Flavor Eigenstates Research Articles

Quantum spread complexity in neutrino oscillations

Quantum information theory has recently emerged as a flourishing area of research and quantum complexity, one of its powerful measures, is being applied for investigating complex systems in many areas of physics. Its application to practical physical situations, however, is still few and far between. Neutrino flavor oscillation is a widely studied physical phenomena with far reaching consequences in understanding the standard model of particle physics and to search for physics beyond it. Oscillation arises because of mixing between the flavor and mass eigenstates, and their evolution over time. It is an inherent quantum system for which flavor transitions are traditionally studied with probabilistic measures. We have applied quantum complexity formalism as an alternate measure to study neutrino oscillations. In particular, quantum spread complexity revealed additional information on the violation of charge-parity symmetry in the neutrino sector. Our results indicate that complexity favors the maximum violation of charge-parity, hinted recently by experimental data.

Improved method to determine the Ξc−Ξc′ mixing

We develop an improved method to explore the Ξc−Ξc′ mixing, which arises from the flavor SU(3) and heavy quark symmetry breaking. In this method, the flavor eigenstates under the SU(3) symmetry are at first constructed, and the corresponding masses can be nonperturbatively determined. Matrix elements of the mass operators, which break the flavor SU(3) symmetry sandwiched by the flavor eigenstates, are then calculated. Diagonalizing the corresponding matrix of Hamiltonian gives the mass eigenstates of the full Hamiltonian and determines the mixing. Following the previous lattice QCD calculation of Ξc and Ξc′, and estimating an off diagonal matrix element, we extract the mixing angle between the Ξc and Ξc′. Preliminary numerical results for the mixing angle confirm the previous observation that such mixing is incapable to explain the large SU(3) symmetry breaking in semileptonic decays of charmed baryons. Published by the American Physical Society 2024

Constraining Vector Dark Matter with neutrino experiments

Vector Dark Matter (VDM) that couples to lepton flavor (Le, Lμ, Lτ) acts similarly to a chemical potential for the neutrino flavor eigenstates and modifies neutrino oscillations. VDM imparts unique signatures such as time and directional dependence with longer baselines giving better sensitivity. We use the non-observation of such a signal at Super-Kamiokande to rule out the existence of VDM in a region of parameter space several orders of magnitude beyond other constraints and show the projected reach of future experiments such as DUNE.

Quark-antiquark states of the lightest scalar mesons within the Nambu-Jona-Lasinio model with flavor-dependent coupling constants

The quark-antiquark components of the U(3) lightest scalar meson nonet are investigated by considering the Nambu-Jona-Lasinio model with flavor-dependent coupling constants that were derived by considering (non-perturbative) gluon exchange. The strange quark effective mass () is varied such that the strangeness content of these scalar mesons can be analyzed further. The neutral states S 0, S 8, and S 3 are adopted as the most relevant quark-antiquark components, respectively, of the σ(500), f 0(980) and mesons. As a result, the mass hierarchy between states S 0 and S 8, and mesons, can be, respectively, inverted and corrected for quite low values of the strange quark constituent mass. In addition, for some particular values of , the masses of σ(500) and f 0(980) can also be obtained by considering the mixing coupling constant G 08. However, the masses of all the nine mesons are not described simultaneously in a self-consistent procedure and this goes along with the need of non-quark-antiquark states to completely describe their masses. A neutral-meson mixing matrix is defined and the leading mixing angle is found by fitting a correct value of the σ(500) − f 0(980) mass difference. Two different estimates for the strengths of the mixings and are proposed, leading to somewhat different behaviors. First by assuming leading transitions to intermediary flavor eigenstates and second by considering a dynamical evolution. The results may be in good agreement with experimental values from BESS-III depending on the value of the strange quark effective mass.

