Mixing Amplitude Research Articles

Search for long-lived heavy neutrinos in the decays of B mesons produced in proton-proton collisions at s\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ \\sqrt{s} $$\\end{document} = 13 TeV

A search for long-lived heavy neutrinos (N) in the decays of B mesons produced in proton-proton collisions at s\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ \\sqrt{s} $$\\end{document} = 13 TeV is presented. The data sample corresponds to an integrated luminosity of 41.6 fb−1 collected in 2018 by the CMS experiment at the CERN LHC, using a dedicated data stream that enhances the number of recorded events containing B mesons. The search probes heavy neutrinos with masses in the range 1 < mN < 3 GeV and decay lengths in the range 10−2 < cτN < 104 mm, where τN is the N proper mean lifetime. Signal events are defined by the signature B → ℓBNX; N → ℓ±π∓, where the leptons ℓB and ℓ can be either a muon or an electron, provided that at least one of them is a muon. The hadronic recoil system, X, is treated inclusively and is not reconstructed. No significant excess of events over the standard model background is observed in any of the ℓ±π∓ invariant mass distributions. Limits at 95% confidence level on the sum of the squares of the mixing amplitudes between heavy and light neutrinos, |VN|2, and on cτN are obtained in different mixing scenarios for both Majorana and Dirac-like N particles. The most stringent upper limit |VN|2 < 2.0 × 10−5 is obtained at mN = 1.95 GeV for the Majorana case where N mixes exclusively with muon neutrinos. The limits on |VN|2 for masses 1 < mN < 1.7 GeV are the most stringent from a collider experiment to date.

Bs → μ+μ− in a two-Higgs-doublet model with flavour-changing up-type Yukawa couplings

We present a Two-Higgs-Doublet Model in which the structure of the quark Yukawa matrices is governed by three spurions breaking the flavour symmetries of the quark Yukawa sector. The model naturally suppresses flavour-changing neutral current (FCNC) amplitudes in the down-type sector, but permits sizable FCNC couplings in the up sector. We calculate the branching ratio of Bs → μ+μ− to leading and next-to-leading order of QCD for the case with FCNC couplings of the heavy neutral Higgs bosons to up-type quarks and verify that all counterterms follow the pattern dictated by the spurion expansion of the Yukawa matrices. We find correlations between Bs → μ+μ−, b → sγ, and the Higgs masses. The \\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$${B}_{s}-{\\overline{B} }_{s}$$\\end{document} mixing amplitude is naturally suppressed in the model but can probe a portion of the parameter space with very heavy Higgs bosons.

Search for keV-scale sterile neutrinos with the first KATRIN data

In this work we present a keV-scale sterile-neutrino search with a low-tritium-activity data set of the KATRIN experiment, acquired in a commissioning run in 2018. KATRIN performs a spectroscopic measurement of the tritium upbeta -decay spectrum with the main goal of directly determining the effective electron anti-neutrino mass. During this commissioning phase a lower tritium activity facilitated the measurement of a wider part of the tritium spectrum and thus the search for sterile neutrinos with a mass of up to 1.6, textrm{keV}. We do not find a signal and set an exclusion limit on the sterile-to-active mixing amplitude of sin ^2theta < 5times 10^{-4} (95% C.L.) at a mass of 0.3 keV. This result improves current laboratory-based bounds in the sterile-neutrino mass range between 0.1 and 1.0 keV.

Momentum dependence of mixing in the pion vector form factor and its effect on * *Supported in part by the Fundamental Research Funds for the Central Universities (FRF-BR-19-001A), and the National Natural Science Foundation of China (11975028, 11974043)

