Decay Widths Of Mesons Research Articles

Charmonium states in a coupled-channel model

We systematically investigate the mass spectrum and two-body open-charm strong decays of charmonium states in a coupled-channel model where the 3P0\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$^3P_0$$\\end{document} quark-antiquark pair creation mechanism is employed. The results of masses, mass shifts, proportions of the cc¯\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$c\\bar{c}$$\\end{document} component, and open-charm decay widths are provided. The S-D wave mixing angles and di-electric decay widths for vector mesons are also presented. Based on our results, we find that the ψ(3770)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\psi (3770)$$\\end{document}, ψ(4040)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\psi (4040)$$\\end{document}, ψ(4160)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\psi (4160)$$\\end{document}, ψ(4360)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\psi (4360)$$\\end{document}, and ψ(4415)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\psi (4415)$$\\end{document} can be assigned as the 13D1\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$1^3D_1$$\\end{document}-, 33S1\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$3^3S_1$$\\end{document}-, 23D1\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$2^3D_1$$\\end{document}-, 43S1\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$4^3S_1$$\\end{document}-, and 33D1\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$3^3D_1$$\\end{document}-dominated charmonium states, respectively. The ψ3(3842)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\psi _3(3842)$$\\end{document} is a good candidate of the ψ3(1D)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\psi _3(1D)$$\\end{document} charmonium state. The calculated mass and strong decay width of χc1(2P)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\chi _{c1}(2P)$$\\end{document} with significant continuum contribution (∼\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\sim $$\\end{document}57%) favor the charmonium interpretation for the mysterious χc1(3872)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\chi _{c1}(3872)$$\\end{document}. When considering the large uncertainty in the observed decay width, the possibility to assign the χc0(3860)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\chi _{c0}(3860)$$\\end{document} as the χc0(2P)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\chi _{c0}(2P)$$\\end{document} charmonium state cannot be ruled out. One may describe well the properties of χc2(3930)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\chi _{c2}(3930)$$\\end{document} with the χc2(2P)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\chi _{c2}(2P)$$\\end{document} charmonium. The predictions on properties of other cc¯\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$c\\bar{c}$$\\end{document} states can be tested by future experiments.

Phenomenology of isospin-symmetry breaking with vector mesons

We study the effect of isospin-symmetry breaking in the framework of the extended linear σ model in vacuum. In this model, several particles mix with each other at tree level, due to the three nonzero scalar condensates (nonstrange, strange, isospin). We resolve these mixings with the help of various field transformations. We compute all possible meson mixings and decay widths at tree level and perform a χ2 fit to PDG data. A very good fit is found if we exclude the (very small ∼130 keV) ω→ππ decay. We also investigate the violation of Dashen’s theorem. Published by the American Physical Society 2024

Mass spectra, Regge trajectories and decay properties of heavy-flavour mesons

In this article, we study the mass spectra, Regge trajectories and decay properties of heavy-flavour mesons $Q\bar{Q}$ $(Q=c,b)$ within a non-relativistic quark model. The spin hyperfine interaction is used to get the prediction for the heavy-meson masses for radial and orbital excitations. By using the radial and orbital excitations, we construct Regge trajectories for the heavy-mesons in the $(J,M^2)$ and $(n,M^2)$ plane and find their slopes and intercepts. We have computed leptonic, photonic and gluonic decay widths of heavy flavour mesons with and without QCD correction factor. We have compared our results of masses as well as decay widths with other theoretical and lattice QCD predictions for each states. Moreover, the known experimental results are also reasonably close to our predicted results.

Analysis of the decay constants and form factors of pseudoscalar mesons in a dirac formalism

We investigate the weak leptonic and semileptonic decay widths of pseudoscalar light and heavy mesons in a Dirac formalism. We take relativistic-independent quark model of the form [Formula: see text], where [Formula: see text]. This is computed using the binding quark eigenfunction and taking the assumptions of a significant relationship between the quark and antiquark momenta inside the decaying meson in the rest frame. To calculate the decay constant [Formula: see text], decay width and branching fractions of pseudoscalar mesons, we employ the model parameters that we used earlier. The experimental findings and various similar models are in good agreement with our predictions such as [Formula: see text] and [Formula: see text]”. Finally, we calculate the form factors and branching fractions for the semileptonic [Formula: see text] decays [Formula: see text], [Formula: see text], [Formula: see text], [Formula: see text] and [Formula: see text]” and find reasonable agreement with the experimental results.

