Modern meson spectroscopy: the fundamental role of unitarity
Eef van Beveren, George Rupp
备注：
Invited review paper, 51 pages, 16 figures, 4 tables; to be published in "Progress in Particle and Nuclear Physics" 2021. v2: several typos corrected, in particular in Eqs. (15), (17), (36), and (37) in Section 2; some accompanying remarks rephrased for clarity; Eq. (41) improved. NOTE: v3 is identical to v2; published version (in print and online) largely corresponds to v1; v3 (=v2) is correct
发表信息：
Progress in Particle and Nuclear Physics 117 (2021) 103845
The importance of $S$-matrix unitarity in realistic meson spectroscopy is reviewed, both its historical development and more recent applications. First the effects of imposing $S$-matrix unitarity on meson resonances is demonstrated in both the elastic and the inelastic case. Then, the static quark model is revisited and its theoretical as well as phenomenological shortcomings are highlighted. A detailed account is presented of the mesons in the tables of the Particle Data Group that cannot be explained at all or only poorly in models describing mesons as pure quark-antiquark bound states. Next the earliest unitarised and coupled-channel models are revisited, followed by several examples of puzzling meson resonances and their understanding in a modern unitarised framework. Also, recent and fully unquenched lattice descriptions of such mesons are summarised. Finally, attention is paid to production processes, which require an unconventional yet related unitary approach. Proposals for further improvement are discussed.
In this time of transition to a new generation of quark flavor experiments we review both the theoretical and the experimental progress on the determination of unitarity triangle angles from penguin-dominated B decays. This summarizes the activities of the Working Group VI at the CKM2010 workshop.
We study the final state interaction in 3-pion decay of meson resonances at the Excited Baryon Analysis Center (EBAC) of JLab. We apply the dynamical coupled-channels formulation which has been extensively used by EBAC to extract N* information. The formulation satisfies the 3-pion unitarity condition which has been missed in the existing works with the isobar models. We report the effect of the 3-pion unitarity on the meson resonance pole positions and Dalitz plot.
This paper has been temporarily withdrawn by the author. A modified version will be resubmitted. One of the trivial solutions was missed with crucial bearing on conclusions.
We present the results of the application of the Dispersion Matrix approach to exclusive semileptonic $B$-meson decays. This method allows to determine the hadronic form factors in a non-perturbative and completely model-independent way. Starting from lattice results available at large values of the momentum transfer, the behaviour of the form factors in their whole kinematical range is obtained without introducing any parameterization of their momentum dependence. We will focus on the determination of the Cabibbo-Kobayashi-Maskawa matrix elements $\vert V_{cb} \vert$ and $\vert V_{ub} \vert$ …
Using the analytic properties of two-point functions in QCD, as well as unitarity, bounds on the B meson form factor F(q^2) can be derived. Heavy quark spin symmetry, correctly taken into account, is shown to improve these bounds significantly.
We compute the one-loop unitarity corrections O(p^6) from K^+ -> pi^+ pi^+ pi^- to K^+ -> pi^+ gamma gamma and we find they are relevant, increasing the leading order prediction for the width in a 30-40%. The contributions of local O(p^6) amplitudes, generated by vector meson exchange, are discussed in several models and we conclude that the vector resonance contribution should be negligible compared to the unitarity corrections.
A method of deriving bounds on the weak meson form factors, based on perturbative QCD, analyticity and unitarity, is generalized in order to fully exploit heavy quark spin symmetry in the ground state $(L=0)$ doublet of pseudoscalar $(B)$ and vector $(B^*)$ mesons. All the relevant form factors of these mesons are taken into account in the unitarity sum. They are treated as independent functions along the timelike axis, being related by spin symmetry only near the zero recoil point. Heavy quark vacuum polarisation up to three loops in perturbative QCD and the experimental cross sections $σ(e^+…
The experimental data on the processes $ππ\toππ,K\bar{K},ηη,ηη^\prime$ in the $I^GJ^{PC}=0^+0^{++}$ channel have been jointly analyzed to study the status and nature of the $f_0$. The method of analysis is based on analyticity and unitarity and uses an uniformization procedure. Some spectroscopic implications from results of the analysis are discussed.
