Mixing and Decay Constants of Pseudoscalar Mesons

Abstract

We propose a new eta-eta' mixing scheme where we start from the quark flavor basis and assume that the decay constants in that basis follow the pattern of particle state mixing. On exploiting the divergences of the axial vector currents - which embody the axial vector anomaly - all basic parameters are fixed to first order of flavor symmetry breaking. That approach naturally leads to a mass matrix, quadratic in the masses, with specified elements. We also test our mixing scheme against experiment and determine corrections to the first order values of the basic parameters from phenomenology. Finally, we generalize the mixing scheme to include the eta(c). Again the divergences of the axial vector currents fix the mass matrix and, hence, mixing angles and the charm content of the eta and eta'.

14 pages, uses feynmp.sty

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• Baryonic D Decay $D_s^{+}\to p\bar{n}$ and Its Implication
• Lepton flavor violating tau decays in type-III seesaw mechanism
• Okubo-Zweig-Iizuka-rule violation and B\to η^{(\prime)}K branching ratios
• Global analysis of charge exchange meson production at high energies
• Meson-Photon Transition Form Factors in the Charmonium Energy Range
• Chiral field theory of $0^{-+}$ glueball
• Resonance $X(3960)$ as a hidden charm-strange scalar tetraquark
• Semileptonic decays of pseudoscalar mesons to scalar "f_0" meson
• Exclusive processes $e^{+}{e}^{-}\to VP$ in $k_T$ factorization
• Model independent analysis of a class of ${\bar{B}}_s^0$ decay modes
• BHLS${}_2$ Upgrade : $\tau$ spectra, muon HVP and the [${\pi }^0,\eta ,{\eta }^{\prime }$] System
• Is $1^{-}+$ Meson a Hybrid?
• Study of ${\Lambda }_b\to \Lambda (\varphi ,{\eta }^{(\prime )})$ and ${\Lambda }_b\to \Lambda K^{+}{K}^{-}$ decays
• A study of the gamma* - f0(980) transition form factors
• Magnetic field induced corrections to the NJL model coupling constant from vacuum polarization
• Insight into $f_0(980)$ through the $B_{(s)}$ charmed decays
• On the heavy quark mass expansion for the operator Qbar gamma_5 Q and the charm content of eta, eta'
• Non-leptonic decays of Charmed mesons into two Pseudoscalars
• ${\eta }^{(\prime )}$ productions in semileptonic B decays
• Semileptonic D decays and eta-eta^prime mixing
• Cabibbo-Kobayashi-Maskawa-favored $B$ decays to a scalar meson and a $D$ meson
• $B_c$ $\to$ $BP$, $BV$ decays with the QCD factorization approach
• Revisiting the radiative decays $J/\psi \to \gamma {\eta }^{(\prime )}$ in perturbative QCD
• Strangeness content of the pion in the U(3) Nambu-Jona-Lasinio model
• Strong $D_s^{\ast }{D}_s{\eta }^{(\prime )}$ and $B_s^{\ast }{B}_s{\eta }^{(\prime )}$ vertices from QCD light-cone sum rules
• eta and eta' in a coupled Schwinger-Dyson and Bethe-Salpeter approach. II. The gamma^* gamma transition form factors
• Anomalous interactions between mesons with nonzero spin and glueballs
• Revisiting the $P$-wave charmonium radiative decays $h_c\to \gamma {\eta }^{(\prime )}$ with relativistic corrections
• Effect of resonance for $CP$ asymmetry of the decay process ${\bar{B}}_s\to P{\pi }^{+}{\pi }^{-}$ in perturbative QCD
• Ordinary and exotic mesons in the extended Linear Sigma Model
• Two-photon decays and transition form factors of ${\pi }^0$, $\eta$, and ${\eta }^{\prime }$ in large-$N_c$ chiral perturbation theory
• From well-known tensor mesons to yet unknown axial-tensor mesons
• Implications of Bbar to D0 h0 Decays on Bbar to D Kbar, Dbar Kbar Decays
• Study of Semileptonic Decays $B^{\pm }\to {\eta }^{(\prime )}l\nu$
• The ${\pi }^0-\eta -{\eta }^{\prime }$ mixing in a generalized multi-quark interaction scheme
• Power corrections to the space-like transition form factor F_{η^{\prime}g^{*}g^{*}}(Q^2,ω)
• Fall-apart decays of polyquark hadrons
• Is $f_2(1950)$ the tensor glueball?
