Measurement Of Direct CP Violation Research Articles

Direct CP violation and the ΔI= 1/2 rule inK→ππdecay in the Standard Model

We discuss the RBC & UKQCD collaborations’ recent [1] lattice calculation of ϵ′, the measure of direct CP-violation in kaon decays. This result significantly improves on our previous 2015 calculation, with nearly 4× the statistics and more reliable systematic error estimates. We discuss how our results demonstrate the Standard Model origin of the ΔI= 1/2 rule, and present our plans for future calculations.

Direct CP violation and the ΔI=1/2 rule in K→ππ decay from the standard model

We present a lattice QCD calculation of the $\Delta I=1/2$, $K\to\pi\pi$ decay amplitude $A_0$ and $\varepsilon'$, the measure of direct CP-violation in $K\to\pi\pi$ decay, improving our 2015 calculation of these quantities. Both calculations were performed with physical kinematics on a $32^3\times 64$ lattice with an inverse lattice spacing of $a^{-1}=1.3784(68)$ GeV. However, the current calculation includes nearly four times the statistics and numerous technical improvements allowing us to more reliably isolate the $\pi\pi$ ground-state and more accurately relate the lattice operators to those defined in the Standard Model. We find ${\rm Re}(A_0)=2.99(0.32)(0.59)\times 10^{-7}$ GeV and ${\rm Im}(A_0)=-6.98(0.62)(1.44)\times 10^{-11}$ GeV, where the errors are statistical and systematic, respectively. The former agrees well with the experimental result ${\rm Re}(A_0)=3.3201(18)\times 10^{-7}$ GeV. These results for $A_0$ can be combined with our earlier lattice calculation of $A_2$ to obtain ${\rm Re}(\varepsilon'/\varepsilon)=21.7(2.6)(6.2)(5.0) \times 10^{-4}$, where the third error represents omitted isospin breaking effects, and Re$(A_0)$/Re$(A_2) = 19.9(2.3)(4.4)$. The first agrees well with the experimental result of ${\rm Re}(\varepsilon'/\varepsilon)=16.6(2.3)\times 10^{-4}$. A comparison of the second with the observed ratio Re$(A_0)/$Re$(A_2) = 22.45(6)$, demonstrates the Standard Model origin of this "$\Delta I = 1/2$ rule" enhancement.

Exploring Brightarrow pi pi , pi K decays at the high-precision frontier

The Brightarrow pi pi ,pi K system offers a powerful laboratory to probe strong and weak interactions. Using the isospin symmetry, we determine hadronic Brightarrow pi pi parameters from data where new measurements of direct CP violation in B^0_drightarrow pi ^0pi ^0 resolve a discrete ambiguity. With the help of the SU(3) flavour symmetry, the Brightarrow pi pi parameters can be converted into their Brightarrow pi K counterparts, thereby allowing us to make predictions of observables. A particularly interesting decay is B^0_drightarrow pi ^0 K_mathrm{S} as it exhibits mixing-induced CP violation. Using an isospin relation, complemented with a robust SU(3) input, we calculate correlations between the direct and mixing-induced CP asymmetries of B^0_drightarrow pi ^0 K_mathrm{S}, which are the theoretically cleanest Brightarrow pi K probes. Interestingly, they show tensions with respect to the Standard Model. Should this Brightarrow pi K puzzle originate from New Physics, electroweak penguins offer an attractive scenario for new particles to enter. We present a strategy to determine the parameters characterising these topologies and obtain the state-of-the-art picture from current data. In the future, this method will allow us to reveal the Brightarrow pi K dynamics and to obtain insights into the electroweak penguin sector with unprecedented precision.

Direct CP violation at LHCb

During 2011, LHCb has collected an integrated luminosity of 1.0fb−1 giving rise to a large variety of measurements. Among these, measurements of direct CP violation in B decays play a central role. Three different analyses are presented: the first evidence of CP violation in the Bs0 system and the observation of CP violation in the B0 system, using B0→Kπ and Bs0→πK decay channels; the evidence of CP violation in B±→DK± decays with the first observation of the suppressed ADS mode; and a preliminary result showing the evidence of CP asymmetry in charmless three-body charged B decays.

