The semihard processes γγ→ΨX, γγ→ΨΨ, γγ→ϱΨ

The cross sections for Ψ-production in the semihard collisions are calculated at s ⪢ |t|, m_Ψ² and at not too large a jet effective mass m_X²≲m_Ψ² + |t| for the process γγ→ΨX. We found these cross sections in the lowest nontrivial QCD order (two-gluon exchange in the t-channel): σ(γγ→ΨX) ≈ 10³⁵ cm², σ(γγ→ΨΨ)=2×10⁻³⁶ cm². The polarization of Ψ in these processes is transversal (contrary to the longitudinal one of light mesons ϱ⁰, ω, ϕ in similar processes).     

Amplitude analysis ofγγ→ππ from threshold to 1.4 GeV

A new amplitude analysis of results onγγ→π ⁺ π ^? from the Mark II andγγ→π ⁰ π ⁰ from the Crystal Ball experiments is reported. Key constraints from the low energy theorem and from analyticity and unitarity that relateγγ→ππ to other meson scattering reactions are built into the trial forms. Despite these restrictions, the limited angular converge of the experiments means that solutions with quite different proportions ofS wave andD waves of both helicities 0 and 2 are admitted above 1 GeV. This leads to a much wider range of possibilities for the couplings of the braod resonancesf _o(?) andf ₂(1270) than is commonly supposed. The better fits have \(\Gamma _{f_0 } \) in excess of 4 keV and a ratio of \(\Gamma _{f_0 } /\Gamma _{f_2 } \) greater than 2.     

OnD→ππ andK\bar K decays

We have analysed the recent data onD→ππ and \(K\bar K\) decays from ARGUS, CLEO and E691. (i) We find that Bauer, Stech and Wirbel (BSW) model does fairly well in explaining all data if we assume that final state interactions simply rotate the amplitudes in the complex plane. However, to get a good fit one needs to raiseD→K transition amplitudes by (5–10)% over the BSW values and lowerD→π amplitudes by a similar amount. (ii) We show that all the data can also be understood in a coupled channel inelastic model. (iii) We also find that the Isgur, Scora, Grinstein and Wise (ISGW) model-form factors, if extrapolated to small momentum transfers (t) by a single pole formula, yield branching ratios too small in comparison to data. We propose an alternate scheme to interpolate between BSW form factors att=0 and ISGW form factors att=t _max.     

The Z → c \bar c → γγ*, Z → b \bar b → γγ* triangle diagrams and the Z → γψ, Z → γϒ decays

The approach to the Z → γψ and Z → γ? decay study is presented in detail, based on the sum rules for the Z → c $ \bar c $ → γγ* and Z → b $ \bar b $ → γγ* amplitudes and their derivatives. The branching ratios of the Z → γψ and Z → γ? decays are calculated for different hypotheses on saturation of the sum rules. The lower bounds of Σ _ψ BR(Z → γψ) = 1.95 × 10^?7 and Σ_υ BR(Z → γ?) = 7.23 × 10^?7 are found. Deviations from the lower bounds are discussed, including the possibility of BR(Z → γJ/ψ(1S)) ～ BR(Z → γ?(1S)) ～ 10^?6, that could be probably measured in LHC. The angular distributions in the Z → γψ and Z → γ? decays are also calculated.     

Model for γγ→VV reactions near threshold

We propose a Veneziano-like model for VV reactions near threshold involving exchanges of 0^– trajectories int- andu-channels. The model is applied to , , , and processes. The model in its simplest form cannot account for the disparities in the cross sections for andK ^*+ K ^*– and for ⁰⁰ and ^+–. Further refinements of the model are suggested.     

Measurements of the γγ＊ → π^0 and γγ＊ → ηc transition form factors at BABAR

We present measurements of the γγ＊ → π^0 transition form factor for the momentum transfer range Q^2=4-40 GeV^2 and the γγ＊ → ηc transition form factor for the range Q^2=2-50 GeV^2. The current status of measurements of the meson-photon transition form factors for the η and η＇ mesons is discussed. The results of the measurement of the ηc mass, total and two-photon widths are also presented.     

The High Energy γγ→γγ Scattering Cross Sections

Contributions of fermion loops, W-boson loops and their sum to the high energy γγ -- γγ scatteringtotal cross sections (1 cosθ＜ cos30) are calculated by analytical expressions of γγ - γγ scattering amplitude. Thesecontributions may be observed in the future photon linear collider and may be uscd to test standard model. Thecontribution of fermions' loops is a half of that in R.K. Arphlus and M. Neuuman's paper (Phys. Rev. 80 (1950) 380;83 (1951) 776).     

