Lepton polarization asymmetries in rare semi-tauonic $$ b \rightarrow s $$ exclusive decays at FCC- ee

We consider measurements of exclusive rare semi-tauonic b-hadron decays, mediated by the \(b \rightarrow s \tau ^+ \tau ^-\) transition, at a future high-energy circular electron–positron collider (FCC-ee). We argue that the high boosts of b-hadrons originating from on-shell Z boson decays allow for a full reconstruction of the decay kinematics in hadronic \(\tau \) decay modes (up to discrete ambiguities). This, together with the potentially large statistics of \(Z\rightarrow b\bar{b}\), opens the door for the experimental determination of \(\tau \) polarizations in these rare b-hadron decays. In the light of the current experimental situation on lepton flavor universality in rare semileptonic B decays, we discuss the complementary short-distance physics information carried by the \(\tau \) polarizations and suggest suitable theoretically clean observables in the form of single- and double-\(\tau \) polarization asymmetries.     

The phenomenon of tristable stochastic resonance driven by $$\alpha $$-noise

In this paper, the tristable stochastic resonance (SR) phenomenon induced by \(\alpha \)-stable noise is analysed. The mechanism for realizing resonance is explored based on research concerning the potential function and resonant output of a system. The rules for resonance system parameters q, p, skewness parameter r and intensity amplification factor Q of \(\alpha \)-stable noise to act on the resonant output are explored under different values of stability index \(\alpha \) and asymmetric skewness \(\beta \) of \(\alpha \)-stable noise. The results will contribute to a reasonable selection of parameter-induced tristable SR system parameters under \(\alpha \)-stable noise, and lay the foundation for a practical engineering application of weak signal detection based on the SR.     

Synthesis and evaluation of bile acid amides of $$\alpha $$-cyanostilbenes as anticancer agents

A series of amino-substituted \(\alpha \)-cyanostilbene derivatives and their bile acid (cholic and deoxycholic acid) amides were designed and synthesized. A comparative study on the anticancer and antibacterial activity evaluation on the synthesized analogs was carried against the human osteosarcoma (HOS) cancer cell line, and two gram ?ve (E. coli and S. typhi) and two gram \(+\)ve (B. subtilis and S. aureus) bacterial strains. All the cholic acid \(\alpha \)-cyanostilbene amides showed an \(\hbox {IC}_{50}\) in the range 2–13 \(\upmu \hbox {M}\) against human osteosarcoma cells (HOS) with the most active analog (6g) possessing an \(\hbox {IC}_{50}\) of \(2\,\upmu \hbox {M}\). One of the amino-substituted \(\alpha \)-cyanostilbene, 4e, was found to possess an \(\hbox {IC}_{50}\) of \(3\,\upmu \hbox {M}\). An increase in the number of cells at the sub-\(\hbox {G}_{1}\) phase of the cell was observed in the in vitro cell cycle analysis of two most active compounds in the series (4e, 6g) suggesting a clear indication toward induction of apoptotic cascade. With respect to antibacterial screening, amino-substituted \(\alpha \)-cyanostilbenes were found to be more active than their corresponding bile acid amides. The synthesized compounds were also subjected to in silico study to predict their physiochemical properties and drug-likeness score.     

Critical Two-Point Function for Long-Range <Emphasis Type="Italic">O</Emphasis>(<Emphasis Type="Italic">n</Emphasis>) Models Below the Upper Critical Dimension

We consider the n-component \(|\varphi |^4\) lattice spin model (\(n \ge 1\)) and the weakly self-avoiding walk (\(n=0\)) on \(\mathbb Z^d\), in dimensions \(d=1,2,3\). We study long-range models based on the fractional Laplacian, with spin-spin interactions or walk step probabilities decaying with distance r as \(r^{-(d+\alpha )}\) with \(\alpha \in (0,2)\). The upper critical dimension is \(d_c=2\alpha \). For \(\varepsilon >0\), and \(\alpha = \frac{1}{2} (d+\varepsilon )\), the dimension \(d=d_c-\varepsilon \) is below the upper critical dimension. For small \(\varepsilon \), weak coupling, and all integers \(n \ge 0\), we prove that the two-point function at the critical point decays with distance as \(r^{-(d-\alpha )}\). This “sticking” of the critical exponent at its mean-field value was first predicted in the physics literature in 1972. Our proof is based on a rigorous renormalisation group method. The treatment of observables differs from that used in recent work on the nearest-neighbour 4-dimensional case, via our use of a cluster expansion.     

