Pionic deuterium

The strong-interaction shift ε _1s ^πD and broadening Γ _1s ^πD in pionic deuterium have been determined in a high statistics study of the πD(3p-1s) X-ray transition using a high-resolution crystal spectrometer. The pionic deuterium shift will provide constraints for the pion-nucleon isospin scattering lengths extracted from measurements of shift and broadening in pionic hydrogen. The hadronic broadening is related to pion absorption and production at threshold. The results are ε _1s ^πD = (?2356 ± 31) meV (repulsive) and Γ _1s ^πD meV yielding for the complex πD scattering length a _πD = [?(24.99±0.33)+i(6.22 _?0.26 ^+0.12 )] × 10^?3 m _π ^?1 . From the imaginary part, the threshold parameter for pion production is obtained to be α = (251 _?11 ⁺⁵ ) μb. This allows, in addition, and by using results from pion absorption in ³He at threshold, the determination of the effective couplings g ₀ and g ₁ for s-wave pion absorption on isoscalar and isovector NN pairs.     

Isospin breaking in the phases of the K e4 form factors

Isospin breaking in the K _?4 form factors induced by the difference between charged and neutral pion masses is studied. Starting from suitably subtracted dispersion representations, the form factors are constructed in an iterative way up to two loops in the low-energy expansion by implementing analyticity, crossing, and unitarity due to two-meson intermediate states. Analytical expressions for the phases of the two-loop form factors of the K ^±→π ⁺ π ^? e ^± ν _e channel are given, allowing one to connect the difference of form-factor phase shifts measured experimentally (out of the isospin limit) and the difference of S- and P-wave ππ phase shifts studied theoretically (in the isospin limit). The isospin-breaking correction consists of the sum of a universal part, involving only ππ rescattering, and a process-dependent contribution, involving the form factors in the coupled channels. The dependence on the two S-wave scattering lengths $a_{0}^{0}$ and $a_{0}^{2}$ in the isospin limit is worked out in a general way, in contrast to previous analyses based on one-loop chiral perturbation theory. The latter is used only to assess the subtraction constants involved in the dispersive approach. The two-loop universal and process-dependent contributions are estimated and cancel partially to yield an isospin-breaking correction close to the one-loop case. The recent results on the phases of K ^±→π ⁺ π ^? e ^± ν _e form factors obtained by the NA48/2 collaboration at the CERN SPS are reanalysed including this isospin-breaking correction to extract values for the scattering lengths $a_{0}^{0}$ and $a_{0}^{2}$ , as well as for low-energy constants and order parameters of two-flavour χPT.     

ΛΛ 6 He and Λ 9 Be systems in the three-body cluster model treated on the basis of differential Faddeev equations

The _ΛΛ ⁶ He and _Λ ⁹ Be hypernuclei are treated as the S=0, T=0 (for the former) and S=1/2, T=0 (for the latter) bound states of the three-cluster systems ΛΛα and Λαα, respectively. The cluster-reduction method is used to solve the s-wave differential Faddeev equations for these systems. On the basis of the MT I–III model, the ΛΛ interaction potential is specified in the form $V_{\Lambda \Lambda } = \frac{2}{3}V_{NN} $ . Phenomenological potentials are used to describe Λα and αα interactions. The binding energies of the _ΛΛ ⁶ He and _Λ ⁹ Be hypernuclei and the parameters of low-energy Λ-hyperon and α-particle scattering on a _Λ ⁵ He hypernucleus are calculated. It is shown that the proposed ΛΛ interaction potential makes it possible to reproduce faithfully the binding energy of the _ΛΛ ⁶ He hypernucleus and that scattering in the Λ _Λ ⁵ He system is similar to neutron scattering on a deuteron.     

Determination of the ππ scattering lengths from data on πN → ππN reactions by the method of Roy equations

Fitted phase-shift curves from the threshold to the dipion mass, which is equal to 1 GeV, are constructed on the basis of all available experimental values of the S-and P-wave phase shifts for five charged channels of pion-pion scattering. The resulting phase-shift curves are introduced in the Roy equations in order to obtain the subtraction constants λ _l ^I (s). By using these subtraction-constant values as functions of the dipion mass, the S ₀-and S ₂-wave pion-pion scattering lengths are found to be a ₀ ⁰ = (0.240 ± 0.023)m _π ^?1 and a ₀ ² = (?0.034 ± 0.013)m _π ^?1 . A strong correlation of the S-wave scattering lengths is demonstrated.     

