\bar \partial -Torsion,foliations and holomorphic vector fields

In this paper, we investigate the relation between -torsion and holomorphic vector fields. We consider complex manifolds which fibrate over the torus having a transverse one dimensional holomorphic foliation. The torsion of the total space is then computed in terms of compact leaves. This can be interpreted as a Lefschetz formula for flows of holomorphic vector fields.     

\bar \partial problem for the generalized Korteweg-de Vries equation

The generalized Korteweg-de Vries equation, which has applications in hydrodynamics, in particular, is essentially the first example of a case in which the dressing of a nonlinear equation is constructed by introducing into the dressing operator an arbitrary function of the independent variables of this equation. The proposed algorithm reveals a class of solutions of this equation which are expressed in terms of the solution of algebraic equations. An example of a new type of solution whose derivative with respect to the independent variables has a power-law singularity at some point is presented. Pis’ma Zh. éksp. Teor. Fiz. 68, No. 9, 715–720 (10 November 1998)     

The\bar \partial -operator on algebraic curves

For a singular algebraic curve we show that all closed extensions of are Fredholm, and we give a general index formula. In particular, we prove a modified version of a conjecture due to MacPherson.     

Multi-\bar K configurations and the limit of kaon condensation

Our recent relativistic mean-field (RMF) calculations of multi?-? $\bar K$ nuclei are briefly reviewed. I discuss the saturation pattern of the $\bar K$ separation energy $B_{\bar K}$ and nuclear densities on increasing the number of antikaons embedded in the nuclear medium. Saturation appears to be a robust feature of multi- $\bar K$ nuclei. Because $B_{\bar K}$ generally does not exceed 200 MeV, it is unlikely that kaon condensation occurs in strong-interaction self-bound strange hadronic matter. Last, I present our calculations of self-bound strange systems made out of neutrons and ${\bar K}^0$ mesons.     

A study of the high-energy reaction\bar PP \to \bar PP

The high-energy behavior of the reaction atP _L =8 GeV/c andP _L =16 GeV/c is studied in the context of O(3,1) symmetry. In view of the many exchanged particles, approximate equivalence relations ins-channel amplitudes are used which cut down the unknown parameters to a manageable set of adjustable constants. Our analysis has essentially explained the characteristic features of this reaction, which are (i) the ending of the forward peak at |t| 0.6 (GeV/c)²; (ii) developing of a shoulder at larger |t|'s; and (iii) decreasing of the differential cross section at the shoulder for 16 GeV/c at a slower rate than 8 GeV/c.On leave of absence from Department of Physics, University of Azarabadgan, Tabriz, Iran.     

Rates for the reactions\bar pp \to \pi \phi andγ φ

We study ¯pp annihilation at rest intoπφ andγφ. Rescattering by ¯K^*K+K^*¯K and ρ⁺ρ^? for ¯pp→πφ states is sizable, of order (0.90 to 2.6) × 10^?4 in the branching ratio, but smaller than experiment. For ¯pp→γφ the rescattering contributions are negligible, but theγφ channel is well explained by aρφ intermediate state combined with vector meson dominance.     

Proton spectrum from\bar pd \to 5\pi p at rest and the elementary\bar pnannihilation

We calculate the shape of the proton spectator distribution in \(\bar pd \to 5\pi p\) at low proton momenta. The sensitivity to atomicS- andP-state orbits and to the size of elementarys- andp-wave annihilation is discussed. Implications for the elementary annihilation amplitude \(\bar pn \to 5\pi \) subthreshold are presented.     

Charmed meson rescattering in the reaction $$ \bar pd \uparrow \bar DDN $$

We examine the possibility to extract information about the DN and interactions from the reaction. We utilize the notion that the open-charm mesons are first produced in the annihilation of the antiproton on one nucleon in the deuteron and subsequently rescatter on the other (the spectator) nucleon. The latter process is then exploited for investigating the DN and interactions. We study different methods for isolating the contributions from the D ⁰ p and D ⁻ p rescattering terms.     

Muon spectra for the processeZ \to Z\mu \bar v_\mu v_e

Energy and angular spectra of muons for the process are calculated within the framework of the conventional V-A theory of weak interactions.     

Charged hadron multiplicities in high energy\bar v_\mu n and\bar v_\mu pinteractions

Charged hadron multiplicity distributions in \(\bar v_\mu n\) and \(\bar v_\mu p\) interactions in the energy range \(5< E_{\bar v}< 150GeV\) GeV are presented. They are obtained from about \(6000\bar v_\mu \) charged current events produced in BEBC filled with deuterium. Multiplicity moments are studied as a function of the invariant mass of the hadronic systemW. Results on multiplicity distributions in the forward and backward directions in the hadronic c.m.s. are presented and discussed within the framework of the quark parton model. Values for the average charge of the forward jet are also determined and compared with other experimental data.     

