Rm Cos Research Articles

Revisiting the transition Ξcc++→Ξc(′)+ to understand the data from LHCb

The LHCb collaboration newly measured the decay rate of doubly charmed baryon $\Xi^{++}_{cc}\to\Xi^{'+}\pi^+$ and a ratio of its branching fraction with respect to that of the decay $\Xi^{++}_{cc}\to\Xi^{+}\pi^+$ is reported as $1.41\pm 0.17\pm 0.10$. This result conflicts with the theoretical predictions made by several groups. In our previous work, following the prescription given in early literature where the $us$ diquark in $\Xi^{+}_{c}$ is assumed to be a scalar whereas in $\Xi^{'+}_{c}$ is a vector i.e. the spin-flavor structure of $\Xi^{+}_{c}$ is $[us]_0 c$ and that of $\Xi^{'+}_{c}$ is $[us]_1 c$, we studied the case of $\Xi^{++}_{cc}\to\Xi^{(')+}$ with the light front quark model. Numerically we obtained $\Gamma(\Xi^{++}_{cc}\to\Xi^{'+}\pi^+)/\Gamma(\Xi^{++}_{cc}\to\Xi^{+}\pi^+)=0.56\pm0.18$ which is about half of the data. While abandoning the presupposition, we suppose the spin-flavor structure of $us$ in $\Xi^{+}_{c}$ may be a mixture of scalar and vector, namely the spin-flavor function of $\Xi^{+}_{c}$ could be ${\rm cos}\theta\, [us]_{0}[c]+{\rm sin}\theta\, [us]_{1}[c]$. An alternative combination $-{\rm sin}\theta\,[us]_{0}[c]+{\rm cos}\theta\, [us]_{1}[c]$ would correspond to $\Xi^{'+}_{c}$. Introducing the mixing mechanism the ratio $\Gamma(\Xi^{++}_{cc}\to\Xi^{'+}\pi^+)/\Gamma(\Xi^{++}_{cc}\to\Xi^{+}\pi^+)$ depends on the mixing angle $\theta$. With the mixing scenario, the theoretical prediction on the ratio between the transition rate of $\Xi^{+}_{cc}\to\Xi^{'+}_c$ and that of $\Xi^{+}_{cc}\to\Xi^{+}_c$ can coincide with the data as long as $\theta=16.27^\circ\pm2.30^\circ$ or $85.54^\circ\pm2.30^\circ$ is set. Definitely, more precise measurements on other decay portals of $\Xi^{+}_{cc}$ are badly needed for testing the mixing mechanism and further determining the mixing angle.

Cylinder–flat-surface contact mechanics during sliding

Using molecular dynamics we study the dependency of the contact mechanics on the sliding speed when an elastic block (cylinder) with a cos(q_{0}x) surface height profile is sliding in adhesive contact on a rigid flat substrate. The atoms on the block interact with the substrate atoms by Lennard-Jones potentials, and we consider both commensurate and (nearly) incommensurate contacts. For the incommensurate system the friction force fluctuates between positive and negative values, with an amplitude proportional to the sliding speed, but with the average close to zero. For the commensurate system the (time-averaged) friction force is much larger and nearly velocity independent. For both types of systems the width of the contact region is velocity independent even when, for the commensurate case, the frictional shear stress increases from zero (before sliding) to ≈0.1MPa during sliding. This frictional shear stress, and the elastic modulus used, are typical for polydimethylsiloxane rubber sliding on a glass surface, and we conclude that the reduction in the contact area observed in some experiments when increasing the tangential force must be due to effects not included in our model study, such as viscoelasticity or elastic nonlinearity.