• The study of $B\to J/\Psi {\eta }^{(\prime )}$ decays and determination of $\eta -{\eta }^{\prime }$ mixing angle
• Weak Annihilation Topologies and Final State Interactions in D -> PP Decays
• $\eta -{\eta }^{\prime }$ mixing
• Probing electroweak physics using B -> XM decays in the endpoint region
• Form factors of ${\eta }_c$ in light front quark model
• Radiative three-body D-meson decays in and beyond the standard model
• Semi-inclusive B Decays and Direct CP Violation in QCD Factorization
• Axial and pseudoscalar current correlators and their couplings to eta and etaprime mesons
• Investigating $D_s^{+}\to {\pi }^0{\ell }^{+}{\nu }_{\ell }$ decay process within QCD sum rule approach
• Decays of the $\hat{\rho }(1^{-+})$ Exotic Hybrid and $\eta$-${\eta }^{\prime }$ Mixing
• Rare Semileptonic $B_s$ Decays to $\eta$ and ${\eta }^{\prime }$ mesons in QCD
• e+e- annihilation to (pi0 pi0 gamma) and (pi0 eta gamma) as a source of information on scalar and vector mesons
• Heavy Baryonic Decays of Λ_b \to Λη^{(\prime)} and Nonspectator Contribution
• $J/\psi$ $\to$ $DP$, $DV$ decays in the QCD factorization approach
• Tension between $e^{+}{e}^{-}\to \eta {\pi }^{-}{\pi }^{+}$ and ${\tau }^{-}\to \eta {\pi }^{-}{\pi }^0{\nu }_{\tau }$ data and non-standard interactions
• A $U_A(1)$ symmetry restoration scenario supported by the generalized Witten-Veneziano relation and its analytic solution
• Quark-antiquark states of the lightest scalar mesons within the Nambu-Jona-Lasinio model with flavor-dependent coupling constants
• The photon to pseudoscalar meson transition form factors
• Quark-hadron duality, axial anomaly and mixing
• Study of transversity GPDs from pseudoscalar mesons production at EIC of China
• ${\bar{B}}_s^0\to ({\pi }^0{\eta }^{(\ast )},{\eta }^{(\ast )}{\eta }^{(\ast )})$ decays and the effects of next-to-leading order contributions in the perturbative QCD approach
• Light Hadron Masses from a Matrix Model for QCD
• Effective-Lagrangian study of ${\psi }^{\prime }(J/\psi )\to VP$ and the insights into $\rho \pi$ puzzle
• A new description of transverse momentum spectra of identified particles produced in proton-proton collisions at high energies
• Ruling out the Weinberg Model of Spontaneous CP Violation
• Perturbative QCD Analysis of Exclusive Processes $e^{+}{e}^{-}\to VP$ and $e^{+}{e}^{-}\to TP$
• Dispersive Approach to Abelian Axial Anomaly, Mixing of Pseudoscalar Mesons and Symmetries
• Radiative decays of $h_c$ to the light mesons ${\eta }^{(\prime )}$: A perturbative QCD calculation
• Hard exclusive pion leptoproduction
• The derivative of the topological susceptibility at zero momentum and an estimate of ${\eta }^{\prime }$ mass in the chiral limit
• $B\to K{\eta }^{(\prime )}\gamma$ decays in the standard model and in scenarios with universal extra dimensions
• Revisiting Final State Interaction in Charmless $B_q\to PP$ Decays
• Pseudoscalar Meson Mixing in Effective Field Theory
• Effects of Flavor-dependent $q\bar{q}$ Annihilation on the Mixing Angle of the Isoscalar Octet-Singlet and Schwinger's Nonet Mass Formula
• Electromagnetic axial anomaly in a generalized linear sigma model
• The doubly virtual $({\pi }^0,\eta ,{\eta }^{\prime })\to {\gamma }^{\ast }{\gamma }^{\ast }$ transition form factors in the light-front quark model
• A contact interaction model for the $\eta$ and ${\eta }^{\prime }$ mesons in a SDE-BSE approach to QCD: masses, decay widths and transition form factors
• Determination of the strangeness contents of light-flavour isoscalars from its production rates in hadronic Z decays measured at LEP