We examine the semileptonic $B \to D^{(*)} \ell ν_\ell$ and $B \to π\ell ν_\ell$ decays adopting the unitarity-based Dispersive Matrix (DM) method, which allows to determine the shape of the relevant hadronic form factors (FFs) in their whole kinematical range, using only lattice QCD results available at large values of the 4-momentum transfer without making any assumption on their momentum dependence. Moreover, the experimental data are not used to constrain the shape of the FFs, but only to obtain our final exclusive determination of $\vert V_{cb} \vert$ and $\vert V_{ub} \vert$, namely: $\v…
An unambiguous definition of meson resonance masses requires a description of the associated phase shifts in terms of a manifestly unitary $S$-matrix and its complex poles. However, the commonly used Breit-Wigner (BW) parametrisations can lead to appreciable deviations. We demonstrate this for a simple elastic resonance, viz. $ρ(770)$, whose pole and BW masses turn out to differ by almost 5 MeV. In the case of the very broad $f_0(500)$ and $K_0^\star(700)$ scalar mesons, the discrepancies are shown to become much larger, while also putting question marks at the listed PDG BW masses and widths.…
Deep-inelastic scattering at low Bjorken x and elastic vector meson electroproduction are analyzed on the basis of the off-shell s-channel unitarity. We discuss behavior of the total cross-section of virtual photon-proton scattering and obtain, in particular, that the exponent in the power-like dependence of $σ^{tot}_{γ^* p}$ is related to the interaction radius of a constituent quark. The explicit mass dependence of the exponent in the power energy behavior of the vector meson electroproduction has been obtained. Angular distributions at large momentum transfers are considered. The energy dep…
The proof of the Khalfin Theorem for neutral meson complex is analyzed. It is shown that the unitarity of the time evolution operator for the total system under considerations assures that the Khalfin's Theorem holds. The consequences of this Theorem for the neutral mesons system are discussed: it is shown, eg., that diagonal matrix elements of the exact effective Hamiltonian for the neutral meson complex can not be equal if CPT symmetry holds and CP symmetry is violated. Properties of time evolution governed by a time--independent effective Hamiltonian acting in the neutral mesons subspace of…
At large virtuality $Q^2$, the coupling to the $ρ$ meson production channels provides us with a natural explanation of the surprisingly large cross section of the $ω$, as well as the $π^+$, meson electroproduction recently measured at backward angles, without destroying the good agreement between the Regge pole model and the data at the real photon point. Together with elastic re-scattering of the outgoing meson it also provides us with a way to explain why the node, that appears at $u\sim -0.15$ GeV$^2$ at the real photon point, disappears at moderate virtuality $Q^2$. Predictions are given f…
Deep-inelastic scattering at low x and elastic vector meson production are considered on the basis of the off-shell extension of the s-channel unitarity. We discuss behavior of the structure function F_2(x,Q^2) at low x and the total cross-section of virtual photon-proton scattering and obtain, in particular, the dependence sigma^{tot}_{gamma^* p}\sim (W^2)^{lambda(Q^2)} where exponent lambda(Q^2) is related to the interaction radius of a constituent quark. The energy dependence of the total cross-section of gamma^*gamma^*-interactions is calculated. The explicit mass dependence of the exponen…
We review recent results of Lattice QCD calculations relevant for flavour physics. We discuss in particular the hadronic parameters entering the amplitudes of K0-K0bar, D0-D0bar and B0-B0bar mixing, the B- and D-meson decay constants and the form factors controlling B-meson semileptonic decays. On the basis of these lattice results, which are extensively collected in the paper, we also derive our averages of the relevant hadronic parameters.
