108 research outputs found
О размерностях контрпримеров к гипотезе Борсука на сферах малого радиуса
In this article there are constructions of counterexamples to the Borsuk's conjecture defined, which are sets laying on spheres of small radii. This work shows how the dimension of a counterexample depends on the radius of the covering sphere.В данной статье воспроизведены конструкции различных контрпримеров к гипотезе Борсука, которые представляют собой множества, лежащие на сфере малого радиуса. В работе отражено, как зависит размерность контрпримера от радиуса сферы, на которой он построен
О хроматических числах R2 и R3 с интервалами запрещённых расстояний
In this article there defined one of generalization of classical notion of chromatic number of a plane or a space defined, that is chromatic number with an interval of forbidden distances. Some upper bounds are obtained for this value with different intervals and the method of finding these results are described.В данной статье представлено одно из обобщений классического понятия хроматического числа плоскости, или пространства, а именно, хроматического числа с интервалом запрещённых расстояний. Были получены верхние оценки для введённой величины при различных интервалах и описан метод получения подобных результатов
Nonresonant Three-body Decays of D and B Mesons
Nonresonant three-body decays of D and B mesons are studied. It is pointed
out that if heavy meson chiral perturbation theory (HMChPT) is applied to the
heavy-light strong and weak vertices and assumed to be valid over the whole
kinematic region, then the predicted decay rates for nonresonant charmless
3-body B decays will be too large and especially B^- --> pi^- K^+ K^- greatly
exceeds the current experimental limit. This can be understood as chiral
symmetry has been applied there twice beyond its region of validity. If HMChPT
is applied only to the strong vertex and the weak transition is accounted for
by the form factors, the dominant B^* pole contribution to the tree-dominated
direct three-body B decays will become small and the branching ratio will be of
order 10^{-6}. The decay modes B^- --> (K^- h^+ h^-)_{NR} and bar{B}^0 -->
(bar{K}^0 h^+h^-)_{NR} for h = pi, K are penguin dominated. We apply HMChPT in
two different cases to study the direct 3-body D decays and compare the results
with experiment. Theoretical uncertainties are discussed.Comment: 24 pages, 2 figures. New experimental results of direct 3-body D
decays as Reported at ICHEP2002 are included. To appear in Phys. Re
Coherent QCD phenomena in the Coherent Pion-Nucleon and Pion-Nucleus Production of Two Jets at High Relative Momenta
We use QCD to compute the cross section for coherent production of a di-jet
(treated as a moving at high relative transverse momentum,). In the target rest frame,the space-time evolution of this reaction is
dominated by the process in which the high component of
the pion wave function is formed before reaching the target. It then interacts
through two gluon exchange. In the approximation of keeping the leading order
in powers of and all orders in
the amplitudes for other processes are
shown to be smaller at least by a power of . The resulting dominant
amplitude is proportional to ( is the fraction
light-cone(+)momentum carried by the quark in the final state) times the skewed
gluon distribution of the target. For the pion scattering by a nuclear target,
this means that at fixed (but ) the nuclear process in which there is only a single interaction is the
most important one to contribute to the reaction. Thus in this limit color
transparency phenomena should occur.These findings are in accord with E971
experiment at FNAL. We also re-examine a potentially important nuclear multiple
scattering correction which is positive and . The
meaning of the signal obtained from the experimental measurement of pion
diffraction into two jets is also critically examined and significant
corrections are identified.We show also that for values of achieved
at fixed target energies, di-jet production by the e.m. field of the nucleus
leads to an insignificant correction which gets more important as
increases.Comment: 23 pages, 9 figure
An attempt to understand exclusive pi+ electroproduction
Hard exclusive pi+ electroproduction is investigated within the handbag
approach. The prominent role of the pion-pole contribution is demonstrated. It
is also shown that the experimental data require a twist-3 effect which ensues
from the helicity-flip generalized parton distribution H_T and the twist-3 pion
wave function. The results calculated from this handbag approach are compared
in detail with the experimental data on cross sections and spin asymmetries
measured with a polarized target. It is also commented on consequences of this
approach for exclusive \pi^0 and vector-meson electroproduction.Comment: 35 pages, 12 figures, using Latex, a number of additional comments
have been included in the text, e.g. in paragraph above (3) or at end of
sect.
