Probing flavor structure in unified theory with scalar spectroscopy

Probing flavor structure in unified Probing flavor structure in unified theory with scalar spectroscopytheory with scalar spectroscopy

June 21, 2007,

Supersymmetry in 2010’sSupersymmetry in 2010’s@Conference Hall, Hokkaido University@Conference Hall, Hokkaido University

Kentaro Kojima (Kyushu univ.)Kentaro Kojima (Kyushu univ.)

K. Inoue (Kyushu univ.), K. K, and K. Yoshioka (Kyoto univ.) [arXiv:hep-ph/0703253]K. Inoue (Kyushu univ.), K. K, and K. Yoshioka (Kyoto univ.) [arXiv:hep-ph/0703253]

““Probing flavor structure in unified theory with scalar spectroscopy”Probing flavor structure in unified theory with scalar spectroscopy”

Based on Based on

2Supersymmetry in 2010’s, K. KojimaSupersymmetry in 2010’s, K. Kojima

IntroductionIntroduction

Terascale direct searches in near future experiments: Terascale direct searches in near future experiments: LHC, ILC,LHC, ILC, ……

Discovery of SuperparticlesDiscovery of Superparticles

• SUSY breakingSUSY breaking• Grand Unified TheoryGrand Unified Theory• Origin of flavorOrigin of flavor• ・・・・・・

e.g. GUT relation for gaugino masses e.g. GUT relation for gaugino masses

Next step is:Next step is:

Terascale rich observables Terascale rich observables

• Higgs particle spectrum• Superparticle spectrum• SUSY induced flavor• ・・・

Extremely high-energy Extremely high-energy underlying theoryunderlying theory

scalar mass spectrumscalar mass spectrum

IndirectIndirectprobeprobe


MSSM Scalar mass spectrum with universal hypothesesMSSM Scalar mass spectrum with universal hypotheses

Generation Generation independentindependentnegligible for i =1, negligible for i =1, 2 2

• highly degenerate 1highly degenerate 1stst and 2 and 2ndnd generation scalars generation scalars• suppression of sparticle-mediated FCNC contributions suppression of sparticle-mediated FCNC contributions

e.g. CMSSM, mSUGRA, etc, …e.g. CMSSM, mSUGRA, etc, …

However, non-degenerate spectrum may be discoveredHowever, non-degenerate spectrum may be discovered

b.c. at a high-scaleb.c. at a high-scale RG induced effectsRG induced effects

Terascale observables Terascale observables

non-degeneracy of MSSM non-degeneracy of MSSM scalar massesscalar masses

high energy high energy physicsphysicsflavor structureflavor structure

in unified theory in unified theory

D-term of broken D-term of broken gauge sym.gauge sym.


ContentsContents

• IntroductionIntroduction

• Matter embedding into grand unified modelsMatter embedding into grand unified models

• Probing unified flavor structure with scalar Probing unified flavor structure with scalar spectroscopyspectroscopy

• Summary and DiscussionsSummary and Discussions


Generation redundancy in GUT modelsGeneration redundancy in GUT models

Successful gauge coupling unification in MSSMSuccessful gauge coupling unification in MSSM

However, matter unification is not simply However, matter unification is not simply realizedrealized

• CKM vs. MNS:CKM vs. MNS:naively conflict with quark-lepton unification

• Yukawa (mass) Yukawa (mass) unification:unification:

possible only for third generation

an available approachan available approach:: un-parallel generation un-parallel generation structurestructure

[Sato, Yanagida, Nomura, Bando, Kugo, maekawa, et. al]

generation dependent matter embedding into GUT multiplets generation dependent matter embedding into GUT multiplets

Generation redundancy Generation redundancy for anti-decoupletsfor anti-decouplets


Generation redundancy and induced scalar non-Generation redundancy and induced scalar non-degeneracydegeneracy

generation twist angeneration twist angles for gles for φφii

have same charge, but have different chargedifferent chargeand

Above the GUT scale, Above the GUT scale, generation dependent scalar non-generation dependent scalar non-

degeneracydegeneracy is induced is induced through through GU/G SM gauge interaction gauge interaction

generation generation dependent!!dependent!!

b.c. at a high-scaleb.c. at a high-scale RG induced effectsRG induced effects D-term of brokenD-term of brokengauge sym.gauge sym.


