Front solutions for the Ginzburg-Landau equation

We prove the existence of front solutions for the Ginzburg-Landau equation $$\partial _t u(x,t) = \partial _x^2 u(x,t) + (1 - |u(x,t)|^2 )u(x,t)$$ , interpolating between two stationary solutions of the form \(u(x) = \sqrt {1 - q^2 } e^{iqx}\) with different values ofq atx=±∞. Such fronts are shown to exist when at least one of theq is in the Eckhaus-unstable domain.     

Exclusive semi-leptonic decays of bottom mesons in the spectator quark model

We calculate the exclusive semileptonic bottom meson decays \(B \to D(D*) + l^ - + \bar v_l \) in the spectator quark model. The helicity structure of the mesonic current transitionsB→D(D ^*) is matched to the helicity structure of the free quark current transitionsb→c at minimum momentum transferq ²=0. The results are continued toq ²≠=0 by pole-dominated form factors. Our results are compared to recent calculations that use quark model dynamics at maximum momentum transferq _max ² = (M ₁ ?M ₂)². We find agreement atq _max ² . Atq ²=0 there are significant differences between the predictions of the two approaches leading to marked differences in the predictions for the shape of the lepton energy spectrum, the shape of theq ²-distribution, and the helicity composition of the transition measurable in the angular distributions of the decaysD ^*→Dπ and \(W_{virtual}^ - \to l^ - + \bar v_l \) .     

The Bloch–Okounkov Correlation Functions, a Classical Half-integral Case

Bloch and Okounkov’s correlation function on the infinite wedge space has connections to Gromov-Witten theory, Hilbert schemes, symmetric groups, and certain character functions of ${\widehat{ \mathfrak{gl} }_\infty}$ -modules of level one. Recent works have calculated these character functions for higher levels for ${\widehat{ \mathfrak{gl} }_\infty}$ and its Lie subalgebras of classical type. Here we obtain these functions for the subalgebra of type D of half-integral levels and as a byproduct, obtain q-dimension formulas for integral modules of type D at half-integral level.     

Characteristics of π−,\bar p,and antinuclei frompp collisions

An investigation of inclusivepp→π^?+? in terms of the covariant Boltzmann factor (BF) including the chemical potential μ indicates a) that the temperatureT increases less rapidly than expected from Stefan's law, b) that a scaling property holds for the fibreball velocity of π^? secondaries, leading to a multiplicity law like ～E _cm ^1/2 at high energy, and c) that μ_π is related to the quark mass: μ_π=2m _q ?m _π the quark massm _q determined by \(T_{\pi ^ - } \) at \(\bar pp\) threshold beingm _q =3T_π?330 MeV. Because ofthreshold effects \(T_{\bar p}< T_{\pi ^ - } \) , whereas \({{\mu _p } \mathord{\left/ {\vphantom {{\mu _p } {\mu _{\pi ^ - } }}} \right. \kern-0em} {\mu _{\pi ^ - } }} \simeq {3 \mathord{\left/ {\vphantom {3 2}} \right. \kern-0em} 2}\) as expected from the quark contents of \(\bar p\) and π. The antinuclei \(\bar d\) and \({{\bar t} \mathord{\left/ {\vphantom {{\bar t} {\overline {He^3 } }}} \right. \kern-0em} {\overline {He^3 } }}\) observed inpp events are formed by coalescence of \(\bar p\) and \(\bar n\) produced in thepp collision. Semi-empirical formulae are proposed to estimate multiplicities of π^?, \(\bar p\) and antinuclei.     

