Strong decay of $$\Lambda _c(2940)$$ as a 2 P state in the $$\Lambda _c$$Λc family

Considering the mass, parity and \(D^0 p\) decay mode, we tentatively assign the \(\Lambda _c(2940)\) as the \(P-\)wave states with one radial excitation. Then, via studying the strong decay behavior of the \(\Lambda _c(2940)\) within the \(^3P_0\) model, we obtain that the total decay widths of the \(\Lambda _{c1}(\frac{1}{2}^-,2P)\) and \(\Lambda _{c1}(\frac{3}{2}^-,2P)\) states are 16.27 and 25.39 MeV, respectively. Compared with the experimental total width \(27.7^{+8.2}_{-6.0}\pm 0.9^{+5.2}_{-10.4}~\mathrm {MeV}\) measured by LHCb Collaboration, both assignments are allowed, and the \(J^P=\frac{3}{2}^-\) assignment is more favorable. Other \(\lambda \)-mode \(\Sigma _c(2P)\) states are also investigated, which are most likely to be narrow states and have good potential to be observed in future experiments.     

Uncertainties of the $$B\rightarrow D$$B→ D transition form factor from the D-meson leading-twist distribution amplitude

The \(B\rightarrow D\) transition form factor (TFF) \(f^{B\rightarrow D}_+(q^2)\) is determined mainly by the D-meson leading-twist distribution amplitude (DA) , \(\phi _{2;D}\), if the proper chiral current correlation function is adopted within the light-cone QCD sum rules. It is therefore significant to make a comprehensive study of DA \(\phi _{2;D}\) and its impact on \(f^{B\rightarrow D}_+(q^2)\). In this paper, we calculate the moments of \(\phi _{2;D}\) with the QCD sum rules under the framework of the background field theory. New sum rules for the leading-twist DA moments \(\left\langle \xi ^n\right\rangle _D\) up to fourth order and up to dimension-six condensates are presented. At the scale \(\mu = 2 \,\mathrm{GeV}\), the values of the first four moments are: \(\left\langle \xi ^1\right\rangle _D = -0.418^{+0.021}_{-0.022}\), \(\left\langle \xi ^2\right\rangle _D = 0.289^{+0.023}_{-0.022}\), \(\left\langle \xi ^3\right\rangle _D = -0.178 \pm 0.010\) and \(\left\langle \xi ^4\right\rangle _D = 0.142^{+0.013}_{-0.012}\). Basing on the values of \(\left\langle \xi ^n\right\rangle _D(n=1,2,3,4)\), a better model of \(\phi _{2;D}\) is constructed. Applying this model for the TFF \(f^{B\rightarrow D}_+(q^2)\) under the light cone sum rules, we obtain \(f^{B\rightarrow D}_+(0) = 0.673^{+0.038}_{-0.041}\) and \(f^{B\rightarrow D}_+(q^2_{\mathrm{max}}) = 1.117^{+0.051}_{-0.054}\). The uncertainty of \(f^{B\rightarrow D}_+(q^2)\) from \(\phi _{2;D}\) is estimated and we find its impact should be taken into account, especially in low and central energy region. The branching ratio \(\mathcal {B}(B\rightarrow Dl\bar{\nu }_l)\) is calculated, which is consistent with experimental data.     

The decays of $$\bar{B}^0$$, $$\bar{B}^0_s$$B¯s0 and $$B^-$$B- into $$\eta _c$$ηc plus a scalar or vector meson

