Strong Phase Difference Research Articles

Role of ρ−ω interference in semileptonic B→π+π−ℓν¯ℓ decays

It is long known that interference effects play an important role in understanding the shape of the π+π− spectrum of resonances near the threshold. In this manuscript, we investigate the role of the ρ−ω interference in the study of semileptonic B→π+π−ℓν¯ℓ decays. We determine for the first time the strong phase difference between B→ρ0ℓν¯ℓ and B→ωℓν¯ℓ from a recent Belle measurement of the mππ spectrum of B→π+π−ℓν¯ℓ. We find ϕρ−ω=(−46−67+155)° and extract the branching fraction of B(B→ρ0ℓν¯ℓ)=(1.41−0.38+0.49)×10−4. In addition, we set a limit on the S-wave component within an mππ window ranging from 2mπ to 1.02 GeV of ΔB(B→[π+π−]Sℓν¯ℓ)<0.51×10−4 at 90% CL. We also determine the absolute value of the Cabibbo-Kobayashi-Maskawa matrix element of |Vub|ρ−ω=(3.03−0.44+0.49)×10−3, which takes into account the ρ−ω interference. Published by the American Physical Society 2024

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A model-independent study of CP\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$C\\!P$$\\end{document} violation in B0→DK∗0\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$${{B} ^0} \\rightarrow {D} {{K} ^{*0}} $$\\end{document} decays is presented using data corresponding to an integrated luminosity of 9\\,fb-1\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\ ext {\\,fb} ^{-1}$$\\end{document} collected by the LHCb experiment at centre-of-mass energies of s=7,8\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\sqrt{s}=7, \\, 8$$\\end{document} and 13\\,TeV\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\ ext {\\,Te\\hspace{-1.00006pt}V}$$\\end{document}. The CKM angle γ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\gamma $$\\end{document} is determined by examining the distributions of signal decays in phase-space bins of the self-conjugate D→KS0h+h-\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$${D} \\rightarrow {{K} ^0_{\ extrm{S}}} h^+ h^-$$\\end{document} decays, where h=π,K\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$h = \\pi , K$$\\end{document}. Observables related to CP\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$C\\!P$$\\end{document} violation are measured and the angle γ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\gamma $$\\end{document} is determined to be γ=(49-19+22)∘\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\gamma =(49^{+ 22}_{-19})^\\circ $$\\end{document}. Measurements of the amplitude ratio and strong-phase difference between the favoured and suppressed B0\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$${B} ^0$$\\end{document} decays are also presented.

Enhanced Charm CP Asymmetries from Final State Interactions.

We show that final state interactions (FSI) within a CPT invariant two-channel framework can enhance the charge-parity (CP) violation difference between D^{0}→π^{-}π^{+} and D^{0}→K^{-}K^{+} decays up to the current experimental value. This result relies upon (i)the dominant tree level diagram, (ii)the well-known experimental values for the D^{0}→π^{-}π^{+} and D^{0}→K^{-}K^{+} branching ratios, and (iii)the ππ→ππ and ππ→KK scattering data to extract the strong phase difference and inelasticity. Based on well-grounded theoretical properties, we find the sign and bulk value of the ΔA_{CP} and A_{CP}(D^{0}→π^{-}π^{+}) recently observed by the LHCb Collaboration.

Improved measurement of the strong-phase difference delta _D^{Kpi } in quantum-correlated D{bar{D}} decays

The decay D rightarrow K^-pi ^+ is studied in a sample of quantum-correlated D{bar{D}} pairs, based on a data set corresponding to an integrated luminosity of 2.93 fb^{-1} collected at the psi (3770) resonance by the BESIII experiment. The asymmetry between C!P-odd and C!P-even eigenstate decays into K^-pi ^+ is determined to be {{mathcal {A}}}_{Kpi } = 0.132 pm 0.011 pm 0.007, where the first uncertainty is statistical and the second is systematic. This measurement is an update of an earlier study exploiting additional tagging modes, including several decay modes involving a K^0_L meson. The branching fractions of the K^0_L modes are determined as input to the analysis in a manner that is independent of any strong phase uncertainty. Using the predominantly C!P-even tag Drightarrow pi ^+pi ^-pi ^0 and the ensemble of C!P-odd eigenstate tags, the observable {{mathcal {A}}}_{Kpi }^{pi pi pi ^0} is measured to be 0.130 pm 0.012 pm 0.008. The two asymmetries are sensitive to r_D^{Kpi }cos delta _D^{Kpi }, where r_D^{Kpi } and delta _D^{Kpi } are the ratio of amplitudes and phase difference, respectively, between the doubly Cabibbo-suppressed and Cabibbo-favoured decays. In addition, events containing D rightarrow K^-pi ^+ tagged by D rightarrow K^0_{S,L} pi ^+pi ^- are studied in bins of phase space of the three-body decays. This analysis has sensitivity to both r_D^{Kpi }cos delta _D^{Kpi } and r_D^{Kpi }sin delta _D^{Kpi }. A fit to {{mathcal {A}}}_{Kpi }, {{mathcal {A}}}_{Kpi }^{pi pi pi ^0} and the phase-space distribution of the D rightarrow K^0_{S,L} pi ^+pi ^- tags yields delta _D^{Kpi }= left( 187.6 {^{+8.9}_{-9.7}}{^{+5.4}_{-6.4}} right) ^{circ }, where external constraints are applied for r_D^{Kpi } and other relevant parameters. This is the most precise measurement of delta _D^{Kpi } in quantum-correlated D{bar{D}} decays.