Stable exponential cosmological solutions with two factor spaces in the Einstein–Gauss–Bonnet model with a $$\Lambda $$-term

We study D-dimensional Einstein–Gauss–Bonnet gravitational model including the Gauss–Bonnet term and the cosmological term \(\Lambda \). We find a class of solutions with exponential time dependence of two scale factors, governed by two Hubble-like parameters \(H >0\) and h, corresponding to factor spaces of dimensions \(m >2\) and \(l > 2\), respectively. These solutions contain a fine-tuned \(\Lambda = \Lambda (x, m, l, \alpha )\), which depends upon the ratio \(h/H = x\), dimensions of factor spaces m and l, and the ratio \(\alpha = \alpha _2/\alpha _1\) of two constants (\(\alpha _2\) and \(\alpha _1\)) of the model. The master equation \(\Lambda (x, m, l,\alpha ) = \Lambda \) is equivalent to a polynomial equation of either fourth or third order and may be solved in radicals. The explicit solution for \(m = l\) is presented in “Appendix”. Imposing certain restrictions on x, we prove the stability of the solutions in a class of cosmological solutions with diagonal metrics. We also consider a subclass of solutions with small enough variation of the effective gravitational constant G and show the stability of all solutions from this subclass.     

Study of the weak annihilation contributions in charmless $$\varvec{B_s\rightarrow VV}$$ decays

In this paper, in order to probe the spectator-scattering and weak annihilation contributions in charmless \(B_s\rightarrow VV\) (where V stands for a light vector meson) decays, we perform the \(\chi ^2\)-analyses for the endpoint parameters within the QCD factorization framework, under the constraints from the measured \(\bar{B}_{s}\rightarrow \) \(\rho ^0\phi \), \(\phi K^{*0}\), \(\phi \phi \) and \(K^{*0}\bar{K}^{*0}\) decays. The fitted results indicate that the endpoint parameters in the factorizable and nonfactorizable annihilation topologies are non-universal, which is also favored by the charmless \(B\rightarrow PP\) and PV (where P stands for a light pseudo-scalar meson) decays observed in previous work. Moreover, the abnormal polarization fractions \(f_{L,\bot }(\bar{B}_{s}\rightarrow K^{*0}\bar{K}^{*0})=(20.1\pm 7.0)\%,(58.4\pm 8.5)\%\) measured by the LHCb collaboration can be reconciled through the weak annihilation corrections. However, the branching ratio of \(\bar{B}_{s}\rightarrow \phi K^{*0}\) decay exhibits a tension between the data and theoretical result, which dominates the contributions to \(\chi _\mathrm{min}^2\) in the fits. Using the fitted endpoint parameters, we update the theoretical results for the charmless \(B_s\rightarrow VV\) decays, which will be further tested by the LHCb and Belle-II experiments in the near future.     

Observational constraints on the jerk parameter with the data of the Hubble parameter

We study the accelerated expansion phase of the universe by using the kinematic approach. In particular, the deceleration parameter q is parametrized in a model-independent way. Considering a generalized parametrization for q, we first obtain the jerk parameter j (a dimensionless third time derivative of the scale factor) and then confront it with cosmic observations. We use the latest observational dataset of the Hubble parameter H(z) consisting of 41 data points in the redshift range of \(0.07 \le z \le 2.36\), larger than the redshift range that covered by the Type Ia supernova. We also acquire the current values of the deceleration parameter \(q_0\), jerk parameter \(j_0\) and transition redshift \(z_t\) (at which the expansion of the universe switches from being decelerated to accelerated) with \(1\sigma \) errors (\(68.3\%\) confidence level). As a result, it is demonstrate that the universe is indeed undergoing an accelerated expansion phase following the decelerated one. This is consistent with the present observations. Moreover, we find the departure for the present model from the standard \(\Lambda \)CDM model according to the evolution of j. Furthermore, the evolution of the normalized Hubble parameter is shown for the present model and it is compared with the dataset of H(z).     

