Precision measurement of neutrino oscillation parameters at INO-ICAL detector

A magnetized Iron CALorimeter (ICAL) detector at the India-based neutrino observatory (INO) is used to study neutrino oscillation sensitivity using atmospheric muon neutrino source. The ICAL detector will be able to detect muon tracks and hadron showers produced by neutrino interactions with the iron target. We have performed precision measurement analysis for the atmospheric neutrino oscillation parameters with the muon neutrino events, generated by Monte Carlo NUANCE event generator. A marginalized χ² analysis based on reconstructed neutrino energy and muon zenith angle binning scheme has been performed to determine the sensitivity for the atmospheric neutrino mixing parameters, \(\sin ^{2}\theta _{23}\) and \(| {\Delta } m^{2}_{23}|\).     

Pinning down neutrino oscillation parameters in the 2–3 sector with a magnetised atmospheric neutrino detector: a new study

We determine the sensitivity to neutrino oscillation parameters from a study of atmospheric neutrinos in a magnetised detector such as the ICAL at the proposed India-based Neutrino Observatory. In such a detector, which can separately count \(\nu _\mu \) and \(\overline{\nu }_\mu \)-induced events, the relatively smaller (about 5%) uncertainties on the neutrino–antineutrino flux ratios translate to a constraint in the \(\chi ^2\) analysis that results in a significant improvement in the precision with which neutrino oscillation parameters such as \(\sin ^2\theta _{23}\) can be determined. Such an effect is unique to all magnetisable detectors and constitutes a great advantage in determining neutrino oscillation parameters using such detectors. Such a study has been performed for the first time here. Along with an increase in the kinematic range compared to earlier analyses, this results in sensitivities to oscillation parameters in the 2–3 sector that are comparable to or better than those from accelerator experiments where the fluxes are significantly higher. For example, the \(1\sigma \) precisions on \(\sin ^2\theta _{23}\) and \(|\Delta {m^2_{32(31)}}|\) achievable for 500 kton year exposure of ICAL are \({\sim }9\) and \({\sim }2.5\)%, respectively, for both normal and inverted hierarchies. The mass hierarchy sensitivity achievable with this combination when the true hierarchy is normal (inverted) for the same exposure is \(\Delta \chi ^2\approx 8.5\) (\(\Delta \chi ^2\approx 9.5\)).     

The effective neutrino mass of neutrinoless double-beta decays: how possible to fall into a well

The neutrinoless double-beta (\(0\nu 2\beta \)) decay is currently the only feasible process in particle and nuclear physics to probe whether massive neutrinos are the Majorana fermions. If they are of a Majorana nature and have a normal mass ordering, the effective neutrino mass term \(\langle m\rangle ^{}_{ee}\) of a \(0\nu 2\beta \) decay may suffer significant cancellations among its three components and thus sink into a decline, resulting in a “well” in the three-dimensional graph of \(|\langle m\rangle ^{}_{ee}|\) against the smallest neutrino mass \(m^{}_1\) and the relevant Majorana phase \(\rho \). We present a new and complete analytical understanding of the fine issues inside such a well, and identify a novel threshold of \(|\langle m\rangle ^{}_{ee}|\) in terms of the neutrino masses and flavor mixing angles: \(|\langle m\rangle ^{}_{ee}|^{}_* = m^{}_3 \sin ^2\theta ^{}_{13}\) in connection with \(\tan \theta ^{}_{12} = \sqrt{m^{}_1/m^{}_2}\) and \(\rho =\pi \). This threshold point, which links the local minimum and maximum of \(|\langle m\rangle ^{}_{ee}|\), can be used to signify observability or sensitivity of the future \(0\nu 2\beta \)-decay experiments. Given current neutrino oscillation data, the possibility of \(|\langle m\rangle ^{}_{ee}| < |\langle m\rangle ^{}_{ee}|^{}_*\) is found to be very small.     