The inverse-amplitude method is applied to the one-loop chiral expansion of the pion, kaon, and $K_{l3}$ form factors. Since these form factors are determined by the same chiral low-energy constants, it is possible to obtain finite predictions for the inverse-amplitude method. It is shown that this method clearly improves one-loop chiral perturbation theory, and a very good agreement between the inverse-amplitude method and the experimental information is obtained. This suggests that the inverse-amplitude method is a rather systematic way of improving chiral perturbation theory.
We study the temperature evolution of the rho and sigma mass and width, using a unitary chiral approach. The one-loop pion-pion scattering amplitude in Chiral Perturbation Theory at finite temperature is unitarized via the Inverse Amplitude Method. Our results predict a clear increase with T of both the rho and sigma widths. The masses decrease slightly for high T, while the rho-pion-pion coupling increases. The rho behavior seems to be favored by experimental results. In the sigma case, it signals chiral symmetry restoration.
We develop a model for describing excited mesons decay into three mesons. The properties of the excited mesons can be extracted with this model. The model maintains the three-body unitarity that has been missed in previous data analyses based on the conventional isobar models. We study an importance of the three-body unitarity in extracting hadron properties from data. For this purpose, we use the unitary and isobar models to analyze the same pseudo data of gamma p -> pi+pi+pi-n, and extract the properties of excited mesons. We find a significant difference between the unitary and isobar model…
We first briefly review a treatment of the scalars in meson meson scattering based on a non-linear chiral Lagrangian, with unitarity implemented by a "local" modification of the scalar propagators. It is shown that the main results are confirmed by a treatment in the SU(3) linear sigma model in which unitarity is implemented "globally". Some remarks are made on the speculative subject of the scalars' quark structure.
We reconsider two classical proposals for the determination of the angle gamma of the unitarity triangle: B^\pm => chi_{c0} π^\pm => π^+π^-π^\pm and B_s => rho^0 K_S => π^+ π^- K_S. We point out the relevance, in both cases, of non resonant amplitudes, where the π^+ π^- pair is produced by weak decay of a B^* (J^P=1^-) or B_0 (J^P=0^+) off-shell meson. In particular, for the B decay channel, the inclusion of the B_0 pole completes some previous analyses and confirms their conclusions, provided a suitable cut in the Dalitz plot is performed; for the B_s decay the inclusion of the B^*, B_0 ampli…
Using the expansions of the heavy meson decay widths in the heavy quark mass and QCD sum rules for estimates of corresponding matrix elements,\, we calculate the $D^{\pm,o,s}$ and $B^{\pm,o,s}$ meson lifetimes. The results for D mesons are in a reasonable agreement with the data,\, while it is predicted: $[Γ(B_d)-Γ(B^\pm)]/Γ_B\se 4\%\,$ (and the lifetime difference of the $B_d$ and $B_s$ mesons is even smaller);\, $[Γ(B_s^{short})-Γ(B_s^{long})]/{\ov Γ}(B_s)\se 8\%\,.$ The role of the weak annihilation and Pauli interference contributions to the lifetime differences is described in detail. In …
By means of a coupled channel non-perturbative unitary approach, it is possible to extend the strong constrains of Chiral Perturbation Theory to higher energies. In particular, it is possible to reproduce the lowest lying resonances in meson-meson scattering up to 1.2 GeV using the parameters of the O(p^2) and O(p^4) Chiral Lagrangian. We report on an update of these results examining their possible relevance for meson spectroscopy.
