Fine-tuning in the models with non-universal gaugino masses Yuji Omura ( Kyoto University) with Hiroyuki Abe ,Tatsuo Kobayashi and Haruhiko Terao

Outline 1.Introduction The Little Hierarchy Problem The ways to analyze the problem 2.The fine-tuning in bottom-up approach 3.The fine-tuning in models with non- universal gaugino masses 4.Conclusion

1.Introduction Minimum Supersymmetric Standard Model (MSSM) Little Hierarchy Problem Lightest Higgs mass bound is as follows : ; This maximum value must be larger than 114.4 GeV (LEP bound). On the other hand, MSSM has the EW constraint; This large stop mass would cause the fine-tuning of . At least 2% fine-tuning is required.

The ways and the tools to analyze the fine-tuning ; The up sector Higgs mass term is evaluated within one-loop calculation, Generally, the Little Hierarchy problem is discussed by tuning these higher-scale parameters. Fine-tuning parameters stand for the sensitivities of b to . EW constraint is within the one-loop approximation. =1 : 100% tuning required =10 : 10% tuning =100 : 1% tuning

2.Fine-tuning in bottom-up approach We regard all parameters at GUT scale as the independent ones . This means we need care about the all fine-tuning parameters. Constraints which limit the parameters at GUT 1. Higgs mass bound; 2. stop mass bound ;(Now our model has only top yukawa coupling.) 3.gaugino mass bounds Assumptions 1.The bottom yukawa can be ignored. 2.Sfermion mass terms are zero at GUT scale. We just concentrate on three gaugino masses and A-term. >95.7GeV

Between the red lines, The black line; Inside the circle, Between the Dot lines, The coefficient of squared gluino mass is 10 times as large as of the others. For all of the fine-tuning parameters to be O(1), 3

Black region; Above Dot line ; Between the thick lines; Between the red lines; The larger wino mass makes the squared stop mass negative.

the fine-tuning parameters ,A-term ,stop masses ,higgs mass bound and gaugino masses are as follows;

3.Fine-tuning in models with non-universal gaugino masses Assumptions One SUSY breaking scale( ) and some relations among gaugino masses. For example, Anomaly mediation; Mirage mediation; Without attention to ,we could look for parameterization, It is just important that the larger It’s easy to be beyond LEP bound. It’s difficult to avoid the fine-tuning. Notice that we also set the sfermion masses at GUT scale to zero. for

Between two red lines Solid lines are Below a blue line

For ; at , ( ) This means where Notice unless , is larger than 10. For example, at

4.Conclusion Bottom-up approach ; The coefficient of SU(3) gaugino mass is ten times as large as the others whithin one-loop calculation. The gluino mass should be set to as small as possible , to avoid the fine-tunings of all parameters. should be less than 120GeV for to be O(1). In some models which have some relations among parameters at GUT scale; Without attentions to and ,we can find the gaugino-mass hierarchy which leads O(1) . 3 at GUT scale. ( ) at weak scale.

For higgs mass above the LEP bound, This large top squark mass causes to be too much larger than . The less than 5% fine-tuning is required.

The larger It’s easy to be beyond LEP bound. It’s difficult to avoid the fine-tuning. If should be cared about , must be as little as possible. For example, But, if it need not be, ;This is solution