CP violations in predictive neutrino mass structures

We study the CP-violation effects from two types of neutrino mass matrices with (i) \((M_\nu )_{ee}=0\), and (ii) \((M_\nu )_{ee}=(M_\nu )_{e\mu }=0\), which can be realized by the high-dimensional lepton number violating operators \(\bar{\ell }_R^c\gamma ^\mu L_L (D_\mu \Phi )\Phi ^2\) and \(\bar{\ell }_R^c l_R (D_\mu {\Phi })^2\Phi ^2\), respectively. In (i), the neutrino mass spectrum is in the normal ordering with the lightest neutrino mass within the range \(0.002\,\mathrm{eV}\lesssim m_0\lesssim 0.007\,\mathrm{eV}\). Furthermore, for a given value of \(m_0\), there are two solutions for the two Majorana phases \(\alpha _{21}\) and \(\alpha _{31}\), whereas the Dirac phase \(\delta \) is arbitrary. For (ii), the parameters of \(m_0\), \(\delta \), \(\alpha _{21}\), and \(\alpha _{31}\) can be completely determined. We calculate the CP-violating asymmetries in neutrino–antineutrino oscillations for both mass textures of (i) and (ii), which are closely related to the CP-violating Majorana phases.     

Fully constrained Majorana neutrino mass matrices using $$\varvec{\varSigma (72\times 3)}$$

In 2002, two neutrino mixing ansatze having trimaximally mixed middle (\(\nu _2\)) columns, namely tri-chi-maximal mixing (\(\text {T}\chi \text {M}\)) and tri-phi-maximal mixing (\(\text {T}\phi \text {M}\)), were proposed. In 2012, it was shown that \(\text {T}\chi \text {M}\) with \(\chi =\pm \,\frac{\pi }{16}\) as well as \(\text {T}\phi \text {M}\) with \(\phi = \pm \,\frac{\pi }{16}\) leads to the solution, \(\sin ^2 \theta _{13} = \frac{2}{3} \sin ^2 \frac{\pi }{16}\), consistent with the latest measurements of the reactor mixing angle, \(\theta _{13}\). To obtain \(\text {T}\chi \text {M}_{(\chi =\pm \,\frac{\pi }{16})}\) and \(\text {T}\phi \text {M}_{(\phi =\pm \,\frac{\pi }{16})}\), the type I see-saw framework with fully constrained Majorana neutrino mass matrices was utilised. These mass matrices also resulted in the neutrino mass ratios, \(m_1:m_2:m_3=\frac{\left( 2+\sqrt{2}\right) }{1+\sqrt{2(2+\sqrt{2})}}:1:\frac{\left( 2+\sqrt{2}\right) }{-1+\sqrt{2(2+\sqrt{2})}}\). In this paper we construct a flavour model based on the discrete group \(\varSigma (72\times 3)\) and obtain the aforementioned results. A Majorana neutrino mass matrix (a symmetric \(3\times 3\) matrix with six complex degrees of freedom) is conveniently mapped into a flavon field transforming as the complex six-dimensional representation of \(\varSigma (72\times 3)\). Specific vacuum alignments of the flavons are used to arrive at the desired mass matrices.     

On non-consensus motions of dynamical linear multiagent systems

The first-principle density functional theory (DFT) calculations were employed to investigate the electronic structures, magnetic properties and half-metallicity of \(\text {Ti}_{2}\text {IrZ}\) (Z \(=\) B, Al, Ga, and In) Heusler alloys with \(\text {AlCu}_{2}\text {Mn}\)- and \(\text {CuHg}_{2}\text {Ti}\)-type structures within local density approximation and generalised gradient approximation for the exchange correlation potential. It was found that \(\text {CuHg}_{2}\text {Ti}\)-type structure in ferromagnetic state was energetically more favourable than \(\text {AlCu}_{2}\text {Mn}\)-type structure in all compounds except \(\text {Ti}_{2}\text {IrB}\) which was stable in \(\text {AlCu}_{2}\text {Mn}\)-type structure in non-magnetic state. \(\text {Ti}_{2}\text {IrZ}\) (Z \(=\) B, Al, Ga, and In) alloys in \(\text {CuHg}_{2}\text {Ti}\)-type structure were half-metallic ferromagnets at their equilibrium lattice constants. Half-metallic band gaps were respectively equal to 0.87, 0.79, 0.75, and 0.73 eV for \(\text {Ti}_{2}\text {IrB}\), \(\text {Ti}_{2}\text {IrAl}\), \(\text {Ti}_{2}\text {IrGa}\), and \(\text {Ti}_{2}\text {IrIn}\). The origin of half-metallicity was discussed for \(\text {Ti}_{2}\text {IrGa}\) using the energy band structure. The total magnetic moments of \(\text {Ti}_{2}\text {IrZ}\) (Z \(=\) B, Al, Ga, and In) compounds in \(\text {CuHg}_{2}\text {Ti}\)-type structure were obtained as \(2\mu _{\mathrm{B}}\) per formula unit, which were in agreement with Slater–Pauling rule (\(M_{\mathrm{tot}} =Z_{\mathrm{tot}}-\)18). All the four compounds were half-metals in a wide range of lattice constants indicating that they may be suitable and promising materials for future spintronic applications.     