Note on Higgs Decay into Two Photons H → γγ

The Higgs decay H →γγ due to the virtual W-loop effect is revisited in the unitary gauge by using the symmetry-preserving and divergent-behavior-preserving loop regularization method,which is realized in the fourdimensional space-time without changing original theory.Though the one-loop amplitude of H →γγ is finite as the Higgs boson in the standard model has no direct interaction with the massless photons at tree level,it involves both tensor-type and scalar-type divergent integrals which can in general destroy the gauge invariance without imposing a proper regularization scheme to make them well-defined.As the loop regularization scheme can ensure the consistency conditions between the regularized tensor-type and scalar-type divergent irreducible loop integrals to preserve gauge invariance,we explicitly show the absence of decoupling in the limit M W /M H → 0 and obtain a result agreeing exactly with the earlier one in the literature.We then clarify the discrepancy of the earlier result from the recent one obtained by R.Gastmans,S.L.Wu and T.T.Wu.The advantage of calculation in the unitary gauge becomes manifest in that the non-decoupling arises from the longitudinal contribution of the W gauge boson.     

What we can learn from γγ→ππ,K \bar K in the resonance region

The two photon couplings of hadronic states are believed to be key pointers to their parton constitutents. With the aim of studying these, we present a method of analysing data on γγ→ππ (andK \(\bar K\) ), which embodies the constraints of unitarity and analyticity while respecting the QED low energy theorem required by gauge invariance. We apply this analysis to presently available data on ππ production and find that within the existing uncertainties few definitive conclusions can yet be drawn in the resonance region. For instance, even the claim that thef-resonance has a largely helicity two coupling is shown not to be established. We illustrate the importance of the angular dependence of the data to reach almost all conclusions not only on the helicity structure off-production but also on the couplings of the scalar states to this vital channel. In the near threshold region, however, we confirm the overwhelming dominance of the QED Born amplitude modified by final state interactions in contradiction with several recent datasets on the π⁺π^? channel. We show how the new Crystal Ball experiment on π⁺0⁰ production not only confirms this conclusion on the near threshold cross-section but angular analysis of their data with its better statistics using the method we present should shed light on the nature of the scalar mesons in the 1 GeV region.     

Impacts of the Soft—Gluon Exchanges on B→ππ Decays

We have investigated the role of soft-gluon exchanges in B→ππ,using the light-cone sum rules in quantum chromodynamics,The calculations are carried out not only for the tree operators but also for the penguin operators.We conclude that soft-gluon exchanges contribute to the decay amplitudes,noticeably on some decay channels,and thus cannot be neglected.     

Calculation of Total Cross Section for γγ→γZ Scattering at High Energy

The total cross sections of γγ→γZ process for γγ c.m.s. energy 91.2—2000GeV are presented. W loop contribution is dominating when γγ c.m.s. energy is larger than 140GeV. The total cross section has a maximum, 220 fb(|cosθ|33cm^－2·s^－1 in which case more than 6000 events for γγ→γZ would be observable. In principle this process provides a test of the non-abelian nature of the standard model, especially the anomalous triple and quartic W-boson vertices.     

Finite-Width Correction to Form Factors of γγ^＊→ π^0 Transition

Instead of the usual zero-width approximation for one resonance, we use the finite-width approximation for the two low resonances, i.e. the ρ- ω mesons, to investigate the light-cone local QCD sum rules for the form factor of the transition γγ^＊→ π^0 ,According to the method of the analytic continuation by duality, the weight function, the polynomial of a low order N, is added to the dispersion integral to annihilate the integrand in the region where both resonance saturation and the QCD asymptotic expression are least reliable. The resultant form factor in the cases for the zero- and finite-widths are almost the same, both agree well with the experimental measurements. A comparison with the result from the Laplacian transformed light-cone sum rules and a brief discussion are given.     

Compton scattering on the charged pion and the process γγ→π0π0

The Compton scattering on a charged pion and the process γγ→π⁰π⁰ are studied using the dispersion relations. Unknown parameters of the S-wave ππ interaction and a sum and a difference of the π⁰ meson polarizabilities are found from a fit to the experimental data for the γγ→π⁰π⁰ process. The found parameters of the ππ interaction are used for the calculation of the cross section of the elastic γπ^± scattering. The analysis of the obtained results shows that the experimental data for the elastic γπ^± scattering in the energy region up to 1 GeV together with the data for the γγ→π⁰π⁰ process could be used both for a determination of the pion polarizability values and for study of the S-wave ππ interaction. Received: 20 November 1998 / Revised version: 22 January 1999     

Measurement of the relative probability of the decay φ → η′γ in the channel η′ → ηπ0π0, η → γγ

The process e ⁺ e ^? → η′γ, η′ → η π⁰π⁰, η → γγ is investigated by an SND detector in experiment on a VEPP-2M equipment with colliding electron-positron beams. The analysis of experimental data yields a value of B(? → η′γ)=(6.7 _?4.2 ^+5.0 ±1.5)×10^?5 for the decay probability. Taking into account a previous measurement of this quantity by an SND detector in the decay channel η′ → π⁺π^?η, one finally obtains B(?→η ′γ)=(6.7 _?2.4 ^+2.8 ±0.8)×10^?5.     

Anomalous couplings of vector bosons and the decay H → γγ: Dimensional regularization versus momentum cutoff

As an illustration of general principles, the W-boson loop contribution to the amplitude for the decay H is calculated within a specific model for the effective lagrangian describing the anomalous gauge boson couplings. Different approaches to the dependence of the result on the scale of new physics are briefly discussed.