Classical {\mathcal{W}}-Algebras and Generalized Drinfeld–Sokolov Hierarchies for Minimal and Short Nilpotents

We derive explicit formulas for λ-brackets of the affine classical \({\mathcal{W}}\) -algebras attached to the minimal and short nilpotent elements of any simple Lie algebra \({\mathfrak{g}}\) . This is used to compute explicitly the first non-trivial PDE of the corresponding integrable generalized Drinfeld–Sokolov hierarchies. It turns out that a reduction of the equation corresponding to a short nilpotent is Svinolupov’s equation attached to a simple Jordan algebra, while a reduction of the equation corresponding to a minimal nilpotent is an integrable Hamiltonian equation on 2h ˇ?3 functions, where h ˇ is the dual Coxeter number of \(\mathfrak{g}\) . In the case when \(\mathfrak{g}\) is \({\mathfrak{sl}_2}\) both these equations coincide with the KdV equation. In the case when \(\mathfrak{g}\) is not of type \({C_n}\) , we associate to the minimal nilpotent element of \(\mathfrak{g}\) yet another generalized Drinfeld–Sokolov hierarchy.     

Benchmark cross sections forp \bar p collisions at 1.8 TeV

High-energyp \(\bar p\) collisions provide many quantitative tests of the standard model. Of particular interest are “hard scattering” processes, which test not only standard model matrix elements and higher order perturbative corrections, but also the distributions of quarks and gluons in the colliding hadrons. We present detailed comparisons of data from the CERNSp \(\bar p\) S collider with theory, incorporating up-to-date parton distributions derived from recent deep inelastic scattering data. Encouraged by the excellent agreement between data and theory at \(\sqrt s \) =630GeV, we present a complete set of “benchmark” predictions for the FNALp \(\bar p\) collider at \(\sqrt s \) =1.8TeV.     

Stability of a singular continuous spectrum of Sturm-Liouville operators

We prove that there exists a continuous potentialq such that the operator generated by $$(lu)(x) = - u^n (x) + \{ q(x) + \upsilon (x)\} u(x), 0 \leqslant (x)< \infty$$ and boundary conditionsu(0) cos α+u′(0) sin α=0 has a singular continuous spectrum in [0, 1] for every locally integrable functionv with compact support and every α ∈ [0, 2π].     

Electroproduction of π0-mesons on protons at very low values of |q 2|

The electroproduction of π⁰-mesons on protons has been measured with electrons of 1.7 and 2.1 GeV energy in the region of the nucleon resonances at \(W = \sqrt {(q + p)^2 } = 1,400 - 2,000MeV\) at rather low values of |q ²|=|(e?e′)²|=0.01–0.1 GeV² but at high values of the nucleon recoil |t|=|(p?p′)²|≈0.6–2.2 GeV² corresponding to \(\Theta _\pi ^{cm} \approx 145^ \circ - 180^ \circ\) . Up toW≈1,650 MeV the cross section for π⁰-production with virtual photons of |q ²|≈0.03 GeV² is only slightly smaller than that with real photons. ForW?1,700 MeV the cross section at |q ²|≈0.03 GeV² is on average a factor of 2 smaller than that atq ²=0 but only slightly higher than that at |q ²|≈0.3–1 GeV².     

Finitely-Generated Projective Modules over the θ-Deformed 4-Sphere

We investigate the “θ-deformed spheres” ${C(S^{3}_{\theta})}$ and ${C(S^{4}_{\theta})}$ , where θ is any real number. We show that all finitely-generated projective modules over ${C(S^{3}_{\theta})}$ are free, and that ${C(S^{4}_{\theta})}$ has the cancellation property. We classify and construct all finitely-generated projective modules over ${C(S^{4}_{\theta})}$ up to isomorphism. An interesting feature is that if θ is irrational then there are nontrivial “rank-1” modules over ${C(S^{4}_{\theta})}$ . In that case, every finitely-generated projective module over ${C(S^{4}_{\theta})}$ is a sum of a rank-1 module and a free module. If θ is rational, the situation mirrors that for the commutative case θ = 0.     

