The effect of extra matter on unification of Yukawa

couplings in The MSSM

A.F.Kord Sabzevar Tarbiat Moallem University (Iran)

September 2011

Outline Supersymmetry The Minimal Supersymmetric Standard Model The scenario of semi-perturbative

unification(SPU) Results Conclusion

Supersymmetry It solves the hierarchy problem Define a tool to unify all forces of nature Produce all the matter that exists Give self-consistent quantum gravity

The Minimal Supersymmetric Standard Model

The Minimal Supersymmetric Standard Model (MSSM) is a very attractive extension of the Standard Model.

In the MSSM, There is a superpartner field for each existing basic field.

For a satisfactory realistic theory there are two Higgs supermultiplets, with opposite values of the weak hypercharge.

The MSSM is a SU (3)C ×SU(2)L×U(1)Y invariant theory with vector supermultiplets for the gauge fields and chiral supermultiplets for the quarks, leptons and two Higgses.

MSSM Field ContentChiral Multiplets

Vector Multiplets

The MSSM Lagrangian Supersymmetry is not an exact symmetry because

superpartners of ordinary particles have not been observed at accessible energies. So, it must be broken in order to give the superpartners large masses. The MSSM Lagrangian is given by:

21112

2 ..

HHHELYHDQYHUQYW

chWdL

LLL

LLL

LDU

Yukawa

Yukawagaugesusy

breakingsoftsusy

Lsoft MM ~qMqMeMeM

~

~

It contains 105 new parameters

Gauge Coupling Unification

Gauge coupling constants change as energy scale changes

In the Minimal Supersymmetric Standard Model three couplings (SU(3), SU(2), U(1)) meet at one point ~2×1016 GeV

accidental? or suggests unification of forces in SUSY!?

4gi

2

Present universeEarly universe

Weak scale Planck scale

Couplings unify with SUSY

Supersymmetry

High energy desert

Standard Model

Log(μ/μ0)

The unification of the Yukawa couplings in the MSSM

In some SO(10) GUT models the top quark Yukawa coupling λt is unified with λb and λτ at the GUT scale. Imposing this constraint one selects a unique value for tanβ and mt.

Problem: mt should be very small, so is inconsistent with experimental measurement.

One could also consider the unification of the Yukawa couplings at some scale other than that at which the gauge couplings unify.

The scenario of semi-perturbative unification(SPU)[1]

In this scenario, one can consider the addition of extra matter, beyond that of the MSSM, at some arbitrary scale Mn≥MZ.

Using α1 and α2 as measured inputs at the weak scale, One can use the renormalization group equation (RGE’s) for the gauge couplings to yield a prediction of the unification scale MG

The scenario of semi-perturbative unification(SPU)

where b'i =bi+ δbi with bi the MSSM β-functions and δbi the contributions of the extra matter.

At one loop, new states which shift all three β-functions identically leave unchanged the predictions for the strong coupling and for the unification scale.

,ln112ln '1

'2

12

21'1

'2

Z

n

Z

G

MM

bbbb

bbMM

The scenario of semi-perturbative unification(SPU)

Nature chooses to unify semiperturbatively One could study the effects of the model on

the phenomenology We consider scenarios of semiperturbative

unification (SPU) in which matter in complete SU(5) is added at some intermediate scale

The scenario of semi-perturbative unification(SPU)

The new extra matter is part of irreps of SU(5)

Two variables n5 and n10 have been introduce as effective numbers.

We study the effects of extra matter by including and varying these effective numbers in the β-functions of the MSSM.

We have no knowledge of dynamics of the underlying model.

Some effects of this model have already been studied on gauge couplings and mass spectrum of sparticles.

1010 and 55

The effects of extra matter on the unification of Yukawa

couplings In order to investigate the effects of extra matter. we run

RGE’s up two loop corrections.

We will focus on the standard treatment with universal boundary conditions at gauge unification, often termed CMSSM or MSUGRA(the minimal super-gravity ).

We run all gauge couplings and third family Yukawa couplings to the scale MG.

Applying the boundary condition on the soft terms at the scale MG. The whole system of the MSSM parameters are evolved to MZ Scale.

We iterate the entire procedure to determine a self-cosistent solution for Yukawa and gauge couplings.

Results In our calculation we have chosen

different values for mt and tanβ and then for each pairs of them we have changed n5 or n10 and have investigated the effects of the variation n5 or n10 over unification of Yukawa couplings.

Which indicate the unification if they rich to 1.

)()(

and )()(

21Gt

G

Gt

Gb

MhMh

RMhMh

R

Sample of Results

n5=-5 n5=-5

mt =165 Gev, tanβ=35

Sample of Results

n10=-2 n10=-2

mt =175 Gev, tanβ=35

Sample of Result

mt= 165Gev, n5=-1 n10=-3.45,tanβ=57

R1=0.99 , R2=1.02

Log(μ/μ0)

log10 ( / 0 )

mt= 170Gev, n5=-4.9 n10=-2,tanβ=59

R1=0.99 , R2=1.007

Log(μ/μ0)

Sample of Result

Log(μ/μ0)

mt= 174.5Gev, n5=1.8 n10=-3.9,tanβ=61

R1=0.99 , R2=1.02

Sample of Result

The Role of Extra Matter on Neutralino

The method of the calculation Two loop β-function including radiative

correction on Neutralino masses[2]: We calculate Nuetralino masses at their

own scales in SPS1a benchmark point[3]: Tan β=10 m1/2=250 Gev m0=100 Gev A=-100 Gev signμ=+ Also we choose mtop=170 Gev

The Role of Extra Matter on Neutralino

N5=-8

N10=1

Sample of Results

N10=0N5=

0

Conclusion

Once n5 and n10 increase then R1 and R2 raise but the increase of R2 is larger then R1.

By using suitable values for n5 and n10, the unification of Yaukawa couplings are possible for large tanβ.

There is no limitation on top quark mass.

Generally all Neutralino are sensitive to both values n10 and n5.

Thank You

References [1]:Christopher Kolda and John March-

Russell, Low-energy signatures of semi-pertubative unification, Physical Review D, Volume 55,Number 7.

[2]S.P. Martin and M.T. Vaughn, Phys. Rev. D50 (1994) 2282.

[3]:B.C. Allanach, et al., Eur. Phys. J. C25 (2002) 113.