\bar pp-Annihilation processes in the tree approximation of SU(3) chiral effective theory

The $\bar pp$ -annihilation reactions $\bar pp \to \eta \eta \eta$ and $\bar pp \to \eta {\rm K}\bar {\rm K}$ at rest are considered in the tree approximation in the framework of SU(3) chiral effective theory at leading order. The calculated branchings are compared with the data. The results for neutral (????, $\eta {\rm K}^0 \bar {\rm K}^0$ ) and charged (??K ⁺ K ^?) channels are essentially different.     

p¯p Annihilation into two mesons in the quark rearrangement model and the quark annihilation model

The relativistic³ P ₀ model is applied to the \(p\bar p\) annihilation into twoS-wave mesons. We calculate the branching ratios of the \(p\bar p\) annihilation at rest into two mesons in the quark rearrangement model and in the quark annihilation model. In the annihilation model, we project the intermediate \(cq\bar q\) state to eigenstates ofSU (4) with the relative angular momentum of \(cq\bar q\) equals orp. In the rearrangement model, no annihilation occurs from theS-wave \(p\bar p\) and certain branching ratios conflict with the experimental data. Detailed comparison with the experiment needs inclusion ofP-wave mesons in the final state, nevertheless we find that the annihilation model gives qualitatively better results than the rearrangement model. The effect of initial state interaction through \(N\bar \Delta \pm \Delta \bar {\rm N}\) or \(\Delta \bar \Delta \) channels is discussed.     

A study of\bar np annihilations between 0.5 and 0.8 GeV/c

A study of \(\bar np\) annihilations with \(\bar n\) momentum between 0.5 and 0.8 GeV/c is presented. The search fors-channel resonances in \(\bar np\) annihilations reveal possibly two narrow structures in the odd pions final state. Inclusiveρ ⁰ andf ⁰ cross sections in \(\bar np\) annihilations have been estimated to be 9.0±0.6 mb and 3.4±0.6 mb respectively. Longitudinal and transverse momentum distributions for inclusiveρ ⁰ production have been presented. A study of resonance production in exclusive final state revealsρ ⁰ production to be dominant in the odd pion final states andρ ⁺,ω ⁰ productions are most important for the even pion final states. Theπ ⁺ π ^? effective mass spectra in the backward and the forward directions in the \(\bar np\) c.m. system have been examined for a possible ?-ω interference effect.     

On scalar resonances in ππ→ππ,K\bar K, ηη reactions

Carried out is the analysis of the new experimental data on theS-wave of the ππ→ \(K\bar K\) reaction in common with ππ→ππ one in the 1–1.6 Gev energy region. It is shown that new resonances are not required for the explanation of the data and for that the well-knownS ^* (980) and ε (1300–1400) resonances and their mixing only are enough. Once more confirmed is the possibility forS ^* (980) to be the \(qq\bar q\bar q\) from (9,0⁺) nonet of the \(qq\bar q\bar q\) mesons predicted by the MIT-bag model. Moreover, it is shown that the ε(1300–1400) resonance can be interpreted as a member of the second four-quark (9,0⁺)-nonet. We predict the bright manifestation of theS ^* and ε-resonances in the π⁺π^? →ηη reaction. The analysis of the data shows that the ε-meson cannot be a pureSU (3)-singlet and therefore it cannot pretend to the role of the gluonium. Discussed is critically the Törnqvist's analysis for scalar mesons.     

Quark-mass dependence in $$\omega \rightarrow 3\pi $$ decays

We study the quark-mass dependence of \(\omega \rightarrow 3\pi \) decays, based on a dispersion-theoretical framework. We rely on the quark-mass-dependent scattering phase shift for the pion–pion P-wave extracted from unitarized chiral perturbation theory. The dispersive representation then takes into account the final-state rescattering among all three pions. The described formalism may be used as an extrapolation tool for lattice QCD calculations of three-pion decays, for which \(\omega \rightarrow 3\pi \) can serve as a paradigm case.     

Chiral SU(3) dynamics and the quasibound K – pp cluster

The prototype of a $\bar{K}$ nuclear cluster, K ^???pp, has been investigated using effective $\bar{K}N$ potentials based on chiral SU(3) dynamics. Variational calculation shows a bound state solution with shallow binding energy B(K ^???pp)?=?20±3 MeV and broad mesonic decay width $\Gamma(\bar{K}NN \rightarrow \pi Y N)=40$ –70 MeV. The $\bar{K}N(I=0)$ pair in the K ^???pp system exhibits a similar structure as the Λ(1405). We have also estimated the dispersive correction, p-wave $\bar{K}N$ interaction, and two-nucleon absorption width.     

Energy dependence of {\bar{K}N} interaction in nuclear medium

When the $\bar{K}N$ system is submerged in nuclear medium the $\bar{K}N$ scattering amplitude and the final state branching ratios exhibit a strong energy dependence when going to energies below the $\bar{K}N$ threshold. A sharp increase of $\bar{K}N$ attraction below the $\bar{K}N$ threshold provides a link between shallow $\bar{K}$ -nuclear potentials based on the chiral $\bar{K}N$ amplitude evaluated at threshold and the deep phenomenological optical potentials obtained in fits to kaonic atoms data. We show the energy dependence of the in-medium K ^??? p amplitude and demonstrate the impact of energy dependent branching ratios on the Λ-hypernuclear production rates.     

