in 4 Dimensional GUT
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πΈ6 Grand Unified Theory and Family Symmetry with Spontaneous CP Violation Nobuhiro Maekawa (Nagoya Univ. KMI) with M. Ishiduki, S.-G. Kim, K. Sakurai, A. Matsuzaki, T. Yoshikawa, H. Kawase, T. Takayama, Y. Muramatsu, Y. Shigekami 1. 2. 3. 4. 5. 6. 7. Introduction π¬π Grand Unified Theory Family Symmetry Spontaneous CP Violation Predictions (FCNC and Nucleon decay) Impact of LHC Summary Overview of this talk ο΅ πΈ6 grand unified theory (GUT) Various hierarchies of quark and lepton masses and mixings can be explained. (ππ3 ~π) ο΅ πΈ6 GUT+non-Abelian family symmetry The explanation is so natural that realistic Yukawa couplings can be realized after breaking the symmetries. Modified universal sfermion masses are predicted. 1 π3 βͺ π is interesting. a. light stop… weak scale stablity b. heavy sfermion…suppress FCNC, CP 2. All FCNC are sufficiently suppressed. 3. Several are within reach of future exp. 4. New type of SUSY CP problem looks serious. π2 . . 2 2 π10 = . π . , . . π3 2 π2 . . 2 2 π5 = . π . . . π2 Overview of this talk ο΅ πΈ6 GUT+family sym. with sp. CP violation (Discrete sym. is introduced.) Not only old type but also new type of SUSY CP problems can be solved. Several bonus (light up quark, ππ’π ~π 4 , predictive power) Examining the neutrino sector Same predictions as the usual πΈ6 GUT but non-trivial. Introduction Grand Unified Theories οΌ οΌ΅ο½ο½ο½ο½ο½ο½ο½ο½ο½ο½ο½ ο΅ Gauge Interactions ο΅ Matter Experimental supports for both unifications GUT is promising Grand Unified Theories ο΅ Unification of gauge interactions quantitative evidence: Non SUSY ο΅ SUSY GUT Unification of matters qualitative evidence: have stronger hierarchy than hierarchies of masses and mixings lepton >>quark (in hierarchies for mixings) ups >> downs, electrons >> neutrinos (in mass hierarchies) Masses & Mixings and GUT 4 Log[Mf/GeV] 2 0 -2 -4 -6 -8 -10 -12 180 160 140 120 100 80 60 40 20 0 up do wn 1st c h arg e d l e pto n 2nd n e u tri n o 3rd up down u, c, t Strongest Neutrinos Weakest e, μοΌτ Middle d, s, b Middle charged neutrino lepton CKM small mixings MNS large mixings These can be naturally realized in SU(5) GUT!! SU(5) SUSY GUT Albright-Barr Sato-Yanagida… have stronger hierarchy than Stronger hierarchy leads to smaller mixings Quark mixings(CKM) Lepton mixing(MNS) Mass hierarchy and mixings ο΅ Stronger hierarchy leads to smaller mixings Stronger hierarchy Smaller mixings SU(5) SUSY GUT have stronger hierarchy than Stronger hierarchy leads to smaller mixings Quark mixings(CKM) Lepton mixing(MNS) Good agreement with masses & mixings πΈ6 Grand Unified Theory The assumption in SU(5) GUT 10π have stronger hierarchy than 5π can be derived. Various Yukawa hierarchies can be induced from one Yukawa hierarchy in πΈ6 GUT. οΌ΅ο½ο½ο½ο½ο½ο½ο½ο½ο½ο½ Three of six Guisey-Ramond-Sikivie, Aichiman-Stech, Shafi, Barbieri-Nanopoulos, Bando-Kugo,… become superheavy after the breaking Once we fix three