Alternative technique for Standard Model estimation of the rare kaon decay branchings \left. {BR(K \to \pi \nu \bar \nu )} \right|_{SM}

We estimate $BR(K \to \pi \nu \bar \nu )$ in the context of the Standard Model by fitting for λ _t≡V _tdV _ts ^* of the “kaon unitarity triangle” relation. To find the vertex of this triangle, we fit data from |? _K|, the CP-violating parameter describing K mixing, and a _ψ,K , the CP-violating asymmetry in B _d ⁰ → J/ψK ⁰ decays, and obtain the values $\left. {BR(K \to \pi \nu \bar \nu )} \right|_{SM} = (7.07 \pm 1.03) \times 10^{ - 11} $ and $\left. {BR(K_L^0 \to \pi ^0 \nu \bar \nu )} \right|_{SM} = (2.60 \pm 0.52) \times 10^{ - 11} $ . Our estimate is independent of the CKM matrix element V _cb and of the ratio of B-mixing frequencies ${{\Delta m_{B_s } } \mathord{\left/ {\vphantom {{\Delta m_{B_s } } {\Delta m_{B_d } }}} \right. \kern-0em} {\Delta m_{B_d } }}$ . We also use the constraint estimation of λ _t with additional data from $\Delta m_{B_d } $ and |V _ub|. This combined analysis slightly increases the precision of the rate estimation of $K^ + \to \pi ^ + \nu \bar \nu $ and $K_L^0 \to \pi ^0 \nu \bar \nu $ (by ?10 and ?20%, respectively). The measured value of $BR(K^ + \to \pi ^ + \nu \bar \nu )$ can be compared both to this estimate and to predictions made from ${{\Delta m_{B_s } } \mathord{\left/ {\vphantom {{\Delta m_{B_s } } {\Delta m_{B_d } }}} \right. \kern-0em} {\Delta m_{B_d } }}$ .     

Direct chargino–neutralino production at the LHC: interpreting the exclusion limits in the complex MSSM

We re-assess the exclusion limits on the parameters describing the supersymmetric (SUSY) electroweak sector of the MSSM obtained from the search for direct chargino–neutralino production at the LHC. We start from the published limits obtained for simplified models, where for the case of heavy sleptons the relevant branching ratio, $\mathrm {BR}(\tilde{\chi}^{0}_{2} \to \tilde{\chi}^{0}_{1} Z)$ , is set to one. We show how the decay mode $\tilde{\chi}^{0}_{2} \to \tilde{\chi}^{0}_{1} h$ , which cannot be neglected in any realistic model once kinematically allowed, substantially reduces the excluded parameter region. We analyze the dependence of the excluded regions on the phase of the gaugino soft SUSY-breaking mass parameter, M ₁, on the mass of the light scalar tau, $m_{{\tilde{\tau}_{1}}}$ , on tanβ as well as on the squark and slepton mass scales. Large reductions in the ranges of parameters excluded can be observed in all scenarios. The branching ratios of charginos and neutralinos are evaluated using a full NLO calculation for the complex MSSM. The size of the effects of the NLO calculation on the exclusion bounds is investigated. We furthermore assess the potential reach of the experimental analyses after collecting 100 fb^?1 at the LHC running at 13 TeV.     

Search for SUSY at LHC in jets + E T miss final states for the case of nonuniversal gaugino masses

We investigate squark and gluino pair production at LHC (CMS) with subsequent decays into quarks and an LSP for the case of nonuniversal gaugino masses. Visibility of a signal by an excess over the SM background in (n≥2)jets+E _T ^miss events depends rather strongly on the relation between the LSP, gluino, and squark masses and decreases with increasing LSP mass. For a relatively heavy LSP mass close to the squark or the gluino mass and for $m_{\tilde q} ,m_{\tilde g} \geqslant 1.5$ TeV, the sygnal is overly small to be observable.     

