f 0(980) and a 0(980) resonances near the thresholds of the γγ → K + K − and γγ → K 0 K̇ 0 reactions

High-statistical data on the γγ → K ⁺ K ^? and γγ → K ⁰ K? ⁰ reactions constitute the last missing link in investigations of light scalar mesons f ₀(980) and a ₀(980) in photon-photon collisions. It is expected that the manifestation of the four-quark structure of the f ₀(980) and a ₀(980) resonances in these reactions will be very peculiar. The possibilities of the observation of scalar contributions in the γγ → K ⁺ K ^? and γγ → K ⁰ K? ⁰ reactions near their thresholds at modern colliders have been estimated.     

Erratum to: Analytic Calculations of the Branching Ratio and CP Violation in $$B_s^0 \to {K^{*0}}{\overline K ^{*0}}$$ B s 0 → K * 0 K ¯ * 0 Decay

Physics of Atomic Nuclei -     

Differential branching fraction and angular analysis of the decay B0 → K*0 μ+ μ-

The angular distributions and the partial branching fraction of the decay B0 → K*0 μ+ μ- are studied by using an integrated luminosity of 0.37 fb(-1) of data collected with the LHCb detector. The forward-backward asymmetry of the muons, A(FB), the fraction of longitudinal polarization, F(L), and the partial branching fraction dB/dq2 are determined as a function of the dimuon invariant mass. The measurements are in good agreement with the standard model predictions and are the most precise to date. In the dimuon invariant mass squared range 1.00-6.00 GeV2/c4, the results are A(FB)=-0.06(-0.14)(+0.13)±0.04, F(L)=0.55±0.10±0.03, and dB/dq2=(0.42±0.06±0.03)×10(-7) c4/GeV2. In each case, the first error is statistical and the second systematic.     

Pure annihilation decays of B_s~0→a_0~+a_0~- and B_d~0→K_0~(*+)K_0~(*-) in the PQCD approach

We study the CP-averaged branching fractions and the CP-violating asymmetries in the pure annihilation decays ofB _s~0→a_0~+a _0~-andB _d~0→K_0~(*+)K_0~(*-),where a_0[K_0~*]denotes the scalar a_0(980) and a_0(1450)[K_0~*(800)(ork)and K_0~*(1430)],with the perturbative QCD factorization approach under the assumption of two-quark structure for the a_0and K_0~*states.The numerical results show that the branching ratios of theB _d~0→K_0~(*+)K_0~(*-)decays are in the order of 10~(-6),while the decay rates of theB_s~0→a_0~+a _0~-modes are in the order of 10~(-5).In light of the measured modes with the same quark components in the pseudoscalar sector,namely,B _d~0→K~+K~-and B_s~0→p p~(+-),the predictions for the considered decay modes in this work are expected to be measured at the Large Hadron Collider beauty and/or Belle-Ⅱ experiments in the (near) future.Meanwhile,it is of great interest to find that the twist-3 distribution amplitudes φ~S and φ~T with inclusion of the Gegenbauer polynomials for the scalar a_0(1450) and K_0~*(1430)states in scenario2 contribute slightly to the branching ratios while significantly to the CP violations in the B_d~0→K_0~*(14 30)~+K_0*(14 30)~-and B_s~0→a_0(1450)~+a_0(1450)~-decays,which indicates that,compared to the asymptotic φ~Sand φ~T,these Gegenbauer polynomials could change the strong phases evidently in these pure annihilation decay channels.These predictions await for the future confirmation experimentally,which could further provide useful information to help explore the inner structure of the scalars and shed light on the annihilation decay mechanism.     

Neutralb→c non leptonic decays and their role in the search forB→K *γ

We estimate the rates ofB ⁰ decays into neutral charmed final states \(B^0 \to \overline {D^{ * 0} } \gamma ,B^0 \to \overline {D^{ * 0} } \pi ^0 ,B^0 \to \overline {D^0 } \pi ^0 ,B^0 \to \overline {D^0 } \omega \) , by considering factorizable, vector meson dominance and long distance contributions. We also discuss the role of these decay modes as a source of background events in the search for exclusiveb→sγ transitions in very high energy experiments, e.g. at LEP.     