Beam spin asymmetries of charged and neutral pion production in semi-inclusive DIS

We present a study on the beam single spin asymmetries $A_{LU}^{\sin\phi_{h}}$ of π ⁺, π ^? and π ⁰ production in semi-inclusive deep inelastic scattering process, by considering Collins effect and the g ^⊥ D ₁ term simultaneously. We calculate the twist-3 distributions $e(x, \boldsymbol{k}_{T}^{2})$ and $g^{\perp}(x, \boldsymbol{k}_{T}^{2})$ for the valence quarks inside the proton in a spectator model. We consider two different options for the form of diquark propagator, as well as two different choices for the model parameters in the calculation. Using the model results, we estimate the beam spin asymmetries $A_{LU}^{\sin\phi_{h}}$ for the charged and neutral pions and compare the results with the measurement from the HERMES Collaboration. We also make predictions on the asymmetries at CLAS with a 5.5 GeV beam using the same model results. It is found that different choices for the diquark propagator will not only lead to different expressions for the distribution functions, but also result in different sizes of the asymmetries. Our study also shows that, although the spectator model calculation can describe the asymmetries for certain pion production in some kinematic regions, it seems difficult to explain the asymmetries of pion production for all three pions in a consistent way from the current versions.     

Open beauty production in high energy π−-tungsten interactions

We present a study of \(B\bar B\) meson pair production inπ ^? interactions at 140, 194 and 286 GeV incident pion energy. At 286 GeV, where we have the best statistics, we find a model-dependent \(B\bar B\) production cross-section \(\sigma _{BB} = 14_{ - 6}^{ + 7} nb/nucleon\) .     

Photonic production ofS- andP-waveB c states and doubly heavy baryons

Numerical calculations for the production ofS-andP-wave levels ofB _c quarkonium inγγ collisions are performed in the leadingO(α _s ² α _em ² ) order of perturbation theory. The total cross-section ofP-wave state production is about 10 % of that for theS-wave levels. The contribution of fragmentation component (6+6 diagrams) is low, and the basic contribution is determined by the recombination mechanism (8 Feynman diagrams). The gauge invariant term of the $\bar b$ →B _c fragmentation (6 diagrams) quite accurately reproduces the result of the fragmentation model, whereas there is a strong deviation of thec→B _c fragmentation term from the predictions of the fragmentation model. The total cross-sections in photonic production of doubly heavy diquark, hadronizing into the baryons, are evaluated.     

Heavy Meson Decay in Three-Mesons and FSI

The final state interaction contribution to charged D decay into \({K \pi \pi}\) is computed within a light-front framework, considering S-wave \({K\pi}\) interactions in 1/2 and 3/2 isospin states. The convergence of the rescattering series is checked computing terms up to the third perturbative order. The role of the resonances above \({K^*_0(1430)}\) , and the contribution of the \({K\pi 3/2}\) isospin channel to charged three-body D decays, are studied against the available phase-shift analysis.     

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.     

Spin-1 particle in a homogeneous magnetic field

The Corben-Schwinger theory gives imaginary values of the energy, forS ₃ ² =1 states, in very intensive magnetic fields. The theory proposed by the author, which is most satisfactory in the nonrelativistic approximation, does not have this defect forS ₃ ² =1 states, but it appears forS ₃ ² =0 states.     

A new determination of the πN sigma term using hyperbolic dispersion relations in the (ν2,t) plane

Dispersion relations in the (ν²,t) plane along hyperbolas are used in order to extrapolate the invariant isospin-even πN amplitude D⁺(ν²,t) to the Cheng-Dashen point, ν=0, t=2μ. The fluctuation of the results obtained with different hyperbolas gives a realistic estimate of the errors, except for errors of the partial wave solution and of the ππ \( - N\bar N\) amplitudes assumed at t < 4μ² —If our ππ \( - N\bar N\) partial waves are used, which are based on the ππs-wave scattering length a ₀ ⁰ =0.28 μ^-1, the result for the sigma term is 64±8 MeV, in agreement with earlier determinations.—The discrepancy with the theoretical prediction σ_πN≈ 30 MeV is smaller by only 8 MeV, if our \( - N\bar N\) amplitudes are modified in such a way that the threshold behaviour of the ππs-wave agrees with Weinberg's prediction a ₀ ⁰ =0.16 μ^-1. Further progress depends on new accurate experimental π^±p scattering data in the Coulomb interference region at low energies.     

Low energy π-π resonances in the Veneziano model

We attempt to impose elastic unitarity on the forward π-π scattering using the Veneziano Amplitude together with a crossing symmetric subtraction term as an input. TheN/D method is used and thep, ? mesons are interpreted as CDD poles. The self consistency requirement led to the evalutation of the low energy parameters and theS andP-wave phase shifts. The values of the scattering lengths obtained area ₀ ⁰ =0.084m _π ^?1 ,a ₂ ⁰ =?0.024m _π ^?1 ,a ₁ ¹ =0.047m _π ^?3 .