Multi-quark structure ofU(3.1)

We interpret the recently observedU(3.1) mesons with the \(\Lambda \bar p\) + pions decays as the bound state of \(\Lambda ,\bar p\) andX ₀(1480). TheX ₀(1480) is a mesonium with \(Q^2 \bar Q^2 \) structures observed in γγ reactions and \(\bar pn\) annihilations. With this interpretation, we can understand its decay modes. Furthermore, we predict the ratio of \(\sigma (\Lambda \bar p\pi ^ + \pi ^ - )/\sigma (\Lambda \bar p\pi ^ + \pi ^ + )\) to be ?3.1 for centrally produced events and that the width of \(U^ - (\Lambda \bar p\pi ^ + \pi ^ - )\) to be greater than that of \(U^ + (\Lambda \bar p\pi ^ + \pi ^ + )\) . Both predictions seem to be in reasonable accord with the available data. We call for the detection of the \(\Lambda \bar p\pi ^ - \pi ^ - \) mode to verify the present interpretation.     

The Isospin Mixing in the X(3872) Decay Spectrum

The large isospin symmetry breaking found in the X(3872) decay is investigated by looking into the transfer strength from the \({{c}\bar{c}}\) quarkonium to the two-meson states: \({c\bar{c} \rightarrow D^{0}\overline{D}^{*0}, D^{+} D^{*-} , J /\psi\omega, {\rm and} \, J /\psi\rho}\) . The widths of the \({\rho}\) and \({\omega}\) mesons are taken into account in the calculation. It is found that very narrow \({J /\psi\omega}\) and \({J /\psi\rho}\) peaks appear at the \({D^{0}\overline{D}^{*0}}\) threshold. These narrow peaks appear provided that the strength of the \({D^{0}\overline{D}^{*0}}\) component is large around the threshold. The large width of the \({\rho}\) meson enhances the isospin-one component in the transfer strength considerably, which reduces the ratio \({{\rm Br}(X \rightarrow J /\psi\omega)/{\rm Br}(X \rightarrow J /\psi\rho)}\) down to 2.5.     

On the nature ofC(1480) resonance

The dynamic interpretation of theC(1480) resonance in the φπ⁰ mass spectrum is discussed in detail. It is shown thatC(1480) can result from a rare decay ρ′(1600)→φπ⁰ originating from OZI rule violation due to coherently amplified intermediate processes ρ′(1600)→ \(K*\bar K + \bar K*K\) →φπ⁰ in the region of logarithmic singularity. Some checks of this interpretation ofC(1480) are given. It is shown that one cannot describe the φπ⁰ data by a nonresonant amplitude π⁰ p→( \(K*\bar K + \bar K*K\) )n→φπ⁰ n with Regge parametrizedK andK ^* exchanges in the block π^?π⁺→ \(K*\bar K + \bar K*K\) →φπ⁰. The decays ρ′(1600)→ωπ⁰, \(K*\bar K + \bar K*K\) ? η are also discussed.     

Faddeev Treatment of the Quasi-Bound and Scattering States in the {\bar{K}NN - \pi\Sigma N} System: New Results

A chiral-motivated \({\bar{K}N - \pi\Sigma - \pi\Lambda}\) potential was constructed and used in Faddeev calculations of different characteristics of \({\bar{K}NN - \pi\Sigma N}\) system. First of all, binding energy and width of the K ^? pp quasi-bound state were newly obtained. The low-energy K ^? d scattering amplitudes, including scattering length, together with the 1s level shift and width of kaonic deuterium were calculated. Comparison with the results obtained with the phenomenological \({\bar{K}N - \pi\Sigma}\) potential demonstrates that the chiral-motivated potential gives more shallow K ^? pp state, while the characteristics of K ^? d system are less sensitive to the form of \({\bar{K}N}\) interaction.     

Nonfactorizable contributions to hadronic decays of charm mesons in the Cabibbo-suppressed modes

We investigate nonfactorizable contributions to charm meson decays into D → ππ/K K?/K K?*/K? K*/D → K*K?* modes. Obtaining the contributions from spectatorquark diagrams for N _c = 3, we determine the nonfactorizable isospin amplitudes required to explain the data for these modes. For these decays, we observe that ππ, πρ, decay modes favor a nonfactorizable-isospin-amplitudes ratio A ₀ ^nf /A ₂ ^nf equal to (1.123±0.158) and for K K?, K K?*, K? K* and K*K?* modes, the ratio of nonfactorizable amplitudes A ₀ ^nf and A ₁ ^nf turns out to be unity.     

