Unraveling the f<Subscript>0</Subscript> nature by connecting KLOE and BABAR data through analyticity

We define a general procedure, based on analyticity and dispersion relations, to estimate low-energy amplitudes for processes like: φ→e ⁺ e ^- M and φ→γM, starting from cross-section data on e ⁺ e ^-→φM, where M is a generic light scalar or pseudoscalar meson. In particular this procedure is constructed to obtain predictions on the radiative decay rate which are crucially linked on the assumed quark structure for the meson M under consideration. Three cases are analyzed: M = η, M = f ₀(qˉ) and M = f ₀(qqˉ). While in the η case the estimate of the branching fraction for the radiative decay φ→ηγ is in agreement with the data, in the case of f ₀, such agreement is obtained only under the hypothesis of a tetraquark scalar meson.     

Selected topics from Belle

The Belle experiment continues to explore the origin of CP violation and test all aspects of standard model inB meson decays. Recent results on CP violating paramter sin2ф₁ and other measurements are presented.     

Meson loops in the f0(980) and a0(980) radiative decays into ρ , ω

We calculate the radiative decay widths of the a ₀(980) and f ₀(980) scalar mesons into ργ and ωγ considering the dynamically generated nature of these scalar resonances within the realm of the chiral unitary approach. The main ingredient in the evaluation of the radiative width of the scalar mesons are the loops coming from the decay into their constituent pseudoscalar-pseudoscalar components and the subsequent radiation of the photon. The dominant diagrams with only pseudoscalar mesons in the loops are found to be convergent while the divergence of those with a vector meson in the loop are written in terms of the two-meson loop function easily regularizable. We provide results for all the possible charge channels and obtain results, with uncertainties, which differ significantly from quark loops models and some version of vector meson dominance.     

K-matrix analysis of the (IJ<Superscript>PC</Superscript> = 00<Superscript>+ +</Superscript>)-wave in the mass region below 1900 MeV

We present the results of the current analysis of the partial wave IJ ^PC = 00^{+ +} based on the available data for meson spectra ( ππ, KˉK,ηη,η,ππππ). In the framework of the K-matrix approach, the analytical amplitude has been reconstructed in the mass region 280 MeV < < 1900 MeV. The following scalar-isoscalar states are seen: comparatively narrow resonances f ₀(980), f ₀(1300), f ₀(1500), f ₀(1750) and the broad state f₀(1200-1600). The positions of the amplitude poles (masses and total widths of the resonances) are determined as well as pole residues (partial widths to meson channels ππ, KˉK,ηη,η,ππππ). The fitted amplitude gives us the positions of the K-matrix poles (bare states) and the values of bare-state couplings to meson channels thus allowing the quark-antiquark nonet classification of bare states. On the basis of the obtained partial widths to the channels ππ, KˉK,ηη,η, we estimate the quark/gluonium content of f ₀(980), f ₀(1300), f ₀(1500), f ₀(1750), f₀(1200-1600). For f ₀(980), f ₀(1300), f ₀(1500) and f ₀(1750), their partial widths testify the qˉq origin of these mesons though being unable to provide precise evaluation of the possible admixture of the gluonium component in these resonances. The ratios of the decay coupling constants for the f₀(1200-1600) support the idea about the gluonium nature of this broad state. Received: 14 May 2002 / Accepted: 20 August 2002 / Published online: 11 February 2003 RID="a" ID="a"e-mail: anisovic@thd.pnpi.spb.ru Communicated by A. Sch?fer     

Exploring the di-photon decay of a light Higgs boson in the MSSM with explicit CP violation

The di-photon decay channel of the lightest Higgs boson is considered as a probe to explore CP violation in the minimal supersymmetric standard model (MSSM). The scalar/pseudo-scalar mixing is considered along with CP violation entering through the Higgs–sfermion–sfermion couplings, with and without light sparticles. The impact of a light stop on the decay width and branching ratio (BR) is established through a detailed study of the amplitude of the process H₁→γγ. The other sparticles have little influence even when they are light. With a suitable combination of other MSSM parameters, a light stop can change the BR by more than 50% with a CP-violating phase φ_μ∼90°, while the change is almost nil with a heavy stop.     

Study of K<Superscript>*</Superscript><Subscript>0</Subscript>(1430) and a<Subscript>0</Subscript>(980) from B→K<Superscript>*</Superscript><Subscript>0</Subscript>(1430)π and B→a<Subscript>0</Subscript>(980)K decays

We use the decay modes B→K^* ₀(1430)π and B→a₀(980)K to study the scalar mesons K^* ₀(1430) and a₀(980) within the framework of perturbative QCD. For B→K^* ₀(1430)π, we perform our calculation in two scenarios for the scalar meson spectrum. The results indicate that scenario II is more favored by the experimental data than scenario I. The important contribution from annihilation diagrams can enhance the branching ratios by about 50% in scenario I and about 30% in scenario II. The direct CP-asymmetries in B→K^* ₀(1430)π are small, which is consistent with the present experiments. The predicted branching ratio of B→a₀(980)K in scenario I differs from the experiments by a factor of 2, which indicates that a₀(980) cannot be interpreted as q̄q.     