Leptonic Decay Widths for the Composite System of Two Relativistic Fermions

The new relativistic semiclassical leptonic decay widths of vector mesons as the relativistic systems of two quarks with arbitrary masses interacting by means of the funnel-type potentials with Coulomb interaction are obtained. The behavior of the relativistic leptonic decay widths of vector mesons is investigated. Comparison of the behavior for new expression with its relativistic spinless analog is given. Consideration is conducted within the framework of completely covariant quasipotential approach in the Hamiltonian formulation of quantum field theory via a transition to the relativistic configurational representation in the case of two relativistic spin particles of arbitrary masses.

Light-front wavefunctions of mesons by design

We develop a mechanism to build the light-front wavefunctions (LFWFs) of meson bound states on a small-sized basis function representation. Unlike in a standard Hamiltonian formalism, the Hamiltonian in this method is implicit, and the information of the system is carried directly by the functional form and adjustable parameters of the LFWFs. In this work, we model the LFWFs for four charmonium states, eta _c, J/psi , psi ', and psi (3770) as superpositions of orthonormal basis functions. We choose the basis functions as eigenfunctions of an effective Hamiltonian, which has a longitudinal confining potential in addition to the transverse confining potential from light-front holographic QCD. We determine the basis function parameters and superposition coefficients by employing both guidance from the nonrelativistic description of the meson states and the experimental measurements of the meson decay widths. With the obtained wavefunctions, we study the features of those meson states, including charge radii and parton distribution functions. We use the J/psi LFWF to calculate the meson production in diffractive deep inelastic scattering and ultra-peripheral heavy-ion collisions, and the eta _c LFWF to calculate its diphoton transition form factor. Both results show good agreement with experiments. The obtained LFWFs have simple-functional forms and can be readily used to predict additional experimental observables.

Study of F-wave bottom mesons in heavy quark effective theory

Abstract We study F-wave bottom mesons in heavy quark effective theory. The available experimental and theoretical data is used to calculate the masses of F-wave bottom mesons. The decay widths of bottom mesons are analyzed to find upper bounds for the associated couplings. We also construct Regge trajectories for our predicted data in the (J, M2) plane, and our results nicely fit on Regge lines. Our results may provide crucial information for future experimental studies.

Study of mass spectra and decay widths of mesons and dimeson molecular states in an analytical approach

Study of mass spectra and decay widths of mesons and dimeson molecular states in an analytical approach

Study of heavy bottom mesons in a variational approach

Using a variational approach we calculate the mass spectra of the bottom mesons in the framework of the phenomenological quark anti-quark potential. Decay constant and Leptonic decay widths of the bottom mesons are also calculated. The obtained results are compared with the available experimental data and other theoretical predictions.

Update on strong and radiative decays of the $$D_{s0}^*(2317)$$ and $$D_{s1}(2460)$$ and their bottom cousins

The isospin breaking and radiative decay widths of the positive-parity charm-strange mesons, $D^{*}_{s0}$ and $D_{s1}$, and their predicted bottom-strange counterparts, $B^{*}_{s0}$ and $B_{s1}$, as hadronic molecules are revisited. This is necessary, since the $B^{*}_{s0}$ and $B_{s1}$ masses used in Eur. Phys. J. A 50 (2014) 149 were too small, in conflict with the heavy quark flavour symmetry. Furthermore, not all isospin breaking contributions were considered. We here present a method to restore heavy quark flavour symmetry, correcting the masses of $B^{*}_{s0}$ and $B_{s1}$, and include the complete isospin breaking contributions up to next-to-leading order. With this we provide updated hadronic decay widths for all of $D^{*}_{s0}$, $D_{s1}$, $B^{*}_{s0}$ and $B_{s1}$. Results for the partial widths of the radiative deays of $D_{s0}^*(2317)$ and $D_{s1}(2460)$ are also renewed in light of the much more precisely measured $D^{*+}$ width. We find that $B_s\pi^0$ and $B_s\gamma$ are the preferred channels for searching for $B_{s0}^*$ and $B_{s1}$, respectively.