Study of the decayf 1(1285)→ρ0(770)γ

The decayf ₁(1285)→ρ⁰(770)γ was studied at VES spectrometer of IHEP. Clear signal off ₁(1285) is seen in the effective mass spectrum of the π⁺π^?γ system in the reaction π^?γN→π⁺π^?π^?γN at the momentum $P_{\pi ^ - } = 37 GeV/c$ . The branching fraction of decayf ₁(1285)→ρ⁰(770)γ has been found to be $$BR(f_1 (1285) \to \rho ^0 (770)\gamma ) = (2.8 \pm 0.7(stat) \pm 0.6(syst)) \cdot 10^{ - 2} .$$ The ratio of the helicity amplitudes for ρ⁰ meson in its rest frame was determined by the analysis of angular distributions: $$\rho _{00} /\rho _{11} = 3.9 \pm 0.9(stat) \pm 1.0(syst).$$      

Φπ production in\bar pp annihilation from S and P states and in J/ψ decaysannihilation from S and P states and in J/ψ decays

Recent experiments at LEAR have found surprisingly large branching ratios for reactions $\bar NN \to \phi \pi $ from S-wave initial states while noφπ production is observed from P states of the $\bar pp$ system. Also, noφπ is seen in radiative J/ψ decays even though the rate forωπ is substantial. We calculate theφπ production rates for these three cases viaKK* intermediate states and $K\bar K$ rescattering using the dispersion relation technique; we find that the largeφπ rate in $\bar pp$ annihilations from S states can be reproduced with a reasonable cut-off for the dispersion integral; for J/ψ decays the calculatedφπ rate is compatible with the observed upper limit. We would, however, expectφπ to be seen from $\bar pp$ P-states, in contrast to experimental findings. Yet the branching ratio for $\bar pp \to K*\bar K$ via isospinI = 1 of $\bar pp$ ,¹ P ₁ state is not known; and therefore no definite conclusion can be drawn. We also compare the Dalitz plots we obtain for directφ production and forφ production via rescattering. Clear differences between the two theoretical distributions are observed; yet very high precision data would be required to establish the origin — direct production or rescattering — of theφ mesons. This observation supports the use of the isobar model in data analyses.     

Few Body Systems Made of Pseudoscalars

Few body systems made of pseudoscalars, like ${K\, K \, \bar K,\,\pi \, K \, \bar K}$ , are studied within a coupled channel approach based on solving the Faddeev equations considering two-body chiral t-matrices as input. As a result, we have found dynamical generation of several states which can be associated with some of the pseudoscalar states listed by the Particle Data Group, like K(1460) or π(1300). The amplitudes obtained have been then used to study systems like f ₀(980) π π and ${f_0(980)K \, \bar K}$ and an evidence for a f ₀ resonance around 1,790 MeV is found.     

Measurements of hyperon semileptonic decays at the CERN Super Proton Synchrotron

The charged hyperon beam at the CERN Super Proton Synchrotron (SPS) has been used to collect data on semileptonic decays of Σ^?, Ξ^?, andΛ. A magnetic channel selected 100 GeV/c negatively charged particles produced in the forward direction by interaction of a 210 GeV/c proton beam on a BeO target. The Σ^? and Ξ^? hyperons were concurrently identified in a DISC ?erenkov counter, and their decay products were analysed by a magnetic spectrometer. Electron-hadron discrimination was achieved by the combined use of lead glass and lead/scintillator counters, transition radiation detectors, and a ?erenkov counter. In this article we report results on the \(\Xi \to \Lambda \pi (\Lambda \to pe\bar v), \Xi \to \Lambda e\bar v(\Lambda \to p\pi ),\) and \(\Xi \to \sum ^0 e\bar v(\sum ^0 \to \Lambda \gamma ) (\Lambda \to p\pi )\) decay modes. Samples of 7,111 \(\Lambda \to pe\bar v, 2,608 \Xi \to \Lambda e\bar v\) , and \(154 \Xi \to \Sigma ^0 e\bar v\) were used in our analysis. The branching ratio measurements gave values of (8.57±0.36)×10^?4, (5.64±0.31)×10^?4, and (0.87±0.17)×10^?4 for \(\Lambda \to pe\bar v, \Xi \to \Lambda e\bar v\) , and \( \Xi \to \sum ^0 e\bar v\) , respectively. Measurements of the Λ polarization and of the centre-of-mass distributions yield the axial vector to vector form factor ratio,g ₁/f ₁=+0.70±0.03 for \(\Lambda \to pe\bar v\) , andg ₁/f ₁=+0.25±0.05 for \(\Xi \to \Lambda e\bar v\) . The effects ofq ²-dependence off ₁ andg ₁ and of radiative corrections, the measurement of the weak magnetism termf ₂, and the effect of possible second-class current terms are discussed. Results on the \(\sum \to \Lambda e\bar v\) and \(\sum \to ne\bar v\) decay modes are reported in separate articles.     