We investigate the decays of \(\bar{B}^0_s\), \(\bar{B}^0\) and \(B^-\) into \(\eta _c\) plus a scalar or vector meson in a theoretical framework by taking into account the dominant process for the weak decay of \(\bar{B}\) meson into \(\eta _c\) and a \(q\bar{q}\) pair. After hadronization of this \(q\bar{q}\) component into pairs of pseudoscalar mesons we obtain certain weights for the pseudoscalar meson-pseudoscalar meson components. In addition, the \(\bar{B}^0\) and \(\bar{B}^0_s\) decays into \(\eta _c\) and \(\rho ^0\), \(K^*\) are evaluated and compared to the \(\eta _c\) and \(\phi \) production. The calculation is based on the postulation that the scalar mesons \(f_0(500)\), \(f_0(980)\) and \(a_0(980)\) are dynamically generated states from the pseudoscalar meson-pseudoscalar meson interactions in S-wave. Up to a global normalization factor, the \(\pi \pi \), \(K \bar{K}\) and \(\pi \eta \) invariant mass distributions for the decays of \(\bar{B}^0_s \rightarrow \eta _c \pi ^+ \pi ^-\), \(\bar{B}^0_s \rightarrow \eta _c K^+ K^-\), \(\bar{B}^0 \rightarrow \eta _c \pi ^+ \pi ^-\), \(\bar{B}^0 \rightarrow \eta _c K^+ K^-\), \(\bar{B}^0 \rightarrow \eta _c \pi ^0 \eta \), \(B^- \rightarrow \eta _c K^0 K^-\) and \(B^- \rightarrow \eta _c \pi ^- \eta \) are predicted. Comparison is made with the limited experimental information available and other theoretical calcualtions. Further comparison of these results with coming LHCb measurements will be very valuable to make progress in our understanding of the nature of the low lying scalar mesons, \(f_0(500), f_0(980)\) and \(a_0(980)\).     

$$\varvec{B^0\rightarrow K^{*0}\mu ^+\mu ^-}$$ decay in the aligned two-Higgs-doublet model

In the aligned two-Higgs-doublet model, we perform a complete one-loop computation of the short-distance Wilson coefficients \(C_{7,9,10}^{(\prime )}\), which are the most relevant ones for \(b\rightarrow s\ell ^+\ell ^-\) transitions. It is found that, when the model parameter \(\left| \varsigma _{u}\right| \) is much smaller than \(\left| \varsigma _{d}\right| \), the charged scalar contributes mainly to chirality-flipped \(C_{9,10}^\prime \), with the corresponding effects being proportional to \(\left| \varsigma _{d}\right| ^2\). Numerically, the charged-scalar effects fit into two categories: (A) \(C_{7,9,10}^\mathrm {H^\pm }\) are sizable, but \(C_{9,10}^{\prime \mathrm {H^\pm }}\simeq 0\), corresponding to the (large \(\left| \varsigma _{u}\right| \), small \(\left| \varsigma _{d}\right| \)) region; (B) \(C_7^\mathrm {H^\pm }\) and \(C_{9,10}^{\prime \mathrm {H^\pm }}\) are sizable, but \(C_{9,10}^\mathrm {H^\pm }\simeq 0\), corresponding to the (small \(\left| \varsigma _{u}\right| \), large \(\left| \varsigma _{d}\right| \)) region. Taking into account phenomenological constraints from the inclusive radiative decay \(B\rightarrow X_{s}{\gamma }\), as well as the latest model-independent global analysis of \(b\rightarrow s\ell ^+\ell ^-\) data, we obtain the much restricted parameter space of the model. We then study the impact of the allowed model parameters on the angular observables \(P_2\) and \(P_5'\) of \(B^0\rightarrow K^{*0}\mu ^+\mu ^-\) decay, and we find that \(P_5'\) could be increased significantly to be consistent with the experimental data in case B.     

On quantum analogue of dynamical stabilisation of inverted harmonic oscillator by time periodical uniform field

