Strong Phase Difference Research Articles

Charm Mixing and D Dalitz Analysis at BESIII

We study D0D‾0 pairs produced in e+e− collisions at s=3.773GeV using a data sample of 2.92fb−1 collected with the BESIII detector. Using world-average values of external parameters, we obtain cosδKπ=1.02±0.11±0.06±0.01, δKπ is the strong phase difference between the doubly Cabibbo-suppressed process D‾0→K−π+ and the Cabibbo-favored process D0→K−π+. A measurement of the parameter yCP in D0−D‾0 oscillations is performed by taking advantage of quantum coherence between pair-produced D0 and D‾0 mesons near threshold, the preliminary result is yCP=(−1.6±1.3±0.6)%. An analysis of the D+→KS0π+π0 Dalitz plot is performed, the Dalitz plot is found to be well presented by a combination of six quasi-two-body decay channels [KS0ρ+, KS0ρ(1450)+, K‾⁎0π+, K‾0(1430)0π+, K‾(1680)0π+, κ‾0π+] plus a small nonresonant component. Using the fit fractions from this analysis, partial branching ratios are updated with higher precision than previous measurements.

Nonleptonic decays of charmed mesons into two pseudoscalars

We examine the role of resonant coupled channel final state interactions (FSI), as well as weak annihilation and exchange contributions in explaining all the two body hadronic $D\rightarrow PP$ decay modes data. In the un-unitarized amplitudes we include modified Wilson coefficients with non-factorizable corrections as parameters. For the hadronic form factors, the z-series expansion method is used to get the $q^2$ dependence. The FSI effects are incorporated via a phenomenological approach with widths of resonances to various channels taken from observations where available, and others as additional parameters to be determined from fits of all the theoretical rates to the measured ones. Our results for the rather hard to explain $D^0\rightarrow K^+K^-, \pi^+\pi^- $ are in agreement with measured values. We demonstrate that both weak exchange as well as FSI effects are required to get the correct branching ratio for the $D^ \rightarrow K^0\bar{K^0}$ mode. Using our unitarized amplitudes we evaluate the strong phase difference between the amplitudes for $D^0\rightarrow K^-\pi^+$ and $D^0\rightarrow K^+\pi^-$ and find it to be in complete agreement with the recent BES III result.

Recent results, status and prospects for the BESIII experiment

We report the measurement of the asymmetry ACP of the branching fractions of D0 → K-π+ in the CP-odd and CP-even eigenstates using a data sample of 2.92 fb-1 collected with the BESIII detector at the center-of-mass energy √s = 3.773 GeV. With the measured ACP, the strong phase difference δKπ between the doubly Cabibbo-suppressed process D̄0 → K−π+ and the Cabibbo-favored process D0 → K−π+ is extracted. Using world- average values of external parameters, we obtain the most precise measurement of δKπ to date: cos δKπ = 1.02 ± 0.11 ± 0.06 ± 0.01. The first and second uncertainties are statistical and systematic, respectively, while the third arises from external input. Based on the same data sample a preliminary results of the parameter yCP in D0D̄0 oscillation is obtained. Finally, a summary of the recent results from charmonium spectroscopy is reported. The high statistics accumulated at the Y(4260) and Y(4360) energies help us to understand the nature and the proprieties of the XYZ states.

Measurement of the [formula omitted] strong phase difference in [formula omitted

We study D0D¯0 pairs produced in e+e− collisions at s=3.773 GeV using a data sample of 2.92 fb−1 collected with the BESIII detector. We measured the asymmetry AKπCP of the branching fractions of D→K−π+ in CP-odd and CP-even eigenstates to be (12.7±1.3±0.7)×10−2. AKπCP can be used to extract the strong phase difference δKπ between the doubly Cabibbo-suppressed process D¯0→K−π+ and the Cabibbo-favored process D0→K−π+. Using world-average values of external parameters, we obtain cosδKπ=1.02±0.11±0.06±0.01. Here, the first and second uncertainties are statistical and systematic, respectively, while the third uncertainty arises from the external parameters. This is the most precise measurement of δKπ to date.

