K.S. Babu Oklahoma State University
Santa Fe 2014 Summer Workshop “LHC After the Higgs” June 30 – July 4, 2014 1 Outline
Why Left-Right Supersymmetry? Higgs Boson spectrum in Supersymmetric Left-Right models . Models with Higgs triplets + bidoublets . Models with Higgs doublets + bidoublets: Inverse seesaw models . Models with Higgs doublets: Universal seesaw models
. E6 motivated Left-Right models Emergence of a Light Doubly Charged Higgs boson and associated phenomenology Conclusions
Based on: K.S. Babu and Ayon Patra, 2014 (to appear); K.S. Babu, Ayon Patra, Santsh Kumar Rai, Phys. Rev. D88, 055006 (2013). 2 Highlights
. Lightest neutral Higgs boson mass can easily be 125 GeV with low tan β ~ 1 , with light stops of mass below 1 TeV and negligible stop mixing. This results in reduced fine- tuning.
. Non-decoupling SU(2)R D-term makes this possible (within MSSM, tan β > 5 and stop mass > 1 TeV is needed). . A light doubly charged Higgs boson is predicted in models with Higgs triplets, which acquires its mass entirely from radiative corrections. . Several variants supersymmetrized for the first time.
3 Why Left-Right Supersymmetry?
Addresses some important open questions of the Standard Model: . Understanding the origin of parity violation. . Natural setting for small neutrino mass via seesaw mechanism. . Provides a simple solution to the Strong CP Problem. . SUSY stabilizes the Higgs boson mass. . Natural dark matter candidate without assuming R-parity. . Solves the SUSY CP problem.
J. C. Pati and A. Salam, Phys. Rev. D (1973) ; R. N. Mohapatra and J. C. Pati, Phys. Rev. D (1975) ; G. Senjanovic and R. N. Mohapatra, Phys. Rev. D (1975). 4 How Left-Right Symmetry solves the Strong CP Problem & SUSY CP Problem
Strong interaction sector admits a term that violates both CP and P: g 2 L GGaa QCD 32 2 Leads to the physical observable
Arg(Det Mq ) Mq quark mass matrix Neutron electric dipole moment limits imply 10 10 .
With left-right symmetry, θ = 0 due to Parity; Mq is Hermitian also due to Parity, and thus 0 at tree level. Induced is small and consistent. Parity symmetry also makes the new SUSY phases zero, thus solving the SUSY CP problem. R.N. Mohaptra and A. Rasin, Phys. Rev. Lett. 76, 3490 (1996); R. Kuchimanchi, Phys. Rev. Lett. 76, 3486 (1996); 5 K.S. Babu, B. Dutta, R.N. Mohapatra, Phys. Rev. D60, 095004 (1999); K.S. Babu, B. Dutta, R.N. Mohapatra, Phys. Rev. D65, 016005 (2002). Higgs Boson masses in Supersymmetric Left-Right models
Supersymmetric versions of left-right symmetry has the
gauge group extended to SU (3) CLRBL SU (2) SU (2) U (1) . BL Electric charge defined as QII 33 LR . 2
The SU (2) RBL U (1) symmetry is broken spontaneously to
U(1)Y at a high scale. Here we consider several variations with different symmetry breaking sectors. Either Higgs triplets or Higgs doublets are used for the high scale symmetry breaking. Higgs boson spectrum is calculated in each case.
6 Fermion Content of Left-Right Models
The common Quark and Lepton sectors of all models are:
c u d Q (3,2,1,1/3) = ; Qc (3*,1,2,-1/3) = d uc
c e e L (1,2,1,-1) = ; Lc (1,1,2,1) = c e e
The Right-handed quarks and leptons are doublets of SU(2)R.
Presence of Right-handed neutrino required by gauge structure.
Each model has to explain
. Consistent symmetry breaking mechanism.
. Quarks and Lepton masses and CKM mixing.
7 . Small neutrino mass generation. Models with Higgs triplets + bidoublets Most straightforward way to break symmetry and generate large mass for right-handed neutrinos.
Under SU(3)CLRBL SU (2) SU (2) U (1)
c c c0 c 2 2 c (1,1,3, 2) c (1,1,3,2) c c c c0 2 2
0 2 2 (1,3,1,2) (1,3,1, 2) 0 2 2 0 (1,2,2,0) 12 a 0 a 1,2 S (1,1,1,0) 12a
R. Kuchimanchi, R. N. Mohapatra, Phys. Rev. D48, 4352 (1993) . C.S. Aulakh, K. Benakli, G. Senjanovic, Phys. Rev. Lett. 79, 2188 (1997); C.S. Aulakh, A. Melfo, G. Senjanovic, Phys. Rev. D57, 4174 (1998). 8 • The SU(2)R Higgs boson triplets ( ) are needed to break
SU (2) RBLY U (1) U (1) without inducing R-Parity violating couplings.
