Inhomogeneous pion condensed phase hosting topologically stable baryons

We discuss the inhomogeneous pion condensed phase within the framework of chiral perturbation theory. We show how the general expression of the condensate can be obtained solving three coupled differential equations, expressing how the pion fields are modulated in space. Upon using some simplifying assumptions, we determine an analytic solution in (3+1)-dimensions. The obtained inhomogeneous condensate is characterized by a non-vanishing topological charge, which can be identified with the baryonic number. In this way, we obtain an inhomogeneous system of pions hosting an arbitrary number of baryons at fixed position in space.

MASS, MATTER, MATERIALIZATION, MATTERGENESIS AND CONSERVATION OF CHARGE

Conservation of mass in classical physics and in chemistry is considered to be equivalent to conservation of matter and is a necessary condition together with other universal conservation laws to account for observed experiments. Indeed matter conservation is associated to conservation of building blocks (molecules, atoms, nucleons, quarks and leptons). Matter is massive but mass and matter are two distinct concepts even if conservation of mass and conservation of matter represent the same reality in classical physics and chemistry. Conservation of mass is a consequence of conservation of atoms. Conservation of mass is valid because in these cases it is a very good approximation, the variation of mass being tiny and undetectable by weighing. However, nuclear physics and particle physics clearly show that conservation of mass is not valid to express conservation of matter. Mass is one form of energy, is a positive quantity and plays a fundamental role in dynamics allowing particles to be accelerated. Origin of mass may be linked to recently discovered Higgs bosons. Matter conservation means conservation of baryonic number A and leptonic number L, A and L being algebraic numbers. Positive A and L are associated to matter particles, negative A and L are associated to antimatter particles. All known interactions do conserve matter thus could not generate, from pure energy, a number of matter particles different from that of number of antimatter particles. But our universe is material and neutral, this double message has to be deciphered simultaneously. Asymmetry of our universe demands an interaction which violates matter conservation but obeys all universal conservation laws, in particular conservation of electric charge Q. Expression of Q shows that conservation of (A–L) and total flavor TF are necessary and sufficient to conserve Q. Conservation of A and L is indeed a trivial case of conservation of (A–L) and is valid for all known interactions of the standard model. Assumption of a novel interaction MC conserving (A–L) but violating simultaneously A and L (not trivial case of conservation) would allow energy to be transformed into a pair of baryon lepton or into a pair of antibaryon antilepton of opposite charges. This model could explain the asymmetric but nevertheless electrically neutral Universe but could not account for the numerical value of the tiny excess of matter over antimatter. The concept of anti-Universe would be superfluous. Observation of matter nonconservation processes would be of great interest to falsify this speculation.

NEGATIVE NUMBERS AND ANTIMATTER PARTICLES

Dirac's equation states that an electron implies the existence of an antielectron with the same mass (more generally same arithmetic properties) and opposite charge (more generally opposite algebraic properties). Subsequent observation of antielectron validated this concept. This statement can be extended to all matter particles; observation of antiproton, antineutron, antideuton … is in complete agreement with this view. Recently antihypertriton was observed and 38 atoms of antihydrogen were trapped. This opens the path for use in precise testing of nature's fundamental symmetries. The symmetric properties of a matter particle and its mirror antimatter particle seem to be well established. Interactions operate on matter particles and antimatter particles as well. Conservation of matter parallels addition operating on positive and negative numbers. Without antimatter particles, interactions of the Standard Model (electromagnetism, strong interaction and weak interaction) cannot have the structure of group. Antimatter particles are characterized by negative baryonic number A or/and negative leptonic number L. Materialization and annihilation obey conservation of A and L (associated to all known interactions), explaining why from pure energy (A = 0, L = 0) one can only obtain a pair of matter particle antimatter particle — electron antielectron, proton and antiproton — via materialization where the mass of a pair of particle antiparticle gives back to pure energy with annihilation. These two mechanisms cannot change the difference in the number of matter particles and antimatter particles. Thus from pure energy only a perfectly symmetric (in number) universe could be generated as proposed by Dirac but observation showed that our universe is not symmetric, it is a matter universe which is nevertheless neutral. Fall of reflection symmetries shattered the prejudice that there is no way to define in an absolute way right and left or matter and antimatter. Experimental observation of CP violation aroused a great hope for explaining why our universe is not exactly matter antimatter symmetric. Sakharov stated that without the violation of baryonic number, it is not possible to obtain from pure energy a universe made of only matter. The fact that our universe is asymmetric (in number) but perfectly neutral, points toward the existence of a hypothetic interaction violating A and L but conserving all charges. This Matter Creation (MC) interaction creating either a pair of matter particles or antimatter particles (instead of a pair of particle antiparticle) would have a charge BAL = (A-L) and a neutral messenger Z*. Even if CP is conserved, MC would allow the creation of a number of matter particles not exactly equal to the number of antimatter particles. Our universe would then correspond to the remaining excess when all matter antimatter pairs have disappeared. Observation of matter nonconservation processes would be of great interest to falsify this speculation. In a plan with A and L as axes, pure energy is represented by the origin (A = 0, L = 0). A symmetric universe is also represented by (A = 0, L = 0) meaning that there are exactly the same number of baryons and antibaryons, and the same number of leptons and antileptons. Our present matter universe is instead represented by a point of the diagonal with A = L = present A value. This value is tiny relative to the number of gammas resulting from the annihilation of matter–antimatter particles.

IS IT POSSIBLE TO CONSERVE ELECTRIC CHARGE WITHOUT SEPARATELY CONSERVING BARYONIC NUMBER AND LEPTONIC NUMBER?

