Angular Dependence of the Polarization Transfer to the Proton in the $$e\vec {p} \to e\vec {p}$$ Process

JETP Letters - The dependence of the longitudinal polarization transfer to the proton in the $$e\vec {p} \to e\vec {p}$$ process on the proton scattering angle has been numerically analyzed for the...     

The polarization of protons from the^{12} C\left( {d,\vec p_0 } \right)^{13} C reaction at low deuteron energies

The polarization of protons produced in the \(^{12} C\left( {d,\vec p_0 } \right)^{13} C\) reaction has been measured at 45° lab for deuteron energies between 0·25 and 1·15 MeV. Besides, the angular distribution of proton polarization at 0·975 MeV has also been measured. The result was analysed in terms of associated Legendre polynomials expansion.     

Strong generators of the subregular $$\mathcal {W}$$W-algebra $$\mathcal {W}^{K-N}(\mathfrak {sl}_N,f_{sub})$$WK-N(slN,fsub) and combinatorial description at critical level

Letters in Mathematical Physics - We construct explicitly strong generators of the affine $$\mathcal {W}$$-algebra $$\mathcal {W}^{K_0-N}(\mathfrak {sl}_N, f_{sub})$$ of subregular type A....     

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.     

2-jet production in polarised\vec p\vec pcollisions

Following recent interest in the subject of polarisation phenomena, we discuss the cross-sections and polarisation asymmetry in 2-jet production in polarised proton-polarised proton ( ) scattering. We set up a complete set of parametrisations for the proton spin-dependent parton densities and use them to demonstrate that this cross-section is dominated by gluonic terms. Hence, a measurement of the asymmetry in such processes will provide information on the gluon spin-dependent density. We further show that a factorisation of the hadronic cross-section a la Combridge and Maxwell's work in unpolarised 2-jet production also applies to the spin-dependent case. Hence, the cross-section can be written in terms of a genericpolarised parton density, which can then be measured in the process.     

Form Factor and rms Radius of Proton Predicted Using Differential Cross-Section Data of $${p\bar{p}}$$ Elastic Scattering at $${\sqrt{s}=31}$$ , 53, 62 and 1960 GeV

Physics of Atomic Nuclei - Using differential cross-section data on $$p\bar{p}$$ elastic scattering at $$\sqrt{s}=31$$ , 53, 62, and 1960 GeV, for low momentum transfer square (...     

Simultaneous Investigation of the Nuclear Reactions $${}^{11}$$ B $$\boldsymbol{(p,3\alpha)}$$ and $${}^{11}$$ B $$\boldsymbol{(p,n)^{11}}$$ C as a New Tool for Determining the Absolute Yield of Alpha Particles in Picosecond Plasmas

Physics of Atomic Nuclei - The results of experimental investigations devoted to initiating the promising nuclear fusion reaction $${}^{11}$$ B $$(p,3\alpha)$$ in picosecond laser plasmas at a...     

\mathfrak{g}-Relative Star Products

We consider Kontsevich star products on the duals of Lie algebras. Such a star product is relative if, for any Lie algebra, its restriction to invariant polynomial functions is the usual pointwise product. Let be a fixed Lie algebra. We shall say that a Kontsevich star product is -relative if, on ^*, its restriction to invariant polynomial functions is the usual pointwise product. We prove that, if is a semi-simple Lie algebra, the only strict Kontsevich -relative star products are the relative (for every Lie algebras) Kontsevich star products.     

Modules over\mathfrak{U}_q (\mathfrak{s}\mathfrak{l}_2 )

The restricted quantum universal enveloping algebra decomposes in a canonical way into a direct sum of indecomposable left (or right) ideals. They are useful for determining the direct summands which occur in the tensor product of two simple . The indecomposable finite-dimensional are classified and located in the Auslander-Reiten quiver.     

