 2013
AXION-HIGGS
Basic idea: Axion and Higgs originate from common strong dynamics. f is fixed by dark matter and the electro-weak scale is tuned.
G
H
f ≈ 1011 GeVHiggs + singlet
Composite Axion: Choi Kim ’85
Wednesday, July 10, 2013
AXION-HIGGS
Basic idea: Axion and Higgs originate from common strong dynamics. f is fixed by dark matter and the electro-weak scale is tuned.
• QCD anomaly from new fermions (KSVZ)
• QCD anomaly from SM fermions (DFSZ)
G
H
f ≈ 1011 GeVHiggs + singlet
Composite Axion: Choi Kim ’85
Wednesday, July 10, 2013
HIGGS + KSVZ AXION
Kim-Shifman-Vainstein-Zakharov:Add new colored fermions + complex scalar
L = LSM + ΨQ∂ΨQ + |∂µσ|2 + (λσ ΨQΨQ + h.c.)− V (σ)
ΨQ → eiαQγ5ΨQ, σ → e−2iαQσ
Wednesday, July 10, 2013
HIGGS + KSVZ AXION
Kim-Shifman-Vainstein-Zakharov:Add new colored fermions + complex scalar
L = LSM + ΨQ∂ΨQ + |∂µσ|2 + (λσ ΨQΨQ + h.c.)− V (σ)
ΨQ → eiαQγ5ΨQ, σ → e−2iαQσ
Spontaneous PQ symmetry breaking
f ≈ �σ� a =√2 Im[σ]
PQ symmetry anomalous under QCD
Wednesday, July 10, 2013
G
H=
SU(6)L × SU(6)RSU(6)L+R
35 = 24⊕ 5⊕ 5⊕ 1
Under SU(5)SM
One Higgs doublet. Two massless singlets are axion candidates.
Wednesday, July 10, 2013
G
H=
SU(6)L × SU(6)RSU(6)L+R
35 = 24⊕ 5⊕ 5⊕ 1
Under SU(5)SM
Under SM 33 charged scalars acquire mass.
m ≈ gSM
4πΛ
One Higgs doublet. Two massless singlets are axion candidates.
Wednesday, July 10, 2013
UV realization: SU(n) gauge theory with 6 flavors
Fermions U(1)Y SU(2)L SU(3)c SU(n)TC
D 13 1 3 n
L − 12 2 1 n
N 0 1 1 nD − 1
3 1 3 nL 1
2 2 1 nN 0 1 1 n
(5 + 1, n)⊕ (5 + 1, n)
Wednesday, July 10, 2013
UV realization: SU(n) gauge theory with 6 flavors
Fermions U(1)Y SU(2)L SU(3)c SU(n)TC
D 13 1 3 n
L − 12 2 1 n
N 0 1 1 nD − 1
3 1 3 nL 1
2 2 1 nN 0 1 1 n
(5 + 1, n)⊕ (5 + 1, n)
�DD� = �LL� = �NN� ≈ Λ3H ∼ (LN)− (LN)∗
Singlets:DD LL NN
anomalyDD + LL+NN
U(1)× SU(n)2TC gTC
4πΛ
Wednesday, July 10, 2013
aE
32π2f�µνρσFµνFρσ
aN
32π2 f�µνρσTr[GµνGρσ]
Axions couple to photon and gluons through anomalies
E =�
QPQQ2em
N =�
QPQT2SU(3)
Wednesday, July 10, 2013
aE
32π2f�µνρσFµνFρσ
aN
32π2 f�µνρσTr[GµνGρσ]
Axions couple to photon and gluons through anomalies
E =�
QPQQ2em
N =�
QPQT2SU(3)
Experiments measure conversion of axion to photons
gaγγ =2(E/N − 1.92)
1016 GeV
ma
µeV
ma ∼ Nfπmπ
2f
√mumd
mu +md
Wednesday, July 10, 2013
4D − 3L− 6N√102
,L− 2N√
3E
N= −5
6
a) If UV interactions respect singlets symmetry
E
N=
8
3D + L− 5N√
30
c) SU(5) is gauged
D − 3L+ 3N√30
E
N= −16
3
b) If all Yukawas allowed
Flavor: 1
Λ22
(qu)(LN)1
Λ21
(qu)(LN)
Wednesday, July 10, 2013
3
1
1
3
1
1
3
1
1
3
2
1
2
1
2
1
2
1
2
1
1
1
1
1
1
1
1
1
1
8
7
6
5
4
3
2
1
0
1
1
1
1
1
1
1
1
1
1
1
2
1
2
1
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1
2
1
2
1
3
1
1
3
1
