Transcript Probing Flavor Structure in Supersymmetric Theories

Phenomenological Aspects of SUSY
B-L Extension of the SM
Shaaban Khalil
Centre for Theoretical Physics
British University in Egypt
1
Outline

TeV scale B-L: Minimal bottom-up extension of the SM

B-L signatures at LHC

Supersymmetric B-L

B-L Right-handed (s)neutrino

(s)neutrino correction to lightest Higgs

Right-sneutrino Dark Matter

Conclusions
2
Introduction
The SM, based on the gauge symmetry SU(3)C x SU(2)L x U(1)Y, is in excellent
agreement with experimental results.
Three firm observational evidences of new physics beyond the Standard Model :
1.
Neutrino Masses.
2.
Dark Matter.
3.
Baryon Asymmetry.
These three problems may be solved by introducing right-handed neutrinos.
The tremendous success of gauge symmetry in describing the SM indicates
that any extension of the SM should be through an extension of its gauge
symmetry.
3
TeV Scale B-L
S.K. (2006)
The minimal extension is based on the gauge group:
GB-L ≡ SU(3)C x SU(2)L x U(1)Y x U(1)B-L
This model can account for the light neutrino masses.
New particles are predicted:
− Three SM singlet fermions (right-handed neutrinos) (cancellation of gauge
anomalies).
− Extra gauge boson corresponding to B−L gauge symmetry.
− Extra SM singlet scalar (heavy Higgs).
These new particles have Interesting signatures at the LHC.
4
ZB-L Discovery at LHC

The interactions of the Z′ boson with the SM fermions are described by



Y
g
Z
'
f

 BL  f
f

Branching ratios:
Yl 2 g 2
( Z   l l ) 
M Z
24
Yq2 g 2

( Z   bb , cc , ss ) 
M Z  (1  s )
8

Yq2 g 2
mt2
4mt2 1/ 2
s
 s mt2
(Z   tt ) 
M Z  (1  2 )(1  2 ) [1 
 O( 2 ))]
8
M Z
M Z

M Z
 

Branching ratios of Z’ → l+l- are relatively high compared to Z’ → qq:
BR(Z   l l  )  30%, BR( Z   qq )  10%
Search for Z’ at LHC via dilepton channels are accessible at LHC.
5
ZB-L Discovery at LHC (Cont.)
 In case of g’’ ~ O(0.1) then MZB-L ~ O(600) GeV.
 In LHC, the neutral gauge boson ZB-L can be produced
through:
qq  Z B L
 The SM background for this production consists
mostly of the Drell-Yan process:
qq   / Z 0  e e
 Therefore, one expects a clear peak at MZB-L
boson in the Me+e- distribution.
 ZB −L boson can be discovered in the e+e− decay
channel in the mass region 800<MZ < 1000 GeV with an
integrated luminosity of 10 fb−1.
Emam, Mine (2008) & Moratti et al. (2009)
6
Signatures for
R
at the LHC
S.K., Huitu, Okada, Rai (2008)
The lightest heavy neutrinos can be (pair)
produced at LHC via Z’B-L exchange.
The main decay channel of
two W bosons.
R
pairs is through
Possible clean signals, which would enable
reconstruction of both the R and Z’B-L
masses, are those involving:
(i) Two pairs of charged leptons and missing
transverse energy.
(ii) Three charged leptons, two jets and
missing transverse energy.
Integrated luminosity ~ 300 fb-1 gives 71 events
for the right handed neutrino mass of 200 GeV
while it gives 46 events for the right handed
neutrino mass of 400 GeV.
7
Higgs Sector



S.K., W. Emam (2007)
One complex SU(2)L doublet and one complex scalar singlet:

Six scalar degrees of freedom.

Four are eaten by C,Z0,W± after symmetry breaking.

Two physical degrees of freedom: φ, χ.
Mass matrix:
3vv / 2 
 1v 2
1 2


M ( ,  )  
2 
2
 3vv / 2 2 v 
Mass eigenstates:
 1   cos  sin    
   
 ,
 2   sin  cos   

Masses:

Mixing is controlled by 3:
3 vv
t an2 
1v 2  2v2
m12, 2  1v 2  2 v2  (1v 2  2 v2 ) 2  32 v 2 v2
3  0  m  1 v, m  2 v
8
Higgs Production

At the LHC, the dominant channel for Higgs boson
production is due to gluon-gluon fusion.