• The SU(2)L Higgs boson triplets ( ) are their parity partners.
• The two bi-doublet Higgs fields a generate the quark and lepton masses and the CKM mixings. • The optional singlet field S makes sure that the right-handed symmetry breaking may occurs in the supersymmetric limit.
• The non-zero vacuum expectation values of the fields are
0 ccv, 0 v , 0 v , 0 v R R12a u a a d a where
vR,, v R v u v d
Previous Higgs boson mass analysis: Zhang, An, Ji, Mohapatra (2008) 9 The Yukawa couplings terms in the superpotential are T c T c T c T c WYQQYQQYLLYLLu212 d 222 212 l 222 * T cT c c i ( f L22 L fL L )
• is heavy and generates small neutrino mass.
The Higgs boson only superpotential is
WSM Tr(* c c ) ' Tr( T ) 2 Higgs ab a22 b R c c T S 2 Tr1 2 Tr( ab 2 2 ) S 22
The Superpotential in invariant under parity transformation. Yukawa coupling matrices are hermitian. * , , S and are real and 12 . If the bi-doublet VEVs are real, it can solve the Strong CP and SUSY CP problem.
10
Higgs Potential VVVVHiggs F D Soft
11 Re1 , Re 2 , Re 3 , Re 4 , Re S
12 Procedure adopted to derive light Higgs mass
• Choose such that M13 , M15 and M35 vanish. This would maximize the lightest Higgs boson mass.
• Lightest neutral scalar tree-level Higgs mass is found to be
, ( MM 2 2 cos 2 2 ) hZMSSM
• Using radiative corrections from top quark and stop squark
where
,
,
mt is top running mass, is the stop mixing, MS is squark mass geometric mean and .
13 Higgs triplets and a singlet
Maximum Higgs mass vs tan β Maximum Higgs mass vs stop mass
. Green shaded region: Xt = 0, Blue shaded region: Xt = 6, Red shaded region: all possible values of parameters.
. Solid red region is for mh between 124 GeV and 126 GeV.
. Solid black line: MSSM result with Xt = 6 and MS = 1.5 TeV (or tanβ = 40). . Plot on the right panel shows that even for a relatively low stop mass
and for small stop mixing the correct Higgs mass is produced. 14 Pseudoscalar Higgs boson mass spectrum
Removing the two Goldstone states, elements of the 33 matrix in a certain basis is
Left-handed triplet Higgs fields decouple and give a complex mass-squared matrix
15 Charged Higgs boson mass spectrum
Removing the two charged Goldstone states, elements of the 22 matrix is
Left-handed charged triplet Higgs fields decouple and has a mass-squared matrix
16 Light doubly charged scalar
• Unlike the charged scalar, which is eaten up by W R , one combination of doubly charged scalars from c and c remains massless at tree level . • This is due to the extra global symmetry of the model. • The charge breaking vacuum turns out to be lower than the desired charge conserving vacuum.1 • Possible solutions with unbroken R Parity: o Planck scale corrections – Would require the right-handed symmetry breaking scale to be of order 1011 GeV.2 o Add new particles, eg: (1,1,3,0).3 o Stay minimal, but rely on radiative corrections to the Higgs mass.4,5
1R. Kuchimanchi, R. N. Mohapatra, Phys. Rev. D48, 4352 (1993) . 2,3C.S. Aulakh, K. Benakli, G. Senjanovic, Phys. Rev. Lett. 79, 2188 (1997); C.S. Aulakh, A. Melfo, G. Senjanovic, Phys. Rev. D57, 4174 (1998). 3 Z. Chacko, R. N. Mohapatra, Phys. Rev. D58, 015003 (1998). 4 K.S. Babu, R. N. Mohapatra, Phys. Lett. B668, 404 (2008). 17 5 K.S. Babu, A. Patra, to appear (2014). Doubly charged Higgs mass from radiative corrections
We have computed the full Majorana Yukawa contribution to the doubly charged Higgs mass.
The Higgs potential studied is a simplified version where electroweak VEVs are ignored.