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3
1
1
2
1
4
1
2
1
4
1
2 �2 �1 0 1 20
1
2
3
4
5
6
�b3��b2
�b 2��b 1
1010
1011
10161017
10181019
102 104 106 108 1010 1012 1014 10160
10
20
30
40
50
60
Energy in GeV
1�Α
�TC
SU�3�c
SU�2�L
U�1�1
SU�6�TC
Incomplete SU(5) multiplets can improve unification(“unificaxion”)
D,L,Q,U,NEx:
Giudice, Rattazzi, Strumia ’12
Wednesday, July 10, 2013
5 GBs:
5 = (2, 2) + 1
Gripaios, Pomarol, Riva, Serra ’09Redi, Tesi ’12
Galloway et. al. ’10
G
H=
SO(6)
SO(5)� SU(4)
Sp(4)
HIGGS + DFSZ AXION
Wednesday, July 10, 2013
5 GBs:
5 = (2, 2) + 1
Gripaios, Pomarol, Riva, Serra ’09Redi, Tesi ’12
Galloway et. al. ’10
G
H=
SO(6)
SO(5)� SU(4)
Sp(4)
Gauging of SM gauge symmetry preserves
SU(2)L × U(1)Y × U(1)PQ
Under singlet shifts. U(1)PQ
HIGGS + DFSZ AXION
Wednesday, July 10, 2013
Partial compositeness
ψSMΨcomp
q+
+q
∆L
∆R
YySM = �L · Y · �R
We can choose
Ψcomp ∈ G
10 = (2, 2) + (3, 1) + (1, 3)
Wednesday, July 10, 2013
PQ symmetry is anomalous due to uR, dR, eR rotations
E = 2
��4
9+
1
9
�3 + 1
�NF + ETC
ETC ∼ nE
N=
8
3+
ETC
6
δqL = 0
Mixing induces a PQ charge on the SM fermions.
δuR = − 1√2uR δdR = − 1√
2dR δeR = − 1√
2eR
N = 2NF
Wednesday, July 10, 2013
HIGGS MASS
Higgs potential is generated by the couplings that break the global symmetry. Minimally gauge and Yukawa couplings.
V (h) =�
i
ai sin2i
�h
f
�
Electro-weak scale:
v � f ai must be tuned
Higgs mass is then “predicted”.
Wednesday, July 10, 2013
Gauge contribution:
1 2 3 4 5 6 7�0.04
�0.03
�0.02
�0.01
0.00
gΡ
HiggsquarticcouplingΛ
ma1� 2 mΡ
ma1� 3 mΡ
V (h)gauge ≈9
4
g2
16π2
m4ρ
g2ρln
�m2
ρ +m2a1
2m2ρ
�sin2
h
f
102 104 106 108 1010 1012 1014 1016�0.04
�0.02
0.00
0.02
0.04
0.06
0.08
0.10
RGE scale Μ in GeV
Hig
gsqu
artic
coup
ling��
1Σ bands inMt � 173.1 � 0.7 GeVΑs�MZ� � 0.1184 � 0.0007Mh � 125.5� 0.5 GeV
λ(mρ)leadinggauge ≈ −3g2 log
3
2
g2ρ(4π)2
V (h)gauge =9
2
�d4p
(2π)4ln
�1 +
1
4
Π1(p2)
Π0(p2)sin2
h
f
�
Wednesday, July 10, 2013
λ(Λ) ∼ g2SMg2ρ
(4π)2∼ few 10−2
• Leading order tuning
125 GeV Higgs implies weak coupling (large n)
Wednesday, July 10, 2013
λ(Λ) ∼ g2SMg2ρ
(4π)2∼ few 10−2
• Leading order tuning
λ(Λ) ∼ g4SM(4π)2
∼ 10−3
• Subleading order tuning
Model I:
Vfermions ∼Nc λ2
t
16π2Λ2f2
2�
α=1
|Tr[Παt · U ]|2 ∝ sin2
h
f
125 GeV Higgs implies weak coupling (large n)
Wednesday, July 10, 2013
CONCLUSIONS
• So far everything is consistent with the SM being valid up to a very large a scale. Maybe scale of new physics is large.
Wednesday, July 10, 2013
CONCLUSIONS
• So far everything is consistent with the SM being valid up to a very large a scale. Maybe scale of new physics is large.
• The idea of the Goldstone boson Higgs can be naturally merged with axions for large compositeness.