Lowering the scale of Pati-Salam breaking through seesaw mixing

We analyse the experimental limits on the breaking scale of Pati-Salam extensions of the Standard Model. These arise from the experimental limits on rare-meson decay processes mediated at tree-level by the vector leptoquark in the model. This leptoquark ordinarily couples to both left- and right-handed SM fermions and therefore the meson decays do not experience a helicity suppression. We find that the current limits vary from mathcal{O} (80–2500) TeV depending on the choice of matrix structure appearing in the relevant three-generational charged-current interactions. We extensively analyse scenarios where additional fermionic degrees of freedom are introduced, transforming as complete Pati-Salam multiplets. These can lower the scales of Pati-Salam breaking through mass-mixing within the charged-lepton and down-quark sectors, leading to a helicity suppression of the meson decay widths which constrain Pati-Salam breaking. We find four multiplets with varying degrees of viability for this purpose: an SU(2)L/R bidoublet, a pair of SU(4) decuplets and either an SU(2)L or SU(2)R triplet all of which contain heavy exotic versions of the SM charged leptons. We find that the Pati-Salam limits can be as low as mathcal{O} (5–150) TeV with the addition of these four multiplets. We also identify an interesting possible connection between the smallness of the neutrino masses and a helicity suppression of the Pati-Salam limits for three of the four multiplets.

Strange mesons in strong magnetic fields

The masses of the strange mesons ([Formula: see text], [Formula: see text] and [Formula: see text]) are investigated in the presence of strong magnetic fields. The changes in the masses of these mesons arise from the mixing of the pseudoscalar and vector mesons in the presence of a magnetic field. For the charged mesons, these mass modifications are in addition to the contributions from the lowest Landau energy levels to their masses. The decay widths, [Formula: see text] and [Formula: see text], in the presence of the magnetic field are studied using a field theoretic model of composite hadrons with constituent quarks/antiquarks. The model uses the free Dirac Hamiltonian in terms of the constituent quark fields as the light quark–antiquark pair creation term and explicit constructions for the meson states in terms of the constituent quarks and antiquarks to study the decay processes. The pseudoscalar–vector (PV) meson mixing leads to a drop (rise) in the mass of the pseudoscalar (longitudinal component of the vector) meson. It is observed that the mass modifications for the hidden strange mesons, arising from [Formula: see text] mixing, are quite prominent, whereas the neutral open strange mesons have only marginal changes in their masses due to mixing. The mass modifications of the charged open strange mesons are due to interplay between the Landau-level contributions and the PV mixing, and, the latter effect is observed to dominate at large values of the magnetic field. The vector meson decay widths ([Formula: see text] and [Formula: see text]) involving the charged mesons are observed to be quite different from the widths involving neutral mesons, due to the additional contribution for the charged mesons from the Landau levels.

ϕ meson mass and decay width in strange hadronic matter

The in-medium mass and decay width of the $\phi$ meson in the hot asymmetric strange hadronic matter are calculated using an effective Lagrangian approach for $\phi$ $K\bar K$ interaction. The in-medium contributions of $K \bar K$ loop to the $\phi$ meson self-energy are computed by the medium modified kaon and antikaon mass which is evaluated using the chiral SU(3) model. To deal with the ultraviolet divergence, we regularize the loop integral of self-energy with a dipole form factor, and present the results for cut-off mass, $\Lambda_c$=3 GeV. In chiral model calculations, for strange matter, we find that the mass of kaons and antikaons decreases with the increase in baryonic density whereas the finite temperature causes an increase in the mass. We observed that the in-medium $\phi$ meson mass decreases slowly with baryonic density whereas the decay width increases rapidly. The results in the present investigation support result in the literature which indicate a small downward shift in mass and a large broadening in the decay width. In the asymmetric strange hadronic matter, the study of the $\phi$ mesons can be relevant for the compressed strange baryonic matter and experimental observables such as dilepton spectra which can result from the experiments in the future FAIR facility at GSI.

