TeV scale Universal seesaw, vacuum stability and Heavy Higgs at the LHC

Yongchao Zhang (张永超 )Center for High-Energy Physics, Peking University

w/ Rabi N. Mohapatra, 1401.6701,JHEP06(2014)072

June 14, 2014Shaanxi Normal University

2

Outline

• Motivation• Modeling• Stabilizing the vacuum• Heavy Higgs• Heavy vector-like fermions• Neutrinos• Conclusion

3

126 GeV Higgs observed!

4

SM vacuum unstable (metastable)

• Running of λ is sensitive to the Higgs and top masses

• What does near criticality of the H and t masses mean? Nearby new physics?......

• Maybe NP are needed to stabilize the SM vacuum, with new particles coupling to the SM Higgs

16¼2¯ ¸ = 12¸ 2 ¡9

5g21 + 9g22 ¸ +

9

4

3

25g41 +

2

5g21g

22 + g42 + 12¸y2t ¡ 12y4t

PDG20131112.3022

5

Main idea of the Left-Right universal Seesaw Model (SLRM)

• Seesaw mechanism SM quarks & charged leptons universal seesaw (Berezhiani 1983, Chang & Mohapatra 1987, Rajpoot 1987, Davidson & Wali 1987, Babu & Mohapatra 1989, 1990)

• Left-right symmetric (Mohapatra & Pati, 1975, Senjanovic & Mohapatra, 1975)

• Providing a solution to the Strong CP problem without an axion (Babu & Mohapatra, 1989, 1990)

GL R ´ SU(2)L £ SU(2)R £ U(1)B ¡ L

6

matter content

• Left-right symmetric• Adding the vector-like fermions to realize the seesaw mechanism

GL R ´ SU(2)L £ SU(2)R £ U(1)B ¡ L

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Simple Higgs sector

• Only two Higgs doublets

• Simple potential

• LR symmetry: softly broken by the mass terms,• LR symmetry: only one extra scalar coupling,• Simple spectrum: only two (neutral) physical Higgs particles

ÂL =Â+LÂ0L

2 (2; 1; 1) ;

ÂR = Â+RÂ0R

2 (1; 2; 1) :

V = ¡ ¹ 2L ÂyL ÂL ¡ ¹ 2R Â

yR ÂR ;

+¸ 1 (ÂyL ÂL )2 + (ÂyR ÂR )

2 + ¸ 2(ÂyL ÂL )(Â

yR ÂR ) :

2¸ 1v2L ¸ 2vL vR¸ 2vL vR 2¸ 1v2R

M 2h = 2¸ 1 1 ¡

¸ 224¸ 21

v2L ;

M 2H = 2¸ 1v

2R :

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Yukawa interaction

• LR symmetric Yukawa interaction

• Seesaw mechanism

• O(1) Yukawa interactions: ultra-heavy partner fermions;TeV RH scale and partner masses: smaller couplings.

• All the flavor structure resides in the Yukawa interactions, e.g., with MP,N,E & Yu diagonal,

¡ L Y = ¹QL Yu ~ÂL PR + ¹QL YdÂL N R + ¹ª L YeÂL E R + (L $ R )

+ ¹PL M P PR + ¹N L M N N R + ¹E L M E E R + h:c: :

0 1p2Ya vL

1p2Ya vR M a

ma 'Y 2a vL vR2M a

Yd = V yC K M Y

diagd VC K M

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Stabilizing the vacuum

• The scalar quartic coupling is larger than in the SM,

• Top Yukawa coupling generally larger than in the SM (the NLO

corrections beyond seesaw is important),

• The other couplings are generally negligible, altough they are larger than in the SM,

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RGEs

• RGEs below the RH scale¯ (g0) =

1

16¼210

9n f +

1

6g03

¯ (g) =1

16¼2¡

43

6¡2

3nf g3

¯ (gs ) =1

16¼2¡ 11 ¡

2

3n f g3s

¯ (¸ ) =1

16¼29

8

1

3g04 +

2

3g02g2 + g4 + 24¸ 2 ¡ 2Y4 ¡ ¸ (3g02 + 9g2) + 4¸Y2 ;

¯ (ht ) =1

16¼2¡ ht

17

12g02 +

9

4g2 + 8g2s +

3

2ht (h

2t ¡ h2b) + ht Y2 ;

¯ (hb) =1

16¼2¡ hb

5

12g02 +

9

4g2 + 8g2s +

3

2hb(h

2b ¡ h2t ) + hbY2 ;

