Mass Eigenstates Research Articles

Mass insertions vs. mass eigenstates calculations in flavour physics

We present and prove a theorem of matrix analysis, the Flavour Expansion Theorem (or FET), according to which, an analytic function of a Hermitian matrix can be expanded polynomially in terms of its off-diagonal elements with coefficients being the divided differences of the analytic function and arguments the diagonal elements of the Hermitian matrix. The theorem is applicable in case of flavour changing amplitudes. At one-loop level this procedure is particularly natural due to the observation that every loop function in the Passarino-Veltman basis can be recursively expressed in terms of divided differences. FET helps to algebraically translate an amplitude written in mass eigenbasis into flavour mass insertions, without performing diagrammatic calculations in flavour basis. As a non-trivial application of FET up to a third order, we demonstrate its use in calculating strong bounds on the real parts of flavour changing mass insertions in the up- squark sector of the MSSM from neutron Electric Dipole Moment (nEDM) measurements, assuming that CP-violation arises only from the CKM matrix.

A second Higgs from the Higgs portal

In the Higgs portal framework, the Higgs field generally mixes with the Standard Model singlet leading to the existence of two states, one of which is identified with the 125 GeV scalar observed at the LHC. In this work, we analyse direct and indirect constraints on the second mass eigenstate and the corresponding mixing angle. The existence of the additional scalar can be beneficial as it can stabilise the otherwise-metastable electroweak vacuum. We find parameter regions where all of the bounds, including the stability constraints, are satisfied. We also study prospects for observing the decay of the heavier state into a pair of the 125 GeV Higgs-like scalars.

NonthermalCPviolation in soft leptogenesis

Soft leptogenesis is a mechanism which generates the matter-antimatter asymmetry of the Universe via the out-of-equilibrium decays of heavy sneutrinos in which soft supersymmetry breaking terms play two important roles: they provide the required $CP$ violation and give rise to the mass splitting between otherwise degenerate sneutrino mass eigenstates within a single generation. This mechanism is interesting because it can be successful at the lower temperature regime $T\ensuremath{\lesssim}1{0}^{9}\text{ }\text{ }\mathrm{GeV}$ in which the conflict with the overproduction of gravitinos can possibly be avoided. In earlier works, the leading $CP$ violation is found to be nonzero only if finite temperature effects are included. By considering generic soft trilinear couplings, we find two interesting consequences: (1) the leading $CP$ violation can be nonzero even at zero temperature realizing nonthermal $CP$ violation, and (2) the $CP$ violation is sufficient even far away from the resonant regime allowing soft supersymmetry breaking parameters to assume natural values at around the TeV scale. We discuss phenomenological constraints on such scenarios and conclude that the contributions to charged lepton flavor violating processes are close to the sensitivities of present and future experiments.

Neutrino flavor oscillations in a curved space-time

Using a WKB approximation of the Dirac equation in a curved spacetime, we obtain the expression for the phase shift between two neutrino mass eigenstates in a generic gravitational field. We apply this expression to two specific space-time geometries, namely the Kerr-Newman metric describing a rotating and charged black hole, and the Friedmann-Robertson-Walker metric.

Newtonian self-gravitation in the neutral meson system

We derive the effect of the Schr\"odinger-Newton equation, which can be considered as a nonrelativistic limit of classical gravity, for a composite quantum system in the regime of high energies. Such meson-antimeson systems exhibit very unique properties, e.g., distinct masses due to strong and electroweak interactions. This raises an immediate question: what does one mean by mass in gravity for a state that is a superposition of mass eigenstates due to strong and electroweak interactions? We find conceptually different physical scenarios due to lacking of a clear physical guiding principle to explain which mass is the relevant one and due to the fact that it is not clear how the flavor wave function relates to the spatial wave function. There seems to be no principal contradiction. However, a nonlinear extension of the Schr\"odinger equation in this manner strongly depends on the relation between the flavor wave function and spatial wave function and its particular shape. In opposition to the continuous spontaneous localization collapse models we find a change in the oscillating behavior and not in the damping of the flavor oscillation.