light modes of six , are determined. We assume all Yukawa matrices Milder hierarchy for Bando-N.M. 01 N.M, T. Yamashita 02 ο΅ fields from become superheavy. Superheavy unless ο΅ Light modes have smaller Yukawa couplings and milder hierarchy than •Larger mixings in lepton sector than in quark sector. •Small •Small neutrino Dirac masses Suppressed radiative LFV How to obtain various Yukawas? SO(10) GUT relations Large ππ3 ∼ π Right-handed neutrinos • The same hierarchy LMA for solar neutrino problem 1st οΌ³ο½ο½ο½ο½ο½ο½ unification explains why the lepton sector has larger mixings than the quark sector.(Large ππ3 ∼ π) ο΅ Suppressed radiative LFV ο΅ A basic Yukawa hierarchy The other Yukawa hierarchies Hierarchy of Three is stronger than that of come from the first 2 generation of Family symmetry All three generation quark and leptons can be unified into a single (or two) field(s) By breaking the horizontal symmetry, realistic quark and lepton masses and mixings can be obtained. Peculiar sfermion mass spectrum is predicted. π10 2 π2 = . . . π2 . . π2 . , π5 2 = . π3 2 . . π2 . . . π2 Family οΌ³ο½ο½ο½ο½ ο½ο½ο½ Dine-Kagan-Leigh Pomarol-Tommasini Barbieri-Hall… •Origin of Yukawa hierarchy •Semi-universal sfermion masses to suppress FCNC • The 1st 2 generation have universal sfermion masses. • Large top Yukawa coupling Not sufficient to suppress FCNC Large neutrino mixings and FCNC • The universal sfermion masses only for the 1st 2 generation do not suppress FCNC sufficiently if οΌ Universality for all three generations is required! unification solves these problems N.M.02,04 • Various Yukawa hierarchies can be obtained from one basic hierarchy. Breaking gives the basic hierarchical structure. • All the three light fields come from and therefore have universal sfermion masses. Important for suppressing FCNC sufficiently, because the mixings of are large. οΌ€ο½ο½ο½ο½ο½ο½ο½ο½ο½ • Extension to is straightforward. All three generation quarks and leptons are unified into a single multiplet • If it is local, D term must be cared. • Peculiar sfermion spectrum Universal Different Experimentο½ • Any mechanisms for the basic hierarchy. Extra dimension Stringy calculation Froggatt-Nielsen mechanism (Anomalous U(1)) • Higgs sector (Doublet-triplet splitting) Anomalous U(1) N.M.-Yamashita 02,03 Generic interactions with O(1) coefficients. Orbifold breaking 2nd οΌ³ο½ο½ο½ο½ο½ο½ • In GUT, one basic hierarchy for Yukawa couplings results in various hierarchical structures for quarks and leptons including larger neutrino mixings. • Family symmetry can easily reproduce the basic hierarchy, and suppress FCNC naturally. • The simpler unification of quarks and leptons explains the more questions. larger neutrino mixings SUSY flavor problem Spontaneous CP violation Old and new type SUSY CP problems can be solved and several bonuses SUSY CP Problem Old type ο΅ EDM constraints => Real SUSY parameters. problem is must be by solved solved anomalous U(1) ο΅ Complex Yukawa couplings => CEDM New type Hisano-Shimizu04 Griffith et.al.09 in E6 GUT with SU(2) Complex Yukawa => is complex generically Additional (discrete) symmetry solves both problems Decoupling features of SUSY CP problem ο΅ EDM constraints from 1 loop ο΅ CEDM from Hg(neutron) even if Hisano-Shimizu ‘04 Contributions through stop loop are not decoupled. Complex Yukawa couplings induce them generically. Spontaneous CP violatoin in SU(2) model ο΅ Doublets under SU(2) family symmetry Real and and require non-trivial discrete charge for . A solution for problem Negative Higgs charges=> massless Higgs SUSY(holomorphic) zero mechanism ο΅ SUSY breaking induces the non-vanishing VEV of superheavy positive charged singlet ο΅ 2 π = ππ»π’ π»π + Λ π + Λππ Additional discrete symmetry π = ππ»π’ π»π + Λ2 1 + πΉπΉ π + Λππ Complex Non trivial discrete charge for to forbid What happens by the discrete symmetry? real complex SUSY zero mechanism is real , is complex A model with a discrete symmetry Ishiduki-Kim-N.M.-Sakurai09 Bonus 1 ο΅ Real up-type Yukawa couplings real CEDM constraints can be satisfied. ο΅ Complex down-type Yukawa couplings KM phase can be induced. ο΅ The point : real, : complex A model with a discrete symmetry ο΅ Bonus 2: small up quark mass is realized. Usually, to obtain the CKM matrix Too large ο¨ good value! A model with a discrete symmetry ο΅ Bonus 3?: # of O(1) parameters =9-12 13 physical parameters ο΅ One of the relations Interesting result(perturbation in ο΅ ) is obtained Kawase, N.M 10 This cancellation depends on the adjoint VEV. (B factory measured the direction of GUT breaking?) ο΅ Numerical calculation Ishiduki-Kim-N.M.-Sakurai09 ο΅ O(1) coefficients(10 parameters) Ref:Ross-Serna07 MSSM 2loop RGE Heavy fields’ contribution must be taken into account. E6 Higgs sector ο΅ N.M.-Yamashita02 Ishiduki-Kim-N.M.-Sakurai 09 E6 can be broken into the SM gauge group. 1, Natural doublet-triplet splitting 2, , is realized 3, consistent with the discrete symmetry Neutrino sector ο΅ N.M.-Takayama 11 5 fields at the low energy are determined as 3 massless modes of this 3 × 6 matrix. . 51 52 53 ′ 51 0 ππ΅−πΏ π5 0 ′ ′ 51 52 53 −ππ΅−πΏ π5 0 0 π4 π2 π5+π 3+π π2 1 π 52 53 π5+π 0 0 π3+π 0 0 ′ ππ ≡ π» πΆ π» ′ ο΅ For lepton doublets, 51 of three massless modes, 53 , because ππ΅−πΏ = 0 for lepton doublets. ο΅ Yukawa couplings of charged lepton in 51 can be obtained through ππΆ 16π 101 16πΆ ο΅ Dirac neutrino Yukawa couplings of 51 through ππ» 1π 101 10π» is vanishing because ππ΅−πΏ = 0. βΆ πππ = 0 That’s a problem. ο΅ Fortunately, we have higher dimensional interactions π ππ 27π» 27π 27π 27π» 27π» βΆ 12 101 10π» We have many parameters on the right-handed neutrino masses. Predictions on neutrino masses and mixings are the same as the usual πΈ6 GUT. 27π» 27π» can couple with many interactions, but the effects are only for the neutrino sector in the model. ο΅ 51 , 51 , 52 , has no mixing with ′ ′ 3rd Summary ο΅ KM theory is naturally realized by spontaneous CP violation in E6 GUT with family symmetry 1, Real and parameters are realized by introducing a discrete symmetry. 