U(1)B−L_{B-L} Symmetry Restoration and Effective Neutrino Species

The U(1)$_{B-L}$ symmetry could be restored during inflation, since the BICEP2 results suggest a GUT-scale inflation with the Hubble parameter, $H_{\rm inf} \simeq 10^{14}$ GeV, close to the U(1)$_{B-L}$ breaking scale. We consider a scenario in which the ${B-L}$ Higgs field dominates the Universe after inflation, and mainly decays into the U(1)$_{B-L}$ gauge bosons, whose subsequent decays reheat the Universe. Interestingly, if one of the right-handed neutrinos is extremely light and behaves as dark radiation or hot dark matter, its abundance is determined by the $B-L$ charge assignment and the relativistic degree of freedom in plasma. We find that $\Delta N_{\rm eff}$ takes discrete values between $0.188$ and $0.220$ in the standard model plus three right-handed neutrinos, depending on whether the decay into heavier right-handed neutrinos are kinematically accessible or not. In the fiveness U(1)$_{\bf 5}$ case, we find that $\Delta N_{\rm eff}$ takes discrete values between $0.313$ and $0.423$. The tension between BICEP2 and {\it Planck} can be partially relaxed by dark radiation.Comment: 14 pages, v2: corrected small errors in calculations, conclusions unchange

Cavitation Characteristics of Restriction Orifices (Experiment for Shock Pressure Distribution by Cavitation on Restriction Orifices and Occurrence of Cavitation at Multiperforated Orifices Due to Interference of Butterfly Valve)

This paper presents two experimental investigations for cavitation characteristics of restriction orifices. The first experiment is about the spatial distribution of cavitation shock pressure in a pipe at the downstream of restriction orifices. The second experiment is the investigation of butterfly valve throttling to the cavitation in a multiperforated orifice installed piping. From the results of the experiment for the cavitation shock pressure, it is concluded the maximum shock pressure remarkably increases with the decrease of cavitation number regardless of the orifice types. The maximum shock pressure becomes smallest on cone type orifice, and largest on single hole orifice. Multiperforated orifice is between this two. The results of the experiment for occurrence of cavitation due to the interference of butterfly valve show that the cavitation occurs at a relatively high cavitation number when the multiperforated orifice is placed at 1D downstream of the butterfly valve. The butterfly valve throttling accelerates the cavitation at the multiperforated orifice because of the closed orifice installation