Monopole Mass Research Articles

Thermal production of superheavy magnetic monopoles in the early universe

Starting with an initial abundance of zero, we calculate the thermal production of magnetic monopoles by using the monopole-antimonopole annihilation cross section and detailed balance. The final abundance of monopoles depends exponentially upon m/ T i ; m is the monopole mass ∼10 16 GeV and T i is the temperature when production commences. For m/ T i ≈35–55 the present monopole to photon ratio is nM/ n γ ≈10 −23−10 −38, less than the bound derived from the present mass density, but possibly large enough to be detected. This calculation provides a lower bound on the monopole abundance for a given m/ T i .

Massive magnetic monopoles: Indirect and direct limits on their number density and flux

The existence of very massive magnetic monopoles is a necessary consequence of most unified theories of the strong, electromagnetic, and weak interactions. Estimates of their masses range from ${10}^{15}$ to ${10}^{17}$ that of a proton. Monopoles should have been produced in the "big bang" and survived to the present, either trapped in matter or in flight. By virtue of their huge mass, these monopoles might have eluded previous searches designed to detect monopoles with much smaller mass. I review the indirect limits which can be placed on monopoles because of the existence of large-scale galactic magnetic fields. I also review the experimental searches and reinterpret them to obtain limits for very massive monopoles. If the monopole masses are \ensuremath{\lesssim}5\ifmmode\times\else\texttimes\fi{}${10}^{14}$ GeV/${\mathit{c}}^{2}$, their concentration must be \ensuremath{\lesssim}${10}^{\ensuremath{-}27}$ monopoles/nucleon from searches for monopoles trapped in meteorites. This limit is several orders of magnitude lower than the astrophysical limits.

Superheavy Magnetic Monopoles

The basic principles of magnetism and the history of thought on the existence of magnetic monopoles are reviewed. The properties of magnetic monopoles as predicted by Dirac, time reversal arguments and unified gauge theories are discussed. Gauge theory predictions of the mass and flux of monopoles suggest why efforts to detect them have not yet been successful and point to promising directions for future experiments. Proposals for experiments are described.

Magnetic monopole in variations on Einstein's nonsymmetric unified field theory

The Einstein-Kur\ifmmode \mbox{\c{s}}\else \c{s}\fi{}uno$\stackrel{\mathrm{\ifmmode \check{}\else \v{}\fi{}}}{\mathrm{g}}$lu and the Einstein-Bonnor unified-field-theory equations for the time-independent, spherically symmetric electric and magnetic fields are reduced to an ordinary integrodifferential equation of the type previously solved by numerical methods. It is found that specifying the mass and charge of the electric monopole along with using Dirac's value for the magnetic charge is sufficient to determine the mass of the magnetic monopole in the Einstein-Kur\ifmmode \mbox{\c{s}}\else \c{s}\fi{}uno\ifmmode \breve{g}\else \u{g}\fi{}lu and the Einstein-Bonnor theories. The observed mass of the electron and the large (unobserved) mass of the magnetic monopole do not disagree with these unified field theories.

A possible SU(7) grand unified model with non-standard charged quarks, lepton and low-mass magnetic monopole

A possible SU(7) grand unified model with non-standard charged quarks, lepton and low-mass magnetic monopole is proposed. In this model, the quarks and leptons of the first and the second generations are the same as in the standard GUM, but the assignment of the fermions of the third and the fourth generations is quite different from the standard GUM. Although the charge of the top quark is 2 3 , the quark Q=− 1 3 , the τ lepton Q=−1, there are also two kinds of quarks with Q= 5 3 , − 4 3 and a lepton with Q=−2. The coupling of e− ν e, μ− ν μ and τ− μ τ is V − A. We break SU(7) down to SU(3) and U(1) em in three steps. We estimate the proton decay lifetime t p and the mass of the magnetic monopole M m . In the experimentally plausible ranges of the weak mixing angle sin 2 θ w( M w) and the strong-coupling constant α s( M w), 0.18⩽sin 2 θ w( M w) ⩽ 0.22, 0.15 ⩽ α s( M w) ⩽ 0.24, respectively, t p > 10 30 yr, which sensitively depends on the mass scale of the grand unified point, and M m ⋍ 10 6 GeV , which is almost independent of sin 2 θ w( M w) and α s( M w) and consistent with the big-bang theory of the universe.