• B decays into two light pseudoscalar mesons and possible effects of enhanced b --> s g
• Rare nonleptonic ${\bar{B}}_s^0$ decays as probes of new physics behind $b\to s\mu \bar{\mu }$ anomalies
• Finite-width Gaussian sum rules for $0^{-+}$ pseudoscalar glueball based on correction from instanton-gluon interference to correlation function
• Analysis of $CP$ violation in $D^0\to K^{+}{K}^{-}{\pi }^0$
• Probing the perturbative dynamics of exclusive meson pair production
• QCD analysis of electromagnetic Dalitz decays $J/\psi \to {\eta }^{(\prime )}{\ell }^{+}{\ell }^{-}$
• Semileptonic Decay of $D_s^{+}\to {\pi }^0{\ell }^{+}{\nu }_{\ell }$ Via Neutral Meson Mixing
• Non-Abelian axial anomaly, axial-vector duality, and the pseudoscalar glueball
• State mixing and masses of the ${\pi }^0$, $\eta$ and ${\eta }^{\prime }$ mesons from $n_f=1+1+1$ lattice QCD+QED
• Role of the short-range dynamics in the formation of $D^{(\ast )}{\bar{D}}^{(\ast )}/B^{(\ast )}{\bar{B}}^{(\ast )}$ hadronic molecules
• Study on the radiative decays of $h_c$ via intermediate meson loops model
• Possibility of searching for $B_c^{\ast }$ $\to$ $B_{u,d,s}V$, $B_{u,d,s}P$ decays
• The B^- -> phi phi K^- decay rate with phi phi invariant mass below charm treshold
• Non Standard $\eta -{\eta }^{\prime }$ mixing and the Nonleptonic B and ${\Lambda }_b$ Decays to $\eta$ and ${\eta }^{\prime }$
• Instantons As Unitary Spin Maker
• f_0(1710) production in exclusive B decays
• The flavour asymmetry and quark-antiquark asymmetry in the ${\Sigma }^{+}$-sea
• Pion-Photon Transition Form Factor and Pion Distribution Amplitude in QCD: Facing the Enigmatic Behavior of the BaBar Data
• $\eta$-$\gamma$ and ${\eta }^{\prime }$-$\gamma$ transition form factors in a nonlocal NJL model
• On the Role of Charm in Decay of B-mesons to η' K
• Study of $B^{-}\to \Lambda \bar{p}{\eta }^{{(}^{\prime })}$ and ${\bar{B}}_s^0\to \Lambda \bar{\Lambda }{\eta }^{{(}^{\prime })}$ decays
• $B_{(s)}\to {\eta }_c(P,V)$ decays and effects of the next-to-leading order contributions in the perturbative QCD approach
• $\eta$ and ${\eta }^{\prime }$ mesons in the Dyson-Schwinger approach using a generalization of the Witten-Veneziano relation
• Quasi-two-body decays $B_c\to D^{\ast }h\to D\pi h$ in the perturbative QCD
• Dispersive approach to non-Abelian axial anomaly
• Penguin induced (B -> eta) transition form factor in light cone QCD
• Model independent investigation of rare semileptonic b \to u l \barν_l decay processes
• Anatomy of $B_s\to PP$ decays and effects of the next-to-leading order contributions in the perturbative QCD approach
• Gluon-pair-Creation Production Model of Strong Interaction Vertices
• Study of the $\psi (1S,2S)$ and ${\eta }_c(1S,2S)$ weak decays into $DM$
• Extracting the unitarity angle gamma in Bs to D0 h0, D0bar h0 Decays
• Exclusive γ*γprocesses
• Glue content and mixing angle of the eta - eta' system. The effect of the isoscalar 0- continuum
• Improved measurement of the branching fraction of $h_c\to \gamma {\eta }^{\prime }/\eta$ and search for $h_c\to \gamma {\pi }^0$
• Study of $B\to PP$ decays in the modified perturbative QCD approach
• Radiative $h_{c/b}$ decays to $\eta$ or ${\eta }^{\prime }$
• On some implications of the BaBar data on the ${\gamma }^{\ast }{\eta }^{\prime }$ transition form factor
• ${\chi }_c$ decays and the gluon content of the ${\eta }^{\prime }$, $\eta$ mesons
• On the $\eta$ and f${}_1$(1420) Couplings to the Nucleon
• Perturbative QCD for B_s \to a_1(1260)(b_1(1235))P(V) Decays
• Can the Mechanism for ${\pi }_1\to \eta \pi ,{\eta }^{\prime }\pi$ Hybrid Decays be Detected?