Two-photon mechanism of scalar meson production by colliding beams

Cross sections of scalar mesons f ₀(980), a ₀(980), and σ(600) production by colliding electron-positron beams are calculated. Two-photon decay widths of scalar mesons obtained in the Nambu-Jona-Lasinio model are used with quark and meson loops taken into account.     

Study of the f<Subscript>2</Subscript>(1270) , f<Subscript>2</Subscript>′(1525) , f<Subscript>0</Subscript>(1370) and f<Subscript>0</Subscript>(1710) in the J/<Emphasis Type="Italic">ψ</Emphasis> radiative decays

In this paper we present an approach to study the radiative decay modes of the J/ψ into a photon and one of the tensor mesons f ₂(1270) , f′ ₂(1525) , as well as the scalar ones f ₀(1370) and f ₀(1710) . Especially, we compare predictions that emerge from a scheme where the states appear dynamically in the solution of vector meson-vector meson scattering amplitudes to those from a (admittedly naive) quark model. We provide evidence that it might be possible to distinguish amongst the two scenarios, once improved data are available.     

On puzzles and non-puzzles in B→ππ,πK decays

Recently, we have seen interesting progress in the exploration of CP violation in B⁰ _d→π⁺π^-: the measurements of mixing-induced CP violation by the BaBar and Belle collaborations are now in good agreement with each other, whereas the picture of direct CP violation is still unclear. Using the branching ratio and direct CP asymmetry of B⁰ _d→π^-K⁺, this situation can be clarified. We predict , which favours the BaBar result, and we extract γ=(70.0^+3.8 _-4.3)^°, which agrees with the unitarity triangle fits. Extending our analysis to other B→πK modes and B⁰ _s→K⁺K^- with the help of the SU(3) flavour symmetry and plausible dynamical assumptions, we find that all observables with colour-suppressed electroweak penguin contributions are measured to be in excellent agreement with the standard model. As far as the ratios R_c,n of the charged and neutral B→πK branching ratios are concerned, which are sizeably affected by electroweak penguin contributions, our standard-model predictions have almost unchanged central values but significantly reduced errors. Since the new data have moved quite a bit towards these results, the “B→πK puzzle” for the CP conserving quantities has been significantly reduced. However, the mixing-induced CP violation of B⁰ _d→π⁰K_S does look puzzling; if confirmed by future measurements, this effect could be accommodated through a modified electroweak penguin sector with a large CP violating new-physics phase. Finally, we point out that the established difference between the direct CP asymmetries of B^±→π⁰K^± and B_d→π^∓K^± appears to be generated by hadronic and not by new physics.     

New physics hints in B decays and collider outlook

There are currently two hints for new physics involving CP violation in b → s transitions: ΔS ≡ S _f − S _J ^ϕK ≠ 0, and difference in direct CP asymmetry ΔA _Kπ ≡ A _K+π ⁰ − A _K+π ⁻ ≠ 0. We explore the two scenarios with a large and unique new CP phase in b ↔ s transitions. Motivated by ΔS ≠ 0, we update on the right-handed strange-beauty squark sb _1R at TeV scale. Motivated by ΔA _Kπ ≠ 0, we explore sequential fourth generation t′ and b′ quarks. Both scenarios can survive constraints such as SM level b → sγ, sll and B _s mixing, and predict sizable CP violation in B _s mixing. The fourth generation picture predicts sizable K _L → π ⁰ vv. Direct search for sb _R, b′ and t′ at hadronic colliders, such as Tevatron Run II and LHC, can complement further CP violation studies at these machines, as well as at the future Super B factory.     

Towards resolution of the scalar meson nonet enigma

By the application of a linear mass spectrum to a composite system of both the pseudoscalar and scalar meson nonets, we find three relations for the masses of the scalar states which suggest the assignment for the scalar meson nonet a₀(1320), K ₀ ^* (1430), f₀(1500), and f₀ ^′(980).     

Form factors,branching ratio and forward–backward asymmetry in B→K<Subscript>1</Subscript>ℓ<Superscript>+</Superscript>ℓ<Superscript>-</Superscript> decays

We study long-distance effects in the rare exclusive semileptonic decays B→K₁ℓ⁺ℓ^-, where K₁ is the axial vector meson. The form factors describing the meson transition amplitudes of the effective Hamiltonian are calculated using the Ward identities, which are then used to calculate the branching ratio and the forward–backward asymmetry in these decay modes. The zero of the forward–backward asymmetry is of special interest and provides us with a precision test of the standard model.     