Distinguishing signatures of top- and bottom-type heavy vectorlike quarks at the LHC

An SU(2) vectorlike singlet quark with a charge either +2/3 (t') or -1/3 (b') is predicted in many extensions of the Standard Model. The mixing of these quarks with the top or bottom lead to Flavor Changing Yukawa Interactions and Neutral Current. The decay modes of the heavier mass eigenstates are therefore different from the Standard Model type chiral quarks. The Large Hadron Collider (LHC) will provide an ideal environment to look for the signals of these exotic quarks. Considering all decays, including those involving Z- and Yukawa interactions, we show how one can distinguish between t' and b' from ratios of event rates with different lepton multiplicities. The ability to reconstruct the Higgs boson with a mass around 125.5 GeV plays an important role in such differentiation.

CP-invariance violation at short-baseline experiments in3+1neutrino scenarios

New neutrino degrees of freedom allow for more sources of CP-invariance violation (CPV). We explore the requirements for accessing CP-odd mixing parameters in the so-called 3+1 scenario, where one assumes the existence of one extra, mostly sterile neutrino degree of freedom, heavier than the other three mass eigenstates. As a first step, we concentrate on the nu_e to nu_mu appearance channel in a hypothetical, upgraded version of the nuSTORM proposal. We establish that the optimal baseline for CPV studies depends strongly on the value of Delta m^2_14 -- the new mass-squared difference -- and that the ability to observe CPV depends significantly on whether the experiment is performed at the optimal baseline. Even at the optimal baseline, it is very challenging to see CPV in 3+1 scenarios if one considers only one appearance channel. Full exploration of CPV in short-baseline experiments will require precision measurements of tau-appearance, a challenge significantly beyond what is currently being explored by the experimental neutrino community.

Dynamically self-regular quantum harmonic black holes

The recently proposed UV self-complete quantum gravity program is a new and very interesting way to envision Planckian/trans-Planckian physics. In this new framework, high energy scattering is dominated by the creation of micro black holes, and it is experimentally impossible to probe distances shorter than the horizon radius. In this letter we present a model which realizes this idea through the creation of self-regular quantum black holes admitting a minimal size extremal configuration. Their radius provides a dynamically generated minimal length acting as a universal short-distance cutoff. We propose a quantization scheme for this new kind of microscopic objects based on a Bohr-like approach, which does not require a detailed knowledge of quantum gravity. The resulting black hole quantum picture resembles the energy spectrum of a quantum harmonic oscillator. The mass of the extremal configuration plays the role of zero-point energy. Large quantum number re-establishes the classical black hole description. Finally, we also formulate a “quantum hoop conjecture” which is satisfied by all the mass eigenstates and sustains the existence of quantum black holes sourced by Gaussian matter distributions.

Future of Neutrino Interaction Models

Neutrino-nucleus cross sections are one of the dominant sources of systematic errors in long-baseline neutrino oscillation experiments. To achieve the goals of precision measurements of the mixing angles and difference of the mass eigenstates squared, and discover the mass hierarchy and CP-violating phase, the underlying neutrino interactions must be better understood. This poster will mention some recent improvements in models in the interaction generators as well as some possible future improvements for proposed experiments.

Wavelet approach to search for sterile neutrinos in tritiumβ-decay spectra

Sterile neutrinos in the mass range of a few keV are candidates for both cold and warm dark matter. An ad-mixture of a heavy neutrino mass eigenstate to the electron neutrino would result in a minuscule distortion - a 'kink' - in a $\beta$-decay spectrum. In this paper we show that a wavelet transform is a very powerful shape analysis method to detect this signature. For a tritium source strength, similar to what is expected from the KATRIN experiment, a statistical sensitivity to active-to-sterile neutrino mixing down to $\sin^2 \theta= 10^{-6}$ ($90\%$ CL) can be obtained after 3 years of measurement time. It is demonstrated that the wavelet approach is largely insensitive to systematic effects that result in smooth spectral modifications. To make full use of this analysis technique a high resolution measurement (FWHM of $\sim100$~eV) of the tritium $\beta$-decay spectrum is required.