A unitary coupled-channels model is presented for investigating the decays of heavy mesons and excited meson states into three light pseudoscalar mesons. The model accounts for the three-mesons final state interactions in the decay processes, as required by both the three-body and two-body unitarity conditions. In the absence of the Z-diagram mechanisms that are necessary consequences of the three-body unitarity, our decay amplitudes are reduced to a form similar to those used in the so-called isobar-model analysis. We apply our coupled-channels model to the three-pions decays of a1(1260), pi2…
This presentation at the conference "50 years of CP violation", 10 - 11 July 2014, held at Queen Mary University of London covers an introduction to time reversal and motion reversal, the phenomenology of K0-K0bar transitions, unitarity relations, the first observation of T violation in 1970, later results from Bell-Steinberger unitarity analyses, searches for T violation in K0 to pi ell nu decay amplitudes and in the transverse muon polarisation of K to pi mu nu decays, direct observation of T violation by motion reversal in K0-K0bar transitions, and "direct T violation" in K0 to pi pi, I=2 d…
Possible effects of noncommutative geometry on weak CP violation and unitarity triangles are discussed by taking account of a simple version of the momentum-dependent quark mixing matrix in the noncommutative standard model. In particular, we calculate nine rephasing invariants of CP violation and illustrate the noncommutative CP-violating effect in a couple of charged D-meson decays. We also show how inner angles of the deformed unitarity triangles are related to CP-violating asymmetries in some typical B_d and B_s transitions into CP eigenstates. B-meson factories are expected to help probe …
We review the physics of purely leptonic decays of $π^\pm$, $K^\pm$, $D^{\pm}$, $D_s^\pm$, and $B^\pm$ pseudoscalar mesons. The measured decay rates are related to the product of the relevant weak-interaction-based CKM matrix element of the constituent quarks and a strong interaction parameter related to the overlap of the quark and antiquark wave-functions in the meson, called the decay constant $f_P$. The leptonic decay constants for $π^\pm$, $K^\pm$, $D^{\pm}$, $D_s^\pm$, and $B^\pm$ mesons can be obtained with controlled theoretical uncertainties and high precision from {\it ab initio} lat…
Studies on the dynamical properties of the $σ$ meson are reviewed and discussed. The important role of fundamental principles such as analyticity, unitarity and crossing symmetry played in the studies are stressed.
The form factors of the light pseudoscalar mesons are investigated in a dispersive formalism based on hadronic unitarity, analyticity and the OPE expansion of the QCD Green functions. We propose generalizations of the original mathematical techniques, suitable for including additional low energy information provided by experiment or Chiral Perturbation Theory (CHPT). The simultaneous treatment of the electroweak form factors of the $π$ and $K$ mesons allows us to test the consistency with QCD of a low energy CHPT theorem. By applying the formalism to the pion electromagnetic form factor, we de…
I describe recent advances in our understanding of the hadronic form factors governing semileptonic meson transitions. The resulting framework provides a systematic approach to the experimental data, as a means of extracting precision observables, testing nonperturbative field-theory methods, and probing a poorly understood limit of QCD.
Recent results and future prospects of the particle physics experiments with neutral and charged K-meson (kaon) decays are reviewed. Topics include CP violation, rare decays, leptons in kaon decays, tests of CPT and quantum mechanics, radiative decays, hadrons in kaon decays, basic observables, Vus and CKM unitarity, and exotic searches. Experimental techniques developed for the kaon decay experiments are discussed.
This article reviews on-shell methods for analytic computation of loop amplitudes, emphasizing techniques based on unitarity cuts. Unitarity techniques are formulated generally but have been especially useful for calculating one-loop amplitudes in massless theories such as Yang-Mills theory, QCD, and QED.
Experimental checks of the second row unitarity of the Cabibbo-Kobayashi-Maskawa (CKM) matrix involve extractions of the matrix element $V_{cd}$, which may be obtained from semileptonic decay rates of $D$ to $π$. These decay rates are proportional to hadronic form factors which parameterize how the quark $c \to d$ transition is realized in $D \to π$ meson decays. The form factors can not yet be analytically computed over the whole range of available momentum transfer $q^2$, but can be parameterized with a varying degree of model dependency. We propose using artificial neural networks trained f…
In the approach, based on analyticity and unitarity and assuming an influence of coupled channels, experimental data on the isovector P-wave of pion-pion scattering have been analyzed to study rho-like mesons below 1.9 GeV.