Wednesday, July 10, 2013
CONCLUSIONS
• So far everything is consistent with the SM being valid up to a very large a scale. Maybe scale of new physics is large.
• Giving up naturalness, strong CP, dark matter, Higgs mass can be explained. Unification and neutrino masses could also fit into the picture.
• The idea of the Goldstone boson Higgs can be naturally merged with axions for large compositeness.
Wednesday, July 10, 2013
HIGGS + DFSZ AXION
Dine-Fischler-Srednicki-Zhitnitsky:Two Higgs doublets and complex singlet
σ → e4iα
σ, qL,R → eiαqL,R Hu → e
−2iαHu, Hd → e
−2iαHd
f =�v2u + v2d + |σ|2
Wednesday, July 10, 2013
HIGGS + DFSZ AXION
Dine-Fischler-Srednicki-Zhitnitsky:Two Higgs doublets and complex singlet
σ → e4iα
σ, qL,R → eiαqL,R Hu → e
−2iαHu, Hd → e
−2iαHd
f =�v2u + v2d + |σ|2
G
H=
SU(6)
SO(6)
20� = (2,2)±2 ⊕ (1,1)±4 ⊕ (1,1)0 ⊕ (3,3)0
Ex:
SO(6) ⊃ SO(4)⊗U(1)PQ
Wednesday, July 10, 2013
Fermions U(1)Y SU(2)L SU(3)c SO(n)TC U(1)PQ
L − 12 2 1 n 0
L12 2 1 n 0
N 0 1 1 n 2N 0 1 1 n −2
�LL� = �NN� = Λ3
UV realization: SO(n) gauge theory with 6 flavors
H1 ∼ LN
H2 ∼ LN
Wednesday, July 10, 2013
Fermions U(1)Y SU(2)L SU(3)c SO(n)TC U(1)PQ
L − 12 2 1 n 0
L12 2 1 n 0
N 0 1 1 n 2N 0 1 1 n −2
�LL� = �NN� = Λ3
UV realization: SO(n) gauge theory with 6 flavors
Yukawas must respect PQ1
Λ2t
(qLtcR)
†(LN) +1
Λ2b
(qLbcR)
†(L N) + h.c.
Anomalies:
ETC = 0E
N=
8
3
H1 ∼ LN
H2 ∼ LN
Wednesday, July 10, 2013
Neutrino masses can be generated by see-saw mechanism
If no right-handed neutrinos
Leptogenesis?
1
Λ5ν
(lL)2N2 1
Λ3ν
(lHu)2σ2 + . . .
1
Λ2ν
(lνcR)†(LN) +m(νcR)
2 + h.c λ lH1νcR +m(νcR)
2 + h.c.
mν ∼ λ2v2
m
Wednesday, July 10, 2013
Fermions U(1)Y SU(2)L SU(3)c Sp(n)TC U(1)PQ
D 0 2 1 n +1S + 1
2 1 1 n −1S − 1
2 1 1 n −1
Sp(n) theories with 4 flavors
Wednesday, July 10, 2013
Fermions U(1)Y SU(2)L SU(3)c Sp(n)TC U(1)PQ
D 0 2 1 n +1S + 1
2 1 1 n −1S − 1
2 1 1 n −1
Sp(n) theories with 4 flavors
Difficult to generate QCD anomaly
(qu)(DS) (qu)(DS)(SS)
We can be build models with partial compositeness
mψΨ+MΨΨ+ gTCΨΨH
Wednesday, July 10, 2013
Minimum ingredients for semi-natural composite Higgs:
- partial compositeness
- custodial symmetry
- L-R symmetry
- split spectrum
- luck with precision tests
- miracle with flavor
Wednesday, July 10, 2013
Despite great improvements difficulties remain:
- flavor
- precision tests
mρ > 3TeV
mρ > 20TeV
Wednesday, July 10, 2013
Despite great improvements difficulties remain:
- flavor
- precision tests
mρ > 3TeV
mρ > 20TeV
- direct exclusionmf > 0.7TeV mρ > 2TeV
Wednesday, July 10, 2013
Despite great improvements difficulties remain:
- flavor
- precision tests
mρ > 3TeV
Redi, Tesi ’12
- Higgs mass
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100 120 140 160 180 200 220500
1000
1500
2000
2500
3000
mH�GeV�
mf�GeV
�
f = 800GeV
mρ > 20TeV
- direct exclusionmf > 0.7TeV mρ > 2TeV
Wednesday, July 10, 2013
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