Analytical study of charged boson stars with large scalar self-couplings

We give good approximate analytic solutions for spherical charged boson stars in the large scalar-self-coupling limit in general relativity. We show that if the charge e and mass m of the scalar field nearly satisfy the critical relation \(e^2\approx Gm^2\) (where G is the Newton constant), our analytic expressions for stable solutions agree well with the numerical solutions.     

Studying the Fourth Generation Quark Contributions to the Double Charm Decays B(s)→D(s)(∗)Ds(∗)

Almost all branching ratios and longitudinal polarization fractions of the double charm decays \(B_{(s)} \to D_{(s)}^{(*)} D_{s}^{(*)}\) have been measured, and the experimental central value of \(f_{L}({B^{0}_{s}}\to D^{*+}_{s}D^{*-}_{s})\) is quite small comparing to its Standard Model prediction. We study the fourth generation quark contributions to the double charm decays \(B_{(s)} \to D_{(s)}^{(*)} D_{s}^{(*)}\). We find that the loop diagrams involving the fourth generation quark t′ have great effects on all branching ratios and CP asymmetries, which are very sensitive to the fourth generation parameter \(\lambda ^{s}_{t^{\prime }}\) and \(\phi _{t^{\prime }}\). Nevertheless, the experimental measurements of all branching ratios can not give effective constraints on relevant new physics parameters. In addition, they have no obvious effect on the relevant polarization fractions. These results could be used to search for the fourth heavy quark t′ via its indirect manifestations in loop diagrams.     

Antiproton-nucleus electromagnetic annihilation as a way to access the proton timelike form factors

Contrary to the reaction \( \bar{{p}}\) p \( \rightarrow\) e ⁺ e ^- with a high-momentum incident antiproton on a free target proton at rest, in which the invariant mass M of the e ⁺ e ^- pair is necessarily much larger than the \( \bar{{p}}\) p mass 2m , in the reaction \( \bar{{p}}\) d \( \rightarrow\) e ⁺ e ^- n the value of M can take values near or below the \( \bar{{p}}\) p mass. In the antiproton-deuteron electromagnetic annihilation, this allows to access the proton electromagnetic form factors in the timelike region of q² near the \( \bar{{p}}\) p threshold. We estimate the cross-section \(d\sigma _{\bar pd \to e^ + e^ - n} /d\mathcal{M}\) for an antiproton beam momentum of 1.5GeV/c. We find that near the \( \bar{{p}}\) p threshold this cross-section is about 1pb/MeV. The case of heavy-nuclei target is also discussed. Elements of experimental feasibility are presented for the process \( \bar{{p}}\) d \( \rightarrow\) e ⁺ e ^- n in the context of the \( \overline{{{\rm P}}}\) ANDA project.     

Characterizing Higgs portal dark matter models at the ILC

We study the dark matter (DM) discovery prospect and its spin discrimination in the theoretical framework of gauge invariant and renormalizable Higgs portal DM models at the ILC with \(\sqrt{s} = 500\) GeV. In such models, the DM pair is produced in association with a Z boson. In the case of the singlet scalar DM, the mediator is just the SM Higgs boson, whereas for the fermion or vector DM there is an additional singlet scalar mediator that mixes with the SM Higgs boson, which produces significant observable differences. After careful investigation of the signal and backgrounds both at parton level and at detector level, we find the signal with hadronically decaying Z boson provides a better search sensitivity than the signal with leptonically decaying Z boson. Taking the fermion DM model as a benchmark scenario, when the DM-mediator coupling \(g_\chi \) is relatively small, the DM signals are discoverable only for benchmark points with relatively light scalar mediator \(H_2\). The spin discriminating from scalar DM is always promising, while it is difficult to discriminate from vector DM. As for \(g_\chi \) approaching the perturbative limit, benchmark points with the mediator \(H_2\) in the full mass region of interest are discoverable. The spin discriminating aspects from both the scalar and the fermion DM are quite promising.     

