# Presentation: 369137

## Probing new CP-odd thresholds with EDMs

- Adam Ritz
- University of Victoria
- Based on work with:
- M. Pospelov,
- S. Huber & Y. Santoso
- [For a review, see hep-ph/0504231]

## Precision Tests as Probes for New Physics

- Precision searches for new physics (at energy scale ):

- Especially powerful for tests of “_*symmetries*_*” *of the SM: e.g. Baryon no., Lepton no., Flavour, T (or CP), etc.

- _e.g: lepton number violation and neutrino mass_

- The Standard Model (above the EW scale) allows a _*single*_ dimension five operator:

- data   ≈ 1011 - 1015 GeV

## Probing the Higgs Sector

## Higgs and CP-violation

- In a complementary way, we can also use precision probes of the couplings

*f**R*

- h

- YfSM + ...

- In particular, we can efficiently probe the CP structure of the (chirality changing) vertex

*f**L*

## Higgs and CP-violation

- With a convenient choice of basis we can associate all SM CP-violation with Yukawa couplings

- [Jarlskog ‘85]

-  Experimentally KM ~ O(1), and consistently explains CP-     violation in K and B meson mixing and decays

-  Experimentally,  < 10-9 ! (strong CP problem)

- Do we anticipate other CP-odd sources ?

## CP-violation and EDMs

- sensitivity through EDMs of neutrons, and para - and       dia-magnetic atoms and molecules (violate T,P)

- _

- Look for CP-violation in flavour diagonal channels, with small SM bkgd

- Within the SM, CP-violation is hidden behind the flavour structure

-  Baryogenesis requires extra CP-violation
-  Most “UV completions” of the SM (e.g. MSSM)  provide additional sources of CP-violation

- YES

- Currently, all experimental data   EDMs vanish to very _high precision_ thus leading to very strong constraints on new physics.

- 

## Outline of the Talk

- Current status of the EDM bounds
- A review of (hadronic) EDM calculations
- EDMs vs supersymmetry
- 		— Review of the (current) SUSY CP problem
- 		— Constraints on new CP-odd thresholds
- EDMs vs baryogenesis
- Concluding remarks

## Measurement

-  Measure Larmor precession frequency in (anti-)aligned E and B fields

**Notes:**
\hbar \omega_L^1 = 2\mu \cdot B + 2 d \cdot E

d = \frac{\hbar}{4 E} (\omega_L^1 - \omega_L^2), \;\;\;\;\;\;\;
\sigma_d \sim \frac{\hbar S}{ET\sqrt{N}}

## Experimental Bounds on the neutron EDM

- Oak Ridge, ILL & PSI

- Log(*d*n)

- [*e* cm]

## Experimental Status

| Neutron EDM |  |    [Baker et al. ‘06]    |
| --- | --- | --- |
| Thallium EDM (paramagnetic) |  |    [Regan et al. ‘02] |
| Mercury EDM (diamagnetic) |  |  [Romalis et al. ‘00] |

- There are ~10 new experiments
- (either operating or in development)
- gain in sensitivity for each channel

- (optimistically) 

**Notes:**
|d_n| < 6 \times 10^{-26} e\ {\rm cm}
|d_{Tl}| < 9 \times 10^{-25} e\ {\rm cm}
|d_{Hg}| < 2 \times 10^{-28} e\ {\rm cm} 
d_n \sim 10^{-32} - 10^{-34} e\ {\rm cm}

## Experimental Status

_*Small*_ SM background (via CKM phase)

- [Khriplovich & Zhitnitsky ‘86]

- EG: for the neutron EDM

**Notes:**
|d_n| < 6 \times 10^{-26} e\ {\rm cm}
|d_{Tl}| < 9 \times 10^{-25} e\ {\rm cm}
|d_{Hg}| < 2 \times 10^{-28} e\ {\rm cm} 
d_n \sim 10^{-32} - 10^{-34} e\ {\rm cm}

## Classification of CP-odd operators at 1GeV

- _Dimension 4_:

- _Dimension “6”_:

- _Dimension “8”_:

- Effective field theory is used to provide a model-independent parametrization of CP-violating operators at 1GeV