2, The symmetry solves CEDM problem. :real :complex 3, Predicted EDM induced by RGE effect is sizable. 4, 5, 6, E6 Higgs sector consistent with the above scenario with natural realization of D-T splitting D term problem ο΅ Non vanishing D terms spoil the universality π2 0 0 π·ππ(2)π» 2 2 π10 = 0 π + 0 2 0 0 π3 2 1 π2 0 0 π· ππ(2) π» π5 2 = 0 π 2 0 + 0 2 0 0 0 π2 1 0 0 0 −1 0 + π·π ′ 0 0 0 0 0 1 1 0 + π·π ′ 0 0 −1 0 1 0 0 0 −2 0 0 1 0 0 1 0 + π·π 0 1 0 0 −3 0 + π·π 0 1 0 0 1 0 0 2 0 This may induce too large FCNC. This problem looks to be serious before LHC. We expected some hints from LHC. 0 0 1 0 0 −3 Predictions of πΈ6 × ππ(2)πΉ × π(1)π΄ Flavor physics : Kim-N.M.-Matsuzaki-Sakurai-Yoshikawa 06,08 π3 must be around the weak scale, because of the stability of the weak scale, while π can be taken larger. 10: 5: Nucleon decay: Y. Muramatsu-N.M. 13,14 Important prediction of Natural (Anomalous U(1)) GUT N.M. 01 Nucleon decay via dim. 6 operators is enhanced, while nucleon decay via dim. 5 is suppressed. Non universal SUSY breaking ο΅ Universal sfermion masses for ο΅ Non universaltiy for fields ο΅ Weak scale stability requires but almost no constraint for fields Structures suppressing FCNC for Small Yukawa couplings ο΅ Small ο΅ Universal sfermion masses for ο΅ can increase without destabilizing the weak scale. (Effective SUSY) ο΅ How does FCNC processes take place in this model? flavor violating 10: No source of flavor violation 5: For example, for the right-handed charged slepton sector, Since 10 contains Q, the form of unitary matrix V is CKM-like. We can parametrize it with Cabibbo angle λ. Non decoupling feature of this model (in lepton flavor violation) ο΅ ο΅ By picking up the 3-2 element, the size of τ→μ transition rate is order . For μ→eγ, there are two passes to change the flavor μ→e. Both they are order . If we raise overall SUSY scale m … Propagator suppression from 1 or 2 generation becomes stronger, but mass difference increase. As a result, both transition rate remain finite, and don’t decouple! Can we discover the LFV at the future experiments? οΎ 7.0 ο΄ 10 οΎ 1.0 ο΄10 ο11 ο8 (exclude) (exclude) MEG experiment (super-)KEKB οΌ 7.0 ο΄ 10ο9 οΌ 1.0 ο΄10 ο14 τ→μγ Detectable, when tanβ is large and μ→eγ Detectable if <400GeV <250GeV This model says that final state lepton tends to be right-handed. ο΅ Final state lepton has different chirality from initial one. q ο½ p ο pο’ ei ο΅ p pο’ Opposite from MSSM+ ej Intermediate state must be right-handed to pick up the . How can we see this feature experimentally? spin ο§ ο Lefthanded e e Righthanded spin ο ο§ It is possible to check this feature experimentally by measuring the angular distribution of final state lepton. Predictions (Quark sector) The maginitudes are the same order as of the RGE effects in the universal mass case. ο΅ New CP phases!! The CP violation in B meson system may be detectable ο΅ CP