The Dynamics of Relativistic Strings Moving in the Minkowski Space $$\mathbb{R}^{1+n}$$

In this paper we investigate the dynamics of relativistic (in particular, closed) strings moving in the Minkowski space . We first derive a system with n nonlinear wave equations of Born-Infeld type which governs the motion of the string. This system can also be used to describe the extremal surfaces in . We then show that this system enjoys some interesting geometric properties. Based on this, we give a sufficient and necessary condition for the global existence of extremal surfaces without space-like point in with given initial data. This result corresponds to the global propagation of nonlinear waves for the system describing the motion of the string in . We also present an explicit exact representation of the general solution for such a system. Moreover, a great deal of numerical analyses are investigated, and the numerical results show that, in phase space, various topological singularities develop in finite time in the motion of the string. Finally, some important discussions related to the theory of extremal surfaces of mixed type in are given.     

$$\mathbb{C}^2/\mathbb{Z}_{n}$$ Fractional Branes and Monodromy

We construct geometric representatives for the fractional branes in terms of branes wrapping certain exceptional cycles of the resolution. In the process we use large radius and conifold-type monodromies, and also check some of the orbifold quantum symmetries. We find the explicit Seiberg-duality which connects our fractional branes to the ones given by the McKay correspondence. We also comment on the Harvey-Moore BPS algebras.     

Coherent Photoproduction of Neutral Pseudoscalar Mesons $$\boldsymbol{\pi^{0}\pi^{0}}$$ and $$\boldsymbol{\pi^{0}\eta}$$ on Light Nuclei

Physics of Atomic Nuclei - The coherent photoproduction of $$\pi^{0}\pi^{0}$$ and $$\pi^{0}\eta$$ on nuclei in the mass-number region of $$A\leqslant 7$$ is studied systematically over the range...     

Photonic decays involving the2^{ + + } \left( {\bar bb} \right): Partial widths and jets from tensor meson dominance

Tensor meson dominance combined with vector meson dominance, QCD-potentials and the experimental leptonic widths of Γ and Γ′ predicts $$\Gamma _{\Upsilon '\left( {10.01} \right) \to \gamma 2^{ + + } \left( {\bar bb} \right)} = 2.8keV$$ and $$\Gamma _{2^{ + + } \left( {\bar bb} \right) \to \gamma \Upsilon \left( {9.46} \right)} = 134keV.$$ The angular distributions of the γ and the jetsj resulting from the decays $$e^ + e^ - \to \Upsilon '\left( {10.01} \right) \to \gamma 2^{ + + } \left( {\bar bb} \right) \to \gamma gg \to \gamma jj$$ and $$e^ + e^ - \to \Upsilon '\left( {10.01} \right) \to \gamma 2^{ + + } \left( {\bar bb} \right) \to \gamma \bar qq \to \gamma jj$$ with massless vector gluonsg, (coupled gauge invariantly) and quarksq are uniquely determined in TMD. The result for the first process agrees with that of perturbative QCD. No perturbative QCD-prediction for the latter is known.     

Parity anomaly in a \mathcal{P}\mathcal{T}-symmetric quartic Hamiltonian

In this paper, two independent methods are used to show that the non-Hermitian -symmetric wrong-sign quartic Hamiltonian H = (1/2m)p ² − gx ⁴ is exactly equivalent to the conventional Hermitian Hamiltonian . First, this equivalence is demonstrated by using elementary differential-equation techniques and second, it is demonstrated by using functional-integration methods. As the linear term in the Hermitian Hamiltonian is proportional to ℏ, this term is anomalous; that is, the linear term in the potential has no classical analog. The anomaly is a consequence of the broken parity symmetry of the original non-Hermitian -symmetric Hamiltonian. The anomaly term in remains unchanged if an x ² term is introduced into H. When such a quadratic term is present in H, this Hamiltonian possesses bound states. The corresponding bound states in are a direct physical measure of the anomaly. If there were no anomaly term, there would be no bound states.     