• D-term D-term correctionscorrections

[Drees, ’86; Kawamura, Murayama, Yamaguchi, ‘94]

multiple D-term correction is spanned by Cartan generators of

• RG effects above the GUT scaleRG effects above the GUT scale[Kawamura, Murayama, Yamaguchi, ‘94, Polonsky, Pomarol, ‘95]

(no intermediate scales)

characterized by quadratic Casimir invariantcharacterized by quadratic Casimir invariant

induced scalar non-degeneracy is directly connected to induced scalar non-degeneracy is directly connected to GGUU//GG SMSM charges, whic charges, which is parametrized by θh is parametrized by θ ii

Twist angles can be probed with the observed non-degeneracyTwist angles can be probed with the observed non-degeneracy


ContentsContents






Relations between observables and twist anglesRelations between observables and twist angles

three 27-plets as the fundamental matter multipletsthree 27-plets as the fundamental matter multiplets

(SU(5) decomposition)(SU(5) decomposition)

RHS: observablesRHS: observablesindependent of high-energy mass parametersindependent of high-energy mass parameters

• Dominant U(1)Dominant U(1)XX D-term case D-term case

(MSSM gauge dependent RG effects)

• General case (including D-term corrections and RG effects)General case (including D-term corrections and RG effects) Yukawa Yukawa dependent dependent MSSM RG MSSM RG effectseffects

•negligible for small tanβnegligible for small tanβ•numerically calculable numerically calculable


Probing into unified flavor structure with scalar spectroscopy Probing into unified flavor structure with scalar spectroscopy

• D-term dominated caseD-term dominated case • General caseGeneral case

scalar non-degeneracy ⇒ non-trivial generation twistingscalar non-degeneracy ⇒ non-trivial generation twisting

A key ingredient of flavor origin in unified theoryA key ingredient of flavor origin in unified theory


ContentsContents






SummarySummary

near future experiments:near future experiments: superparticle spectrumsuperparticle spectrum

generation dependent matter embedding into GUT multipletsgeneration dependent matter embedding into GUT multiplets

different different GGUU//GGSM SM

interactioninteraction

and scalar non-degeneracy is scalar non-degeneracy is induced through gauge induced through gauge interactions aboveinteractions above MMGG

TeV scale observables TeV scale observables

MSSM scalar massesMSSM scalar masses

high energy high energy physicsphysics

generation twisting angles:generation twisting angles:Origin of flavorOrigin of flavor

in unified theoryin unified theory


Discussion: Implications from FCNC constraints Discussion: Implications from FCNC constraints

non-degenerate scalarsnon-degenerate scalars

⇒ superparticle mediated flavor violation would be large

slepton mediated flavor violation ⇒ slepton mediated flavor violation ⇒

diagonalizes Yediagonalizes Ye

constraints from FCNC processes rather constraints from FCNC processes rather depend on the forms of Yukawa matricesdepend on the forms of Yukawa matrices

generation twisting is consistent with generation twisting is consistent with FCNCFCNC


generation twisting andgeneration twisting and large 2large 2ndnd and 3 and 3rdrd generation mixing generation mixing in charged lepton sector enhance τ→μγ process as reachin charged lepton sector enhance τ→μγ process as reach

able in near future experimentsable in near future experiments

In general, generation twisting enhances FCNC processes and In general, generation twisting enhances FCNC processes and flavor violation searches may give us implication of generation flavor violation searches may give us implication of generation

twistingtwisting



appendixappendix



Relation between observations and twist anglesRelation between observations and twist anglese.g. GU=E6: three 27-plets as the fundamental matter multipletsthree 27-plets as the fundamental matter multiplets

(SU(5) decomposition)

Dominant U(1)Dominant U(1)XX D-term case D-term case

Dominant U(1)Dominant U(1)ZZ D-term case D-term case

General case (including D-term corrections and RG effects)General case (including D-term corrections and RG effects)

Yukawa dependent MSSM RG effects

•negligible for small tanβ•numerically calculable

gauge gauge dependent dependent MSSM RG MSSM RG effects are effects are canceled outcanceled out


Lepton flavor violating processLepton flavor violating process

Large 2-3 entry of Ye RGE between RGE between induces large 2-3 mixing induces large 2-3 mixing in slepton mass matricesin slepton mass matrices

Relatively light sparticle spectrum leads sizable B(τRelatively light sparticle spectrum leads sizable B(τμγ)μγ)

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Probing flavor structure in unified theory with scalar spectroscopy