Measurement of the decay rate and the parameter αK* of the decay KL → μμγ

The rate of the decay of the neutral K meson into K _L ⁰ → μμγ has been measured with the NA48 detector at the CERN SPS. A total of 59 events has been observed with an estimated background of 14 events. The overall Kaon flux was determined to be 1.2 × 10⁹. This observation corresponds to a branching ratio of (3.4 ± 0.6_stat ± 0.4_sys × 10^-7. Using this branching ratio the parameter α_K* describing the relative strength of the two contributing amplitudes to this decay, through intermediate pseudoscalar or vectorlike mesons, was measured to be α_K* = -0.04+ _-0.21 ^+0.24 .     

Determination of the branching ratiosΓ(K L→3π0)/Γ(K L→π+ - 0) andΓ(K L→3π0)/Γ(K L→πev)

Improved branching ratios were measured for theK _L3⁰ decay in a neutral beam at the CERN SPS with the NA31 detector:

N\bar N annihilation at rest into πππ andK\bar K\pi in the3 P 0 model and selection rules on the πρ,K\bar K* and\bar KK* production

\(N\bar N\) annihilation into three pseudoscalar mesons especially πππ and \(K\bar K\pi \) are studied in the quark pair creation model or the³ P ₀ model in which two \(q\bar q\) pairs are annihilated and two \(q\bar q\) pairs are created with quantum numbers of the vacuum or³ P ₀. The correlations of two pions to form ?,f ₂ and the resonance AX(1565) which is recently found by the ASTERIX group are taken into account. A proper treatment of the symmetry among the three pions in the final state shows that the \({}^{31}S_0 p\bar p\) annihilation into ?π is suppressed in agreement with the experiment. We calculate the cosθ distribution or the distribution of the Dalitz plot as the function of the angle between the direction of emission of one decay pion in the resonance centre of mass and the line of flight of the resonance. The interferences of π⁺ρ⁺, π^?ρ⁺ and π⁰ρ⁰ in the isospin 0 channels and π^±ρ^? and π⁰ f ₂ in the isospin 1 channel reproduce the peaks. The cos θ distribution for the P-wave \(p\bar p\) annihilation into πAX depends strongly on the size of the pion since the amplitude interfers with the π^±ρ^? amplitude which is sensitive to the size of the pion. The same model qualitatively explains the \(p\bar p\) annihilation into \(K\bar K\pi \) in whichK or \(\bar K\) and π are correlated to formK* \(\bar K\) or \(\bar K\) *K final states. We can qualitatively reproduce different patterns of the cos θ distribution for theK ^*+ andK ^*0.     

Form factors of γ * ρ → π and γ * γ → π 0 transitions and light-cone sum rules

The method of light-cone QCD sum rules is applied to the calculation of the form factors of and transitions. We consider the dispersion relation for the amplitude in the variable . At large virtualities and , this amplitude is calculated in terms of light-cone wave functions of the pion. As a next step, the light-cone sum rule for the form factor is derived. This sum rule, together with the quark-hadron duality, provides an estimate of the hadronic spectral density in the dispersion relation. Finally, the form factor is obtained taking the limit in this relation. Our predictions are valid at and have a correct asymptotic behaviour at large . Received: 16 January 1998 / Revised version: 14 May 1998 / Published online: 26 August 1998     

Annihilation contribution and B → a 0π, f 0 K decays

We analyze the and B^–,0 → f₀K^–,0 decays and show that a consistent phenomenological picture can be obtained within the factorization approximation. In this approach the O₆ operator provides the dominant contributions to the suppressed channel . An estimate of the annihilation form factor using perturbative QCD indicates that this contribution is not negligible, moreover interference with other penguin contributions includes a free parameter since the phase of the annihilation amplitude is not determined. Assumptions based on SU(2) isospin symmetry provide relations between different B decays involving one scalar and one pseudoscalar meson.     

