Mass Gap Problem Research Articles

Neutral Electron (e°) or Neutrino (ν): e° ≡ ν

In order to solve the Neutron decay mass gap problem, Pauli proposed a precise solution. The brilliant idea of a 3rd particle came to Pauli (fully shared by Fermi) to compensate the energy-mass gap that emerged from the disintegration of the neutron, or negative b decay (bd-): N® P + e-.
 
 The basic requirements originally requested by Pauli and Fermi for the new particle, later called neutrino, are essentially three: it is electrically neutral and it must have the same mass and spin of an electron. Hence, if the mass of the neutrino (n) corresponded to that assumed by Pauli and Fermi, the βd- mass gap problem would be brilliantly solved.
 
 However, the current upper limits of the mass of the n are < 2eV.
 
 Here we show that a clear incongruity comes out: the mass attributed to the n will never be able to solve the energy gap problem of the βd- : it takes ≃ 250,000 n to compensate the energy-mass gap. 
 
 Unless we consider, instead of n, another particle, probably still unknown, as the 3rd particle of βd-. To find a solution, we hypothesized the existence of an electron with no electric charge: a neutral electron (e°).

Can Cosmologically Coupled Mass Growth of Black Holes Solve the Mass Gap Problem?

Observations of elliptical galaxies suggest that black holes (BHs) might serve as dark energy candidates, coupled to the expansion of the Universe. According to this hypothesis, the mass of a BH could increase as the Universe expands. BH low-mass X-ray binaries (LMXBs) in the Galactic disk were born several gigayears ago, making the coupling effect potentially significant. In this work, we calculate the evolution of BH binaries with a binary population synthesis method to examine the possible influence of cosmologically coupled growth of BHs, if it really exists. The measured masses of the compact objects in LMXBs show a gap around ∼2.5–5 M ⊙, separating the most-massive neutron stars from the least-massive BHs. Our calculated results indicate that considering the mass growth seems to (partially) account for the mass gap and the formation of compact BH LMXBs, alleviating the challenges in modeling the formation and evolution of BH LMXBs with traditional theory. However, critical observational evidence like the detection of intermediate-mass BH binaries is required to test this hypothesis.

Revisiting Black Hole Hyperaccretion in the Center of Gamma-Ray Bursts for the Lower Mass Gap

The ultrarelativistic jets triggered by neutrino annihilation processes or Blandford–Znajek (BZ) mechanisms in stellar-mass black hole (BH) hyperaccretion systems are generally considered to power gamma-ray bursts (GRBs). Due to the high accretion rate, the central BHs might grow rapidly on a short timescale, providing a new way to understand the lower mass gap problem. In this paper, we use the BH hyperaccretion model to investigate BH mass growth based on observational GRB data. The results show that (i) if the initial BH mass is set as 3 M ⊙, the neutrino annihilation processes are capable of fueling the BHs to escape the lower mass gap for more than half of long-duration GRBs (LGRBs), while the BZ mechanism is inefficient in triggering BH growth for LGRBs; (ii) the mean BH mass growth in the case of LGRBs without observable supernova (SN) association is much larger than that in the case of LGRBs associated with SNe for both mechanisms, which implies that more massive progenitors or lower SN explosion energies prevail throughout the former cases; (iii) for the short-duration GRBs, the mean BH mass growth is satisfied with the mass supply limitation in the scenario of compact object mergers, but the hyperaccretion processes are unable to rescue BHs from the gap in binary neutron star (NS) mergers or the initial BH mass being 3 M ⊙ after NS−BH mergers.

Mass gap problem and Planck constant

The mass gap problem is about defining the constant that defines the minimal excitation of the vacuum. Planck’s constant is defining the minimal possible excitation of the vacuum from the point of quantum mechanics. The mass gap problem can be solved in quantum mechanics by the formulation of the photon’s mass according to the Planck‐Einstein relation.

Towards non-perturbative quantization and the mass gap problem for the Yang–Mills field

In this paper, we reduce the problem of quantization of the Yang–Mills field Hamiltonian to a problem for defining a probability measure on an infinite-dimensional space of gauge equivalence classes of connections on [Formula: see text]. We suggest a formally self-adjoint expression for the quantized Yang–Mills Hamiltonian as an operator on the corresponding Lebesgue [Formula: see text]-space. In the case when the Yang–Mills field is associated to the abelian group [Formula: see text], we define the probability measure which depends on two real parameters [Formula: see text] and [Formula: see text]. This yields a non-standard quantization of the Hamiltonian of the electromagnetic field, and the associated probability measure is Gaussian. The corresponding quantized Hamiltonian is a self-adjoint operator in a Fock space the spectrum of which is [Formula: see text], i.e. it has a gap.