• Form factors for semileptonic $B_c$ decays into ${\eta }^{{(}^{\prime })}$ and Glueball
• Eta' gluonic content and J/psi->VP decays
• Light-Front Quark Model Analysis of Meson-Photon Transition Form Factor
• $B_{(s)}\to D_{s0}^{\ast }(2317)P(V)$ decays in perturbative QCD approach
• Mixing effects of $\eta -{\eta }^{\prime }$ in ${\Lambda }_b\to \Lambda {\eta }^{{(}^{\prime })}$ decays
• $1/N_c$ Nambu -- Jona-Lasinio model: ${\pi }^0$, $\eta$ and ${\eta }^{\prime }$ mesons
• Strong and electromagnetic contributions to the U_A(1) anomaly and the P^0 to gamma gamma decays
• Novel insights into the $\gamma {\gamma }^{\ast }\to {\pi }^0$ transition form factor
• Semi-classical Description of Exclusive Meson Pair Production in ${\gamma }^{\ast }\gamma$ Scattering
• Pion-photon transition form factor. Living on the QCD frontier
• Quantum algebra in the mixed light pseudoscalar meson states
• Modification of Kawai model about the mixing of the pseudoscalar mesons
• Charmless hadronic $B\to (f_1(1285),f_1(1420))P$ decays in the perturbative QCD approach
• $B_s^0\to {\eta }^{(\prime )}{\eta }^{(\prime )}$ decays in the pQCD approach
• Study of X(1812) as a $(K^{\ast }{\bar{K}}^{\ast })$ Molecular State
• Contributions of $\rho (770,1450)\to \omega \pi$ for the Cabibbo-favored $D\to h\omega \pi$ decays
• On the mass relation of a meson nonet
• Eta decays involving photons
• QCD analysis of the $P$-wave charmonium electromagnetic Dalitz decays $h_c\to {\eta }^{(\prime )}{\ell }^{+}{\ell }^{-}$
• Weak decays of bottom-charm baryons: ${\mathcal{B}}_{bc}\to {\mathcal{B}}_{b}P$
• Study of $B\to \rho \eta$, $\rho {\eta }^{\prime }$ decays in the modified perturbative QCD approach
• LFV couplings of the extra gauge boson Z' and leptonic decay and production of pseudoscalar mesons
• Looking for meson molecules in B decays
• On the Dalitz plot analysis of the B --> K eta gamma decays
• Semi-inclusive hadronic B decays as null tests of the Standard Model
• Study of the ${\bar{B}}_q^{\ast }$ $\to$ $DM$ decays with perturbative QCD approach
• Transition form factors of ${\pi }^0$, $\eta$ and ${\eta }^{\prime }$ mesons: What can be learned from anomaly sum rule?