Nonleptonic Weak Decays of Bottom Baryons
Cabibbo-allowed two-body hadronic weak decays of bottom baryons are analyzed.
Contrary to the charmed baryon sector, many channels of bottom baryon decays
proceed only through the external or internal W-emission diagrams. Moreover,
W-exchange is likely to be suppressed in the bottom baryon sector.
Consequently, the factorization approach suffices to describe most of the
Cabibbo-allowed bottom baryon decays. We use the nonrelativistic quark model to
evaluate heavy-to-heavy and heavy-to-light baryon form factors at zero recoil.
When applied to the heavy quark limit, the quark model results do satisfy all
the constraints imposed by heavy quark symmetry. The decay rates and up-down
asymmetries for bottom baryons decaying into and
are calculated. It is found that the up-down asymmetry is negative except for
decay and for decay modes with in the final
state. The prediction for
is consistent with the recent CDF measurement. We also present
estimates for decays and compare with various model
calculations.Comment: 24 pages, to appear in Phys. Rev. Uncertainties with form factor q^2
dependence are discusse
Constraining fundamental constants of physics with quasar absorption line systems
We summarize the attempts by our group and others to derive constraints on
variations of fundamental constants over cosmic time using quasar absorption
lines. Most upper limits reside in the range 0.5-1.5x10-5 at the 3sigma level
over a redshift range of approximately 0.5-2.5 for the fine-structure constant,
alpha, the proton-to-electron mass ratio, mu, and a combination of the proton
gyromagnetic factor and the two previous constants, gp(alpha^2/mu)^nu, for only
one claimed variation of alpha. It is therefore very important to perform new
measurements to improve the sensitivity of the numerous methods to at least
<0.1x10-5 which should be possible in the next few years. Future
instrumentations on ELTs in the optical and/or ALMA, EVLA and SKA pathfinders
in the radio will undoutedly boost this field by allowing to reach much better
signal-to-noise ratios at higher spectral resolution and to perform
measurements on molecules in the ISM of high redshift galaxies.Comment: 11 pages, 3 figure
Negative Kaons in Dense Baryonic Matter
Kaon polarization operator in dense baryonic matter of arbitrary isotopic
composition is calculated including s- and p-wave kaon-baryon interactions. The
regular part of the polarization operator is extracted from the realistic
kaon-nucleon interaction based on the chiral and 1/N_c expansion. Contributions
of the Lambda(1116), Sigma(1195), Sigma*(1385) resonances are taken explicitly
into account in the pole and regular terms with inclusion of mean-field
potentials. The baryon-baryon correlations are incorporated and fluctuation
contributions are estimated. Results are applied for K- in neutron star matter.
Within our model a second-order phase transition to the s-wave K- condensate
state occurs at rho_c \gsim 4 \rho_0 once the baryon-baryon correlations are
included. We show that the second-order phase transition to the p-wave
condensate state may occur at densities in
dependence on the parameter choice. We demonstrate that a first-order phase
transition to a proton-enriched (approximately isospin-symmetric) nucleon
matter with a p-wave K- condensate can occur at smaller densities, \rho\lsim 2
\rho_0. The transition is accompanied by the suppression of hyperon
concentrations.Comment: 41 pages, 24 figures, revtex4 styl
Energy and decay width of the pi-K atom
The energy and decay width of the pi-K atom are evaluated in the framework of
the quasipotential-constraint theory approach. The main electromagnetic and
isospin symmetry breaking corrections to the lowest-order formulas for the
energy shift from the Coulomb binding energy and for the decay width are
calculated. They are estimated to be of the order of a few per cent. We display
formulas to extract the strong interaction S-wave pi-K scattering lengths from
future experimental data concerning the pi-K atom.Comment: 37 pages, 5 figures, uses Axodra
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