1. 1 Aslı Sabancı University of Helsinki and Helsinki Insititute of Physics (HIP) Electric Dipole Moments in U(1)’ Models DESY Theory Workshop (Collider Phenomenology) 2009

2. 2  Motivation: µ Problem  Theoretical Background about U’(1) Models  Neutralino and Chargino sector in U’(1) Models  Numerical Analysis

3. 3 μ Problem The superpotential of the MSSM is defined as Yukawa couplings (Dimensionless parameters) What is the scale of this mass parameter ???? (Dimensionful parameter) The µ parameter has a mass dimension but supersymmetry does not explain why it must be order of TeV not a higher scale (Planck scale (M PL ) ) SOLUTION: U(1)’ MODELS

4. 4 U(1)’ Model Along with U(1)’ we introduce a new SM-singlet chiral superfield whose VEV can generate an effective μ upon spontenous U(1)’ breakdown. Dimensionless U(1)’ model = MSSM + singlet chiral superfield S + extra U(1) gauge symmetry O( )~ TeV U(1)’ Model New gauge boson Z’ SU(3)XSU(2)XU(1)XU(1)’

5. 5 U(1)’ Model MSSM New gauge singlet field coming from U(1)’ model We enlarge the MSSM by adding new gauge group and this group lead to new charges that are unknown and vary for different U(1)’ Models adds new gauge boson and its gaugino to the spectrum

6. 6 U(1)’ Model There are various sources of U(1)’ models : *Grand Unified Theories *Extra dimensions *Little Higgs Models *String Theories Grand Unified Theories E6 SO(10) x U(1)  SU(5) x U(1)  x U(1)  SU(3)xSU(2)xU(1)x U(1)’ U(1)’ = Cos(  ) U(1)  - Sin(  ) U(1)  Some spec ific models;  0-  /2ArcSin[  1 ]ArcSin[  2 ] U(1)’U(1)  U(1)  U(1)  U(1) I  1 = (3/8) 1/2  2 = -(5/8) 1/2 U(1)’ is the combination of  and  symmetries

7. 7 Well Known U(1)’ Models Common gauge coupling constant ψ, η, , N models come from E(6) GUT and S model comes from the string theory Charge Assignment

8. 8 Features of Models After the kinetic mixing the gauge part of the lagrangian becomes = the field strength tensor Sinχ = the kinetic mixing angle With the presence of kinetic mixing the part of covariant derivative becomes Since the field strength tensor itself is invariant under the gauge transformations, in theories involving more than one U(1) factor, the kinetic terms can mix.

9. 9 Features of Models The most general holomorphic case of soft breaking terms then becomes In general all trilinear couplings, gaugino masses can be the source of CP violation. For simplicity and definiteness, in our study, we assume that all CP violating effects are confined into the gaugino mass M 1 (bino) and the rest are real. Additional terms coming from U(1)’

10. 10 Neutralino Sector In U(1)’ models the neutralino sector of the MSSM is enlarged by “Singlino” and “Z’ino or B’ino” (supersymmetric partners of S field and Z’ boson) 6X6 Neutralino Mass matrix in a basis of MSSM U(1)’

11. Neutralino Sector The additional neutralino mass eigenstates due to new higgsino and gaugino fields encode effects of U(1)’ models Moreover we can see the effects of these contributions in the neutralino-sfermion exchanges that contribute to EDMs of both quarks and leptons Where the neutralino vertex is given as The EDM of spin ½ particles can be defined as

12. Unlike the Neutralino Sector, the Chargino sector does not have any additional gaugino or higgsino fields its structure remains the same as in the MSSM. However chargino mass eigenstates become dependent on U(1)’ through μ eff The fermion EDMs through fermion-sfermion-chargino interactions are given by

13. 13 Total EDM of electron (eEDM) is sum of the one loop diagrams with neutralino and chargino exchanges eEDM and nEDM For nEDM, we need to add 1-loop gluino exchange contribution and 3 other contributions coming from quark chromoelectric dipole moments of quarks

14. 14 nEDM Contributions from chargino exchange Contribution coming from 2-loop gluino-top-stop diagram Contributions arising from quark chromoelectric dipole moment of quarks EDM for quark-squark-gluino interaction If all the parameters but are real From neutralino exchange

15. 15 Constraints for EDMs Mixing angle between Z and Z’ is Phenomenological constraints (from LEPII and neutral weak current data ) The strongest constraints arise from the mixing mass term between the Zand Z’

16. 16 For simplicity, in our analysis we take into account just one CP-odd phase corresponding to complex bino (and bino-prime) mass and rest of parameters are real quantities. Numerical Analysis During the analysis we rescept the collider bounds for m h, m sfermions, m charginos and M z ’ The Z-Z ’ mixing angle is taken less than 3 x 10 -3 Phys. Rev. D78: 055011 (2008) A. Hayreter, A. Sabanci,L.Solmaz, S. Solmaz

17. 17 Phys. Rev. D78: 055011 (2008) MSSM ▲ U(1)’ Gray crosses The phase of M 1 versus EDM’s For S and I models eEDm predictions are well below the MSSM predictions tanβ=3 and all sfermion masses are scanned 0.5 to 1 TeV. The EDM’s are given in log 10 base.

18. 18 Dark triangles  N model Gray crosses  MSSM 0≤M YX ≤0.5 TeV tanβ= 5, m sleptons =500 GeV, m squarks =750 GeV EDM’s versus the argument of M 1

19. 19 tanβ versus EDMs tanβ is scanned up 10 and most striking difference between the MSSM and U(1)’ models that tanβ can be as small as 0.5 Which is ruled out for the MSSM. For most of the models eEDM and nEDM Predictions decrease with decreasing tanβ as in the MSSM.

20. 20 Thank You

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23. 23 Dipole moments of Particles If a charged particle is moving through the electric and magnetic fields, The Interaction Energy is given as: μ = Magnetic Dipole Moment d = Electric Dipole Moment Magnetic dipole interaction respects all the continuous and discrete symmetry of the nature. Its existence does not lead to Parity (P) and Time (T) violations. BUT ?

24. 24 Dipole moments of Particles The sign of electric dipole interaction is changed both time and space reversal. This means that the existence of this interaction breaks both T and P symmetry of nature. RESPECT CPT T odd  CP odd

25. 25 Respects C,P, T symmetries CP conserving Violate P, T symmetry and respects Charge symmetry CP Violating Case That is why, determining the electric dipole moment has grabbed the scientists’ attention. Dipole Moments of Particles Measurement of electric dipole moments can say a lot about strength and sources of CP violation

26. 26 Electron, neutron, muon, thallium… can have non-zero electric dipole moment and it is necessary to analyse in different theories. We have the experimental upper limits of these electric dipole moments i.e Dipole moments of Particles

27. 27 If we have reasonably large values of the electric dipole moments It would be clear evidence of the new physics beyond the SM !!!!! Predictions in theories beyond the SM The SM edm predictions are vanishingly small

28. 28 In this sense, We have analysed both electron and neutron EDM in MSSM and U(1)’ models Large value of electric dipole moments are the evidence of the existence of the new pyhsics beyond the Standard Model (SM) These SM extended theories are needed to explain the baryogenesis (because the phase in the SM is not sufficient to explain the huge difference between the amount of matter and antimatter in the universe. ) Importance of edm’s

29. 29 In this figure, It is seen that with increasing μ eff eEDm predictions start to raise from S to η models. Moreover, for large value of μ eff eEDM predictions seem to bound μ term in η and ψ models. In right panels, with increasing μ eff the nEDM decreases from S to η models. μ eff versus EDMs Phys. Rev. D78: 055011 (2008)