The Finite-Size Scaling Study of the Ising Model for the Fractals

The fractals are obtained by using the model of diffusion-limited aggregation (DLA) for 40 ≤ L ≤ 240. The two-dimensional Ising model is simulated on the Creutz cellular automaton for 40 ≤ L ≤ 240. The critical exponents and the fractal dimensions are computed to be β = 0.124(8), γ = 1.747(10), α = 0.081(21), δ = 14.994(11), η = 0.178(10), ν = 0.960(23) and \(d_{f}^{\beta } =1.876(8), \,d_{f}^{\gamma } =3.747(10), \,d_{f}^{\alpha } =2.081(68), \,d_{f}^{\delta } =1.940(22)\), \(d_{f}^{\eta } =2.178(10)\), \(d_{f}^{\nu } =2.960(22)\), which are consistent with the theoretical values of β = 0.125, γ = 1.75, α = 0, δ = 15, η = 0.25, ν = 1 and \(d_{f}^{\beta } =1.875, \,d_{f}^{\gamma } =3.75, \,d_{f}^{\alpha } =2, \,d_{f}^{\delta } =1.933, \,d_{f}^{\eta } =2.25, \,d_{f}^{\nu } =3\).     

Universality in the partially anisotropic three-dimensional Ising lattice

Using transfer-matrix extended phenomenological renormalization-group methods, we study the critical properties of the spin-1/2 Ising model on a simple-cubic lattice with partly anisotropic coupling strengths \(\mathop J\limits^ \to = (J',J',J)\). The universality of both fundamental critical exponents y _t and y _h is confirmed. It is shown that the critical finite-size scaling amplitude ratios \(U = A_{\chi ^{(4)} } A_\kappa /A_\chi ^2 ,Y_1 = A_{\kappa ''} /A_\chi\), and \(Y_2 = A_{\kappa ^{(4)} } /A_{\chi ^{(4)} }\) are independent of the lattice anisotropy parameter Δ=J′/J. For the Y² invariant of the three-dimensional Ising universality class, we give the first quantitative estimate Y²≈2.013 (shape L×L×∞, periodic boundary conditions in both transverse directions).     

Investigation of the <Emphasis Type="Italic">Hττ</Emphasis> and <Emphasis Type="Italic">Hbb</Emphasis> coupling constants for a scalar (pseudoscalar) Higgs boson at a future linear electron-positron collider

The possibility of setting constraints on the couplings of a scalar (pseudoscalar) Higgs boson to the tau lepton and the b quark in the reactions \(e^ + e^ - \to \nu \bar \nu \tau ^ + \tau ^ - \) and \(e^ + e^ - \to \nu \bar \nu b\bar b\) at a future linear electron-positron collider of total energy \(\sqrt s = 500 GeV\) is studied. The admixture of a new hypothetical pseudoscalar state of the Higgs boson in the H ff vertex is parametrized in the form (m _f /ν)(a+iγ₅b). On the basis of an analysis of differential distributions for the processes under study, it is shown that data from the future linear collider TESLA will make it possible to constrain the parameters a and b as ?0.32≤Δa≤0.24 and ?0.73≤b≤0.73 in the case of the reaction \(e^ + e^ - \to \nu \bar \nu \tau ^ + \tau ^ - \) and as ?0.026≤Δa≤0.027 and ?0.23≤b≤0.23 in the case of the reaction \(e^ + e^ - \to \nu \bar \nu b\bar b\). It is emphasized that the contribution of the fusion subprocess WW → H in the channel involving an electron neutrino is of particular importance, since this contribution enhances the sensitivity of data to the parameters being analyzed.     