Modularity of logarithmic parafermion vertex algebras

The parafermionic cosets \(\mathsf {C}_{k} = {\text {Com}} ( \mathsf {H} , \mathsf {L}_{k}(\mathfrak {sl}_{2}) )\) are studied for negative admissible levels k, as are certain infinite-order simple current extensions \(\mathsf {B}_{k}\) of \(\mathsf {C}_{k}\). Under the assumption that the tensor theory considerations of Huang, Lepowsky and Zhang apply to \(\mathsf {C}_{k}\), irreducible \(\mathsf {C}_{k}\)- and \(\mathsf {B}_{k}\)-modules are obtained from those of \(\mathsf {L}_{k}(\mathfrak {sl}_{2})\). Assuming the validity of a certain Verlinde-type formula likewise gives the Grothendieck fusion rules of these irreducible modules. Notably, there are only finitely many irreducible \(\mathsf {B}_{k}\)-modules. The irreducible \(\mathsf {C}_{k}\)- and \(\mathsf {B}_{k}\)-characters are computed and the latter are shown, when supplemented by pseudotraces, to carry a finite-dimensional representation of the modular group. The natural conjecture then is that the \(\mathsf {B}_{k}\) are \(C_2\)-cofinite vertex operator algebras.     

Leptoquark mechanism of neutrino masses within the grand unification framework

We demonstrate the viability of the one-loop neutrino mass mechanism within the framework of grand unification when the loop particles comprise scalar leptoquarks (LQs) and quarks of the matching electric charge. This mechanism can be implemented in both supersymmetric and non-supersymmetric models and requires the presence of at least one LQ pair. The appropriate pairs for the neutrino mass generation via the up-type and down-type quark loops are \(S_3\)–\(R_2\) and \(S_{1,\,3}\)–\(\tilde{R}_2\), respectively. We consider two distinct regimes for the LQ masses in our analysis. The first regime calls for very heavy LQs in the loop. It can be naturally realized with the \(S_{1,\,3}\)–\(\tilde{R}_2\) scenarios when the LQ masses are roughly between \(10^{12}\) and \(5 \times 10^{13}\) GeV. These lower and upper bounds originate from experimental limits on partial proton decay lifetimes and perturbativity constraints, respectively. Second regime corresponds to the collider accessible LQs in the neutrino mass loop. That option is viable for the \(S_3\)–\(\tilde{R}_2\) scenario in the models of unification that we discuss. If one furthermore assumes the presence of the type II see-saw mechanism there is an additional contribution from the \(S_3\)–\(R_2\) scenario that needs to be taken into account beside the type II see-saw contribution itself. We provide a complete list of renormalizable operators that yield necessary mixing of all aforementioned LQ pairs using the language of SU(5). We furthermore discuss several possible embeddings of this mechanism in SU(5) and SO(10) gauge groups.     

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.     

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 \(p>0\).     

The Exoticness and Realisability of Twisted Haagerup–Izumi Modular Data

The quantum double of the Haagerup subfactor, the first irreducible finite depth subfactor with index above 4, is the most obvious candidate for exotic modular data. We show that its modular data \({\mathcal{D}{\rm Hg}}\) fits into a family \({\mathcal{D}^\omega {\rm Hg}_{2n+1}}\) , where n ≥  0 and \({\omega\in \mathbb{Z}_{2n+1}}\) . We show \({\mathcal{D}^0 {\rm Hg}_{2n+1}}\) is related to the subfactors Izumi hypothetically associates to the cyclic groups \({\mathbb{Z}_{2n+1}}\) . Their modular data comes equipped with canonical and dual canonical modular invariants; we compute the corresponding alpha-inductions, etc. In addition, we show there are (respectively) 1, 2, 0 subfactors of Izumi type \({\mathbb{Z}_7, \mathbb{Z}_9}\) and \({\mathbb{Z}_3^2}\) , and find numerical evidence for 2, 1, 1, 1, 2 subfactors of Izumi type \({\mathbb{Z}_{11},\mathbb{Z}_{13},\mathbb{Z}_{15},\mathbb{Z}_{17},\mathbb{Z}_{19}}\) (previously, Izumi had shown uniqueness for \({\mathbb{Z}_3}\) and \({\mathbb{Z}_5}\)), and we identify their modular data. We explain how \({\mathcal{D}{\rm Hg}}\) (more generally \({\mathcal{D}^\omega {\rm Hg}_{2n+1}}\)) is a graft of the quantum double \({\mathcal{D} Sym(3)}\) (resp. the twisted double \({\mathcal{D}^\omega D_{2n+1}}\)) by affine so(13) (resp. so\({(4n^2+4n+5)}\)) at level 2. We discuss the vertex operator algebra (or conformal field theory) realisation of the modular data \({\mathcal{D}^\omega {\rm Hg}_{2n+1}}\) . For example we show there are exactly 2 possible character vectors (giving graded dimensions of all modules) for the Haagerup VOA at central charge c = 8. It seems unlikely that any of this twisted Haagerup-Izumi modular data can be regarded as exotic, in any reasonable sense.     