The cross section of this process is proportional to the
Higgs boson couplings to the heavy quark mass.

In B-L, the production cross section for the light Higgs
state is reduced respect to the SM one by a factor ~
cos2.

Heavy Higgs production is suppressed by two effects: a
small ~ sin2 and a large mH’ (compared to mH).
9
 Both Higgs particles tend to decay into the heaviest gauge bosons and fermions
allowed by the phase space.
 Branching Ratios of Light Higgs are very close to those of SM: Couplings are
cancelled in the ratio.
 In addition to SM-like decay channels, either or both Higgs bosons can decay in
genuine B-L final states, like R and/or Z’B-L pairs, with sizable rates.
This opens up then the intriguing possibility of all the new states predicted by the
B-L model being simultaneously detected at the LHC.
10
Neutrino Masses and Mixing
lL
eR
SU(2)Lx U(1)Y
(2,-1/2)
(1,-1)
(1,0)
(2,-1/2)
(1,0)
U(1)B-L
-1
-1
-1
0
2
A type I seesaw can be obtained from:
R
1
~
LB  L   l  R   R v cR  R  h.c.
2
Majorana mass: After B-L symmetry breaking
MR  R v v ~ O(TeV), R ~ O(1)  MR  O(TeV)
Dirac mass: After Electroweak symmetry breaking
Thus:
 0 mD 
 

 mD M R 
mD   v
mD  O(104 )GeV   ~ e
11
TeV Scale B-L with Inverse Seesaw Mechanism
S.K. (2010)

Type-I seesaw mechanism implies  ~ 10-6 , which may be unnatural small.

A new modification for TeV scale B-L model, based on the inverse seesaw
mechanism, has been recently proposed.

If U(1)B-L is spontaneously broken by a SM singlet scalar  with B-L charge
=+1.
SM singlet fermions S1 with B-L =+2 and S2 with B-L =-2 are introduced, an
inverse seesaw mechanism may be implemented.
 The Lagrangian of the leptonic sector in this model is given by

12

After B-L and EW symmetry breaking, the neutrino Yukawa interaction terms
lead to the following mass terms:

Lepton number is broken but a remnant symmetry: (-1)L+S is survived.

After (-1)L+S is broken at much lower scale, a mass term for S2 is generated.
The 9x9 neutrino mass matrix takes the form:
Diagonalization
Light neutrino mass ~ eV is obtained for a TeV scale MN, if S << MN. No
restriction imposed on the mD.
13
B-L Symmetry Breaking Scale
The scale of B- L symmetry breaking is unknown, ranging from TeV to much
higher scales (GUT or Planck NP).
In MSSM, the electroweak and SUSY breaking scale are nicely correlated through
the mechanism of radiative breaking of the EW symmetry.
Radiative corrections may drive the squared Higgs mass from positive initial
values at the GUT scale to negative values at the EW scale.
The size of the Higgs VEV responsible for the EW breaking is determined by the
size of the top Yukawa coupling and of the soft SUSY breaking terms.
Analogously, in a SUSY B-L, it is possible to radiatively induce the breaking of B−L
having the scale of such breaking directly linked to the soft SUSY breaking scale.
14
SUSY and B-L Radiative Symmetry Breaking
S.K., A. Masiero, 2007
The minimal SUSY version of B-L model has the following superpotential:
The RGE of relevant scalar masses are:
From MX to MW, m21 and m22 are renormalized
differently.
At O(1) TeV, m21 becomes negative, the
minimization condition is satisfied & B-L gauge
symmetry is broken.
15
SUSY B-L with Inverse Seesaw
 In this mode, B-L is spontaneously broken by chiral singlet superfields 1 with
a charge = +1 and 2 with −1.
 Also three chiral singlet superfields S1 with charge +2 and three chiral singlet
superfields S2 with charge −2 are considered to implement the inverse seesaw
mechanism.
 The superpotential of the leptonic sector of this model is
 The relevant soft SUSY breaking terms, assuming the usual universality
assumptions, are