violation in B meson SM O(0.04) E6 O(0.006) <0.15 0.006 <0.01 very small very small For Bd ο φKs,η’Ks is possible. Gluino contribution is decoupled. Chargino contribution is not decoupled. in the limit O(0.1) deviation in B factory may be confirmed in SuperB factory. Summary table of E6 predictions SM O(0.04) E6 O(0.006) <0.15 0.006 <0.01 very small Discussions ο΅ Strictly speaking, when e.g. This can be consistent with the experiments, but the predictions can be changed. If we take , this model dependent parts can be neglected. No weak scale instability!! Nucleon decay N.M.-Y.Muramatsu 13,14 Natural(Anomalous U(1)) GUT N.M. 01 N.M. T. Yamashita, 02 ο΅ ο΅ ο΅ ο΅ ο΅ ο΅ ο΅ ο΅ ο΅ Natural: All the interactions which are allowed by the symmetry are introduced with O(1) coefficients. (incl. higher dimensional int.) We can define the model only by fixing the symmetry of the model(except O(1) coefficients) . The parameters for the definition are mainly about 10 charges for the fields. The predictions are expected to be stable under the quantum corrections or gravity effects. This assumption is quite natural. Infinite number of interactions can be controlled. Doublet-triplet splitting problem can be solved. Realistic quark and lepton masses and mixings. Non trivial explanation for gauge coupling unification. Anomalous U(1) gauge symmetry plays an essential role Natural Gauge Coupling Unification New Explanation for the success ο΅ ο΅ ο΅ ο΅ N.M. 01, N.M-Yamashita 02 Fix a model with Calculate οΌ£ο½ο½ο½ο½ο½ο½ο½ο½ ο½ο½ο½ο½ οΌ‘ο½ο½ο½ο½ο½ ο½ο½ ο½ ο½ ο½ο½ a scale οΌοΌ³οΌ³οΌ Nucleon decay via dim. 6 is enhanced ο΅ Unification scale becomes lower. ο΅ ο΅ Proton decay via dimension 6 op. π π → ππ ∼ 2 − 8 × 1034 years (Λ π ∼ Λ πΊ /2) πππ₯π π → ππ > 1.4 × 1034 years ο΅ Generic interactions GUT model identification by nucleon decay two important ratios of partial decay widths to identify GUT model to identify grand unification group to identify Yukawa structure at GUT scale GUT GUT GUT : dimension-6 operators which have anti electron in final state : dimension-6 operators which have anti neutrino in final state ππ3 model points πΉπ = πππ model points πΉπ = 4th Summary ο΅ Observed (or observing) π13 ∼ π, ( πΏππππ‘ππ ∼ π 1 ) (ππ’π ∼ π4 ) ο΅ Not yet Nucleon decay FCNC large Unfortunately most of FCNC processes are decoupled when SUSY breaking scale is large. Impact of LHC 125 GeV Higgs Stop mass (π3 ) must be larger than 1 TeV ο΅ No SUSY particle ⇒ SUSY breaking scale may be larger than we expected. The little hierarchy problem is more serious. FCNC problem (D term problem) is milder. ο΅ The little hierarchy problem -Very serious problem must be solved! N.M.