Equilibration in the Kac Model Using the GTW Metric $$d_2$$

We use the Fourier based Gabetta–Toscani–Wennberg metric \(d_2\) to study the rate of convergence to equilibrium for the Kac model in 1 dimension. We take the initial velocity distribution of the particles to be a Borel probability measure \(\mu \) on \(\mathbb {R}^n\) that is symmetric in all its variables, has mean \(\vec {0}\) and finite second moment. Let \(\mu _t(dv)\) denote the Kac-evolved distribution at time t, and let \(R_\mu \) be the angular average of \(\mu \). We give an upper bound to \(d_2(\mu _t, R_\mu )\) of the form \(\min \left\{ B e^{-\frac{4 \lambda _1}{n+3}t}, d_2(\mu ,R_\mu )\right\} ,\) where \(\lambda _1 = \frac{n+2}{2(n-1)}\) is the gap of the Kac model in \(L^2\) and B depends only on the second moment of \(\mu \). We also construct a family of Schwartz probability densities \(\{f_0^{(n)}: \mathbb {R}^n\rightarrow \mathbb {R}\}\) with finite second moments that shows practically no decrease in \(d_2(f_0(t), R_{f_0})\) for time at least \(\frac{1}{2\lambda }\) with \(\lambda \) the rate of the Kac operator. We also present a propagation of chaos result for the partially thermostated Kac model in Tossounian and Vaidyanathan (J Math Phys 56(8):083301, 2015).     

Nature of the $$\Omega (2012)$$ through its strong decays

We extend our previous analysis on the mass of the recently discovered \(\Omega (2012)\) state by investigation of its strong decays and calculation of its width employing the method of light cone QCD sum rule. Considering two possibilities for the quantum numbers of \(\Omega (2012)\) state, namely 1P orbital excitation with \(J^P=\frac{3}{2}^-\) and 2S radial excitation with \(J^P=\frac{3}{2}^+\), we obtain the strong coupling constants defining the \(\Omega (1P/2S)\rightarrow \Xi K\) decays. The results of the coupling constants are then used to calculate the decay width corresponding to each possibility. Comparison of the obtained results on the total widths in this work with the experimental value and taking into account the results of our previous mass prediction on the \(\Omega (2012)\) state, we conclude that this state is 1P orbital excitation of the ground state \(\Omega \) baryon, whose quantum numbers are \(J^P=\frac{3}{2}^-\).     

Chern–Simons,Wess–Zumino and other cocycles from Kashiwara–Vergne and associators

Descent equations play an important role in the theory of characteristic classes and find applications in theoretical physics, e.g., in the Chern–Simons field theory and in the theory of anomalies. The second Chern class (the first Pontrjagin class) is defined as \(p= \langle F, F\rangle \) where F is the curvature 2-form and \(\langle \cdot , \cdot \rangle \) is an invariant scalar product on the corresponding Lie algebra \(\mathfrak g\). The descent for p gives rise to an element \(\omega =\omega _3+\omega _2+\omega _1+\omega _0\) of mixed degree. The 3-form part \(\omega _3\) is the Chern–Simons form. The 2-form part \(\omega _2\) is known as the Wess–Zumino action in physics. The 1-form component \(\omega _1\) is related to the canonical central extension of the loop group LG. In this paper, we give a new interpretation of the low degree components \(\omega _1\) and \(\omega _0\). Our main tool is the universal differential calculus on free Lie algebras due to Kontsevich. We establish a correspondence between solutions of the first Kashiwara–Vergne equation in Lie theory and universal solutions of the descent equation for the second Chern class p. In more detail, we define a 1-cocycle C which maps automorphisms of the free Lie algebra to one forms. A solution of the Kashiwara–Vergne equation F is mapped to \(\omega _1=C(F)\). Furthermore, the component \(\omega _0\) is related to the associator \(\Phi \) corresponding to F. It is surprising that while F and \(\Phi \) satisfy the highly nonlinear twist and pentagon equations, the elements \(\omega _1\) and \(\omega _0\) solve the linear descent equation.     