More corrections to the sixth-order anomalous magnetic moment of the muon

The contribution to the sixth-order muon anomaly from second-order electron vacuum polarization is determined analytically to orderm _e/m _μ. The result, including the contributions from graphs containing proper and improper fourth-order electron vacuum polarization subgraphs, is $$\begin{gathered} \left( {\frac{\alpha }{\pi }} \right)^3 \left\{ {\frac{2}{9}\log ^2 } \right.\frac{{m_\mu }}{{m_e }} + \left[ {\frac{{31}}{{27}}} \right. + \frac{{\pi ^2 }}{9} - \frac{2}{3}\pi ^2 \log 2 \hfill \\ \left. { + \zeta \left( 3 \right)} \right]\log \frac{{m_\mu }}{{m_e }} + \left[ {\frac{{1075}}{{216}}} \right. - \frac{{25}}{{18}}\pi ^2 + \frac{{5\pi ^2 }}{3}\log 2 \hfill \\ \left. { - 3\zeta \left( 3 \right) + \frac{{11}}{{216}}\pi ^4 - \frac{2}{9}\pi ^2 \log ^2 2 - \frac{1}{9}log^4 2 - \frac{8}{3}a_4 } \right] \hfill \\ + \left[ {\frac{{3199}}{{1080}}\pi ^2 - \frac{{16}}{9}\pi ^2 \log 2 - \frac{{13}}{8}\pi ^3 } \right]\left. {\frac{{m_e }}{{m_\mu }}} \right\} \hfill \\ \end{gathered} $$ . To obtain the total sixth-order contribution toa _μ?a _e, one must add the light-by-light contribution to the above expression.     

Heavy gluino and squark decays atp \bar p collider

The recent limits, \(m_{\tilde g} , m_{\tilde q} \gtrsim 40\) , GeV for gluino and squark masses obtained from experiments at the collider are based on jet +p _T analysis, in the hypothesis that the gluino or the squark decays into photino+quarks with a branching ratio near to one. We show that this hypothesis is generally not justified for higher masses of the gluino and the squarks, 50 GeV \( \lesssim m_{\tilde g,\tilde q} \lesssim \) 150 GeV, relevant to present and future \(\bar p\) colliders. In an interesting range of the parameters we study the different decay modes and the related signatures, among which isolated leptons or photons in the final states.     

B^0 - \bar B^0 mixing within and beyond the standard model

The standard model with three fermion families is found to be compatible with the Argus observation of a relatively large amount of \(B_{^d }^0 - \bar B_d^0 \) mixing provided that the top quark is rather heavy. From an analysis of the existing information on mixing angles, and of the constraints imposed by the kaon system, in particular by the ε parameter, we conclude that almost certainlym _t <45 GeV and probablym _t >90 GeV. In view of the Argus result the standard model unambiguously leads to the prediction of a nearly maximal amount of \(B_{^s }^0 - \bar B_s^0 \) mixing. Apart from the rather obvious case of a fourth family of quarks, most “minimal” extensions of the standard model preserve the prediction of a large \(B_{^s }^0 - \bar B_s^0 \) mixing. We discuss \(B^0 - \bar B^0 \) mixing in minimal supersymmetric models compatible with the UA1 lower bounds on gluino and squark masses. Contributions from charged Higgs exchange in the box diagrams are also discussed. While supersymmetry (although marginally) and charged Higgses can lead to an appreciable enhancement of \(B^0 - \bar B^0 \) mixing, minimal left-right symmetric models actually predict a modest suppression of the effect with respect to the standard model.     

LHC (CMS) discovery potential for models with effective supersymmetry and nonuniversal gaugino masses

We investigate squark and gluino pair production at LHC (CMS) with subsequent decays into quarks, leptons, and the lightest supersymmetric particles (LSP) in models with effective supersymmetry, where the third generation of squarks is relatively light, whilst the first two generations of squarks are heavy. We consider the general case of nonuniversal gaugino masses. The visibility of a signal through an excess over Standard Model background in (n≥2) jets+(m≥0) leptons+E _T ^miss events depends rather strongly on the relation between the LSP, second-neutralino, gluino, and squark masses and decreases with increasing LSP mass. We find that, for a relatively heavy gluino, it is very difficult to detect a SUSY signal even for light third-generation squarks $(m_{\tilde q_3 } \leqslant 1TeV)$ if the LSP mass is close to the third-generation squark mass.     

