Radiative Electroweak Symmetry Breaking with Neutrino Effects in Supersymmetric SO(10) Unifications

KEKPH06 p.1/17 Radiative Electroweak Symmetry Breaking with Neutrino Effects in Supersymmetric SO(10) Unifications Kentaro Kojima Based on the work with Kenzo Inoue and Koichi Yoshioka (Department of Physics, Kyushu University) KEK Theory Meeting 2006 Particle Physics Phenomenology Plan of the talk Overview Yukawa unification with neutrino Yukawa coupling SO(10) GUT with lopsided texture

Ñ Ê Ñ Þ µ Ú À Ó Ý Ê Overview I: t-b- coupling unification in the MSSM MSSM allows t-b- Yukawa coupling unification [Carena, Pokorski, Wagner (1993)] The complete unification of third generation Yukawa couplings SO(10) unifications µ Ý ½ ½ ½¼ À ÉÝ Ø ØÀ Ù ÉÝ À ÄÝ À Ý Ø Å µ Ý Å µ Ý Å µ Ý Å ½¼ ½ Î MSSM renormalization group evolution Ñ Ê Ñ Þ µ Ú À Ò Ý Ê Ñ Þ µ½ Ø Ø Ñ Ê Ñ Þ µ Ú À Ó Ý Ê Ø Ñ Þ µ½ Ñ Þ µ½ µ ÑÊ Ø ØÒ Ê Ñ Ú À ³ ½ Î Ç ¼µ Ø are weak scale SUSY threshold corrections fermion mass estimation µ sparticle spectrum KEKPH06 p.2/17

¼ ½ Å Á ¼ Ø Á Ø KEKPH06 p.3/17 Overview II: large threshold corrections to Ñ can be easily large as Ç ½µ; ³ ØÒ ³ maximum of ], [Å ¾ Ѿ Á Á Ø maximum of ] [ ¾ Ñ ¾ Ø [Hempfling (1994); Hall et al. (1994); Carena et al. (1994)] In order to achieve correct fermion masses, must be much smaller than its naively expected size [Hall, Rattazzi, Sarid (1994); Tobe, Wells (2003)] Suppression of is ensured with approximate symmetries: PQ sym. ( ¾ Å ¾ ËÍË ) R sym. (Å ¾ ½¾ ¾ ¾ Å ¾ ËÍË )

Ñ ¾ ½¼ (Higgs), Ѿ ½ (matter), Å ½¾, ¼, ¼ ¾ ¼ Ѿ½¼ Ѿ ½ ¾ Ñ Ñ¾ ½¼ Ѿ ½ Ñ ¾ ½¼ Ѿ ½ Å ¾ Å ËÍ˵³ Ñ À Å ËÍË µ ¾ Ñ ÀÙ Å ËÍË µ ¾ Ñ Þ Å ËÍË µ ¾ KEKPH06 p.4/17 Overview III: difficulties in minimal SO(10) The minimal SO(10): unification of t-b- Yukawa couplings, and the SO(10) symmetric soft terms at Å ; ¼½ ¼¼ Ñ ¾ ¼ ¼½Å ¾ ½¾ ¼¼½¾ ¼ ¼¼ ¼Å ½¾ Ñ ¾ Þ ³ ½¾ ² Ñ ¼ µ large violation of R sym. Å Also is strongly constrained: ¾ ³ Ñ ¾ À Ù Ñ ¾ Þ ¾ ² Å ½¾ µ large violation of PQ sym. [Bando et al.(1992); Carena et al.(1994)] Ç ¼µ: minimal SO(10) cannot lead to correct fermion masses

KEKPH06 p.5/17 Our work Sources of the splitting between Ñ ¾ À Ù and Ñ ¾ À are needed previous approaches: SO(10) asymmetric non-universality [Olechowski, Pokorski (1995)] D-term arise from SO(10) SU(5) U(1) [Murayama et al.(1996)]

Ñ Ý ¾ Ò ¾ Ú ¾ À ³ Å Our work Sources of the splitting between Ñ ¾ À Ù and Ñ ¾ À are needed To the issue, we include effects expected from neutrino properties, and consider two scenarios in SO(10) unification tiny masses: Yukawa unification with Ý and seesaw mech.: large mixing: the atmospheric large mixing comes from : and have lopsided forms We examined radiative EWSB, fermion masses and constraint, which is severe for large ØÒ KEKPH06 p.6/17

Yukawa unification with Ý KEKPH06 p.7/17

Ï ÅËËÅ Ä µ À Ù ½ Ï Å µ ¾ KEKPH06 p.8/17 Yukawa unification with neutrino Yukawa coupling 16 rep. includes a singlet, RH neutrino Ý µ Ý Å µ ³ Å ³ ½¼ ½ Î Ý alters the RG evolution gauge couplings: very small (1-loop RGE s are unchanged) [Casas et al.(2001)] Yukawa couplings: b-tau mass ratio is slightly raised for Ñ fixed ÔÓÐ Ø [Vissani, Smirnov (1994); Allanach, King (1995)] Suppressed is still useful for correct fermion masses We focus on Ý effects on Å ¾

