Reaction pp \rightarrow pp \pi \pi \pi as a background for hadronic decays of the \eta^{{\prime}}_{} meson

Isospin violating hadronic decays of the $ \eta$ and $ \eta{^\prime}$ mesons into 3 $ \pi$ mesons are driven by a term in the QCD Lagrangian proportional to the mass difference of the d and u quarks. The source giving large yield of the mesons for such decay studies are pp interactions close to the respective kinematical thresholds. The most important physics background for $ \eta$ , $ \eta{^\prime}$ $ \rightarrow$ $ \pi$ $ \pi$ $ \pi$ is coming from direct three-pion production reactions. In case of the $ \eta$ meson the background for the decays is relatively low ( $ \approx$ 10% . The purpose of this article is to provide an estimate of the direct pion production background for the $ \eta{^\prime}$ $ \rightarrow$ 3 $ \pi$ decays. Using the inclusive data from the COSY-11 experiment we have extracted the differential cross-section for the pp $ \rightarrow$ pp -multipion production reactions with the invariant mass of the pions equal to the $ \eta{^\prime}$ meson mass and estimated an upper limit for the signal to background ratio for studies of the $ \eta{^\prime}$ $ \rightarrow$ $ \pi^{+}_{}$ $ \pi^{-}_{}$ $ \pi^{0}_{}$ decay.     

Synthesis and anti-cancer activity of a glycosyl library of \varvec{N}-acetylglucosamine-bearing oleanolic acid

N-Acetylglucosamine-bearing triterpenoid saponins (GNTS) were reported to be a unique type of saponins with potent anti-tumor activity. In order to study the structure–activity relationship of GNTS, 24 oleanolic acid saponins with ( $1 \rightarrow 3$ )-linked, ( $1\rightarrow 4$ )-linked, ( $1\rightarrow 6$ )-linked $N$ -acetylglucosamine oligosaccharide residues were synthesized in a combinatorial and concise method. The cytotoxicity of these compounds toward the leukemia cell line HL-60 and the colorectal cancer cell line HT-29 could not be improved. Half maximal inhibition below $10\,\upmu \hbox {M}$ was achieved in one single case. The study revealed that the activity decreased following the order of $3^{\prime }>4^{\prime }>6^{\prime }$ glycosyl modifications. GNTS that incorporated (d/l)-xylose and l-arabinose at positions $3^{\prime }$ and $4^{\prime }$ were more potent than those bearing other sugars.     

Influence of temperature on the electric,dielectric and AC conductivity properties of nano-crystalline zinc substituted cobalt ferrite synthesized by solution combustion technique

Cobalt–zinc nanoferrites with formulae Co $_{1-x}$ Zn $_{x}$ Fe $_{2}$ O $_{4}$ , where x = 0.0, 0.1, 0.2 and 0.3, have been synthesized by solution combustion technique. The variation of DC resistivity with temperature shows the semiconducting behavior of all nanoferrites. The dielectric properties such as dielectric constant ( $\varepsilon $ ’) and dielectric loss tangent (tan $\delta )$ are investigated as a function of temperature and frequency. Dielectric constant and loss tangent are found to be increasing with an increase in temperature while with an increase in frequency both, $\varepsilon $ ’ and tan $\delta $ , are found to be decreasing. The dielectric properties have been explained on the basis of space charge polarization according to Maxwell–Wagner’s two-layer model and the hopping of charge between Fe $^{2+}$ and Fe $^{3+}$ . Further, a very high value of dielectric constant and a low value of tan $\delta $ are the prime achievements of the present work. The AC electrical conductivity ( $\sigma _\mathrm{AC})$ is studied as a function of temperature as well as frequency and $\sigma _\mathrm{AC}$ is observed to be increasing with the increase in temperature and frequency.     