On the chiral limit in lattice gauge theories with Wilson fermions

The chiral limit κ ? κ _c (β) in lattice gauge theories with Wilson fermions and problems related to near-to-zero (’exceptional’) eigenvalues of the fermionic matrix are studied. For this purpose we employ compact lattice QED in the confinement phase. A new estimator $\tilde m_\pi$ for the calculation of the pseudoscalar mass m _π is proposed which does not suffer from ’divergent’ contributions at κ ? κ _c (β)We conclude that the main contribution to the pion mass comes from larger modes, and ’exceptional’ eigenvalues play no physical role. The behaviour of the subtracted chiral condensate $\left\langle {\bar \psi \psi } \right\rangle _{subt}$ near κ _c (β) is determined. We observe a comparatively large value of $\left\langle {\bar \psi \psi } \right\rangle _{subt} \cdot Z_P^{ - 1}$ , which could be interpreted as a possible effect of the quenched approximation.     

Theoretical study of collision and collision-free radiative lifetimes of {{\text{S}}_2}\left( {{{\text{B}}^3}\Sigma_{\text{u}}^{-} \left( {{\upsilon^{\prime}} = 0 - 9} \right)} \right)

We calculate multireference configuration-interaction wavefunctions and the potential-energy curves for the $ {B^3}\Sigma_u^{-} $ and $ {X^3}\Sigma_g^{-} $ states of the collision-free S₂ molecule and the T-shape collision complex S₂?CHe using cc-pVQZ basis sets. We obtain the transition dipole moments of the $ {{\text{S}}_2}\left( {{B^3}\Sigma_u^{-} \to {X^3}\Sigma_g^{-} } \right) $ and the Franck?CCondon factors between the vibrational levels of this two states. We evaluate the radiative lifetimes of $ {{\text{S}}_2}\left( {{B^3}\Sigma_u^{-} \left( {{\upsilon^{\prime}} = 0 - 9} \right)} \right) $ levels of the collision complex and the collision-free molecule and compare them with the experiments. The collision provides little change in the radiative lifetimes of $ {{\text{S}}_2}\left( {{B^3}\Sigma_u^{-} \left( {{\upsilon^{\prime}} = 0 - 9} \right)} \right) $ according to the previous calculations. We obtain excellent agreement between the theoretical results and the experiments. The data calculated are very useful in the study of the microwave-driven high-pressure sulfur lamp and an S₂ laser pumped by a transverse fast discharge.     

Polarization-optical and X-ray diffraction investigations on the symmetry of distorted phases of ammonium cryolite (NH4)3 ScF6

Single-crystal plates of different sections of the (NH₄)₃ScF₆ crystal have been investigated by polarization-optical microscopy and X-ray diffraction over a wide temperature range, including the temperatures of two known phase transitions and the third transition found recently. It is established that the symmetry of 5 phases changes in the following sequence: $\begin{gathered} O_h^5 - Fm3m(Z = 4) \leftrightarrow C_{2h}^5 - {{P12_1 } \mathord{\left/ {\vphantom {{P12_1 } {n1}}} \right. \kern-0em} {n1}}(Z = 2) \leftrightarrow C_{2h}^3 - {{I12} \mathord{\left/ {\vphantom {{I12} {m1}}} \right. \kern-0em} {m1}} \\ (Z = 16) \leftrightarrow C_i^1 - I\bar 1(Z = 16) \\ \end{gathered} $ .     

Distinction between avalanche and tunneling breakdown in one-sided abrupt junctions

The distinction between avalanche and tunneling breakdown in one-sided abrupt junctions is made on the basis of a new, simple expression for the tunneling breakdown field strengthF _t. It is shown thatF _t [V/cm] depends upon the temperatureT [K], the reduced tunneling effective massm _eff ⁺ /m _o and the semiconductor energy band gapE _g [eV] according to the following equation $$F_t = 1.76 \cdot 10^6 \cdot \left( {\frac{T}{{300}}} \right) \cdot \left( {\frac{{m_{eff}^ + }}{{m_0 }} \cdot E_g } \right)^{{1 \mathord{\left/ {\vphantom {1 2}} \right. \kern-\nulldelimiterspace} 2}} [V/cm].$$ Using published calculations for the avalanche breakdown voltage, the result is applied to the semiconductors Ge, Si, GaAs and GaP at 300 K and InSb at 77K.     

