Low-Energy Precision Tests of Supersymmetric Models -- Proton decay & EDMs -- Junji Hisano (ICRR, Univ. of Tokyo) Supersymmetry in 2010's June 20 (Wed.) -22 (Fri.), 2007 Conference Hall, Hokkaido University, Sapporo

SM works well to explain phenomena at low energy, but it has many mysteries. What can we solve or understand better when SUSY is discovered at LHC? Section 0 Introduction Hierarchy problem Three gauge groups Dark matter Three generations and origin of flavor violation Strong CP and EDMs Proton stability and baryogensis. Origin of neutrino masses

SM works well to explain phenomena at low energy, but it has many mysteries. What can we solve or understand when SUSY is discovered at LHC? SUSY is a Pandora’s box New Flavor/CP/Baryon #/Lepton # violation sources can be introduced in SUSY. They are rather lower dimensional operators than in SM. Section 0 Introduction Hierarchy problem Three gauge groups Dark matter Three generations and origin of flavor violation Strong CP and EDMs Proton stability and baryogensis. Origin of neutrino masses We may get a clue. Mysteries become more mysterious. Precision tests play important roles in frontier to physics beyond SUSY SM.

Contents of My talk Sec. 0: Introduction Sec. 1: Review of proton decay in SUSY models Sec. 2: Review of EDMs in SUSY models Sec. 3: Summary Sorry for low coherence of my talk…

Section 1 Proton Decay in SUSY Models

After SuperK started on 96’, bounds on every modes are improved by a factor of ~10. (Thanks to Shiozawa-san) Further improvements of a factor of 10 require Mton-class detectors, such as HuperK, UNO, MEMPHYS, etc. (Talk by Nakamura-san) But, we have to know more precise proton lifetime predicted in models before them. Current status of proton decay search Baryon # violating operators in SM are automatically suppressed, since the lowest operators are dim-six. (B-L) is conserved automatically in them.

Lattice simulation of hadron matrix elements Traditionally, chiral perturbation theory is used, and  and  are evaluated by QCD models or Lattice QCD. Latest Lattice QCD by RBC collabo. (hep-lat/ ) Domain-wall fermion NP renormalization Dynamical fermions (Nf=2) They found. It is consistent with continuum limit of CP-PACS& JLQCD (04). (From Y.Aoki et al, 06’) For proton to pion processes, we need to evaluate,

Direct v.s. indirect evaluation of hadron matrix elements Soft pion limit is taken in chiral perturbation theory, while meson momentum in final state is half of proton mass. (Y.Aoki et al, 06’) RBC collabo. compares two evaluations in various processes. Direct evaluation by lattice Indirect evaluation using Ch-P. Difference of a factor ~2 is observed. Now systematic errors seem to be under control, and the difference should be taken to be serious.

Baryon # operators in SUSY models D=6 operators In GUTs, (extra) X gauge boson generates D=6 operators. D=5 operators in SUSY models In SUSY GUTs, colored Higgs, SU(5) partner of Higgs doublet, generates D=5 operators.. D=4 operators in SUSY models Forbidden by R parity Related to stability of LSP DM.

Proton decay & R party violation When L and B are violating, the coupling is severely constrained from proton decay. But, quantum gravity might violate it. Anomaly-free discrete gauge symmetry. (Ibanez&Ross) Ex. R parity comes from U(1) B-L gauge symmetry. R parity might be partially broken in only lepton or baryon. In the case, gravitino LSP might be a DM candidate. When B is violating but, gravitino is almost stable. Proton decay is possible, Some anomaly-free discrete gauge symmetries are systematically studied. It is found that D=4 and 5 B operators are forbidden by a symmetry. (Dreiner et al, 05) (K.Choi et al, 96’)

Proton decay induced by D=5 operators Dressing D=5 operators induces proton decay with dressing. When squark masses are degenerate, charged Wino or Higgsino exchange is dominant. SUSY spectrum measurement at LHC or LC reduces large theoretical uncertainties. Typically, from null results. D=5 operators depend on detail of underlying physics since symmetries can suppress them. Ex.

In Minimal SUSY SU(5) GUT, colored Higgs, SU(5) partner of Higgs doublet, generates D=5 operators. Proton decay is suppressed by light fermion masses. But, from null result Improvement of a factor 30 reaches to reduced Planck scale. Upperbound on MHc in Minimal model. Produced from Nihei-Goto (98). Now Planck scale physics can be constrained. Ex. U(1) flavor symmetry controls Yukawa and D=5 operators. (Harnik et al, 04’) where.