Studying the possibility of recovering np and nn helicity amplitudes on the basis of \vec p + \vec d and \vec n + \vec d scattering data at intermediate energies

In this work, we study the possibility of direct recovery of np helicity amplitudes, which are unknown at incident neutron energies T _n > 1.1 GeV, and nn helicity amplitudes, which are unknown at any energy, from data on $\vec p + \vec d$ and $\vec n + \vec d$ scattering. For the inversion of $\vec N + \vec d$ data, we use formulas that relate N _d- and NN amplitudes derived in terms of a refined Glauber model. It is found that the critical factors for solving the inverse problem under study are the accuracy and completeness of the set of input $\vec N + \vec d$ observables.     

Analysis of the \frac{1} {2}^ - and \frac{3} {2}^ - heavy and doubly heavy baryon states with QCD sum rules

In this article, we study the $\frac{1} {2}^ -$ and $\frac{3} {2}^ -$ heavy and doubly heavy baryon states $\Sigma _Q \left( {\frac{1} {2}^ - } \right)$ , $\Xi '_Q \left( {\frac{1} {2}^ - } \right)$ , $\Omega _Q \left( {\frac{1} {2}^ - } \right)$ , $\Xi _{QQ} \left( {\frac{1} {2}^ - } \right)$ , $\Omega _{QQ} \left( {\frac{1} {2}^ - } \right)$ , $\Sigma _Q^* \left( {\frac{3} {2}^ - } \right)$ , $\Xi _Q^* \left( {\frac{3} {2}^ - } \right)$ , $\Omega _Q^* \left( {\frac{3} {2}^ - } \right)$ , $\Xi _{QQ}^* \left( {\frac{3} {2}^ - } \right)$ and $\Omega _{QQ}^* \left( {\frac{3} {2}^ - } \right)$ by subtracting the contributions from the corresponding $\frac{1} {2}^ +$ and $\frac{3} {2}^ +$ heavy and doubly heavy baryon states with the QCD sum rules in a systematic way, and make reasonable predictions for their masses.     

Study of semileptonic decay of ${\bar{B}}_{s}^{0} \rightarrow \phi {l}^{+}{l}^{-}$ in QCD sum rule

In this work we study the semileptonic decay of ${\bar{B}}_{s}^{0}\to \phi {l}^{+}{l}^{-}$ (l=e, μ, τ) with the QCD sum rule method. We calculate the ${\bar{B}}_{s}^{0}\to \phi $ translation form factors relevant to this semileptonic decay, then the branching ratios of ${\bar{B}}_{s}^{0}\to \phi {l}^{+}{l}^{-}$ (l=e, μ, τ) decays are calculated with the form factors obtained here. Our result for the branching ratio of ${\bar{B}}_{s}^{0}\to \phi {\mu }^{+}{\mu }^{-}$ agree very well with the recent experimental data. For the unmeasured decay modes such as ${\bar{B}}_{s}^{0}\to \phi {e}^{+}{e}^{-}$ and ${\bar{B}}_{s}^{0}\to \phi {\tau }^{+}{\tau }^{-}$, we give theoretical predictions.     

Results of the Further Analysis of Data from the Tien Shan Array in the Energy Spectrum of Primary Cosmic Rays in the Energy Range of $${2\times 10^{13}{-}3\times 10^{17}}$$ eV

Physics of Atomic Nuclei - The energy spectrum of primary cosmic rays at energies between 2 $$\times 10^{13}$$ and 3 $$\times 10^{17}$$ eV is presented according to data from the Tien Shan array on...     

On \mathbb{Z}-Gradations of Twisted Loop Lie Algebras of Complex Simple Lie Algebras

We define the twisted loop Lie algebra of a finite dimensional Lie algebra as the Fréchet space of all twisted periodic smooth mappings from to . Here the Lie algebra operation is continuous. We call such Lie algebras Fréchet Lie algebras. We introduce the notion of an integrable -gradation of a Fréchet Lie algebra, and find all inequivalent integrable -gradations with finite dimensional grading subspaces of twisted loop Lie algebras of complex simple Lie algebras.On leave of absence from the Institute for Nuclear Research of the Russian Academy of Sciences, 117312 Moscow, Russia.