Mathematical Simulations of Deformation for the Rotation Shells with Variable Wall Thickness

Well-posed boundary value problems are constructed for calculating rotation shells of with a stiffness variable along the meridian in two directions, and also with variable bilateral with respect to the reference surface with the shell wall thickness. Algorithms for the numerical integration of systems of differential equations with variable coefficients are discussed.Well-posed boundary value problems are constructed for calculating rotation shells of with a stiffness variable along the meridian in two directions, and also with variable bilateral with respect to the reference surface with the shell wall thickness. Algorithms for the numerical integration of systems of differential equations with variable coefficients are discussed

Prospects of introducing microgrids in Russian industry

Improving energy efficiency keeps on being one of the most pressing problems for Russian industry. The paper aims to examine the prospects of using microgrids in Russian regions, including in the old industrial ones, to reduce energy costs of industrial enterprises. The methodological basis of the study comprises theoretical aspects of pricing within the models of retail and wholesale energy markets, tenets of uneven demand for energy under the use of microgrids. The authors apply analysis, synthesis, systematisation and statistical observation, create matrices and positioning maps and explore the parameters of energy consumption schedules at industrial enterprises of various types as well as the values of ‘common pot’ electricity transmission tariffs introduced in the subjects of the Russian Federation. The researchers develop own system of indicators for assessing the variability in the cost of electricity transmission services and present a map of Russian regions that illustrate the prospects of using microgrids and mechanisms of demand management in industrially developed regions with a view to cutting energy costs

Search for the rare hadronic decay Bs0→ppˉB_s^0\to p \bar{p}

A search for the rare hadronic decay Bs0→pp¯ is performed using proton-proton collision data recorded by the LHCb experiment at a center-of-mass energy of 13 TeV, corresponding to an integrated luminosity of 6  fb-1. No evidence of the decay is found and an upper limit on its branching fraction is set at B(Bs0→pp¯)&lt;4.4(5.1)×10-9 at 90% (95%) confidence level; this is currently the world’s best upper limit. The decay mode B0→pp¯ is measured with very large significance, confirming the first observation by the LHCb experiment in 2017. The branching fraction is determined to be B(B0→pp¯)=(1.27±0.15±0.05±0.04)×10-8, where the first uncertainty is statistical, the second is systematic and the third is due to the external branching fraction of the normalization channel B0→K+π-. The combination of the two LHCb measurements of the B0→pp¯ branching fraction yields B(B0→pp¯)=(1.27±0.13±0.05±0.03)×10-8.A search for the rare hadronic decay $B_s^0\to p \bar{p}$ is performed using proton-proton collision data recorded by the LHCb experiment at a center-of-mass energy of 13 TeV, corresponding to an integrated luminosity of 6 fb$^{-1}$. No evidence of the decay is found and an upper limit on its branching fraction is set at ${\cal B}(B_s^0\to p \bar{p}) < 4.4~(5.1) \times 10^{-9}$ at 90% (95%) confidence level; this is currently the world's best upper limit. The decay mode $B^0\to p \bar{p}$ is measured with very large significance, confirming the first observation by the LHCb experiment in 2017. The branching fraction is determined to be ${\cal B}(B^0\to p \bar{p}) = \rm (1.27 \pm 0.15 \pm 0.05 \pm 0.04) \times 10^{-8}$, where the first uncertainty is statistical, the second is systematic and the third is due to the external branching fraction of the normalization channel $B^0\to K^+\pi^-$. The combination of the two LHCb measurements of the $B^0\to p \bar{p}$ branching fraction yields ${\cal B}(B^0\to p \bar{p}) = \rm (1.27 \pm 0.13 \pm 0.05 \pm 0.03) \times 10^{-8}$

Amplitude analysis of the Λc+→pK−π+\Lambda^+_c\to pK^-\pi^+ decay and Λc+\Lambda^+_c baryon polarization measurement in semileptonic beauty hadron decays