The sneutrino mass matrix of one generation is 8x8 matrix, decomposed into 6x6
~ ~  ~ ~  T and 2x 2 mass matrix of the
mass matrix in the basis of (~L ,~L  , N
, N , S2 , S2 )
~ ~ T
basis: (S1, S1 ) .
16
B-L Right-Handed Sneutrino
 The sneutrino mass matrix is obtained from the scalar potential that contains
sneutrino fields:
where
 The sneutrino mass matrix can be written as a 3x3 matrix, with entries
multiplied by the identity 2x2 matrix

If (12) and (23) elements vanish, the sneutrino masses are:
17
(s)Neutrino Correction to Lightest Higgs

In MSSM, the mass of the lightest Higgs at one loop is given by
 For stop mass of order TeV, this correction implies that
This upper limit on the lightest Higgs boson mass barely consistent with
experimental data.
 The genuine B−L corrections to the lightest SM-like Higgs boson mass
can be obtained from one-loop radiative corrections, due to the righthanded neutrinos and sneutrinos,
Elsayed, S.K. Moretti, 2011
18

The one-loop correction in the effective potential is given by the relation:
where the supertrace is defined as follow:

ΔV, due to one generation of neutrinos and sneutrinos, is given by:

Substituting and differentiating gives
with
19

for MN ϵ[0.4, 2.5] TeV, Yν ϵ[0.1, √(4π)], and cos2θ = 0, lightest Higgs boson
massas function of the lightest sneutrino mass is given as follow:

B-L (s)neutrino corrections lead to an absolute upper limit on it at around 180 GeV.

If the effect of three generations is considered the upper bound reaches 200 GeV.
20
Sneutrino Dark Matter in SUSY B-L
S.K., Okada, Toma, 2011
 In the MSSM, the lightest neutralino is an attractive candidate for cold DM.
 The current experimental constraints: LHC limits, WMAP results and CDMS,
impose stringent limits on the lightest neutralino even if it consists of
gaugino-Higgsino mixture.

In SUSY B-L, the lightest sneutrino is given by (large tan β and small tan θ limits):
 The relevant interactions of the B−L right-handed sneutrino are:
21
Possible annihilation channels of sneutrino. 2nd diagram gives a sub-dominant
contribution, however it may be relevant for indirect detection processes.
The thermal average annihilation cross section is given
with
22
The sneutrino relic abundance is given by
23
Sneutrino Direct Detection
The general form of the elastic scattering
cross section between DM sneutrino &
nuclei N is given by
Where
Here M is the the nuclei mass, A and Z are the mass number and the atomic
number. The effective Lagrangian parameters bu and bd are defined as
24
 The sneutrino effective interaction is
 Thus, the elastic scattering cross section of
B−L right-handed sneutrino is given by
 The following upper bound on elastic
cross section is obtained:

The elastic cross section is quite insensitive to the B−L sneutrino mass.

The limits from CDMS II and XENON experiments indicate to a lower-bound of
order 3.7×10−44 cm2. Thus, our B−L sneutrino DM can be detected in near
future.
25
Sneutrino Indirect Detection
 B−L sneutrino annihilates into ℓ+ℓ- channels,

However, these channels give sub-dominate
contribution to the annihilation process.
 Therefore, the corresponding annihilation
cross section is < 10−27 cm3s−1.

A huge, unexplained, boost factor must be introduced in order to account for
Pamela results.

As a result, it is difficult for our B−L sneutrino to explain the controversial results
of PAMELA experiment.
26
Summary

The SM gauge group can be minimally extended by adding U(1)B−L

B-L extension contains (at least) three right handed neutrinos, extra gauge
boson, and extra scalar Higgs. Promising signatures at LHC.

SUSY B-L is just as exciting:

It incorporates well known benefits of SUSY models (gauge coupling
unification, solution to the hierarchy problem).

It alleviates well known flaws of more minimal SUSY realizations (such an
upper limit on the lightest Higgs boson mass barely consistent with
experimental data).

The right-handed sneutrino in the SUSY B-L model with inverse seesaw
mechanism is also a viable candidate for cold DM.

Like its SM counterpart, right-handed sneutrino can be a long-lived particle and
be pair produced at the LHC through ZB-L. Then, it decays into same-sign dileptons, with a total cross section of order O(1) pb.

This signal is a striking sparticle signature of the SUSY B-L gauged model.
27
Thank you
28