Historical research guide · 1084 · 2012
Charged Lepton Spectra from Hot-Spot Evaporation
Julian Moosmann · Ralf Hofmann
In one minute
Julian Moosmann and Ralf Hofmann work inside a reformulation of Yang-Mills theory in which each charged lepton — electron, muon, tau — has its own SU(2) gauge theory, and the lepton itself is a loop of magnetic flux that crosses itself once. Just above the temperature at which such a theory condenses there is a narrow phase whose ground state carries negative pressure. Deposit enough energy in a small enough region and you make a droplet of it: a hot spot. This paper computes what a droplet radiates as it boils away. For the electron theory the answer lands on something measured long ago and never explained — the narrow electron and positron peaks seen in supercritical heavy-ion collisions at GSI Darmstadt in the 1980s, whose width corresponds to a lifetime of about ten to the minus twentieth of a second, which is exactly the droplet lifetime the model predicts. For the muon theory they compute pair-mass spectra and show how sharply the shape depends on the cuts an experiment applies to its own data.
Connection
Chapter 13 is the unified picture — the attempt to get matter, charge and the forces out of the structure of a field rather than adding them by hand — and Hofmann’s SU(2) programme is the most fully worked version of that in the literature. This paper is where it touches data: a droplet of a new phase of the vacuum, a predicted lifetime, and an experimental peak that has been waiting for an explanation since the 1980s.
From the source
The framework in one paragraph. Pure SU(2) Yang-Mills thermodynamics has a narrow preconfining phase in which monopole-antimonopole pairs are condensed, arising as isolated defects through caloron dissociation in the hotter deconfining phase. Below the Hagedorn temperature the infinitely extended condensate decays non-thermally into single and self-intersecting centre-vortex loops, which are interpreted as spin one-half fermions; only loops with exactly one self-intersection are absolutely stable in an SU(2) theory, and it is those that are identified with the charged leptons. The consequence is one SU(2) Yang-Mills theory per lepton family, with each theory’s Yang-Mills scale matching the mass of its charged lepton.Section 1, Introduction, opening paragraph
The apparent point-likeness of leptons is accounted for rather than contradicted. On this account, when a lepton is probed by a high-momentum-transfer Standard Model process, the interaction region contains a large number of unstable excitations whose combined effect, together with the free shiftability of the vortex intersection point, is exactly what perturbation theory describes so successfully — a succession of vertices and off-shell propagators mediating structureless initial states into structureless final ones. Structure shows up only where large hot spots of preconfining ground state can form: very high collision energies, high temperatures in extended systems, or local energy densities above the fourth power of the electron mass, about ten to the eleventh in units of keV to the fourth.Section 1, Introduction, second paragraph
The GSI signature the model addresses. In supercritical heavy-ion systems — uranium on thorium, thorium on thorium, thorium on curium, uranium on uranium, uranium on curium — with combined nuclear charge between 180 and 188, well above the critical value of 173, narrow positron peaks of several tens of keV width were detected, centred at 250, 330 and 400 keV, sitting on a broad background that conventional parameter-free theory already explains. Correlated narrow electron peaks with similar characteristics followed. Doppler broadening puts the emitting source at a speed of at most five hundredths of the speed of light, and the absence of back-to-back emission excludes a two-particle decay of a neutral state between 1.5 and 2 MeV. The peak features are independent of the combined nuclear charge, where strong-field QED predicts strong power laws in it.Section 1.1.1
The lifetime is the paper’s sharpest number. The observed width of the electron and positron peaks corresponds to an inverse width of about one over seventy keV, that is 9.4 times ten to the minus twenty-first of a second. The evaporation time computed for an SU(2) hot spot in the electron theory, assuming recoil-free thermal emission, varies only weakly with the deposited energy: setting the two order-unity parameters to one, a centre-of-mass energy of 10 MeV gives 1.0 times ten to the minus twenty-first of a second and 10 GeV gives 1.0 times ten to the minus twentieth. The energy density available at closest approach in a supercritical collision is estimated at about ten times the fourth power of the electron mass — larger than the minimum needed to cross the Hagedorn transition, though not hierarchically larger, which is why the droplets should be small.Section 1.1.1, and Section 2, equations 2.9 and 2.10
The single-lepton spectrum itself. Treating the leptons far from the emitting surface as a thermal Fermi distribution at the Hagedorn temperature, with a fourfold degeneracy for spin and charge, the differential yield per unit energy, time and surface is proportional to the squared energy minus the squared lepton mass, divided by one plus the exponential of the energy over the Hagedorn temperature. Multiplying by the shrinking spherical surface of the droplet and integrating over its lifetime gives the number of emitted leptons per energy bin. The deposited energy and the fraction of it that goes into hot-spot creation enter only the normalisation, never the shape.Section 2, equations 2.1 to 2.4 and 2.13
The lesson the authors draw for collider analysis, and the resonance they name. Kinematic cuts applied while extrapolating known physics into the unknown necessarily hide potentially important signatures: the computed dimuon mass spectra move their maximum from about 0.6 GeV with no cuts to about 2.3 GeV once a representative transverse-momentum cut is imposed. If metastable droplets of a new phase form in isolated TeV-range proton-antiproton collisions, the collision energy would be redistributed into a large multiplicity of low-energy charged leptons rather than a few energetic secondaries — and only the leptonic sector, which has no confinement mechanism here, would show that multiplicity. The authors also name a check: two further and much heavier copies of vector-boson triplets must eventually be excited, and they point to the potential resonance near 240 GeV in the electron-positron invariant-mass spectrum reported from Tevatron Run II as a plausible candidate for the decoupling dual gauge mode of the muon theory.Section 4, Summary and Conclusions
The way in
https://doi.org/10.5402/2012/509793How to cite it
Julian Moosmann, Ralf Hofmann (2012) Charged Lepton Spectra from Hot-Spot Evaporation doi:10.5402/2012/509793