Near Threshold Photoproduction of {K\Sigma} in Four Isospin Channels

Photoproduction of ${K\Sigma}$ on the nucleon in four isospin channels has been investigated near their production thresholds by means of an isobar model. It is shown that in the proton channels ( ${K^+\Sigma^0}$ and ${K^0\Sigma^+}$ channels) the model can nicely reproduce experimental data. Due to the uncertainties in the neutron helicity amplitudes our predictions imply some uncertainties in the observables of the neutron channels ( ${K^+\Sigma^-}$ and ${K^0\Sigma^0}$ channels).     

Large N approach to Kaon decays and mixing 28 years later: \Delta I=1/2 rule, \hat{B}_K,and \Delta M_K

We review and update our results for $K\rightarrow \pi \pi $ decays and $K^0$ – $\bar{K}^0$ mixing obtained by us in the 1980s within an analytic approximate approach based on the dual representation of QCD as a theory of weakly interacting mesons for large $N$ , where $N$ is the number of colors. In our analytic approach the Standard Model dynamics behind the enhancement of $\hbox {Re}A_0$ and suppression of $\hbox {Re}A_2$ , the so-called $\Delta I=1/2$ rule for $K\rightarrow \pi \pi $ decays, has a simple structure: the usual octet enhancement through the long but slow quark–gluon renormalization group evolution down to the scales $\mathcal{O}(1\, {\hbox { GeV}})$ is continued as a short but fast meson evolution down to zero momentum scales at which the factorization of hadronic matrix elements is at work. The inclusion of lowest-lying vector meson contributions in addition to the pseudoscalar ones and of Wilson coefficients in a momentum scheme improves significantly the matching between quark–gluon and meson evolutions. In particular, the anomalous dimension matrix governing the meson evolution exhibits the structure of the known anomalous dimension matrix in the quark–gluon evolution. While this physical picture did not yet emerge from lattice simulations, the recent results on $\hbox {Re}A_2$ and $\hbox {Re}A_0$ from the RBC-UKQCD collaboration give support for its correctness. In particular, the signs of the two main contractions found numerically by these authors follow uniquely from our analytic approach. Though the current–current operators dominate the $\Delta I=1/2$ rule, working with matching scales $\mathcal{O}(1 \, {\hbox { GeV}})$ we find that the presence of QCD-penguin operator $Q_6$ is required to obtain satisfactory result for $\hbox {Re}A_0$ . At NLO in $1/N$ we obtain $R=\hbox {Re}A_0/\hbox {Re}A_2= 16.0\pm 1.5$ which amounts to an order of magnitude enhancement over the strict large $N$ limit value $\sqrt{2}$ . We also update our results for the parameter $\hat{B}_K$ , finding $\hat{B}_K=0.73\pm 0.02$ . The smallness of $1/N$ corrections to the large $N$ value $\hat{B}_K=3/4$ results within our approach from an approximate cancelation between pseudoscalar and vector meson one-loop contributions. We also summarize the status of $\Delta M_K$ in this approach.     

Asymptotic Behavior for a Version of Directed Percolation on the Triangular Lattice

We consider a version of directed bond percolation on the triangular lattice such that vertical edges are directed upward with probability $y$ , diagonal edges are directed from lower-left to upper-right or lower-right to upper-left with probability $d$ , and horizontal edges are directed rightward with probabilities $x$ and one in alternate rows. Let $\tau (M,N)$ be the probability that there is at least one connected-directed path of occupied edges from $(0,0)$ to $(M,N)$ . For each $x \in [0,1]$ , $y \in [0,1)$ , $d \in [0,1)$ but $(1-y)(1-d) \ne 1$ and aspect ratio $\alpha =M/N$ fixed for the triangular lattice with diagonal edges from lower-left to upper-right, we show that there is an $\alpha _c = (d-y-dy)/[2(d+y-dy)] + [1-(1-d)^2(1-y)^2x]/[2(d+y-dy)^2]$ such that as $N \rightarrow \infty $ , $\tau (M,N)$ is $1$ , $0$ and $1/2$ for $\alpha > \alpha _c$ , $\alpha < \alpha _c$ and $\alpha =\alpha _c$ , respectively. A corresponding result is obtained for the triangular lattice with diagonal edges from lower-right to upper-left. We also investigate the rate of convergence of $\tau (M,N)$ and the asymptotic behavior of $\tau (M_N^-,N)$ and $\tau (M_N^+ ,N)$ where $M_N^-/N\uparrow \alpha _c$ and $M_N^+/N\downarrow \alpha _c$ as $N\uparrow \infty $ .     

