The effect of extra matter on unification of Yukawa couplings in The MSSM

1. The effect of extra matter on unification of Yukawa couplings inTheMSSM A.F.Kord SabzevarTarbiatMoallem University (Iran) September 2011

2. Outline • Supersymmetry • The Minimal SupersymmetricStandard Model • The scenario of semi-perturbative unification(SPU) • Results • Conclusion

3. 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

4. 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 chiralsupermultiplets for the quarks, leptons and two Higgses.

5. MSSM Field Content ChiralMultiplets Vector Multiplets

6. 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: Lsoft It contains 105 new parameters

7. 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 ~2×1016GeV • accidental? or suggests unification of forces in SUSY!?

8. Present universe Early universe Weak scale Planck scale Couplings unify with SUSY Standard Model Supersymmetry High energy desert Log(μ/μ0)

9. The unification of the Yukawa couplings in the MSSM • In some SO(10) GUT models the top quark Yukawa coupling λt is unified with λband λτat the GUT scale. Imposing this constraint one selects a unique value for tanβ and mt. • Problem: mtshould 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.

10. 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

11. The scenario of semi-perturbativeunification(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.

12. The scenario of semi-perturbativeunification(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

13. The scenario of semi-perturbative unification(SPU) • The new extra matter is part of irrepsof SU(5) • Two variables n5and 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.

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

15. Results • In our calculation we have chosen different values for mt and tanβand 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.

16. Sample of Results mt=165 Gev, tanβ=35 n5=-5 n5=-5

17. Sample of Results mt=175 Gev, tanβ=35 n10=-2 n10=-2

18. Sample of Result mt= 165Gev, n5=-1 n10=-3.45,tanβ=57 R1=0.99 , R2=1.02 Log(μ/μ0)

19. Sample of Result mt= 170Gev, n5=-4.9 n10=-2,tanβ=59 R1=0.99 ,R2=1.007 Log(μ/μ0)

20. Sample of Result mt= 174.5Gev, n5=1.8 n10=-3.9,tanβ=61 R1=0.99 ,R2=1.02 Log(μ/μ0)

21. 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

22. The Role of Extra Matter on Neutralino N10=1 N5=-8

23. Sample of Results N5=0 N10=0

24. 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.

25. Thank You

26. 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.