An amplitude analysis of $\Lambda^+_c \to pK^-\pi^+$ decays together with a measurement of the $\Lambda^+_c$ polarization vector in semileptonic beauty hadron decays is presented. A sample of $400\,000$ candidates is selected from proton-proton collisions recorded by the LHCb detector at a center-of-mass energy of 13 TeV. An amplitude model is developed and the resonance fractions as well as two- and three-body decay parameters are reported. The mass and width of the $\Lambda(2000)$ state are also determined. A significant $\Lambda^+_c$ polarization is found. A large sensitivity of the $\Lambda^+_c \to pK^-\pi^+$ decay to the polarization is seen, making the amplitude model suitable for $\Lambda^+_c$ polarization measurements in other systems.An amplitude analysis of Λc+→pK-π+ decays together with a measurement of the Λc+ polarization vector in semiōleptonic beauty hadron decays is presented. A sample of 400 000 candidates is selected from proton-proton collisions recorded by the LHCb detector at a center-of-mass energy of 13 TeV. An amplitude model is developed and the resonance fractions as well as two- and three-body decay parameters are reported. The mass and width of the Λ(2000) state are also determined. A significant Λc+ polarization is found. A large sensitivity of the Λc+→pK-π+ decay to the polarization is seen, making the amplitude model suitable for Λc+ polarization measurements in other systems.An amplitude analysis of $\Lambda^+_c \to pK^-\pi^+$ decays together with a measurement of the $\Lambda^+_c$ polarization vector in semileptonic beauty hadron decays is presented. A sample of $400\,000$ candidates is selected from proton-proton collisions recorded by the LHCb detector at a center-of-mass energy of 13 TeV. An amplitude model is developed and the resonance fractions as well as two- and three-body decay parameters are reported. The mass and width of the $\Lambda(2000)$ state are also determined. A significant $\Lambda^+_c$ polarization is found. A large sensitivity of the $\Lambda^+_c \to pK^-\pi^+$ decay to the polarization is seen, making the amplitude model suitable for $\Lambda^+_c$ polarization measurements in other systems

Search for CPCP violation using T^\hat{T}-odd correlations in B0→ppˉK+π−B^{0} \to p \bar p K^{+} \pi^{-} decays

A search for $CP$ and $P$ violation in charmless four-body $B^{0} \to p \bar p K^{+} \pi^{-}$ decays is performed using triple-product asymmetry observables. It is based on proton-proton collision data collected by the LHCb experiment at centre-of-mass energies of $7$, $8$ and $13$ TeV, corresponding to a total integrated luminosity of $8.4$ fb$^{-1}$. The $CP$- and $P$-violating asymmetries are measured both in the integrated phase space and in specific regions. No evidence is seen for $CP$ violation. $P$-parity violation is observed at a significance of 5.8 standard deviations.A search for CP and P violation in charmless four-body B0→pp¯K+π- decays is performed using triple-product asymmetry observables. It is based on proton-proton collision data collected by the LHCb experiment at center-of-mass energies of 7, 8 and 13 TeV, corresponding to a total integrated luminosity of 8.4  fb-1. The CP- and P-violating asymmetries are measured both in the integrated phase space and in specific regions. No evidence is seen for CP violation. P-parity violation is observed at a significance of 5.8 standard deviations.A search for $CP$ and $P$ violation in charmless four-body $B^{0} \to p \bar p K^{+} \pi^{-}$ decays is performed using triple-product asymmetry observables. It is based on proton-proton collision data collected by the LHCb experiment at centre-of-mass energies of $7$, $8$ and $13$ TeV, corresponding to a total integrated luminosity of $8.4$ fb$^{-1}$. The $CP$- and $P$-violating asymmetries are measured both in the integrated phase space and in specific regions. No evidence is seen for $CP$ violation. $P$-parity violation is observed at a significance of 5.8 standard deviation