**Notes:**
{\mathcal L} = \sum_i \frac{c_i}{M^{d-4}} {\mathcal O}_d^{(i)}

\bar{\theta} \alpha_s G\tilde{G}

\sum_{q=u,d,s} d_q \bar{q} F\sigma\gamma_5 q + \sum_{q=u,d,s}\tilde{d}_q \bar{q}G\sigma\gamma_5 q + d_e \bar{e} F\sigma\gamma_5 e + w g_s^3 GG\tilde{G}

\sum_{q=u,d,s} C_{qq} \bar{q} q \bar{q} i\gamma_5 q + C_{qe} \bar{q} q \bar{e} i\gamma_5 e

\bar{\theta} = \theta_0 + {\rm Arg Det}(M_q)

## Classification of CP-odd operators at 1GeV

- _Dimension 4_:

- _Dimension “6”_:

- _Dimension “8”_:

- Effective field theory is used to provide a model-independent parametrization of CP-violating operators at 1GeV

**Notes:**
{\mathcal L} = \sum_i \frac{c_i}{M^{d-4}} {\mathcal O}_d^{(i)}

\bar{\theta} \alpha_s G\tilde{G}

\sum_{q=u,d,s} d_q \bar{q} F\sigma\gamma_5 q + \sum_{q=u,d,s}\tilde{d}_q \bar{q}G\sigma\gamma_5 q + d_e \bar{e} F\sigma\gamma_5 e + w g_s^3 GG\tilde{G}

\sum_{q=u,d,s} C_{qq} \bar{q} q \bar{q} i\gamma_5 q + C_{qe} \bar{q} q \bar{e} i\gamma_5 e

\bar{\theta} = \theta_0 + {\rm Arg Det}(M_q)

## Origin of the EDMs

- TeV

- Energy

- QCD

- nuclear

- atomic

- pion-nucleon coupling (         )

- EDMs of paramagnetic atoms (      )

- EDMs of diamagnetic  atoms (       )

- Neutron EDM (    )

## Origin of the EDMs

- TeV

- Energy

- QCD

- nuclear

- atomic

- EDMs of paramagnetic molecules
-  (YbF, PbO, HfF+)
- Atoms in traps (Rb,Cs)

- EDMs of diamagnetic atoms (Hg,Xe,Ra,Rn)

- Neutron EDM (    )

- EDMs of nuclei and ions   (deuteron, etc)

## Next-generation Experiments

- TeV

- Energy

- QCD

- nuclear

- atomic

- EDMs of paramagnetic molecules
-  (YbF, PbO, HfF+)
- Atoms in traps (Rb,Cs)

- EDMs of diamagnetic atoms (Hg,Xe,Ra,Rn)

- Neutron EDM (    )

- EDMs of nuclei and ions  atoms (deuteron, etc)

- Deuteron EDM @ BNL !

## Calculating the EDMs - Tl

- _1. Tl EDM_ (paramagnetic)

- [Salpeter ‘58; Sandars ‘65]

- relativistic violation of Schiff thm

- arises from

- [Bouchiat ‘75; Khatsymovsky et al. ‘86]

- [Liu & Kelly ‘92]

**Notes:**
\alpha^2 Z^3 \vec{E}

d_{Tl}\ \sim\ -10\,alpha^2 Z^3 d_e(1\ {\rm GeV})- e \sum_{q=d,s,b} C_{qe}(1\ {\rm GeV}) \frac{2\ {\rm GeV}^2}{m_q}

## Future - e.g. paramagnetic molecules

- e.g. YbF, PbO

- [Kozlov et al.]

- [Hinds; DeMille]

**Notes:**
\alpha^2 Z^3 \vec{E}

d_{Tl}\ \sim\ -10\,alpha^2 Z^3 d_e(1\ {\rm GeV})- e \sum_{q=d,s,b} C_{qe}(1\ {\rm GeV}) \frac{2\ {\rm GeV}^2}{m_q}

## Calculating the EDMs - n

- _2. neutron EDM_

-  Chiral Logarithm:  [Crewther, Di Vecchia, Veneziano & Witten ‘79]

- [also Baluni ‘79]