These lectures describe CP violation and rare decays of K and B mesons and consist of ten chapters: i) Grand view of the field including CKM matrix and the unitarity triangle, ii) General aspects of the theoretical framework, iii) Particle-antiparticle mixing and CP violation, iv) Standard analysis of the unitarity triangle, v) The ratio epsilon'/epsilon including most recent developments, vi) Rare decays K^+ -> pi^+ nu barnu and K_L -> pi^0 nu barnu, vii) Express review of other rare decays, viii) Express review of CP violation in B decays, ix) A brief look beyond the Standard Model including…
In view of the observed strong hierarchy of quark masses, we propose a new description of flavor mixing which is particularly suited for models of quark mass matrices based on flavor symmetries. The necessary and sufficient conditions for CP violation are clarified. The emergence of CP violation is primarily linked to a large phase difference (near 90^{\circ}) in the light quark sector. The unitarity triangle is determined by the mass ratios of the light quarks. We conclude that the unitarity triangle should be close or identical to a rectangular triangle, and CP violation is maximal in this s…
We study the linking between the CP violating phase of the lepton sectors and the unitarity triangle of the B0 meson system. Antusch, King, Malinsky and Spinrath have shown that the quark mass matrices with the negligible 1-3 mixing give an interesting relation between the phase of the quark mixing matrices and CP violating measure phi_2(alpha). This approach is extended by considering the SO(10) GUT including the Pati-Salam symmetry, which links the Yukawa matrices of the quark sector to the one of the lepton sector. We discuss the relation of the CP violating phases between both quark and le…
The effect of finite hadronization time is considered in the recombination model, and it is shown that the hadron multiplicity turns out to be proportional to the initial quark density and unitarity is conserved in the model. The baryon to meson ratio increases rapidly with the initial quark density due to competition among different channels.
We discuss the problem of unitarity for Yang-Mills theory in the Landau gauge with a mass term a la Stueckelberg. We assume that the theory (non-renormalizable) makes sense in some subtraction scheme (in particular the Slavnov-Taylor identities should be respected!) and we devote the paper to the study of the space of the unphysical modes. We find that the theory is unitary only under the hypothesis that the 1-PI two-point function of the vector mesons has no poles (at p^2=0). This normalization condition might be rather crucial in the very definition of the theory. With all these provisos the…
The unitarity triangles of the $3\times 3$ Cabibbo-Kobayashi-Maskawa (CKM) matrix are studied in a systematic way. We show that the phases of the nine CKM rephasing invariants are indeed the outer angles of the six unitarity triangles and measurable in the $CP$-violating decay modes of $B_{d}$ and $B_{s}$ mesons. An economical notation system is introduced for describing properties of the unitarity triangles. To test unitarity of the CKM matrix we present some approximate but useful relations among the sides and angles of the unitarity triangles, which can be confronted with the accessible exp…
The study of charmless hadronic two-body decays of B mesons is one of the most fascinating topics in B physics. A construction of the unitarity triangle based on such decays is presented, which is independent of B-B(bar) and K-K(bar) mixing. It provides stringent tests of the Standard Model with small theoretical uncertainties.