Search for the doubly heavy baryon Ξbc+\it{\Xi}_{bc}^{+} decaying to J/ψΞc+J/\it{\psi} \it{\Xi}_{c}^{+}

A first search for the decay is performed by the LHCb experiment with a data sample of proton-proton collisions, corresponding to an integrated luminosity of 9 fb$^{−1}$ recorded at centre-of-mass energies of 7, 8, and 13 TeV. Two peaking structures are seen with a local (global) significance of and standard deviations at masses of 6571 and 6694 MeV/, respectively. Upper limits are set on the baryon production cross-section times the branching fraction relative to that of the decay at centre-of-mass energies of 8 and 13 TeV, in the and in the rapidity and transverse-momentum ranges from 2.0 to 4.5 and 0 to , respectively. Upper limits are presented as a function of the mass and lifetime.A first search for the $\it{\Xi}_{bc}^{+}\to J/\it{\psi}\it{\Xi}_{c}^{+}$ decay is performed by the LHCb experiment with a data sample of proton-proton collisions, corresponding to an integrated luminosity of $9\,\mathrm{fb}^{-1}$ recorded at centre-of-mass energies of 7, 8, and $13\mathrm{\,Te\kern -0.1em V}$. Two peaking structures are seen with a local (global) significance of $4.3\,(2.8)$ and $4.1\,(2.4)$ standard deviations at masses of $6571\,\mathrm{Me\kern -0.1em V\!/}c^2$ and $6694\,\mathrm{Me\kern -0.1em V\!/}c^2$, respectively. Upper limits are set on the $\it{\Xi}_{bc}^{+}$ baryon production cross-section times the branching fraction relative to that of the $B_{c}^{+}\to J/\it{\psi} D_{s}^{+}$ decay at centre-of-mass energies of 8 and $13\mathrm{\,Te\kern -0.1em V}$, in the $\it{\Xi}_{bc}^{+}$ and in the $B_{c}^{+}$ rapidity and transverse-momentum ranges from 2.0 to 4.5 and 0 to $20\,\mathrm{Ge\kern -0.1em V\!/}c$, respectively. Upper limits are presented as a function of the $\it{\Xi}_{bc}^{+}$ mass and lifetime

Search for the lepton-flavour violating decays B0→K∗0μ±e∓B^0 \to K^{*0} \mu^\pm e^\mp and Bs0→ϕμ±e∓B_s^0 \to \phi \mu^\pm e^\mp