**Notes:**
d_n(\theta) = c_1 \ln \frac{\Lambda}{m_\pi} + c_2

## Calculating the EDMs - n

- _2. neutron EDM_

-  QCD Sum Rules:  [Pospelov & AR ‘99-’00, Chan & Henley ‘99]

- — Neutron current:
- — Correlator:

**Notes:**
\int d^4 x e^{ip\cdot x} \langle \bar{j}_n(x), j_n(0) \rangle_{\,\slash \!\!\!\!\!\! {\rm CP}, F} = \Pi_0(p) + \Pi_1^{\mu\nu}(p)F_{\mu\nu}+\cdots

j_n \sim d^T C\gamma_5 u d

\Pi_1(p,\theta,d_q,\tilde{d}_q) \cdot F \sim \frac{d_n \lambda^2 m_n}{(p^2-m_n^2)^2}\{F\sigma\gamma_5,\slash\!\!\!\!\!p\}+\cdots

## Calculating the EDMs - n

- _2. neutron EDM_

-  QCD Sum Rules:  [Pospelov & AR ‘99-’00, Chan & Henley ‘99]

- — Neutron current:
- — Correlator:

**Notes:**
\int d^4 x e^{ip\cdot x} \langle \bar{j}_n(x), j_n(0) \rangle_{\,\slash \!\!\!\!\!\! {\rm CP}, F} = \Pi_0(p) + \Pi_1^{\mu\nu}(p)F_{\mu\nu}+\cdots

j_n \sim d^T C\gamma_5 u d

\Pi_1(p,\theta,d_q,\tilde{d}_q) \cdot F \sim \frac{d_n \lambda^2 m_n}{(p^2-m_n^2)^2}\{F\sigma\gamma_5,\slash\!\!\!\!\!p\}+\cdots

## Calculating the EDMs - n

- _2. neutron EDM_

-  QCD Sum Rules: _Results_

- — Important condensates:

- [Pospelov & AR ‘99,’00]

- Sensitive only to ratios of light quark masses

- NB: PQ axion used to remove

- Future developments: dn() in LQCD

- [Berruto et al; Shintani et al.]

**Notes:**
\langle \bar{q} \sigma_{\mu\nu} q\rangle_F = \chi e_q F_{\mu\nu}\langle \bar{q}q\rangle

\langle \bar{q} G\sigma q\rangle = -m_0^2\langle \bar{q}q\rangle

d_n = (0.4\pm 0.2) \frac{|\langle \bar{q}q\rangle|}{(225\ {\rm MeV})^3} \left[ 4d_d-d_u + \frac{1}{2}\chi m_0^2 (4 e_d \tilde{d}_d - e_u \tilde{d}_u)+\cdots\right] +{\mathcal O}(d_s,w,C_{qq})

## Calculating the EDMs - Hg

- _3. Hg EDM_ (diamagnetic)

- charge distribution

- nuclear EDM

- [Schiff ‘63]

**Notes:**
V \sim - e S (J \cdot \nabla)\delta(r)

d_{Hg} \sim -3 \times 10^{-17} S\ fm^{-3} + {\mathcal O}(d_e,C_{qq})

S \sim -0.06 g_{\pi NN} \bar{g}_{\pi NN}^{(1)} \, e\ fm^{3} + \cdots

## Calculating the EDMs - Hg

- _3. Hg EDM_ (diamagnetic)

- charge distribution

- nuclear EDM

-  Misalignment of nuclear charge and dipole moment distribution

- Schiff moment

- [Schiff ‘63]

- [Dzuba et al ‘02]

- [Flambaum et al. ‘86; Dmitriev & Senkov ’03; de Jesus & Engel ‘05]

**Notes:**
V \sim - e S (J \cdot \nabla)\delta(r)

d_{Hg} \sim -3 \times 10^{-17} S\ fm^{-3} + {\mathcal O}(d_e,C_{qq})

S \sim -0.06 g_{\pi NN} \bar{g}_{\pi NN}^{(1)} \, e\ fm^{3} + \cdots

## Calculating the EDMs - Hg

- _3. Hg EDM_ (diamagnetic)

-  EDM (predominantly) due to CP-odd pion-nucleon coupling:

**Notes:**
\bar{g}_{\pi NN}(\tilde{d}_q) = \frac{\tilde{d}_u-\tilde{d}_d}{2f_\pi} \left\langle N \left| \sum_{q=u,d} \bar{q} g_s G\sigma q - m_0^2 \bar{q}q\right| N \right\rangle +\cdots

\bar{g}_{\pi NN}(\tilde{d}_q) = (1-6) \frac{|\langle \bar{q}q\rangle|}{(225 {\rm MeV})^3} (\tilde{d}_u - \tilde{d}_d) + {\mathcal O}(\tilde{d}_u+\tilde{d}_d,\tilde{d}_s,w)

## Calculating the EDMs - Hg

- _3. Hg EDM_ (diamagnetic)

-  EDM (predominantly) due to CP-odd pion-nucleon coupling:

**Notes:**
\bar{g}_{\pi NN}(\tilde{d}_q) = \frac{\tilde{d}_u-\tilde{d}_d}{2f_\pi} \left\langle N \left| \sum_{q=u,d} \bar{q} g_s G\sigma q - m_0^2 \bar{q}q\right| N \right\rangle +\cdots

\bar{g}_{\pi NN}(\tilde{d}_q) = (1-6) \frac{|\langle \bar{q}q\rangle|}{(225 {\rm MeV})^3} (\tilde{d}_u - \tilde{d}_d) + {\mathcal O}(\tilde{d}_u+\tilde{d}_d,\tilde{d}_s,w)

## Calculating the EDMs - Hg

- _3. Hg EDM_ (diamagnetic)

-  EDM (predominantly) due to CP-odd pion-nucleon coupling:

- NB: large errors due to cancelations

- Using QCD sum-rules: [Pospelov ‘01]

- [or, using LETs: Falk et al ‘99; Hisano & Shimizu ‘04]

**Notes:**
\bar{g}_{\pi NN}(\tilde{d}_q) = \frac{\tilde{d}_u-\tilde{d}_d}{2f_\pi} \left\langle N \left| \sum_{q=u,d} \bar{q} g_s G\sigma q - m_0^2 \bar{q}q\right| N \right\rangle +\cdots

\bar{g}_{\pi NN}(\tilde{d}_q) = (1-6) \frac{|\langle \bar{q}q\rangle|}{(225 {\rm MeV})^3} (\tilde{d}_u - \tilde{d}_d) + {\mathcal O}(\tilde{d}_u+\tilde{d}_d,\tilde{d}_s,w)

## Future - charged nuclei & octupoles

- _Deuteron EDM @ BNL_

- [Lebedev, Olive, Pospelov, AR ‘04]

- [Khriplovich & Korkin ‘00; Liu & Timmermans ‘04]

-  Same (leading) dependence as Hg (but without Schiff suppression)

- [SREDM Collab.]

- _Ra, Rn EDM_

- [Holt et al, Chupp et al]

-  Nuclear octupole deformations enhance the Schiff moment,   by O(100-1000) relative to Hg

- [Flambaum et al.]

- Sensitivity:

- 

**Notes:**
d_D \sim (d_n + d_p) + d_D^{\pi NN}

d_D^{\pi NN} \sim -2 \times 10^{-14} \bar{g}_{\pi NN}^{(1)}\, e\ cm

## Origin of the EDMs

- TeV

- Energy

- QCD

- nuclear

- atomic

- pion-nucleon coupling (         )

- EDMs of paramagnetic atoms (      )

- EDMs of diamagnetic  atoms (       )

- Neutron EDM (    )

## Origin of the EDMs

- TeV

- Energy

- QCD

- nuclear

- atomic

- pion-nucleon coupling (         )

- EDMs of paramagnetic atoms (      )

- EDMs of diamagnetic  atoms (       )

- Neutron EDM (    )

- EDM constraints

## Resulting Bounds on fermion EDMs & CEDMs

|   Tl EDM
    (20%) |  |
| --- | --- |
|   Neutron
    EDM
   (50 %) |  |
|       Hg 
    EDM 
 (+200%) |  |

- Sensitivity:                       

**Notes:**
\left| d_e + e(26 {\rm MeV})^2\left(3\frac{C_{ed}}{m_d} + 11 \frac{C_{es}}{m_s} + 5 \frac{C_{eb}}{m_b}\right)\right| < 1.6 \times 10^{-27}\, e\ cm