Precision Measurement ofCPViolation inBS0→J/ΨK+K−Decays

The time-dependent CP asymmetry in B(s)(0)→J/ψK+K- decays is measured using pp collision data, corresponding to an integrated luminosity of 3.0 fb-1, collected with the LHCb detector at center-of-mass energies of 7 and 8 TeV. In a sample of 96,000 B(s)(0)→J/ψK+K- decays, the CP-violating phase ϕs is measured, as well as the decay widths ΓL and ΓH of the light and heavy mass eigenstates of the B(s)(0)-B[over ¯]s0 system. The values obtained are ϕs=-0.058±0.049±0.006 rad, Γs≡(ΓL+ΓH)/2=0.6603±0.0027±0.0015 ps-1, and ΔΓs≡ΓL-ΓH=0.0805±0.0091±0.0032 ps-1, where the first uncertainty is statistical and the second, systematic. These are the most precise single measurements of those quantities to date. A combined analysis with Bs0→J/ψπ+π- decays gives ϕs=-0.010±0.039 rad. All measurements are in agreement with the standard model predictions. For the first time, the phase ϕs is measured independently for each polarization state of the K+K- system and shows no evidence for polarization dependence.

Minimal3+2sterile neutrino model at LBNE

In this paper we examine the sensitivity of the Long Baseline Neutrino Oscillation Experiment to the inclusion of two new sterile neutrino flavors with masses in the eV range. We implement a model with a modified Casas-Ibarra parametrization which can accommodate medium scale mass eigenstates and introduces a new complex mixing angle. We explore the new mixing angle parameter space and demonstrate how LBNE can be used to either provide evidence for or rule out a particular model of sterile neutrinos. Certain three-flavor CP-violation scenarios cannot be distinguished from the sterile neutrinos. Constraints from the Daya Bay reactor experiment and T2K are used to help lift this degeneracy.

Quasi-Classical Gravity Effect on Neutrino Oscillations in a Gravitational Field of a Heavy Astrophysical Object

In the framework of quantum field theory, a graviton interacts locally with a quantum state having definite mass, that is, the gravitational mass eigenstate, while a weak boson interacts with a state having definite flavor, that is, the flavor eigenstate. An interaction of a neutrino with an energetic graviton may trigger the collapse of the neutrino to a definite mass eigenstate with probability expressed in terms of PMNS mixing matrix elements. Thus, gravitons would induce quantum decoherence of a coherent neutrino flavor state similarly to how weak bosons induce quantum decoherence of a neutrino in a definite mass state. We demonstrate that such an essentially quantum gravity effect may have strong consequences for neutrino oscillation phenomena in astrophysics due to relatively large scattering cross sections of relativistic neutrinos undergoing large angle radiation of energetic gravitons in gravitational field of a classical massive source (i.e., the quasi-classical case of gravitational Bethe-Heitler scattering). This graviton-induceddecoherenceis compared todecoherencedue to propagation in the presence of the Earth matter effect. Based on this study, we propose a new technique for the indirect detection of energetic gravitons by measuring the flavor composition of astrophysical neutrinos.

Mass eigenstates in bimetric theory with matter coupling

In this paper we study the ghost-free bimetric action extended by a recently proposed coupling to matter through a composite metric. The equations of motion for this theory are derived using a method which avoids varying the square-root matrix that appears in the matter coupling. We make an ansatz for which the metrics are proportional to each other and find that it can solve the equations provided that one parameter in the action is fixed. In this case, the proportional metrics as well as the effective metric that couples to matter solve Einstein's equations of general relativity including a matter source. Around these backgrounds we derive the quadratic action for perturbations and diagonalize it into generalized mass eigenstates. It turns out that matter only interacts with the massless spin-2 mode whose equation of motion has exactly the form of the linearized Einstein equations, while the field with Fierz-Pauli mass term is completely decoupled. Hence, bimetric theory, with one parameter fixed such that proportional solutions exist, is degenerate with general relativity up to linear order around these backgrounds.