Measurements of DirectCPViolating Asymmetries in Charmless Decays of Strange Bottom Mesons and Bottom Baryons

We report measurements of direct CP-violating asymmetries in charmless decays of neutral bottom hadrons to pairs of charged hadrons with the upgraded Collider Detector at the Fermilab Tevatron. Using a data sample corresponding to 1 fb(-1) of integrated luminosity, we obtain the first measurements of direct CP violation in bottom strange mesons, A(CP)(B(s)(0)→K(-)π(+))=+0.39±0.15(stat)±0.08(syst), and bottom baryons, A(CP)(Λ(b)(0)→pπ(-))=+0.03±0.17(stat)±0.05(syst) and A(CP)(Λ(b)(0)→pK(-))=+0.37±0.17(stat)±0.03(syst). In addition, we measure CP violation in B(0)→K(+)π(-) decays with 3.5σ significance, A(CP)(B(0)→K(+)π(-))=-0.086±0.023(stat)±0.009(syst), in agreement with the current world average. Measurements of branching fractions of B(s)(0)→K(+)K(-) and B(0)→π(+)π(-) decays are also updated.

Chiral Perturbation Theory from Charged Kaon Decays at NA48/2

Chiral Perturbation Theory, as a low-energy effective field theory of strong interactions, is a very useful tool to study the interactions of kaons. The NA48/2 experiment, whose primary goal was the measurement of direct CP violation in the decays of charged kaons, has however collected enough statistics to check the ChPT predictions for several decay modes of charged kaons.

Bs,d→ππ,πK,KK: status and prospects

Several years ago, it was pointed out that the U-spin-related decays Bd→π+π-, Bs→K+K- and Bd→π∓K±, Bs→π±K∓ offer interesting strategies for the extraction of the angle γ of the unitarity triangle. Using the first results from the Tevatron on the Bs decays and the B-factory data on Bu,d modes, we compare the determinations of γ from both strategies, study the sensitivity on U-spin-breaking effects, discuss the resolution of discrete ambiguities, predict observables that were not yet measured but will be accessible at LHCb, explore the extraction of the width difference ΔΓs from untagged Bs→K+K- rates, and address the impact of new physics. The data for the Bd→π+π-, Bs→K+K- system favour the BaBar measurement of direct CP violation in Bd→π+π-, which will be used in the numerical analysis and result in a fortunate situation, yielding γ=(66.6+4.3+4.0 -5.0-3.0)°, where the latter errors correspond to a generous estimate of U-spin-breaking effects. On the other hand, the Bd→π∓K±, Bs→π±K∓ analysis leaves us with 26°≤γ≤70°, and points to a value of the Bs→π±K∓ branching ratio that is larger than the current Tevatron result. An important further step will be the measurement of mixing-induced CP violation in Bs→K+K-, which will also allow us to extract the B0 s–B0 s mixing phase unambiguously with the help of Bs→J/ψφ at the LHC. Finally, the measurement of direct CP violation in Bs→K+K- will make the full exploitation of the physics potential of the Bs,d→ππ,πK,KK modes possible.

Direct CP violation and rare decays at BaBar

We present recent time integrated and time dependent measurements of Direct CP violation at the BaBar experiment.

First observation and precision measurement of direct CP violation: the experiments NA31 and NA48

The CP violating decay of the CP odd eigenstate of the neutral kaon into two pions has first been observed by the NA31 experiment at CERN. The strength of direct CP violation has been measured precisely more recently as expressed by the parameter |ε′/ε|=(1.7±0.2)×10-3. This implies a difference in the dipionic decay rates of neutral kaons and their antiparticles at a level of 10-5.

Direct CP violation in $B \rightarrow \pi^{ + }\pi^{-}\pi$ : determination of $\alpha$ without discrete ambiguity

Direct CP violation in the hadronic decays $\Bar{B}^{0} \to \pi^{+}\pi^{-} \pi^{0}$ is investigated near the peak of the $\rho^{0}$ taking into account the effect of $\rho - \omega$ mixing. Branching ratios for processes $B^{\pm,0} \to \rho^{\pm,0}\pi^{\pm,0}$ and $B^{-} \to \omega \pi^{-}$ are calculated as well. We find that the CP violating asymmetry is strongly dependent on the CKM matrix elements. For a fixed $N_{c}^{eff}$, the CP violating asymmetry, $a$, has a maximum of order -40% to -70% for $\Bar{B}^{0} \to \rho^{0}(\omega) \pi^{0}$ when the invariant mass of the $\pi^{+}\pi^{-}$ pair is in the vicinity of the $\omega$ resonance. The sensitivity of the asymmetry to $N_{c}^{eff}$ is small in that case. Moreover, we find that in the range of $N_{c}^{eff}$ which is allowed by the most recent experimental branching ratios from the BABAR, BELLE and CLEO Collaborations, the sign of $\sin \delta$ is always positive. Thus, a measurement of direct CP violation in decays $\Bar{B}^{0} \to \pi^{+}\pi^{-} \pi^{0}$ would remove the mod$(\pi)$ ambiguity in the determination of the CP violating phase angle $\alpha$.