Alternative technique for Standard Model estimation of the rare kaon decay branchings \left. {BR(K \to \pi \nu \bar \nu )} \right|_{SM}

We estimate $BR(K \to \pi \nu \bar \nu )$ in the context of the Standard Model by fitting for λ _t≡V _tdV _ts ^* of the “kaon unitarity triangle” relation. To find the vertex of this triangle, we fit data from |? _K|, the CP-violating parameter describing K mixing, and a _ψ,K , the CP-violating asymmetry in B _d ⁰ → J/ψK ⁰ decays, and obtain the values $\left. {BR(K \to \pi \nu \bar \nu )} \right|_{SM} = (7.07 \pm 1.03) \times 10^{ - 11} $ and $\left. {BR(K_L^0 \to \pi ^0 \nu \bar \nu )} \right|_{SM} = (2.60 \pm 0.52) \times 10^{ - 11} $ . Our estimate is independent of the CKM matrix element V _cb and of the ratio of B-mixing frequencies ${{\Delta m_{B_s } } \mathord{\left/ {\vphantom {{\Delta m_{B_s } } {\Delta m_{B_d } }}} \right. \kern-0em} {\Delta m_{B_d } }}$ . We also use the constraint estimation of λ _t with additional data from $\Delta m_{B_d } $ and |V _ub|. This combined analysis slightly increases the precision of the rate estimation of $K^ + \to \pi ^ + \nu \bar \nu $ and $K_L^0 \to \pi ^0 \nu \bar \nu $ (by ?10 and ?20%, respectively). The measured value of $BR(K^ + \to \pi ^ + \nu \bar \nu )$ can be compared both to this estimate and to predictions made from ${{\Delta m_{B_s } } \mathord{\left/ {\vphantom {{\Delta m_{B_s } } {\Delta m_{B_d } }}} \right. \kern-0em} {\Delta m_{B_d } }}$ .     

Inclusive γ-production in\bar pp interactions at 0.76 and 2.0 GeV/c

The inclusive production of photons in \(\bar pp\) interactions has been studied at incident momenta of 0.76 and 2.0 GeV/c. The inclusive cross sections for γ-production and the average multiplicities of γ, «n _γ», are presented as a function of the charged prong topology. Results on the two particle correlation parametersf ⁰⁰ andf ^?0 are presented. The inclusive distributions of the Feynman variablex and of the transverse momentump _T of the photons are compared with the expectations from charged pion distributions on the basis of charge independence. A search has been made for direct γ-production in \(\bar pp\) interactions at 0.76 GeV/c by looking for events which fit uniquely the hypothesis \(\bar pp \to m\pi ^ + + m\pi ^ - + \gamma \) . An estimate of the ratio $$R = \frac{{\sigma (\bar pp \to m\pi ^ + + m\pi ^ - + \gamma )}}{{\sigma (\bar pp \to m\pi ^ + + m\pi ^ - + \pi ^0 )}}$$ is given.     

Charged Higgs observability through associated production with W ± at a muon collider

The observability of a charged Higgs boson produced in association with a W boson at future muon colliders is studied. The analysis is performed within the MSSM framework. The charged Higgs is assumed to decay to $t\bar{b}We study $B_{s}^{0} \to J/\psi f_{0}(980)$ decays, the quark content of f ₀(980) and the mixing angle of f ₀(980) and ??(600). We calculate not only the factorizable contribution in the QCD factorization scheme but also the nonfactorizable hard spectator corrections in QCDF and pQCD approach. We get a result consistent with the experimental data of $B_{s}^{0} \to J/\psi f_{0}(980)$ and predict the branching ratio of $B_{s}^{0}$ ?CJ/???. We suggest two ways to determine f ₀?C?? mixing angle ??. Using the experimental measured branching ratio of $B_{s}^{0} \to J/\psi f_{0}(980)$ , we can get the f ₀?C?? mixing angle ?? with some theoretical uncertainties. We suggest another way to determine the f ₀?C?? mixing angle ?? using both experimental measured decay branching ratios $B_{s}^{0} \to J/\psi f_{0}(980) (\sigma)$ to avoid theoretical uncertainties.     