Resonance structures in the \Lambda \bar \Lambda system

The results of studying the $\Lambda \bar \Lambda $ system produced in the reaction π^? p→ $\Lambda \bar \Lambda $ n at a π^?-meson energy of 40 GeV are reported. Experimental data (～2300 events) were obtained on the ITEP 6-meter spectrometer with a beam of the IHEP U-70 accelerator. The invariant-mass spectra for the events dominated by the singlet or triplet $\Lambda \bar \Lambda $ states were found to differ considerably from each other. The data give evidence for the existence of resonance $\Lambda \bar \Lambda $ states of the system in the mass regions near 2.3, 2.5, and 2.8 GeV.     

Rescattering mechanisms for\bar pd \to pX reactions

Inclusive proton spectra for the reactions¯pd→3πp, ¯pd→5πp, and¯p d →K¯Kmπp are calculated. In addition to nucleon exchange, the rescattering of pions and kaons, and the production and absorption of heavy mesons is evaluated. In the proton spectator momentum regime of 200 to 600 MeV/c, the role of heavy mesons is found to be negligible. The proper counting of the topological variants of pion and kaon rescattering can explain the cross sections with the exception of the¯pd→3πp channel.     

Rho-omega-mixing and the mass difference between the spin oneu\bar u andd\bar d configurations

The mixing between the rho and omega mesons is treated in the frame of a nonrelativistic and nonhermitean effective Hamiltonian, in which the charge symmetry is broken only by the mass difference between the spin one \(u\bar u\) and \(d\bar d\) configurations. The mass difference obtained from the fit to the Novosibirsk data is ¦m¦=5.4(4) MeV.     

Corrections of order O(\bar \alpha \bar \alpha _s ) and O(\overline \alpha ^2 ) to the \bar bb-decay width of the neutral Higgs boson

Analytical expressions are presented for contributions of order $O(\overline \alpha \overline \alpha _s )$ and $O(\overline \alpha ^2 )$ to the $\bar bb$ -decay width of the neutral Higgs boson of the standard model of electroweak interactions. The numerical value of the mixed QED and QCD correction of order $O(\overline \alpha \overline \alpha _s )$ is comparable to other computed terms in the perturbation series.     

Suggestion for Einstein-Podolsky-Rosen experiments using reactions likee^ + e^ - \to \Lambda \bar \Lambda \to \pi ^ - p\pi ^ + \bar p

Since weakly decaying particles are their own polarimeters, reactions like \(\eta _c \to \Lambda \bar \Lambda , \psi \to \Lambda \bar \Lambda ,e^ + e^ - \to \mu ^ + \mu ^ -\) , etc. are interesting for testing the non-locality of quantum mechanical predictions. Although such reactions, in principle, do not exclude all classes of hidden variable theories, they can be used to complement current experiments with external polarimeters. The reaction \(\eta _c \to \Lambda \bar \Lambda \to \pi ^ - p\pi ^{ + - } \bar p\) is conceptually the simplest and most useful as agedanken experiment, although it has not yet been seen experimentally. The reaction \(e^ + e^ - \to \Lambda \bar \Lambda \to \pi ^ - p\pi ^ + \bar p\) near threshold or at the φ resonance can be used for essentially the same test. This is feasible with presently available data and would be the first EPR experiment involving weak interactions.     

GLSMs for partial flag manifolds

In this paper we outline some aspects of nonabelian gauged linear sigma models. First, we review how partial flag manifolds (generalizing Grassmannians) are described physically by nonabelian gauged linear sigma models, paying attention to realizations of tangent bundles and other aspects pertinent to (0, 2) models. Second, we review constructions of Calabi–Yau complete intersections within such flag manifolds, and properties of the gauged linear sigma models. We discuss a number of examples of nonabelian GLSMs in which the Kähler phases are not birational, and in which at least one phase is realized in some fashion other than as a complete intersection, extending previous work of Hori–Tong. We also review an example of an abelian GLSM exhibiting the same phenomenon. We tentatively identify the mathematical relationship between such non-birational phases, as examples of Kuznetsov’s homological projective duality. Finally, we discuss linear sigma model moduli spaces in these gauged linear sigma models. We argue that the moduli spaces being realized physically by these GLSMs are precisely Quot and hyperquot schemes, as one would expect mathematically.     

Properties ofe^ + e^ - \to h\bar h in the\Upsilon (b\bar b)-continuum

The unflavored hadrons frome ⁺ e ^? annihilation in the \(\Upsilon (b\bar b)\) -continuum are analyzed in terms of the covariant Boltzmann distribution with an equilibrium temperature 151 MeV according to the Stefan's law. It is found that the effective fugacities of quark contents are approximately equal to the reciprocals of those from othere ⁺ e ^? annihilations outside the γ-continuum, whereas the fireballs are practically stationary, reflecting the decay at rest of \(B\bar B\) mesons produced by thee ⁺ e ^? annihilation.