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Radiative generation of the Higgs potential
Hyun Min Lee(KIAS)
NRF workshop on particle physics and cosmologyJune 8, 2013
Ref: E.J.Chun, S.Jung, HML, arXiv:1204.5815 [hep-ph]
2013년 6월 8일 토요일
Outline
• Motivation
• Scale symmetry breaking
• B-L gauge symmetry and radiative EWSB
• Conclusions
2013년 6월 8일 토요일
Higgs mechanism is now real!• Discovered 126 GeV boson consistent
with the SM Higgs.
mass (GeV)1 2 3 4 5 10 20 100 200
1/2
or (
g/2v
)!
-210
-110
1W Z
t
b
"
68% CL95% CL68% CL95% CL
CMS Preliminary -1 19.6 fb# = 8 TeV, L s -1 5.1 fb# = 7 TeV, L s
(GeV)!!m110 120 130 140 150S/
(S+B
) Wei
ghte
d Ev
ents
/ 1.
5 G
eV
0
1000
2000
3000
4000
5000 DataS+B FitBkg Fit Component
"1 ±
"2 ±
(MVA)-1 = 8 TeV, L = 19.6 fbs (MVA)-1 = 7 TeV, L = 5.1 fbs
CMS Preliminary
mH = 125.5± 0.2(stat)+0.5−0.6(sys)GeV
mH = 125.7± 0.3(stat)± 0.3(sys)GeV
CMS:ATLAS:
2013년 6월 8일 토요일
Higgs boson and unitarity• Higgs boson couplings to W/Z bosons hint that Higgs
degrees of freedom provide longitudinal modes to W/Z spin-1 bosons, making the SM renormalizable and unitary.
• WW-scattering matrix is unitary:
E2
v2
�
W
WHiggs
−E2
v2− 2M2
H
v2
: MH < 870GeV.
E=c.m. energy
W
|ReA(WW → WW )| = 2M2H
v2< 8π
S†S = 1; |A|2 ≤ ImA.
2013년 6월 8일 토요일
Higgs potential
• Higgs mass measurement fully determines the Higgs potential.
V (H) = −µ2|H|2 + λH |H|4
“Fermi constant”
“Higgs mass”
v =
�
− µ2
λH
= 246GeV,
GF =g2
4√2M2
W
=1√2v2
λH =m2
H
2v2= 0.131
(|µ| = 89GeV)
• Is the end of the SM ?
2013년 6월 8일 토요일
Hierarchy problem• SM loops leads to quadratic divergent Higgs mass.
∆µ2 � − 1
16π2
�18λH +
3
4g2Y+
9
4g2 − 6y2
t
�Λ2.
Need a tuning of the bare mass parameter.
• repetitive cancellation of new-physics contributions. “Hierarchy problem”Λ � mH :
Motivation for new symmetry at TeV, such as low-energy supersymmetry.
µ2 +∆µ2 = −(89GeV)2.
Log-sensitive−M2Z
2� |µ|2 +m2
Hu.
2013년 6월 8일 토요일
Vacuum instability• Higgs quartic coupling turns negative at high
energies. We might live in a catastrophic universe.[Degrassi et al (2012)]
βλH< 0
• Problem of vacuum selection in early universe, conflict with inflation, etc.
2013년 6월 8일 토요일
Scale invariance in SM
• Scale invariance could be a solution to the hierarchy problem, if there is no large (induced) scale breaking.
• But, it is broken by explicit mass scales, “cutoff or renormalization scale”, in the regularization of loop corrections.
• New particles for neutrino masses, dark matter, ect. could correct the Higgs mass parameter,
µ2 ∼ κiM2i .
κi � 1 and/or Mi � MP .
[Meissner, Nicolai(2006); Shaposhnikov et al(2008)]
2013년 6월 8일 토요일
Scale anomalies• Scale invariance.
• Scale anomalies.
• Dilaton as pseudo-Goldstone.
δxµ = εxµ
scale current: Sµ(x) = xν Tνµ +Kµ(x)
∂µSµ = 0, Tµ
µ = −∂µKµ. local Op. with
no explicit x dep.cf. conformal inv: Tµ
µ = ∂µ∂νLνµ, D ≥ 3.
Tµν → ∂σ∂ρYµσνρ : redundancyΘµν ≡ Tµν + δTµν , Θµ
µ = 0.
�0|∂µJµ|0� = �0|Θµµ|0� = −fσM
2σ , M2
σ � βλf2σ .
δxµ = ε vµ(x),
improved E-M, “RG-inv.”
Θµµ = −βa(g)
2gaF aµνF
aµν + (4γφλ− βλ) + γφφ�φ+ · · ·
2013년 6월 8일 토요일
Coleman-Weinberg mechanism• Spontaneous breaking of hidden
gauge symmetry.