Magnetic-dipole corrections to RK and RK* in the Standard Model and dark photon scenarios

In this work we evaluate the long-distance QED contributions, induced by the magnetic-dipole corrections to the final charged leptons, on the B meson decay widths B → (K, K*)ℓ+ℓ− and ratios RK,K* = Γ(B → (K, K*)μ+μ−)/Γ(B → (K, K*)e+e−), as well as on {R}_{K,Kast}^{tau } (with μ replaced by the τ lepton). QED long-distance contributions induced by the Coulomb potential corrections (Fermi-Sommerfeld factors) were also included. Corresponding corrections to the inclusive decay widths of B → Xsℓ+ℓ−, with ℓ = e, μ, τ, are also analyzed for completeness. The magnetic-dipole corrections, which are manifestly Lepton Flavor Universality violating and gauge-invariant, are expected to be particularly enhanced in RK* for the dilepton mass region close to the threshold. However, we find that the largest contribution of all these corrections to the RK,K* observables do not exceed a few per mille effect, thus reinforcing the validity of previous estimates about the leading QED corrections to RK,K*. Finally, viable new physics contributions to RK,K* induced by the exchange of a massless dark-photon via magnetic-dipole interactions, which provide the leading contribution to the corresponding B → (K, K*)ℓ+ℓ− amplitudes in this scenario, are analyzed in light of the present RK,K* anomalies.

Decays of higher charmonium above the D¯ D threshold

The charmonium resonances that are heavier than the D^(-0) D^0 threshold at 3.73 GeV are kinematically allowed to decay into D meson pairs and are commonly expected to be more extensive than the states under the threshold. Study the potential decays of the light–quarks at various incident energies is a method to investigate the meson structure and decay width. In heavy Q Q systems, hadronic transitions function an important probe of their internal structures and help ascertain the understanding of light quark coupling with a significant degree of freedom.Hadronic transitions of JPC = 1- - higher charmonia are studied in the framework of the quark pair creation model. The model shows its potential to reproduce the observed decay widths and make predictions for the unobserved channels. Computed decay widths are in a good agreement with experimental data. Keywords: Hadronic transitions, quark pair creation model, heavy quarkonium, higher charmonia, decay widths

Strong coupling constants and radiative decays of the heavy tensor mesons

In this article, we analyze tensor-vector-pseudoscalar(TVP) type of vertices D_{2}^{*+}D^{+}rho , D_{2}^{*0}D^{0}rho , D_{2}^{*+}D^{+}omega , D_{2}^{*0}D^{0}omega , B_{2}^{*+}B^{+}rho , B_{2}^{*0}B^{0}rho , B_{2}^{*+}B^{+}omega , B_{2}^{*0}B^{0}omega , B_{s2}^{*}B_{s}phi and D_{s2}^{*}D_{s}phi in the frame work of three point QCD sum rules(QCDSR). According to these analysis, we calculate their strong form factors which are used to fit into analytical functions of Q^{2}. Then, we obtain the strong coupling constants by extrapolating these strong form factors into deep time-like regions. As an application of this work, the coupling constants for radiative decays of these heavy tensor mesons are also calculated at the point of Q^{2}=0. With these coupling constants, we finally obtain the radiative decay widths of these tensor mesons.

Updated measurement of time-dependent CP-violating observables in {{B} ^0_{s}} rightarrow J/psi K^+ K^- decays

The decay-time-dependent CP asymmetry in {{B} ^0_{s}} rightarrow J/psi {{K} ^+} {{K} ^-} decays is measured using proton–proton collision data, corresponding to an integrated luminosity of 1.9,mathrm{fb}^{-1} , collected with the LHCb detector at a centre-of-mass energy of 13,mathrm {TeV} in 2015 and 2016. Using a sample of approximately 117 000 signal decays with an invariant {{K} ^+} {{K} ^-} mass in the vicinity of the phi (1020) resonance, the CP-violating phase phi _s is measured, along with the difference in decay widths of the light and heavy mass eigenstates of the {{B} ^0_{s}} -{{overline{B}{}} {}^0_{s}} system, Delta Gamma _s. The difference of the average {{B} ^0_{s}} and {{B} ^0} meson decay widths, Gamma _s-Gamma _d, is determined using in addition a sample of {{B} ^0} rightarrow J/psi {{K} ^+} {{pi } ^-} decays. The values obtained are phi _s = -0.083pm 0.041pm 0.006mathrm { ,rad} , Delta Gamma _s = 0.077 pm 0.008 pm 0.003 {mathrm { ,ps^{-1}}} and Gamma _s-Gamma _d = -0.0041 pm 0.0024 pm 0.0015{mathrm { ,ps^{-1}}} , where the first uncertainty is statistical and the second systematic. These are the most precise single measurements of these quantities to date and are consistent with expectations based on the Standard Model and with a previous LHCb analysis of this decay using data recorded at centre-of-mass energies 7 and 8 TeV. Finally, the results are combined with recent results from {{B} ^0_{s}} rightarrow J/psi {{pi } ^+} {{pi } ^-} decays obtained using the same dataset as this analysis, and with previous independent LHCb results.