Isospin relation and SU(3) breaking effects of strong phases in charmless B decays

Isospin and flavor SU(3) relations in charmless hadronic B decays $B\to \pi \pi, \pi K$ are investigated in detail with paying attention to the SU(3) symmetry breaking effects in both amplitudes and strong phases. In general, the isospin and the flavor SU(3) structure of the effective Hamiltonian provide several relations among the amplitudes and strong phases. Whereas a global fit to the latest data shows that some relation seems not to be favorable for a consistent explanation to the current data within the standard model (SM). By considering several patterns of SU(3) breaking, the amplitudes and the corresponding strong phases are extracted and compared with the theoretical estimations. It is found that in the case of SU(3) limits and also the case with SU(3) breaking only in amplitudes, the fitting results lead to an unexpected large ratio between two isospin amplitudes $a^{c}_{3/2}/a^{u}_{3/2}$, which is about an order of magnitude larger than the SM prediction. The results are found to be insensitive to the weak phase $\gamma$. By including SU(3) breaking effects on the strong phases, one is able to obtain a consistent fit to the current data within the SM, which implies that the SU(3) breaking effect on strong phases may play an important role in understanding the observed charmless hadronic B decay modes $B\to \pi \pi$ and $\pi K$. It is possible to test those breaking effects in the near future from more precise measurements of direct CP violation in B factories.

A precision measurement of direct CP violation in the decay of neutral kaons into two pions

The direct CP violation parameter Re(ϵ′/ϵ) has been measured from the decay rates of neutral kaons into two pions using the NA48 detector at the CERN SPS. The 2001 running period data was collected under varied conditions compared to earlier years (1997–1999). The new data result is Re( ϵ′/ ϵ) = (13.7 ± 3.1) × 10 −4. The overall value of Re( ϵ′/ ϵ) = (14.7 ± 2.2) × 10 −4 is obtained from the complete NA48 data set.

Measurements of direct CP violation in two-body decays of B meson with Belle

We report measurements of partial rate asymmetries in charge conjugate modes using two-body B decays with flavor-specific final states at the Belle experiment. A time-integrated analysis is applied on data samples of 31–85 million B B pairs. All asymmetries are null consistent within errors.

Measurements of direct CP violation

We review the experimental searches and determinations of direct CP violation in meson decays and other systems.

A precision measurement of direct CP violation in the decay of neutral kaons into two pions

A precision measurement of direct CP violation in the decay of neutral kaons into two pions

A precision measurement of direct CP violation in the decay of neutral kaons into two pions

The direct CP violation parameter Re(ϵ′/ϵ) has been measured from the decay rates of neutral kaons into two pions using the NA48 detector at the CERN SPS. The 2001 running period was devoted to collecting additional data under varied conditions compared to earlier years (1997–1999). The new data yield the result: Re(ϵ′/ϵ)=(13.7±3.1)×10−4. Combining this result with that published from the 1997, 98 and 99 data, an overall value of Re(ϵ′/ϵ)=(14.7±2.2)×10−4 is obtained from the NA48 experiment.

Recent measurements of CP violation in the neutral kaon system

During the last ten years the measurement of direct CP violation in the K 0 — K 0 system has been vigorously carried out by expriments NA48 at CERN and KTeV at Fermilab. The measurement of the parameter Re(ε′/ε) has been achieved with an accuracy of 2 × 10 −4 . We review some important results obtained by these two experiments among which the clear evidence of direct CP violation. The CPLEAR contribution to the precision determination of parameters in the kaon sector is briefly discussed.

Recent measurements of CP violation in the neutral kaon system

During the last ten years the measurement of direct CP violation in the K 0 — K 0 system has been vigorously carried out by expriments NA48 at CERN and KTeV at Fermilab. The measurement of the parameter Re(ε′/ε) has been achieved with an accuracy of 2 × 10 −4 . We review some important results obtained by these two experiments among which the clear evidence of direct CP violation. The CPLEAR contribution to the precision determination of parameters in the kaon sector is briefly discussed.

A new measurement of direct CP-violation by experiment NA48 at CERN

The NA48 experiment at CERN has performed a new measurement of the CP-violating parameter Re(ϵ′/ϵ). The experiment collects K L and K S decays into π 0π 0 and π +π − from the same decay region simultaneously. A new measurement of the Re(ϵ′/ϵ) parameter based on the data collected during the 1998 run is presented. The preliminary result for the Re(ϵ′/ϵ) based on data collected in 1997 and 1998 is (14.0±4.3) · 10 −4.

Future NA48 programs for hyperon rare decays and CP violation measurements

The NA48 Collaboration has submitted two proposals to extend its physics program after the completion of the ϵ′/ϵ measurement. The first will address several topics in rare hyperon and K S decays, using an high intensity K S beam. In the second proposal the focus is on the measurement of direct CP violation in charged kaon decay, using simultaneous K ± beams.