Scaling exponents of forced polymer translocation through a nanopore

We investigate several properties of a translocating homopolymer through a thin pore driven by an external field present inside the pore only using Langevin Dynamics (LD) simulations in three dimensions (3D). Motivated by several recent theoretical and numerical studies that are apparently at odds with each other, we estimate the exponents describing the scaling with chain length (Nof the average translocation time \(\ensuremath \langle\tau\rangle\) , the average velocity of the center of mass \(\ensuremath \langle v_{{\rm CM}}\rangle\) , and the effective radius of gyration \(\ensuremath \langle {R}_g\rangle\) during the translocation process defined as \(\ensuremath \langle\tau\rangle \sim N^{\alpha}\) , \(\ensuremath \langle v_{{\rm CM}} \rangle \sim N^{-\delta}\) , and \(\ensuremath {R}_g \sim N^{\bar{\nu}}\) respectively, and the exponent of the translocation coordinate (s -coordinate) as a function of the translocation time \(\ensuremath \langle s^2(t)\rangle\sim t^{\beta}\) . We find \(\ensuremath \alpha=1.36 \pm 0.01\) , \(\ensuremath \beta=1.60 \pm 0.01\) for \(\ensuremath \langle s^2(t)\rangle\sim \tau^{\beta}\) and \(\ensuremath \bar{\beta}=1.44 \pm 0.02\) for \(\ensuremath \langle\Delta s^2(t)\rangle\sim\tau^{\bar{\beta}}\) , \(\ensuremath \delta=0.81 \pm 0.04\) , and \(\ensuremath \bar{\nu}\simeq\nu=0.59 \pm 0.01\) , where \( \nu\) is the equilibrium Flory exponent in 3D. Therefore, we find that \(\ensuremath \langle\tau\rangle\sim N^{1.36}\) is consistent with the estimate of \(\ensuremath \langle\tau\rangle\sim\langle R_g \rangle/\langle v_{{\rm CM}} \rangle\) . However, as observed previously in Monte Carlo (MC) calculations by Kantor and Kardar (Y. Kantor, M. Kardar, Phys. Rev. E 69, 021806 (2004)) we also find the exponent α = 1.36 ± 0.01 < 1 + ν. Further, we find that the parallel and perpendicular components of the gyration radii, where one considers the “cis” and “trans” parts of the chain separately, exhibit distinct out-of-equilibrium effects. We also discuss the dependence of the effective exponents on the pore geometry for the range of N studied here.     

Excited state mass spectra of doubly heavy $$\Xi $$ baryons

In this paper, the mass spectra are obtained for doubly heavy \(\Xi \) baryons, namely, \(\Xi _{cc}^{+}\), \(\Xi _{cc}^{++}\), \(\Xi _{bb}^{-}\), \(\Xi _{bb}^{0}\), \(\Xi _{bc}^{0}\) and \(\Xi _{bc}^{+}\). These baryons consist of two heavy quarks (cc, bb, and bc) with a light (d or u) quark. The ground, radial, and orbital states are calculated in the framework of the hypercentral constituent quark model with Coulomb plus linear potential. Our results are also compared with other predictions, thus, the average possible range of excited states masses of these \(\Xi \) baryons can be determined. The study of the Regge trajectories is performed in (n, \(M^{2}\)) and (J, \(M^{2}\)) planes and their slopes and intercepts are also determined. Lastly, the ground state magnetic moments of these doubly heavy baryons are also calculated.     

