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

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Outline


Motivation: µ Problem



Theoretical Background about U’(1) Models
Neutralino and Chargino sector in U’(1) Models





Numerical Analysis

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The superpotential of the MSSM is defined as

Yukawa couplings (Dimensionless parameters)

(Dimensionful parameter)
What is the scale of this mass 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 (MPL) )

SOLUTION: U(1)’ MODELS
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SU(3)XSU(2)XU(1)XU(1)’




eff  hs S

Along with U(1)’ we introduce a new SM-singlet chiral superfield whose VEV can generate an effective μ upon spontenous U(1)’ breakdown.

O(<S>)~ TeV

Dimensionless
U(1)’ model = MSSM + singlet chiral superfield S + extra U(1) gauge symmetry

U(1)’ Model



New gauge boson Z’
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MSSM
adds new gauge boson and its gaugino to the spectrum

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

New gauge singlet field coming from U(1)’ model
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There are various sources of U(1)’ models : *Grand Unified Theories *Extra dimensions Grand Unified Theories *Little Higgs Models E6 *String Theories

SO(10) x U(1)
U(1)’ is the combination of  and  symmetries

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 specific models;


U(1)’

0
U(1)

-/2
U(1)

ArcSin[1]
U(1)

ArcSin[2]
U(1)I

1 = (3/8)1/2

2 = -(5/8)1/2

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Charge Assignment
ψ, η , , N models come from E(6) GUT and S model comes from the string theory
Common gauge coupling constant

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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.
After the kinetic mixing the gauge part of the lagrangian becomes

With the presence of kinetic mixing the derivative becomes

part of covariant

= the field strength tensor
Sinχ = the kinetic mixing angle
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Features of Models
The most general holomorphic case of soft breaking terms then becomes

Additional terms coming from U(1)’

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 M1 (bino) and the rest are real.

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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)’

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Neutralino Sector
The EDM of additional neutralino mass eigenstates due to new higgsino The spin ½ particles can be defined as

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

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 μeff

The fermion EDMs through fermion-sfermion-chargino interactions are given by

eEDM and nEDM
Total EDM of electron (eEDM) is sum of the one loop diagrams with neutralino and chargino exchanges

For nEDM, we need to add 1-loop gluino exchange contribution and 3 other contributions coming from quark chromoelectric dipole moments of quarks

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Contributions from chargino exchange

From neutralino exchange

EDM for quark-squark-gluino interaction

Contributions arising from quark chromoelectric dipole moment of quarks
1 Im(q k )  0

If all the parameters but M1 are real

Contribution coming from 2-loop gluino-top-stop diagram
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The strongest constraints arise from the mixing mass term between the Zand Z’

Mixing angle between Z and Z’ is

Phenomenological constraints (from LEPII and neutral weak current data )

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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.

During the analysis we rescept the collider bounds for mh , msfermions , mcharginos and Mz’

The Z-Z’ mixing angle is taken less than 3 x 10-3

A. Hayreter, A. Sabanci,L.Solmaz, S. Solmaz

Phys. Rev. D78: 055011 (2008)
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The phase of M1 versus EDM’s
Gray crosses ▲

U(1)’ MSSM

tanβ=3 and all sfermion masses are scanned 0.5 to 1 TeV. The EDM’s are given in log10 base.

For S and I models eEDm predictions are well below the MSSM predictions

Phys. Rev. D78: 055011 (2008)

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EDM’s versus the argument of M1
Dark triangles N model Gray crosses  MSSM

0≤MYX≤0.5 TeV

0≤MYX≤0.5 TeV
tanβ= 5, msleptons=500 GeV, msquarks =750 GeV

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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.

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If a charged particle is moving through the electric and magnetic fields, The Interaction Energy is given as:

     B  S  dE  S
μ = Magnetic 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.

  BS

d = Electric Dipole Moment

BUT ?
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Dipole moments of Particles
    P( E  S )   E  S

    T (E  S )  E  S
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
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Dipole Moments of Particles

0

Respects C,P, T symmetries

CP conserving

d 0

Violate P, T symmetry and respects Charge symmetry CP Violating Case

That is why, determining the electric dipole moment has grabbed the scientists’ attention.
Measurement of electric dipole moments can say a lot about strength and sources of CP violation
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Dipole moments of Particles
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 i.e dipole moments

d neutron  1026 e.cm d electron  1.6 x1027 e.cm

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Predictions in theories beyond the SM

The SM edm predictions are vanishingly small

If we have reasonably large values of the electric dipole moments It would be clear evidence of the new physics beyond the SM !!!!!

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• 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. )

In this sense, We have analysed both electron and neutron EDM in MSSM and U(1)’ models

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In this figure, •It is seen that with increasing μeff eEDm predictions start to raise from S to η models. •Moreover, for large value of μeff eEDM predictions seem to bound μ term in η and ψ models.

• In right panels , with increasing μeff the nEDM decreases from S to η models.
Phys. Rev. D78: 055011 (2008)

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