CP Asymmetries
(through End of May 2021)

CP Asymmetries in D⁺ decays

CP Asymmetries in D_s⁺ decays

CP Asymmetries in decays of charm baryons

For charm baryons CP asymmetry has been accessed through comparison of P asymmetry in decays of, for instance, Λ_c⁺ and Λ_c^-, measured with the weak-asymmetry parameters, respectively α(Λ_c⁺) and α(Λ_c^-). As under P-parity conservation: α(Λ_c⁺) = -α(Λ_c^-), the CP-violating asymmetry is defined as: A^α_CP = [α(Λ_c⁺) + α(Λ_c^-)] /[α(Λ_c⁺) - α(Λ_c^-]. The α(Λ_c) can be measured through an angular analysis exploiting a helicity angle of weakly-decaying baryon in Λ_c decay chain, for instance Λ->pπ^- in Λ_c⁺->Λπ⁺ decays.
This method of accessing CP violation occuring through P-violation can be applied also to other charm baryons, like Ξ_c⁰->Ξ^-π⁺ with Ξ^-->Λπ^-.

Year	Experiment	CP Asymmetry in the decay mode Λc+ to Λ e+ ν	[α(Λc+)+α(Λc-)]/[α(Λc+)-α(Λc-]
2005	CLEO	J.W. Hinson et al. (CLEO Collab.), Phys. Rev. Lett. 94, 191801 (2005).	0.00 ± 0.03 ± 0.01 ± 0.02
Year	Experiment	CP Asymmetry in the decay mode Λc+ to Λπ+	[α(Λc+)+α(Λc-)]/[α(Λc+)-α(Λc-]
2006	FOCUS	J.M. Link et al. (FOCUS Collab.), Phys. Lett. B 34, 165 (2006).	-0.07 ± 0.19 ± 0.12
Year	Experiment	CP Asymmetry in the decay mode Ξc0 to Ξ-π+	[α(Ξc0)+α(Ξc0)]/[α(Ξc0)-α(Ξc0))]
2021	BELLE	Y.B. Li et al. (BELLE Collab.), arXiv:2103.06496 [PRL].	+0.015 ± 0.052 ± 0.017

ΔA_CP measurements

Probing CP violation through differences between A_CP asymmetries of similar decay channels allows for cancelation of nuisance asymmetries, like charm-production asymmetry and/or charge-track detection asymmetry. It significantly facilitates experimental measurements and increases sensitivity.

Measurements of ΔA_CP for D⁰->h⁺h^- decays, defined as A_CP(D⁰->K⁺K^-)-A_CP(D⁰->π⁺π^-), are discussed here.
Notably, the LHCb measurement in R. Aaij et al. (LHCb Collab.), Phys. Rev. Lett. 122, 211803 (2019) yields an LHCb combination of
ΔA_CP(D⁰->h⁺h^-) = (-15.4 ± 2.9)×10^-4, comprising the discovery of CP violation in charm sector.

ΔA_CP is also measured for three-body Λ_c⁺->ph⁺h^- decays, in a phase-space integrated manner, in R. Aaij et al. (LHCb Collab.), JHEP 03 182 (2018) giving
ΔA_CP(Λ_c⁺->ph⁺h^-) = (+0.30 ± 0.91 ± 0.61)×10^-2.

Sum rule for D->ππ decays

This sume rule was proposed in Y. Grossman, A.L. Kagan, J. Zupan, Phys. Rev. D 85, 114036 (2012) and for the first time experimentally tested in V. Babu et al. (BELLE Collab.), Phys. Rev. D 97, 011101 (2018).
An isospin decomposition of D->ππ decay amplitudes gives:

where A₁ and A₃ are amplitudes of decays with an isospin change of, respectively, ΔI = 1/2 and ΔI = 3/2 (i.e. transitions to ππ final states with I=0 and I=2). Therefore the following sum holds for decay amplitudes of D->ππ channels:

It translates into the following sum for differences between D and D decay rates:

The above sum being non-zero would mean that CP violation arises from the ΔI = 1/2 amplitude. If the sum is zero, while individual CP asymmetries of D->ππ modes are non-zero, it would suggest New Physics contributing to the ΔI = 3/2 amplitude. As penguin amplitude is, to a good approximation, ΔI = 1/2 within the Standard Model, while D⁺->π⁺π⁰ decay is purely a ΔI = 3/2 transistion, any CP asymmetry observed for this mode would point to New Physics in the ΔI = 3/2 amplitude.

To facilitate an experimental test, the left-hand side of the above sum is rewritten as:

Using the relation between amplitude and branching fraction, |A|²~B/τ_D, and employing A_CP definition, |A|² - |A|² = A_CP(|A|² + |A|²), the above turns into:

where B_+-, B₀₀ and B₊₀ denote branching fractions of D⁰->π⁺π^-, D⁰->π⁰π⁰ and D⁺->π⁺π⁰ decays, respectively, whereas τ_D0 and τ_D+ are lifetimes of D⁰ and D⁺.
The sum R is calculated using HFLAV averages for A_CP given in the tables above, and PDG averages for branching fractions and lifetimes from P.A. Zyla et al. (PDG), Prog. Theor. Exp. Phys. 2020, 083C01 (2020).

The result is R = (+0.06 ± 2.44)×10^-3, and is consistent with zero.

More details are given in Sec.9.2 of Y. Amhis et al. (HFLAV), Eur. Phys. J. C 81:226 (2021).

 

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