Phenomenological applications of<Emphasis Type="Italic">k</Emphasis><Subscript>T</Subscript>factorization

We discuss applications of the perturbative QCD approach in the exclusive non-leptonic two-bodyB-meson decays. We briefly review its ingredients and some important theoretical issues on the factorization approach. PQCD results are compatible with present experimental data for charmless B-meson decays. We predict the possibility of large direct CP asymmetry in B⁰ → π⁺π⁻ (23 +7%) and B⁰ →K ⁺π⁻ (− 17 ± 5%). We also investigate the branching ratios, CP asymmetry and isospin symmetry breaking in radiativeB →(K*/ρ)γ decays.     

CP violation in a multi higgs doublet model

We study CP violation in a multi-Higgs doublet model based on aS ₃×Z ₃ horizontal symmetry. We consider two mechanisms for CP violation in this model: a) CP violation due to complex Yukawa couplings; and b) CP violation due to scalarpseudoscalar mixings. We find that the predictions for ε′/ε, CP violation in B decays and the electric dipole moments of neutron and electron are different between these two mechanisms. These predictions are also dramatically different from the minimal Standard Model predictions.     

The quark‐level linear σ model

This review of the quark‐level linear σ model (QLLσM) is based upon the dynamical realization of the pseudoscalar and scalar mesons as a linear representation of SU(2)× SU(2) chiral symmetry, with the symmetry weakly broken by current quark masses. In its simplest SU(2) incarnation, with two non‐strange quark flavors and three colors, this nonperturbative theory, which can be selfconsistently bootstrapped in loop order, is shown to accurately reproduce a host of low‐energy observables with only one parameter, namely the pion decay constant f_π. Extending the scheme to SU(3) by including the strange quark, equally good results are obtained for many strong, electromagnetic, and weak processes just with two extra constants, viz. f_K and <π |H_weak|K>. Links are made with the vector‐meson‐dominance model, the BCS theory of superconductivity, and chiral‐symmetry restoration at high temperature. Finally, these ideas are cautiously generalized to the electroweak sector, including the W, Z, and Higgs bosons, and also to CP violation.     

Two Higgs bi-doublet left-right model with spontaneous P and CP violation

A left-right symmetric model with two Higgs bi-doublet is shown to be a consistent model for both spontaneous P and CP violation. The flavor changing neutral currents can be suppressed by the mechanism of approximate global U(1) family symmetry. The constraints from neural K meson mass difference Δm _K are calculated and it is demonstrated that a right-handed gauge boson W ₂ contribution in box-diagrams with mass well below 1 TeV is allowed due to a cancelation caused by a light-charged Higgs boson with a mass range of 150–300 GeV. The W ₂ contribution to ε _K can be suppressed from an appropriate choice of additional CP phases appearing in the right-handed Cabbibo-Kobayashi-Maskawa matrix. The model is also found to be fully consistent with B ⁰ mass difference Δm _B and the mixing induced CP violation sin2β _{J/ Ψ}, which is usually difficult for the model with only one Higgs bi-doublet. The new physics beyond the standard model can be directly searched at the colliders LHC and ILC. Supported by the National Natural Science Foundation of China (NSFC) (Grant Nos. 10475105 and 10491306) and the Key Project of Chinese Academy of Sciences (CAS)     

Beauty-conserving strangeness-changing rare semileptonic decays ofB s meson

The beauty-conserving strangeness-changing decays ofB _s meson are examined. In the charm sector, charm-conserving strangeness changing (Δc = 0, Δs ≠ 0) decays are Cabibbo suppressed and are governed by the CKM elementV _us which is much smaller than the CKM diagonal elementV _cs, so may be of little interest. On the other hand, in theb-sector, beauty-conserving strangeness changing (Δb = 0, Δs ≠ 0) decays are CKM allowed as the CKM matrix elementV _us governing such decays is much larger thanV _bc orV _bu which govern respectively theb →c orb →u transitions. The phase space available, however, is too small for the decays considered here. The numerical estimates for the decay widths of two such modes ofB _s meson are presented.     

Radiative scalar-meson decays f0(980) → ρ(ω)γ and a0(980) → ρ(ω)γ within the local Nambu-Jona-Lasinio model

The widths with respect to the radiative decays f ₀(980) → ργ and a ₀(980) → ωγ were calculated within the local Nambu-Jona-Lasinio model. The contributions of both quark and meson loops were taken into account. The latter and the former play a dominant role for the radiative decays of, respectively, the f ₀(980) and the a ₀(980) meson.