Quantum analogue of stabilised forced oscillations around an unstable equilibrium position is explored by solving the non-stationary Schrödinger equation (NSE) of the inverted harmonic oscillator (IHO) driven periodically by spatial uniform field of frequency \(\Omega \), amplitude \(F_{0}\) and phase \(\phi \), i.e. the system with the Hamiltonian of \(\hat{{H}}=(\hat{{p}}^{2}/2m)-(m\omega ^{2}x^{2}/2)-F_0 x\sin \) \(\left( {\Omega t+\phi } \right) \). The NSE has been solved both analytically and numerically by Maple 15 in dimensionless variables \(\xi = x\sqrt{m\omega /\hbar }\hbox {, }f_0 =F_0 /\omega \sqrt{\hbar m\omega }\) and \(\tau =\omega t\). The initial condition (IC) has been specified by the wave function (w.f.) of a generalised Gaussian type which suits well the corresponding quantum IC operator. The solution obtained demonstrates the non-monotonous behaviour of the coordinate spreading \(\sigma \left( \tau \right) \hbox { =}\sqrt{\big ( {\overline{\Delta \xi ^{2}\big ( \tau \big )} } \big )}\) which decreases first from quite macroscopic values of \(\sigma _{0} =2^{12,\ldots ,25}\) to minimal one of \(\sim \!(1/\sqrt{2})\) at times \(\tau <\tau _0 =0.125\ln \!\left( {16\sigma _0^4 +1} \right) \) and then grows back unlimitedly. For certain phases \(\phi \) depending on the \(\Omega /\omega \) ratio and \(n=\log _2\!\sigma _0 \), the mass centre of the packet \(\xi _{\mathrm {av}}( \tau )= \overline{\hat{{x}}(\tau )} \cdot \sqrt{m\omega /\hbar }\) delays approximately two natural ‘periods’ \(\sim \!(4\pi /\omega )\) in the area of the stationary point and then escapes to ‘\(+\)’ or ‘?’ infinity in a bifurcating way.  For ‘resonant’ \(\Omega =\omega \), the bifurcation phases \(\phi \) fit well with the regression formula of Fermi–Dirac type of argument n with their asymptotic \(\phi ( {\Omega ,n\rightarrow \infty } )\) obeying the classical formula \(\phi _{\mathrm {cl}} ( \Omega )=-\hbox {arctg} \, \Omega \) for initial energy \(E = 0\) in the wide range of \(\Omega =2^{-4},...,2^{7}\).     

On Blow-up Profile of Ground States of Boson Stars with External Potential

We study minimizers of the pseudo-relativistic Hartree functional \({\mathcal {E}}_{a}(u):=\Vert (-\varDelta +m^{2})^{1/4}u\Vert _{L^{2}}^{2}+\int _{{\mathbb {R}}^{3}}V(x)|u(x)|^{2}\mathrm{d}x-\frac{a}{2}\int _{{\mathbb {R}}^{3}}(\left| \cdot \right| ^{-1}\star |u|^{2})(x)|u(x)|^{2}\mathrm{d}x\) under the mass constraint \(\int _{{\mathbb {R}}^3}|u(x)|^2\mathrm{d}x=1\). Here \(m>0\) is the mass of particles and \(V\ge 0\) is an external potential. We prove that minimizers exist if and only if a satisfies \(0\le a<a^{*}\), and there is no minimizer if \(a\ge a^*\), where \(a^*\) is called the Chandrasekhar limit. When a approaches \(a^*\) from below, the blow-up behavior of minimizers is derived under some general external potentials V. Here we consider three cases of V: trapping potential, i.e. \(V\in L_{\mathrm{loc}}^{\infty }({\mathbb {R}}^3)\) satisfies \(\lim _{|x|\rightarrow \infty }V(x)=\infty \); periodic potential, i.e. \(V\in C({\mathbb {R}}^3)\) satisfies \(V(x+z)=V(x)\) for all \(z\in \mathbb {Z}^3\); and ring-shaped potential, e.g. \( V(x)=||x|-1|^p\) for some \(p>0\).     