Analysis of the {3\over 2}^{+} heavy and doubly heavy baryon states with QCD sum rules

In this article, we study the ${3\over 2}^{+}$ heavy and doubly heavy baryon states $\varXi^{*}_{cc}$ , $\varOmega^{*}_{cc}$ , $\varXi^{*}_{bb}$ , $\varOmega^{*}_{bb}$ , $\varSigma_{c}^{*}$ , $\varXi_{c}^{*}$ , $\varOmega_{c}^{*}$ , $\varSigma_{b}^{*}$ , $\varXi_{b}^{*}$ and $\varOmega_{b}^{*}$ by subtracting the contributions from the corresponding ${3\over 2}^{-}$ heavy and doubly heavy baryon states with the QCD sum rules, and we make reasonable predictions for their masses.     

Charmonium rescattering effects in \psi(2S) \rightarrow \gamma \eta_{c}^{} decay

Charmonium rescattering effects in the M1 transition of $ \psi$ (2S) $ \rightarrow$ $ \gamma$ $ \eta_{c}^{}$ are investigated by modeling a $ \chi_{{cJ}}^{}$ or J/ $ \psi$ rescattering into a $ \eta_{c}^{}$ final state. The absorptive and dispersive part of the transition amplitudes for the rescattering loops of $ \eta$ $ \psi$ ( $ \gamma^{{\ast}}_{}$ ) and $ \gamma$ $ \chi$ ( $ \psi$ ) are separately evaluated. The numerical results show that the contribution from the $ \gamma$ $ \chi$ ( $ \psi$ ) rescattering process is negligible. Compared with the virtual D $ \bar{{D}}$ (D ^*) rescattering processes, the $ \eta$ $ \psi$ ( $ \gamma^{{\ast}}_{}$ ) process may be regarded as the next-leading order of the hadronic loop mechanism, which only offers the partial decay width of ～ 0.045 keV to the $ \psi$ (2S) $ \rightarrow$ $ \gamma$ $ \eta_{c}^{}$ .     

Positivity constraints on the low-energy constants of the chiral pion–nucleon Lagrangian

Positivity constraints on the pion–nucleon scattering amplitude are derived in this article with the help of general S-matrix arguments, such as analyticity, crossing symmetry, and unitarity, in the upper part of the Mandelstam triangle, $\mathcal{R}$ . Scanning inside the region $\mathcal{R}$ , the most stringent bounds on the chiral low-energy constants of the pion–nucleon Lagrangian are determined. When just considering the central values of the fit results from covariant baryon chiral perturbation theory using the extended-on-mass-shell scheme, it is found that these bounds are well respected numerically both at the $O(p^3)$ and the $O(p^4)$ level. Nevertheless, when taking the errors into account, only the $O(p^4)$ bounds are obeyed in the full error interval, while the bounds on the $O(p^3)$ fits are slightly violated. If one disregards the loop contributions, the bounds always fail in certain regions of $\mathcal{R}$ . Thus, at a given chiral order these terms are not numerically negligible and one needs to consider all possible contributions, i.e., both tree-level and loop diagrams.We have provided the constraints for special points in $\mathcal {R}$ where the bounds are nearly optimal in terms of just a few chiral couplings, which can easily be implemented and employed to constrain future analyses. Some issues concerned with calculations with an explicit $\Delta $ resonance are also discussed.     

