Mass Gap Problem and Hodge Conjecture (original) (raw)
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Atomic bonding energies by β-decay and electric and magnetic energies can have mass gap. Their process to the mass gap can be expressed by quantum mechanics of holographical potential energies. Kinetic energy is a circumferential one, which is transitted from radial one. This is a kind of super symmetry. Laplace equation is derived from mass gap condition of quantum mechanics to the radial energy. Kinetic energy and static one (0 2 , − 0 2) make zero point one and harmonic vibrational one. And then the zero point one and the harmonic vibration one make the kinetic one and the static mass (0 2 , − 0 2). Any geometry can be configured by the super symmetry and Riemann hypothesis. Scalar, vector and complex are the same by the super symmetry. The super symmetries can configure any geometry. The cosmological constants (leftwise positive, rightwise positive, leftwise negative and rightwise negative) can generate the super symmetries.
A Possible Quantum-Gravitational Origin of the Neutrino Mass Difference ?
We discuss the theoretical possibility that the neutrino mass differences have part of their origin in the quantum-decoherence-inducing medium of space-time foam, which characterises some models of quantum gravity, in much the same way as the celebrated MSW effect, responsible for the contribution to mass differences when neutrinos pass through ordinary material media. We briefly describe consequences of such decoherent media in inducing CPT violation at a fundamental level, which would affect the neutrino oscillation probability; we speculate on the connection of such phenomena with the rôle of neutrinos for providing one possible source of a cosmological constant in the Universe, of the phenomenologically right order of magnitude. Finally we discuss possible experimental constraints on the amount of neutrino mass differences induced by quantum gravity, which are based on fits of a simple decoherence model with all the currently available neutrino data.
Yang–Mills theory is the (non-Abelian) quantum field theory underlying the Standard Model of particle physics; mathbb{R}^4 is Euclidean 4-space; the mass gap Δ is the mass of the least massive particle predicted by the theory. Therefore, the winner must first prove that Yang–Mills theory exists and that it satisfies the standard of rigor that characterizes contemporary mathematical physics, in particular constructive quantum field theory, which is referenced in the papers 45 and 35 cited in the official problem description by Jaffe and Witten.
Annual Review of Nuclear and Particle Science, 2006
▪ We review the present state and future outlook of our understanding of neutrino masses and mixings. We discuss what we think are the most important perspectives on the plausible and natural scenarios for neutrinos and attempt to throw light onto the flavor problem of quarks and leptons. This review focuses on the see-saw mechanism, which fits into a big picture of particle physics such as supersymmetry and grand unification, providing a unified approach to the flavor problem of quarks and leptons. We argue that, in combination with family symmetries, this may be at the heart of a unified understanding of the flavor puzzle. We also discuss other new physics ideas, such as neutrinos in models with extra dimensions, and possible theoretical implications of sterile neutrinos. We outline some tests for the various schemes.
Existence of Neutrino Mass : A New Mathematical Formulation
It is assumed that there exists a transformation law, even in the standard model framework, that transforms mass eigen states of neutrino to the flavour eigen states. The transformation matrix from mass eigen states to flavor states is assumed to be singular and therefore becomes unable to generate any mass of the neutrino. It is considered that a small deviation from that singular matrix leads to unitary PMNS matrix, which is able to diagonalize the mass matrix. A formulation is done to indicate the possible spontaneous symmetry breaking which can generate physical neutrino mass in eV scale. A mapping between symmetry transformations and a set of real numbers (0,k) is defined on the backdrop of the neutrino mass generation. Keywords: Neutrino mass, Beyond Standard Model, CKM Matrix, Mass and flavor eigen states of neutrinos.
Quantum correlations and the neutrino mass degeneracy problem
The European Physical Journal C, 2018
Many facets of nonclassicality are probed in the context of three flavour neutrino oscillations including matter effects and CP violation. The analysis is carried out for parameters relevant to two ongoing experiments NOνA and T2K, and also for the upcoming experiment DUNE. The various quantum correlations turn out to be sensitive to the mass-hierarchy problem in neutrinos. This sensitivity is found to be more prominent in DUNE experiment as compared to NOνA and T2K experiments. This can be attributed to the large baseline and high energy of the DUNE experiment. Further, we find that to probe these correlations, the neutrino (antineutrino) beam should be preferred if the sign of mass square difference ∆31 turns out to be positive (negative).
Neutrino Discrepancies and Higgs Neutrino Oscillation Masses
Neutrino Discrepancies and Higgs Neutrino Oscillation Masses, 2022
A history of neutrino measurements is described as a reply to a published video by Sabine Hossenfelder from September 21 st , 2021 https://youtu.be/p118YbxFtGg The sterile neutrino can be called a Higgs neutrino, as it derives from the Goldstone boson form of the Higgs Boson also coupled to the dark matter particle here called RMP for RestMass Photon. The problem with the Majorana form of the neutrinos is that they are indeed massless as fist proposed by the Standard Model and so are in fact their own antiparticles in the massless state. They do however assume a mass value as Dirac particles when mixing with the sterile scalar Higgs neutrinos explained by Sabine Hossenfelder in the link above.
Massive neutrinos and the Higgs boson mass window
Physical Review D, 2000
If neutrino masses are produced by a see-saw mechanism the Standard Model prediction for the Higgs mass window (defined by upper (perturbativity) and lower (stability) bounds) can be substantially affected. Actually the Higgs mass window can close completely, which settles an upper bound on the Majorana mass for the right-handed neutrinos, M , ranging from 10 13 GeV for three generations of quasi-degenerate massive neutrinos with mν ≃ 2 eV, to 5 × 10 14 GeV for just one relevant generation with mν ≃ 0.1 eV. A slightly weaker upper bound on M , coming from the requirement that the neutrino Yukawa couplings do not develop a Landau pole, is also discussed. PACS: 14.80.Bn, 14.60.Pq, Observations of the flux of atmospheric neutrinos by SuperKamiokande [1] provide strong evidence for neutrino oscillations, which in turn imply that (at least two species of) neutrinos must be massive. Additional support to this hypothesis is given by the need of neutrino oscillations to explain the solar neutrino flux deficit and the possible essential role of the neutrinos in the large scale structure of the universe [2]. Much work has been devoted in the last months in order to guess and to explain the structure and the origin of the neutrino mass matrices capable to account for the different observations .