The Padé interpolation method applied to <Emphasis Type="Italic">q</Emphasis>-Painlevé equations II (differential grid version)

Recently, we studied Padé interpolation problems of q-grid, related to q-Painlevé equations of type \(E_7^{(1)}\), \(E_6^{(1)}\), \(D_5^{(1)}\), \(A_4^{(1)}\) and \((A_2+A_1)^{(1)}\). By solving those problems, we could derive evolution equations, scalar Lax pairs and determinant formulae of special solutions for the corresponding q-Painlevé equations. It is natural that the q-Painlevé equations were derived by the interpolation method of q-grid, but it may be interesting in terms of differential grid that the Padé interpolation method of differential grid (i.e. Padé approximation method) has been applied to the q-Painlevé equation of type \(D_5^{(1)}\) by Ikawa. In this paper, we continue the above study and apply the Padé approximation method to the q-Painlevé equations of type \(E_6^{(1)}\), \(D_5^{(1)}\), \(A_4^{(1)}\) and \((A_2+A_1)^{(1)}\). Moreover, determinant formulae of the special solutions for q-Painlevé equation of type \(E_6^{(1)}\) are given in terms of the terminating q-Appell Lauricella function.     

Recent results on kaon decays by the NA48/2 experiment at CERN

The NA48/2 experiment reports the first observation of the rare decay K^± → π^±π⁰e⁺e^?, based on about 2000 candidates from 2003 data. The preliminary branching ratio in the full kinematic region is \(\mathcal {B}(K^{\pm } \to \pi ^{\pm }\pi ^{0}e^{+}e^{-})=(4.06\pm 0.17)\cdot 10^{-6}\). A sample of 4.687 × 10⁶\(K^{\pm }\to \pi ^{\pm }{\pi ^{0}_{D}}\) events collected in 2003/4 is analyzed to search for the dark photon (\(A^{\prime }\)) via the decay chain K^± → π^±π⁰, \(\pi ^{0}\to \gamma A^{\prime }\), \(A^{\prime }\to e^{+}e^{-}\). No signal is observed, limits in the plane mixing parameter ε² versus its mass \(m_{A^{\prime }}\) are reported.     

Kinetically modified non-minimal inflation with exponential frame function

We consider supersymmetric (SUSY) and non-SUSY models of chaotic inflation based on the \(\phi ^n\) potential with \(n=2\) or 4. We show that the coexistence of an exponential non-minimal coupling to gravity \(f_\mathcal{R}=\mathrm{e}^{c_\mathcal{R}\phi ^{p}}\) with a kinetic mixing of the form \(f_{\mathrm{K}}=c_{\mathrm{K}}f_\mathcal{R}^m\) can accommodate inflationary observables favored by the Planck and Bicep2/Keck Array results for \(p=1\) and 2, \(1\le m\le 15\) and \(2.6\times 10^{-3}\le r_{\mathcal {R}\mathrm{K}}=c_\mathcal{R}/c_{\mathrm{K}}^{p/2}\le 1,\) where the upper limit is not imposed for \(p=1\). Inflation is of hilltop type and it can be attained for subplanckian inflaton values with the corresponding effective theories retaining the perturbative unitarity up to the Planck scale. The supergravity embedding of these models is achieved employing two chiral gauge singlet supefields, a monomial superpotential and several (semi)logarithmic or semi-polynomial Kähler potentials.     

Systems of conservation laws with third-order Hamiltonian structures

We investigate n-component systems of conservation laws that possess third-order Hamiltonian structures of differential-geometric type. The classification of such systems is reduced to the projective classification of linear congruences of lines in \(\mathbb {P}^{n+2}\) satisfying additional geometric constraints. Algebraically, the problem can be reformulated as follows: for a vector space W of dimension \(n+2\), classify n-tuples of skew-symmetric 2-forms \(A^{\alpha } \in \varLambda ^2(W)\) such that

$$\begin{aligned} \phi _{\beta \gamma }A^{\beta }\wedge A^{\gamma }=0, \end{aligned}$$

for some non-degenerate symmetric \(\phi \).

