CP VIOLATIONIN TAU DECAYS

Nita SinhaThe Institute of Mathematical Sciences

Chennai

CPV in Charged Leptons CP violation has been observed in K meson and B meson decays and perhaps (?) recently even in the D meson decays

SM cannot produce the observed matter vs antimatter asymmetry

Look elsewhere—Neutrinos Charged leptons Electric Dipole Moments

Will hopefully simultaneously be able to pin down the kind of New Physics

Search for CP violation in the decay

BABARRapid

Communications

PRD 85, 031102 (2012)

Naively one would not expect any CPV in this decay mode as there is no weak phase involved. However, - mix

t: (VtsV*td)2 ~ 10, mt

2 c: (VcsV*

cd)2 ~ 2, mc2

u: (VusV*ud)2 ~ 2, mu

2 c dominates

𝐾−𝐾

The BaBar collaboration reported a measurement of a rate asymmetry in this tau decay mode

In the presence of CPV, the observed neutral Kaon states of definite mass and lifetime are:

Asymmetry from Neutral Kaon Mixing

In the limit of CP conservation and reduce to CP eigenstates, > =|> , where

Bigi and Sanda estimated the asymmetry in the SM due to mixing to be--

The observed asymmetry has the opposite sign!

Sign of the AsymmetryIn fact, the sign of such an CP asymmetry expected to be opposite to the CP Asymmetry in charged D decays

𝑢 𝑢𝑑𝑑𝜋−

𝐾 0𝑠𝑐𝑑

𝑑𝑠

𝜋−

𝐾 0

𝜏− 𝜈𝜏 𝐷−

Careful AnalysisThe measured CP asymmetry has the opposite sign to the theoretical expectation, leading to a ~2.8

Babar has done a rather careful analysis—including corrections pointed out by theorists:

1

2

The discrepancy from expectation (if confirmed with higher statistical significance) needs to be explained

Except for neutral K mixing, tau decays can only be affected by Direct CPV

CP asymmetries in semi-hadronic final states can probe both CPV coming from New hadronic and leptonic physics.

Once the well measured Kaon oscillation contribution to CP asymmetry is accounted for, any further deviations provide clean signals of New Physics

Why is this interesting?

Decay Rate

In Standard Model

Kpi system will only allow and

The differential decay rate for may be written as:

Where, the leptonic term:

and the hadronic term

is given in terms of the hadronic vector current

which is parameterized in terms of scalar and vector form factors as:

No Vector –Scalar

Interference term

Form Factors parameterized in terms of Briet -Wigner forms with energy dependent widths

l=1 p wave vector state l=0 s wave scalar state

) is the momentum ofKaon in hadron rest frame

Fits to data, possible by using and OR and

𝛽 , 𝜒 𝑎𝑛𝑑𝜅 ,𝛾 are complex coefficients for the relative contributions of the other Resonances wrt the dominant contribution.

Note: For CP asymmetry need strong and weak phases

Strong phase-provided by the resonances!

No Weak phase in SM, can come from New Physics (complex coupling)

CP Asymmetry

) is the ratio of NSI amp. to SM amp

CP asymmetry being linear in NP has higher sensitivity to it than effects like lfv or edms

For charged Higgs, no new FF, only modification, so calculable

Interference of scalar and vector FF term vanishes after the angular integration, so cannot give the decay rate asymmetry although can give asymmetry in distributions

The Vector contribution being odd under parity, interference of vector-scalar is odd, hence vanishes when integrated over the full (parity even) phase space

BUT

Additional Scalar Interaction (Charged Higgs) ? Naively expect a charged scalar boson to provide the additional NSI amplitude, With a complex weak coupling and strong phase difference of scalar and vector FF CP Asymmetry

Belle and Cleo Analysis

Other Options-Tensor interaction?

Complex coupling

NP amplitude

Hadronic Current

This interference survives even after full phase space integration, as both vector and tensor terms are odd under parity

Use the observed BR and ACP to determine the coupling strength of this new tensor interaction and its CP violating phase.

Small coupling will not affect the fits to BR, as it will appeared squared, yet its linear interference term will be sufficient to generate the asymmetry.

Strong phases determined from the complex form of the form factors (vector and scalar)

Numerical estimates of NP Parameters

Case I and

Case II and

Future

Hadronic form factors for tensor contribution could be estimated from lattice calculations

Larger data sample could be analyzed by the experimental groups, including fits with tensorial contribution

Some handle on tensor form factor can pin down the coupling strength and weak phase further.

Note that the dependence of tensor mod-squared term is quite different from other terms which will enable its extraction from data.

Summary

KM Mechanism of CPV verified, explains all measured CPV

BAU requires larger CPV

Explore the lepton sector– Neutrinos Charged leptons

Other possible sources of CPV and NP need to be explored

Observation of a CP asymmetry in the tau decay mode is interesting and if the deviation from the expected SM value confirmed at higher statistical significance It will be an excellent probe of NP

In a model independent way we explored the possibility if tensor interactions could possibly explain the observed asymmetry.

Thank You