Figure 4 - uploaded by Paul Soler
Content may be subject to copyright.
Efficiency function used in the isobar model fits, corresponding to the average efficiency over the full data set. The coordinates mKS0π2 and mKS0K2 are used to highlight the approximate symmetry of the efficiency function. The z units are arbitrary.
Source publication
Amplitude models are applied to studies of resonance structure in D 0 → K 0 S K − π þ and D 0 → K 0 S K þ π − decays using pp collision data corresponding to an integrated luminosity of 3.0 fb −1 collected by the LHCb experiment. Relative magnitude and phase information is determined, and coherence factors and related observables are computed for b...
Similar publications
Fractional Repetition (FR) codes break the data into smaller fragments and distribute these fragments across multiple storage nodes. This paper focuses on extension-based construction methods for obtaining new FR codes from existing FR codes. Additionally, it formulates a particular case of extension codes as an exact cover problem, enabling an alg...
This study investigates the h-fractional difference operators with h-discrete generalized Mittag-Leffler kernels (h E , (Θ, t − h (sh)) in the sense of Riemann type (namely, the ABR) and Caputo type (namely, the ABC). For which, we will discuss the region of convergent. Then, we study the h-discrete Laplace transforms to formulate their correspondi...
Abstract A fractional-order eco-epidemiological model with disease in the prey population is formulated and analyzed. Mathematical analysis and numerical simulations are performed to clarify the characteristics of the proposed fractional-order model. The existence, uniqueness, non-negativity and boundedness of the solutions are proved. The local an...
This study aims to analyze student errors in resolving word problems, which are then formulated into characteristics of student errors according to gender. The subject selection was done randomly from male and female students of grade VII who made mistakes in solving the questions. Research data from the test results of 2 items word problem type. T...
In this article, we formulate the concept of generalize bonvexity/pseudobonvexity functions. We formulate duality results for second-order fractional symmetric dual programs of G-Wolfe-type model. In the next section, we explain the duality theorems under generalize bonvexity/pseudobonvexity assumptions. We identify a function lying exclusively in...
Citations
... However, even the 2018 PDG [43] did not list the K(1460) as an 'established particle'. In the most recent studies of the resonance structure in D 0 → K m π ± π ± π m decays using pp collision, data collected at 7 and 8 TeV with the LHCb experiment [44], and the precise measurements of the + a 1 (1260), -K 1 (1270) and K(1460) resonances are made. Within a model-independent partial-wave analysis performed for the K (1460) resonance, it is found that the mass is roughly consistent with previous studies [41,42]. ...
... MeV for the parameter sets A and B for KK and KK interactions, respectively. The mass of the charged resonance K + (1460) in the ABC ( [51] did not reproduce the quite sizeable experimental width, 335.60 ± 6.20 ± 8.65 MeV [44,46]. In [48] reported the width of approximately 200 MeV for the + + K K K 0 resonance and [49] presented the estimation for the width of Γ 100 MeV for K(1460) resonance. ...
... These channels require two-body dynamics either beyond s-wave (to form K * (892) or ρ) or well above 1 GeV (to form K * (1430)), and these effects are not included in [49,50,54]. It is then natural that the width reported in those and present works is much smaller than the one quoted indicated in [41,42] (Γ ∼ 250 MeV) or in the recent LHCb analysis [44] (Γ ∼ 335 MeV). ...