Gluino reach and mass extraction at the LHC in radiatively-driven natural SUSY

Radiatively-driven natural SUSY (RNS) models enjoy electroweak naturalness at the 10% level while respecting LHC sparticle and Higgs mass constraints. Gluino and top-squark masses can range up to several TeV (with other squarks even heavier) but a set of light Higgsinos are required with mass not too far above \(m_h\sim 125\) GeV. Within the RNS framework, gluinos dominantly decay via \(\tilde{g}\rightarrow t\tilde{t}_1^{*},\ \bar{t}\tilde{t}_1 \rightarrow t\bar{t}\widetilde{Z}_{1,2}\) or \(t\bar{b}\widetilde{W}_1^-+c.c.\), where the decay products of the higgsino-like \(\widetilde{W}_1\) and \(\widetilde{Z}_2\) are very soft. Gluino pair production is, therefore, signaled by events with up to four hard b-jets and large \(\not \!\!{E_T}\). We devise a set of cuts to isolate a relatively pure gluino sample at the (high-luminosity) LHC and show that in the RNS model with very heavy squarks, the gluino signal will be accessible for \(m_{\tilde{g}} < 2400 \ (2800)\) GeV for an integrated luminosity of 300 (3000) fb\(^{-1}\). We also show that the measurement of the rate of gluino events in the clean sample mentioned above allows for a determination of \(m_{\tilde{g}}\) with a statistical precision of 2–5% (depending on the integrated luminosity and the gluino mass) over the range of gluino masses where a 5\(\sigma \) discovery is possible at the LHC.     

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.     

Likelihood analysis of the minimal AMSB model

We perform a likelihood analysis of the minimal anomaly-mediated supersymmetry-breaking (mAMSB) model using constraints from cosmology and accelerator experiments. We find that either a wino-like or a Higgsino-like neutralino LSP, \(\tilde{\chi }^0_{1}\), may provide the cold dark matter (DM), both with similar likelihoods. The upper limit on the DM density from Planck and other experiments enforces \(m_{\tilde{\chi }^0_{1}} \lesssim 3 \,\, \mathrm {TeV}\) after the inclusion of Sommerfeld enhancement in its annihilations. If most of the cold DM density is provided by the \(\tilde{\chi }^0_{1}\), the measured value of the Higgs mass favours a limited range of \(\tan \beta \sim 5\) (and also for \(\tan \beta \sim 45\) if \(\mu > 0\)) but the scalar mass \(m_0\) is poorly constrained. In the wino-LSP case, \(m_{3/2}\) is constrained to about \(900\,\, \mathrm {TeV}\) and \(m_{\tilde{\chi }^0_{1}}\) to \(2.9\pm 0.1\,\, \mathrm {TeV}\), whereas in the Higgsino-LSP case \(m_{3/2}\) has just a lower limit \(\gtrsim 650\,\, \mathrm {TeV}\) (\(\gtrsim 480\,\, \mathrm {TeV}\)) and \(m_{\tilde{\chi }^0_{1}}\) is constrained to \(1.12 ~(1.13) \pm 0.02\,\, \mathrm {TeV}\) in the \(\mu >0\) (\(\mu <0\)) scenario. In neither case can the anomalous magnetic moment of the muon, \((g-2)_\mu \), be improved significantly relative to its Standard Model (SM) value, nor do flavour measurements constrain the model significantly, and there are poor prospects for discovering supersymmetric particles at the LHC, though there are some prospects for direct DM detection. On the other hand, if the \(\tilde{\chi }^0_{1}\) contributes only a fraction of the cold DM density, future LHC Open image in new window -based searches for gluinos, squarks and heavier chargino and neutralino states as well as disappearing track searches in the wino-like LSP region will be relevant, and interference effects enable \(\mathrm{BR}(B_{s, d} \rightarrow \mu ^+\mu ^-)\) to agree with the data better than in the SM in the case of wino-like DM with \(\mu > 0\).     

Further studies on the exclusive productions of $$J/\psi +\chi _{cJ}$$ ($$J=0,1,2$$J=0,1,2) via $$e^+e^-$$e+e- annihilation at the B factories