Charming synergies: the role of charm-threshold studies in the search for physics beyond the Standard Model

Measurements performed with pairs of charm mesons produced at threshold from the decay of the $\psi(3770)$ resonance are of great value in flavour physics. The quantum correlation that exists between the two mesons allows unique access to strong-phase information, which is essential input to flavour-physics studies conducted in other environments. An excellent example from the BESIII collaboration is a recent determination of the strong-phase difference between $D^0$ and $\bar{D}^0$ mesons in the decay $D^0 \to K^0_S\pi^+\pi^-$, which has enabled recent measurements to be performed of the $C\!P$-violating phase $\gamma$ and $D^0-\bar{D}^0$ oscillations by the LHCb experiment at CERN. These $\psi(3770)$ data, and also those collected just above the thresholds for $D_s^+$ and $\Lambda_c^+$ production, can also be exploited in many other ways that are of benefit to flavour-physics studies. These synergies are reviewed, and the need for larger threshold data samples in the near future is emphasised.

Measurement of the D \u2192 K\u2212\u03c0+\u03c0+\u03c0\u2212 and D \u2192 K\u2212\u03c0+\u03c00 coherence factors and average strong-phase differences in quantum-correlated Doverline{D} decays

The decays D → K−π+π+π− and D → K−π+π0 are studied in a sample of quantum-correlated Doverline{D} pairs produced through the process e+e− → ψ(3770) → Doverline{D} , exploiting a data set collected by the BESIII experiment that corresponds to an integrated luminosity of 2.93 fb−1. Here D indicates a quantum superposition of a D0 and a {overline{D}}^0 meson. By reconstructing one neutral charm meson in a signal decay, and the other in the same or a different final state, observables are measured that contain information on the coherence factors and average strong-phase differences of each of the signal modes. These parameters are critical inputs in the measurement of the angle γ of the Unitarity Triangle in B− → DK− decays at the LHCb and Belle II experiments. The coherence factors are determined to be RK3π = {0.52}_{-0.10}^{+0.12} and {R}_{K{pi pi}^0} = 0.78 ± 0.04, with values for the average strong-phase differences that are {delta}_D^{K3pi }=left({167}_{-19}^{+31}right){}^{circ} and {delta}_D^{K{pi pi}^0}=left({196}_{-15}^{+14}right){}^{circ} , where the uncertainties include both statistical and systematic contributions. The analysis is re-performed in four bins of the phase-space of the D → K−π+π+π− to yield results that will allow for a more sensitive measurement of γ with this mode, to which the BESIII inputs will contribute an uncertainty of around 6°.

Exploring new physics contributions to CP violation in tau ^- rightarrow K^-pi ^0nu _{tau }

A general analysis of possible violation of CP in processes like tau rightarrow Kpi nu , for unpolarized tau is presented. In this paper, we derive the new contributions to the effective Hamiltonian governs vert Delta S vert =1 semileptonic tau decays in the framework of two Higgs doublet model with generic Yukawa structure and Leptoquarks models. Within these models, we list all operators, in the effective Hamiltonian and provide analytical expression for their corresponding Wilson coefficients. Moreover, we analyze the role of the different contributions, originating from the scalar, vecor and tensor hadronic currents, in generating direct CP asymmetry in the decay rate of tau ^-rightarrow K^-pi ^0nu _tau . We show that non vanishing direct CP asymmetry in the decay rate of tau ^-rightarrow K^-pi ^0nu _tau can be generated due to the presence of both, the weak phase in the Wilson coefficient corresponding to the tensor operator and the strong phase difference resulting from the interference between the form factors expressing the matrix elements of the vector and tensor hadronic currents. After taking into account all relevant constraints, we find that the generated direct CP asymmetry is of order 10^{-8} which is several orders of magnitude larger than the standard model prediction. We show also that, in two Higgs doublet model with generic Yukawa structure , direct local or non integrated CP violation can be as large as 0.3 % not far from experimental possibilities. This kind of asymmetry can be generated due to the interference between vector and scalar contributions with different weak phases which is not the case in the SM.