This article surveys the important questions attached to unitarity tests of the Cabibbo-Kobayashi-Maskawa matrix, with a focus on the direct determinations of the magnitude of CKM matrix elements. The current CKM anomalies are discussed and the clear-cut prospects at LHCb and Belle II envisaged. The anticipated precision on $C\!P$-conserving and $C\!P$-violating observables at the projected upgrades of the LHCb and Belle~II experiments is examined from the point of view of the search for New Physics in $B$-meson mixing, addressing the bottlenecks in precision for the interpretation of the meas…
We study physics on $ρ(770)$ and $ω(782)$ in framework of chiral constituent quark model. The effective action is derived by proper vertex method, which can capture all order information of chiral expansion. The $N_c^{-1}$ expansion is also studied systematically. It is shown that the momentum expansion at vector meson energy scale converges slowly, and the loop effects of pseudoscalar meson play an important role at this energy scale. We provide a method to prove the unitarity of S-matrix in any low-energy effective theory of QCD. Phenomenologically, we study decays for $ρ\toππ$, $ρ\to e^+e^-…
The study of charmless two-body decays of B mesons is currently one of the hottest topics in B physics. QCD factorization provides the theoretical framework for a systematic analysis of such decays. A global fit to B->pi K,pi pi branching fractions, combined with knowledge on |V(ub)|, establishes the existence of a CP-violating phase in the bottom sector of the CKM matrix and tends to favor values of gamma near 90 degrees, somewhat larger than those suggested by the standard analysis of the unitarity triangle. A novel construction of the unitarity triangle is presented, which is independent of…
We review our recent work on thermal meson properties within the Chiral Perturbation Theory framework. We will focus on the pion electromagnetic form factor, stressing its importance for Relativistic Heavy Ion Collisions. We obtain model-independent predictions (based only on chiral symmetry) such as the temperature dependence of the pion electromagnetic charge radius. Imposing unitarity allows to describe the thermal effects of resonances such as the $ρ$ meson.
We present a lattice QCD computation and preliminary results for the leptonic decay constants of the pseudoscalar mesons $K$, $D$ and $D_{s}$ in the isosymmetric QCD limit. The computation is based on simulations of $N_f = 2+1+1$ dynamical quarks performed by the Extended Twisted Mass Collaboration (ETMC), where the light, strange and charm quark masses are all tuned at their physical values. We also present preliminary unitarity checks for the first and second rows of the Cabibbo-Kobayashi-Maskawa matrix.
We study the $B$ meson radiative decay $B \to X_s γ$ in the vector quark model. Deviation from the Standard Model arises from the non-unitarity of the charged current KM matrix and related new FCNC interactions. We establish the relation between the non-unitarity of charged current mixing matrix and the mixing among the vector quark and the ordinary quarks. We also make explicitly the close connection between this non-unitarity and the flavor changing neutral currents. The complete calculation including leading logarithmic QCD correction is carefully carried out. Using the most updated data an…
We present preliminary results for the chiral behavior of charged pseudo-Goldstone-boson masses and decay constants. These are obtained in simulations with N_f=2+1 flavors of tree-level, O(a)-improved Wilson sea quarks. In these simulations, mesons are composed of either valence quarks discretized in the same way as the sea quarks (unitary simulations) or of overlap valence quarks (mixed-action simulations). We find that the chiral behavior of the pseudoscalar meson masses in the mixed-action calculations cannot be explained with continuum, partially-quenched chiral perturbation theory. We sho…
We construct several classes of hadronic matrix elements and relate them to the low-energy constants in Chiral Perturbation Theory that describe the electromagnetic effects in the semileptonic beta decay of the pion and the kaon. We propose to calculate them using lattice QCD, and argue that such a calculation will make an immediate impact to a number of interesting topics at the precision frontier, including the outstanding anomalies in $|V_{us}|$ and the top-row Cabibbo-Kobayashi-Maskawa matrix unitarity.