The inclusion of the mixing effect is essential for a precise description of the pion electromagnetic form factor in the process, which quantifies the two-pion contribution to the anomalous magnetic moment of muon . In this study, we analyze the momentum dependence of mixing by considering loop contributions at the next-to-leading order in expansion within the framework of resonance chiral theory. We revisit a previous study [Y. H. Chen, D. L. Yao, and H. Q. Zheng, Commun. Theor. Phys. 69, 1 (2018)] and consider the contribution arising from the kaon mass splitting in the kaon loops and latest experimental data. We perform two types of fits (with momentum-independent or momentum-dependent mixing amplitude) to describe and data within the energy region of 600900 MeV and decay width of . Furthermore, we compare their results. Our findings indicate that the momentum-independent and momentum-dependent mixing schemes provide appropriate descriptions of the data. However, the momentum-dependent scheme exhibits greater self-consistency, considering the reasonable imaginary part of the mixing matrix element obtained. Regarding the contribution to the anomalous magnetic moment of the muon, , the results obtained from the fits considering the momentum-dependent mixing amplitude are in good agreement with those obtained without incorporating the momentum dependence of mixing, within the margin of errors. Furthermore, based on the fitted values of the relevant parameters, we observe that the decay width of is predominantly influenced by the mixing effect.

Neutron-neutral particle mixing and its observable consequences

In this work, we explore the mixing between neutron ($n$) and elementary neutral particle ($\eta$), which violates both the baryon number ($\mathcal{B}$) and the lepton number ($\mathcal{L}$) by one unit but conserves their difference $(\mathcal{B}-\mathcal{L})$. Such mixing may give rise to non-trivial effects that are different from the Standard Model predictions. We organize our discussions based on two scenarios, roughly depending on whether an interference between oscillation and decay occurs, or whether the new-physics effects associated with the $n$-$\eta$ mixing contribute to the absorptive mixing amplitude. If an oscillation process is not accompanied by an interference between oscillation and decay, or the new-physics interactions do not contribute to the absorptive mixing amplitude, such a process can be classified as pure oscillation. Otherwise, it can be classified as impure oscillation. In the scenario of pure oscillation, CP-violation arising from the Majorana phase can manifest itself through the $n$-$\bar{n}$ oscillation process and may lead to observable effects. In the scenario of impure oscillation, we analyze the testable implications on the masses and lifetimes of the mass eigenstates formed as a result of the $n$-$\bar{n}$ oscillation mediated by $\eta$. In this scenario, we also suggest a unified interpretation of the neutron lifetime anomaly and the $n$-$\bar{n}$ oscillation measurements based on the $n$-$\eta$ mixing. In both scenarios, we present the lower bounds imposed by the experimental searches for $n$-$\bar{n}$ oscillations on the masses of the color multiplet bosons and point out that they could be within the reach of a direct detection at the LHC or future high-energy experiments.

Consistent Theory of Kinetic Mixing and the Higgs Low-Energy Theorem.

Extensions of the standard model of particle physics with new Abelian gauge groups allow for kinetic mixing between the new gauge bosons and the hypercharge gauge boson, resulting in mixing with the photon. In many models, the mixing with the hypercharge gauge boson captures only part of the kinetic mixing term with the photon, since the new gauge bosons can also mix with the neutral component of the SU(2)_{L} gauge bosons. We take these contributions into account and present a consistent description of kinetic mixing for general Abelian gauge groups both in the electroweak symmetric and the broken phase. We identify an effective operator that captures the kinetic mixing with SU(2)_{L} and demonstrate how renormalizable contributions arise if the charged fields only obtain their masses from electroweak symmetry breaking. For the first time, a low-energy theorem for the couplings of novel Abelian gauge bosons with the standard model Higgs boson is derived from the one-loop kinetic mixing amplitudes.

