Supremum of the Airy2 Process Minus a Parabola on a Half Line

Let $\mathcal {A}_{2}(t)$ be the Airy₂ process. We show that the random variable $$\sup_{t\leq\alpha} \bigl\{\mathcal {A}_2(t)-t^2 \bigr\}+\min\{0,\alpha \}^2 $$ has the same distribution as the one-point marginal of the Airy_2→1 process at time α. These marginals form a family of distributions crossing over from the GUE Tracy-Widom distribution F _GUE(x) for the Gaussian Unitary Ensemble of random matrices, to a rescaled version of the GOE Tracy-Widom distribution F _GOE(4^1/3 x) for the Gaussian Orthogonal Ensemble. Furthermore, we show that for every α the distribution has the same right tail decay $e^{-\frac{4}{3} x^{3/2} }$ .     

Radiative open charm decay of the Y(3940) , Z(3930) , X(4160) resonances

We determine the radiative decay amplitudes for the decay into D^* and $ \bar{{D}}$ $ \gamma$ , or D ^* _s and $ \bar{{D}}_{s}^{}$ $ \gamma$ of some of the charmonium-like states classified as X , Y , Z resonances, plus some other hidden charm states which are dynamically generated from the interaction of vector mesons with charm. The mass distributions as a function of the $ \bar{{D}}$ $ \gamma$ or $ \bar{{D}}_{s}^{}$ $ \gamma$ invariant mass show a peculiar behavior as a consequence of the D ^* $ \bar{{D}}^{*}_{}$ nature of these states. The experimental search of these magnitudes can shed light on the nature of these states.     

Hadroproduction of ψψ

We calculate the cross sections \(q\bar q \to \psi \psi \) andgg→ψψ in 0(α _s ⁴ ) QCD. We compare our results with measurements in πN interactions, and give predictions forpN and \(\bar p\) interactions. The cross section foryy→ψψ is computed.     

Gas-Like Cluster States in Finite Nuclei

Gas-like α cluster states are investigated in ¹⁶O with the use of 4α OCM (orthogonality condition model) and GEM (Gauss expansion method). α-particle condensed state is found slightly above the 4α threshold as the ${0_6^+}$ state. The candidates of the ${\alpha + {^{12}{\rm C}(0_2^+)}}$ rotational states are also found at a few megaelectron volt above the condensate. The ${0_6^+}$ state is shown to have an analogue structure to the Hoyle state ${({^{12}{\rm C}}(0_2^+))}$ and its relation with the α+ Hoyle-like rotational states is also discussed.     

Constant volume exponential solutions in Einstein–Gauss–Bonnet flat anisotropic cosmology with a perfect fluid

In this paper we investigate the constant volume exponential solutions (i.e. the solutions with the scale factors change exponentially over time so that the comoving volume remains the same) in the Einstein–Gauss–Bonnet gravity. We find conditions for these solutions to exist and show that they are compatible with any perfect fluid with the equation of state parameter \(\upomega <1/3\) if the matter density of the Universe exceeds some critical value. We write down some exact solutions which generalize ones found in our previous paper for models with a cosmological constant.     

Studying bi-partite entangled state representations via the integration over ket-bra operators in \mathfrak{Q}-ordering or \mathfrak{P}-ordering

For two particles＇ relative position and total momentum we have introduced the entangled state representation ｜μ〉, and its conjugate state｜ξ〉 In this work, for the first time; we study theln via the integration over ket bra operators in -ordering or -ordering, where Q-ordering means all Qs are to the left, of all Ps and -ordering means all Ps are to the left of all Qs. In this way we newly derive -ordered （or Q-ordered） expansion formulas of the two-mode squeezing operator which can show the squeezing effect on both the two-mode coordinate and momentum eigenstates. This tells that not only the integration over ket bra operators within normally ordered, but also within - ordered （or -ordered） are feasible and useful in developing quantum mechanical representation and transtbrlnation theory.     

Coupling constant in dispersive model

The average of the moments for event shapes in e ^?+? e??→hadrons within the context of next-to-leading order (NLO) perturbative QCD prediction in dispersive model is studied. Moments used in this article are $\langle {1-T}\rangle$ , $\langle \rho\rangle$ , $\langle {B_{\rm T}}\rangle$ and $\langle {B_{\rm W} }\rangle$ . We extract α _s, the coupling constant in perturbative theory and α ₀ in the non-perturbative theory using the dispersive model. By fitting the experimental data, the values of $\alpha_{\rm s} ({M_{\rm Z^0} })=0.1171\pm 0.00229$ and $\alpha_0 \left( {\mu_{\rm I} =2\,{\rm GeV}} \right)=0.5068\pm 0.0440$ are found. Our results are consistent with the above model. Our results are also consistent with those obtained from other experiments at different energies. All these features are explained in this paper.     