     

Leptonic decays of the <Emphasis Type="Italic">W</Emphasis> boson in a strong electromagnetic field

The probability of W-boson decay into a lepton and a neutrino, \(W^ \pm \to \ell ^ \pm \bar \nu _\ell \), in a strong electromagnetic field is calculated. On the basis of the method for deriving exact solutions to relativistic wave equations for charged particles, an exact analytic expression is obtained for the partial decay width \(\Gamma () = \Gamma (W^ + \to \ell ^ + \bar \upsilon _\ell )\) at an arbitrary value of the external-field-strength parameter \( = eM_W^{ - 3} \sqrt { - (F_{\mu \upsilon } q^\upsilon )^2 } \). It is found that, in the region of comparatively weak fields (??1), field-induced corrections to the standard decay width of theW boson in a vacuum are about a few percent. As the external-field-strength parameter is increased, the partial width with respect to W-boson decay through the channel in question, Γ(?), first decreases, the absolute minimum of Γ_min=0.926Γ(0) being reached at ?=0.6116. A further increase in the external-field strength leads to a monotonic growth of the decay width of the W boson. In superstrong fields (??1), the partial width with respect to W boson decay is greater than the corresponding partial width \(\Gamma ^{(0)} (W^ \pm \to \ell ^ \pm \bar \upsilon _\ell )\) in a vacuum by a factor of a few tens.     

Transition from non-fermi liquid behavior to Landau–Fermi liquid behavior induced by magnetic fields

We show that a strongly correlated Fermi system with a fermion condensate which exhibits strong deviations from Landau–Fermi liquid behavior is driven into the Landau–Fermi liquid by applying a small magnetic field B at temperature T=0. This field-induced Landau–Fermi liquid behavior provides constancy of the Kadowaki–Woods ratio. A re-entrance into the strongly correlated regime is observed if the magnetic field B decreases to zero; the effective mass M* then diverges as \(M^* \propto {1 \mathord{\left/ {\vphantom {1 {\sqrt B }}} \right. \kern-\nulldelimiterspace} {\sqrt B }}\). At finite temperatures, the strongly correlated regime is restored at some temperature \(T^* \propto \sqrt B \). This behavior is of a general form and takes place in both three-dimensional and two-dimensional strongly correlated systems. We demonstrate that the observed \({1 \mathord{\left/ {\vphantom {1 {\sqrt B }}} \right. \kern-\nulldelimiterspace} {\sqrt B }}\) divergence of the effective mass and other specific features of heavy-fermion metals are accounted for by our consideration.     

A Mysterious Cluster Expansion Associated to the Expectation Value of the Permanent of 0–1 Matrices

We consider two ensembles of \(0-1\) \(n\times n\) matrices. The first is the set of all \(n\times n\) matrices with entries zeroes and ones such that all column sums and all row sums equal r, uniformly weighted. The second is the set of \(n \times n\) matrices with zero and one entries where the probability that any given entry is one is r / n, the probabilities of the set of individual entries being i.i.d.’s. Calling the two expectation values E and \(E_B\) respectively, we develop a formal relation

$$\begin{aligned} E({{\mathrm{perm}}}(A)) = E_B({{\mathrm{perm}}}(A)) e^{\sum _2 T_i}.\quad \quad \quad \quad \mathrm{(A1)} \end{aligned}$$

We use two well-known approximating ensembles to E, \(E_1\) and \(E_2\). Replacing E by either \(E_1\) or \(E_2\) we can evaluate all terms in (A1). For either \(E_1\) or \(E_2\) the terms \(T_i\) have amazing properties. We conjecture that all these properties hold also for E. We carry through a similar development treating \(E({{\mathrm{perm}}}_m(A))\), with m proportional to n, in place of \(E({{\mathrm{perm}}}(A))\).