New determination of the [formula omitted] and [formula omitted] coherence factors and average strong-phase differences

Measurements of the coherence factors (RKππ0 and RK3π) and the average strong-phase differences (δDKππ0 and δDK3π) for the decays D0→K−π+π0 and D0→K−π+π+π− are presented. These parameters are important inputs to the determination of the unitarity triangle angle γ in B∓→DK∓ decays, where D designates a D0 or D¯0 meson decaying to a common final state. The measurements are made using quantum correlated DD¯ decays collected by the CLEO-c experiment at the ψ(3770) resonance, and augment a previously published analysis by the inclusion of new events in which the signal decay is tagged by the mode D→KS0π+π−. The measurements also benefit from improved knowledge of external inputs, namely the D0D¯0 mixing parameters, rDKπ and several D-meson branching fractions. The measured values are RKππ0=0.82±0.07, δDKππ0=(164−14+20)°, RK3π=0.32−0.28+0.20 and δDK3π=(225−78+21)°. Consideration is given to how these measurements can be improved further by using the larger quantum-correlated data set collected by BESIII.

On the ∆ACPsaga

We discuss a model in which the large SU(3) flavor violations in singly Cabibbo suppressed decays of neutral D mesons are ascribed exclusively to the final state interactions. The agreement with the experimental data on the branching ratios is obtained with large strong phase differences which are also necessary for substantial direct CP violation. While the value of the CP violating asymmetries depends on the strength of the penguin contribution, we predict an asymmetry for the decays into charged pions more than twice larger than that for charged kaons and having opposite sign.

Measurement of strong phase in D0 → Kπ decay at BESIII

Based on 2.92 fb-1 of e+e- collision data collected with the BESIII detector at [Formula: see text] GeV, we measured the asymmetry [Formula: see text] of the branching fractions of DCP± → K-π+ (DCP± are the CP-odd and CP-even eigenstates) to be [Formula: see text]. [Formula: see text] is used to extract the strong phase difference δKπ between the doubly Cabibbo-suppressed process [Formula: see text] and Cabibbo-favored D0 → K-π+. By taking inputs of other parameters in world measurements, we obtain cos δKπ = 1.03 ± 0.12 ± 0.04 ± 0.01. This is the most accurate result of cos δKπ to date and can improve the world constrains on the mixing parameters and on γ/ϕ3 in the CKM matrix.

Highlight of Charm Physics at BESIII

In this talk, we present the recent results of charm physics from the BESIII collaboration. This talk covers the studies of the leptonic and semi-leptonic decays of D mesons, and the measurement of the strong phase difference based on the quantum correlation.

Charm mixing as input for model-independent determinations of the CKM phase γ

The coherence factor and average strong phase difference of D0 and D¯0 decay amplitudes to the same final state play an important role in the precision determination of the CKM parameter γ using B±→DK± and related decay modes. So far, this important input from the charm sector could only be obtained from measurements based on quantum-correlated DD¯ pairs produced at the charm threshold. We propose to constrain these parameters using charm mixing, using the large charm samples available at the B factories and LHCb. We demonstrate for the example of D→K+π−π+π− that a substantial improvement in the precision of the coherence factor and average strong phase difference can be obtained with this method, using existing data.

CPviolation inDmeson decays: Would it be a sign of new physics?

Ascribing the large SU(3) violations in the Cabibbo forbidden decays of neutral D mesons to the final state interactions, one gets large strong phase differences, necessary for substantial direct CP violation. While the absolute value of the CP violating asymmetries depend on the uncertain strength of the penguin contribution, we predict an asymmetry for the decays into charged pions more than twice as large and having opposite sign with respect to that for charged kaons.