We point out that hints of deviations from unitarity in the first row of the CKM matrix may be explained by the presence of a single vector-like top. We study how the stringent experimental constraints arising from CP Violation in the kaon sector and from meson mixing such as $D^0$-$\overline{D}^0$, $K^0$-$\overline{K}^0$ and $B^0_{d,s}$-$\overline{B}^0_{d,s}$ can be satisfied in the proposed framework. In order for the deviations from unitarity to be of the required size while keeping the theory perturbative, the new top quark should have a mass $m_T \lesssim 7$ TeV which could be probed in u…
The measurement of time-dependent CP asymmetries in charm decays can provide a unique insight into the flavor changing structure of the Standard Model. We examine a number of different CP eigenstate decays of D mesons and describe a method that can be used to measure time-dependent CP asymmetries at existing and future experiments, with a preliminary assessment, based on statistical considerations, of their various capabilities. Any asymmetry observed in time-dependent analysis of neutral D mesons could signify new physics. We discuss the measurements required to perform direct and indirect te…
We consider the production and scattering amplitudes of heavy mesons in a situation, where there are two closely spaced narrow resonances, which structure we refer to as a diresonance. Assuming strong overlapping of the resonances coupled to common channels, it is found, using the unitarity and analyticity constraints, that the production amplitudes in different channels should have similar behavior with energy. In particular the ratio of the coefficients for each pole contribution to the production amplitude is fixed at -1.
We examine a simple Composite Higgs Model (CHM) with vector resonances in addition to the Standard Model (SM) fields in perturbation theory by using the $K$-matrix method to implement unitarity constraints. We find that the $W_LW_L$ scattering amplitude has an additional scalar pole (analogous to the $σ$ meson of QCD) as in generic strongly interacting extensions of the SM. The mass and width of this dynamically generated scalar resonance are large and the mass behaves contrary to the vector one, so that when the vector resonance is lighter, the scalar one is heavier, and vice versa. We also a…
At large virtuality $Q^2$, the coupling to the vector meson production channels provides us with a natural explanation of the surprisingly large cross section of the neutral pion electroproduction recently measured at Jefferson Laboratory, without destroying the good agreement between the Regge pole model and the data at the real photon point. Elastic rescattering of the $π^0$ provides us with a way to explain why the node, that appears at $t\sim -0.5$ GeV$^2$ at the real photon point, disappears as soon as $Q^2$ differs from zero.
We investigate the rare decays $B_c \rightarrow D_s(1968) \ell \bar{\ell}$ and $B_c\rightarrow D_s^*(2317) \ell \bar{\ell}$ in the framework of the light-cone quark model (LCQM). The transition form factors are calculated in the space-like region and then analytically continued to the time-like region via exponential parametrization. The branching ratios and longitudinal lepton polarization asymmetries (LPAs) for the two decays are given and compared with each other. The results are helpful to investigating the structure of $B_c$ meson and to testing the unitarity of CKM quark mixing matrix. A…
Recent studies of hadronic -meson decays are reported. Some experimental searches of CP-symmetry violation using model independent methods are presented. An importance of unitarity constraints in construction of phenomenological models of the D-meson decays is underlined. The theoretical model of the D0 --> K0S pi+ pi- decays, including some two-body unitarity constraints, is described. Then a comparison of the model results with the Belle collaboration data is made. The results on the CP-violation in the D0 --> K0S pi+ pi- decays are given and the necessity to consider the CP-violation in the…
We report on recent nonperturbative techniques that combine the information of chiral Lagrangians (with and without resonances) with unitarity in coupled channels and other requirements of the S-matrix theory of the strong interactions. As a result, the region of applicability of such techniques is much larger than the one of Chiral Perturbation Theory allowing one to study also resonance physics. Applications to meson-meson and meson-baryon scattering, as well as to problems where pairs of mesons or a meson and a baryon appear in the initial or final state are shown. Implications in several n…
From recent analysis of the $ππ$ scattering amplitude, it has been claimed that there exists a broad and light $σ$ meson. However, if this meson really exists, it must also appear in other observables such as the pion scalar form factor. With the use of unitarity and dispersion relations together with chiral perturbation theory, this form factor is analyzed in the complex energy plane. The result agrees well with the empirical information in the elastic region and reveals a resonance pole at $\sqrt{s}=445-i235$ MeV. This gives further strong evidence for the existence of the $σ$ meson.