     

Spherically Symmetric Solutions of Light Galileon

We have been studied the model of light Galileon with translational shift symmetry ? → ? + c. The matter Lagrangian is presented in the form \(\mathcal {L}_{\phi }= -\eta (\partial \phi )^{2}+\beta G^{\mu \nu }\partial _{\mu }\phi \partial _{\nu }\phi \). We have been addressed two issues: the first is that, we have been proven that, this type of Galileons belong to the modified matter-curvature models of gravity in type of \(f(R,R^{\mu \nu }T_{\mu \nu }^{m})\). Secondly, we have been investigated exact solution for spherically symmetric geometries in this model. We have been found an exact solution with singularity at r = 0 in null coordinates. We have been proven that the solution has also a non-divergence current vector norm. This solution can be considered as an special solution which has been investigated in literature before, in which the Galileon’s field is non-static (time dependence). Our scalar-shift symmetrized Galileon has the simple form of ? = t, which it is remembered by us dilaton field.     

Decays of a neutral particle with zero spin and arbitrary CP parity into two off-mass-shell <Emphasis Type="Italic">Z</Emphasis> bosons

We investigate effects of CP symmetry violation in the decay of a scalar particle X (the Higgs boson) into two off-mass-shell Z bosons both decaying into a fermion–antifermion pair, \(X \to {Z_1}*{Z_2}* \to {f_1}{\bar f_1}{f_2}{\bar f_2}\). The most general form of the amplitude of the transition X → Z₁*Z₂*, wherein the boson X may not have definite CP parity, is considered. The applicability limits of the narrow-Z-width approximation used in obtaining differential widths of the decay under consideration are determined. Various observables connected with the structure of the amplitude of the decay X → Z₁*Z₂* are studied. These observables are analyzed in the Standard Model as well as in models conceding indefinite CP parity of the Higgs boson. An experimental measurement of angular and invariant mass distributions of the decay \(X \to {Z_1}*{Z_2}* \to {f_1}{\bar f_1}{f_2}{\bar f_2}\) at the LHC can give information about the CP properties of the Higgs boson and its interaction with the Z boson.     

Quantifying Contextuality of Empirical Models in Terms of Trace-Distance

In order to quantify contextuality of empirical models, the quantity of contextuality (QoC) of empirical models is introduced in terms of the trace-distance. Let Q C(e) denote the QoC of an empirical model e. The following conclusions are proved. (i) An empirical model e is non-contextual if and only if Q C(e)=0, and then it is contextual if and only if Q C(e)>0; (ii) the QoC function QC is convex, contractive and continuous. Finally, the QoC of some famous models is computed, including PM-isotropic boxes P M ^α , M-isotropic boxes M ^α , C H _n -isotropic boxes \(CH_{n}^{\alpha }\) as well as K box, where α∈[0,1]. Moreover, P M ^α is non-contextual if and only if \(\alpha \in [\frac {1}{6},\frac {5}{6}]\); M ^α is non-contextual if and only if \(\alpha \in [0,\frac {4}{5}]\); when n is even, \(CH_{n}^{\alpha }\) is non-contextual if and only if \(\alpha \in [\frac {1}{n},\frac {n-1}{n}]\), and when n is odd, \(CH_{n}^{\alpha }\) is non-contextual if and only if \(\alpha \in [0,\frac {n-1}{n}]\). The most important thing is that it is very easy to compare the QoC of any two isotropic boxes discussed in the above.     

Dynamical generation of flavour

We propose the generation of Standard Model fermion hierarchy by the extension of renormalizable SO(10) GUT with O(N_g) family gauge symmetry. In this scenario, Higgs representations of SO(10) also carry family indices and are called Yukawons. Vacuum expectation values of these Yukawon fields break GUT and family symmetry and generate MSSM Yukawa couplings dynamically. We have demonstrated this idea using \({\mathbf {10}}\oplus {\mathbf {210}} \oplus {\mathbf {126}} \oplus {\overline {\mathbf {126}}}\) Higgs irrep, ignoring the contribution of 120-plet which is, however, required for complete fitting of fermion mass-mixing data. The effective MSSM matter fermion couplings to the light Higgs pair are determined by the null eigenvectors of the MSSM-type Higgs doublet superfield mass matrix \(\mathcal {H}\). A consistency condition on the doublet ([1,2,±1]) mass matrix (\(\text {Det}(\mathcal {H})=\) 0) is required to keep one pair of Higgs doublets light in the effective MSSM. We show that the Yukawa structure generated by null eigenvectors of \(\mathcal {H}\) are of generic kind required by the MSSM. A hidden sector with a pair of (S_ab; ?_ab) fields breaks supersymmetry and facilitates \(D_{O(N_{g})}\hspace *{-1pt}=\) 0. SUSY breaking is communicated via supergravity. In this scenario, matter fermion Yukawa couplings are reduced from 15 to just 3 parameters in MSGUT with three generations.     