Theoretical Investigation into Production of Double-Λ Hypernuclei from Stopped Ξ − on 6Li

We have investigated theoretically a feasible nuclear reaction to produce light double-Λ hypernuclei by choosing a suitable target. In the reaction from stopped Ξ ^? on ⁶Li target light doubly-strange nuclei, ${^5_{\Lambda\Lambda}{\rm H}}$ and ${^6_{\Lambda\Lambda}{\rm He}}$ , are produced: we have calculated the formation ratio of ${^5_{\Lambda\Lambda}{\rm H}}$ to ${^6_{\Lambda\Lambda}{\rm He}}$ for Ξ ^? absorptions from 2S, 2P and 3D orbitals of Ξ ^?–⁶Li atom by assuming a d?α cluster model for ⁶Li. From this cluster model the d?α relative wave functions has a node due to Pauli exclusion among nucleons belonging to d and α clusters. Two kinds of d?α wave functions, namely 1s relative wave function with a phenomenological one-range Gaussian (ORG) potential and that of an orthogonality-condition model (OCM) are used. It is found that the probability of ${^5_{\Lambda\Lambda}{\rm H}}$ formation is larger than that of ${^6_{\Lambda\Lambda}{\rm He}}$ for all absorption orbitals: in the case of the major 3D absorption their ratio is 1.08 for ORG and 1.96 for OCM. The dominant low momentum component of the d?α relative wave function favors the ${^5_{\Lambda\Lambda}{\rm H}}$ formation with a low Q value compared to the ${^6_{\Lambda\Lambda}{\rm He}}$ formation with a high Q value. We have also calculated momentum distributions of emitted particles, d and n, displaying continuum spectra for single-Λ hypernuclei, ${^4_{\Lambda}{\rm H}}$ and ${^5_{\Lambda}{\rm He}}$ , and line spectra for the ${^5_{\Lambda\Lambda}{\rm H}}$ and ${^6_{\Lambda\Lambda}{\rm He}}$ nuclei. Thus, our present theoretical analysis would be a significant contribution to experiments in the strangeness ?2 sector of hypernuclear physics.     

Spherical top-hat collapse of a viscous unified dark fluid

In this paper, we test the spherical collapse of a viscous unified dark fluid (VUDF) which has constant adiabatic sound speed and show the nonlinear collapse for VUDF, baryons, and dark matter, which are important in forming the large-scale structure of our Universe. By varying the values of the model parameters $\alpha $ and $\zeta _{0}$ , we discuss their effects on the nonlinear collapse of the VUDF model, and we compare its result to the $\Lambda $ CDM model. The results of the analysis show that, within the spherical top-hat collapse framework, larger values of $\alpha $ and smaller values of $\zeta _{0}$ make the structure formation earlier and faster, and the other collapse curves are almost distinguished with the curve of $\Lambda $ CDM model if the bulk viscosity coefficient $\zeta _{0}$ is less than $10^{-3}$ .     

Atomic number dependence ofL-shell vacancy rearrangement probabilities onKα X-ray satellites induced by 6 MeV/amu N4+ impacts

L-shell vacancy rearrangement probabilities, \(\tilde f\) 's, prior toKα X-ray emission andL-shell widths were determined from intensity distributions of theKα satellite structures. Characteristic X-rays were induced by 6 MeV/amu N⁴⁺ impacts on atoms with various chemical compositions and with different bonding structures, whose atomic numbers range from 9 to 30. In the region where target atomic numberZ ₂≦12, the experimentally deduced \(\tilde f\) values exceed theoretical ones to large extent. On the other hand, the theoretical \(\tilde f\) values give upper limits to the experimental ones in the regionZ ₂≧13. No significant chemical effect could be found in \(\tilde f\) values for all the atoms investigated except forF.     

Consequences of f(R) theories of gravity on gravitational leptogenesis

$f(R)$ f ( R ) -theories of gravity are reviewed in the framework of the matter-antimatter asymmetry in the Universe. The asymmetry is generated by the gravitational coupling of heavy (Majorana) neutrinos with the Ricci scalar curvature. In order that the mechanism works, a time varying non-zero Ricci curvature is necessary. The latter is provided by $f(R)$ f ( R ) cosmology, whose Lagrangian density is of the form $\mathcal{L}(R)\sim f(R)$ L ( R ) ～ f ( R ) , with $f(R)\sim R+\alpha R^n$ f ( R ) ～ R + α R n .     

Direct measurements of (p, \gamma) cross-sections at astrophysical energies using radioactive beams and the Daresbury Recoil Separator

There are a number of astrophysical environments in which the path of nucleosynthesis proceeds through proton-rich nuclei. These nuclei have traditionally not been available as beams, and thus proton-capture reactions on these nuclei could only be studied indirectly. At the Holifield Radioactive Ion Beam Facility (HRIBF), some of the first direct measurements of (p, $ \gamma$ ) cross-sections on radioactive beams have been made. The Daresbury Recoil Separator (DRS) has been used to separate the recoils of interest from the unreacted primary beam and identify them in an isobutane-filled ionization counter. First data from ¹⁷F (p, $ \gamma$ ¹⁸Ne and ⁷Be (p, $ \gamma$ ⁸B measurements are presented.     