Outer rotation curve of the Galaxy with VERA. IV. Astrometry of IRAS 01123+6430 and the possibility of cloud–cloud collision

Abstract As part our investigation into the Galactic rotation curve, we carried out Very Long Baseline Interferometry (VLBI) observations towards the star-forming region IRAS 01123+6430 using VLBI Exploration of Radio Astrometry (VERA) to measure its annual parallax and proper motion. The annual parallax was measured to be 0.151 ± 0.042 mas, which corresponds to a distance of $D = 6.61^{+2.55}_{-1.44}\:{\rm kpc}$, and the obtained proper motion components were $(\mu _\alpha {\rm cos}\delta ,\, \mu _\delta ) = (-1.44 \pm 0.15,\, -0.27 \pm 0.16)\:{\rm mas\:yr^{-1}}$ in equatorial coordinates. Assuming Galactic constants of $(R_0,\, \Theta _0) = (8.05 \pm 0.45\:{\rm kpc},\, 238 \pm 14\:{\rm km\:s^{-1}})$, the Galactocentric distance and rotation velocity were measured to be $(R,\, \Theta ) = (13.04 \pm 2.24\:{\rm kpc},\, 239 \pm 22\:{\rm km\:s^{-1}})$, which are consistent with a flat Galactic rotation curve. The newly estimated distance provides a more accurate bolometric luminosity of the central young stellar object, $L_{\rm Bol} = (3.11 \pm 2.86) \times 10^{3}\, L_{\odot }$, which corresponds to a spectral type of B1–B2. Analysis of ${}^{12}{\rm{CO}}$ (J = 1–0) survey data obtained with the Five College Radio Astronomical Observatory (FCRAO) 14 m telescope shows that the molecular cloud associated with IRAS 01123+6430 consists of arc-like and linear components, which matches well a structure predicted by numerical simulation of the cloud–cloud collision phenomenon. The coexistence of arc-like and linear components implies that the relative velocity of the two initial clouds was as slow as 3–$5\:{\rm km\, s^{-1}}$, which meets the expected criteria of massive star formation where the core mass is effectively increased in the presence of low relative velocity (∼3–5 km s−1), as suggested by Takahira, Tasker, and Habe (2014, ApJ, 792, 63).

Impact of magnetic-field fluctuations on measurements of the chiral magnetic effect in collisions of isobaric nuclei

We investigate the properties of electromagnetic fields in isobaric $_{44}^{96}\textrm{Ru}+\,_{44}^{96}\textrm{Ru}$ and $_{40}^{96}\textrm{Zr}+\,_{40}^{96}\textrm{Zr}$ collisions at $\sqrt{s}$ = 200 GeV by using a multiphase transport model, with special emphasis on the correlation between magnetic field direction and participant plane angle $\Psi_{2}$ (or spectator plane angle $\Psi_{2}^{\rm SP}$), i.e. $\langle{\rm cos}\ 2(\Psi_B - \Psi_{2})\rangle$ [or $\langle{\rm cos}\ 2(\Psi_B - \Psi_{2}^{\rm SP})\rangle$]. We confirm that the magnetic fields of $_{44}^{96}\textrm{Ru}+\,_{44}^{96}\textrm{Ru}$ collisions are stronger than those of $_{40}^{96}\textrm{Zr}+\,_{40}^{96}\textrm{Zr}$ collisions due to their larger proton fraction. We find that the deformation of nuclei has a non-negligible effect on $\langle{\rm cos}\ 2(\Psi_B - \Psi_{2})\rangle$ especially in peripheral events. Because the magnetic-field direction is more strongly correlated with $\Psi_{2}^{\rm SP}$ than with $\Psi_{2}$, the relative difference of the chiral magnetic effect observable with respect to $\Psi_{2}^{\rm SP}$ is expected to be able to reflect much cleaner information about the chiral magnetic effect with less influences of deformation.