Die absolute Intensität der durch Elektronenstoß in einer dicken Wolfram-Antikathode erzeugtenL α -Strahlung

The number\(N_{L_\alpha }^{dir} \) (produced) ofL _α -photons produced by electron-bombardment in a thick target of tungsten per incident electron has been measured absolutely with the Ross-filter method and relatively with the crystal-spectrometer method in the energyregion up to the 3.6 times theL _III-ionization energy\(E_{L_{III} } \). The result can be presented in the following empirical form:\(N_{L_\alpha }^{dir} \) (produced)=4π·?·(U ₀?1) ⁿ with ?=0.52·10^?4±5% andn=1.44±0.02\((U_0 = E_0 /E_{L_{III} }< 3.6)\). Out of this the number\(n_{L_{III} } \) ofL _III-ionizations per electron which is slowed down to the energy\(E_{L_{III} } \) within the target, has been evaluated. The computation of\(n_{L_{III} } \) out of the elementary process by usingBethe's non-relativistic formulae for totalL _III-ionization cross sectionQ _L and energy loss-dE/ds is in full agreement with experiment in the region 2<U ₀<3.6, if the constants in\(Q_{L_{III} } \) are chosen as follows:\(B = 4E_{L_{III} } , b_{L_{III} } = 0.25 \cdot 5.89\). By comparison of this result for\(b_{L_{III} } \) with the corresponding value ofb _K in the totalK-ionization cross-sectionQ _K for copper (b _K=0.35·2.26) it is concluded that\(Q_{L_{III} } \) is considerably higher than predicted by theory. The necessary correction factors as e.g. loss ofL _III-ionizations by rediffusion of electrons and portion of indirectly producedL _α -radiation-radiation are determined for tungsten quantitatively.     

Method of uniform effective field in structure-dynamic approach of nanoionics

In the structure-dynamic approach of nanoionics, the method of a uniform effective field \( {F}_{\mathrm{eff}}^{j,k} \) of a crystallographic planeX ^j has been substantiated for solid electrolyte nanostructures. The \( {F}_{\mathrm{eff}}^{j,k} \)is defined as an approximation of a non-uniform field \( {F}_{\mathrm{dis}}^j \)of X ^j with a discrete- random distribution of excess point charges. The parameters of \( {F}_{\mathrm{eff}}^{j,k} \)are calculated by correction of the uniform Gauss field \( {F}_{\mathrm{G}}^j \) of X ^j . The change in an average frequency of ionic jumps X ^k ?→?X ^k?+?1 between adjacent planes of nanostructure is determined by the sum of field additives to the barrier heights η _k , _k?+?1, and for \( {F}_{\mathrm{G}}^j \) and \( {F}_{\mathrm{dis}}^j \), these sums are the same decimal order of magnitude. For nanostructures with length ~4 nm, the application of \( {F}_{\mathrm{G}}^j \) (as \( {F}_{\mathrm{eff}}^{j,k} \)) gives the accuracy ~20 % in calculations of ion transport characteristics. The computer explorations of the “universal” dynamic response (Reσ ^??∝?ω ⁿ ) show an approximately the same power n < ≈1 for\( {F}_{\mathrm{G}}^j \) and \( {F}_{\mathrm{eff}}^{j,k} \).