Fast proton conduction path in {\text{Ni}} - {\text{BaCe}}_{{0.8}} {\text{Y}}_{{0.2}} {\text{O}}_{{2.9 - \delta }} membrane

The effect of metal-to-oxide grain boundary layer in $ {\text{Ni}} - {\text{BaCe}}_{{0.8}} {\text{Y}}_{{0.2}} {\text{O}}_{{3 - \delta }} $ (BCY) cermet membrane on hydrogen permeation was studied by applying the different size of oxide grain on Ni-BCY membranes. Two types of cermet membranes having different grain size of oxide were prepared by using different starting particle size of oxide powder. The hydrogen flux of coarse-oxide-grain membrane showed higher flux than that of small-oxide-grain membrane. It was understood that the negative potential at metal-to-oxide grain boundary, reference to the bulk oxide ( $ \phi _{0} < \phi _{\infty } = 0 $ ), was developed, and the accumulation of the effectively positively charged protons may occur at the grain boundary layer (space charge layer), which may result in providing highly conductive proton path by shifting the charge neutrality condition from $ {\left[ {OH^{ \bullet }_{O} } \right]} = {\left[ {Y^{/}_{{Ce}} } \right]} $ to $ {\left[ {OH^{ \bullet }_{O} } \right]} = n $ .     

One-range Addition Theorems for Noninteger n Slater Functions using Complete Orthonormal Sets of Exponential Type Orbitals in Standard Convention

By the use of complete orthonormal sets of ${\psi ^{(\alpha^{\ast})}}$ -exponential type orbitals ( ${\psi ^{(\alpha^{\ast})}}$ -ETOs) with integer (for α ^* = α) and noninteger self-frictional quantum number α ^*(for α ^* ≠ α) in standard convention introduced by the author, the one-range addition theorems for ${\chi }$ -noninteger n Slater type orbitals ${(\chi}$ -NISTOs) are established. These orbitals are defined as follows $$\begin{array}{ll}\psi _{nlm}^{(\alpha^*)} (\zeta ,\vec {r}) = \frac{(2\zeta )^{3/2}}{\Gamma (p_l ^* + 1)} \left[{\frac{\Gamma (q_l ^* + )}{(2n)^{\alpha ^*}(n - l - 1)!}} \right]^{1/2}e^{-\frac{x}{2}}x^{l}_1 F_1 ({-[ {n - l - 1}]; p_l ^* + 1; x})S_{lm} (\theta ,\varphi )\\ \chi _{n^*lm} (\zeta ,\vec {r}) = (2\zeta )^{3/2}\left[ {\Gamma(2n^* + 1)}\right]^{{-1}/2}x^{n^*-1}e^{-\frac{x}{2}}S_{lm}(\theta ,\varphi ),\end{array}$$ where ${x=2\zeta r, 0<\zeta <\infty , p_l ^{\ast}=2l+2-\alpha ^{\ast}, q_l ^{\ast}=n+l+1-\alpha ^{\ast}, -\infty <\alpha ^{\ast} <3 , -\infty <\alpha \leq 2,_1 F_1 }$ is the confluent hypergeometric function and ${S_{lm} (\theta ,\varphi )}$ are the complex or real spherical harmonics. The origin of the ${\psi ^{(\alpha ^{\ast})} }$ -ETOs, therefore, of the one-range addition theorems obtained in this work for ${\chi}$ -NISTOs is the self-frictional potential of the field produced by the particle itself. The obtained formulas can be useful especially in the electronic structure calculations of atoms, molecules and solids when Hartree–Fock–Roothan approximation is employed.     