Proton decay induced by D=6 operators D=6 proton decay is predicted in almost grand unified models. One of exceptions is some orbifold GUTs, in which quarks and leptons are not unified. Proton lifetime is sensitive to precise value of  since Theoretical evaluation of  is quite important. In SUSY SU(5) GUT, X gauge boson generates D=6 proton decay. We need to know physics between GUT and weak scale to predict proton decay. Ex. Low-energy gauge-mediation model. Gauge coupling at GUT scale depends on matter contents below the GUT scale. # of messenger in GMSB(JH, 00’)

Summary (Proton decay) Proton stability is more mysterious in SUSY models than in SM. Proton decay is induced by lower dimensional operators, and it may be related with DM in the universe. Ten years have passed after SK started, but null result. We have to evaluate proton lifetime predicted in models more precisely. Lattice simulation for hadron matrix elements are working well to reduce the systematic errors. Precise determination of the model parameters of SUSY SM is also important to reduce systematic errors in prediction, especially, D=5 proton decay.

Section 2 EDMs in SUSY models

Current status of EDM measurements and future Electric Dipole moments: T and P-odd. They are sensitive to CP violation. Current experimental bounds on EDMs : Paramagnetic atom (Tl) : Diamagnetic atom (Hg): Neutron: (Schiff theorem: Atomic EDMs vanish in NR and point-like nucleus limits.) → CP in nuclear force → SM prediction: CKM phase is unique CP source. Electron EDM: (four-loop) (three-loop) Neutron EDM: (long-distance effect) EDMs are sensitive to CP in models beyond SM.

Future prospects for EDM measurements: Electron EDM: Polarized Molecule: large enhancement factor YbF(Imperial College) and PbO (Yale) in a few yrs. Neutron EDM: Cryogenic UCN. ILL: Construction started. in a few yrs, and after beamline upgraded. SNS: Planed. Prospect is. Charged particle EDM: Strong motional E field for relativistic particles in B field. Measure of tilt of spin precession plane in E field. Prospects: muon EDM, deuteron EDM, H, 2H, and 3H EDM measurements, in addition to neutron one, will make anatomic studies of hadronic EDMs possible. (From Czarnecki at LEPT06)

CP-violating effective operators up dim 6 at parton level QCD theta (NF) EDM CEDM (NF) Weinberg op (NF) 4 fermi (NF/EN) NF: contribution to EDM via nuclear force. EN: contribution via interaction between electron and nucleus. (From Onderwateri at LEPT06) Hadronic EDM evaluation is a difficult task. Neutron EDM evaluation method. NR SU(6) quark model, Chiral lagrangian method, QCD sum rule, lattice. Issues in sea-quark contribution, strange quark contribution and so on. Strong CP problem. EDM prediction depends on presence of axion. Hadronic EDM prediction suffers from uncertainties of O(1) at present. Evaluation of EDMs

EDMs in MSSM and SUSY CP problem MSSM has many CP parameters in SUSY breaking terms. F term SUSY breakings are complex. Gaugino massB massA mass Physical phases in MSUGRA convention, From electron EDM From neutron EDM SUSY CP problem: phases should be suppressed by less than ~1% or SUSY particle mass are larger than ~10TeV. A term contribution is suppressed when A~0, however, B term contribution is enhanced when B~0, since tan  1 

How to suppress EDMs F-term SUSY breakings are real. Ex. Dilaton mediation. Radiative CP phases in supergravity theories. (Endo et al,04’) A and B terms are zero at boundary condition (tree level) They are radiatively generated from gaugino masses. Highly predictive and large tan   Minimal gauge mediation model.  Current values of muon g-2 and b→s  favor low messenger scale (~100TeV) and gluino mass~1TeV. Gaugino mass: ←Anomaly mediation Future EDM measurements give a clue of the sub-leading contribution. (JH&Shimizu,07’)

1st generation sfermions are superheavy. When some SUSY particles stay at weak scale, EDMs still give constraints on model. SUSY particles are coupled with H1 and H2. The Higgs coupling with gauge fields are generated from their loops. Two-loop contribution is suppressed by at most loop factors. When tan  is large, model is constrained. (Chang et al, 99’) Stop/sbottom loop contribution to EDMs

Physical phases are removed by extra fields. One-loop contributions to EDMs are proportional to Majorana gaugino masses. Dirac gauginos suppress EDMs. U(1) D term SUSY breaking generates them. → U(1)-R breaking generates Sigma mass term and Majorana gaugino mass term so that EDMs are generated. Models in which EDMs are suppressed have some specific features in spectrum or model parameters. Those models predict non-vanishing EDMs to be measure in future. If model is determined by experiments, it would be possible to predict more reliable values for EDMs.