-K.Takayama 14 . Little hierarchy problem ο΅ πβ ~125 GeV (LHC) → ππ‘ > 1TeV (π΄π‘ ~2ππ‘ ) ππ‘ > 5TeV (π΄π‘ βͺ ππ‘ ) πβ 2 ~ππ 2 πππ 2 2β ο΅ + 3πΊπΉ ππ‘ 4 2π2 ln ππ‘ 2 ππ‘ 2 + π΄π‘ 2 ππ‘ 2 1− π΄π‘ 2 12ππ‘ 2 Higgs mass is fixed by π΄π‘ and ππ‘ at weak energy scale. Heavy stop leads to parameters tuning Δππ»π’ 2~ 3π¦π‘ 2 − 2 8π 2ππ‘ 2 + π΄π‘ 2 ln Λ ππ‘ 1 2 β« πβ 2 ππ‘ = 5TeV, π΄π‘ βͺ ππ‘ , Λ = ΛπΊ → O(0.01%) tuning ππ‘ = 1TeV, π΄π‘ = 2ππ‘ , Λ = Λ πΊ → O(0.1%) tuning ππ‘ = 1TeV, π΄π‘ = 2ππ‘ , Λ~π(Λ ππππ ) → O(1%) tuning Correction depends on π΄π‘ , ππ‘ at higher scale and Λ. Low mediation scale and π΄π‘ ~2ππ‘ are preferable. Low mediation scale scenarios ο΅ ο΅ Gauge mediation Mass of the messenger particles can be small. Unfortunately it is difficult to obtain large π΄π‘ Mirage mediation Choi-Falkowski-Nilles-Olechowski-Pokorski04, Jeong-Kobayashi-Okumura05, Kitano-Nomura05 Due to the cancellation between anomaly mediation and RG effects of moduli contribution, the mediation scale can be lower effectively. Special boundary conditions are required π1/2 = π΄π‘ = 2ππ‘ Unfortunately, π΄π‘ is not sufficiently large. What happens if special boundary conditions are not required? Cosmological Gravitino Problem SUSY is still promising Decay of gravitino produced in early universe spoils BBN. Kawasaki-Kohri-Moroi-Yotsuyanagi08 One solution O(100TeV) gravitino It decays before BBN! High scale SUSY but destabilizes the weak scale. Roughly π3/2 > 50 TeV What we would like to show ο΅ Gravitino mass π3/2 = O(100) TeV to solve the cosmological gravitino problem ο΅ The other SUSY breaking parameters = O(1) TeV for the naturalness As in mirage mediation The little hierarchy problem can be less severe. O(%) tuning is realized. Point: anomaly mediation cancels the RG contribution. π΄π‘ can be larger without changing βππ»π’ 2 Cancellation property of anomaly mediation ο΅ Gaugino mass RGE π π ππ‘ π = 1 2 π π ππ π π 8π2 ππ π |πππππππ¦ = ππ π |ππππ£ππ‘π¦ = ππ ππ 2 π3/2 16π2 ππ ππ 2 ππ + ππ 8π2 ln π Λ ππ π = ππ π |πππππππ¦ + ππ π |ππππ£ππ‘π¦ = π1/2 + ΛπΊ ln ππππ = ππ ππ 2 π π ln 1/2 8π2 ππππ π3/2 2π1/2 π1 = π2 = π3 = π1/2 ππππ ~1 TeV↔ π3/2 π1/2 ~60 Cancellation property(no Yukawa) ο΅ π΄πππ π΄πππ π = π΄πππ − 1 8π2 π πΎπ + πΎπ + πΎπ π1/2 ln π ππππ πΎπ = 2 π πΆ π ππ 2 2 ο΅ Scalar fermion mass square ππ 1 π 1 π 2 2 2 2 ππ π = ππ − 2 πΎπ π1/2 ln − 2 πΎπ π1/2 ln 4π ππππ 8π ππππ + ο΅ 3 2 π ln π π π 40π2 π 1 Λ 2 π ≠ π‘πΏ , π‘π , π»π’ π = π ππ ππ 2 These parameters at the mirage scale ππππ become gravity contribution at the cutoff Λ if π = 0 What happens for sfermions with large top Yukawa? ο΅ ο΅ π΄π‘ π = π΄π‘ + 6π π΄π‘ − π1/2 − 2 1 8π2 πΎπ»π’ + πΎπ‘πΏ + πΎπ‘π π1/2 ln π ππππ 2 ππ π = ππ − ππ π π΄π‘ − π1/2 1 + 6π + Σπ‘ − π1/2 2 1 π 2 2 − 2 πΎπ π1 + ππ π΄π‘ − π1/2 1 + 6π π¦π‘ ln 4π ππππ 2 2 1 π 2 − 2 πΎπ π1 ln π = π‘πΏ , π‘π , π»π’ 8π ππππ 2 2 Special boundary conditions π1/2 = π΄π‘ = Σπ‘ β ππ‘πΏ 2 + ππ‘π 2 + ππ»π’ 2 → π΄π‘ = 2ππ‘ ππ»π’ = 0 are required to obtain ππ 2 ππππ = π2 and π΄π‘ ππππ = π΄π‘ Generalization of mirage mediation ο΅ ο΅ ο΅ ο΅ In the usual mirage mediation, universal sfermion masses are adopted. If the conditions π1/2 = π΄π‘ = Σπ‘ β ππ‘πΏ 2 + ππ‘π 2 + ππ»π’ 2 are satisfied, any values for the other parameters are OK for mirage phenomena when π = 0. For example, natural(effective) SUSY