¯ (h¿ ) =1

16¼2¡9

4h¿

5

3g02 + g2 +

3

2h3¿ + h¿ Y2 ;

Y2 = 3h2t + 3h2b + h2¿ ;

Y4 = 3h4t + 3h4b + h4¿ :

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RGEs

• RGEs above the RH scale¯ (gB L ) =

1

16¼241

2g3B L

¯ (g) =1

16¼2¡19

6g3

¯ (gs ) =1

16¼2¡ 3g3s

¯ (¸ 1 ) =1

16¼29

8

3

4g4B L + g2B L g

2 + g4 + (24¸ 21 + 2¸ 22 ) ¡ 2~Y4

¡ ¸ 19

2g2B L + 9g2 + 4¸ 1 ~Y2 ;

¯ (¸ 2 ) =1

16¼227

16g4B L + (24¸ 1¸ 2 + 4¸ 22 ) ¡ ¸ 2

9

2g2B L + 9g2 + 4¸ 2 ~Y2

¯ (Y t ) =1

16¼23

2Y t (Y

2t ¡ Y 2

b ) ¡ Y t17

8g2B L +

9

4g2 + 8g2s + Y t ~Y2

¯ (Yb) =1

16¼23

2Yb(Y

2b ¡ Y 2

t ) ¡ Yb5

8g2B L +

9

4g2 + 8g2s + Yb ~Y2

¯ (Y¿ ) =1

16¼23

2Y 3¿ ¡

9

4Y¿

5

2g2B L + g2 + Y¿ ~Y2 ;

~Y2 = 3Y 2t + 3Y 2

b + Y 2¿ ;

~Y4 = 3Y 4t + 3Y 4

b + Y 4¿ :

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Matching conditions

• Gauge couplings in the context of GUT (Mohapatra, 2002, book),

• Scalar quartic couplings

• Yukawa couplings

1

®Y (vR )=3

5

1

®I 3R (vR )+2

5

1

®B L (vR )

~g0 =5

3g0 and ~gB L =

2

3gB L

¸ (vR ) = ¸ 1(vR ) 1 ¡¸ 22(vR )

4¸ 21(vR )

hf (vR )p2

'Y 2f (vR )vR2M F

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Vacuum stability

• Vacuum stability conditions

• Gauge interactions grand unified: RGE run only up to the GUT scale but not to the Planck scale

• Perturbativity: λ1 < 3• Simplifying the heavy mass parameters,

Given vR & MF, all the Yukawa couplings are fixed

• Free parameters in the simplified case

¸ 1 > 0 & 2¸ 1 + ¸ 2 > 0

M F = M P 3 = MN 3 = M E 3

λ1vR MF

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Vacuum stability: examples

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Vacuum stability: parameter scan

Colliderconstraint

ATLAS-CONF-2013-051

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Vacuum stability: if λ2<0…

¸ (vR ) = ¸ 1(vR ) 1 ¡¸ 22(vR )

4¸ 21(vR )

Colliderconstraint

Colliderconstraint

ATLAS-CONF-2013-051

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Constraints on heavy Higgs (H) mass

• Heavy Higgs mass is determined by the RH scale and λ1

• The matching condition of λ1 says that λ1 > λ,• The parameter scan shows that when λ1 is large enough it

would enter the non-perturbative region at high energy scales,

M 2H = 2¸ 1v

2R

[p2 £ 0:1;

p2£ 0:25]vR ' [0:4; 0:7]vR

NOT consider constraint on the heavy vector-like fermions

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Constraints on the fermion masses

• Large Yukawa couplings would worsen the stability problem.

• One important implication is that the partners of bottom and tauon is below the RH scale.

• The large top Yukawa coupling contribute significantly to the top partner mass.