Measurement of the CKM angle \u03b3 in B\xb1 \u2192 DK\xb1 and B\xb1 \u2192 D\u03c0\xb1 decays with D \u2192 {K}_{mathrm{S}}^0 h+h\u2212

A measurement of CP-violating observables is performed using the decays B± → DK± and B± → Dπ±, where the D meson is reconstructed in one of the self-conjugate three-body final states {K}_{mathrm{S}}^0 π+π− and {K}_{mathrm{S}}^0 K+K− (commonly denoted {K}_{mathrm{S}}^0 h+h−). The decays are analysed in bins of the D-decay phase space, leading to a measurement that is independent of the modelling of the D-decay amplitude. The observables are inter- preted in terms of the CKM angle γ. Using a data sample corresponding to an integrated luminosity of 9 fb−1 collected in proton-proton collisions at centre-of mass energies of 7, 8, and 13 TeV with the LHCb experiment, γ is measured to be left({68.7}_{-5.1}^{+5.2}right){}^{circ} . The hadronic parameters {r}_B^{D K},{r}_B^{Dpi},{delta}_B^{D K},kern0.5em mathrm{and}kern0.5em {delta}_B^{Dpi} , which are the ratios and strong-phase differences of the suppressed and favoured B± decays, are also reported.

Strong-Phase Measurement in Charmed-Hadron Decays in Belle II Experiment and $${c{-}}{\tau}$$ Factory

A method of employing semileptonic $$K^{0}$$ -meson decays is proposed. Combined with a time-dependent analysis of decay parameters of initially produced combination, it permits extracting $$K^{0}{-}\bar{K}^{0}$$ . These measurements could be applied to heavy-flavor physics problems—in particular, charm physics. A feasibility study for the strong-phase difference in charm decays is performed.

Improved model-independent determination of the strong-phase difference between D0 and D¯0→KS,L0K+K− decays

We present a measurement of the strong-phase difference between $D^{0}$ and $\bar{D}^{0}\to K^{0}_{\rm S,L}K^{+}K^{-}$ decays, performed through a study of quantum-entangled pairs of charm mesons. The measurement exploits a data sample equivalent to an integrated luminosity of 2.93~fb$^{-1}$, collected by the BESIII detector in $e^{+}e^{-}$ collisions corresponding to the mass of the $\psi(3770)$ resonance. The strong-phase difference is an essential input to the determination of the Cabibbo-Kobayashi-Maskawa (CKM) angle $\gamma/\phi_3$ through the decay $B^{-}\to DK^{-}$, where $D$ can be either a $D^{0}$ or a $\bar{D}^{0}$ decaying to $K^{0}_{\rm S,L}K^{+}K^{-}$. This is the most precise measurement to date of the strong-phase difference in these decays.

Measurement of {D}^0-overline{D} 0 Mixing Parameters Using Semileptonic Decays of Neutral Kaon

We propose a new method to extract {D}^0-overline{D} 0 mixing parameters using the D0→ overline{K} 0π0 decay with the overline{K} 0 reconstructed in the semileptonic mode. Although a K0 → π±ℓ∓vℓ decay suffers from low statistics and complexity of the secondary vertex reconstruction in comparison to the standard {K}_S^0to {pi}^{+}{pi}^{-} vertex, it provides much richer, sometimes unique information about the initial state of a K0-meson produced in a heavy-flavor hadron decay. In this paper it is shown that the reconstruction of the chain D0 → K0(π±ℓ∓vℓ)π0 allows one to extract the strong phase difference between the doubly Cabibbo-suppressed and Cabibbo-favored decay amplitudes, which is of key importance for determination of the {D}^0-overline{D} 0 -mixing parameters.

Improved sensitivity to the CKM phase γ through binning phase space in B− → DK−, D → K+π−π−π+ decays

A binning scheme is proposed for D→K+π−π−π+ phase space that will improve the sensitivity of a B−→DK− analysis to the angle γ of the Cabibbo-Kobayashi-Maskawa Unitarity Triangle. The scheme makes use of amplitude models recently reported by the LHCb collaboration. Assuming that a four-bin scheme optimised on the models retains a similar sensitivity when applied in data, it is estimated that the statistical uncertainty on γ from the B-meson sample so far collected by the LHCb experiment will be as low as 5 degrees. This will be one of the most precise results available for any single decay mode in a B−→DK− measurement. Quantum-correlated DD¯ data accumulated by the CLEO-c experiment are analysed to provide first constraints on the coherence factors and average strong-phase differences in the four bins, which are necessary inputs for the measurement. These constraints are compared with the predictions of the model, and consequences for the measurement of γ are discussed.