Quantum Decoherence of Neutrino Oscillation and Weak Measurement about Its Group Velocity

We theoretically explore the possibility of observing the quantum decoherence of neutrino oscillation due to the vacuum dispersion, that the wave-packet of neutrino spatially splits according to the different velocities of two mass eigenstates. We find that if this decoherence could be observed and the range of values of the mixing angle is known, then the superluminal neutrino phenomena could occur for some mixing angles as the consequence of a weak measurement about flavor mixing in the neutrino propagation. Our calculation gives the explicit dependence of group velocity shift to the decoherence factor and the weak value of neutrino's pre and post-selected states. We also study the related problems for the neutrino oscillation with three generations.

One-loop decaysA0→ZZ,Zγ,γγwithin the 2HDM and its search at the LHC

The general two-higgs doublet model (2HDM) contains a rich spectrum of neutral and charged Higgs bosons, whose detection would be a clear signal of new physics. When the Higgs potential is CP-conserving, the spectrum includes a pseudoscalar mass eigenstate $A^{0}$, which does not couple to vector bosons at tree-level. However, fermionic loops (top and bottom mainly) induce the coupling $AVV'$ (with $V,V'=\gamma, Z$) at higher orders. We evaluate the amplitude for the decays ${A^0} \to ZZ, Z\gamma, \gamma\gamma$, including a generic fermionic loop contribution, and present results on the branching ratios for 2HDM-I,II and III. Current LHC searches on heavy Higgs bosons are used as an estimate to constrain the allowed mass range for $A^0$.

Dark matter in the minimal inverse seesaw mechanism

We consider the possibility of simultaneously addressing the dark matter problem and neutrino mass generation in the minimal inverse seesaw realisation. The Standard Model is extended by two right-handed neutrinos and three sterile fermionic states, leading to three light active neutrino mass eigenstates, two pairs of (heavy) pseudo-Dirac mass eigenstates and one (mostly) sterile state with mass around the keV, possibly providing a dark matter candidate, and accounting for the recently observed and still unidentified monochromatic 3.5 keV line in galaxy cluster spectra. The conventional production mechanism through oscillation from active neutrinos can account only for ∼ 43% of the observed relic density. This can be slightly increased to ∼ 48% when including effects of entropy injection from the decay of light (with mass below 20 GeV) pseudo-Dirac neutrinos. The correct relic density can be achieved through freeze-in from the decay of heavy (above the Higgs mass) pseudo-Dirac neutrinos. This production is only effective for a limited range of masses, such that the decay occurs not too far from the electroweak phase transition. We thus propose a simple extension of the inverse seesaw framework, with an extra scalar singlet coupling to both the Higgs and the sterile neutrinos, which allows to achieve the correct dark matter abundance in a broader region of the parameter space, in particular in the low mass region for the pseudo-Dirac neutrinos.