Poisson Algebras of Block-Upper-Triangular Bilinear Forms and Braid Group Action

In this paper we study a quadratic Poisson algebra structure on the space of bilinear forms on ${\mathbb{C}^{N}}$ C N with the property that for any ${n, m \in \mathbb{N}}$ n , m ∈ N such that n m = N, the restriction of the Poisson algebra to the space of bilinear forms with a block-upper-triangular matrix composed from blocks of size ${m \times m}$ m × m is Poisson. We classify all central elements and characterise the Lie algebroid structure compatible with the Poisson algebra. We integrate this algebroid obtaining the corresponding groupoid of morphisms of block-upper-triangular bilinear forms. The groupoid elements automatically preserve the Poisson algebra. We then obtain the braid group action on the Poisson algebra as elementary generators within the groupoid. We discuss the affinisation and quantisation of this Poisson algebra, showing that in the case m = 1 the quantum affine algebra is the twisted q-Yangian for ${\mathfrak{o}_{n}}$ o n and for m = 2 is the twisted q-Yangian for ${(\mathfrak{sp}_{2n})}$ ( sp 2 n ) . We describe the quantum braid group action in these two examples and conjecture the form of this action for any m > 2. Finally, we give an R-matrix interpretation of our results and discuss the relation with Poisson–Lie groups.     

Pair production of exotic particles at\mathop p\limits^{( - )} p colliding beams

A maximally complete set of differential cross section has been obtained in Born approximation for pair production of exotic particles with various spinsJ=0,1/2, 1 and quantum numbers (colored and colorless) both inq \(\bar q\) - andgg-collisions. For vector boson processes we systematically use the connection of the unitary of their interaction with gauge invariance, factorization properties of nonabelian gauge amplitudes and the presence of kinematic zeros. Besides, the problem of admissibility of massless limit for these processes is being discussed. The, yields of exotic particle pairs at \(\mathop p\limits^{( - )} \) p colliding beams in TeV energy range have been calculated and limits for the accessible mass range have been found.     

New Integrable Models from the Gauge/YBE Correspondence

We introduce a class of new integrable lattice models labeled by a pair of positive integers N and r. The integrable model is obtained from the Gauge/YBE correspondence, which states the equivalence of the 4d $\mathcal {N} =1$ $S^{1}\times S^{3}/ \mathbb {Z} _{r}$ index of a large class of SU(N) quiver gauge theories with the partition function of 2d classical integrable spin models. The integrability of the model (star-star relation) is equivalent with the invariance of the index under the Seiberg duality. Our solution to the Yang-Baxter equation is one of the most general known in the literature, and reproduces a number of known integrable models. Our analysis identifies the Yang-Baxter equation with a particular duality (called the Yang-Baxter duality) between two 4d $\mathcal {N} =1$ supersymmetric quiver gauge theories. This suggests that the integrability goes beyond 4d lens indices and can be extended to the full physical equivalence among the IR fixed points.     

Neutral strange particle production in proton-proton collisions at\sqrt s = 63 GeV

The inclusive cross section for the production ofK _s ⁰ mesons, Λ and \(\bar \Lambda\) particles in proton-proton interactions at \(\sqrt s = 63\) GeV is presented. The produced particles have been detected in the full phase space. Behaviour of the longitudinal and transversal depandences of the cross sections are discussed. The total production cross sections for _s ⁰ mesons and Λ particles was determined to \(\sigma _{{\rm K}_S^0 } = (25.5 \pm 1.4)\) mb andσ _Λ =(7.8±1.2) mb respectively. A strong energy dependence of the production cross sections is observed.     

Form factor π0 → γ* + γ* at different photon virtualities

The π⁰ γγ vertex for virtual photons of squared masses q ₁ ² and q ₂ ² plays a vital rôle in several physical processes; for example for q ₁ ² < 0, q ₂ ² < 0, in the two-photon physics reaction e ⁺ e ^? → e ⁺ e ^?π⁰, and for q ₁ ² > 0, q ₂ ² > 0, in the annihilation process e ⁺ e ^? → π⁰ l ⁺l^?. It is also of interest because of its link to the axial anomaly. We suggest a new approach to this problem. We have obtained a closed analytic expression for the vertex in the limit in which at least one of ¦q ₁ ² ¦ and ¦q ₂ ² ¦ is large for arbitrary fixed values of the ratio q ₁ ² /q ₂ ² . We compare our results with those obtained previously by Brodsky and Lepage. It should be straightforward to test our predictions experimentally.