\left| e(\tilde{d}_d+0.5\tilde{d}_u)+1.3(d_d-0.25d_u) + {\mathcal O}(\tilde{d}_s,w,C_{qq})\right| < 2\times 10^{-26}\, e\ cm

e|\tilde{d}_d-\tilde{d}_u +{\mathcal O}(d_e,\tilde{d}_s,C_{qq},C_{qe})| < 2 \times 10^{-26}\, e\ cm

## Constraints on TeV-Scale models

-  _E.G. MSSM__:_ In general, the MSSM contains many new parameters, including multiple new CP-violating phases, e.g.

**Notes:**
\frac{d_d}{m_d} \sim \frac{1}{16\pi^2}\frac{\mu m_{\tilde{g}}}{M^4}\sin\theta_\mu

\Delta {\mathcal L} &\sim&\;\; -\mu\; \bar{\tilde{H}}_1\tilde{H}_2 + B\mu\; H_1H_2 + h.c. \\
&& -\;\frac{1}{2}\left(M_3\; \bar{\lambda}_3 \lambda_3 +M_2 \;\bar{\lambda}_2\lambda_2+M_1\; \bar{\lambda}_1 \lambda_1\right)+h.c.\\
&&- \;A^d_{ij}\; H_1 \tilde{q}_{Li}\tilde{q}_{Rj} + h.c + \cdots

## Constraints on TeV-Scale models

- With a universality assumption, 2 new physical CP-odd phases

-  _E.G. MSSM__:_ In general, the MSSM contains many new parameters, including multiple new CP-violating phases, e.g.

- _ __EG:1-loop EDM contribution__:_

- [Ellis, Ferrara & Nanopoulos ‘82]

- Complex  CP-odd phase

- M ~ sfermion mass

**Notes:**
\frac{d_d}{m_d} \sim \frac{1}{16\pi^2}\frac{\mu m_{\tilde{g}}}{M^4}\sin\theta_\mu

\Delta {\mathcal L} &\sim&\;\; -\mu\; \bar{\tilde{H}}_1\tilde{H}_2 + B\mu\; H_1H_2 + h.c. \\
&& -\;\frac{1}{2}\left(M_3\; \bar{\lambda}_3 \lambda_3 +M_2 \;\bar{\lambda}_2\lambda_2+M_1\; \bar{\lambda}_1 \lambda_1\right)+h.c.\\
&&- \;A^d_{ij}\; H_1 \tilde{q}_{Li}\tilde{q}_{Rj} + h.c + \cdots

## SUSY CP Problem

- Soft CP-odd phases

- [Also: Barger et al. ‘01, Abel et al. ‘01, Pilaftsis ‘02]

- Generic Implications   

- [Olive, Pospelov, AR, Santoso ‘05]

## SUSY CP Constraints

- Decoupling 1st/2nd generation

- 2 HDM

- MSSM         parameter space

- split SUSY

- large tan

- EW baryogenesis

- [Barr ‘92; Lebedev & Pospelov ‘02]

- [Weinberg ‘89; Dai et al. 90]

- [Chang, Keung & Pilaftsis ‘98]

- [Barr, Zee ‘92]

## SUSY threshold sensitivity

- If soft terms (approximately) conserve CP & flavour, what is the sensitivity to irrelevant operators (new thresholds) ?

- _Dim 5:_

- [Pospelov, AR, Santoso ‘05, ‘06]

-  Contributions to e.g. EDMs will scale as “dim=5”
-  Sensitivity depends on flavor structure of Yff

- — we will assume

**Notes:**
{\mathcal W} = {\mathcal W}_{MSSM} + \frac{y_h}{\Lambda} (H_uH_d)^2 + \frac{Y^{qe}}{\Lambda} QULE + \frac{Y^{qq}}{\Lambda}QUQD + {\rm seesaw}+{\rm baryon}

\Delta m_e \sim m_e \Rightarrow \Lambda > 10^6 GeV

&& d_{Tl}(C_S), d_{Hg}(C_S), \mu\rightarrow e \\ && \;\;\;\; \Rightarrow \Lambda > 10^8 GeV