By including the interference effect between the QCD and the QED diagrams, we carry out a complete analysis on the exclusive productions of \(e^+e^- \rightarrow J/\psi +\chi _{cJ}\) (\(J=0,1,2\)) at the B factories with \(\sqrt{s}=10.6\) GeV at the next-to-leading-order (NLO) level in \(\alpha _s\), within the nonrelativistic QCD framework. It is found that the \({\mathcal {O}} (\alpha ^3\alpha _s)\)-order terms that represent the tree-level interference are comparable with the usual NLO QCD corrections, especially for the \(\chi _{c1}\) and \(\chi _{c2}\) cases. To explore the effect of the higher-order terms, namely \({\mathcal {O}} (\alpha ^3\alpha _s^2)\), we perform the QCD corrections to these \({\mathcal {O}} (\alpha ^3\alpha _s)\)-order terms for the first time, which are found to be able to significantly influence the \({\mathcal {O}} (\alpha ^3\alpha _s)\)-order results. In particular, in the case of \(\chi _{c1}\) and \(\chi _{c2}\), the newly calculated \({\mathcal {O}} (\alpha ^3\alpha _s^2)\)-order terms can to a large extent counteract the \({\mathcal {O}} (\alpha ^3\alpha _s)\) contributions, evidently indicating the indispensability of the corrections. In addition, we find that, as the collision energy rises, the percentage of the interference effect in the total cross section will increase rapidly, especially for the \(\chi _{c1}\) case.     

Stochastic Averaging Principle for Spatial Birth-and-Death Evolutions in the Continuum

We study a spatial birth-and-death process on the phase space of locally finite configurations \({\varGamma }^+ \times {\varGamma }^-\) over \({\mathbb {R}}^d\). Dynamics is described by an non-equilibrium evolution of states obtained from the Fokker-Planck equation and associated with the Markov operator \(L^+(\gamma ^-) + \frac{1}{\varepsilon }L^-\), \(\varepsilon > 0\). Here \(L^-\) describes the environment process on \({\varGamma }^-\) and \(L^+(\gamma ^-)\) describes the system process on \({\varGamma }^+\), where \(\gamma ^-\) indicates that the corresponding birth-and-death rates depend on another locally finite configuration \(\gamma ^- \in {\varGamma }^-\). We prove that, for a certain class of birth-and-death rates, the corresponding Fokker-Planck equation is well-posed, i.e. there exists a unique evolution of states \(\mu _t^{\varepsilon }\) on \({\varGamma }^+ \times {\varGamma }^-\). Moreover, we give a sufficient condition such that the environment is ergodic with exponential rate. Let \(\mu _{\mathrm {inv}}\) be the invariant measure for the environment process on \({\varGamma }^-\). In the main part of this work we establish the stochastic averaging principle, i.e. we prove that the marginal of \(\mu _t^{\varepsilon }\) onto \({\varGamma }^+\) converges weakly to an evolution of states on \({\varGamma }^+\) associated with the averaged Markov birth-and-death operator \({\overline{L}} = \int _{{\varGamma }^-}L^+(\gamma ^-)d \mu _{\mathrm {inv}}(\gamma ^-)\).     

$$f_0(500)$$, $$f_0(980)$$f0(980), and $$a_0(980)$$a0(980) production in the $$\chi _{c1} \rightarrow \eta \pi ^+\pi ^-$$χc1→ηπ+π- reaction

We study the \(\chi _{c1} \rightarrow \eta \pi ^+ \pi ^-\) decay, paying attention to the production of \(f_0(500)\), \(f_0(980)\), and \(a_0(980)\) from the final state interaction of pairs of mesons that can lead to these three mesons in the final state, which is implemented using the chiral unitary approach. Very clean and strong signals are obtained for the \(a_0(980)\) excitation in the \(\eta \pi \) invariant mass distribution and for the \(f_0(500)\) in the \(\pi ^+ \pi ^-\) mass distribution. A smaller, but also clear signal for the \(f_0(980)\) excitation is obtained. The results are contrasted with experimental data and the agreement found is good, providing yet one more test in support of the picture where these resonances are dynamically generated from the meson–meson interaction.     