Search for cosmic-ray-related magnetic monopoles at ground level

Magnetic monopoles have been sought at ground level using the large magnetic moment of the Fermilab 15-foot bubble-chamber magnet for collection and acceleration and Lexan polycarbonate for particle detection. The 100 days of operation with proper polarity provides an (area) x (time) factor of 8.4 x 10/sup 14/ cm/sup 2/ sec for slowed north-seeking monopoles. The 3.5 years of exposure also provides 10/sup 13/ cm/sup 2/ sec for high-energy directly penetrating monopoles of both polarities. The lack of observable poles sets new limits on monopole mass and charge for experiments that make no assumptions about long-term trapping of magnetic charges.

Grand unification magnetic monopoles inside the Earth

Elementary particle grand unification theories admit the possibility of very massive magnetic monopoles, but standard cosmology gives too many poles. Massive monopoles are affected both by gravity and magnetism, requiring reassessment of existing monopole searches. Monopoles inside the Earth would be able to annihilate with each field reversal, thereby giving rise to additional internal heat. This perspective is used to estimate an upper limit for the monopole-to-baryon ratio at accretion of 10−28.

Phase Transitions and Magnetic Monopole Production in the Very Early Universe

In grand unified models, the abundance of superheavy magnetic monopoles in the universe can be suppressed if (1) the phase transition which creates the monopoles occurs after much supercooling; and (2) immediately after the phase transition, the effective monopole mass is large compared with the temperature. These requirements impose constraints on the history of the early universe. The Georgi-Glashow SU(5) group probably breaks to SU(4) \ensuremath{\bigotimes} U(1) before it reaches SU(3) \ensuremath{\bigotimes} SU(2) \ensuremath{\bigotimes} U(1).

The masses of monopoles in grand unified theories

The form the Bogomol'nyi bound takes in grand unified theories is considered. In the context of certain approximations, which are detailed, the ratio of the mass of a monopole to that of a superheavy boson is calculated. Lower bounds on the masses of these particles are given in terms of the mixing angles of the theory. The results are applied to the spin (10) theory.

Optimum analysing electrode radius for a fourfold monopole mass spectrometer

Values are presented for the optimum radius of curvature of the analysing electrode in a fourfold monopole mass spectrometer. Computer simulation of the operation of the device demonstrates that residual field non-linearity present, even when using an opti-mum radius, does not impair device operation and peaks are well formed. Half-peak-height resolutions in excess of 200 are shown to be possible at 100% transmission. Experimental results reported previously support the values of electrode radius given.

Exact monopole solutions in gauge theories for an arbitrary semisimple compact group

We construct an exact n-parametric monopole and dyon solutions for an arbitrary compact gauge group G of rank n by using the symmetry between cylindrically symmetric instanton equations in Euclidean space R4 and monopole equations in Minkowski space R3,1 (with Higgs scalar field in adjoint representation). The solutions are spherically symmetric with respect to the total momentum operator \( - \overrightarrow {ir} \times \overrightarrow \nabla + \overrightarrow T , where \overrightarrow T \) represents the minimal embedding of SU(2) in G. Explicit expressions for the monopole magnetic charge and mass matrices are obtained. The remarkable aspect of our results is the existence of discrete series of the monopole solutions, which are labelled by n ‘quantum’ numbers and degenerated in the latter ones at a fixed monopole mass matrix.

Creation of magnetic monopoles in pulsars

THE symmetry of the free Maxwell equations under transformation of electric field into magnetic field led Dirac1 to suggest the existence of magnetic monopoles. Many experimental searches for these particles have been made on different accelerators and using cosmic ray interactions; no magnetic monopoles having been detected, upper limits of the cross sections for the creation of monopoles have been obtained. The data of Ross et al.2 are the best and can be fitted by: where σpn is the proton–nucleon cross-sections in cm2, and mg the monopole mass in GeV c−2. It is believed3,4 that very energetic particles are created in pulsars. These particles can interact between themselves and/or be smashed onto the neutron star surface to produce pairs of magnetic monopoles and antimonopoles. These monopoles (if they exist or are effectively produced) would be accelerated in the pulsar magnetic field, one species towards the interstellar medium, the other towards the neutron star, producing a decrease in the magnetic field. Such a phenomenon can be related to observations, particularly to the discrepancy between the characteristic and the kinematical ages. We show here that these observations can be explained by a production of magnetic monopoles, inherent to the pulsars, with a cross-section lower than equation (1), (that is, without contraction with the negative results of the terrestrial searches). More specifically, we will consider the magnetic monopoles production on the neutron star surface, in the Ruderman and Sutherland model4. Other models (with and without gaps) will be considered elsewhere.