Enhanced CP violation in D 0→ρ 0(ω)ρ 0(ω)→π + π − π + π −

In the factorization approach we study the direct CP violation in D0→ρ0(ω)ρ0(ω)→π+π−π+π− (with unpolarized ρ0(ω)) via the ρ−ω mixing mechanism. We find that the CP violation can be enhanced due to a large strong phase difference when the masses of the π+π− pairs are in the vicinity of the ω resonance. The CP violation parameter depends on the effective parameter Nc which includes nonfactorizable effects and is determined by the experimental data. Taking into account double ρ−ω mixing contributions, we find the CP violating asymmetry is larger than these in the cases where no ρ−ω mixing or single ρ−ω mixing is taken into account. We also discuss the possibility to observe the predicted CP violation at BEPCII.

Studies of the decaysD0→KS0K−π+andD0→KS0K+π−

The first measurements of the coherence factor R_{K_S^0K\pi} and the average strong--phase difference \delta^{K_S^0K\pi} in D^0 \to K_S^0 K^\mp\pi^\pm decays are reported. These parameters can be used to improve the determination of the unitary triangle angle \gamma\ in B^- \rightarrow $\widetilde{D}K^-$ decays, where $\widetilde{D}$ is either a D^0 or a D^0-bar meson decaying to the same final state, and also in studies of charm mixing. The measurements of the coherence factor and strong-phase difference are made using quantum-correlated, fully-reconstructed D^0D^0-bar pairs produced in e^+e^- collisions at the \psi(3770) resonance. The measured values are R_{K_S^0K\pi} = 0.70 \pm 0.08 and \delta^{K_S^0K\pi} = (0.1 \pm 15.7)$^\circ$ for an unrestricted kinematic region and R_{K*K} = 0.94 \pm 0.12 and \delta^{K*K} = (-16.6 \pm 18.4)$^\circ$ for a region where the combined K_S^0 \pi^\pm invariant mass is within 100 MeV/c^2 of the K^{*}(892)^\pm mass. These results indicate a significant level of coherence in the decay. In addition, isobar models are presented for the two decays, which show the dominance of the K^*(892)^\pm resonance. The branching ratio {B}(D^0 \rightarrow K_S^0K^+\pi^-)/{B}(D^0 \rightarrow K_S^0K^-\pi^+) is determined to be 0.592 \pm 0.044 (stat.) \pm 0.018 (syst.), which is more precise than previous measurements.

Formula omitted] mixing studies with the decays [formula omitted

We demonstrate how a time-dependent analysis of the decays D0→KS0K∓π± can be used to determine the D0–D¯0 mixing parameter y with a precision that is competitive with established methods. The proposed analysis is an inclusive study which makes use of the measurements of the coherence factor and mean strong phase difference for these decays recently performed by CLEO.

Model-independent determination of the strong-phase difference betweenD0andD¯0→KS,L0h+h−(h=π,K) and its impact on the measurement of the CKM angleγ/ϕ3

We report the first determination of the relative strong-phase difference between D^0 -> K^0_S,L K^+ K^- and D^0-bar -> K^0_S,L K^+ K^-. In addition, we present updated measurements of the relative strong-phase difference between D^0 -> K^0_S,L pi^+ pi^- and D^0-bar -> K^0_S,L pi^+ pi^-. Both measurements exploit the quantum coherence between a pair of D^0 and D^0-bar mesons produced from psi(3770) decays. The strong-phase differences measured are important for determining the Cabibbo-Kobayashi-Maskawa angle gamma/phi_3 in B^- -> K^- D^0-tilde decays, where D^0-tilde is a D^0 or D^0-bar meson decaying to K^0_S h^+ h^- (h=pi,K), in a manner independent of the model assumed to describe the D^0 -> K^0_S h^+ h^- decay. Using our results, the uncertainty in gamma/phi_3 due to the error on the strong-phase difference is expected to be between 1.7 and 3.9 degrees for an analysis using B^- K^- D^0-tilde D^0-tilde -> K^0_S pi^+ pi^- decays, and between 3.2 and 3.9 degrees for an analysis based on B^- -> K^- D^0-tilde, D^0-tilde -> K^0_S K^+ K^- decays. A measurement is also presented of the CP-odd fraction, F_-, of the decay D^0 -> K^0_S K^+ K^- in the region of the phi -> K^+ K^- resonance. We find that in a region within 0.01 GeV^2/c^4 of the nominal phi mass squared F_- > 0.91 at the 90% confidence level.

