Flavor Vacuum Research Articles

On the quark spectral function in QCD

We calculate the spectral function of light quark flavours in 2+1 flavour vacuum QCD in the isospin-symmetric approximation. We employ spectral Dyson-Schwinger equations and compute the non-perturbative quark propagator directly in real-time, using recent spectral reconstruction results from Gaussian process regression of gluon propagator data in 2+1 flavour lattice QCD. Our results feature a pole-like peak structure at time-like momenta larger than the propagator’s gapping scale as well as a negative scattering continuum, which we exploit assuming an analytic pole-tail split during the iterative solution. The computation is augmented with a general discussion of the impact of the quark-gluon vertex and the gluon propagator on the analytic structure of the quark propagator. In particular, we investigate under which conditions the quark propagator shows unphysical complex poles. Our results offer a wide range of applications, encompassing the ab-initio calculation of transport as well as resonance properties in QCD.

Non-Abelian gauge structure and flavor mixing in quantum field theory1

The quantum field theory formalism describing the phenomenon of neutrino mixing and oscillations is reviewed in its essential aspects. The condensate structure of the flavor vacuum state is considered and its non-perturbative nature is discussed within the existence in the quantum field theory of the manifold of unitarily inequivalent representations of the anticommutation relations. The Poincaré structure of the theory is discussed in connection with the gauge theory features of neutrino mixing, where the possibility arises to describe flavored neutrinos as on-shell fields with definite masses. The flavor vacuum state may be thought of as a refractive medium where different refraction indexes are related to the different neutrino masses. Neglecting the condensate structure of the flavor vacuum implies neglecting second-order contributions in the gauge field coupling and leads to experimentally inconsistent results.

Boson mixing and flavor vacuum in the expanding Universe: A possible candidate for the dark energy

We analyze the boson mixing in curved spacetime and compute the expectation value of the energy-momentum tensor of bosons on the flavor vacuum in spatially flat Friedmann-Lemaître-Robertson-Walker metrics. We show that the energy-momentum tensor of the flavor vacuum behaves as the effective energy-momentum tensor of a perfect fluid. Assuming a fixed de Sitter background, we show that the equation of state can assume values in the interval [−1,1], and, in the flat space-time limit has a value −1, which is the one of the dark energy. The results here presented show that vacuum of mixed bosons like neutrino super-partners, can represent a possible component of the dark energy of the Universe.

Field Mixing in Curved Spacetime and Dark Matter

An extensive review of recent results concerning the quantum field theory of particle mixing in curved spacetime is presented. The rich mathematical structure of the theory for both fermions and bosons, stemming from the interplay of curved space quantization and field mixing, is discussed, and its phenomenological implications are shown. Fermionic and bosonic oscillation formulae for arbitrary globally hyperbolic spacetimes are derived and the transition probabilities are explicitly computed on some metrics of cosmological and astrophysical interest. The formulae thus obtained are characterized by a pure QFT correction to the amplitudes, which is absent in quantum mechanics, where only the phase of the oscillations is affected by the gravitational background. Their deviation from the flat space probabilities is demonstrated, with the aid of numerical analyses. The condensate structure of the flavor vacuum of mixed fermions is studied, assessing its role as a possible dark matter component in a cosmological context. It is shown that the flavor vacuum behaves as a barotropic fluid, satisfying the equation of the state of cold dark matter. New experiments on the cosmic neutrino background, as PTOLEMY, may validate these theoretical results.

Neutrino capture on tritium as a probe of flavor vacuum condensate and dark matter

We show that the study of neutrino capture on tritium, for non-relativistic neutrinos, can allow to distinguish among the various neutrino models, eventually prove the quantum field theory condensation effects and permit to test the hypothesis according to which the flavor vacuum energy gives a contribution to the dark matter of the universe. Indeed, we show that the capture rate depends on the neutrino model considered, and that it brings an imprint of the flavor vacuum condensate. Experiments like PTOLEMY, designed to reveal the cosmic neutrino background, then can give an indication of the existence of the dark matter component induced by neutrino mixing.

Quantum flavor vacuum in the expanding universe: A possible candidate for cosmological dark matter?

We analyze fermion mixing in the framework of field quantization in curved spacetime. We compute the expectation value of the energy momentum tensor of mixed fermions on the flavor vacuum. We consider spatially flat Friedmann-Lemaitre-Robertson-Walker metrics, and we show that the energy momentum tensor of the flavor vacuum is diagonal and conserved. Therefore it can be interpreted as the effective energy momentum tensor of a perfect fluid. In particular, assuming a fixed De Sitter background, the equation of state of the fluid is consistent with that of dust and cold dark matter. Our results establish a new link between quantum effects and classical fluids, and indicate that the flavor vacuum of mixed fermions may represent a new component of dark matter.