First measurement of the CKM angle \u03d53 with B\xb1\u2192 D( {K}_{mathrm{S}}^0 \u03c0+\u03c0\u2212\u03c00) K\xb1 decays

We present the first model-independent measurement of the CKM unitarity triangle angle ϕ3 using B±→ D( {K}_{mathrm{S}}^0 π+π−π0) K± decays, where D indicates either a D0 or overline{D} 0 meson. Measurements of the strong-phase difference of the D → {K}_{mathrm{S}}^0 π+π−π0 amplitude obtained from CLEO-c data are used as input. This analysis is based on the full Belle data set of 772 × 106B overline{B} events collected at the Υ(4S) resonance. We obtain ϕ3 = ( {5.7}_{-8.8}^{+10.2} ±3.5±5.7)° and the suppressed amplitude ratio rB = 0.323±0.147±0.023±0.051. Here the first uncertainty is statistical, the second is the experimental systematic, and the third is due to the precision of the strong-phase parameters measured from CLEO-c data. The 95% confidence interval on ϕ3 is (−29.7, 109.5)°, which is consistent with the current world average.

Comparison of <i>H</i> component geomagnetic field time series obtained at different sites over South America

Abstract. The geomagnetic field in the Brazilian sector is influenced by the South American Magnetic Anomaly (SAMA) that causes a decrease in the magnitude of the local geomagnetic field when compared to other regions in the world. Thus, the magnetometer network and data set of space weather over Brazil led by Embrace are important tools for promoting the understanding of geomagnetic fields over Brazil. In this sense, in this work we used the H component of geomagnetic fields obtained at different sites in South America in order to compare results from the phase coherence obtained from wavelet transform (WT). Results from comparison between Cachoeira Paulista (CXP) and Eusébio (EUS), and Cachoeira Paulista and São Luis (SLZ), indicated that there exist some phenomena that occur simultaneously in both locations, putting them in the same phase coherence. However, there are other phenomena putting both locations in a strong phase difference as observed between CXP and Rio Grande, Argentina (RGA). This study was done for a specific moderate geomagnetic storm that occurred in March 2003. The results are explained in terms of nonlinear interaction between physical phenomena acting in distinct geographic locations and at different times and scales. Keywords. Geomagnetism and paleomagnetism (time variations – diurnal to secular)

Model-independent determination of the strong phase difference between D0 and {overline{D}}^0to {pi}^{+}{pi}^{-}{pi}^{+}{pi}^{-} amplitudes

For the first time, the strong phase difference between D0 and {overline{D}}^0to {pi}^{+}{pi}^{-}{pi}^{+}{pi}^{-} amplitudes is determined in bins of the decay phase space. The measurement uses 818 pb−1 of e+e− collision data that is taken at the ψ(3770) resonance and collected by the CLEO-c experiment. The measurement is important for the determination of the CP -violating phase γ in B± → DK± (and similar) decays, where the D meson (which represents a superposition of D0 and {overline{D}}^0 ) subsequently decays to π+π−π+π−. To obtain optimal sensitivity to γ, the phase space of the D → π+π−π+π− decay is divided into bins based on a recent amplitude model of the decay. Although an amplitude model is used to define the bins, the measurements obtained are model-independent. The CP -even fraction of the D → π+π−π+π− decay is determined to be F+4π = 0.769 ± 0.021 ± 0.010, where the uncertainties are statistical and systematic, respectively. Using simulated B± → DK±, D → π+π−π+π− decays, it is estimated that by the end of the current LHC run, the LHCb experiment could determine γ from this decay mode with an uncertainty of (±10 ± 7)°, where the first uncertainty is statistical based on estimated LHCb event yields, and the second is due to the uncertainties on the parameters determined in this paper.

Quantum-correlated measurements of D\u2009\u2192\u2009KS0\u03c0+\u03c0\u2212\u03c00 decays and consequences for the determination of the CKM angle \u03b3

We perform quantum-correlated measurements of the decay D → KS0π+π−π0 using a data sample corresponding to an integrated luminosity of 0.82 fb−1 collected at the ψ(3770) resonance by the CLEO-c detector. The value of the CP -even fraction F+ is determined to be 0.238 ± 0.012 ± 0.012. The strong-phase differences are also measured in different regions of KS0π+π−π0 phase space by binning around the intermediate resonances present. The potential sensitivity of the results for determining the CKM angle γ from B± → D(KS0π+π−π0)K± decays is also discussed.