Performance and application of a fourfold monopole mass spectrometer

Some preliminary tests with an experimental fourfold monopole mass spectrometer are described, illustrating that the device performs acceptably (at the low resolutions used) despite the fact that the field-forming surfaces of the driven electrodes are only one quadrant of a cylinder. Coupling between adjacent channels is shown not to be a problem so that applications requiring simultaneous measurements using two or more of the monopole channels can be entertained. Owing to its parallel structure the instrument is suggested as being suited particularly to isotope ratio measurements with precisions which could be significantly better than would be possible with a quadrupole device.

Supersymmetric magnetic monopoles and dyons

We construct the supersymmetric generalization of the 't Hooft-Polyakov magnetic monopole and of the Julia-Zee dyon. We show that the quantum corrections to the monopole mass are vanishing as a consequence of the supersymmetry of the theory.

A variable-frequency voltage supply for a monopole mass spectrometer

The focusing properties of the quadrupole field can be utilized in a quadrupole mass spectrometer by sweeping the frequency of the impressed voltage instead of the amplitude. A method of obtaining electronic frequency-sweeping is described, including a method of compensating for the presence of harmonic distortions in the waveform. A resolution of 200 is obtained using a monopole of 1.1 cm radius and 29 cm length.

Massive photons and tachyon monopoles

Massive photons and tachyon monopoles

Simulation of a monopole mass spectrometer with a view to determining operating parameter tolerances

Results from a computer model of the operation of a monopole mass spectrometer are presented and used to illustrate the dependence of peak shape, transmission, and resolution upon various waveform and geometric parameters. In addition, the parameter tolerances necessary for highly stable operation are derived and shown to be within the capabilities of present electronic techniques. In particular, for a duty cycle (rectangular waveform operation) or dc–rf ratio (sinusoidal excitation) tolerance of the order of 10 ppm, peak height stability of about 0.1% is seen to be attainable at high resolution and high transmission. This is an order of magnitude better than is possible with a quadrupole mass filter.

Phase-space calculations of monopole mass spectrometer performance

The phase-space techniques recently developed for quadrupole mass filter calculations are applied to the monopole mass spectrometer. As an illustration, exact matching of the ion source emittance to the monopole acceptance is assumed and peak-shapes, resolution and relative sensitivity are determined as a function of the length of the monopole field in rf cycles.

Relation between Monopole Mass and Primary Monopole Flux

We give quantitative results concerning the simple idea that the probability of observing a monopole at Earth with $\ensuremath{\beta}\ensuremath{\simeq}0.5$ decreases as the monopole mass decreases, for masses \ensuremath{\lesssim}${10}^{4}$ Gev/${\mathit{c}}^{2}$: The effective cross section of Earth is roughly the geometric cross section times the ratio of the monopole mass to 8000 GeV/${\mathit{c}}^{2}$.

Theoretical Limits on Interstellar Magnetic Poles Set by Nearby Magnetic Fields

The interstellar magnetic field limits the monopole flux to ${10}^{\ensuremath{-}16}$ pole ${\mathrm{cm}}^{\ensuremath{-}2}$ ${\mathrm{sec}}^{\ensuremath{-}1}$ and gives the average monopole energy ${10}^{11}$ GeV. They can be detected nonrelativistically only if their mass is \ensuremath{\gtrsim} ${10}^{11}$ GeV/${\mathit{c}}^{2}$ and, being produced at $E{10}^{22}$ GeV, require ${10}^{21}$ g ${\mathrm{cm}}^{\ensuremath{-}2}$ matter for ionization loss to make them nonrelativistic. Massive monopoles can only be primordial or cosmologically produced. Low-mass monopoles trapped in dust grains and released in the atmosphere are possible.