type sfermion masses π32 = ππ‘πΏ 2 = ππ‘π 2 = ππ2π βͺ π02 = ππ2 (π ≠ π‘π , π‘πΏ , ππ ) LHC and FCNC constraints become milder than the usual mirage mediation with fixed π3 Asano-Higaki12 In this talk, we do not address π0 so much because the value is not so important in our arguments What happens without special boundary conditions? π1/2 = π΄π‘ = Σπ‘ Without these boundary conditions, the situation becomes just the situation in which the gravity mediation and anomaly mediation contribute at the same time. Sizable anomaly mediation It is known that anomaly mediation leads to negative mass square of some of the sfermions. → upper bound of π3/2 π3/2 π1/2 = 60 ↔ ππππ = 1TeV π1/2 = 2ππ‘ at mirage point Wide region where ππ2 Λ πΊ > 0 in general setup. ππ‘ /π1/2 Mirage point Little hierarchy problem 2 2 2 βππ» = ππ» πππππ − ππ» π’ π’ π’ from π3/2 , π1/2 , ππ‘ , π΄π‘ . We fixed π3/2 = 60 π1/2 ππ‘ = 2 TeV πβ 2 /βππ»π’ 2 2 1, O(%) tuning is realized! (←Width of 1% band is O(TeV)) 2, Mild dependence on π΄π‘ (Important to obtain heavy Higgs.) 2 πβ /2βππ»π’ 2 π3/2 = 50 π1/2 π3/2 = 70 π1/2 for π3/2 π1/2 = 50, 60, 70, 80 ππ‘ = 2 TeV π3/2 = 60 π1/2 π3/2 = 80 π1/2 1, O(%) tuning is realized! (←Width of 1% band is O(TeV)) 2, Mild dependence on π΄π‘ (Important to obtain heavy Higgs.) Little hierarchy problem 2 βππ»π’ 2 1πππ = π0 π1/2 2 + π1 Σπ‘ + π2 π΄π‘ + π3 π΄π‘ π1/2 ο΅ In CMSSM, π0 = −1.6, π1 = −0.40, π2 = −0.082, π3 = −0.26 βππ»π’ 2 = −2.34π1/2 2 if π1/2 = π΄π‘ = Σπ‘ . ο΅ In mirage (anomaly mediation with π3/2 /π1/2 = 60), π0 = 0.29, π1 = −0.40, π2 = −0.082, π3 = 0.16 βππ»π’ 2 = −0.031π1/2 2 if π1/2 = π΄π‘ = Σπ‘ . Reasons for this improvement 1, Smaller coefficients ππ 2, Cancellation (Different signature) (Naturalness arguments strongly depend on high energy physics) What happens for other values of π3/2 /π1/2 ? ο΅ What happens for other values of π3/2 /π1/2 ? π1 = −0.40, π2 = −0.082 1, Smaller coefficients ππ 2, Different signature Improvement is generally expected Mild dependence on π΄π‘ βππ»π’ 2 1πππ = π0 π1/2 2 + π1 Σπ‘ + π2 π3 2 π0 − 4π2 π3 π΄π‘ + π1/2 2π2 < 0, π1 < 0, π2 < 0 → βππ»π’ 2 ≠ 0 ο΅ In CMSSM, π0 = ο΅ With anomaly mediation, π0 > 0 when π3/2 ≥ 47π1 2 → βππ»π’ 2 = 0 is possible ο΅ 2 βππ»π’ = 0 and πβππ»π’ 2 π π΄π‘ 2 = 0 → π΄π‘ ~2ππ‘ Important observation ο΅ Gravitino mass π3/2 = O(100) TeV ο΅ to solve the cosmological gravitino problem The other SUSY breaking parameters = O(1) TeV for the naturalness The little hierarchy problem can be less severe. O(%) tuning is realized. Point: anomaly mediation cancels the RG contribution. π΄π‘ can be larger without changing βππ»π’ 2 If ππππ ~ O(TeV), we may observe directly the GUT signatures through the mass spectrum of the other sfermions than stops. (ex. D-term contributions of GUT.) Sizable D-term contribution as a signature of π¬π × πΊπΌ π π × πΌ π π¨ N.M.