A search for the lepton-flavour violating decays $B^0 \to K^{*0} \mu^\pm e^\mp$ and $B_s^0 \to \phi \mu^\pm e^\mp$ is presented, using proton-proton collision data collected by the LHCb detector at the LHC, corresponding to an integrated luminosity of $9\,\text{fb}^{-1}$. No significant signals are observed and upper limits of \begin{align} {\cal B}( B^0 \to K^{*0} \mu^+ e^- ) &< \phantom{1}5.7\times 10^{-9}~(6.9\times 10^{-9}),\newline {\cal B}( B^0 \to K^{*0} \mu^- e^+ ) &< \phantom{1}6.8\times 10^{-9}~(7.9\times 10^{-9}),\newline {\cal B}( B^0 \to K^{*0} \mu^\pm e^\mp ) &< 10.1\times 10^{-9}~(11.7\times 10^{-9}),\newline {\cal B}( B_s^0 \to \phi \mu^\pm e^\mp ) &< 16.0\times 10^{-9}~(19.8\times 10^{-9}) \end{align} are set at $90\%~(95\%)$ confidence level. These results constitute the world's most stringent limits to date, with the limit on the decay $B_s^0 \to \phi \mu^\pm e^\mp$ the first being set. In addition, limits are reported for scalar and left-handed lepton-flavour violating New Physics scenarios.A search for the lepton-flavour violating decays B$^{0}$ → K$^{*0}$μ$^{±}$e$^{∓}$ and ${B}_s^0$→ ϕμ$^{±}$e$^{∓}$ is presented, using proton-proton collision data collected by the LHCb detector at the LHC, corresponding to an integrated luminosity of 9 fb$^{−1}$. No significant signals are observed and upper limits of${\displaystyle \begin{array}{c}\mathcal{B}\left({B}^0\to {K}^{\ast 0}{\mu}^{+}{e}^{-}\right)<5.7\times {10}^{-9}\left(6.9\times {10}^{-9}\right),\\ {}\mathcal{B}\left({B}^0\to {K}^{\ast 0}{\mu}^{-}{e}^{+}\right)<6.8\times {10}^{-9}\left(7.9\times {10}^{-9}\right),\\ {}\mathcal{B}\left({B}^0\to {K}^{\ast 0}{\mu}^{\pm }{e}^{\mp}\right)<10.1\times {10}^{-9}\left(11.7\times {10}^{-9}\right),\\ {}\mathcal{B}\left({B}_s^0\to \phi {\mu}^{\pm }{e}^{\mp}\right)<16.0\times {10}^{-9}\left(19.8\times {10}^{-9}\right)\end{array}}$are set at 90% (95%) confidence level. These results constitute the world’s most stringent limits to date, with the limit on the decay ${B}_s^0$→ ϕμ$^{±}$e$^{∓}$ the first being set. In addition, limits are reported for scalar and left-handed lepton-flavour violating New Physics scenarios.[graphic not available: see fulltext]A search for the lepton-flavour violating decays $B^0 \to K^{*0} \mu^\pm e^\mp$ and $B_s^0 \to \phi \mu^\pm e^\mp$ is presented, using proton-proton collision data collected by the LHCb detector at the LHC, corresponding to an integrated luminosity of $9\,\text{fb}^{-1}$. No significant signals are observed and upper limits of \begin{align} {\cal B}( B^0 \to K^{*0} \mu^+ e^- ) &< \phantom{1}5.7\times 10^{-9}~(6.9\times 10^{-9}),\newline {\cal B}( B^0 \to K^{*0} \mu^- e^+ ) &< \phantom{1}6.8\times 10^{-9}~(7.9\times 10^{-9}),\newline {\cal B}( B^0 \to K^{*0} \mu^\pm e^\mp ) &< 10.1\times 10^{-9}~(11.7\times 10^{-9}),\newline {\cal B}( B_s^0 \to \phi \mu^\pm e^\mp ) &< 16.0\times 10^{-9}~(19.8\times 10^{-9}) \end{align} are set at $90\%~(95\%)$ confidence level. These results constitute the world's most stringent limits to date, with the limit on the decay $B_s^0 \to \phi \mu^\pm e^\mp$ the first being set. In addition, limits are reported for scalar and left-handed lepton-flavour violating New Physics scenarios

A study of C ⁣PC\!P violation in the decays B±→[K+K−π+π−]Dh±B^\pm\to[K^+K^-\pi^+\pi^-]_D h^{\pm} (h=K,πh = K, \pi) and B±→[π+π−π+π−]Dh±B^\pm\to[\pi^+\pi^-\pi^+\pi^-]_D h^{\pm}