## SUSY threshold sensitivity

- [Pospelov, AR, Santoso ‘05, ‘06]

- _Models:_ e.g. MSSM + extended Higgs sector

- SPS1a

- 2

- 8

- 4

## (Electroweak) Baryogenesis

- The SM satisfies, in principle, all 3 Sakharov criteria for baryogenesis

- _BUT_

-  mh too large for a strong 1st order PT
-  insufficient CP-violation

- _Alternatives:_

- [Gavela et al. ‘94]

- [Kajantie et al. ‘96]

- [WMAP3 + BBN]

-  EWBG still possible in the MSSM
-  Leptogenesis

- —needs one light stop, a large M1-phase, and a rather tuned spectrum

- — decoupled from EW scale, difficult to test

- [Archambault, Czarnecki & Pospelov ‘04]

## Minimal EW Baryogenesis 

-  What is the minimal SM modification required for viable EWBG ?

- [Grojean et al. ‘04; Huber et al ‘05]

-  makes predictions for the top-Higgs coupling, cf. LHC

- require

- Do EDM bounds really allow such a scenario ?

- Tuning of other operators at such low thresholds ?

- _Questions:_

- * NB: Can also flip sign of quartic Higgs coupling

- (*)

## Barr-Zee diagrams

- Assuming MFV structure

- CP-odd top-Higgs coupling

## Constraints

- [Huber, Pospelov, AR ‘06 ]

- Next-generation EDM sensitivity:

## Concluding Remarks

-  Precision tests can play a crucial role in probing fundamental symmetries  at scales well beyond the reach of colliders.
-  EDMs currently provide stringent constraints on CP-phases in the          soft-breaking sector of the MSSM.

## Concluding Remarks

-  Precision tests can play a crucial role in probing fundamental symmetries at scales well beyond the reach of colliders.
-  EDMs currently provide stringent constraints on CP-phases in the          soft-breaking sector of the MSSM.
-  If the soft sector is real, EDMs and other precision flavor physics provide impressive sensitivity to new SUSY thresholds.
-  Current EDM bounds still allow for electroweak baryogenesis in a   minimal dim=6 extension of the SM.

- next generation tests will push the scale close to that of RH neutrinos, etc.

- next-generation expts will provide a conclusive test.

## Next-generation Experiments

- TeV

- Energy

- QCD

- nuclear

- atomic

- EDMs of paramagnetic molecules
-  (YbF, PbO, HfF+)
- Atoms in traps (Rb,Cs)

- EDMs of diamagnetic atoms (Hg,Xe,Ra,Rn)

- Neutron EDM (    )

- EDMs of nuclei and ions  atoms (deuteron, etc)

## Next-generation Experiments

- TeV

- Energy

- QCD

- nuclear

- atomic

- EDMs of paramagnetic molecules
-  (YbF, PbO, HfF+)
- Atoms in traps (Rb,Cs)

- EDMs of diamagnetic atoms (Hg,Xe,Ra,Rn)

- Neutron EDM (    )

- EDMs of nuclei and ions  atoms (deuteron, etc)

- Deuteron EDM @ BNL !

## Appendices

## Future experimental progress

-  _Paramagnetic atoms & molecules_

| PbO |  |   [DeMille et al. (Yale ‘06/07)] |
| --- | --- | --- |
| YbF |  |  [Hinds et al. (Imperial ‘06/07)] |
| solid state (garnet) |  |           [LANSCE ‘06/07] |

-  _Neutron_

-  _Diamagnetic atoms_

| UCN bottle (Hg comag) |  | [PSI ‘07/09] |
| --- | --- | --- |
| UCN in liquid He4    (He3 comag) |  | [LANSCE ‘07/10;       
Sussex et al. ‘07/10 ] |

- + many others ....

| Deuteron |  |    [SR EDM collab. (BNL)] |
| --- | --- | --- |

| Hg |  |     [Fortson, (Washington)] |
| --- | --- | --- |
| Liquid Xe |  |       [Romalis, (Princeton)] |

## CP-violation and EDMs

- sensitivity through EDMs of neutrons, and para - and       dia-magnetic atoms and molecules (violate T,P)

- _

-  Look for CP-violation in flavour diagonal channels

- Within the SM, CP-violation is hidden behind the flavour structure

- 

- Are CP and flavour intrinsically linked ?