Fully coupled-channel study of K−pp resonance in a chiral SU(3)-based [formula omitted] potential

We have investigated the most essential kaonic nucleus “K−pp” as a resonant state of the K¯NN-πΣN- πΛN coupled-channel system using a chiral SU(3)-based K¯N potential. We treat the “K−pp” resonance adequately with a fully coupled-channel complex scaling method (full ccCSM). Self-consistency needs to be considered for the energy dependence of the chiral SU(3)-based potential. In the present study, we propose a simple prescription for the treatment of self-consistency, considering the averaged threshold and averaged binding energy of mesons. With this prescription, we have successfully found the self-consistent solutions of the “K−pp” three-body resonance. The results indicate that the “K−pp” system is bound rather shallowly. In particular, when the potential parameters are constrained with the latest K¯N scattering length, the binding energy and half of the mesonic decay width are obtained as 14–50 MeV and 8–19 MeV, respectively.

The reactions $\pi\pi \rightarrow \pi\pi$ π π → π π and $\gamma\gamma \rightarrow \pi\pi$ γ γ → π π in $\chi$ χ PT with an isosinglet scalar resonance

The lowest-lying resonance in the QCD spectrum is the $0^{++}$ isoscalar $\sigma$ meson, also known as the $f_0(500)$. We augment SU(2) chiral perturbation theory ($\chi$PT) by including the $\sigma$ meson as an additional explicit degree of freedom, as proposed by Soto, Talavera, and Tarr\'us and others. In this effective field theory, denoted $\chi$PT$_S$, the $\sigma$ meson's well-established mass and decay width are not sufficient to properly renormalize its self energy. At $\mathcal{O}(p^4)$ another low-energy constant appears in the dressed $\sigma$-meson propagator; we adjust it so that the isoscalar pion-pion scattering length is also reproduced. We compare the resulting amplitudes for the $\pi\pi\rightarrow\pi\pi$ and $\gamma\gamma\rightarrow\pi\pi$ reactions to data from threshold through the energies at which the $\sigma$-meson resonance affects observables. The leading-order (LO) $\pi \pi$ amplitude reproduces the $\sigma$-meson pole position, the isoscalar $\pi \pi$ scattering lengths and $\pi \pi$ scattering and $\gamma \gamma \rightarrow \pi \pi$ data up to $\sqrt{s} \approx 0.5$ GeV. It also yields a $\gamma\gamma\rightarrow\pi\pi$ amplitude that obeys the Ward identity. The value obtained for the $\pi^0$ polarizability is, however, only slightly larger than that obtained in standard $\chi$PT.

Fully coupled-channels complex scaling method for the K−pp system

We have developed a fully coupled-channels complex scaling method (ccCSM) for the study of the simplest (and thus most important) kaonic nucleus, $``{K}^{\ensuremath{-}}pp$'', which is a resonant state of a $\overline{K}NN\text{\ensuremath{-}}\ensuremath{\pi}\mathrm{\ensuremath{\Sigma}}N\text{\ensuremath{-}}\ensuremath{\pi}\mathrm{\ensuremath{\Lambda}}N$ coupled-channel system based on theoretical viewpoint. By employing the ccCSM and imposing the correct boundary condition for a resonance, the coupled-channel problem is solved using a phenomenological energy-independent potential. As a result of the ccCSM calculation of $``{K}^{\ensuremath{-}}pp$'', in which all three channels are treated explicitly, we have obtained a three-body resonance as a Gamow state. The resonance pole indicates that the binding energy of $``{K}^{\ensuremath{-}}pp$'' and the half value of its mesonic decay width are 51 and 16 MeV, respectively. In the analysis of the ccCSM resonant wave function, we clarify the spatial configuration and channel composition of $``{K}^{\ensuremath{-}}pp$''. Compared with past single-channel calculations based on effective $\overline{K}N$ potentials, the current study provides a guideline for the determination of the $\overline{K}N$ energy to be used in such effective potentials.