Inflationary flavor oscillations and the cosmic spectroscopy

Inflationary scenarios motivated by high-energy physics generically contain a plethora of degrees of freedom beyond the primordial curvature perturbation. The latter interacts in a simple way with what we name "inflationary flavor eigenstates", which differ, in general, from freely propagating "mass eigenstates". We show that the mixing between these misaligned states results in new striking behaviors in the squeezed limit of the curvature perturbation three-point function, depending not only on the mass spectrum but also on the "mixing angles" of the theory. These results bring about a new perspective on the cosmological collider program: contrary to a widespread belief, the primordial signal needs not be dominated by the lightest extra degree of freedom. Instead, we show that it may display either modulated oscillations, a broken power law, or a transition from oscillations to a power law, thus offering a detailed cosmic spectroscopy of the particle content of inflation.

Geometric phases in neutrino mixing

Neutrinos can acquire both dynamic and geometric phases due to the nontrivial mixing between mass and flavor eigenstates. In this paper, we derive the general expressions for all plausible gauge invariant diagonal and off-diagonal geometric phases in the three- flavor neutrino model using the kinematic approach. We find that diagonal and higher-order off-diagonal geometric phases are sensitive to the mass ordering and the Dirac CP violating phase [Formula: see text]. We show that, third-order off-diagonal geometric phase [Formula: see text] is invariant under any cyclic or non-cyclic permutations of flavor indices when the Dirac CP phase is zero. For nonzero [Formula: see text], we find that [Formula: see text]. We also prove that, only the third-order off-diagonal geometric phase is sensitive to the sign of [Formula: see text]. Further, we explore the effects of matter background using a two-flavor neutrino model and show that the diagonal geometric phase is either [Formula: see text] or [Formula: see text] in the MSW resonance region and takes nontrivial values elsewhere. The transition between zero and [Formula: see text] occurs at the point of complete oscillation inversion called the nodal point, where the diagonal geometric phase is not defined. Also, in two-flavor approximations, two distinct diagonal geometric phases are co-functions with respect to the mixing angle. Finally, in the two-flavor model, we show that the only second-order off-diagonal geometric phase is a topological invariant quantity and is always [Formula: see text].

Neutrino physics in TeV scale gravity theories

In this paper, the general features of the neutrino sector in TeV scale quantum gravity theories, such as ADD and Many Species Theory, is investigated. This class of theories has an inherent way to generate small neutrino masses. After reviewing this mechanism it is generalized to a realistic three-flavour case. Furthermore, a procedure is presented how to diagonalize a mass matrix which is generated by this class of theories and how one can find the Standard Model flavour eigenstates. The developed general approach is applied to two specific scenarios within ADD and Many Species Theory and possible effects on neutrino oscillations and on unitarity of the lepton mixing matrix are calculated. Finally, a short overview of phenomenology which can be potentially testable by the nowadays neutrino experiments is presented.

Suppression of fast neutrino flavor conversions occurring at large distances in core-collapse supernovae

Neutrinos propagating in dense neutrino mediasuch as core-collapse supernovaeand neutron star merger remnantscan experience the so-called fast flavorconversions on scalesmuch shorter than those expected in vacuum. A very generic class of fast flavor instabilities is the ones which are produced by the backward scatteringof neutrinos off the nuclei at relatively large distances from the supernova core.In this study we demonstrate that despite their ubiquity, such fast instabilities are unlikelyto cause significant flavor conversionsif the population of neutrinos in the backward direction is not large enough.Indeed, the scattering-induced instabilities can mostly impact theneutrinos traveling in the backward direction, which represent only a small fraction of neutrinos at large radii.We show that this can be explained by the shapeof the unstable flavor eigenstates, which can be extremely peaked at the backward angles.

Precise determination of the B_{mathrm{s}}^0\u2013overline B_{mathrm{s}}^0 oscillation frequency

Mesons comprising a beauty quark and strange quark can oscillate between particle ({B}_{mathrm{s}}^{0}) and antiparticle ({overline{B}}_{mathrm{s}}^{0}) flavour eigenstates, with a frequency given by the mass difference between heavy and light mass eigenstates, Δms. Here we present a measurement of Δms using {B}_{mathrm{s}}^{0}to {D}_{mathrm{s}}^{-}π+ decays produced in proton–proton collisions collected with the LHCb detector at the Large Hadron Collider. The oscillation frequency is found to be Δms = 17.7683 ± 0.0051 ± 0.0032 ps−1, where the first uncertainty is statistical and the second is systematic. This measurement improves on the current Δms precision by a factor of two. We combine this result with previous LHCb measurements to determine Δms = 17.7656 ± 0.0057 ps−1, which is the legacy measurement of the original LHCb detector.