18 • The charge-conserving VEV structure for the right-handed triplet Higgs boson is 0v c 00 c R v0 00 R
while we can consider a charge-breaking vacuum given by
1 0v 1 0v c R c R v0 2 v0R 2 R • The SU(2) D-term vanishes for the charge-breaking vacuum. R • Charge-conserving vacuum has a positive D-term. • The charge-breaking vacuum has a lower minima than the charge- conserving. • The charge conserving vacuum leads to a massless (or negative squared mass) doubly charged scalar boson.
19 R. Kuchimanchi and R. N. Mohapatra, Phys. Rev. D (1993) Right-handed doubly-charged Higgs boson mass-squared matrix (tree- level) is
where
Eigenvalues of the matrix
One of the eigenvalues is negative. Becomes zero if gauge couplings vanish. However, radiative corrections can make the squared mass positive.
K. S. Babu and R. N. Mohapatra, Phys. Lett. B (2008) 20 The problem solves itself through the one-loop Majorana Yukawa corrections, which break the accidental global symmetry of the tree- level Higgs potential. • Corrections to pseudo-goldstone bosons must remain finite, which is a nontrivial check of the calculation. • We neglect gauge couplings and calculate correction from Yukawa sector. • This pseudo-Goldstone state is identified as
• The neutral Higgs boson couplings are written as
where XVˆ Mass eigenstate, Unitary diagonalizing matrix
21 Feynman diagrams and corresponding contributions
c
h0
S. Weinberg (1973) 22 ec
Adding all these contributions
• Quadratic divergences cancelled.
• Log divergences cancelled.
23 Final expression for one-loop correction to the mass of the right-handed doubly-charged Higgs boson:
2 222 11 mmcc f vR v S A f v R 2 2 2 2 ee M f v m c ln ln 1 2 2 2R e 2 22 2 16 v v Mcc2 vv M RR RR 2 f m c 221 vR v S 2 f v R A f v R m c ln 2 4 1 M c 2 f m c 22 2 vR v S 2 f v R A f v R m c ln 2 2 4 M c All the one-loop terms in the mass-square eigenvalues are of order 22 M SUSY /16 . If right-handed gauge symmetry breaks at a high scale, the squared mass is negative. However, for vR of order SUSY breaking scale, the mass squared is positive. If SUSY is broken at the TeV scale, the doubly-charged Higgs boson mass has to be of electroweak symmetry breaking order ( ). 24 Back to Light Neutral Higgs: Special Cases
1. Case without a Singlet Higgs S
• Higgs superpotential is: c c T WHiggs 1Tr 2 Tr Tr( 2 2 ) 2 • Higgs mass is MM22cos 2 . hZ 12 • Same as in MSSM.
2. Case with the Singlet Higgs S integrated out . The Higgs superpotential is c c T c c 2 WHiggs 1Tr 2 Tr Tr( 2 2 ) Tr 2 . The lightest Higgs boson mass is 22 MMhW2 cos 2 12 .
25 Higgs triplets and a heavy singlet
Maximum Higgs mass vs tan β Maximum Higgs mass vs stop mass
. Green shaded region: Xt = 0, Blue shaded region: Xt = 6, Red shaded region: all possible values of parameters.
. Solid red region is for mh between 124 GeV and 126 GeV.
. Solid black line: MSSM result with Xt = 6 and MS = 1.5 TeV (or tanβ = 40). . Plot on the right panel shows that even for a relatively low stop mass and for small stop mixing the correct Higgs mass is produced. 26 Symmetry breaking with Higgs doublets: Inverse Seesaw Models Higgs sector is simple with doublets, and no triplets. 0 H L H L H R H L (1,2,1, 1) , H L (1,2,1,1) , H R (1,1,2,1) , H H 0 H 0 L L R
H 0 0 H (1,1,2, 1)R , 12 R a (1,2,2,0) , (a 1,2) H 0 R 12a
• HH RR and breaks the right-handed symmetry.
• Allows right-handed symmetry breaking scale naturally of order TeV.
• a generates the quark and lepton masses and CKM mixing.
• Need extra singlet heavy neutrino N to generate small neutrino mass.
R. N. Mohapatra, J.W.F. Valle, Phys. Rev. D34, 1642 (1986). 27 . The non-zero vacuum expectation values of Higgs fields
H0 v, H 0 v , H 0 v , H 0 v , 0 v , 0 v RRRRLLLL 1a 1 a 2 a 2 a
. Yukawa terms in the superpotential are 2 j T c j T c T WY Y q Q2 j 2 Q Y l L 2 j 2 L ifL 2 H L N j1
ccT N + if L 2 HL N NN . 2 . Neutrino mass matrix – Inverse seesaw:
S.M. Barr, Phys. Rev. Lett. 92, 101601 (2004).
