A.F.Kord Sabzevar Tarbiat Moallem University (Iran) September 2011

 Supersymmetry  The Minimal Supersymmetric Standard Model  The scenario of semi-perturbative unification(SPU)  Results  Conclusion

 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 (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.

Chiral Multiplets Vector Multiplets

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: L soft It contains 105 new parameters

 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 ~2×10 16 GeV  accidental? or suggests unification of forces in SUSY!?

Present universe Early universe Weak scale Planck scale Supersymmetry High energy desert Standard Model Log(μ/μ0)

 In some SO(10) GUT models the top quark Yukawa coupling λ t is unified with λ b and λ τ at the GUT scale. Imposing this constraint one selects a unique value for tan β and m t.  Problem: m t 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.

 In this scenario, one can consider the addition of extra matter, beyond that of the MSSM, at some arbitrary scale M n ≥M Z.  Using α 1 and α 2 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 M G

 where b' i =b i + δ b i with b i the MSSM β -functions and δ b i th e 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.

 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 new extra matter is part of irreps of SU(5)  Two variables n 5 and n 10 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.

 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 M G.  Applying the boundary condition on the soft terms at the scale M G. The whole system of the MSSM parameters are evolved to M Z Scale.  We iterate the entire procedure to determine a self-cosistent solution for Yukawa and gauge couplings.

 In our calculation we have chosen different values for m t and tan β 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.

n5=-5 m t =165 Gev, tanβ=35

n10=-2 m t =175 Gev, tanβ=35

m t = 165Gev, n 5 =-1 n 10 =-3.45,tanβ=57 R 1 =0.99, R 2 =1.02 Log(μ/μ0)

m t = 170Gev, n 5 =-4.9 n 10 =-2,tanβ=59 R 1 =0.99, R 2 =1.007 Log(μ/μ0)

m t = 174.5Gev, n 5 =1.8 n 10 =-3.9,tanβ=61 R 1 =0.99, R 2 =1.02

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 sign μ =+ Also we choose mtop=170 Gev

N5=-8 N10=1

N10=0 N5=0

 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 tan β.  There is no limitation on top quark mass.  Generally all Neutralino are sensitive to both values n10 and n5.

Thank You

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