Measurement of the difference between CP-violating asymmetries in D⁰ → K⁺K^- and D⁰ → π⁺π^- Decays at CDF

Primary authors: A. Di Canto, M. J. Morello, G. Punzi, L. Ristori, D. Tonelli

This webpage provides a concise summary of the analysis. See the PRL publication, the CDF Public Note 10784, and the previous measurement of individual asymmetries for details.

Introduction and motivation

Time-integrated CP-violating asymmetries of singly-Cabibbo suppressed transitions as D⁰ → π⁺π^- and D⁰ → K⁺K^- are powerful probes of new physics (NP). Contributions from "penguin" amplitudes are negligible in the Standard Model [1], but as in D⁰-D⁰ oscillations, NP particles could enhance the CP-violation with respect to the CKM hierarchy expectation. Any asymmetry significantly larger than 1% is believed to unambiguously indicate non-SM physics [1]. Accurate predictions of the size for the individual CP-violating asymmetries are challenging due to hadronic uncertainties, but consensus is that the direct components of the asymmetries in D⁰ → π⁺π^- and D⁰ → K⁺K^- have opposite signs. Hence, a measurement of the difference between asymmetries in the two decays is maximally sensitive to detect CP violation. Also experimentally, measuring the difference is convenient because most systematic uncertainties due to instrumental effects cancel.

The LHCb collaboration reported recently a precise measurement of the difference of asymmetries, Δ A_CP = (-0.82 ± 0.21 ± 0.11)% [2]. This is the first evidence for CP violation in the charm sector, with a size that may indicate the presence of NP. An independent confirmation of this measurement is crucial to establish the effect and improve the precision on its size. The sample of hadronic charm decays collected by the CDF displaced-trigger is the only one currently available in which this can be attained with sufficient precision. Buiding upon the techniques used in our previous analysis of individual asymmetries, we report a measurement of difference of asymmetries that uses the full dataset collected in Run II.

Analysis overview

Building upon the techniques developed for our previous measurement of individual asymmetries [3], we updated and optimized the analysis towards the measurement of difference of asymmetries. We use an event sample collected with the displaced-track trigger from March 2001 through September 2011, which corresponds to about 9.7 fb^-1 of integrated luminosity. The trigger requires presence of two charged particles with transverse momenta greater than 2 GeV/c, impact parameters greater than 100 microns and basic cuts on azimuthal separation and scalar sum of momenta.

The decays used are D*-tagged D⁰ → K⁺K^- and D⁰ → π⁺π^- decays (charge conjugate states are implied). The reconstruction uses only tracking information without any particle identification. We first reconstruct a signal consistent with a D⁰ → h⁺h^- decay. Then we associate a low-momentum charged track to construct a D*⁺ candidate. The offline selection relies on confirmation of trigger requirements and basic additional requirements on track and vertex quality. The selection has been loosened with respect to the measurement of individual asymmetries, since the difference of asymmetries is much less sensitive to instrumental effects allowing for a more inclusive selection.

The flavor of the charmed meson is unambiguously determined from the charge of the pion in the strong D*⁺ → D⁰π⁺ decay. Primary D⁰ and D⁰ mesons are produced in equal number in strong pp interactions. Any asymmetry between the number of D⁰ and D⁰ decays is due to either CP non-conservation or instrumental asymmetries. However, the only possible instrumental effect in D⁰ → h⁺h^- and decays is the one induced by the difference in reconstruction efficiency between positive and negative soft pions. Provided that the relevant kinematic distributions are equalized in the two decay channels, this asymmetry cancels to an excellent level of accuracy in the difference between CP-violating asymmetries.

Results

Using 550K D*-tagged D⁰ → π^-π⁺ decays and 1.21M D*-tagged D⁰ → K^-K⁺ decays, we obtain:
ΔA_CP = (-0.62 ± 0.21 ± 0.10)%

which is 2.7σ different from zero and consistent with the LHCb result, suggesting that CDF data support CP violation in charm.

The observed CP-violating asymmetry describes a straight line in the plane (a_CP^ind,ΔA_CP^dir) with angular coefficient -<Δt>/τ. Using the observed values of 2.4τ (2.65τ) for the D⁰ → π^-π⁺ (D⁰ → K^-K⁺) as resulting from the proper-decay time bias of the displaced track trigger, we graphically compare our result with the no-CPV point and previous measurements in the figure below. The combination of our result with the LHCb measurements, assuming Gaussian, fully uncorrelated uncertainties, yields ΔA_CP^dir = (-0.67 ± 0.16)% and A_CP^ind = (-0.02 ± 0.22)%, which deviates by approximately 3.8σ from the no-CP violation point.

The measured value of ΔA_CP in the subsample of additional events selected by the new criteria is combined with the statistically independent results of Ref. [3], to obtain a more precise determination of the individual asymmetries:

A_CP(D⁰→π⁺π^-) = (+0.31 ± 0.22)%,
A_CP(D⁰→K⁺K^-) = (-0.32 ± 0.21)%,

where the uncertainties include both the statistical and systematic components. The correlation between the two asymmetries is 0.412.

Additional material

More plots are available here.

References

D.-S. Du, "CP violation for neutral charmed meson decays into CP eigenstates", Eur. Phys. J. C 50 (2007) 579; Y. Grossman, A. Kagan, and Y. Nir, "New Physics and CP Violation in Singly Cabibbo Suppressed D Decays", Phys. Rev. D75, 036008 (2006); I. I. Y. Bigi, "Could Charm 'Third-time' Be the Real Charm ? A Manifesto", arXiv:0902.3048 [hep-ph]; S. Bianco et al. "A Cicerone for the physics of charm" Riv. Nuovo Cim. 26 N7, 1 (2003); Z.-Z. Xing, "D⁰-D⁰ mixing and CP violation in neutral D-meson decays", Phys. Rev. D55, 196 (1997).
R. Aaij et al. [LHCb Collaboration], "Evidence for CP violation in time-integrated D⁰→ h⁺h^- decay rates ", arXiv:1112.0938.
T. Aaltonen et al. [CDF Collaboration], "Measurement of CP-violating asymmetries D⁰ → K⁺K^- and D⁰ → π⁺π^- decays at CDF", Phys. Rev. D 85 012009 (2012);