Possible Explanation of the Quark Confinement and Asymptotic Freedom, and Possible Solution to the Yang-Mills Mass Gap Problem

With this work, we try to answer 3 fundamental questions that have plagued mathematicians and physicists for several decades. As known, the spontaneous symmetry breaking (SSB) and the Brout-Englert-Higgs Mechanism (BEH-M) solved the Yang-Mills Mass Gap Problem. However, various mathematicians, even prestigious ones, consider the basic assumptions of the gauge theories to be wrong, as well as in conflict with the experimental evidences and in clear disagreement with the facts, distorcing the physical reality itself. Likewise, the Quantum Fields Theory (QFT) is mathematically inconsistent, adopting a mathematical structure somewhat complicated and arbitrary, which does not satisfy the strong demands for coherence. The weakest point of the gauge theories, in our opinion, consists in imposing that all the particles must be free of an intrinsic mass (massless).
 On the contrary, even for the particle considered universally massless, i.e. the photon (P), our calculations show a dynamic-mass, a push-momentum (p) of 1.325⋅10−22[g⋅cm/s]. That is, an optic P hits a particle with an energy-mass greater than 100 protons rest-mass’. It is clear that if we replaced this value with the full value of the P inserted in the equations of the Perturbation Theory, QFT and Yang-Mills theories, all divergences, that is all zeroes and infinities, would suddenly disappear.
 Consequently, the limits imposed by the SSB disappear so that there is no longer any need to deny the mass to the Nuclear Forces bosons, including the Yang-Mills b quantum. Still, the photons (Ps) are the basis of the quantum vacuum energy, which is distributed ubiquitously, also within the intra-atomic spaces. It is likely that a lot of Ps were trapped in atomic nuclei (at the time of nucleosynthesis) and among quarks (Qs) at the time of primordial nucleonic synthesis. We believe that when Qs get too close to each other, till repelling each other (Asymptotic Freedom of Qs), this may depend on the presence of a multitude of Ps that, no further compressible, begin to exert an antigravity repulsive force, just as a Dark Energy. This limit to Compressibility (C) of the radiation is shown in equation: PV 4/3 = C, where V is the volume, and P is the Pressure of the photonic gas. Quantum Mechanics plays a crucial role, through the Uncertainty Principle, in the spatial Confinement of Qs, which have remained eternally confined in an extremely narrow space by the Strong Interaction, but in primis by the very short range (likely ≈8.44[±1.44]⋅10-16cm) and lifetime of gluon(G) which, from our calculations, is ≈2.73[±0.564]⋅10-26 sec. Therefore, a new parameter may be added to the Qs and G spatial Confinement: the b quantum or G Temporal Confinement (and of their Colours and anti-Colours).

Yang-Mills Mass Gap Clay Institute Problem Solution

Here is the solution to the Yang-Mills Mass Gap Problem as described below. The Mass in the material universe is a balance between the resistance to mass formation (cuz=Pi-base e), squeezing Energy, and Gravity pulling it apart. There is an explanation as to why there are 116 sable elements in the material universe. The calculations are verified by predicting the size of the universe within experimental error.

Yang–Mills mass gap at large-N, noncommutative YM theory, topological quantum field theory and hyperfiniteness