¾ Ѿ ¾ ÑÀ ½¾ Ù ÀÙ ÐÒ É É ÐÒ ½ Å ¾ Å ËÍ˵ ³ Ñ À Å ËÍË µ ¾ Ñ ÀÙ Å ËÍË µ ¾ Ñ Þ Å ËÍË µ ¾ Ñ Ñ Ñ Æ ¾ ½ µ Ñ ¾ ¼ Å Å ¾ ½¾ ¾ ¼ Å ¼ Å ½¾ Ñ ¾ Þ KEKPH06 p.9/17 Novel way of radiative EWSB On the up-type Higgs soft masses: Ý ¾ Ñ ¾ À Ù Ñ ¾ Ä Ñ¾ ¾ µ ÅËËÅ Ñ ¾ À Ù is lowered µ Å ¾ is increased through Ý effects : e.g. Ñ ¾ Ѿ ½ ½ ½µ ÓØÖ ÒÐØ Ê Æ ¾ contributions can became large ¾ Ñ With large Ñ ¾, Å ½¾ Ñ ¼ type EWSB is possible ¾ ½ Ñ ¾ ¼ ½Å ¾ ½¾ : positive and large Ñ ¼ lowers

¾¼ µ ½¼ KEKPH06 p.10/17 Parameter space analysis, fermion masses and constraint Æ ¾ ¼ Å ½¾ ¼¼ Î ¼ ¼ the experimental ranges Ñ ÅË Ñ µ ½ to GeV Approximate R Å sym.: ¼ ¼ Ñ ¼ ½¾ Approximate PQ ¼ sym.; Ñ and Å ½¾ ½ ¼ Suppression of We obtaine allowed values of fermion masses µ and

SO(10) unification with lopsided texture KEKPH06 p.11/17

KEKPH06 p.12/17 SO(10) GUT with Lopsided Texture Small mixings in the Î ÃÅ and large mixings in the Î ÅÆË One of the attractive approaches: highly asymmetric Yukawa texture, referred to as lopsided ¼ ½ µ µ Ì In SO(10) models, non-minimal field contents are useful to realize the lopsided texture: e.g. ½¼À (others) À [Albright et al.(1998); Nomura, Yanagida (1999); Babu et al.(2000)] SO(10) unification leads quite different picture of radiative EWSB from the third generation Yukawa unifications

KEKPH06 p.13/17 Higgs mixing and Fermion masses We consider following Yukawa matrices: ¼ ½ ¼ ½ µ µ Ì Ý Ó Ù µ Ò µ ½ ½ Ý Ó parametrizes the À mixing between ½¼À and others µ the nearly maximal atmospheric mixing angle ² For, ¼, that is ¼, is needed Æ In the wide range of, suppressed is needed to achieve correct bottom mass

À ½¼ À µ Ó ½ À µ Ò ¾ ¼ Ñ ¼ ¾ KEKPH06 p.14/17 The model The freedom of is a key ingredient [Nomura, Yanagida (1999)] ¾ Ñ Ñ¼ ¾ Ѿ À Ñ ¾ ¾ ¼ Ó ¾ Ò ¾ À Ù ¾ Ó ¾ Ò ¾ Ñ ¾ ٠Ѿ É Ñ¾ Ѿ ¼ Æ Ñ ¾ Ѿ ¼ Æ ¼ ½ Ñ ¾ ¼ Ñ ¾ Ä Ñ¾ ¾ Ñ parametrizes gaugino dependent RG contribution between Å ÔÐ and Å

KEKPH06 p.15/17 Higgs mixing and radiative EWSB Å ¾ Å ËÍ˵ Ñ Ñ Ñ ¾ ¼ Å Å ¾ ½¾ ¾ ¼ Å ¼ Å ½¾ Ñ ¾ Þ Å Large raises even Å ½¾ Ñ ¾ ¼ Positive D-term decreases ; ¾ ¾ ½Å ¾ ½¾ ¾¼ For ² ¼ Æ, approximate PQ and R symmetric spectrum is possible

¾¼ µ ½¼ Ñ Correct Ñ ÅË µ is obtained with a small but sizable KEKPH06 p.16/17 Parameter space analysis Æ ¼ Ñ ¼ ¼½ ¼ ¼ the experimental ranges Ñ ÅË Ñ µ ½ to GeV Approximate PQ and R symmetric spectrum suppresses constraint is evaded with relatively heavy sparticles for ¼

KEKPH06 p.17/17 Conclusions We investigated the radiative EWSB, fermion masses and constraint in SO(10) models with effects Including Ý the effects, Ñ large and R sym. allow small ¾. raises CP-odd Higgs mass, and PQ In the model with lopsided texture, non-minimal Higgs content and down-type Higgs mixing allow PQ and R symmetric radiative EWSB with ² ¼ Æ, and thus small sizable is achieved In both Ñ cases, Ñ ÅË µ µ and are consistent with experiments.