Gauged B-L Leptogenesis Shaaban Khalil Center for Fundamental - - PowerPoint PPT Presentation

Gauged B-L Leptogenesis

Center for Fundamental Physics Zewail City of Science and Technology

Shaaban Khalil

• The recent observations indicate that the asymmetry between number density of

baryon (!") and of anti-baryon (!#

") of the universe is given

• In the SM, the baryon asymmetry is $" ≈ &'()* , which is too small to account for

the observed baryon asymmetry.

• Leptogenesis through the decay of a heavy singlet neutrino is considered as the best

scenario for understanding the observed baryon asymmetry of the Universe.

• In this mechanism, the lepton asymmetry YL can be converted to baryon asymmetry

YB via the electroweak sphaleron according to this relation $" = , , − & $. / =

* 01 23 04 )) 01 2&5 04 , and 01 is the number of fermions and 04 is the number of Higgses.

Introduction

• The lepton asymmetry is given by
• Lepton asymmetry arises due to interference between tree & loop contributions
• Thus
• Therefore, the necessary condition for leptogenesis is
• Due to the unitarity of UMNS, leptogenesis does not depend on low energy phase

appears in the leptonic mixing matrix. If the matrices R and MR are real the !1 =0.

• Finally, the baryon asymmetry is given by

!" =

$ $%& !'= $ $%& ( )& *∗ ≈ &-%.( )&

The coffecient ( parametrize the wash out effect due to the inverse decay and the scattering processes. It depends on the ratio / = 0

12&/4; (( ~1/K).

• For 612& ~ &-&- 789 ⇒ ( ~; & and !" ≈ &-%. )&
• For 612& ≪ 612., 612> ;(&-&>)
• Thus, the required baryon asymmetry can be obtained.
• In this case, the energy scale involved in a successful application is in the range

109 to 1013 GeV, which renders the idea impossible to verify experimentally

TeV scale Leptogenesis

• We now consider TeV scale Seesaw mechanism. In this case, after the TeV scale

symmetry (e.g., B−L) breaking, the neutrino mass matrix is given by

• With mD = Yν v2, MN = YNv1ʹ. The neutrino masses are
• Therefore, if MN ∼ O(1) TeV, the light neutrinos νℓ mass can be of order one eV if the

Yukawa coupling Yν ~ 10−6.

• This small coupling is of order the electron Yukawa coupling, so it is not quite

unnatural.

• In TeV scale type I seesaw, !"~ $ %&'(

and )*~ $ +,- , the lepton asymmetry can be written as

• Thus, for /) = )1 − )%~ $(%&'4), the required baryon asymmetry can be
• btained.
• Based on this fine tuning, a “Resonant Leptogenesis” is defined.

Inverse Seesaw Mechanism

• In this class of models, the SM is extended with three right-handed neutrinos, !"

# and

three singlet fermions $#.

• The Lagrangian of neutrino masses, in the flavor basis, is given by:

ℒ = (() ̅ +,-. + 01 2

• .

34 + h. c. ) + 9: ̅

434

Leptogenesis with Inverse Seesaw

Gauged B − L Leptogenesis

• In supersymmetry, the addition of the singlet superfield !

"# with B − L = 1 implies a fermion "# and a scalar $ "#.

• After the B−L symmetry breaking by the VEVs < &',) > = ,',), a bilinear

coupling -./

) $

".

0 $

"/

0 is obtained and it is given by

• 1

) = −,3' 4" 5 + 4",3'7′∗

• Here, we assume that -1

)= 0 so that the off-diagonal elements of sneutrino $

"# mass matrix, in the ($ ".

0, $

".

0∗) basis, vanish.

• Therefore, $

"#, $ "#∗ are mass eigenstates with mass squared <1

∗ <1 = + >

?1

) + ' @ <A3 ) BCD2F

• They have lepton numbers G = ∓I respectively. Moreover, if cos 2θ is negative,

$ "# can be lighter than "#.

• This is the crucial assumption of our proposal.

• The Lagrangian, in flavor eigenstates, relevant for our analysis is given by
• The Lagrangian in mass eigenstate is given by

Where

• The four-component Majorana spinors are defined as
• Now, we consider leptogenesis by !" → $%&

!'

( , assuming the mass hierarchy

)!" ≪ )!+,-. We assume that only the lightest B − L neutralino $ ≡ $" and sneutrino of the third generation & !-

( are lighter than !" , and satisfy the relation

./

0 + )& !-

2 < )!"

• Due to the fact that 4! = 6, &

!-

( carries lepton number, the decay:

!" → $ & !-

( violates lepton number.

• CP asymmetry of !" → $ %

!&

' decay

processes is generated by the interference between tree and one- loop level diagrams of vertex and self-energy correction

• CP asymmetry of !" → $ %

!&

' decay processes is generated by the interference

between tree and one-loop level diagrams of vertex and self-energy correction

• It is defined as
• The decay rate ( at one-loop level is given by

Where the phase space integral of two-body decay )* is given by

• We found that the CP asymmetry !" → $ %

!&

' decay has the structure:

where we assumed diagonal right-handed mass matrix. One finds (

"&~*+, - ≪ ", as

required by out-of equilibrium condition: ((!" → $ % !&

')< 0(2 = "), for 2 = 5!" 6 .

Also(

&&~789 :~", which leads to a large CP asymmetry. This situation is realized if the

mixing matrix ( is almost diagonal.

• In our model, baryon asymmetry is obtained through the following procedure:
• 1. !" → $ %

!&

' decay generates %

!&

' asymmetry ;∆% ! .

• 2. %

!&

' decays into (s)lepton by Dirac Yukawa couplings, soft SUSY breaking A-term

and =-term, and resulting (s)lepton asymmetry ;∆>(∆?

@) is obtained by solving

the Boltzmann equations.

• 3. Sphaleron converts total lepton asymmetry ;> = ;∆> + ;∆?

@ to baryon

asymmetry ;A.

Boltzmann Equations

• The Boltzmann equation describing the evolution of !" is

!" is the number of particle in a comoving volume element, which is given by the ratio of #" and the entropy density s.

Enough baryon asymmetry is obtained.

Conclusion

• We have shown that a successful TeV scale leptogenesis can take place in

gauged B − L supersymmetric model.

• In this model, if the right-sneutrino bilinear term is absent, then the lightest

sneutrino is assigned a lepton number. Therefore if ! "#

$ is lighter than "% and

scalar mass matrix of ! "& is almost diagonal, a large lepton asymmetry can be generated by B−L neutralino interactions of O (1) couplings '()* and/or +" through the one-loop exchange of "#

$ for the decay "% → - !

"#

$ .

• This asymmetry of !

"#

$ is transmitted into asymmetry of lepton and slepton

through the Yukawa coupling, trilinear coupling, and μ-term, and sphaleron converts lepton asymmetry to baryon asymmetry.