We review a number of old and new concepts in quantum gauge theories, some of which are well-established but not widely appreciated, some are most recent, that may have analogs in gauge formulations of quantum gravity, loop quantum gravity, and their topological versions, and may be of general interest. Such concepts involve noncommutative gauge theories and their relation to the large-N limit, loop equations and the change to the anti-selfdual (ASD) variables also known as Nicolai map, topological field theory (TFT) and its relation to localization and Morse–Smale–Floer homology, with an emphasis both on the mathematical aspects and the physical meaning. These concepts, assembled in a new way, enter a line of attack to the problem of the mass gap in large-NSU(N) Yang–Mills (YM), that is reviewed as well. Algebraic considerations furnish a measure of the mathematical complexity of a complete solution of large-NSU(N) YM: In the large-N limit of pure SU(N) YM the ambient algebra of Wilson loops is known to be a type II1 nonhyperfinite factor. Nevertheless, for the mass gap problem at the leading 1/N order, only the subalgebra of local gauge-invariant single-trace operators matters. The connected two-point correlators in this subalgebra must be an infinite sum of propagators of free massive fields, since the interaction is subleading in [Formula: see text], a vast simplification. It is an open problem, determined by the growth of the degeneracy of the spectrum, whether the aforementioned local subalgebra is in fact hyperfinite. Moreover, the sum of free propagators that occurs in the two-point correlators in the aforementioned local subalgebra must be asymptotic for large momentum to the result implied by the asymptotic freedom and the renormalization group: This fundamental constraint fixes asymptotically the residues of the poles of the propagators in terms of the mass spectrum and of the anomalous dimensions of the local operators. For the mass gap problem, in the search of a hyperfinite subalgebra containing the scalar sector of large-N YM, a major role is played by the existence of a TFT underlying the large-N limit of YM, with twisted boundary conditions on a torus or, which is the same by Morita duality, on a noncommutative torus. The TFT is trivial at the leading large-N order and localized on a set of critical points by means of a quantum version of Morse–Smale–Floer homology, that involves loop equations in the ASD variables. A hyperfinite sector arises by fluctuations around the trivial TFT, in which the joint spectrum of scalar and pseudoscalar glueballs is linear in the square of the masses [Formula: see text] with degeneracy k = 1, 2,…, and the two-point correlator satisfies the aforementioned fundamental constraint arising by the asymptotic freedom and the renormalization group.

On the Yang-Mills mass gap problem

Theorem 4.1 of the author’s paper “Quantum Yang-Mills-Weyl dynamics in the Schroedinger paradigm”, RJMP 21 (2), 169–188 (2014) claims the relative ellipticity of cutoff Yang-Mills quantum energy-mass operators in von Neumann algebras with regular traces. This implies that the spectra of cutoff self-adjoint Yang-Mills energy-mass operators in a nonperturbative quantum Yang-Mills theory (with an arbitrary compact simple gauge group) are nonnegative sequences of the eigenvalues converging to +∞. The spectra are self-similar in the inverse proportion to the running coupling constant. In particular, they have self-similar positive spectral mass gaps. Presumably, this is a solution of the Yang-Mills Millennium problem.

The Gribov phenomenon in flat and curved spaces

The quantization of Yang–Mills theories relies on the gauge-fixing procedure. However, in the non-Abelian case this procedure leads to the well-known Gribov ambiguity. In order to solve the ambiguity a modification of the functional integral formula must be introduced. As a consequence of this, the Green functions get deep modifications in the infrared. We consider, in particular, the SU (N) case and show that in the pure gauge case the ghost propagator is enhanced, while the gluon propagator is suppressed in this limit, therefore the study of the Gribov ambiguity may shed some light on the mass gap problem and on color confinement. We discuss some recent developments on the subject in the case of a curved background. We argue that the concurrent presence of a spacetime curvature and the Gribov ambiguity may introduce further modifications to the Green functions in the infrared.

Glueball mass from quantized knot solitons and gauge-invariant gluon mass

We propose an approach which enables one to obtain simultaneously the glueball mass and the gluon mass in the gauge-invariant way to shed new light on the mass gap problem in Yang-Mills theory. First, we point out that the Faddeev (Skyrme--Faddeev-Niemi) model can be induced through the gauge-invariant vacuum condensate of mass dimension two from SU(2) Yang-Mills theory. Second, we obtain the glueball mass spectrum by performing the collective coordinate quantization of the topological knot soliton in the Faddeev model. Third, we demonstrate that a relationship between the glueball mass and the gluon mass is obtained, since the gauge-invariant gluon mass is also induced from the relevant vacuum condensate. Finally, we determine physical values of two parameters in the Faddeev model and give an estimate of the relevant vacuum condensation in Yang-Mills theory. Our results indicate that the Faddeev model can play the role of a low-energy effective theory of the quantum SU(2) Yang-Mills theory.

Precanonical quantization of Yang-Mills fields and the functional Schrödinger representation

Precanonical quantization of pure Yang-Mills fields, which is based on the covariant De Donder-Weyl (DW) Hamiltonian formulation, and its connection with the functional Schrödinger representation in the temporal gauge are discussed. The mass gap problem is related to the finite-dimensional spectral problem for a generalized Clifford-valued magnetic Schrödinger operator which represents the DW Hamiltonian operator.