Mixing angles between the tetraquark states with two heavy quarks within QCD sum rules

LHCb Collaboration has recently announced the observation of a doubly charmed tetraquark $T_{cc \bar{u} \bar{d}}^+$ state with spin parity $J^P = 1^+$. This exotic state can be explained as a molecular state with small binding energy. According to conventional quark model, both $D^+ D^{0\ast}$ and $(D^0 D^{+\ast})$ multiquark states are expected to have the same mass and flavor in the exact $SU(3)$ symmetry. However, since the quark masses are different, $SU(3) (SU(2))$ symmetry is violated, hence, the mass and flavor eigenstates do not coincide. The mass eigenstates can be represented as a linear combination of the flavor eigenstates, which is characterized by the mixing angle $\theta$. In the present work, the possible mixing angles between the $T_{cc}$ states are calculated. Moreover, the analysis are extended for all the possible tetraquarks scenarios with two heavy and two light quarks within the molecular picture although those states have not been observed yet. Our prediction on mixing angle between doubly charmed tetraquark states shows that $SU(3)$ symmetry breaking is around $7\%$ maximally.

Flavor-mass majorization uncertainty relations and their links to the mixing matrix

Uncertainties in flavor and mass eigenstates of neutrinos are considered within the majorization approach. Nontrivial bounds reflect the fact that neutrinos cannot be simultaneously in flavor and mass eigenstates. As quantitative measures of uncertainties, both the Rényi and Tsallis entropies are utilized. Within the current amount of experience concerning the mixing matrix, majorization uncertainty relations need to put values of only two parameters, viz. [Formula: see text] and [Formula: see text]. That is, the majorization approach is applicable within the same framework as the Maassen–Uffink relation recently utilized in this context. We also consider the case of detection inefficiencies, since it can naturally be incorporated into the entropic framework. Short comments on applications of entropic uncertainty relations with quantum memory are given.

Spatiotemporal linear instability analysis of collective neutrino flavor conversion in four-dimensional spacetime

In an environment with high-density neutrinos formed in a core-collapse supernova (CCSN), the neutrinos exhibit nonlinear and complex oscillation behaviors due to their self-interactions. The onset of this nonlinear oscillation can be investigated by linearizing the evolution equation for small perturbations around the flavor eigenstates. While the condition under which the flavor eigenstates are unstable has been investigated in many studies, how the perturbations evolve in spacetime has yet to be elucidated. In this paper, we analytically and correctly derive the asymptotic behaviors of the linear perturbations in 4-dimensional spacetime in the linear regime for a 2-beam neutrino model using the recently proposed Lefschetz thimble formulation. The result suggests that the perturbations grow in the directions between the two neutrino beams. We also briefly discuss the possible effects of neutrino flavor conversion on the explosion mechanism of a CCSN. In particular, the result implies that the flavor instability in the preshock region may propagate into the postshock region, contrary to the previous study focusing on the group velocity in 1-dimensional space. How to treat the case of a more realistic continuous spectrum is also discussed.

Neutrino invisible decay at DUNE: a multi-channel analysis

The hypothesis of the decay of neutrino mass eigenstates leads to a substantial modification of the appearance and disappearance probabilities of flavor eigenstates. We investigate the impact on the standard oscillation scenario caused by the decay of the heaviest mass eigenstate ν 3 (with a mass m 3 and a mean life τ 3) to a sterile state in deep underground neutrino experiment. We find that the lower bound of 5.1 × 10−11 s eV−1 at 90% confidence level on the decay parameter τ 3/m 3 can be set if the neutral current data are included in the analysis, thus providing the best long-baseline expected limit so far. We also show that the ν τ appearance channel would give only a negligible contribution to the decay parameter constraints. Our numerical results are corroborated by analytical formulae for the appearance and disappearance probabilities in vacuum (which is a useful approximation for the study of the invisible decay model) that we have developed up to the second order in the solar mass splitting and to all orders in the decay factor t/τ 3.

