The Higgs boson mass in a natural MSSM with nonuniversal gaugino masses

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1 PASCOS 2013, Taipei Taiwan The Higgs boson mass in a natural MSSM with nonuniversal gaugino masses Hajime Otsuka (Waseda University) with H. Abe and J. Kawamura PTEP 2013 (2013) 013B02, arxiv : [hep-ph] 1/15

2 A Standard Model-like Higgs particle has been discovered. ATLAS CMS 2/15

3 Fine-tuning problem in the Standard Model If the cut-off scale is of order GUT scale, In the MSSM, 0 One of motivations for SUSY ; Solution of the fine-tuning problem. 3/15

4 Fine-tuning problem in the Standard Model If the cut-off scale is of order GUT scale, In the MSSM, 0 One of motivations for SUSY ; Solution of the fine-tuning problem. 4/15

5 SUSY little hierarchy problem in the MSSM (Fine-tuning problem for EWSB) We need to avoid the tuning problem. 5/15

6 We examined the possibility to realize ~125 GeV Higgs and avoid the SUSY little hierarchy problem. 6/15

7 [1]M. S. Carena, M. Quiros and C. E. M. Wagner, Nucl. Phys. B 461 (1996) 407. In the MSSM, lightest CP-even Higgs boson mass is evaluated as[1] There are two possibilities to realize ~125 GeV Higgs. 1 High-scale SUSY breaking( >10 [TeV]) > SUSY little hierarchy problem 2 Large stop mixing Higgs mass is maximaly enhanced. 7/15

8 [1]M. S. Carena, M. Quiros and C. E. M. Wagner, Nucl. Phys. B 461 (1996) 407. In the MSSM, lightest CP-even Higgs boson mass is evaluated as[1] There are two possibilities to realize ~125 GeV Higgs. 1 High-scale SUSY breaking( >10 [TeV]) > SUSY little hierarchy problem 2 Large stop mixing Higgs mass is maximaly enhanced. 8/15

9 [1]M. S. Carena, M. Quiros and C. E. M. Wagner, Nucl. Phys. B 461 (1996) 407. In the MSSM, lightest CP-even Higgs boson mass is evaluated as[1] There are two possibilities to realize ~125 GeV Higgs. 1 High-sale SUSY breaking( >10 [TeV]) > SUSY little hierarchy problem 2 Large stop mixing is large. Higgs mass is maximally enhanced. 9/15

10 2 Large stop mixing How do we get the large stop mixing? After running a one-loop RG eq. from the GUT scale to the EW scale, Ratios of the gaugino masses Stop mixing is enhanced due to the RG effects. Higgs mass is enhanced. 10/15

11 2 Large stop mixing Solution of the SUSY little hierarchy problem. After running a one-loop RG eq. from the GUT scale to the EW scale, SUSY little hierarchy problem is relaxed due to the RG effects. Gaugino mass ratio is almost same as the large stop mixing. 11/15

12 Higgs mass and tuning There are the parameter spaces which realize the 125 GeV Higgs and avoid the tuning problem. Tuning parameter Input parameter at the GUT scale Universal Gaugino masses 12/15

13 Sparticle spectrums Reference point : In Summary, LSP is Higgsino. Wino is heavier than gluino. Stop is relatively light. 13/15

14 SUSY breaking mechanism There are two interesting candidates to realize the nonuniversal gaugino masses at the GUT scale. i) Moduli mixing( in the higher-dimensional theory) SU(2) gauge field Moduli( Volume) SU(3) gauge field Moduli mediation Nonuniversal gaugino masses ii) Mirage mediation Moduli mediation + Anomaly mediation Nonuniversal gaugino masses 14/15

15 Summary Nonuniversal gaugino masses at the GUT scale We can realize ~125 GeV Higgs and avoid the SUSY little hierarchy problem at the same time. Universal Gaugino masses 15/15

16 Appendix

17 RG eq. Casmir Invariant Casmir Invariant, gauge couplings and the value of Yukawa coupling determine the ratio of the gaugino masses.

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19 CCB breaking minima CCB breaking minima exist unless the following condition is satisfied. This inequality is guaranteed.