Neutrino Mixing and Oscillations in Quantum Field Theory: A Comprehensive Introduction

We review some of the main results of the quantum field theoretical approach to neutrino mixing and oscillations. We show that the quantum field theoretical framework, where flavor vacuum is defined, permits giving a precise definition of flavor states as eigenstates of (non-conserved) lepton charges. We obtain the exact oscillation formula, which in the relativistic limit reproduces the Pontecorvo oscillation formula and illustrates some of the contradictions arising in the quantum mechanics approximation. We show that the gauge theory structure underlies the neutrino mixing phenomenon and that there exists entanglement between mixed neutrinos. The flavor vacuum is found to be an entangled generalized coherent state of SU(2). We also discuss flavor energy uncertainty relations, which impose a lower bound on the precision of neutrino energy measurements, and we show that the flavor vacuum inescapably emerges in certain classes of models with dynamical symmetry breaking.

Flavor-vacuum entanglement in boson mixing

Mixing transformations in quantum field theory are nontrivial, since they are intimately related to the unitary inequivalence between Fock spaces for fields with definite mass and fields with definite flavor. Considering the superposition of two neutral scalar (spin-0) bosonic fields, we investigate some features of the emerging condensate structure of the flavor vacuum. In particular, we quantify the flavor vacuum entanglement in terms of the von Neumann entanglement entropy of the reduced state. Furthermore, in a suitable limit, we show that the flavor vacuum has a structure akin to the thermal vacuum of thermo field dynamics, with a temperature dependent on both the mixing angle and the particle mass difference.

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.

Chiral symmetry-breaking schemes and dynamical generation of masses and field mixing

In this paper we review dynamical generation of field mixing after chiral symmetry breaking. We also study the explicit form of discrete transformations of flavor states in a two-flavor scalar model with field mixing. We find that CPT symmetry is spontaneously broken on flavor vacuum because of its dynamically generated condensate structure.

Some nontrivial aspects of Poincaré and CPT invariance of flavor vacuum

We study the explicit form of Poincar\'e and discrete transformations of flavor states in a two-flavor scalar model, which represents the simplest example of the field mixing. Because of the particular form of the flavor vacuum condensate, we find that the aforementioned symmetries are spontaneously broken. The ensuing vacuum stability group is identified with the Euclidean group E(3). With the help of Fabri-Picasso theorem, we show that flavor vacua with different time labels and in different Lorentz frames are unitarily inequivalent to each other and they constitute a manifold of zero-flavor-charge states. Despite the spontaneous breakdown of Poincar\'e and CPT symmetries that characterises such vacua, we provide arguments on the absence of Goldstone Bosons. We also prove that the phenomenologically relevant oscillation formula is invariant under these transformations.

Dynamical generation of flavor vacuum and Lorentz invariance

In this paper we review dynamical generation of field mixing after chiral symmetry breaking. We also study the explicit form of Lorentz boosts transformations of flavor states in a two-flavor scalar model with field mixing. We find that Lorentz symmetry is spontaneously broken on flavor vacuum because of its dynamically generated condensate structure.

Dynamical generation of field mixing via flavor vacuum condensate

In this paper we study dynamical chiral symmetry breaking of a generic quantum field theoretical model with global chiral flavor symmetry. By purely algebraic means we analyze the vacuum structure for different symmetry breaking schemes and show explicitly how the ensuing non-trivial flavor vacuum condensate characterizes the phenomenon of field mixing. In addition, with the help of Ward-Takahashi identities we demonstrate the emergence of a correct number of Nambu-Goldstone modes in the physical spectrum.

Generating functional for the Green’s functions of a two-flavor bosonic model

We examine a simple two-flavor scalar model with a non-diagonal mass matrix. We argue that the conventional definition of the QFT partition function does not allow to evaluate the Green’s functions with respect to the flavor vacuum as it favors only the mass vacuum. By using functional-integral techniques, we derive new generating functional for Green’s functions on the flavor vacuum.

Noncommutative spectral geometry, Bogoliubov transformations and neutrino oscillations

In this report we show that neutrino mixing is intrinsically contained in Connes’ noncommutatives pectral geometry construction, thanks to the introduction of the doubling of algebra, which is connected to the Bogoliubov transformation. It is known indeed that these transformations are responsible for the mixing, turning the mass vacuum state into the flavor vacuum state, in such a way that mass and flavor vacuum states are not unitary equivalent. There is thus a red thread that binds the doubling of algebra of Connes’ model to the neutrino mixing.