Transition probabilities for flavor eigenstates of non-Hermitian Hamiltonians in the PT-broken phase

We investigate the transition probabilities for the “flavor” eigenstates in the two-level quantum system, which is described by a non-Hermitian Hamiltonian with the parity and time-reversal (PT) symmetry. Particularly, we concentrate on the so-called PT-broken phase, where two eigenvalues of the non-Hermitian Hamiltonian turn out to be a complex-conjugate pair. In this case, we find that the transition probabilities will be unbounded in the limit of infinite time t → +∞. However, after performing a connection between a non-Hermitian system, which exhibits passive PT symmetry and global decay, and the neutral-meson system in particle physics, we observe that the diverging behavior of the transition probabilities is actually applicable to the gauge-transformed neutral-meson states, whereas the transition probabilities for physical states are exponentially suppressed by the global decay. We also present a brief review on the situation at the so-called exceptional point, where both the eigenvalues and eigenvectors of the Hamiltonian coalesce.

General Quantum Field Theory of Flavor Mixing and Oscillations

We review the canonical transformation in quantum physics known as the Bogoliubov transformation and present its application to the general theory of quantum field mixing and oscillations with an arbitrary number of mixed particles with either boson or fermion statistics. The mixing relations for quantum states are derived directly from the definition of mixing for quantum fields and the unitary inequivalence of the Fock space of energy and flavor eigenstates is shown by a straightforward algebraic method. The time dynamics of the interacting fields is then explicitly solved and the flavor oscillation formulas are derived in a unified general formulation with emphasis on antiparticle content and effect introduced by nontrivial flavor vacuum.

HUNTER: precision massive-neutrino search based on a laser cooled atomic source

We describe a project that brings together researchers from atomic physics, nuclear physics and sub-atomic particle physics, to develop a high-precision laboratory-scale experiment able to search for very weakly coupled sterile neutrinos in the mass range extending from 5–10 keV/c 2 to several 100 keV/c 2. Observed neutrino flavor eigenstates are known to be quantum mixtures of at least three sub-eV/c 2 mass eigenstates. There is a strong theoretical belief that there may exist further neutrino mass eigenstates at higher mass levels, and which, if in the keV/c 2 mass range, might form all or part of the galactic dark matter. This has led to many searches for anomalous events in both astrophysical and particle physics experiments, and searches for distortions in beta decay spectra. The present experiment will utilize K-capture events in a population of 131Cs atoms suspended in vacuum by a magneto-optical trap (MOT). Using AMO and nuclear physics techniques, individual events will be fully reconstructed kinematically. Normally each event would be consistent with an emitted neutrino mass close to zero, but the existence of a sterile neutrino of keV/c 2 mass that mixes with the electron type neutrino produced in the decay would result in a separated population of events with non-zero reconstructed missing mass (up to the Q = 352 keV available energy of the reaction). Detailed calculations and simulations of all significant background processes have been made, in particular for scattering in the source itself, radiative K-capture, local radioactivity, cosmic ray muons, and knock-out of electrons by x-rays. A phase 1 of the experiment, under construction with funding from the W M Keck Foundation, has the potential to reach sterile neutrino mixing angles down to sin2 θ ∼ 10−4. With further upgrades this technique could be progressively improved to eventually reach much lower coupling levels ∼10−10, in particular reaching the level needed to be consistent with galactic dark matter below the astrophysical x-ray limits.