In the framework of the Faddeev equations in configuration space, we
investigate the $K$(1460) meson as a resonant state of the $KK\bar{K}$
kaonic system. We perform calculations for the particle configurations $%
K^{0}K^{+}K^{-}$ and $K^{0}K^{+}\overline{{K}^{0}}$ within two models: the $%
ABC $ model, in which all three particles are distinguishable, and the $AAC$
model when two particles are identical. The models differ in their treatment
of the kaon mass difference and the attractive Coulomb force between the $%
K^{+}K^{-}$ pair. We found that the Coulomb shift adds over 1 MeV to the
three-body binding energy. The expected correction to the binding energy due
to mass redistribution from $AA$ to $AB$ is found to be negligible, up to a
maximum of 6\% of the relative mass correction. At the same time, the
symmetry of the wave function is distorted depending on the mass ratio
value. We found that the repulsive $KK$ interaction plays essential role in the binding energy of the $KK\bar K$ system and report the mass of 1461.8 or 1464.1 MeV for the neutral $K^{0}$(1460) and 1466.5 or 1468.8 MeV for the charged $K^{+}$(1460) resonances, respectively,
depending on the parameter sets for $KK$ and $K\bar{K}$ interactions.
... First, we perform the PQCD prediction of B → a 0 ð980Þ½→ηπK decays that go beyond the single pole approximation, trying to explain the measurement status. Second, we consider the roles of a 0 ð1450Þ and a 0 ð1950Þ in the B → KKK decays inspired by the recent measurements of charm meson decays where a 0 ð1450Þ and a 0 ð1950Þ are observed in the KK invariant mass spectral [29][30][31], supplementing to the B → ηπK decays observed first at the Crystal Barrel Collaboration a long time ago [32,33]. The study would be executed in parallel by taking two different scenarios of a 0 states, where the first one says that a 0 ð980Þ is the lowest lying qq state and a 0 ð1450Þ is the first excited state, and the second one states that a 0 ð1450Þ and a 0 ð1950Þ are the lowest lying qq state and the first excited state, respectively. ...
We propose to study the multiparticle configurations of isovector scalar mesons, a0(980) and a0(1450), in the charmless three-body B decays by considering the width effects. Two scenarios of a0 configurations are assumed in which the first one takes a0(980) as the lowest-lying qq¯ state and a0(1450) as the first radial excited state, the second one takes a0(1450) as the lowest-lying qq¯ state and a0(1950) as the first radial excited state while a0(980) is not a qq¯ state. Within these two scenarios, we do the perturbative QCD (PQCD) calculation for the quasi-two-body B→a0[→KK¯/πη]h decays and extract the corresponding branching fractions of two-body B→a0h decays under the narrow width approximation. Our predictions show that the first scenario of the a0(980) configuration cannot be excluded by the available measurements in B decays, and the contributions from a0(1450) to the branching fractions in most channels are comparable in the first and second scenarios. Several channels are suggested for the forthcoming experimental measurements to reveal the multiparticle configurations of a0, such as the channel B0→a0−(980)[→π−η]π+ with the largest predicted branching fraction, the channels B0→a0±(1450)[→K±K¯0,π±η]π∓ whose branching fractions obtained in the second scenario is about three times larger in magnitude than that obtained in the first scenario, and also the channels B+→a0+(1950)[K+K¯0/π+η]K0 whose branching fractions are linearly dependent on the partial width Γa0(1950)→KK/πη.
... Due to their small nonresonant components and abundant intermediate states, three-body D decays as well as their subprocesses were widely employed to study the properties and substructures of various resonant states [4][5][6][7][8][9][10][11][12][13][14][15][16][17], to analyze hadron-hadron interactions [18][19][20][21][22][23][24], and to extract information on the ππ, Kπ, and KK S-wave amplitude in the low energy region [25][26][27][28][29][30][31][32][33][34][35]. In the experimental analyses for relevant decay amplitudes [26,[36][37][38][39][40][41][42], Dalitz plot technique [43] was widely adopted in recent years. The corresponding expressions of the decay amplitudes are usually composed of the coherent sum of the resonant and nonresonant contributions within the isobar formalism [44][45][46]. ...
... The contributions for the kaon pair in the final states of three-body D decays from the ρ family resonances, such as ρð1450Þ AE and ρð1700Þ AE for K 0 S K AE in the decays D þ → K 0 S K þ π 0 and D 0 → K 0 S K AE π ∓ , have been noticed by BESIII [47], LHCb [40], and CLEO [48] Collaborations. In addition, the subprocess ρð1450Þ 0 → K þ K − was found to contribute a surprising large fit fraction for the threebody decays B AE → π AE K þ K − by LHCb Collaboration in Ref. [49]. ...