Evidence for prolate-oblate shape coexistence in the odd- ABr383573 nucleus

The excited states in $^{73}\mathrm{Br}$ nucleus have been investigated through the fusion evaporation reaction $^{50}\mathrm{Cr}(^{28}\mathrm{Si}$, $\ensuremath{\alpha}p)^{73}\mathrm{Br}$ at a beam energy of 90 MeV using the Indian National Gamma Array. The $\ensuremath{\gamma}\text{\ensuremath{-}}\ensuremath{\gamma}$ coincidence technique has been used to add eight new $\ensuremath{\gamma}$-ray transitions in the level scheme. The mixing ratio of $\mathrm{\ensuremath{\Delta}}I=0$ (mixed with $E2$ and $M1$) transitions have been determined using angular distribution and ${R}_{\mathrm{DCO}}$-polarization measurement. The half-life of the ${9/2}^{+}$ isomeric state has been measured to be ${\ensuremath{\tau}}_{1/2}=52(2)$ ns from the variation in the intensity of delayed $\ensuremath{\gamma}$-ray transition as a function of coincidence time window. The two state mixing model calculations were performed to obtain the mixing amplitude, and mixing interaction of two different configurations of $^{73}\mathrm{Br}$. The calculated mixing amplitudes along with the deformations of two different configurations provide the monopole transition strength ${\ensuremath{\rho}}^{2}(E0)$ for Se, Br, and Kr isotopes in a semiempirical approach. These results support a prolate-oblate shape coexistence in the odd-$A\phantom{\rule{4pt}{0ex}}^{73}\mathrm{Br}$ nucleus. The observed structural properties have been discussed in terms of projected shell model calculations.

Theory of collective topologically protected Majorana fermion excitations of networks of localized Majorana modes

Predictions of localized Majorana modes, and ideas for manipulating these degrees of freedom, are the two key ingredients in proposals for physical platforms for Majorana quantum computation. Several proposals envisage a scalable network of such Majorana modes coupled bilinearly to each other by quantum-mechanical mixing amplitudes. Here, we develop a theoretical framework for characterizing collective topologically protected zero-energy Majorana fermion excitations of such networks of localized Majorana modes. A key ingredient in our work is the Gallai-Edmonds decomposition of a general graph, which we use to obtain an alternate ``local'' proof of a ``global'' result of Lov\'asz and Anderson on the dimension of the topologically protected null space of real skew-symmetric (or pure-imaginary Hermitian) adjacency matrices of general graphs. Our approach to Lov\'asz and Anderson's result constructs a maximally localized basis for the said null space from the Gallai-Edmonds decomposition of the graph. Applied to the graph of the Majorana network in question, this gives a method for characterizing basis-independent properties of these collective topologically protected Majorana fermion excitations, and relating these properties to the correlation function of monomers in the ensemble of maximum matchings (maximally packed dimer covers) of the corresponding network graph. Our approach can also be used to identify signatures of zero-energy excitations in systems modeled by a free-fermion Hamiltonian with a hopping matrix of this type; an interesting example is provided by vacancy-induced Curie tails in generalizations (on nonbipartite lattices) of Kitaev's honeycomb model.

Coexistence and configuration mixing in 112Cd

I have performed a two-state mixing analysis between so-called rotational intruder 0+, 2+ and yrast 0+, 2+ states in 112Cd, fitting E2 transition matrix elements to obtain mixing amplitudes and matrix elements connecting basis states. Mixing is found to be small for both 0+ and 2+ states. Of two possible solutions, one provides a 0+ mixing amplitude of 0.251– identical to the one derived years ago from 2n transfer data.

Effects of the Skyrme tensor force on 0+ , 2+ , and 3− states in O16 and Ca40 nuclei within the second random-phase approximation

The effects of the Skyrme tensor force on the natural-parity ${0}^{+}$, ${2}^{+}$, and ${3}^{\ensuremath{-}}$ states in $^{16}\mathrm{O}$ and $^{40}\mathrm{Ca}$ are studied with the subtracted second random-phase approximation (SSRPA) adopting the Skyrme energy density functional. The strength distribution of these normal parity states are calculated with and without tensor interactions. The tensor force produces a small effect on ${0}^{+}$ and ${2}^{+}$ states in the random-phase approximation (RPA). However, our study shows that the tensor force has a significant effect on these states due to the coupling between one particle-one hole (1p-1h) and two particle-twp hole (2p-2h) model space in SSRPA; i.e., it increases strength for the low-lying ${0}^{+}$ and ${2}^{+}$ states below 10 MeV and shifts the main peak of ${2}^{+}$ transition downwards by about 1 to 2 MeV. For the negative-parity ${3}^{\ensuremath{-}}$ state, the tensor force shifts the lowest state downwards obviously, which helps the prediction of experimental data. The effect of the tensor force on the ${3}^{\ensuremath{-}}$ state is even visible in the 1p-1h RPA model space. We introduce two different parameter sets of tensor forces to clarify the role of the triplet-odd tensor term on the low-lying states. The microscopic structures of the lowest ${0}^{+}$, ${2}^{+}$, and ${3}^{\ensuremath{-}}$ states are examined looking at their 1p-1h and 2p-2h mixing amplitudes.

