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Register a new userThe Theoretical Power Law Exponent for Electron and Positron Cosmic Rays: A Comment on the Recent Letter of the AMS Collaboration
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In a recent letter, the AMS collaboration reported the detailed and extensive data concerning the distribution in energy of electron and positron cosmic rays. A central result of the experimental work resides in the energy regime $30 {rm GeV}< E < 1 {rm TeV}$ wherein the power law exponent of the energy distribution is measured to be $alpha ({rm experiment})=3.17$. In virtue of the Fermi statistics obeyed by electrons and positrons, a theoretical value was predicted as $alpha ({rm theory})=3.151374$ in very good agreement with experimental data. The consequences of this agreement between theory and experiment concerning the sources of cosmic ray electrons and positrons are briefly explored.
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The AMS-02 collaboration has just released its first result of the cosmic positron fraction $e^+/(e^-+e^+)$ with high precision up to $sim 350$ GeV. The AMS-02 result shows the same trend with the previous PAMELA result, which requires extra electron/positron sources on top of the conventional cosmic ray background, either from astrophysical sources or from dark matter annihilation/decay. In this paper we try to figure out the nature of the extra sources by fitting to the AMS-02 $e^+/(e^-+e^+)$ data, as well as the electron and proton spectra by PAMELA and the $(e^-+e^+)$ spectrum by Fermi and HESS. We adopt the GALPROP package to calculate the propagation of the Galactic cosmic rays and the Markov Chain Monte Carlo sampler to do the fit. We find that the AMS-02 data have implied essential difference from the PAMELA data. There is {rm tension} between the AMS-02 $e^+/(e^-+e^+)$ data and the Fermi/HESS $(e^-+e^+)$ spectrum, that the AMS-02 data requires less contribution from the extra sources than Fermi/HESS. Then we redo the fit without including the Fermi/HESS data. In this case both the pulsars and dark matter annihilation/decay can explain the AMS-02 data. The pulsar scenario has a soft inject spectrum with the power-law index $sim 2$, while the dark matter scenario needs $tau^+tau^-$ final state with mass $sim 600$ GeV and a boost factor $sim 200$.
We have recently shown that the cosmic ray energy distributions as detected on earthbound, low flying balloon or high flying satellite detectors can be computed by employing the heats of evaporation of high energy particles from astrophysical sources. In this manner, the experimentally well known power law exponents of the cosmic ray energy distribution have been theoretically computed as 2.701178 for the case of ideal Bose statistics, 3.000000 for the case of ideal Boltzmann statistics and 3.151374 for the case of ideal Fermi statistics. By ideal we mean virtually zero mass (i.e. ultra-relativistic) and noninteracting. These results are in excellent agreement with the experimental indices of 2.7 with a shift to 3.1 at the high energy ~ PeV knee in the energy distribution. Our purpose here is to discuss the nature of cosmic ray power law exponents obtained by employing conventional thermal quantum field theoretical models such as quantum chromodynamics to the cosmic ray sources in a thermodynamic scheme wherein gamma and zeta function regulation is employed. The key reason for the surprising accuracy of the ideal boson and ideal fermion cases resides in the asymptotic freedom or equivalently the Feynman parton structure of the ultra-high energy tails of spectral functions.
The DArk Matter Particle Explorer (DAMPE) experiment has recently announced the first results for the measurement of total electron plus positron fluxes between 25 GeV and 4.6 TeV. A spectral break at about 0.9 TeV and a tentative peak excess around 1.4 TeV have been found. However, it is very difficult to reproduce both the peak signal and the smooth background including spectral break simultaneously. We point out that the numbers of events in the two energy ranges (bins) close to the 1.4 TeV excess have $1sigma$ deficits. With the basic physics principles such as simplicity and naturalness, we consider the $-2sigma$, $+2sigma$, and $-1sigma$ deviations due to statistical fluctuations for the 1229.3~GeV bin, 1411.4~GeV bin, and 1620.5~GeV bin. Interestingly, we show that all the DAMPE data can be explained consistently via both the continuous distributed pulsar and dark matter interpretations, which have $chi^{2} simeq 17.2 $ and $chi^{2} simeq 13.9$ (for all the 38 points in DAMPE electron/positron spectrum with 3 of them revised), respectively. These results are different from the previous analyses by neglecting the 1.4 TeV excess. At the same time, we do a similar global fitting on the newly released CALET lepton data, which could also be interpreted by such configurations. Moreover, we present a $U(1)_D$ dark matter model with Breit-Wigner mechanism, which can provide the proper dark matter annihilation cross section and escape the CMB constraint. Furthermore, we suggest a few ways to test our proposal.
For explaining the AMS-02 cosmic positron excess, which was recently reported, we consider a scenario of thermally produced and decaying dark matter (DM) into the standard model (SM) leptons with an extremely small decay rate, Gamma_{DM} sim 10^{-26} sec.^{-1}. Since the needed DM mass is relatively heavy (700 GeV < m_{DM} < 3000 GeV), we introduce another DM component apart from the lightest supersymmetric particle (LSP). For its (meta-) stability and annihilation into other particles, the new DM should be accompanied with another Z_2 symmetry apart from the R-parity. Sizable renormalizable couplings of the new DM with SM particles, which are necessary for its thermalization in the early universe, cannot destabilize the new DM because of the new Z_2 symmetry. Since the new DM was thermally produced, it can naturally explain the present energy density of the universe. The new DM can decay into the SM leptons (and the LSP) only through non-renormalizable operators suppressed by a superheavy squared mass parameter after the new symmetry is broken around TeV scale. We realize this scenario in a model of gauged vector-like leptons, which was proposed recently for the naturalness of the Higgs boson.
We consider indirect detection of meta-stable dark matter particles decaying into a stable neutral particle and a pair of standard model fermions. Due to the softer energy spectra from the three-body decay, such models could potentially explain the AMS-02 positron excess without being constrained by the Fermi-LAT gamma-ray data and the cosmic ray anti-proton measurements. We scrutinize over different final state fermions, paying special attention to handling of the cosmic ray background and including various contributions from cosmic ray propagation with the help of the textsc{LikeDM} package. It is found that primary decays into an electron-positron pair and a stable neutral particle could give rise to the AMS-02 positron excess and, at the same time, stay unscathed against the gamma-ray and anti-proton constraints. Decays to a muon pair or a mixed flavor electron-muon pair may also be viable depending on the propagation models. Decays to all other standard model fermions are severely disfavored.
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