K 0 → \bar K^0 and B 0 → \bar B^0 transitions in the minimal supersymmetric standard model involving explicit CP violation in the Higgs sector

Mixing in the systems of neutral K ⁰ and B ⁰ mesons is considered within the minimal supersymmetric standard model (MSSM) containing a type-II Yukawa sector and featuring an explicitCP violation in the Higgs potential. In the case of a strong mixing of CP-even and CP-odd states, the model admits the presence of a light charged Higgs boson. Basic mixing parameters are calculated. These include the mass difference Δm _LS between neutral kaons and the parameter ε, which characterizes the amount of an indirect CP violation (that is, that which arises owing to an ultraweak mixing of CP-invariant and CP-noninvariant components). In the limit of the low-energy one-loop approximation, it is shown that, for the K ⁰ mesons, the contribution of nonstandard-physics effects to the mass splitting of the neutral kaons and an indirect CP violation are very small and are weakly dependent on the mass of the charged Higgs boson. Under certain conditions, the nonstandard contributions for the B ⁰- $ \bar B_d^0 $ and B ⁰- $ \bar B_s^0 $ systems may become somewhat more substantial, which constrains the MSSM parameter space.     

B0d→φK*0极化反常和Bd→φKs CP不对称的研究

在模型Ⅲ下,仅考虑来自于中性规范玻色子H0,H0和A0产生的树图阶味改变中性流的贡献,并利用QCD因子化方法,对B0d→φK(≠)0衰变过程的极化反常和Bd→φKs衰变过程的CP不对称进行了研究,经过计算发现,在147＜|λbsλss|＜165的参数范围内,这两个过程中存在的反常现象能够同时给予解释.     

Nonfactorization and the decaysD s +→φπ +,φρ + andφl + ν l

Using the experimentally measured values ofx=A ₂(0)/A ₁(0) andy=V(0)/A ₁(0) and the measured ratiosR _st=Γ(D _s ⁺ →φl ⁺ ν _l)/Γ(D _ins ⁺ →φπ ⁺) andR _h=Γ(D _s ⁺ →φρ ⁺)/Γ(D _s ⁺ →φπ ⁺), we present evidence for significant nonfactorization contribution in the decay amplitude forD _s ⁺ →φπ ⁺. We analyze the role of nonfactorization inD _s ⁺ →φρ ⁺ and conclude that present data onR _h are consistent with factorization inD _s ⁺ →φρ ⁺. A measurement of polarization inD _s ⁺ →φρ ⁺ would greatly assist our analysis.     

K~* production in the KN → Kπp reaction

We investigate the K^∗ production in the KN→Kπp reaction using the effective Lagrangian approach and the isobar model.To describe this reaction,we first take into account the contributions from the π,ρ and ω exchanges,as in previous studies.We find that although the experimental data can be generally described,there are some obvious discrepancies between the model and the experiments.To improve the model,we consider the contributions of the axial-vector meson and hyperon exchange.It is shown that a large contribution of the axial-vector meson exchange can significantly improve the results.This may indicate that the coupling of the axial-vector meson,e.g.a1(1260),is large in the KK^∗ channel.To verify our model,measurements of the angular distributions and spin density matrix elements of K^∗0 in the KLp→K^∗0p reaction would be helpful,and we make predictions for this reaction for a future comparison.     

Study of the K − → e − νπ 0 decay

The decay K ^? → e ^? νπ ⁰ has been studied using in-flight decays detected with the ISTRA₊ setup working at the 25-GeV negative secondary beam of the U-70 PS. About 130K events were used for the analysis. The λ ₊ parameter of the vector form factor has been measured: λ ₊=0.0293±0.0015(stat.)±0.002(syst.). The limits on the possible tensor and scalar couplings have been derived: f _T/f ₊(0)=?0.045±0.060(stat.) and f _S/f ₊(0)=?0.019 _?0.016 ^+0.025 (stat.).