We construct the theoretical framework for quasi-two-body D meson decays with the help of pion and kaon electromagnetic form factors and with which we study the contributions of the subprocesses ρ(770,1450)→KK¯ for the three-body D decays within the flavor SU(3) symmetry. Because of the limitations imposed by phase space and strong coupling, the contributions for the kaon pair from the virtual bound state ρ(770) are channel dependent and generally small for the concerned three-body D decays, but some quasi-two-body processes could still be observed in the Dalitz plot analyses for related decays, such as D0→K−ρ(770)+→K−K+KS0 and D+→KS0ρ(770)+→KS0K+KS0, they are predicted to have the branching fractions B=(0.82±0.04)×10−4 and B=0.47−0.03+0.05×10−4, which are (1.86±0.16)% and (1.84−0.16+0.21)%, respectively, of the total branching fractions for the corresponding three-body D decays. We find in this work that the normal subprocesses like ρ(1450)+→π+π0 or ρ(1450)+→K+K¯0, which are bound by the masses of decaying initial states, will provide virtual contributions in some special decays.
... The method is efficient to extract information on the role played by different resonances but has its limitations. We quote Ref. [14]: "This approach, albeit largely employed [15], has conceptual limitations. The outcome of isobar model analyses are resonance parameters such as fit fractions, masses and widths, which are neither directly related to any underlying dynamical theory nor provide clues to the identification of two-body substructures. ...
... Our model has three parameters: one for the global normalization C in Eq. (6) and two for the global weight of the ϕ meson amplitude, complex D in Eq. (10), which we fit to the experimental [13] K þ K − distribution [only Fig. 4(a)]. The other parts in Fig. 4 represent the K þ K þ distribution and the distributions s high K þ K − and s low K þ K − where, according to Ref. [13], s high K þ K − and s low K þ K − represent the highest and lowest values among s 12 and s 23 ; see Fig. 5. Theoretically, we evaluate the s low K þ K − distribution including θðs 23 − s 12 Þ in the integrand of Eq. (15), with θ the step function. ...
We study theoretically the resonant structure of the double Cabibbo suppressed D+→K−K+K+ decay. We start from an elementary production diagram, considered subleading in previous approaches, which cannot produce a final K−K+ pair at the tree level but which we show to be able to provide the strength of the decay through final meson-meson state interaction. The different meson-meson elementary productions are related through SU(3), and the final rescattering is implemented from a suitable implementation of unitary extensions of chiral perturbation theory, which generate dynamically the scalar resonances f0(980) and a0(980). We obtain a good agreement with recent experimental data from the LHCb Collaboration with a minimal freedom in the fit and show the dominance of the a0(980) contribution close to the threshold of the K−K+ spectrum.
... CP -violation searches in phase space can be performed in either a model-dependent or -independent manner. In the former, an amplitude model is constructed and then fitted separately to the charm and anti-charm decay samples [122,125,127,128]. Significant differences in the amplitude modulus, phase or fit-fraction of any resonance contribution between the two data sets would signify the presence of CP violation. ...
In recent years charm physics has undergone a renaissance, one which has been catalysed by an unexpected and impressive set of experimental results from the $B$-factories, the Tevatron and LHCb. The existence of $D^0\bar{D}{}^0$ oscillations is now well established, and the recent discovery of $CP$ violation in $D^0$ decays has further renewed interest in the charm sector. In this article we review the current status of charm-mixing and $CP$-violation measurements, and assess their agreement with theoretical predictions within the Standard Model and beyond. We look forward to the great improvements in experimental precision that can be expected over the coming two decades, and the prospects for corresponding advances in theoretical understanding.