Probe CP violation in H→γZ through forward-backward asymmetry

We suggest that the forward-backward asymmetry $(A_{FB})$ of the charged leptons in $gg\to H\to\gamma Z\to\gamma \ell^-\ell^+$ process could be used to probe the CP violating $H\gamma Z$ coupling when the interference from $gg\to\gamma Z\to\gamma \ell^-\ell^+$ process is included. With CP violation in $H\gamma Z$ coupling, the interference effect leads to a non-vanishing $A_{FB}$, which is also sensitive to the strong phase differences. The resonant and non-resonant strong phases together make $A_{FB}(\hat{s})$ change sign around Higgs mass $M_H$. For phenomenology study, we suggest the integral over one-side mass region below $M_H$ to magnify the $A_{FB}$ strength.

Charm physics at BESIII

The study of mesons and baryons which contain at least one charm quark is referred to as open charm physics. It offers the possibility to study up-type quark transitions. Since the c quark can not be treated in any mass limit, theoretical predictions are difficult and experimental input is crucial. BESIII collected large data samples of e+e- collisions at several charm thresholds. The at-threshold decay topology offers special opportunities to study open charm decays.We present a selection of recent BESIII results. The D+s decay constant is measured using the leptonic decays to μ+ν and τ+ ν. Using the semi-leptonic decays of D0 and D± to Ke+νe and πe+νe, a measurement of the form factors f+K (q2) and f+π (q2) is performed and furthermore, we show preliminary results of a model independent measurement of the strong phase difference between D0 and D0 in the channel D0 → Ks0π+π- which is an experimental input to the measurement of the CKM angle γ/ϕ3.

Model-independent measurement of the CKM angle γ using B0 → DK∗0 decays with D → K S 0 π + π − and K S 0 K+K−

A binned Dalitz plot analysis of the decays $B^0 \to D K^{\ast 0}$, with $D \to K_{S}^{0} \pi^{+} \pi^{-}$ and $K_{S}^{0} K^{+} K^{-}$, is performed to measure the observables $x_\pm$ and $y_\pm$, which are related to the CKM angle $\gamma$ and the hadronic parameters of the decays. The $D$ decay strong phase variation over the Dalitz plot is taken from measurements performed at the CLEO-c experiment, making the analysis independent of the $D$ decay model. With a sample of proton-proton collision data, corresponding to an integrated luminosity of $3.0\,\rm{fb}^{-1}$, collected by the LHCb experiment, the values of the $CP$ violation parameters are found to be $x_+ = 0.05 \pm 0.35 \pm 0.02$, $x_-=-0.31\pm 0.20 \pm 0.04$, $y_+=-0.81\pm 0.28\pm 0.06$ and $y_-=0.31\pm 0.21 \pm 0.05$, where the first uncertainties are statistical and the second systematic. These observables correspond to values $\gamma$ = $(71 \pm 20)^\circ$, $r_{B^0} = 0.56\pm 0.17$ and $\delta_{B^0} = (204\,^{+21}_{-20})^\circ$. The parameters $r_{B^0}$ and $\delta_{B^0}$ are the magnitude ratio and strong phase difference between the suppressed and favoured $B^0$ decay amplitudes, and have been measured in a region of $\pm 50$ MeV/$c^2$ around the $K^{\ast}(892)^{0}$ mass and with the magnitude of the cosine of the $K^{\ast}(892)^{0}$ helicity angle larger than 0.4.

Improved determination of the D → K − π + π + π − coherence factor and associated hadronic parameters from a combination ofe+e−→ψ(3770)→cc¯andpp→cc¯Xdata

Measurements of the coherence factor $R_{K3\pi}$, the average strong-phase difference $\delta^{K3\pi}_D$ and mean amplitude ratio $r_D^{K3\pi}$ for the decay $D \to K^-\pi^+\pi^+\pi^-$ are presented. These parameters are important inputs to the determination of the unitarity triangle angle $\gamma$ in $B^- \to DK^-$ decays, where $D$ designates a superposition of $D^0$ and $\bar{D}{}^0$ mesons decaying to a common final state. The results are based on a combined fit to observables obtained from a re-analysis of the CLEO-c $\psi(3770)$ data set and those measured in a $D^0\bar{D}^0$ mixing study performed by the LHCb collaboration.