Likelihood analysis of the pMSSM11 in light of LHC 13-TeV data

We use MasterCode to perform a frequentist analysis of the constraints on a phenomenological MSSM model with 11 parameters, the pMSSM11, including constraints from \(\sim 36\)/fb of LHC data at 13 TeV and PICO, XENON1T and PandaX-II searches for dark matter scattering, as well as previous accelerator and astrophysical measurements, presenting fits both with and without the \((g-2)_\mu \) constraint. The pMSSM11 is specified by the following parameters: 3 gaugino masses \(M_{1,2,3}\), a common mass for the first-and second-generation squarks \(m_{\tilde{q}}\) and a distinct third-generation squark mass \(m_{\tilde{q}_3}\), a common mass for the first-and second-generation sleptons \(m_{\tilde{\ell }}\) and a distinct third-generation slepton mass \(m_{\tilde{\tau }}\), a common trilinear mixing parameter A, the Higgs mixing parameter \(\mu \), the pseudoscalar Higgs mass \(M_A\) and \(\tan \beta \). In the fit including \((g-2)_\mu \), a Bino-like \(\tilde{\chi }^0_{1}\) is preferred, whereas a Higgsino-like \(\tilde{\chi }^0_{1}\) is mildly favoured when the \((g-2)_\mu \) constraint is dropped. We identify the mechanisms that operate in different regions of the pMSSM11 parameter space to bring the relic density of the lightest neutralino, \(\tilde{\chi }^0_{1}\), into the range indicated by cosmological data. In the fit including \((g-2)_\mu \), coannihilations with \(\tilde{\chi }^0_{2}\) and the Wino-like \(\tilde{\chi }^\pm _{1}\) or with nearly-degenerate first- and second-generation sleptons are active, whereas coannihilations with the \(\tilde{\chi }^0_{2}\) and the Higgsino-like \(\tilde{\chi }^\pm _{1}\) or with first- and second-generation squarks may be important when the \((g-2)_\mu \) constraint is dropped. In the two cases, we present \(\chi ^2\) functions in two-dimensional mass planes as well as their one-dimensional profile projections and best-fit spectra. Prospects remain for discovering strongly-interacting sparticles at the LHC, in both the scenarios with and without the \((g-2)_\mu \) constraint, as well as for discovering electroweakly-interacting sparticles at a future linear \(e^+ e^-\) collider such as the ILC or CLIC.     

The Quest for the Ultimate Anisotropic Banach Space

We present a new scale \(\mathcal {U}^{t,s}_p\) (\(s<-t<0\) and \(1\le p <\infty \)) of anisotropic Banach spaces, defined via Paley–Littlewood, on which the transfer operator \(\mathcal {L}_g \varphi = (g \cdot \varphi ) \circ T^{-1}\) associated to a hyperbolic dynamical system T has good spectral properties. When \(p=1\) and t is an integer, the spaces are analogous to the “geometric” spaces \(\mathcal {B}^{t,|s+t|}\) considered by Gouëzel and Liverani (Ergod Theory Dyn Syst 26:189–217, 2006). When \(p>1\) and \(-1+1/p<s<-t<0<t<1/p\), the spaces are somewhat analogous to the geometric spaces considered by Demers and Liverani (Trans Am Math Soc 360:4777–4814, 2008). In addition, just like for the “microlocal” spaces defined by Baladi and Tsujii (Ann Inst Fourier 57:127–154, 2007) (or Faure–Roy–Sjöstrand in Open Math J 1:35–81, 2008), the transfer operator acting on \(\mathcal {U}^{t,s}_p\) can be decomposed into \(\mathcal {L}_{g,b}+\mathcal {L}_{g,c}\), where \(\mathcal {L}_{g,b}\) has a controlled norm while a suitable power of \(\mathcal {L}_{g,c}\) is nuclear. This “nuclear power decomposition” enhances the Lasota–Yorke bounds and makes the spaces \(\mathcal {U}^{t,s}_p\) amenable to the kneading approach of Milnor–Thurson (Dynamical Systems (Maryland 1986–1987), Springer, Berlin, 1988) (as revisited by Baladi–Ruelle, Baladi in Dynamical Zeta Functions and Dynamical Determinants for Hyperbolic Maps, Monograph, 2016; Baladi and Ruelle in Ergod Theory Dyn Syst 14:621–632, 1994; Baladi and Ruelle in Invent Math 123:553–574, 1996) to study dynamical determinants and zeta functions.     