... in the approach of Ref. [20]. From the study of Ref. [43], the partial decay widths of K(1460) ...
... Considering now the decay widths listed in Tables I-III, we can calculate the ratios in Eqs. (42), (43), (44). We present the results in Tables IV-VI As can be seen from Table V, the value of B 2 depends on the description considered for K + 1 (1270). ...
... • A ratio B 2 [defined in Eq. (43)] for the φ(2170) decay to final states involving K(1460) and K 1 (1270) is obtained using yet another model (model A) for the latter one, besides the two mentioned in the previous point. Within model A, K 1 (1270) is interpreted as a state, related to two poles in the complex energy plane, arising from pseudoscalarvector meson dynamics. ...
In this work we study the strong decays of $\phi(2170)$ to final states involving the kaonic resonances $K(1460)$, $K_1(1270)$ and $K_1(1400)$, on which experimental data have recently been extracted by the BESIII Collaboration. The formalism developed here is based on interpreting $\phi(2170)$ and $K(1460)$ as states arising from three-hadron dynamics, which is inspired by our earlier works. For $K_1(1270)$ and $K_1(1400)$ we investigate different descriptions, such as a mixture of states belonging to the nonet of axial resonances, or the former one as a state originating from the vector-pseudoscalar dynamics. The ratios among the partial widths of $K^+(1460)K^-$, $K^+_1(1400)K^-$ and $K^+_1(1270)K^-$ obtained are compatible with the experimental results, reinforcing the three-body nature of $\phi(2170)$. Within our formalism, we can also explain the suppressed decay of $\phi(2170)$ to $K^*(892) \bar K^*(892)$, as found by the BESIII Collaboration. Furthermore, our results can be useful in clarifying the properties of $K(1460)$, $K_1(1270)$ and $K_1(1400)$ when higher statistics data would be available.
... However, still the PDG does not yet list it as an "established particle" [67]. In the most recent study [68] intermediate decays of the K(1460) meson are found to be roughly consistent with previous studies [65,66], with approximately equal partial widths toK * (892)π − and [π + π − ] L=0 K − , and its resonant nature is confirmed using a model-independent partial-wave analysis. This resonance can be considered as a 2 1 S 0 excitation of the kaon in a unified quark model, which leads to the mass 1450 MeV [69]. ...
... The second case is complicated by isospin dependence of the KK potential, when the strength of the isospin singlet and triplet parts of the potential are different and related by the condition of obtaining a quasi-bound three-body state. Results of our calculations are compared with the SLAC and ACCMOR collaboration experimental values for the mass of K(1460) resonance [65,66] and the recent experimental study [68]. ...
... The comparison of our calculations with the recent experimental study 1482.40±3.58±15. 22 MeV [68], where the first uncertainty is statistical and the second systematic, shows that the mass of the K(1460) resonance is in a satisfactory agreement with the mass upper bound, calculated within our three-body model with isospin splitting KK potential. Due to the experimental uncertainties in the relevant observable, one can explore the possible range for the ratio of the strengths of isospin triplet and singlet components of the KK interaction. ...
The three-body $KK\bar K$ model for the $K(1460)$ resonance is developed on the basis of the Faddeev equations in configuration space. A single-channel approach is using with taking into account the difference of masses of neutral and charged kaons. It is demonstrated that a splitting the mass of the $K(1460)$ resonance takes a place around 1460 MeV according to $K^0K^0{\bar K}^0$, $K^0K^+K^-$ and $K^+K^0{\bar K}^0$, $ K^+K^+K^-$ neutral and charged particle configurations, respectively. The calculations are performed with two sets of $KK$ and $K\bar K$ phenomenological potentials, where the latter interaction is considered the same for the isospin singlet and triplet states. The effect of repulsion of the $KK$ interaction on the mass of the $KK\bar K$ system is studied and the effect of the mass polarization is evaluated. The first time the Coulomb interaction for description of the $K(1460)$ resonance is considered. The mass splitting in the $K$(1460) resonances is evaluated to be in range of 10 MeV with taking into account the Coulomb force. The three-body model with the $K\bar K$ potential, which has the different strength of the isospin singlet and triplet parts that are related by the condition of obtaining a quasi-bound three-body state is also considered. Our results are in reasonable agreement with the experimental mass of the $K(1460)$ resonance.