Universal Probability Distribution for the Wave Function of a Quantum System Entangled with its Environment

A quantum system (with Hilbert space \({\mathcal {H}_{1}}\)) entangled with its environment (with Hilbert space \({\mathcal {H}_{2}}\)) is usually not attributed to a wave function but only to a reduced density matrix \({\rho_{1}}\). Nevertheless, there is a precise way of attributing to it a random wave function \({\psi_{1}}\), called its conditional wave function, whose probability distribution \({\mu_{1}}\) depends on the entangled wave function \({\psi \in \mathcal {H}_{1} \otimes \mathcal {H}_{2}}\) in the Hilbert space of system and environment together. It also depends on a choice of orthonormal basis of \({\mathcal {H}_{2}}\) but in relevant cases, as we show, not very much. We prove several universality (or typicality) results about \({\mu_{1}}\), e.g., that if the environment is sufficiently large then for every orthonormal basis of \({\mathcal {H}_{2}}\), most entangled states \({\psi}\) with given reduced density matrix \({\rho_{1}}\) are such that \({\mu_{1}}\) is close to one of the so-called GAP (Gaussian adjusted projected) measures, \({GAP(\rho_{1})}\). We also show that, for most entangled states \({\psi}\) from a microcanonical subspace (spanned by the eigenvectors of the Hamiltonian with energies in a narrow interval \({[E, E+ \delta E]}\)) and most orthonormal bases of \({\mathcal {H}_{2}}\), \({\mu_{1}}\) is close to \({GAP(\rm {tr}_{2} \rho_{mc})}\) with \({\rho_{mc}}\) the normalized projection to the microcanonical subspace. In particular, if the coupling between the system and the environment is weak, then \({\mu_{1}}\) is close to \({GAP(\rho_\beta)}\) with \({\rho_\beta}\) the canonical density matrix on \({\mathcal {H}_{1}}\) at inverse temperature \({\beta=\beta(E)}\). This provides the mathematical justification of our claim in Goldstein et al. (J Stat Phys 125: 1193–1221, 2006) that GAP measures describe the thermal equilibrium distribution of the wave function.     

Beyond antihydrogen: testing CPT with the molecular antihydrogen ion

Measurements of Zeeman, Zeeman-hyperfine and ro-vibrational transitions in \(\bar {H}_{2}^{-}(\bar {p}e^{+}\bar {p})\) compared to \(H_{2}^{+}\) have the potential for more precise tests of CPT than can be obtained from antiprotons and antihydrogen. In particular, measurements of ro-vibrational transitions have a potential sensitivity to a difference between antiproton and proton mass three orders of magnitude higher than antihydrogen/hydrogen. Methods are outlined for precision measurements on a single \(\bar {H}_{2}^{-}\) or \({H}_{2}^{+}\) ion in a cryogenic Penning trap, with non-destructive state identification using the continuous Stern-Gerlach effect or changes in mass. \(\bar {H}_{2}^{-}\) can be produced using the \(\bar {H}^{+}+\bar {p} \rightarrow \bar {H}_{2}^{-} + e^{+}\) reaction.     

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.     