Spin density matrix of the $$\omega $$ in the reaction $${\bar{p}p}\,\rightarrow \,\omega \pi ^0$$p¯p→π0

The spin density matrix of the \(\omega \) has been determined for the reaction \({\bar{p}p}\,\rightarrow \,\omega \pi ^0\) with unpolarized in-flight data measured by the Crystal Barrel LEAR experiment at CERN. The two main decay modes of the \(\omega \) into \(\pi ^0 \gamma \) and \(\pi ^+ \pi ^- \pi ^0\) have been separately analyzed for various \({\bar{p}}\)momenta between 600 and 1940 MeV/c. The results obtained with the usual method by extracting the matrix elements via the \(\omega \) decay angular distributions and with the more sophisticated method via a full partial wave analysis are in good agreement. A strong spin alignment of the \(\omega \) is clearly visible in this energy regime and all individual spin density matrix elements exhibit an oscillatory dependence on the production angle. In addition, the largest contributing orbital angular momentum of the \({\bar{p}p~}\)system has been identified for the different beam momenta. It increases from \(L^{max}_{{\bar{p}p~}}\) \(=\) 2 at 600 MeV/c to \(L^{max}_{{\bar{p}p~}}\) \(=\) 5 at 1940 MeV/c.     

Two Higgs doublet models and $$b\rightarrow s$$ exclusive decays

We computed the leading order Wilson coefficients relevant to all the exclusive \(b\rightarrow s\ell ^+\ell ^-\) decays in the framework of the two Higgs doublet model (2HDM) with a softly broken \(\mathbb {Z}_2\) symmetry by including the \(\mathcal {O}(m_b)\) corrections. We elucidate the issue of appropriate matching between the full and the effective theory when dealing with the (pseudo-)scalar operators for which keeping the external momenta different from zero is necessary. We then make a phenomenological analysis by using the measured \({\mathcal {B}}(B_s\rightarrow \mu ^+\mu ^-)\) and \({\mathcal {B}}(B\rightarrow K \mu ^+\mu ^-)_{\mathrm {high}-q^2}\), for which the hadronic uncertainties are well controlled, and we discuss their impact on various types of 2HDM. A brief discussion of the decays with \(\tau \)-leptons in the final state is provided too.     

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).     

A Theory of Hydrodynamic Turbulence Based on Non-equilibrium Statistical Mechanics

In earlier papers, we have studied the turbulent flow exponents \(\zeta _p\), where \(\langle |\Delta \mathbf{v}|^p\rangle \sim \ell ^{\zeta _p}\) and \(\Delta \mathbf{v}\) is the contribution to the fluid velocity at small scale \(\ell \). Using ideas of non-equilibrium statistical mechanics we have found

$$\begin{aligned} \zeta _p={p\over 3}-{1\over \ln \kappa }\ln \Gamma \left( {p\over 3}+1\right) \end{aligned}$$

where \(1/\ln \kappa \) is experimentally \(\approx \,0.32\,\pm \,0.01\). The purpose of the present note is to propose a somewhat more physical derivation of the formula for \(\zeta _p\). We also present an estimate \(\approx \,100\) for the Reynolds number at the onset of turbulence.

     

Isospin analysis of charmless <Emphasis Type="Italic">B</Emphasis>-meson decays

We discuss the determination of the CKM angle \(\alpha \) using the non-leptonic two-body decays \(B\rightarrow \pi \pi \), \(B\rightarrow \rho \rho \) and \(B\rightarrow \rho \pi \) using the latest data available. We illustrate the methods used in each case and extract the corresponding value of \(\alpha \). Combining all these elements, we obtain the determination \(\alpha _\mathrm{dir}={({86.2}_{-4.0}^{+4.4} \cup {178.4}_{-5.1}^{+3.9})}^{\circ }\). We assess the uncertainties associated to the breakdown of the isospin hypothesis and the choice of the statistical framework in detail. We also determine the hadronic amplitudes (tree and penguin) describing the QCD dynamics involved in these decays, briefly comparing our results with theoretical expectations. For each observable of interest in the \(B\rightarrow \pi \pi \), \(B\rightarrow \rho \rho \) and \(B\rightarrow \rho \pi \) systems, we perform an indirect determination based on the constraints from all the other observables available and we discuss the compatibility between indirect and direct determinations. Finally, we review the impact of future improved measurements on the determination of \(\alpha \).