Higher harmonics of azimuthal anisotropy in relativistic heavy-ion collisions in HYDJET++ model

The LHC data on azimuthal anisotropy harmonics from PbPb collisions at center-of-mass energy 2.76 TeV per nucleon pair are analyzed and interpreted in the framework of the HYDJET++ model. The cross-talk of elliptic $v_2$ and triangular $v_3$ flow in the model generates both even and odd harmonics of higher order. Comparison with the experimental data shows that this mechanism is able to reproduce the $p_\mathrm{T}$ and centrality dependencies of quadrangular flow $v_4$ , and also the basic trends for pentagonal $v_5$ and hexagonal $v_6$ flows.     

On Gravitational Effects in the Schrödinger Equation

The Schrödinger  equation for a particle of rest mass $m$ and electrical charge $ne$ interacting with a four-vector potential $A_i$ can be derived as the non-relativistic limit of the Klein–Gordon  equation $\left( \Box '+m^2\right) \varPsi =0$ for the wave function $\varPsi $ , where $\Box '=\eta ^{jk}\partial '_j\partial '_k$ and $\partial '_j=\partial _j -\mathrm {i}n e A_j$ , or equivalently from the one-dimensional  action $S_1=-\int m ds +\int neA_i dx^i$ for the corresponding point particle in the semi-classical approximation $\varPsi \sim \exp {(\mathrm {i}S_1)}$ , both methods yielding the equation $\mathrm {i}\partial _0\varPsi \approx \left( \frac{1}{2m}\eta ^{\alpha \beta }\partial '_{\alpha }\partial '_{\beta } + m + n e\phi \right) \varPsi $ in Minkowski  space–time  , where $\alpha ,\beta =1,2,3$ and $\phi =-A_0$ . We show that these two methods generally yield equations  that differ in a curved background  space–time   $g_{ij}$ , although they coincide when $g_{0\alpha }=0$ if $m$ is replaced by the effective mass $\mathcal{M}\equiv \sqrt{m^2-\xi R}$ in both the Klein–Gordon  action $S$ and $S_1$ , allowing for non-minimal coupling to the gravitational  field, where $R$ is the Ricci scalar and $\xi $ is a constant. In this case $\mathrm {i}\partial _0\varPsi \approx \left( \frac{1}{2\mathcal{M}'} g^{\alpha \beta }\partial '_{\alpha }\partial '_{\beta } + \mathcal{M}\phi ^{(\mathrm g)} + n e\phi \right) \varPsi $ , where $\phi ^{(\mathrm g)} =\sqrt{g_{00}}$ and $\mathcal{M}'=\mathcal{M}/\phi ^{(\mathrm g)} $ , the correctness of the gravitational  contribution to the potential having been verified to linear order $m\phi ^{(\mathrm g)} $ in the thermal-neutron beam interferometry experiment due to Colella et al. Setting $n=2$ and regarding $\varPsi $ as the quasi-particle wave function, or order parameter, we obtain the generalization of the fundamental macroscopic Ginzburg-Landau equation of superconductivity to curved space–time. Conservation of probability and electrical current requires both electromagnetic gauge and space–time  coordinate conditions to be imposed, which exemplifies the gravito-electromagnetic analogy, particularly in the stationary case, when div ${{\varvec{A}}}=\hbox {div}{{\varvec{A}}}^{(\mathrm g)}=0$ , where ${{\varvec{A}}}^{\alpha }=-A^{\alpha }$ and ${{\varvec{A}}}^{(\mathrm g)\alpha }=-\phi ^{(\mathrm g)}g^{0\alpha }$ . The quantum-cosmological Schrödinger  (Wheeler–DeWitt) equation is also discussed in the $\mathcal{D}$ -dimensional  mini-superspace idealization, with particular regard to the vacuum potential $\mathcal V$ and the characteristics of the ground state, assuming a gravitational  Lagrangian   $L_\mathcal{D}$ which contains higher-derivative  terms up to order $\mathcal{R}^4$ . For the heterotic superstring theory  , $L_\mathcal{D}$ consists of an infinite series in $\alpha '\mathcal{R}$ , where $\alpha '$ is the Regge slope parameter, and in the perturbative approximation $\alpha '|\mathcal{R}| \ll 1$ , $\mathcal V$ is positive semi-definite for $\mathcal{D} \ge 4$ . The maximally symmetric ground state satisfying the field equations is Minkowski  space for $3\le {\mathcal {D}}\le 7$ and anti-de Sitter  space for $8 \le \mathcal {D} \le 10$ .     