Dark matter and dark energy via nonperturbative (flavor) vacua

A non-perturbative field theoretical approach to flavour physics (Blasone-Vitiello formalism) has been shown to imply a highly non-trivial vacuum state. In a previous work, we implemented the approach on a simple supersymmetric model (free Wess-Zumino), with flavour mixing, which was regarded as a model for free neutrinos and sneutrinos. The resulting effective vacuum (called "flavour vacuum") was found to be characterized by a strong SUSY breaking. In this paper we explore the phenomenology of the model and we argue that the flavour vacuum is a consistent source for both Dark Energy (thanks to the bosonic sector of the model) and Dark Matter (via the fermionic one). Quite remarkably, besides the parameters connected with neutrino physics, in this model no other parameters have been introduced, possibly leading to a predictive theory of Dark Energy/Matter. Despite its oversimplification, such a toy model already seems capable to shed some light on the observed energy hierarchy between neutrino physics, Dark Energy and Dark Matter. Furthermore, we move a step forth in the construction of a more realistic theory, by presenting a novel approach for calculating relevant quantities and hence extending some results to interactive theories, in a completely non-perturbative way.

D-foam-induced flavor condensates and breaking of supersymmetry in free Wess-Zumino fluids

Recently we argued that a particular model of string-inspired quantum space-time foam (D-foam) may induce oscillations and mixing among flavoured particles. As a result, rather than the mass-eigenstate vacuum, the correct ground state to describe the underlying dynamics is the flavour vacuum, proposed some time ago by Blasone and Vitiello as a description of quantum field theories with mixing. At the microscopic level, the breaking of target-space supersymmetry is induced in our space-time foam model by the relative transverse motion of brane defects. Motivated by these results, we show that the flavour vacuum, introduced through an inequivalent representation of the canonical (anti-) commutation relations, provides a vehicle for the breaking of supersymmetry (SUSY) at a low-energy effective field theory level; on considering the flavour-vacuum expectation value of the energy-momentum tensor and comparing with the form of a perfect relativistic fluid, it is found that the bosonic sector contributes as dark energy while the fermion contribution is like dust. This indicates a strong and novel breaking of SUSY, of a non-perturbative nature, which may characterize the low energy field theory of certain quantum gravity models.

Quantum gravity, flavour vacua and supersymmetry

AbstractI review a novel and non‐perturbative way of breaking Supersymmetry in the flavour sector of electrically neutral particles, as a result of flavour mixing in the presence of stringy quantum gravity space‐time foam backgrounds that violate Lorentz and CPT symmetries. In these models, part of the mixing may itself be induced dynamically by the interactions of the flavoured particles with the space‐time foam.

An AdS/QCD model from tachyon condensation: II

A simple holographic model is presented and analyzed that describes chiral symmetry breaking and the physics of the meson sector in QCD. This is a bottom-up model that incorporates string theory ingredients like tachyon condensation which is expected to be the main manifestation of chiral symmetry breaking in the holographic context. As a model for glue the Kuperstein-Sonnenschein background is used. The structure of the flavor vacuum is analyzed in the quenched approximation. Chiral symmetry breaking is shown at zero temperature. Above the deconfinement transition chiral symmetry is restored. A complete holographic renormalization is performed and the chiral condensate is calculated for different quark masses both at zero and non-zero temperatures. The 0^{++},0^{-+},1^{++},1^{--} meson trajectories are analyzed and their masses and decay constants are computed. The asymptotic trajectories are linear. The model has one phenomenological parameter beyond those of QCD that affects the 1^{++},0^{-+} sectors. Fitting this parameter we obtain very good agreement with data. The model improves in several ways the popular hard-wall and soft wall bottom-up models.

Stable periodic regime in a scalar field cosmology

Motivated by a microscopic model of string-inspired foam, in which foamy structures are provided by brany point-like defects (D-particles) in space-time, we discuss flavour mixing in curved space-time for spin-0 and spin-1/2 particles. This can be view as the low energy limit of flavour non-preserving interactions of stringy matter excitations with the defects, and non-trivial space-time background induced by quantum fluctuations of the D-particles. We show, at late epochs of the Universe, that both the fermionic and the bosonic vacuum condensate behaves as a fluid with negative pressure and positive energy; however the equation of state has wfermion > -1/3 and therefore the contribution of fermion-fluid flavour vacuum alone could not yield accelerating Universes. On the other hand, for the boson fluid the equation of state is, for late eras, close to wboson → -1, and hence overall the D-foam universe appears accelerating at late eras.