. If v L 0 and N 0 , one of the eigenvalues of this matrix is zero.
28 • Consider the case with one bidoublet for simplicity. • The Higgs only superpotential is
TTT WHiggs i1 H L 2 H L i 1 H R 2 H R H L 2 2 H R
+HHTT Tr LR2 2 2 2 • Calculate the Higgs potential and the minimization conditions. • Change the basis so that only one field gets EW VEV. • Compute the neutral scalar Higgs boson mass-squared matrix. • Mass of the lightest neutral Higgs boson
42 2 4MMWW 4 2 2 2 2 MhW2 M sin 22 cos sin 2 + v sin 2 12 22MMWZ
29 Higgs doublets: Inverse seesaw models
Maximum Higgs mass vs tan β Maximum Higgs mass vs stop mass
. Green shaded region: Xt = 0, Blue shaded region: Xt = 6, Red shaded region: all possible values of parameters.
. Solid red region is for mh between 124 GeV and 126 GeV.
. Solid black line: MSSM result with Xt = 6 and MS = 1.5 TeV (or tanβ = 40). . Plot on the right panel shows that even for a relatively low stop mass and for small stop mixing the correct Higgs mass is produced. 30 Universal Seesaw Models Higgs sector of the model is 0 H L H L H R H L (1,2,1, 1) , H L (1,2,1,1) , H R (1,1,2,1) , H H 0 H 0 L L R H 0 H (1,1,2, 1)R , S(1,1,1,0) R H R
• HH RR and breaks the right-handed symmetry. • No bidoublet to generate the quarks and lepton masses and mixings. • Need extra heavy quarks and leptons
42
PRE(3,1,1, 33 ), (3,1,1, ), (1,1,1,2)
c42 c c
PRE(3,1,1,33 ), (3,1,1, ), (1,1,1, 2)
A. Davidson, KC. Wali, Phys. Rev. Lett. 59, 393 (1987); 31 K.S. Babu and R.N. Mohapatra, Phys. Rev. Lett. 62, 1079 (1989). • An optional heavy singlet neutrino N .
• Yukawa coupling terms in the superpotential
WY Y u QH L P Y d QH L R Y l LH L E Y LH L N cc ccc ccc c cc + YQHPYQHRYLHEYLHNu R d R l R R c c c + mu PP m d RR m l EE m NN
• Mass of fermions are generated via the seesaw mechanism.
0 YvuL Mu c Y v m u R u • Neutrino mass can also be generated at the two-loop level from
WL and WR exchange.
32 • The Higgs only superpotential is TT2 WHiggs S i H L 22 H L i H R H R M .
• Mass of the lightest neutral scalar Higgs boson
4 MW 2 2 2 2 Mvh 22cos 2 + sin 2 12 2MMWZ
33 Higgs doublets: Universal seesaw
Maximum Higgs mass vs tan β Maximum Higgs mass vs stop mass
. Green shaded region: Xt = 0, Blue shaded region: Xt = 6, Red shaded region: all possible values of parameters.
. Solid red region is for mh between 124 GeV and 126 GeV.
. Solid black line: MSSM result with Xt = 6 and MS = 1.5 TeV (or tanβ = 40). . Plot on the right panel shows that even for a relatively low stop mass and for small stop mixing the correct Higgs mass is produced. 34 Universal seesaw model without singlet
• Higgs superpotential terms are
TT WHiggs i1 H L 2 H L i 1 H R 2 H R.
• Calculate the Higgs potential and the minimization conditions.
• Calculate the Higgs boson mass-squared matrix.
• Lightest neutral scalar Higgs boson mass
22 MMhZ cos 2 12 .
• Same result as in MSSM.
35 E6 motivated left-right SUSY model
• Low energy manifestation of superstring theory.