-Y.Muramatsu-Y.Shigekami 14 Natural (Effective) SUSY type sfermion masses 10: 5: Most of models which predict natural SUSY sferimion masses are suffering from CEDM constraints. If natural SUSY sfermion masses are observed, this scenario is implied. Small deviation from natural SUSY sfermion masses can be a signature of πΈ6 GUT with family symmetry. A signature from sizable D-term contributions π2 0 0 π·ππ(2)πΉ 2 2 π10 = 0 π + 0 2 0 0 π3 2 π2 0 0 π·ππ(2)πΉ 1 2 π5 = 0 π 2 0 + 0 2 0 0 0 π2 1 0 0 0 −1 0 + π·π ′ 0 0 0 0 0 1 1 0 + π·π ′ 0 0 −1 0 1 0 0 1 0 0 1 0 + π·π 0 1 0 0 1 0 0 0 0 −3 0 −2 0 + π·π 0 2 0 1 0 0 2 2 2 Δπ10,2 ≡ π10,2 − π10,1 = −DSU 2 2 2 2 Δπ5,2 ≡ π5,2 − π5,1 2 2 2 Δπ5,3 ≡ π5,3 − π5,1 An important prediction How large D-term can be allowed? We consider FCNC constraints F = −3Dπ ′ + 5π·π = −DSU 2 F 2 2 Δπ10,2 = Δπ5,3 0 0 1 0 0 −3 FCNC constraints for mass insertion parameters mass insertion parameter diagonalizing matrices π for 10 matters 1 πΏπ’ ∼ πΏπ ∼ π π’ ∼ π π ∼ π π3 π 1 π2 π3 π2 1 for 5 matters 1 πΏπ ∼ πΏπ ∼ π π ∼ π0.5 π Constraints from ππΎ is the strongest because decoupling feature is weak. π0.5 1 π0.5 π π0.5 1 0 0 FCNC constraints from πΎ − πΎ mixing(ππΎ ) Ciuchini et al. (1998) mass insertion parameter in this model π ∼ 0.22 average down type squark mass : ππ :constraint from π¦= :constraint from π₯= Result 1 When ππ = 10 TeV π₯ ∼ π¦ ∼ 0.1 = D-term can be 1 TeV! signature of πΈ6 × ππ 2 πΉ × π 1 π΄ SUSY GUT model in future experiments (100 TeV proton collider or muon collider) 5th Summary ο΅ Gravitino mass π3/2 = O(100) TeV ο΅ to solve the cosmological gravitino problem The other SUSY breaking parameters = O(1) TeV for the naturalness The little hierarchy problem can be less severe. O(%) tuning is realized. Point: anomaly mediation cancels the RG contribution. π΄π‘ can be larger without changing βππ»π’ 2 If ππππ ~ O(TeV), we may observe directly the GUT signatures through the mass spectrum of the other sfermions than stops. (ex. D-term contributions of GUT.) ο΅ Natural SUSY type sfermion masses may be directly observed. 2 2 2 2 π10,2 − π10,1 = π5,3 − π5,1 ο΅ An important prediction ο΅ D term can be 1 TeV! (ππΎ ) Summary ο΅ GUT is promising Experimental supports for two unifications ο΅ πΈ6 GUT is interesting An assumption in ππ(5) GUT can be derived. Various Yukawa hierarchies in SM can be obtained from one hierarchy. ο΅ +Family symmetry Unification of three generation quark and leptons with realistic Yukawa SUSY flavor problem is solved (Natural SUSY type sfermion masses) ο΅ +Spontaneous CP violation Origin of KM phase can be understand SUSY CP problem is solved. (Even CEDM constraints can be satisfied.) ο΅ Natural (anomalous U(1)) GUT The doublet-triplet splitting problem is solved under natural assumption. Summary ο΅ Predictions Observed π13 ∼ π, (πΏ ∼ π 1 , ππ’π ∼ π4 ) Not yet Nucleon decay Sfermion mass spectrum (Natural SUSY type) D-term contribution can be a smoking gun. 2 2 2 2 π10,2 − π10,1 = π5,3 − π5,1 Signatures for future flavor experiments? ο΅ Future works Cosmology (Inflation, DM, Baryogenesis etc) More predictions Issues (generic int., gauge coupling unif. etc)