On the production of \pi^{+}_{} \pi^{+}_{} pairs in pp collisions at 0.8 GeV

Data accumulated recently for the exclusive measurement of the pp $ \rightarrow$ pp $ \pi^{+}_{}$ $ \pi^{-}_{}$ reaction at a beam energy of 0.793GeV using the COSY-TOF spectrometer have been analyzed with respect to possible events from the pp $ \rightarrow$ nn $ \pi^{+}_{}$ $ \pi^{+}_{}$ reaction channel. The latter is expected to be the only $ \pi$ $ \pi$ production channel, which contains no major contributions from resonance excitation close to threshold and hence should be a good testing ground for chiral dynamics in the $ \pi$ $ \pi$ production process. No single event has been found, which meets all conditions for being a candidate for the pp $ \rightarrow$ nn $ \pi^{+}_{}$ $ \pi^{+}_{}$ reaction. This gives an upper limit for the cross-section of 0.16μb (90% C.L.), which is more than an order of magnitude smaller than the cross-sections of the other two-pion production channels at the same incident energy.     

Dynamically Generated Resonances from Two Vectors in the Charm Sector and their Decays

In this talk we study dynamically generated resonances from two-vector mesons within the hidden gauge formalism in a coupled channel unitary approach. We focus on the sectors with charm and/or strangeness and double charm, being some of them flavor exotic. Concretely, by looking for poles in the complex plane, we get three poles in the T-matrix around 2,460, 2,640 and 2,572 MeV that we identify with the ${D^*_2(2,460), D^*(2,640)}$ and ${D^*_{s2}(2,573)}$ , coupling strongly to D*ρ (the first two) and D*K* respectively. In addition, we obtain resonances in other exotic sectors such as (charm = 1; strangeness = ?1), (charm = 2; strangeness = 0, 1). This ’flavor-exotic’ states are interpreted as ${D^*\bar{K}^*, D^*D^*}$ and ${D^*_sD^*}$ molecular states and have not been observed yet. The observation of these peculiar states is a challenge for the experimentalist.     

Optimal Paths for Symmetric Actions in the Unitary Group

Given a positive and unitarily invariant Lagrangian ${\mathcal{L}}$ defined in the algebra of matrices, and a fixed time interval ${[0,t_0]\subset\mathbb R}$ , we study the action defined in the Lie group of ${n\times n}$ unitary matrices ${\mathcal{U}(n)}$ by $$\mathcal{S}(\alpha)=\int_0^{t_0} \mathcal{L}(\dot\alpha(t))\,dt, $$ where ${\alpha:[0,t_0]\to\mathcal{U}(n)}$ is a rectifiable curve. We prove that the one-parameter subgroups of ${\mathcal{U}(n)}$ are the optimal paths, provided the spectrum of the exponent is bounded by π. Moreover, if ${\mathcal{L}}$ is strictly convex, we prove that one-parameter subgroups are the unique optimal curves joining given endpoints. Finally, we also study the connection of these results with unitarily invariant metrics in ${\mathcal{U}(n)}$ as well as angular metrics in the Grassmann manifold.     

Pseudo-fermions in an Electronic Loss-Gain Circuit

In some recent papers a loss-gain electronic circuit has been introduced and analyzed within the context of PT-quantum mechanics. In this paper we show that this circuit can be analyzed using the formalism of the so-called pseudo-fermions. In particular we discuss the time behavior of the circuit, and we construct two biorthogonal bases associated to the Liouville matrix $\mathcal {L}$ used in the treatment of the dynamics. We relate these bases to $\mathcal {L}$ and $\mathcal {L}^{\dagger}$ , and we also show that a self-adjoint Liouville-like operator could be introduced in the game. Finally, we describe the time evolution of the circuit in an Heisenberg-like representation, driven by a non self-adjoint Hamiltonian.     

Perturbative QCD coherence ine + e − annihilation

We study the pattern of soft parton radiation in the hard annihilation processes \(e^ + e^ - \to q\bar q\gamma \) and \(e^ + e^ - \to q\bar qg\) by explicit evaluation of the cross sections for \(e^ + e^ - \to q\bar q\gamma g\) and \(e^ + e^ - \to q\bar qgg + q\bar qq\bar q\) taken care of correct normalization. We find the coherence effects as observed experimentally and discuss why these effects are not present in the usual models based onO(α _s ² ) perturbation theory with subsequent independent fragmentation.     

Analysis of the {1\over2}^{\pm} flavor antitriplet heavy baryon states with QCD sum rules

In this article, we study the masses and pole residues of the ${1\over2}^{\pm}$ flavor antitriplet heavy baryon states ( $\varLambda _{c}^{+}$ , $\varXi _{c}^{+},\varXi _{c}^{0})$ and ( $\varLambda _{b}^{0}$ , $\varXi _{b}^{0},\varXi _{b}^{-})$ by subtracting the contributions from the corresponding ${1\over2}^{\mp}$ heavy baryon states with the QCD sum rules, and observe that the masses are in good agreement with the experimental data and make reasonable predictions for the unobserved ${1\over2}^{-}$ bottom baryon states. Once reasonable values of the pole residues λ _Λ and λ _Ξ are obtained, we can take them as basic parameters to study the relevant hadronic processes with the QCD sum rules.