• Matter multiplets belong to 27 of E6 group. • Previously discussed by others but some parameters were zero, here we keep everything. • Particle spectrum given as
c1 c c 1 1 X(3,1,2, ) h u , Q(3,2,1, ) u d , hh(3,1,1, )L , 6 L 6 L 3
cc 1 1 cc1 L(1,1,2, ) e n , EE(1,2,1, ) E , dd(3,1,1, ) L , 2 L 2 L 3 Ec e NNcc(1,1,1,0) . F(1,2,2,0) c , L eN E L • Discrete R-parity symmetry under which c u, d , e ,e Even, ( h , E , n , N E , E ) Odd
K. S. Babu, X. G. He and E. Ma, Phys. Rev. D 36, 878 (1987). 36 • The Higgs fields are identified as
• The superpotential is W Qdc E QX c F hX c L c FL c E FN c F hd c N c 1 2 3 4 5 6 • The quark and lepton masses are generated from this superpotential. c • The neutrino mass matrix is a 33 matrix in basis (,,) EE Nn given as
37 • The Higgs only superpotential is TT WHHHiggs L 2 2 R Tr 2 2 . • The non-zero vacuum expectation values are given as
0 0 0 0 HRRLL v, H v , 1 v 1 , 2 v 2
• Calculate the Higgs potential and the minimization conditions. • Change basis so that only one field gets EW vev. • Compute the Higgs boson mass-squared matrix. • Mass of the lightest neutral Higgs boson
22 MMhW2 cos 2 12
38 Experimental search for doubly-charged Higgs boson at LHC
Direct pair-production of doubly-charged Higgs Boson
39 The mass limit on the right-handed doubly-charged Higgs boson from ATLAS experiment.
S. Chatrchyan et al. [CMS Collaboration], Eur. Phys. J. C 72, 2189 (2012); G. Aad et al. [ATLAS Collaboration], Eur.Phys. J. C 72, 2244 (2012). 40 New signals of doubly-charged particles at the LHC
Production and decay of the doubly -charged Higgsino.
The final state signal is 4 leptons and missing energy (a new channel for doubly-charged Higgs boson search at the LHC).
K. S. Babu, A. Patra, S. Rai, Phys.Rev. D88 (2013) 055006 41 Three cases we must consider
1.
2.
3.
We take two parameter space
• BP1 for which M 300 GeV , M ± ± = 5 0 0 G e V and M 0 80 GeV . d 1 R R
• BP2 for which , M ±± = 4 0 0 G e V and . dR
42 1000 Right-handed Higgs Boson Right-handed Higgsino Left-handed Higgsino
100
)
b
f
(
n 10
o
i
t
c
e
s
- s
s 1
o
r C
0.1
0.01 300 400 500 600 700 800 Mass (GeV) Direct production of the light doubly-charged Higgsinos and Higgs boson at LHC at 14 TeV.
43 1 Opposite sign Leptons Same sign Leptons The same-sign lepton plot peaks at a low value of while the opposite- sign leptons peak at a much higher
0.1 value. R
D
d
/
s d
Expected as the same-sign leptons
s / 1 come from the decay of one particle 0.01 while the opposite sign leptons come from much further apart.
0.001 Measurement at the LHC for a four 0 0.5 1 1.5 2 2.5 3 3.5 4 lepton final state can give definite DR indication of existence of doubly- plot for the same-sign charged particles if distribution is and opposite-sign final state similar to our analysis. leptons.
44 10 Opposite sign Leptons No events between 80 GeV and 100 GeV in Same sign Leptons the same-sign lepton plot because of the Z peak cut applied. 1
) V
e A clear peak in the same sign invariant
G
/
b
f (
mass while no such peak in the opposite
v 0.1
n i
M sign plot at a mass of 300 GeV.
d
/ s d 0.01 The Peak came due to the decay of the right-handed doubly-charged Higgs bosons into two same-sign leptons. 0.001 0 200 400 600 800 1000 Invariant Mass (GeV) Difficult to see in experiments without a priori knowledge of the Higgs boson mass. Invariant Mass plot for the same- sign and opposite-sign If seen, will be a definite signature of a final state leptons. doubly-charged particle.
45 Conclusions
The Left-Right Supersymmetric models solve many of the problems in the Standard Model.
Examineed various models with different symmetry breaking sectors. The tree-level neutral Higgs boson mass can be significantly increased.
Experimentally observed Higgs boson mass of 125 GeV can be easily achieved with low stop mass and mixing.
Models with triplets admit zero mass states of doubly-charged Higgs bosons which remains light after radiative corrections.
46 47 The kinematic cuts applied
• The final state lepton must have a rapidity cut . • between the final state leptons where and is the azimuthal angle. • Each lepton must have a transverse momentum . • Invariant mass cut between the opposite sign same flavor OS leptons such that M inv 10 GeV . • OS A further invariant mass cut of 80 GeV M inv 100 GeV to get rid of the Z-boson peak.
We study the MET, and the invariant mass of the final state leptons.
48