eft approach for the electron edm at two loops

1

EFT approach for the electron EDMat two loops

Marc RiembauUniversité de Genève

HEFT, April 2019

Based on 1810.09413, with G. Panico and A. Pomarol

2

relativistic limit

Nonvanishing d breaks CP

SM

3

relativistic limit

Nonvanishing d breaks CP

SM prediction:

e e3

1

2 2

3SM contribution is ridiculously small,EDM is a clear sign of New Phisics

SM

4Hints for this simplicity are old, coming from non-violations of accidental and approximate SM symmetries.In particular, CP:

5Evolution of electron EDM constraints

Current: ACME II

6

Translation of ACME constraints to particle physics:

Two loops Chirality flip log enhanced

Relevant constraints even at two loops.

We want to characterize all effects that enter with

This is the key to help organize the contributions

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Only 4-fermion to enter at one loopThe others do not have the correct structure

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It is useful to write the parameters in a more physical wayIt is useful to write the parameters in a more physical way

Due to approximate accidental cancellation, 1/2+2 Qe sin^2 0.04, Z boson ∼ 0.04, Z boson

contribution negligible.

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enters through ,only 4-fermion that renormalizes it

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This one is interesting, since a two loop, log^2 contribution competes with the single loop, no log contribution

Compared with 1loop,

which is O(1) for 5TeV

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Accidental cancellation makes it smaller and only hypercharge contributes to EDM

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The other 4-fermions enter only at 2 loops, single log

Again, a cancellation for ledq:

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Impact on BSM

16

Impact on BSM

ACME

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Power counting of the Wilson coefficients

Fix

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Leptoquarks

EDM sets strong constraints to leptoquarks that couple to both left and right leptons

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Supersymmetry: 1 loop + tree

One loop EDMs are very important in SUSY.Exact expressions are very complicated, but now we know superpartners are heavy.

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Supersymmetry: 2 loop + tree

At two loops, a Barr-Zee diagram gives sensitivity to stops.

Also understood via RGE of AFF to dipole. After integrating out the stops,

Nakai, Reece, 1612.08090

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Supersymmetry: 1 loop + 1loop, HHFF

Since the decoupling 1/scalars^4, EDM via HHFF relevant in Split SUSY

For tan beta ~ CP phases ~ O(1)

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Supersymmetry: 1 loop + 1loop, luqe

Contribution to luqe via squark-gauginos loop

with

For degenerate superpartner masses,

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Consequences for Composite models

Take SO(5)/SO(4):

CMS B2G-16-019-pas

G.Panico, MR, T.Vantalon 1712.06337

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Take SO(5)/SO(4):

arXiv: 1409.0100

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Take SO(5)/SO(4):

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CPV controled by

For complete, degenerate multiplets the diagram is proportional to

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HL-LHC projections:Constraints from ACME II

Electron EDM constraints and comparison with direct searches

Im(ct) has to be of order 0.01 if we want to be within LHC reach

32The future of the electron EDM


- After some time of promises of improvements with nothing happening, it seems that there will be further progress in a short time scale.- If there is a positive signal, we’ll have confirmation very quickly.- There are some proposals for a total breakthrough.

Projected datesare approximate

35Conclusions

36Conclusions

- Map of the most relevant effects at two loops:

- Bounds of 1-100TeV for generic theories of leptoquarks

- Characterization of relevant constraints for the MSSM

- In composite models, CPV from top sector important. Top partners pushed outside LHC range, unless they have CP preserving couplings

- Unless there is a reason why, contrary to SM, BSM sector respects CP, ACME result makes these theories much less natural

- CPV in Higgs sector pushed way outside any current or future collider reach

37Conclusions

- Map of the most relevant effects at two loops:

- Bounds of 1-100TeV for generic theories of leptoquarks

- Characterization of relevant constraints for the MSSM

- In composite models, CPV from top sector important. Top partners pushed outside LHC range, unless they have CP preserving couplings

- Unless there is a reason why, contrary to SM, BSM sector respects CP, ACME result makes these theories much less natural

- CPV in Higgs sector pushed way outside any current or future collider reach

Thanks!

38Backup & extra slides

39Selection rules for the RGEs

Elias-Miro, Espinosa, Pomarol, 1412.7151

Cheung, Shen, 1505.01844

Rodrigo Alonso, Jenkins, Manohar, 1409.0868

Since Tom Melia already talked about it yesterday,let me just state again the recipe...

40

Recipe by Cheung, Shen, 1505.01844

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Recipe by Cheung, Shen, 1505.01844

Recipe is not final...The steps are necessary, but clearly not sufficientThe recipe does not have flavour

An increasing group of people is trying to bake a better one

42Dimension 8

If , dim 8 operators are parametrically leading

Only interested in wrong hypercharge 4fermion operators

43Finite contributions

Phases in the Yukawas of 3rd family fermions enter only via threshold correctionsat the EW scale.Due to their relevance, we include them despite being 2 loop and no log.

Both give similar result, since mt infinity with mt/mh fixed in both.→infinity with mt/mh fixed in both.

Finite contribution for electron Yukawa larger than log enhanced due to accidental cancelations, but only for below 10TeV.

44Finite contributions

Phases in the Yukawas of 3rd family fermions enter only via threshold correctionsat the EW scale.Due to their relevance, we include them despite being 2 loop and no log.

Double log enhancement for bottom, tau...(loop)^2 RGE after integrating out the Higgs

( For the bottom, the RGE below the EW scale has to be compared with the accidental cancellation in the RGE above the EW scale for the ledq operator! )

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A word on

Neither the Weinberg operator nor its SU(2) counterpart can be generated at one loop by weakly coupled, spin ≤ 1 theories. At least, one needs two loops!

Couplings to field strength have to be modified, so extra loop seems to be always needed...

46Weinberg operator and neutron EDM

ACME II

Relative importance of Weinberg operator w/respect dipole grows with , but electron EDM more relevant

eft approach for the electron edm at two loops

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