DEMOGRAPHIC MECHANISMS DETERMINING THE DYNAMICS OF THE RELATIVE ABUNDANCE OF PHASES IN BIPHASIC LIFE CYCLES1

Studies investigating the demographic traits that drive the patterns of phase dominance (the ploidy ratio) in isomorphic biphasic life cycles have not found an integrative solution. Either fertility or survival has been suggested independently as the main driver. Here, we provide a global theoretical framework on how demographic mechanisms determine the ploidy ratio, unifying previous numerical and observational attempts at this question. The analytical solutions of both the ploidy ratio and its elasticities to model parameters of a stage/size‐structured model patterned after the life cycle of a marine alga were derived and analyzed. A complex interaction among vital rates determines the patterns of phase dominance of biphasic life cycles. Three co‐occurring processes—growth, fertility, and looping—may dominate the dynamics of the population, determining both its growth rate and ploidy ratio. Our analyses show that in species where fertility is low, the ploidy ratio is highly elastic to looping transitions (survival, breakage, and clonal growth). Consequently, the subtle morphological, ecophysiological, and biochemistry phase differences that have been reported in isomorphic life cycles as not explaining the observed ploidy ratios, may, in fact, explain them if they translate into slight phase differences in looping transitions. In species where fertility is low, the looping dissimilarities between phases cannot be too high favoring simultaneously one phase, as the population structure would be completely dominated by that phase. In the case of ecological similarity between phases (equal looping and growth rates between phases), a ploidy ratio different from one can only be set by strong phase differences in fertility.

Measurement ofCPobservables inB±→DCPK±decays and constraints on the CKM angleγ

Using the entire sample of 467 million Y(4S) --> BBbar decays collected with the BaBar detector at the PEP-II asymmetric-energy B factory at SLAC, we perform a "GLW" analysis of B+- --> D K+- decays, using decay modes in which the neutral D meson decays to either CP-eigenstates or non-CP-eigenstates. We measure the partial decay rate charge asymmetries for CP-even and CP-odd D final states to be A_CP+ = 0.25+-0.06+-0.02 and A_CP- = -0.09+-0.07+-0.02, respectively, where the first error is the statistical and the second is the systematic uncertainty. The parameter A_CP+ is different from zero with a significance of 3.6 standard deviations, constituting evidence for direct CP violation. We also measure the ratios of the charged-averaged B partial decay rates in CP and non-CP decays, R_CP+ = 1.18+-0.09+-0.05 and R_CP- = 1.07+-0.08+-0.04. We infer frequentist confidence intervals for the angle gamma of the (db) unitarity triangle, for the strong phase difference delta_B, and for the amplitude ratio r_B, which are related to the B- --> DK- decay amplitude by r_Be^{i(delta_B-gamma)} = A(B- --> anti-D0 K^-)/A(B- --> D0 K-). Including statistical and systematic uncertainties, we obtain 0.24<r_B<0.45 (0.06<r_B<0.51) and, modulo 180 degrees, 11.3 degrees < gamma < 22.7 degrees or 80.9 degrees < gamma < 99.1 degrees or 157.3 degrees < gamma < 168.7 degrees (7.0 degrees < gamma < 173.0 degrees) at the 68% (95%) confidence level.