Time evolution of lepton number carried by Majorana neutrinos

Abstract We revisit the time evolution of the lepton family number for an SU(2) doublet consisting of a neutrino and a charged lepton. The lepton family number is defined through the weak basis of the SU(2) doublet, where the charged lepton mass matrix is real and diagonal. The lepton family number carried by the neutrino is defined by the left-handed current of the neutrino family. For this work we assume that the neutrinos have Majorana mass. This Majorana mass term is switched on at time $t=0$ and the lepton family number evolves. Since the operator in the flavor eigenstate is continuously connected to that of the mass eigenstate, the creation and annihilation operators for the two eigenstates are related to each other. We compute the time evolution of all lepton family numbers by choosing a specific initial flavor eigenstate for a neutrino. The evolution is studied for relativistic and non-relativistic neutrinos. The non-relativistic region is of particular interest for the cosmic neutrino background predicted from Big Bang models. In that region we find that the lepton family numbers are sensitive to the Majorana and Dirac phases, the absolute mass, and the mass hierarchy of neutrinos.

Mixing angles between the tetraquark states with two heavy quarks within QCDsum rules

LHCb collaboration has recently announced the observation of a doubly charmed tetraquark $T_{cc \bar{u} \bar{d}}^+$ state with spin parity $J^P = 1^+$. This exotic state can be explained as a molecular state with small binding energy. According to conventional quark model, both $D^+ D^{0\ast}$ and $(D^0 D^{+\ast})$ multiquark states are expected to have the same mass and flavor in the exact $SU(3)$ symmetry. However, since the quark masses are different, $SU(3) (SU(2))$ symmetry is violated; hence, the mass and flavor eigenstates do not coincide. The mass eigenstates can be represented as a linear combination of the flavor eigenstates, which is characterized by the mixing angle $\theta$. In the present work, the possible mixing angles between the $T_{cc}$ states are calculated. Moreover, the analyses are extended for all the possible tetraquarks scenarios with two heavy and two light quarks within the molecular picture although those states have not been observed yet. Our prediction on mixing angle between doubly charmed tetraquark states shows that $SU(3)$ symmetry breaking is around $7\%$ maximally.

Neutrino flavor-mass uncertainty relations and an entanglement-assisted determination of the PMNS matrix

As a result of a non-trivial mixing matrix, neutrinos cannot be simultaneously in a flavor and mass eigenstate. We formulate and discuss information entropic relations that quantify the associated quantum uncertainty. We also formulate a protocol to determine the Pontecorvo-Maki-Nakagawa-Sakata (PMNS) matrix from quantum manipulations and measurements on an entangled lepton-neutrino pair. The entangled state features neutrino oscillations in a conditional probability involving measurements on the lepton and the neutrino. They can be switched off by choosing a specific observable on the lepton side which is determined by the PMNS matrix. The parameters of the latter, including the CP-violating phase $\delta$, can be obtained by guessing them and improving the guess by minimizing the remaining oscillations.

Dark energy and neutrino mass from a transient vacuum particle pair model

We propose that the transient vacuum fluctuations of quantum fields can be represented by transient vacuum quanta where both the lifetime and spatial extent are given by the Heisenberg Uncertainty Principle, HUP. Accordingly, a quantum field fluctuation at any spatial site results in the creation of a transient HUP-limited vacuum pair, corresponding to the particle and the antiparticle associated with that quantum field. All HUP-limited vacuum pairs, both massive and massless, are found to be on-shell particles, and are indistinguishable from each other except for differences related to their exchange symmetry. We find that the net vacuum energy density of all HUP-limited vacuum pairs is identically zero at any energy where both bosonic and fermionic transient vacuum pairs are present. The net vacuum energy density, from zero energy to the Planck limit, is found to be proportional to that of the rest mass of the lightest fermion, the lowest mass neutrino eigenstate. This net energy density is equal to the observed dark energy density if the mass of the lightest neutrino eigenstate is 3.2[Formula: see text]meV. The model predicts the absolute values of the masses of the three neutrino mass eigenstates and of the three neutrino flavor eigenstates for both normal and inverted ordering. The sum of the neutrino masses is found to be below the Planck satellite upper limit of 120[Formula: see text]meV, and the neutrino mass sum for normal ordering is below the most stringent upper bound of 78[Formula: see text]meV, indicating a preference for normal ordering.