Dispersive and absorptive CP violation in D0−D¯0 mixing

CP violation (CPV) in $D^0-\overline{D^0}$ mixing is described in terms of the dispersive and absorptive `weak phases' $\phi_f^M$ and $\phi_f^\Gamma$. They parametrize CPV originating from the interference of $D^0$ decays with and without dispersive mixing, and with and without absorptive mixing, respectively, for CP conjugate hadronic final states $f$, $\bar f$. These are distinct and separately measurable effects. For CP eigenstate final states, indirect CPV only depends on $\phi_f^M$ (dispersive CPV), whereas $\phi_f^\Gamma$ (absorptive CPV) can only be probed with non-CP eigenstate final states. Measurements of the final state dependent phases $\phi_f^M$, $\phi_f^\Gamma$ determine the intrinsic dispersive and absorptive mixing phases $\phi_2^M$ and $\phi_2^\Gamma$. The latter are the arguments of the dispersive and absorptive mixing amplitudes $M_{12}$ and $\Gamma_{12}$, relative to their dominant ($\Delta U=2$) $U$-spin components. The intrinsic phases are experimentally accessible due to approximate universality: in the SM, and in extensions with negligible new CPV phases in Cabibbo favored/doubly Cabibbo suppressed (CF/DCS) decays, the deviation of $\phi_f^{M,\Gamma}$ from $\phi_2^{M,\Gamma}$ is negligible in CF/DCS decays $D^0 \to K^\pm X$, and below $10\% $ in CF/DCS decays $D^0 \to K_{S,L} X$ (up to precisely known $O(\epsilon_K)$ corrections). In Singly Cabibbo Suppressed (SCS) decays, QCD pollution enters at $O(\epsilon)$ in $U$-spin breaking and can be significant, but is $O(\epsilon^2)$ in the average over $f=K^+K^-$, $\pi^+\pi^-$. SM estimates yield $\phi_2^M, \phi_2^\Gamma = O(0.2\%)$. A fit to current data allows $O(10)$ larger phases at $2\sigma$, from new physics. A fit based on naively extrapolated experimental precision suggests that sensitivity to $\phi_2^{M}$ and $\phi_2^{\Gamma}$ in the SM may be achieved at the LHCb Phase II upgrade.

Spherical-deformed mixing in Zr94

I have applied a simple two-state mixing model to $E2$ strengths from a recent $^{94}\mathrm{Zr}(n,{n}^{\ensuremath{'}}\ensuremath{\gamma})$ experiment in order to obtain the mixing amplitudes between spherical and deformed basis states in $^{94}\mathrm{Zr}$. The fits also provide the transition matrix elements connecting the basis states.

The effect of initial amplitude and convergence ratio on instability development and deposited fluctuating kinetic energy in the single-mode Richtmyer–Meshkov instability in spherical implosions

This paper investigates the growth of perturbations on the inner surface of a dense imploding spherical shell due to hydrodynamic instabilities. The perturbations change in amplitude due to Richtmyer–Meshkov instability and Rayleigh-Taylor instability, geometric convergence, and compressibility. Two mode numbers (ℓ=5,50) and three different perturbation amplitudes (a0=0.1λ,0.01λ,0.001λ) are applied to the surface of the dense inner shell. Two independent codes were used to perform simulations with these six perturbation profiles at four convergence ratios, ranging from 3.6 to 7.3, for a total of 48 cases. The mixing layer amplitudes show good agreement between the two simulation codes across the range of convergence ratios, mode numbers, and initial amplitudes. The growth of the mixing layer is employed to validate an extension of a recently proposed Bell-Plesset model, showing good agreement across the range of convergence ratios. Persistent and substantial shock-deposited fluctuating kinetic energy is observed within the light core, away from the perturbed interface. Temporal evolution of fluctuating kinetic energy indicates a time delay between the peak radial and theta directions, consistent with a build-up of vortical motion. A “jet” like phenomena is observed at the peaks and troughs of the initial perturbations in both simulation codes across a variety of cases. It is postulated that these occur due to the shape singularity shown to develop in spatially periodic perturbed planar shock waves in ideal gas dynamics. Significant anisotropy of kinetic energy components is present at all times.

