CP violating mode of thestoponium decay into Zh
Po-Yan Tseng (Kavli IPMU)
Collaborators:
Kingman Cheung (NTHU,NCTS)
Wai-Yee Keung (UIC)JHEP 1807 (2018) 025,
arXiv: 1804.06089

The 4th IPMU-IPPP-KEK-KIAS workshop, 1st Oct. 2018

Introduction
In the MSSM (Minimal Supersymmetry SM), the lighter
Stop,superpartner of top, can be lighter than othersquarks.
Because, i) top is heavy, large mixing angle between,. ii) if squarks have equal mass at high scale,the radiative correction will reduce the mass of.
M. Drees, Mihoko M. Nojiri, PRL 72, 2324(1994)

Stop cancel with the top quadratic divergence in theradiative correction to the Higgs mass. Hierarchy
problem.
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Introduction
The LHC has put the Stop mass above 1 TeV:ATLAS, 1711.11520, CMS,1711.00752.

is compress just above the lightest neutralinomass, there is not much missing momentum for
tagging events at LHC.
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Introduction
Lighter Stop is long-lived in comparison to the timescale QCD hadronization.
Stoponium,state, can be formed.

stop-anti-stop bound
V.D. Bager, W.Y. Keung, PRL 211, 355(1988)

It produced through gluon-gluon fusion and beidentified by its distinctive decays:
M. Drees, Mihoko M. Nojiri, PRL 72, 2324(1994)

Studies the QCD corrections, lattice calculation, andMartin, J.E. Younkin, PRD 80, 035026(2009),
dark matter co-annihilation. S.P.
S. Kim, PRD 92, no.9 094505,
F.Luo, J.Ellis et al, EPJ C78 (2018) no.5, 425.

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Introduction
The stoponium decay into channel hZ is forbidden by
the assumption of CP conservation.
There is no strong argument against CP violation inthe stop sector.
We will show
can have significant
branching ratio withing the constraint from eEDM
(electron electric dipole moment).

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CP-violation in the Stop sector
The Z-boson couplings to the Stops
convection Feynman vertex amplitude:, through theWhere the convection current isfor incoming

and outgoing

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CP-violation in the Stop sector
The Z-boson couplings to the Stops
convection Feynman vertex amplitude:, through theUnder the charge conjugation

We need to make C-odd transformation for Z:

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CP-violation in the Stop sector
The Z-boson couplings to the Stops
convection Feynman vertex amplitude:, through theThe hermiticity of the unitary interaction
requires.
If Charge conjugation is good symmetry,

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p.7

CP-violation in the Stop sector
Summarizing above discussion: Complex
if its phase is NOT removable implies C-parityviolation.
We can makebetween.

real by redefining the relative phase

To have C-parity violation, additional complex
coupling coefficientfrom Higgs vertex ofis needed.

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CP-violation in the Stop sector
The P-parity is conserved in the Z-vertex.
Because for the renormalizable interaction of the purebosonic sector, operators of dim 4 or less do not
involve the P-odd Levi-Civita
symbol.
C-parity violation is CP-violation.

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CP-violation in the Stop sector
Our example is the decay of the ground state
stoponium in.

The exchange

appear in t-channel and u-channel.

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CP-violation in the Stop sector
Our example is the decay of the ground state
stoponium in.

The phase ofis tied with vertex
thus overall unremovable.
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CP-violation in the Stop sector
Our example is the decay of the ground state
stoponium in.

The two amplitudes of t- and u-channels cancel if thecoupling factor is real, but add up if imaginary.
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CP-violation in the Stop sector
Our example is the decay of the ground state
stoponium in.

The production of Zh from stoponium decay is a signof CP-violation.
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CP-violation in the Stop sector
Our example is the decay of the ground state
stoponium in.

Direct coupling of pseudoscalar A to the Stops, which is CP-violating.
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CP-violation in the Stop sector
Our example is the decay of the ground state
stoponium in.

will enhance the Zh decay mode, but
restricted by the eEDM.
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Decay width of Stoponium
The process.

In the non-relativistic approximation, the amplitude is

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Decay width of Stoponium
The process.

In the non-relativistic approximation, the amplitude is

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Decay width of Stoponium
The process.

In the non-relativistic approximation, the amplitude is

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Decay width of Stoponium
The process.

In the non-relativistic approximation, the amplitude is

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Decay width of Stoponium
The process.

In the non-relativistic approximation, the amplitude is

The partial decay width:

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Contribution to the Electron EDM
The eEDM constraint:
ACME Collaboration, Science 343, 269(2014)

In MSSM, CP-violating contribution in Stop sector via
two-loop Barr-Zee diagram. D.Chang, W.Y.Keung, A.Pilaftsis,, PRL 82, 900 (1999)

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Contribution to the Electron EDM
The eEDM constraint:
ACME Collaboration, Science 343, 269(2014)

In MSSM, CP-violating contribution in Stop sector via
two-loop Barr-Zee diagram. D.Chang, W.Y.Keung, A.Pilaftsis,, PRL 82, 900 (1999)

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Contribution to the Electron EDM
The eEDM constraint:
ACME Collaboration, Science 343, 269(2014)

In MSSM, CP-violating contribution in Stop sector via
two-loop Barr-Zee diagram. D.Chang, W.Y.Keung, A.Pilaftsis,, PRL 82, 900 (1999)

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Contribution to the Electron EDMThe eEDM constraint:
ACME Collaboration, Science 343, 269(2014)

In MSSM, CP-violating contribution in Stop sector via
two-loop Barr-Zee diagram. D.Chang, W.Y.Keung, A.Pilaftsis,, PRL 82, 900 (1999)

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Contribution to the Electron EDM
The eEDM constraint:
ACME Collaboration, Science 343, 269(2014)

In MSSM, CP-violating contribution in Stop sector via
two-loop Barr-Zee diagram. D.Chang, W.Y.Keung, A.Pilaftsis,, PRL 82, 900 (1999)

We ignore one-loop contribution from neutralinoselectron, and chargino-sneutrino diagrams, involve
different CP-violating parameters.

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Analysis
Interplay between Zh channel and eEDM:

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Analysis
Interplay between Zh channel and eEDM:

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Observability at LHC
The Stoponium LO production cross section at LHC
through the gluon-gluon fusion:

Including NLO, at 13 TeV LHC, the cross section is

At LHC, the signal would be

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Observability at LHC
At LHC, the signal would be

The Z and Higgs bosons are very boosted in contrast
to the conventional QCD background.
The current limit from ATLAS and CMS:
300 fb^-1 luminosity at Run-II, 15 events for

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Conclusions
The Zh channel decay mode from the ground state ofstoponium is clean signal of CP-violation.
Under the eEDM constraint,significant branching ratio.

can have aIf stoponium is around 1.2 TeV, highly boosted Z andHiggs bosons are distinguishable from the QCD
background.

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Thank You!

AS, HEP seminar 2018,

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Back Up

AS, HEP seminar 2018,

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Conclusions
The Stop mixing:

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Conclusions
The Higgs-Stop-Stop couplings:

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Conclusions
The Z-Stop-Stop couplings:

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Conclusions
The A-Stop-Stop couplings:

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Analysis
Interplay between Zh channel and eEDM:

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Analysis
Interplay between Zh channel and eEDM:

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p.14