Light quark masses in quantum chromodynamics and chiral symmetry breaking

We derive model independent lower bounds for the sums of effective quark masses \(\bar m_u + \bar m_d \) and \(\bar m_u + \bar m_s \) . The bounds follow from the combination of the spectral representation properties of the hadronic axial currents two-point functions and their behavior in the deep euclidean region (known from a perturbative QCD calculation to two loops and the leading non-perturbative contribution). The bounds incorporate PCAC in the Nambu-Goldstone version. If we define the invariant masses \(\hat m\) by $$\bar m_i = \hat m_i \left( {{{\frac{1}{2}\log Q^2 } \mathord{\left/ {\vphantom {{\frac{1}{2}\log Q^2 } {\Lambda ^2 }}} \right. \kern-\nulldelimiterspace} {\Lambda ^2 }}} \right)^{{{\gamma _1 } \mathord{\left/ {\vphantom {{\gamma _1 } {\beta _1 }}} \right. \kern-\nulldelimiterspace} {\beta _1 }}} $$ and <F ²> is the vacuum expectation value of $$F^2 = \Sigma _a F_{(a)}^{\mu v} F_{\mu v(a)} $$ , we find, e.g., $$\hat m_u + \hat m_d \geqq \sqrt {\frac{{2\pi }}{3} \cdot \frac{{8f_\pi m_\pi ^2 }}{{3\left\langle {\alpha _s F^2 } \right\rangle ^{{1 \mathord{\left/ {\vphantom {1 2}} \right. \kern-\nulldelimiterspace} 2}} }}} $$ ; with the value <α _u F ²?0.04GeV⁴, recently suggested by various analysis, this gives $$\hat m_u + \hat m_d \geqq 35MeV$$ . The corresponding bounds on \(\bar m_u + \bar m_s \) are obtained replacingm _π ² f _π bym _K ² f _K . The PCAC relation can be inverted, and we get upper bounds on the spontaneous masses, \(\hat \mu \) : $$\hat \mu \leqq 170MeV$$ where \(\hat \mu \) is defined by $$\left\langle {\bar \psi \psi } \right\rangle \left( {Q^2 } \right) = \left( {{{\frac{1}{2}\log Q^2 } \mathord{\left/ {\vphantom {{\frac{1}{2}\log Q^2 } {\Lambda ^2 }}} \right. \kern-\nulldelimiterspace} {\Lambda ^2 }}} \right)^d \hat \mu ^3 ,d = {{12} \mathord{\left/ {\vphantom {{12} {\left( {33 - 2n_f } \right)}}} \right. \kern-\nulldelimiterspace} {\left( {33 - 2n_f } \right)}}$$ .     

The Spectrum of the Cubic Oscillator

We prove the simplicity and analyticity of the eigenvalues of the cubic oscillator Hamiltonian, $$\begin{array}{ll}H(\beta)=-\frac{d^2}{dx^2}+x^2+i\sqrt{\beta}x^3\end{array}$$ , for β in the cut plane ${\mathcal{C}_c:=\mathcal{C}\backslash \mathcal{R}_-}$ . Moreover, we prove that the spectrum consists of the perturbative eigenvalues {E _n (β)} _{n ≥ 0} labeled by the constant number n of nodes of the corresponding eigenfunctions. In addition, for all ${\beta \in \mathcal{C}_c, E_n(\beta)}$ can be computed as the Stieltjes-Padé sum of its perturbation series at β = 0. This also gives an alternative proof of the fact that the spectrum of H(β) is real when β is a positive number. This way, the main results on the repulsive PT-symmetric and on the attractive quartic oscillators are extended to the cubic case.     

Self-Avoiding Walk is Sub-Ballistic

We prove that self-avoiding walk on ${\mathbb{Z}^d}$ is sub-ballistic in any dimension d ≥ 2. That is, writing ${\| u \|}$ for the Euclidean norm of ${u \in \mathbb{Z}^d}$ , and ${\mathsf{P_{SAW}}_n}$ for the uniform measure on self-avoiding walks ${\gamma : \{0, \ldots, n\} \to \mathbb{Z}^d}$ for which γ ₀ = 0, we show that, for each v > 0, there exists ${\varepsilon > 0}$ such that, for each ${n \in \mathbb{N}, \mathsf{P_{SAW}}_n \big( {\rm max}\big\{\| \gamma_k \| : 0 \leq k \leq n\big\} \geq vn \big) \leq e^{-\varepsilon n}}$ .     