The first study of $C\!P$ violation in the decay mode $B^\pm\to[K^+K^-\pi^+\pi^-]_D h^{\pm}$, with $h=K,\pi$, is presented, exploiting a data sample of proton-proton collisions collected by the LHCb experiment that corresponds to an integrated luminosity of $9$ fb$^{-1}$. The analysis is performed in bins of phase space, which are optimised for sensitivity to local $C\!P$ asymmetries. $C\!P$-violating observables that are sensitive to the angle $\gamma$ of the Unitarity Triangle are determined. The analysis requires external information on charm-decay parameters, which are currently taken from an amplitude analysis of LHCb data, but can be updated in the future when direct measurements become available. Measurements are also performed of phase-space integrated observables for $B^\pm\to[K^+K^-\pi^+\pi^-]_D h^{\pm}$ and $B^\pm\to[\pi^+\pi^-\pi^+\pi^-]_D h^{\pm}$ decays.The first study of $C\!P$ violation in the decay mode {{B} ^\pm } \rightarrow [{{K} ^+} {{K} ^-} {{\uppi } ^+} {{\uppi } ^-} ]_{D} h^\pm , with $h=K,\pi$, is presented, exploiting a data sample of proton–proton collisions collected by the LHCb experiment that corresponds to an integrated luminosity of $9\text {\,fb} ^{-1}$. The analysis is performed in bins of phase space, which are optimised for sensitivity to local $C\!P$ asymmetries. $C\!P$-violating observables that are sensitive to the angle $\gamma$ of the Unitarity Triangle are determined. The analysis requires external information on charm-decay parameters, which are currently taken from an amplitude analysis of LHCb data, but can be updated in the future when direct measurements become available. Measurements are also performed of phase-space integrated observables for {{B} ^\pm } \rightarrow [{{K} ^+} {{K} ^-} {{\uppi } ^+} {{\uppi } ^-} ]_{D} h^\pm and {{B} ^\pm } \rightarrow [{{\uppi } ^+} {{\uppi } ^-} {{\uppi } ^+} {{\uppi } ^-} ]_{D} h^\pm decays.The first study of $C\!P$ violation in the decay mode $B^\pm\to[K^+K^-\pi^+\pi^-]_D h^\pm$, with $h=K,\pi$, is presented, exploiting a data sample of proton-proton collisions collected by the LHCb experiment that corresponds to an integrated luminosity of $9$ fb$^{-1}$. The analysis is performed in bins of phase space, which are optimised for sensitivity to local $C\!P$ asymmetries. $C\!P$-violating observables that are sensitive to the angle $\gamma$ of the Unitarity Triangle are determined. The analysis requires external information on charm-decay parameters, which are currently taken from an amplitude analysis of LHCb data, but can be updated in the future when direct measurements become available. Measurements are also performed of phase-space integrated observables for $B^\pm\to[K^+K^-\pi^+\pi^-]_D h^\pm$ and $B^\pm\to[\pi^+\pi^-\pi^+\pi^-]_D h^\pm$ decays

Observation of the Bs0 ⁣→D∗+D∗−B^0_s\!\to D^{*+}D^{*-} decay

International audienceThe first observation of the ${B}_s^0$→ D$^{∗+}$D$^{∗−}$ decay and the measurement of its branching ratio relative to the B$^{0}$→ D$^{∗+}$D$^{∗−}$ decay are presented. The data sample used corresponds to an integrated luminosity of 9 fb$^{−1}$ of proton-proton collisions recorded by the LHCb experiment at centre-of-mass energies of 7, 8 and 13 TeV between 2011 and 2018. The decay is observed with more than 10 standard deviations and the time-integrated ratio of branching fractions is determined to be$\frac{\mathcal{B}\left({B}_s^0\to {D}^{\ast +}{D}^{\ast -}\right)}{\mathcal{B}\left({B}^0\to {D}^{\ast +}{D}^{\ast -}\right)}=0.269\pm 0.032\pm 0.011\pm 0.008,$where the first uncertainty is statistical, the second systematic and the third due to the uncertainty of the fragmentation fraction ratio f$_{s}$/f$_{d}$. The ${B}_s^0$→ D$^{*+}$D$^{*−}$ branching fraction is calculated to be$\mathcal{B}\left({B}_s^0\to {D}^{\ast +}{D}^{\ast -}\right)=\left(2.15\pm 0.26\pm 0.09\pm 0.06\pm 0.16\right)\times {10}^{-4},$where the fourth uncertainty is due to the B$^{0}$→ D$^{*+}$D$^{*−}$ branching fraction. These results are calculated using the average ${B}_s^0$ meson lifetime in simulation. Correction factors are reported for scenarios where either a purely heavy or a purely light ${B}_s^0$ eigenstate is considered.[graphic not available: see fulltext