Non-minimal flavor violation and EDMs In SM a phase in CKM is unique origin of CP violation. Quark EDMs are proportional to generation-diagonal Jarlskog invariants as where. This impliesat. Yukawa coupling Non-minimal flavor violation enhances EDMs. New Jarskog invariants involving flavor violation in squark or slepton mass terms contribute to EDMs. Mass insertion parameters:

SUSY GUTs favor nonzero Gluino contributes to EDMs at one-loop level and they are enhanced by heavy quark masses. (Here, we assume max phase.) and. and or and Charged Higgsino generates EDMs at one-loop level. In minimal flavor violation, these vanish. or No one-loop contribution. But, two-loop contribution by charged Higgs can be comparable to above one-loop one. This is non-decoupling due to anomalous coupling of charged Higgs even if SUSY scale is high. (JH, Nagai, Paradisi)

Hadronic flavor violation and EDMs Flavor mixing in squark sector is constrained from K/D/Bd/Bs meson mixing. When both left- and right-handed squarks have mixing, where. Neutron (Hg) EDM also gives constraints as up quark down quark where and. EDMs work well to give constraints except for 1-2 mixing. strange quark

(JH, Kakizaki, Nagai, Shimizu) Neutron deuteron strange quark CEDM down quark CEDM ×1/2 (current bound) SUSY GUT with right-handed neutrinos Quarks and leptons are unified. In MUGRA case, CKM mixing → LH squark & RH slepton mixing Neutrino mixing → LH slepton & RH down squark mixing Rich (non-minimal) flavor structure is predicted in the SUSY breaking. Future neutron and deuteron EDM measurements will give big impacts on this model.

Summary (EDMs) SUSY models, in which EDMs are suppressed, have some specific features in spectrum or model parameters. Many of those models predict non-vanishing EDMs to be measure in future. If model is determined by experiments, it would be possible to predict reliable values for EDMs. We have prospects on improvements of neutron and electron EDMs in near future due to experimentalists’ efforts. And, measurements of charged particles, such as proton, deuteron and triton, give a change an anatomic studies of EDMs. EDMs also give constraints on flavor violation in SUSY breaking terms. But, when non-zero EDMs are measured, we cannot identify the origin. In that case, experimental studies of the FCNC processes and also more serious studies of the hadronic systems would be important.

Sec. 3: Summary Proton decay Proton stability is more mysterious in SUSY models than in SM. Proton decay is induced by lower dimensional operators, and it may be related with DM in the universe. Ten years have passed after SK started, but null result. We have to evaluate proton lifetime predicted in models precisely. Lattice simulation for hadron matrix elements are working well to reduce the systematic errors. Precise determination of the model parameters of SUSY SM is also important to reduce systematic errors in prediction, especially, D=5 proton decay. EDMs SUSY models in which EDMs are suppressed have some specific features in spectrum or model parameters. Those models predict non-vanishing EDMs to be measure in future. If model is determined by experiments, it would be possible to predict reliable values for EDMs. We have good prospects on improvements of neutron and electron EDMs in near future due to experimentalists’ efforts. And, measurements of charged particles, such as proton, deuteron and triton, give a change an anatomic studies of EDMs. EDMs also give constraints on flavor violation in SUSY breaking terms. But, when non-zero EDMs are measured, we cannot identify the origin. In that case, experimental studies of the FCNC processes and also more serious studies of the hadronic systems would be important.

Backup

Notation: Mass insertion parameters Yukawa coupling Ratio of Higgs vevs, for Here, is averaged value. (Yukawa unification)

Only charged Higgsino contributes to them at one-loop level,then. In minimal flavor violation, and the EDMs vanish. (max phase) or One-loop contribution is absent. ( ) Future EDM measurements might cover it.

Higgs mediation contribution at two-loop level in a case of Charged Higgs coupling: Radiative correction to down quark mass matrix This is not decoupled even in Where. Charged Higgs contributes to EDMs. Right-handed down coupling is enhanced by heavy quark mass. (JH, Nagai, Paradisi)

Higgs mediation contribution at two-loop level in a case of (cont.) Charged Higgs contribution is already constrained from EDMs. This may dominate over 1-loop (gluino) contribution for SUSY parameter dependence is almost cancelled out in ratio of the gluino and charged Higgs loops, and the ratio is sensitive to only. It is more smoothly decoupled for heavy charged Higgs mass.

Leptonic EDM induced by flavor violation Sources of flavor violation: and. New Jarskog invariants: Bino contributes to them at one-loop level and EDM is ehnanced by heavy lepton mass. (max phase) Models has been already constrained from current EDM bound. Charged Higgs contribution is not present. Neutral Higgs might contribute to EDM for large..

3, Hadronic EDMs in SUSY GUTs and FCNCs Let us adopt flavor violation motivated by SUSY GUTs as working hypothesis. In MSSM with right-handed neutrinos, (top quark Yukawa with CKM) (neutrino Yukawa) Colored Higgs, which is SU(5) partner of SU(2) Higgs, induces right-handed mixing. (top quark Yukawa with CKM) (neutrino Yukawa) (bottom quark Yukawa with CKM) Under some assumptions neutrino sector, and

In Split SUSY model, only fermionic SUSY particles have weak-scale masses, and bosonic ones are superheavy. Even in this case, sizable EDMs are predicted. CP phases come from chargino and neutralino mass matrixes. (Giudice and Romanino,05’)