• Account for axial vector mesons in the $\eta \to {\pi }^{+}{\pi }^{-}\gamma$ and ${\eta }^{\prime }\to {\pi }^{+}{\pi }^{-}\gamma$ decays
• Charm Radiative Decays with Neutral Mesons D^0 -> K^0(bar) pi^0 gamma, D^0 -> K^0(bar) eta (eta') gamma
• $\eta$ and ${\eta }^{\prime }$ transition form factors from Padé approximants
• Quasi-two-body decays $B\to P{f}_0(500)\to P{\pi }^{+}{\pi }^{-}$ in the perturbative QCD approach
• On modeling the scalar meson dynamics with Resonance Chiral Theory
• Near-threshold structures in the $D_s^{+}{D}_s^{-}$ mass distribution of the decay $B^{+}\to D_s^{+}{D}_s^{-}{K}^{+}$
• The B\to D_s^{(*)}η^{(\prime)} decays in the perturbative QCD
• The semileptonic decays of $B/B_s$ meson in the perturbative QCD approach: A short review
• Study of conventional and non-conventional scalar and vector mesons
• Rescattering-induced $D\to SS$ weak decays
• Improved measurement of $\eta /{\eta }^{\prime }$ mixing in $B_{(s)}^0\to J/\psi {\eta }^{(\prime )}$ decays
• Mixing of $\eta -{\eta }^{\prime }$ in charge-exchange reactions and decays of mesons with heavy quarks
• Charged pions asymmetry from the decay of light neutral axial mesons due to interference
• Model Dependent Analysis of D_((s))^+ arrows η^((')) l^+ ν_l Decays in Beyond Standard Model
• Possible candidate of 0^+ s\bar{s}s\bar{s} state
• Role of Resonances in Heavy Meson Processes within Standard Model and Beyond
• Study of B^{0}_{s} \rightarrow \ TT(a_{2}(1320),K^{*}_{2}(1430),f_{2}(1270),f^{'}_{2}(1525)) in the perturbative QCD approach
• The nonleptonic decays of double-charmed baryon ${\Omega }_{cc}^{+}$ within the nonrelativistic quark model
• Pseudoscalar transition form factors: $(g-2)$ of the muon, pseudoscalar decays into lepton pairs, and the $\eta -{\eta }^{\prime }$ mixing
• $B \to K \etap$ decays in the SM with fourth generation fermions
• Study on the effects of the light CP-odd Higgs via the leptonic decays of pseudoscalar mesons
• Rare weak decays of ${\eta }^{\prime }\to K\pi$
• Hadronic contributions to $a_{\mu }$ within Resonance Chiral Theory
• Study of $C$ parity violating and strangeness changing $J/\psi$ $\to$ $PP$ weak decays
• Valence structures of light and strange mesons from the basis light-front quantization framework
• Charmonium decay in the C3P0 Model
• Analysis of Exotic Hybrid eta pion, eta-prime pion Decays
• The hidden strangeness mechanism in Ds^+ -> omega pi^+ and Ds^+ -> rho^0 pi^+ decays
• Probing neutrino-night-quark effective scalar interactions from neutrino masses
• Study of the two-body nonleptonic $B_c(2S)$ weak decays with the QCD factorization approach
• Elastic and transition form factors of light pseudoscalar mesons from QCD sum rules
• Branching ratios and CP asymmetries in charmless nonleptonic B decays to radially excited mesons
• Novel method for determining the light quark mass ratio using ${\eta }^{\prime }\to \eta \pi \pi$ decays
• Symmetry breaking effects in pion couplings to constituent quark currents
• Probing leptophobic dark sector with a pseudoscalar portal in the NA64 experiment at CERN
• Radiative vertex $VP\gamma$ and $\eta -{\eta }^{\prime }$ mixing in light-cone sum rules
• Contributions of the subprocess $K_0^{\ast }(1430)\to K{\eta }^{\prime }$ in the charmless three-body $B$ meson decays
• Mirror matter admixtures in K_L to mu^+ mu^-
• Estimating QCD-factorization amplitudes through $SU(3)$ symmetry in $B\to PP$ decays
• Scrutinizing new physics of $B_d\to \varphi ({\eta }^{{(}^{\prime })},\pi ,\omega )$ decay modes
• An analysis of B meson decays to two light pseudoscalar nonets with deltaS=1 in QCD factorization approach
• Sub-leading power corrections to transition form factors of $\eta$ and ${\eta }^{\prime }$ mesons from twist-six contributions
• Eta-Eta' mixing and the derivative of the topological susceptibility at zero momentum transfer