Logarithmic Finite-Size Correction in Non-neutral Two-Component Plasma on Sphere

We consider a general two-component plasma of classical pointlike charges \(+e\) (e is say the elementary charge) and \(-Z e\) (valency \(Z=1,2,\ldots \)), living on the surface of a sphere of radius R. The system is in thermal equilibrium at the inverse temperature \(\beta \), in the stability region against collapse of oppositely charged particle pairs \(\beta e^2 < 2/Z\). We study the effect of the system excess charge Qe on the finite-size expansion of the (dimensionless) grand potential \(\beta \varOmega \). By combining the stereographic projection of the sphere onto an infinite plane, the linear response theory and the planar results for the second moments of the species density correlation functions we show that for any \(\beta e^2 < 2/Z\) the large-R expansion of the grand potential is of the form \(\beta \varOmega \sim A_V R^2 + \left[ \chi /6 - \beta (Qe)^2/2\right] \ln R\), where \(A_V\) is the non-universal coefficient of the volume (bulk) part and the Euler number of the sphere \(\chi =2\). The same formula, containing also a non-universal surface term proportional to R, was obtained previously for the disc domain (\(\chi =1\)), in the case of the symmetric \((Z=1)\) two-component plasma at the collapse point \(\beta e^2=2\) and the jellium model \((Z\rightarrow 0)\) of identical e-charges in a fixed neutralizing background charge density at any coupling \(\beta e^2\) being an even integer. Our result thus indicates that the prefactor to the logarithmic finite-size expansion does not depend on the composition of the Coulomb fluid and its non-universal part \(-\beta (Qe)^2/2\) is independent of the geometry of the confining domain.     

The Fermi–Pasta–Ulam Problem and Its Underlying Integrable Dynamics: An Approach Through Lyapunov Exponents

FPU models, in dimension one, are perturbations either of the linear model or of the Toda model; perturbations of the linear model include the usual \(\beta \)-model, perturbations of Toda include the usual \(\alpha +\beta \) model. In this paper we explore and compare two families, or hierarchies, of FPU models, closer and closer to either the linear or the Toda model, by computing numerically, for each model, the maximal Lyapunov exponent \(\chi \). More precisely, we consider statistically typical trajectories and study the asymptotics of \(\chi \) for large N (the number of particles) and small \(\varepsilon \) (the specific energy E / N), and find, for all models, asymptotic power laws \(\chi \simeq C\varepsilon ^a\), C and a depending on the model. The asymptotics turns out to be, in general, rather slow, and producing accurate results requires a great computational effort. We also revisit and extend the analytic computation of \(\chi \) introduced by Casetti, Livi and Pettini, originally formulated for the \(\beta \)-model. With great evidence the theory extends successfully to all models of the linear hierarchy, but not to models close to Toda.     

Hyperscaling for Oriented Percolation in $$$$ Space–Time Dimensions

Consider nearest-neighbor oriented percolation in \(d+1\) space–time dimensions. Let \(\rho ,\eta ,\nu \) be the critical exponents for the survival probability up to time t, the expected number of vertices at time t connected from the space–time origin, and the gyration radius of those vertices, respectively. We prove that the hyperscaling inequality \(d\nu \ge \eta +2\rho \), which holds for all \(d\ge 1\) and is a strict inequality above the upper-critical dimension 4, becomes an equality for \(d=1\), i.e., \(\nu =\eta +2\rho \), provided existence of at least two among \(\rho ,\eta ,\nu \). The key to the proof is the recent result on the critical box-crossing property by Duminil-Copin et al. [6].     