SMEFT atlas of \u2206F = 2 transitions

We present a model-independent anatomy of the ∆F = 2 transitions K0− {overline{K}}^0 , Bs,d− {overline{B}}_{s,d} and D0− {overline{D}}^0 in the context of the Standard Model Effective Field Theory (SMEFT). We present two master formulae for the mixing amplitude [M12]BSM. One in terms of the Wilson coefficients (WCs) of the Low-Energy Effective Theory (LEFT) operators evaluated at the electroweak scale μew and one in terms of the WCs of the SMEFT operators evaluated at the BSM scale Λ. The coefficients {P}_a^{ij} entering these formulae contain all the information below the scales μew and Λ, respectively. Renormalization group effects from the top-quark Yukawa coupling play the most important role. The collection of the individual contributions of the SMEFT operators to [M12]BSM can be considered as the SMEFT atlas of ∆F = 2 transitions and constitutes a travel guide to such transitions far beyond the scales explored by the LHC. We emphasize that this atlas depends on whether the down-basis or the up-basis for SMEFT operators is considered. We illustrate this technology with tree-level exchanges of heavy gauge bosons (Z′, G′) and corresponding heavy scalars.

Description of the low-lying collective states of Zr96 based on the collective Bohr Hamiltonian including the triaxiality degree of freedom

Experimental data on $^{96}$Zr indicate coexisting spherical and deformed structures with small mixing amplitudes. Several collective low-lying states and E2 and M1 transitions are observed for this nucleus. The quadrupole-collective Bohr Hamiltonian depending on both $\beta$ and $\gamma$ shape variables with a potential having spherical and deformed minima, is applied consideration of these data. The relative depth of two minima, height and width of the barrier, rigidity of the potential near both minima are determined so as to achieve a satisfactory description of the observed properties of the low-lying collective quadrupole states of $^{96}$Zr. Good agreement with the experimental data on the excitation energies, $B(E2)$ and $B(M1; 2^+_2\rightarrow 2^+_1)$ reduced transition probabilities is obtained. It is shown that the low-energy structure of $^{96}$Zr can be described in a satisfactory way within the Geometrical Collective Model with a potential function supporting shape coexistence without other restrictions of its shape. However, the excitation energy of the $2^+_2$ state can be reproduced only if the rotation inertia coefficient is taken by four times smaller than the vibrational one in the region of the deformed well. It is shown also that shell effects are important for the description of the $B(M1; 2^+_2 \rightarrow 2^+_1)$ and $B(M1; 3^+_1 \rightarrow 2^+_1)$ transition probabilities. An indication for the influence of the pairing vibrational mode on the $0^+_2 \rightarrow 0^+_1$ transition is confirmed in agreement with the previous result.

Measurements with a TRISTAN prototype detector system at the “Troitsk nu-mass” experiment in integral and differential mode

Sterile neutrinos emerge in minimal extensions of the Standard Model which can solve a number of open questions in astroparticle physics. For example, sterile neutrinos in the keV-mass range are viable dark matter candidates. Their existence would lead to a kink-like distortion in the tritium β-decay spectrum. In this work we report about the instrumentation of the Troitsk nu-mass experiment with a 7-pixel TRISTAN prototype detector and measurements in both differential and integral mode. The combination of the two modes is a key requirement for a precise sterile neutrino search, as both methods are prone to largely different systematic uncertainties. Thanks to the excellent performance of the TRISTAN detector at high rates, a sterile neutrino search up to masses of about 6 keV could be performed, which enlarges the previous accessible mass range by a factor of 3. Upper limits on the neutrino mixing amplitude in the mass range < 5.6 keV (differential) and < 6.6 keV (integral) are presented. These results demonstrate the feasibility of a sterile neutrino search as planned in the upgrade of the KATRIN experiment with the final TRISTAN detector and read-out system.