Scaling Limit of Symmetric Random Walk in High-Contrast Periodic Environment

It is shown that the deterministic infinite trigonometric products

$$\begin{aligned} \prod _{n\in \mathbb {N}}\left[ 1- p +p\cos \left( \textstyle n^{-s}_{_{}}t\right) \right] =: {\text{ Cl }_{p;s}^{}}(t) \end{aligned}$$

with parameters \( p\in (0,1]\ \& \ s>\frac{1}{2}\), and variable \(t\in \mathbb {R}\), are inverse Fourier transforms of the probability distributions for certain random series \(\Omega _{p}^\zeta (s)\) taking values in the real \(\omega \) line; i.e. the \({\text{ Cl }_{p;s}^{}}(t)\) are characteristic functions of the \(\Omega _{p}^\zeta (s)\). The special case \(p=1=s\) yields the familiar random harmonic series, while in general \(\Omega _{p}^\zeta (s)\) is a “random Riemann-\(\zeta \) function,” a notion which will be explained and illustrated—and connected to the Riemann hypothesis. It will be shown that \(\Omega _{p}^\zeta (s)\) is a very regular random variable, having a probability density function (PDF) on the \(\omega \) line which is a Schwartz function. More precisely, an elementary proof is given that there exists some \(K_{p;s}^{}>0\), and a function \(F_{p;s}^{}(|t|)\) bounded by \(|F_{p;s}^{}(|t|)|\!\le \! \exp \big (K_{p;s}^{} |t|^{1/(s+1)})\), and \(C_{p;s}^{}\!:=\!-\frac{1}{s}\int _0^\infty \ln |{1-p+p\cos \xi }|\frac{1}{\xi ^{1+1/s}}\mathrm{{d}}\xi \), such that

$$\begin{aligned} \forall \,t\in \mathbb {R}:\quad {\text{ Cl }_{p;s}^{}}(t) = \exp \bigl ({- C_{p;s}^{} \,|t|^{1/s}\bigr )F_{p;s}^{}(|t|)}; \end{aligned}$$

the regularity of \(\Omega _{p}^\zeta (s)\) follows. Incidentally, this theorem confirms a surmise by Benoit Cloitre, that \(\ln {\text{ Cl }_{{{1}/{3}};2}^{}}(t) \sim -C\sqrt{t}\; \left( t\rightarrow \infty \right) \) for some \(C>0\). Graphical evidence suggests that \({\text{ Cl }_{{{1}/{3}};2}^{}}(t)\) is an empirically unpredictable (chaotic) function of t. This is reflected in the rich structure of the pertinent PDF (the Fourier transform of \({\text{ Cl }_{{{1}/{3}};2}^{}}\)), and illustrated by random sampling of the Riemann-\(\zeta \) walks, whose branching rules allow the build-up of fractal-like structures.

     

On the Convexity of the KdV Hamiltonian

Motivated by perturbation theory, we prove that the nonlinear part \({H^{*}}\) of the KdV Hamiltonian \({H^{kdv}}\), when expressed in action variables \({I = (I_{n})_{n \geqslant 1}}\), extends to a real analytic function on the positive quadrant \({\ell^{2}_{+}(\mathbb{N})}\) of \({\ell^{2}(\mathbb{N})}\) and is strictly concave near \({0}\). As a consequence, the differential of \({H^{*}}\) defines a local diffeomorphism near 0 of \({\ell_{\mathbb{C}}^{2}(\mathbb{N})}\). Furthermore, we prove that the Fourier-Lebesgue spaces \({\mathcal{F}\mathcal{L}^{s,p}}\) with \({-1/2 \leqslant s \leqslant 0}\) and \({2 \leqslant p < \infty}\), admit global KdV-Birkhoff coordinates. In particular, it means that \({\ell^{2}_+(\mathbb{N})}\) is the space of action variables of the underlying phase space \({\mathcal{F}\mathcal{L}^{-1/2,4}}\) and that the KdV equation is globally in time \({C^{0}}\)-well-posed on \({\mathcal{F}\mathcal{L}^{-1/2,4}}\).     

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.     

Rapid communication: $$K_{S}^{0}$$ Production from beryllium target using 120 $$\hbox {GeV}/\hbox {c}$$GeV/c protons beam interactions at the MIPP experiment

We have measured the cross-section for the \(K_{S}^{0}\) production from beryllium target using 120 \(\hbox {GeV}/\hbox {c}\) protons beam interactions at the main injector particle production (MIPP) experiment at Fermilab. The data were collected with target having a thickness of 0.94% of the nuclear interaction length. The \(K_{S}^{0}\) inclusive differential cross-section in bins of momenta is presented covering momentum range from \(0.4\,\hbox {GeV}/\hbox {c}\) to \(30\,\hbox {GeV}/\hbox {c}\). The measured inclusive \(K_{S}^{0}\) production cross-section amounts to \(39.54\pm 1.46\delta _{\mathrm {stat}}\pm 6.97\delta _{\mathrm {syst}}\) mb and the value is compared with the prediction of FLUKA hadron production model.     

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.