New feature of low $$p_{T}$$ charm quark hadronization in pp collisions at $$\sqrt{s}=7$$s=7 TeV

Treating the light-flavor constituent quarks and antiquarks whose momentum information is extracted from the data of soft light-flavor hadrons in pp collisions at \(\sqrt{s}=7\) TeV as the underlying source of chromatically neutralizing the charm quarks of low transverse momenta (\(p_{T}\)), we show that the experimental data of \(p_{T}\) spectra of single-charm hadrons \(D^{0,+}\), \(D^{*+}\) \(D_{s}^{+}\), \(\varLambda _{c}^{+}\) and \(\varXi _{c}^{0}\) at mid-rapidity in the low \(p_{T}\) range (\(2\lesssim p_{T}\lesssim 7\) GeV/c) in pp collisions at \(\sqrt{s}=7\) TeV can be well understood by the equal-velocity combination of perturbatively created charm quarks and those light-flavor constituent quarks and antiquarks. This suggests a possible new scenario of low \(p_{T}\) charm quark hadronization, in contrast to the traditional fragmentation mechanism, in pp collisions at LHC energies. This is also another support for the exhibition of the soft constituent quark degrees of freedom for the small parton system created in pp collisions at LHC energies.     

Light deflection and Gauss–Bonnet theorem: definition of total deflection angle and its applications

In this paper, we re-examine the light deflection in the Schwarzschild and the Schwarzschild–de Sitter spacetime. First, supposing a static and spherically symmetric spacetime, we propose the definition of the total deflection angle \(\alpha \) of the light ray by constructing a quadrilateral \(\varSigma ^4\) on the optical reference geometry \({\mathscr {M}}^\mathrm{opt}\) determined by the optical metric \(\bar{g}_{ij}\). On the basis of the definition of the total deflection angle \(\alpha \) and the Gauss–Bonnet theorem, we derive two formulas to calculate the total deflection angle \(\alpha \); (1) the angular formula that uses four angles determined on the optical reference geometry \({\mathscr {M}}^\mathrm{opt}\) or the curved \((r, \phi )\) subspace \({\mathscr {M}}^\mathrm{sub}\) being a slice of constant time t and (2) the integral formula on the optical reference geometry \({\mathscr {M}}^\mathrm{opt}\) which is the areal integral of the Gaussian curvature K in the area of a quadrilateral \(\varSigma ^4\) and the line integral of the geodesic curvature \(\kappa _g\) along the curve \(C_{\varGamma }\). As the curve \(C_{\varGamma }\), we introduce the unperturbed reference line that is the null geodesic \(\varGamma \) on the background spacetime such as the Minkowski or the de Sitter spacetime, and is obtained by projecting \(\varGamma \) vertically onto the curved \((r, \phi )\) subspace \({\mathscr {M}}^\mathrm{sub}\). We demonstrate that the two formulas give the same total deflection angle \(\alpha \) for the Schwarzschild and the Schwarzschild–de Sitter spacetime. In particular, in the Schwarzschild case, the result coincides with Epstein–Shapiro’s formula when the source S and the receiver R of the light ray are located at infinity. In addition, in the Schwarzschild–de Sitter case, there appear order \({\mathscr {O}}(\varLambda m)\) terms in addition to the Schwarzschild-like part, while order \({\mathscr {O}}(\varLambda )\) terms disappear.     

Phase Transition and Uniqueness of Levelset Percolation

The main purpose of this paper is to introduce and establish basic results of a natural extension of the classical Boolean percolation model (also known as the Gilbert disc model). We replace the balls of that model by a positive non-increasing attenuation function \(l:(0,\infty ) \rightarrow [0,\infty )\) to create the random field \(\Psi (y)=\sum _{x\in \eta }l(|x-y|),\) where \(\eta \) is a homogeneous Poisson process in \({\mathbb {R}}^d.\) The field \(\Psi \) is then a random potential field with infinite range dependencies whenever the support of the function l is unbounded. In particular, we study the level sets \(\Psi _{\ge h}(y)\) containing the points \(y\in {\mathbb {R}}^d\) such that \(\Psi (y)\ge h.\) In the case where l has unbounded support, we give, for any \(d\ge 2,\) a necessary and sufficient condition on l for \(\Psi _{\ge h}(y)\) to have a percolative phase transition as a function of h. We also prove that when l is continuous then so is \(\Psi \) almost surely. Moreover, in this case and for \(d=2,\) we prove uniqueness of the infinite component of \(\Psi _{\ge h}\) when such exists, and we also show that the so-called percolation function is continuous below the critical value \(h_c\).