Analysis of the vertexes \Xi_{Q}^{*}′QV , \Sigma_{Q}^{*} \Sigma_{Q}^{}V and radiative decays \Xi_{Q}^{*} \rightarrow ′Q \gamma , \Sigma_{Q}^{*} \rightarrow \Sigma_{Q}^{} \gamma

In this article, we study the vertexes $ \Xi_{Q}^{*}$ ′_Q V and $ \Sigma_{Q}^{*}$ $ \Sigma_{Q}^{}$ V with the light-cone QCD sum rules, then assume the vector meson dominance of the intermediate $ \phi$ (1020) , $ \rho$ (770) and $ \omega$ (782) , and calculate the radiative decays $ \Xi_{Q}^{*}$ $ \rightarrow$ ′_Q $ \gamma$ and $ \Sigma_{Q}^{*}$ $ \rightarrow$ $ \Sigma_{Q}^{}$ $ \gamma$ .     

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 $10^{-3}$ .     

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 Alpha Decay Chains of Superheavy Nuclei and Magic Number Beyond Z = 82 and N = 126

We study various $\alpha $ -decay chains on the basis of the preformed cluster decay model. Our work targets the superheavy elements, which are expected to show extra stability at shell closure. Our computations identify the following combinations of proton and neutron numbers as the most stable nuclei: $Z=112$ , $N=161, 163$ ; $Z=114$ , $N=171, 178, 179$ ; and $Z=124$ , $N=194$ . We also investigate the alternative of heavy cluster emissions in the decay chain of ³⁰¹120, instead of $\alpha $ decay. Our study of cluster radioactivity shows that the half-life for ¹⁰Be decay in ²⁸⁹114 is larger, indicating enhanced stability at $Z=114$ , $N=175$ . Similar calculations concerning the emission of $\ ^{14}{\rm C}$ and $\ ^{34}{\rm Si}$ from ³⁰¹120 find the more stable combinations $Z=114$ , $N=173$ , and $Z=106$ , $N=161$ , respectively. From the same parent, ³⁰¹120, the emission of a $\ ^{49-51}{\rm Ca}$ cluster yielding a $Z=100$ , $N=152$ daughter is the most probable.     

Identification of \mathrm{\ensuremath J^{\pi} = 19/2^+} and \mathrm{\ensuremath 23/2^+} isomeric states in 127Sb

The nucleus $\ensuremath {\rm ^{127}Sb}$ , which is on the neutron-rich periphery of the $\ensuremath \beta$ -stability region, has been populated in complex nuclear reactions involving deep-inelastic and fusion-fission processes with $\ensuremath {\rm {}^{136}Xe}$ beams incident on thick targets. The previously known isomer at 2325 keV in $\ensuremath {\rm {}^{127}Sb}$ has been assigned spin and parity $\ensuremath 23/2^+$ , based on the measured $\ensuremath \gamma$ - $\ensuremath \gamma$ angular correlations and total internal conversion coefficients. The half-life has been determined to be 234(12) ns, somewhat longer than the value reported previously. The 2194 keV state has been assigned $\ensuremath J^{\pi} = 19/2^+$ and identified as an isomer with $\ensuremath T_{1/2} = 14(1) {\rm ns}$ , decaying by two $\ensuremath E2$ branches. The observed level energies and transition strengths are compared with the predictions of a shell model calculation. Two $\ensuremath 15/2^+$ states have been identified close in energy, and their properties are discussed in terms of mixing between vibrational and three-quasiparticle configurations.     