Isospin mixing \bar{K}N\hbox{-}{\pi}{\Sigma} interaction and \bar{K}NN\hbox{-}{\pi} {\Sigma}N quasi-bound state

A phenomenological isospin-dependent $\bar{K}N\hbox{-}\pi\Sigma$ potential reproducing a medium KEK value of 1s kaonic hydrogen level shift instead of a K ^? p scattering length is constructed. The corresponding three-body $\bar{K}NN\hbox{-}\pi\Sigma N$ calculation using the obtained potential is performed.     

Charmonium and Meson–Molecule Hybrid Tetraquarks

In the X (3872) decay, both of the ${{J/{\psi\pi\pi}}}$ and ${{J/{\psi\pi\pi\pi}}}$ branching fractions are observed experimentally, and their sizes are comparable to each other. In order to clarify the mechanism to cause such a large isospin violation, we investigate X(3872) employing a model of coupled-channel two-meson scattering with a ${{\rm c}\bar{c}}$ core. The two-meson states consist of ${{D^0\overline{D}^{*0}}}$ , D ⁺ D ^*?, ${{J/{\psi\rho}}}$ , and ${{J/{\psi\omega}}}$ . The effects of the ρ and ω meson width are also taken into account. We calculate the transfer strength from the ${{{\rm c}\bar{c}}}$ core to the final two-meson states. It is found that very narrow ${{J/{\psi\rho}}}$ and ${{J/{\psi\omega}}}$ peaks appear very close to the ${{D^0\overline{D}^{*0}}}$ threshold for a wide range of variation in the parameter sets. The size of the ${{J/{\psi\rho}}}$ peak is almost the same as that of ${{J/{\psi\omega}}}$ , which is consistent with the experiments. The large width of the ρ meson makes the originally small isospin violation by about five times larger.     

Coupled-Channel Faddeev Calculations of K ? d Scattering Length

Dependence of the K ^? d scattering length on the different models of ${\bar{K}N - \pi \Sigma}$ interaction describing ??(1405) resonance in terms of one or two poles is investigated. The ${\bar{K}NN - \pi \Sigma N}$ system is described by coupled-channel Faddeev equations in AGS form. The two-body ${\bar{K}N - \pi \Sigma}$ interaction models reproduce all existing experimental data on K ^? p scattering and K ^? p atom level shift. The comparison with several approximations, commonly used for such calculations, is done.     

Antiproton-proton annihilation at rest intoπ + π − η ′ andπ + π − η from atomicS andP states

We have measured the branching ratios for \(\bar pp\) annihilation at rest intoπ ⁺ π ^? η andπ ⁺ π ^? η′ in hydrogen gas in two data samples that have different fractions ofS-wave andP-wave initial states. The branching ratios are derived from a comparison with the topological branching ratio for \(\bar pp\) annihilations into four charged pions of (49±4)% and the branching ratio intoπ ⁺ π ^? π ⁺ π ^? π ⁰ of (18.7±1.6)%. We find a significant reduction of the branching ratios fromP-states for \(\bar pp \to \pi ^ + \pi ^ - \eta \) andπ ⁺ π ^? η′ in comparison toS-state annihilation. $$\begin{gathered} BR(S - wave \to \pi ^ + \pi ^ - \eta ) = (13.7 \pm 1.46) \cdot 10^{ - 3} \hfill \\ BR(P - wave \to \pi ^ + \pi ^ - \eta ) = (3.35 \pm 0.84) \cdot 10^{ - 3} \hfill \\ BR(S - wave \to \pi ^ + \pi ^ - \eta ') = (3.46 \pm 0.67) \cdot 10^{ - 3} \hfill \\ BR(P - wave \to \pi ^ + \pi ^ - \eta ') = (0.61 \pm 0.33) \cdot 10^{ - 3} . \hfill \\ \end{gathered} $$ In a partial wave analysis of theπ ⁺ π ^? η Dalitz plot we find the following contributions: Phase space, \(a_2^ + (1320)\pi ^ \mp \) ,ηρ⁰ andf ₂(1270)η: $$\begin{gathered} BR(S - wave \to \pi ^ + \pi ^ - \eta PS) = (6.31 \pm 1.22) \cdot 10^{ - 3} \hfill \\ BR(P - wave \to \pi ^ + \pi ^ - \eta PS) = (0.47 \pm 0.26) \cdot 10^{ - 3} \hfill \\ BR(^1 S_0 \to a_2^ \pm (1320)\pi ^ \mp ) = (2.59 \pm 0.73) \cdot 10^{ - 3} \hfill \\ BR(^3 S_1 \to a_2^ \pm (1320)\pi ^ \mp ) = (1.31 \pm 0.48) \cdot 10^{ - 3} \hfill \\ BR(P - wave \to a_2^ \pm (1320)\pi ^ \mp ) = (1.31 \pm 0.69) \cdot 10^{ - 3} \hfill \\ BR(^3 S_1 \to \rho \eta ) = (3.29 \pm 0.90) \cdot 10^{ - 3} \hfill \\ BR(^1 P_1 \to \rho \eta ) = (0.94 \pm 0.53) \cdot 10^{ - 3} \hfill \\ BR(^1 S_0 \to f_2 (1270)\eta ) = (0.083 \pm 0.086) \cdot 10^{ - 3} \hfill \\ BR(P - wave \to f_2 (1270)\eta ) = (0.64 \pm 0.26) \cdot 10^{ - 3} . \hfill \\ \end{gathered} $$ We find a 2 σ effect for the reaction \(\bar pp \to a_0^ \pm (980)\pi ^ \mp \) , \(a_0^ \pm \to \eta \pi ^ \pm \) , with a branching ratio of (0.13±0.07)·10^?3. For η' production we give a branching ratio of \(\bar pp \to \rho \eta '\) of (1.81±0.44)·10^?3 from³ S ₁. We estmate a contribution of about 0.3·10^?3 for ρη' fromP-states. The ratio of ρη and ρη' rpoduction is used to test the validity of the quark line rule. In theπ ⁺ π ^? π ⁺ π ^? γ final state we do not observe the reaction \(\bar pp \to \pi ^ + \pi ^ - \omega \) , ω→π ⁺ π ^? λ and derive an upper limit of 3·10^?3 for decay modeω→π ⁺ π ^? λ.     