The origin and status of the third neutrino

1. The three lepton families The elementary particles known today fall in two categories: twelve spin particles (fermions), the building blocks of matter, and twelve spin 1 particles (bosons), which are the mediators of all the forces but gravity. The last element in the Standard Model is a spin 0 particle, thought to be at the origin of the masses and called the “Higgs” after the name of one of the discoverers of the theory. Not yet detected, it is searched for at the new CERN LHC collider. The fermions come in three different groups, called families, of identical structure. The reason for that is unknown. Each family is made of a doublet of quarks, of charge +2/3 q and –1/3 q (q is the proton charge), and a doublet of leptons, one of charge –q and one neutral. The neutral leptons are collectively called neutrinos, but are three different particles, distinguished by an additive quantum number called “lepton flavour”. The electron (e) and the electron-neutrino ( e) have one unit of electronic flavour (–1 their antiparticles); the muon ( ) and the muon-neutrino ( μ) have one unit of muonic flavour and similarly for the tau ( ) and the tau-neutrino ( ). The charged leptons are distinguished by their masses (increasing with the family number) and lifetimes, neutrinos only by their lepton flavours. Neutrinos are produced in states of definite flavour, as e, μ or , in pairs with an antiparticle of the same and opposite flavour. Elementary interactions conserve flavours. So that, by definition, the electron-neutrino ( e) is the neutral lepton produced with a positron (e), the μ is the one produced with a + and the is the one produced with a . And electron-anti-neutrino is the neutral particle produced with an e, etc. Neutrinos cannot be detected directly. However, when one of them interacts with the matter producing a charged lepton, the latter can be detected. The identification of the charged lepton gives the flavour of the neutrino: if it is an electron (e) it was a e etc. Experiments show that neutrinos born with a flavour produce charged leptons of the same flavour, provided the ratio L/E between distance from production to interaction points and neutrino energy is not very large, namely if the oscillation phenomenon has no time to develop. Indeed, experiments in underground laboratories have shown that neutrinos do not behave as assumed in the Standard Model, they do change, “oscillate”, between one flavour and another. The evidence has gradually grown in the last four decades, by studying the es produced by the fusion reactions in the core of the Sun and the μs indirectly produced by the cosmic rays collisions in the atmosphere. Confirmations came by experiments with artificial neutrino sources: proton accelerators (producing mainly μ) and nuclear power reactors ( e ). There two types of experiments. In a disappearance experiment the flux of neutrinos of a certain flavour is known at production; if the flux is measured at a (large) distance and found to be less than expected, the oscillation to another flavour is inferred. In an appearance experiment a flavour not present at production is searched. Oscillations happen because neutrinos of definite flavour are not stationary states (mass eigenstates). The latter, 1, 2 and 3, do not change and have definite masses, m1, m2 and m3. The two basis are linked by an orthogonal transformation that can be expressed in terms of three rotations, through angles that we shall call 12, 23 and 13, and of phase factors. If neutrinos are Dirac particles, as assumed in the Standard Model, all but one of the phase factors can be absorbed, as in the case of quarks, in the wave functions of the states. However, neutrino and antineutrino might be two states of the same particle, namely ‘Majorana particles’. In this case two more phases, which we shall call M

Next-generation atmospheric neutrino experiments

Abstract A short review on the next-generation experiments aiming to study the neutrinos produced in cosmic-ray induced atmospheric showers is presented. The projects currently proposed rely on different complementary detection techniques, from the successful water Cherenkov and magnetized tracko-calorimeter techniques to the more innovative Liquid Argon technology. As all of the proposed detectors must be deeply buried to mitigate the atmospheric muon background, many experiments are expected to be placed deep underground. Following the neutrino telescope approach, the largest ones will be located deep under the sea/ice. Several future projects are part of a wider physics program which includes a neutrino beam. For such cases, the focus is put on the expected performances with only using atmospheric neutrinos. The main physics thread of the review is the question of the determination of the ordering of the neutrino mass eigenstates, referred to as the neutrino mass hierarchy. This falls into the broader context of the precise measurement of the neutrino mixing parameters. The expected reach of the future planned detectors in this respect is also addressed.

Spectroscopy of family gauge bosons

Spectroscopy of family gauge bosons is investigated based on a U(3) family gauge boson model proposed by Sumino. In his model, the family gauge bosons are in mass eigenstates in a diagonal basis of the charged lepton mass matrix. Therefore, the family numbers are defined by (e1,e2,e3)=(e,μ,τ), while the assignment for quark sector are free. For possible family-number assignments (q1,q2,q3), under a constraint from K0–K¯0 mixing, we investigate possibilities of new physics, e.g. production of the lightest family gauge boson at the LHC, μ−N→e−N, rare K and B decays, and so on.