An Averaging Theorem for FPU in the Thermodynamic Limit

Consider an FPU chain composed of $N\gg 1$ particles, and endow the phase space with the Gibbs measure corresponding to a small temperature $\beta ^{-1}$ . Given a fixed $K$ , we construct $K$ packets of normal modes whose energies are adiabatic invariants (i.e., are approximately constant for times of order $\beta ^{1-a}$ , $a>0$ ) for initial data in a set of large measure. Furthermore, the time autocorrelation function of the energy of each packet does not decay significantly for times of order $\beta $ . The restrictions on the shape of the packets are very mild. All estimates are uniform in the number $N$ of particles and thus hold in the thermodynamic limit $N\rightarrow \infty $ , $\beta >0$ .     

Structure of neutron-rich nuclei around the N = 126 closed shell; the yrast structure of 205Au126 up to spin-parity I^{\pi} = (19/2+)

Heavy neutron-rich nuclei have been populated through the relativistic fragmentation of a $\ensuremath ^{208}_{\ 82}{\rm Pb}$ beam at $\ensuremath E/A = 1$ GeV on a $\ensuremath 2.5 {\rm g/cm^2}$ thick Be target. The synthesised nuclei were selected and identified in-flight using the fragment separator at GSI. Approximately 300 ns after production, the selected nuclei were implanted in an $\ensuremath \sim 8$ mm thick perspex stopper, positioned at the centre of the RISING $\ensuremath \gamma$ -ray detector spectrometer array. A previously unreported isomer with a half-life $\ensuremath T_{1/2} = 163(5)$ ns has been observed in the N = 126 closed-shell nucleus $\ensuremath ^{205}_{\ 79}{\rm Au}$ . Through $ \gamma$ -ray singles and $ \gamma$ - $ \gamma$ coincidence analysis a level scheme was established. The comparison with a shell model calculation tentatively identifies the spin-parity of the excited states, including the isomer itself, which is found to be $\ensuremath I^{\pi} = (19/2^+)$ .     

Galton–Watson Trees with Vanishing Martingale Limit

We show that an infinite Galton–Watson tree, conditioned on its martingale limit being smaller than  $\varepsilon $ , agrees up to generation $K$ with a regular $\mu $ -ary tree, where $\mu $ is the essential minimum of the offspring distribution and the random variable $K$ is strongly concentrated near an explicit deterministic function growing like a multiple of $\log (1/\varepsilon )$ . More precisely, we show that if $\mu \ge 2$ then with high probability, as $\varepsilon \downarrow 0$ , $K$ takes exactly one or two values. This shows in particular that the conditioned trees converge to the regular $\mu $ -ary tree, providing an example of entropic repulsion where the limit has vanishing entropy. Our proofs are based on recent results on the left tail behaviour of the martingale limit obtained by Fleischmann and Wachtel [11].     

A brief review of antimatter production

In this article, we present a brief review of the discoveries of kinds of antimatter particles, including positron ( $ \bar e $ ), antiproton ( $ \bar p $ ), antideuteron ( $ \bar d $ ) and antihelium-3 ( $ ^3 \overline {He} $ ). Special emphasis is put on the discovery of the antihypertriton( $ \frac{3} {\Lambda }\overline H $ ) and antihelium-4 nucleus ( $ ^4 \overline {He} $ , or $ \bar \alpha $ ) which were reported by the RHIC-STAR experiment very recently. In addition, brief discussions about the effort to search for antinuclei in cosmic rays and study of the longtime confinement of the simplest antimatter atom, antihydrogen are also given. Moreover, the production mechanism of anti-light nuclei is introduced.