• A small scale from dimensional transmutation:
V =1
4λφφ
4 +1
64π2(10λ2
φ + 3e4φ)�ln
φ2
M2− 25
6
�
�φ� = ΛUV exp�116
�exp
�− 8π2
3
λφ(ΛUV)
e4φ(ΛUV)
�.
λφ(ΛUV) ∼ e4φ(ΛUV) �φ� � ΛUV.
minimization condition: λφ(�φ�) ≈11
16π2e4φ(�φ�)
m2ϕ =
3e4φ8π2
�φ� � m2X = e2φ�φ�.
0 1 2 3 4
0
1
2
3
4
!
V!!"
2013년 6월 8일 토요일
EWSB from Higgs-portal term
• Higgs-portal coupling to singlet scalar induces Higgs mass due to singlet VEV.
• Need of a small portal coupling.
λHφφ2h2
If �φ� ∼ v, λHφ ∼ O(1) :
λHφ < 0
µ2 = λHφ�φ2� < 0.
M2 ∼�
λφv2 λHφv2
λHφv2 λHv2
�
( Higgs data: )|λHφ| � λH
�φ� � v
|λHφ| � λH
(λφ � 1)
[Hempfling(96)]
m21 ∼ v2
�λH + λφ −
�(λH − λφ)2 + λ2
Hφ
�> 0
2013년 6월 8일 토요일
B-L gauge symmetry• See-saw mechanism requires right-handed(RH)
neutrinos with lepton # violating masses.
• B-L gauge symmetry is an anomaly-free U(1) with “SM + 3 RH neutrinos”, generating neutrino masses after B-L breaking.
L = − cv2
MNνν, MN/c � 1014 GeV.mν =
cv2
MN� 0.1eV :
LB−L = −yν l̄LνR(iσ2H
∗)− yN (νR)cνRΦ.
MN = 2yN �Φ�.
covariant deriv.:2013년 6월 8일 토요일
Radiative B-L breaking
• One-loop Coleman-Weinberg for B-L.
• Minimization condition:
• Masses:
∼ βλφ
> 0.
[Iso et al (2009, 2013)]
� M∗.
� 1.
2013년 6월 8일 토요일
Radiative B-L breaking
• Vanishing potential + no kinetic mixing at MI.
Blue: B-L quartic,Red: B-L min. condition.
Mt = 173GeV
βλφ changes sign.
MI
2013년 6월 8일 토요일
EWSB from B-L breaking
• Mixing between B-L and SM sectors.
• Higgs quartic coupling as in the SM.
Higgs-portal term at two-loop leads to EWSB.
Gauge kinetic mixing at one-loop.
g̃ � − 2
3π2gB−Lg
2Y ln
ΛUV
vφ.
λHΦ � − 3
4π2g̃2g2
B−Lln
ΛUV
vφµ2 =
1
2λHΦv
2φ < 0.
negligible loop corrections
B
Z’
h
h
φ
φ
BZ’
,
2013년 6월 8일 토요일
Numerical results
• MI =1018 GeV (M =171.3 GeV)
larger running: vφ ~ a few TeV, gB-L ~ 0.35.
e.g. vφ =5.1TeV, MB-L = 3.6TeV, mφ =460GeV, MN =4.9TeV.2013년 6월 8일 토요일
Bounds on RH neutrino masses• Heavy RH neutrinos have Yukawa couplings to
Higgs, contributing to Higgs mass.
δµ2 =y2ν
(4π)2M2
N∼ m2
H
• Lower bound from leptogenesis.
cf. Resonant leptogenesis: Pilaftsis et al(2003); Iso et al(2010)
[Davidson,Ibarra(2002); Giudice et al(2003)]
[Farina et al (2013)]
: Upper bound.MN � mH
�16π2mH
mν
�1/3
∼ 107 GeV
∼ 10−10,
M1 > 2× 107−9 GeV
M1 � M2 � M3 :
( )
2013년 6월 8일 토요일
B-L Z’ at the LHC
• MB-L > (gY / gB-L) 2.86 TeV @ 95% C.L.
• HE-LHC will probe the higher mass region.
2013년 6월 8일 토요일
Conclusions
• Natural radiative EWSB can occur via the Higgs-portal term in the presence of hidden-sector gauge symmetry breakdown.
• B-L gauge symmetry leads to a small Higgs-portal term at loops, being consistent with EWSB and LHC bounds on extra gauge bosons.
• Vanishing potential at instability scale gives rise to a predictive mass spectrum for B-L sector.
• Conformality of scalar potential may come from a shift or global symmetry in the scalar sector.
2013년 6월 8일 토요일