QCD calculation ofB \to \pi l\bar v_l and the matrix element |V bu|

Using QCD sum rules for a two-point function involving beauty vector currents, together with current algebra-PCAC sum rules, we estimate the hadronic matrix element in \(B \to \pi l\bar v_l \) . We find \(\Gamma \left( {\bar {\rm B}^0 \to \pi ^ + l\bar v_l } \right) = \left( {1.45 \pm 0.59} \right) \times 10^{13} \left| {V_{bu} } \right|^2 s^{ - 1} \) . As a byproduct, the vector current contribution to the decay \(B \to \rho l\bar v_l \) is also estimated.     

Three-loop on-shell charge renormalization without integration:\Lambda _{QED}^{\overline {MS} } to four loops

Using algebraic methods, we find the three-loop relation between the bare and physical couplings of one-flavourD-dimensional QED, in terms of Γ functions and a singleF ₃₂ series, whose expansion nearD=4 is obtained, by wreath-product transformations, to the order required for five-loop calculations. Taking the limitD→4, we find that the \(\overline {MS} \) coupling \(\bar \alpha (\mu )\) satisfies the boundary condition $$\begin{gathered} \frac{{\bar \alpha (m)}}{\pi } = \frac{\alpha }{\pi } + \frac{{15}}{{16}}\frac{{\alpha ^3 }}{{\pi ^3 }} + \left\{ {\frac{{11}}{{96}}\zeta (3) - \frac{1}{3}\pi ^2 \log 2} \right. \hfill \\ \left. { + \frac{{23}}{{72}}\pi ^2 - \frac{{4867}}{{5184}}} \right\}\frac{{\alpha ^4 }}{{\pi ^4 }} + \mathcal{O}(\alpha ^5 ), \hfill \\ \end{gathered} $$ wherem is the physical lepton mass and α is the physical fine structure constant. Combining this new result for the finite part of three-loop on-shell charge renormalization with the recently revised four-loop term in the \(\overline {MS} \) β-function, we obtain $$\begin{gathered} \Lambda _{QED}^{\overline {MS} } \approx \frac{{me^{3\pi /2\alpha } }}{{(3\pi /\alpha )^{9/8} }}\left( {1 - \frac{{175}}{{64}}\frac{\alpha }{\pi } + \left\{ { - \frac{{63}}{{64}}\zeta (3)} \right.} \right. \hfill \\ \left. { + \frac{1}{2}\pi ^2 \log 2 - \frac{{23}}{{48}}\pi ^2 + \frac{{492473}}{{73728}}} \right\}\left. {\frac{{\alpha ^2 }}{{\pi ^2 }}} \right), \hfill \\ \end{gathered} $$ at the four-loop level of one-flavour QED.