Connection Probabilities for Conformal Loop Ensembles

The goal of the present paper is to explain, based on properties of the conformal loop ensembles {{rm CLE}_kappa} (both with simple and non-simple loops, i.e., for the whole range {kappa in (8/3, 8)}), how to derive the connection probabilities in domains with four marked boundary points for a conditioned version of {{rm CLE}_kappa} which can be interpreted as a {{rm CLE}_kappa} with wired/free/wired/free boundary conditions on four boundary arcs (the wired parts being viewed as portions of to-be-completed loops). In particular, in the case of a square, we prove that the probability that the two wired sides of the square hook up so that they create one single loop is equal to {1/(1 - 2 {rm cos} (4 pi / kappa ))} . Comparing this with the corresponding connection probabilities for discrete O(N) models. For instance, indicates that if a dilute O(N) model (respectively a critical FK(q)-percolation model on the square lattice) has a non-trivial conformally invariant scaling limit, then necessarily this scaling limit is {{rm CLE}_kappa} where {kappa} is the value in (8/3, 4] such that {-2 {rm cos} (4 pi / kappa )} is equal to N (resp. the value in [4,8) such that {-2 {rm cos} (4pi / kappa)} is equal to {sqrt q}). On the one hand, Our arguments and computations build on Dubédat’s SLE commutation relations (as developed and used by Dubédat, Zhan or Bauer-Bernard-Kytölä) and on the other hand, on the construction and properties of the conformal loop ensembles and their relation to Brownian loop-soups, restriction measures, and the Gaussian free field (as recently derived in works with Sheffield and with Qian).

Angular momentum evolution in dark matter haloes: a study of the Bolshoi and Millennium simulations

We use three different cosmological dark matter simulations to study how the orientation of the angular momentum vector (AM) in dark matter haloes evolve with time. We find that haloes in this kind of simulations are constantly affected by a spurious change of mass, which translates into an artificial change in the orientation of the AM. After removing the haloes affected by artificial mass change, we found that the change in the orientation of the AM vector is correlated with time. The change in its angle and direction (i.e. the angle subtended by the AM vector in two consecutive timesteps) that affect the AM vector has a dependence on the change of mass that affects a halo, the time elapsed in which the change of mass occurs and the halo mass. We create a Monte-Carlo simulation that reproduces the change of angle and direction of the AM vector. We reproduce the angular separation of the AM vector since a look back time of 8.5 Gyrs to today ( $\rm \alpha$) with an accuracy of approximately 0.05 in $\rm cos(\alpha)$. We are releasing this Monte-Carlo simulation together with this publication. We also create a Monte Carlo simulation that reproduces the change of the AM modulus. We find that haloes in denser environments display the most dramatic evolution in their AM direction, as well as haloes with a lower specific AM modulus. These relations could be used to improve the way we follow the AM vector in low-resolution simulations.

Magnetocaloric Effect and Magnetoresistance Due to Itinerant Electron Metamagnetic Transition in <inline-formula> <tex-math notation="TeX">${\rm Co}({\rm S}_{1-x}{\rm Se}_{x})_{2}$ </tex-math></inline-formula>

The ${\rm Co}({\rm S}_{1-x}{\rm Se}_{x})_{2}$ compounds with the cubic Pyrite structure show itinerant electron metamagnetism for $0.12\leq x$ . We studied the magnetocaloric effect and magnetoresistance (MR) of this system. It was found that a substantial magnetic entropy change was obtained for ${\rm Co}({\rm S}_{0.88}{\rm Se}_{0.12})_{2}$ , which has a paramagnetic ground state. We observed giant positive MR associated with the itinerant electron metamagnetic transition for ${\rm Co}({\rm S}_{1-x}{\rm Se}_{x})_{2}$ . The magnitude of the MR jump is independent of temperature and concentration for $0.13\leq x\leq 0.15$ . These results are discussed in terms of a simple band structure of ${\rm CoS}_{2}$ , in which high-spin polarization is realized in a ferromagnetic state.