Newest results from the Mainz neutrino-mass experiment

The Mainz neutrino-mass experiment investigates the endpoint region of the tritium β-decay spectrum with a MAC-E spectrometer to determine the mass of the electron antineutrino. By the recent upgrade, the former problem of dewetting T₂ films has been solved, and the signal-to-background ratio was improved by a factor of 10. The latest measurement leads to $m_\nu ^2 = - 3.7 \pm 5.3(stat.) \pm 2.1(syst.){{eV^2 } \mathord{\left/ {\vphantom {{eV^2 } {c^4 }}} \right. \kern-0em} {c^4 }}$ , from which an upper limit of $m_\nu < 2.8{{eV^2 } \mathord{\left/ {\vphantom {{eV^2 } {c^2 }}} \right. \kern-0em} {c^2 }}(95\% C.L.)$ is derived. Some indication for the anomaly, reported by the Troitsk group, was found, but its postulated half-year period is contradicted by our data. To push the sensitivity on the neutrino mass below 1 eV/c ², a new larger MAC-E spectrometer is proposed. Besides its integrating mode, it could run in a new nonintegration operation MAC-E-TOF mode.     

Neutrino production of dimuons

Neutrino interactions with two muons in the final state have been studied using the Fermilab narrow band beam. A sample of 18v _μ like sign dimuon events withP _μ>9 GeV/c yields 6.6±4.8 events after backgroud subtraction and a prompt rate of (1.0±0.7)×10^?4 per single muon event. The kinematics of these events are compared with those of the non-prompt sources. A total of 437v _μ and 31 \(\bar v_\mu \) opposite sign dimuon events withP _μ>4.3 GeV/c are used to measure the strange quark content of the nucleon: \(\kappa = {{2s} \mathord{\left/ {\vphantom {{2s} {\left( {\bar u + \bar d} \right) = 0.52_{ - 0.15}^{ + 0.17} \left( {or\eta _s \frac{{2s}}{{u + d}} = 0.075 \pm 0.019} \right) for 100< E_v< 230 GeV\left( {\left\langle {Q^2 } \right\rangle = {{23 GeV^2 } \mathord{\left/ {\vphantom {{23 GeV^2 } {c^2 }}} \right. \kern-0em} {c^2 }}} \right)}}} \right. \kern-0em} {\left( {\bar u + \bar d} \right) = 0.52_{ - 0.15}^{ + 0.17} \left( {or\eta _s \frac{{2s}}{{u + d}} = 0.075 \pm 0.019} \right) for 100< E_v< 230 GeV\left( {\left\langle {Q^2 } \right\rangle = {{23 GeV^2 } \mathord{\left/ {\vphantom {{23 GeV^2 } {c^2 }}} \right. \kern-0em} {c^2 }}} \right)}}\) using a charm semileptonic branching ratio of (10.9±1.4)% extracted from measurements ine ⁺ e ^? collisions and neutrino emulsion data.     

A new determination of the capture ratior_c = \frac{{\sum ^ - p \to \sum ^0 n}}{{(\sum ^ - p \to \sum ^0 n) + (\sum ^ - p \to \Lambda ^0 n)}}, the Λ0-lifetime and the ∑−-Λ0 mass difference

The two∑ ^? reactions at rest∑ ^? p→Λ ⁰ n and∑ ^? p→Λ ⁰ n have been studied in order to determine the capture ratio $$r_c = \frac{{\sum ^ - p \to \sum ^0 n}}{{(\sum ^ - p \to \sum ^0 n) + (\sum ^ - p \to \Lambda ^0 n)}}$$ , theΛ ⁰-lifetime and the∑ ^?-Λ ⁰ mass difference. The following results were obtained: $$\begin{gathered} rc = 0.474 \pm 0.016 \hfill \\ \tau _{\Lambda ^0 } = (2.47 \pm 0.08) \times 10^{ - 10} \sec \hfill \\ M_{\sum ^ - } - M_{\sum ^0 } = 81.64 \pm 0.09{{MeV} \mathord{\left/ {\vphantom {{MeV} {c^2 }}} \right. \kern-\nulldelimiterspace} {c^2 }} \hfill \\ \end{gathered} $$ The∑ ^?-mass was determined from the range of the stopping∑ ^?-hyperons,M _∑} =1197.19±0.32 MeV/c ².