radiative generation of the higgs...

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


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:


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.


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 ?


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.


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.


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)]


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+ · · ·


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!!"


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


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.


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


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’

,


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 :

( )


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.


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.


radiative generation of the higgs...

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