Electroproduction of K+ Λ at JLab Hall-C

A Λ hypernuclear spectroscopic experiment, JLab E05-115 was performed at JLab Hall-C in 2009 by the (e, e′K+) reaction. Data of Λ hypernuclei with mass numbers from A = 7 to A = 52 were successfully taken, and the analyses are in progress. A polyethylene (CH2) target was used as a proton target to calibrate energy scales, and to study elementary process of the p(e, e′K+)Λ, Σ0 reaction. A preliminary differential cross section of K+Λ electro-production at low Q2 [~0.01 (GeV/c)2] and at small kaon angles \({({\rm cos} \theta_{\rm K}^{\rm CM} \sim 0.97)}\) is reported in the present article.

Non-resonant boundary value problems with singular $${\phi}$$ -Laplacian operators

In this paper, using Leray–Schauder degree arguments, critical point theory for lower semicontinuous functionals and the method of lower and upper solutions, we give existence results for periodic problems involving the relativistic operator \({u \mapsto \left(\frac{u^\prime}{\sqrt{1-u^\prime 2}}\right)^\prime+r(t)u}\) with \({\int_0^Tr dt\neq 0}\) . In particular we show that in this case we have non-resonance, that is periodic problem $$\left(\frac{u^\prime}{\sqrt{1-u^\prime 2}}\right)^\prime+r(t)u=e(t),\quad u(0)-u(T)=0=u^\prime(0)-u^\prime(T),$$ has at least one solution for any continuous function \({e : [0, T] \to \mathbb {R}}\) . Then, we consider Brillouin and Mathieu-Duffing type equations for which \({r(t) \equiv b_1 + b_2 {\rm cos} t {\rm and} b_1, b_2 \in \mathbb{R}}\) .

Closed form solution of a periodically forced logistic model

We give the exact closed form solution of the following ordinary differential equation: $$\left\{ \begin{array}{ll} \dot{x}(t)&=a\,x(t)-b\,x^{2}(t)+c\, {\rm cos} (\omega t)-h,\\ x(0)&=x_{0} \end{array}\right.$$ which is a modified logistic one, wherein x(t) is the population of a homogeneous species x at time t. Other than integrating the above nonlinear differential equation by means of Mathieu functions of the first kind, we also provide a condition of a couple of inequalities involving a, b, c, h and x 0 whose fulfillment is sufficient to ensure that a bounded solution for x(t) there exists.

On the Instability Intervals of the Mathieu–Hill Operator

Consider the Mathieu–Hill operator $${Ly=-y^{\prime\prime}+(2h {\rm cos}2x)y,\quad -\infty < x < +\infty,}$$ in \({L_{2}({\mathfrak{R}})}\) , where \({h \in {\mathfrak{R}}\setminus\{0\}}\) . We obtain the precise asymptotic formulas for the widths γk of the instability intervals of L. The formula states the isolated terms of arbitrary number in the asymptotics of the sequence γk for large k and verifies the results of Harrell (Am J Math suppl:139–150, 1981) and Avron and Simon (Ann Phys 134:76–84, 1981).

Quantum Phase Dynamics of Interaction between Photon Field and Magnetic System: Effects of Magnetic Quantum Tunnelling

We investigate the dynamics of probability distributions of an initially one-mode coherent field interacting with a four-state molecular system, which is a single magnet with a tunneling across an anisotropic barrier, using a numerically exact approach. The population for each state, the phase properties of and \(\langle{\rm cos}^2 \hat{\varphi}\rangle\), and \(\triangle {\rm cos}^2 \varphi(\equiv \langle {\rm cos}^2 \hat{\varphi}\rangle-{\langle {\rm cos} \hat{\varphi}\rangle}^2\)), the entropy are calculated for a model system. The model predicts that the molecule and field become asymptotically disentangled at half of the revival time, and that optical Schrodinger-cat and magnetic Schrodinger-cat states are generated.

On entire functions extremal for the ${\rm cos}\,\pi \rho $ theorem having prescribed asymptotic growth

On entire functions extremal for the ${\rm cos}\,\pi \rho $ theorem having prescribed asymptotic growth

Numerical Evaluation of Continued Fractions

Numerical Evaluation of Continued Fractions