ExtractingCPviolation and strong phase inDdecays by using quantum correlations inψ(3770)→D0D¯0→(V1V2)(V3V4)andψ(3770)→D0D¯0→(V1V2)(Kπ)

The charm quark offers interesting opportunities to cross check the mechanism of $CP$ violation precisely tested in the strange and beauty sectors. In this paper, we exploit the angular and quantum correlations in the $D\overline{D}$ pairs produced through the decay of the $\ensuremath{\psi}(3770)$ resonance in a charm factory to investigate $CP$-violation in two different ways. We build $CP$-violating observables in $\ensuremath{\psi}(3770)\ensuremath{\rightarrow}D\overline{D}\ensuremath{\rightarrow}({V}_{1}{V}_{2})({V}_{3}{V}_{4})$ to isolate specific new physics effects in the charm sector. We also consider the case of $\ensuremath{\psi}(3770)\ensuremath{\rightarrow}D\overline{D}\ensuremath{\rightarrow}({V}_{1}{V}_{2})(K\ensuremath{\pi})$ decays, which provide a new way to measure the strong phase difference $\ensuremath{\delta}$ between Cabibbo- favored and doubly-Cabibbo suppressed $D$ decays required in the determination of the Cabibbo-Kobayashi-Maskawa quark-mixing matrix angle $\ensuremath{\gamma}$. Neglecting the systematics, we give a first rough estimate of the sensitivities of these measurements at BES-III with an integrated luminosity of $20\text{ }\text{ }{\mathrm{fb}}^{\ensuremath{-}1}$ at $\ensuremath{\psi}(3770)$ peak and at a future Super $\ensuremath{\tau}$-charm factory with a luminosity of ${10}^{35}\text{ }\text{ }{\mathrm{cm}}^{\ensuremath{-}2}\text{ }{\mathrm{s}}^{\ensuremath{-}1}$.

Determination of theD0→K−π+π0andD0→K−π+π+π−coherence factors and average strong-phase differences using quantum-correlated measurements

The first measurements of the coherence factors (R_Kpipi0 and R_K3pi) and the average strong-phase differences (delta_D^Kpipi0 and delta_D^K3pi) for D0->K-pi+pi0 and D0->K-pi+pi+pi- are presented. These parameters can be used to improve the determination of the unitarity triangle angle gamma in B^- -> DK^- decays, where D is a D^0 or Dbar^0 meson decaying to the same final state. The measurements are made using quantum-correlated, fully-reconstructed D^0Dbar^0 pairs produced in e+e- collisions at the psi(3770) resonance. The measured values are: R_Kpipi0=0.84+/-0.07, delta_D^Kpipi0=(227+14-17) deg, $R_K3pi=0.33+0.20-0.23, and delta_D^K3pi=(114+26-23) deg. These results indicate significant coherence in the decay D0->K-pi+pi0, whereas lower coherence is observed in the decay D0->K-pi+pi+pi-. The analysis also results in a small improvement in the knowledge of other D-meson parameters, in particular the strong-phase difference for D0->K-pi+, delta_D^Kpi, and the mixing parameter, y.

First model-independent determination of the relative strong phase betweenD0andD¯0→KS0π+π−and its impact on the CKM angleγ/ϕ3measurement

We exploit the quantum coherence between pair-produced D0 and D0B in psi(3770) decays to make a first determination of the relative strong phase differences between D0--> K0Spi+pi- and D0B--> K0Spi+pi-, which are of great importance in determining the CKM angle gamma/phi3 in B- --> D0 (D0B) K- decays. Using 818 1/pb of e+e- collision data collected with the CLEO-c detector at Ecm = 3.77 GeV, we employ a binned Dalitz-plot analysis of K0S pi+pi- and K0Lpi+pi- decays recoiling against flavor-tagged, CP-tagged and K0Spi+pi- tagged events to determine these strong phase differences.

Phenomenological studies on D0-D0 mixing and strong phase difference

Most recently, both BABAR and Belle experiments found evidences of neutral D mixing. In this paper, we discuss the constraints on the strong phase difference in D0→Kπ decay from the measurements of the mixing parameters y′, yCP, and x at the B-factories. With CP tag technique at ψ（3770） peak, the extraction of the strong phase difference at BES-Ⅲ is discussed. The sensitivity of the measurement of the mixing parameter y is estimated in BES-Ⅲ experiment at ψ（3770） peak. Finally, we make an estimate on the measurements of mixing rate RM.