Unified description of pairing and quarteting correlations within the particle-hole-boson approach

We study the description of single-species and isovector pairing correlations in the framework of the projected-BCS (PBCS) and the Quartet Condensation Model (QCM) from a particle-hole perspective and we introduce the representation of the QCM quartet condensate state in terms of particle-hole excitations with respect to the Hartree-Fock state. We also present a new bosonic approximation for both PBCS and QCM. In each case, the starting point is the reformulation of the pair/quartet condensate state in terms of particle-hole excitations with respect to the Hartree-Fock state. The main simplification of our approach is the assumption that the pair operators corresponding to both particle and hole states obey bosonic commutation relations. This simplifies tremendously the computations and allows for an analytic derivation of the averaged Hamiltonian on the condenstate state as a function of the mixing amplitudes. We study both the pure bosonic approach and the renormalized version, and compare the particle-hole bosonic version to the naive prescription of applying the boson approximation directly to the original condensate state. We compare the fermionic and the renormalized particle-hole bosonic approach in the case of a picket fence model of doubly degenerate states and in a realistic shell model space with an effective interaction for the $N=Z$ nuclei above $^{100}$Sn.

Description of shape coexistence in Zr96 based on the quadrupole-collective Bohr Hamiltonian

Experimental data on $^{96}$Zr indicate coexisting spherical and deformed structures with small mixing amplitudes. We investigate the properties of the low-lying collective states of $^{96}$Zr based on the collective quadrupole Bohr Hamiltonian. The $\beta$-dependent collective potential having two minima -- spherical and deformed, is fixed so to describe experimental data in the best way.Good agreement with the experimental data on the excitation energies, $B(E2)$ and $B(M1)$ reduced transition probabilities is obtained. It is shown that the low-energy structure of $^{96}$Zr can be reproduced in a satisfactory way in the geometrical model with a potential function supporting shape coexistence. However, the excitation energy of the $2^+_2$ state can be reproduced only if the rotation inertia coefficient is taken five times smaller then the vibrational one in the region of the deformed well. It is shown also that shell effects are important for the description of the $B(M1;2^+_2 \rightarrow 2^+_1)$ value. An indication on the influence of the pairing vibrational mode on the $\rho^2 (0^+_2 \rightarrow 0^+_1)$ value is obtained.

Analytical approach for the quartet condensation model

Within the Quartet Condensation Model (QCM), the isovector pairing correlations for $N = Z$ nuclei are described with a very high accuracy by a condensate of $\alpha$-like quartets. The usual approach involves cumbersome recurrence relations in order to compute numerically the relevant quantities of the model: the norm of the quartet states and the mean value of the isovector pairing Hamiltonian as functions of the pair mixing amplitudes. We present the final analytical expressions for the above mentioned quantities, for all cases up to four quartets in the valence shell. The analytical QCM expressions were obtained by a straightforward implementation of the SO(5) algebra in the symbolic computer algebra system Cadabra2. The norm of the quartet states and the mean value of the Hamiltonian are polynomial functions of the mixing amplitudes. The numerical implementation of the QCM model is thus made trivial as matter of copying and pasting the presented formulas. We introduce in this work the method of computer aided analytical calculus for a many body setting. In particular, we provide precise and easy to use tools for the description of isovector pairing correlations.

Band mixing in 154Gd

I have applied a simple two-state mixing model to members of the first two rotational bands in 154Gd. Resulting mixing amplitudes are similar for $0^{+}$ , $2^{+}$ , $4^{+}$ , and $6^{+}$ , with mixing decreasing slightly with increasing J. The analysis indicates that 154Gd is very similar to 152Sm for these first two bands. Results suggest that the larger of the two experimental strengths that are available for the $2_{2}\rightarrow 0_{2}$ transition in 154Gd is the correct one.