-  Baryogenesis requires extra CP-violation
-  Most “UV completions” of the SM (e.g. MSSM)        provide additional sources of CP-violation

- YES

- Currently, all experimental data   EDMs vanish to very _high precision_ thus leading to very strong constraints on new physics.

## Computations

- _1. Tl EDM (paramagnetic)_

- _2. neutron EDM_

- _3. Hg EDM (diamagnetic)_

- [Dzuba et al. ‘02; Flambaum et al. ‘86; Dmitriev & Senkov ‘03]

- [Pospelov ‘01]

- [Liu & Kelly ‘92; Khatsymovsky et al. ‘86]

- [Pospelov & AR ‘99,’00]

- (chiralPT, NDA, QCD sum rules, ...) 

- (atomic)

- (atomic+nuclear+QCD)

## Comments on the SR NEDM calculation

- 

- 

-  Chiral properties
-  Mixing with CP-conjugate currents
-  Generic treatment of all CP-odd sources (...)

-  Dependence on sea-quark EDMs
-  Improvements in precision (?)

- Lattice ?

## Future - charged nuclei

- _Deuteron EDM_

- [Lebedev, Olive, Pospelov, AR ‘04]

- [Khriplovich & Korkin ‘00]

-  Same (leading) dependence as Hg (but without Schiff suppression)

**Notes:**
d_D \sim (d_n + d_p) + d_D^{\pi NN}

d_D^{\pi NN} \sim -2 \times 10^{-14} \bar{g}_{\pi NN}^{(1)}\, e\ cm

## SUSY CP Problem

- Soft CP-odd phases

- [Also: Barger et al. ‘01, Abel et al. ‘01, Pilaftsis ‘02]

- Generic Implications   

- [Olive, Pospelov, AR, Santoso ‘05]

## SUSY CP Constraints

- Decoupling 1st/2nd generation

- 2 HDM

- MSSM parameter space:

- large tan

- [Barr ‘92; Lebedev & Pospelov ‘02]

- [Weinberg ‘89; Dai et al. 90]

- [Chang, Keung & Pilaftsis ‘98]

- [Barr, Zee ‘92]

- Decoupling scalars (split SUSY, EW baryogenesis)

- Decoupling fermions

|  |
| --- |
|  |
|  |

- [Arkani-Hamed et al. ‘04]

## Naturalness and new CP-odd thresholds

- Success of CKM CP-violation (with natural O(1) phase) in K and B-meson mixing, and e.g. constraints on soft-SUSY phases

-  Can this scenario provide a viable  baryogenesis mechanism ?
-  What is the threshold sensitivity?

- Questions:

- 

- Assumption:  non-CKM CP-violation is “_*irrelevant*_”               (to leading order) at the weak scale

## SUSY threshold sensitivity

- Dimension-3,6 operators generated at the soft threshold

**Notes:**
{\mathcal W} = {\mathcal W}_{MSSM} + \frac{y_h}{\Lambda} (H_uH_d)^2 + \frac{Y^{qe}}{\Lambda} QULE + \frac{Y^{qq}}{\Lambda}QUQD + {\rm seesaw}+{\rm baryon}

\Delta m_e \sim m_e \Rightarrow \Lambda > 10^6 GeV

&& d_{Tl}(C_S), d_{Hg}(C_S), \mu\rightarrow e \\ && \;\;\;\; \Rightarrow \Lambda > 10^8 GeV

## SUSY threshold sensitivity

- Dimension-3,6 operators generated at the soft threshold

**Notes:**
{\mathcal W} = {\mathcal W}_{MSSM} + \frac{y_h}{\Lambda} (H_uH_d)^2 + \frac{Y^{qe}}{\Lambda} QULE + \frac{Y^{qq}}{\Lambda}QUQD + {\rm seesaw}+{\rm baryon}

\Delta m_e \sim m_e \Rightarrow \Lambda > 10^6 GeV

&& d_{Tl}(C_S), d_{Hg}(C_S), \mu\rightarrow e \\ && \;\;\;\; \Rightarrow \Lambda > 10^8 GeV