Upper bounds

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SM Higgs in the extended model

• Higgs Production: The top partner loop is suppressed by the scalar mixing or the LH fermion top mixing angle,The top quark loop dominates…

• Higgs decayBelow the RH scale, all the beyond SM particles are integrated out, and we recover the SM as an effective theory

¡ L =1p2¹tL Yt hL TR +

1p2¹TL Yt hR tR + h:c:

¡ L '1p2¹bL YbhB R +

1p2¹B L YbH bR + h:c:

)1p2sin®bR ¹b

mL Ybhb

mR + h:c: sin®bR '

1p2YbvR =M F

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Heavy Higgs production at LHC14

• Top loop gluon fusion channel is suppressed by the scalar mixing or LH top mixing angle,

• Dominate channel: gluon fusion via top partner loop¡ L =

1p2¹tL Yt hL TR +

1p2¹TL Yt hR tR + h:c:

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Heavy Higgs decay

• Dominate decay channels

• Theses 2nd-4th channels are suppressed, respectively, by

• The diphoton channel is dominated by the WR, t and T loops,generally of order 10-5, not practically observable

¡ (H ! hh) =1

8¼

m2H hh

M H1 ¡

4m2h

M 2H

1=2

¡ (H ! t¹t) =3

16¼¢y2H t ¹tM H 1 ¡

4m2t

M 2H

3=2

¡ (H ! WW ) =1

8¼

m2H W W

M H1 ¡

4m2W

M 2H

1=2

1+1

21 ¡

M 2H

2m2W

2

¡ (H ! ZZ ) =1

16¼

m2H Z Z

M H1 ¡

4m2Z

M 2H

1=2

1+1

21 ¡

M 2H

2m2Z

2

" or ®tL ; " ; with " =¸ 22¸ 1

vLvR

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Quartering rule in the massive limit

• In the massive limit vR→, the fermion channel is suppressed by the LR scale ratio, and the other three channels,

• This originate from the coupling of H to the four component of χL in the potential.

¡ (H ! hh) =1

8¼

¸ 224p2¸ 1

vR ;

¡ (H ! WW ) =1

8¼

¸ 222p2¸ 1

vR ;

¡ (H ! ZZ ) =1

8¼

¸ 224p2¸ 1

vR :

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Quartering rule in the massive limit

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What if MH>2MF?...

• In a large parameter space, the di-top-partner channel is not allowed

• The bottom and tau partner channels are suppressed by the small scalar mixing and light-heavy fermion mixing anglesgenerally of order 10-3

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Neutrinos in SLRM without

• Dirac neutrino masses generated at 2-loop level (Babu & X-G He, 1989)

N

mº a 'g42

(16¼2)2mtmbm`a

M 2W R

I (M P 3 ; M N 3 ; M W R )

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Neutrinos in SLRM with

• With only Dirac masses for the neutrino partners:Ultrahigh energy scale of MN or ultra-small Yukawa couplings

• With both Dirac and Majorana masses of MN, in the basis of

• The neutrino masses read, when MN ≤ ML,R

N

0 0 0 1p2Y vL

0 M L1p2Y T vR M N

0 1p2Y vR 0 0

1p2Y T vL M N 0 M R

(º; N ; º C ; N C )

M º ' ¡1

2v2L Y M R ¡ M T

N M¡ 1L M N

¡ 1Y T

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Conclusion

• Vacuum stabilized in the left-right universal seesaw model• Simple Higgs sector: only one heavy neutral Higgs H,• Higgs H mass is constrained below the RH scale,

• The phenomenology of H could be tested at LHC14, with the characteristic quartering decay rule,

• The vector-like heavy fermions are at or below the RH scale, and are accessible at LHC.

0:4vR < MH < 0:7vR

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Open questions

• Neutrino physics in SLRM?

• SLRM Higgs inflation?

• CP violation and baryogenesis in SLRM?

Thank you very much!!!

Backup slides

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Strong CP problem

• Strong CP parameter

• With parity soft broken, θ=0,• Then the strong CP violation can be generated at 2-loop level

(Babu & Mohapatra, 1990)

¹µ= µ+argdet(MuMd)

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Vacuum stability: parameter scan

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Vacuum stability: parameter scan

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Collider constraint on MFATLAS-CONF-2013-051

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SM Higgs coupling

• Triple Higgs coupling¸ 1 vL h

3L + vR h

3R +

1

2¸ 2 vL hL h

2R + vR h

2L hR

) ¸ 1vL h3 1 ¡

¸ 22¸ 1

2

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Couplings in H decay

• Couplings beyond SM in the H decay widths

With ε and α, respectively, the scalar mixing angle and Light-Heavy fermion mixing angle

mH hh =1

2" 6¸ 1 + "2 ¡ 2 ¸ 2 vL +

1

26"2¸ 1 + 1 ¡ 2"2 ¸ 2 vR

'1

2¸ 2vR ;

yH t ¹t = Yt (" sin®tR + sin®tL cos®

tR ) ;

mH W W = 2"M 2W =v ;

mH Z Z = 2"M 2Z =v :