... The generalized LASS model [29,30] is used to parametrize the Kπ and Kη S-wave contributions: ...
We present the results of the first Dalitz plot analysis of the decay D0→K−π+η. The analysis is performed on a data set corresponding to an integrated luminosity of 953 fb−1 collected by the Belle detector at the asymmetric-energy e+e− KEKB collider. The Dalitz plot is well described by a combination of the six resonant decay channels K¯*(892)0η, K−a0(980)+, K−a2(1320)+, K¯*(1410)0η, K*(1680)−π+ and K2*(1980)−π+, together with Kπ and Kη S-wave components. The decays K*(1680)−→K−η and K2*(1980)−→K−η are observed for the first time. We measure ratio of the branching fractions, B(D0→K−π+η)B(D0→K−π+)=0.500±0.002(stat)±0.020(syst)±0.003(BPDG). Using the Dalitz fit result, the ratio B(K*(1680)→Kη)B(K*(1680)→Kπ) is measured to be 0.11±0.02(stat)−0.04+0.06(syst)±0.04(BPDG); this is much lower than the theoretical expectations (≈1) made under the assumption that K*(1680) is a pure 13D1 state. The product branching fraction B(D0→[K2*(1980)−→K−η]π+)=(2.2−1.9+1.7)×10−4 is determined. In addition, the πη′ contribution to the a0(980)± resonance shape is confirmed with 10.1σ statistical significance using the three-channel Flatté model. We also measure B(D0→K¯*(892)0η)=(1.41−0.12+0.13)%. This is consistent with, and more precise than, the current world average (1.02±0.30)%, deviates with a significance of more than 3σ from the theoretical predictions of (0.51–0.92)%.
... The value in Eq. (3.3) is smaller than the one in Eq. (3.2), because A sd (K * 0 K S ) and A sd (K * 0 K S ) do not vanish in the SU(3) F limit. The prediction in Eq. (3.3) uses data from an LHCb analysis of the D 0 → K ∓ π ± K S Dalitz plot [23]. ...
... The value in Eq. (3.3) is smaller than the one in Eq. (3.2), because A sd (K * 0 K S ) and A sd (K * 0 K S ) do not vanish in the SU(3) F limit. The prediction in Eq. (3.3) uses data from an LHCb analysis of the D 0 → K ∓ π ± K S Dalitz plot [23]. ...
I discuss hadronic decays of $D$ mesons with emphasis on the recent discovery of charm CP violation in $D^0\to K^+K^-,\pi^+\pi^-$ decays. The measured difference $\Delta a_{CP} \, \equiv \; a_{CP}^{\mathrm{dir}}(D^0\rightarrow K^+K^-) - a_{CP}^{\mathrm{dir}}(D^0\rightarrow\pi^+\pi^-) = \; (-15.4\pm 2.9)\cdot 10^{-4}$ of two direct CP asymmetries exceeds the SM prediction by a factor of 7. A possible explanation is an enhancement of the penguin amplitude entering $ a_{CP}^{\mathrm{dir}}$ by QCD effects which are not understood yet. Alternatively, $\Delta a_{CP}$ could be dominated by contributions from new physics. In order to distinguish these two hypotheses further CP asymmetries should be measured. To this end CP asymmetries resulting from the interference of two tree-level amplitudes auch as $a_{CP}^{\mathrm{dir}}(D^0\rightarrow K_SK_S)$ or $a_{CP}^{\mathrm{dir}}(D^0 \to K^{*0} K_S)$ are especially interesting.