Charges that are sources of fields must be universally conserved. Any quantity which is proved to be violated in certain circumstance cannot be a source of field. To account for the asymmetry of our Universe baryon number A has to be violated; thus A cannot be a charge. We postulate a new interaction, matter creation, with (A–L) as charge and Z * as messenger. Conservation of (A–L) instead of (3A–L) suggested by Sakharov is deduced on the one hand from observational facts (our Universe is both material and neutral) and on the other hand from the generalized Gell-Mann and Nishijima formula. Conservation of (A–L) forbids neutrinoless double beta decay and neutron antineutron oscillations. The union of four interactions — electromagnetism, the MC interaction, the weak interaction and the strong interaction — considered as the product U(1) × U(1) × SU(2) × SU(3) would account for available experimental and observational data. Observation of processes violating baryon number conservation would be of great interest in falsifying this suggestion.

WHAT IS THE SIGNIFICANCE OF THE CONSERVATION OF ELECTRIC CHARGE Q?

The conservation of electric charge Q is a universal law in the sense that it should be conserved in any interaction, known or yet unknown. However, Q should not be considered as a simple number but as the half sum of two irreducible quantities, the baryon lepton asymmetric number BAL = A-L (where A is the baryonic number and L is the leptonic number) and total flavor TF. Conservation of electric charge implies obviously conservation of Q (considered as a simple number) but also BAL and TF. We verify that electromagnetism and strong interaction which conserve Q, A and L and all individual flavors conserve obviously BAL and TF; that weak interaction which conserves Q, A and L conserves also BAL and TF. However, conservation of BAL does not necessarily imply conservation of A and L. In effect Δ BAL = 0 has another solution ΔA = ΔL = ±1 which points to a possible solution to explain how a material and neutral universe could arise evolving from an A = 0, L = 0, Q = 0 state to an A > 0, Q = 0 state through a process which would conserve BAL and TF without conserving separately A and L.

CAPTURE CONDITIONS FOR STRANGELETS IN THE GEOMAGNETIC FIELD

Strangelets coming from the interstellar medium are an interesting target in experiments searching for evidence of this hypothetic state of hadronic matter. For a stationary population of strangelets to be trapped by the geomagnetic field, these particles would have to fulfill certain conditions, namely having magnetic rigidities above the geomagnetic cutoff and below a certain threshold for adiabatic motion. For totally ionized strangelets these two conditions prevent them to be stably trapped if one considers that a similar mechanism resulting in the anomalous cosmic rays belt should also be responsible for strangelet trapping. The situation could be different if those particles could reach the earth with an effective charge less than total ionization, since it would lower the particle's magnetic rigidity, but cross sections are much too low to allow interstellar electronic recombination for strangelets in the low baryonic number range. If traces of strangelets are indeed measured as a component of the radiation belt, alternative methods for their capture have to be proposed.

ARE NEUTRON-RICH ELEMENTS PRODUCED IN THE COLLAPSE OF STRANGE DWARFS?

The structure of strange dwarfs and that of hybrid stars with the same baryonic number is compared. There is a critical mass (M ≈ 0.24M⊙) in the strange dwarf branch, below which configurations with the same baryonic number in the hybrid star branch are more stable. If a transition occurs between both branches, the collapse releases an energy of about of 3 × 1050 erg , mostly in the form of neutrinos resulting from the conversion of hadronic matter onto strange quark matter. Only a fraction (~ 4%) is required to expel the outer neutron-rich layers. These events may contribute significantly to the chemical yield of nuclides with A ≥ 80 in the Galaxy, if their frequency is of about one per 1,500 years.

WHAT IS A TRULY NEUTRAL PARTICLE?

An electrically charged particle is necessarily different from its antiparticle while an electrically neutral particle is either identical with or different from its antiparticle. A truly neutral particle is a particle identical to its antiparticle, which means that all its algebraic intrinsic properties are equal to zero since particle and antiparticle have all their algebraic intrinsic properties opposite. We propose two complementary methods to recognize the true nature of any electrically neutral particle. On the one hand, any non-null algebraic intrinsic property of a particle (properties such as Q, magnetic moment already known from classical physics, or quantum numbers such as baryonic number A, lepton number L or flavors, which are meaningful only in the quantum world) reveals that it is distinct from its antiparticle. On the other hand, any particle decaying through a self-conjugate channel or/and through both two conjugate channels is a truly neutral particle implying then that all algebraic intrinsic properties, known or yet unknown, of this particle are null. According to these methods, the neutrino, like any fermion, cannot be its own antiparticle, so neutrinoless double beta decay cannot take place in nature. We point out the internal contradiction required by the existence of hypothetical neutrinoless double beta decay. We suggest that persistent failure to find experimental evidence for this decay mechanism despite huge efforts dedicated to this aim is consistent with the physics of this process. The immediate consequence would be that limits of neutrino mass deduced from neutrinoless double beta decay cannot be used as constraints in contrast with mass limits deduced from the behavior of the end-point in simple beta spectra.

Line Formation in U Gem and T Leo

We present 3-D LTE radiative transfer calculations [1] for H, He and Ca in accretion disks (AD) of dwarf novae in quiescence. The model disk is assumed to be in hydrostatic equilibrium vertically, and to rotate with Keplerian velocities. Calculated emission lines are fitted to phase-averaged, continuum-subtracted spectra of U Gem (Fig. 1) and T Leo (Fig. 2). Up to four parameters of the AD have been fitted: distance D, baryonic number density N, isotropic turbulence Vtu and disk temperature T; the latter two are assumed to be constant throughout the disk. Geometrical parameters are from [2] and [3].