We compute the energy dependence of the P_T-integrated cross section of directly produced quarkonia in pp collisions at next-to-leading order (NLO), namely up to alpha_s^3, within nonrelativistic QCD (NRQCD). Our analysis is based on the idea that th
e P_T-integrated and the P_T-differential cross sections can be treated as two different observables. The colour-octet NRQCD parameters needed to predict the P_T-integrated yield can thus be extracted from the fits of the P_T-differential cross sections at mid and large P_T. For the first time, the total cross section is evaluated in NRQCD at full NLO accuracy using the recent NLO fits of the P_T-differential yields at RHIC, the Tevatron and the LHC. Both the normalisation and the energy dependence of the J/psi, psi and Upsilon(1S), we obtained, are in disagreement with the data irrespective of the fit method. The same is true if one uses CEM-like colour-octet NRQCD parameters. If, on the contrary, one disregards the colour-octet contribution, the existing data in the TeV range are well described by the alpha_s^3 contribution in the colour-singlet model --which, at alpha_s^4, however shows an unphysical energy dependence. A similar observation is made for eta(c,b). This calls for a full NNLO or for a resummation of the initial-state radiation in this channel. In any case, past claims that colour-octet transitions are dominantly responsible for low-P_T quarkonium production are not supported by our results. This may impact the interpretation of quarkonium suppression in high-energy proton-nucleus and nucleus-nucleus collisions.
A calibration is made for the correlation between the X-ray Variability Amplitude (XVA) and Black Hole (BH) mass. The correlation for 21 reverberation-mapped Active Galactic Nuclei (AGN) appears very tight, with an intrinsic dispersion of 0.20 dex. T
he intrinsic dispersion of 0.27 dex can be obtained if BH masses are estimated from the stellar velocity dispersions. We further test the uncertainties of mass estimates from XVAs for objects which have been observed multiple times with good enough data quality. The results show that the XVAs derived from multiple observations change by a factor of 3. This means that BH mass uncertainty from a single observation is slightly worse than either reverberation-mapping or stellar velocity dispersion measurements; however BH mass estimates with X-ray data only can be more accurate if the mean XVA value from more observations is used. Applying this relation, the BH mass of RE J1034+396 is found to be $4^{+3}_{-2} times 10^6$ $M_{odot}$. The high end of the mass range follows the relationship between the 2$f_0$ frequencies of high-frequency QPO and the BH masses derived from the Galactic X-ray binaries. We also calculate the high-frequency constant $C= 2.37 M_odot$ Hz$^{-1}$ from 21 reverberation-mapped AGN. As suggested by Gierlinski et al., $M_{rm BH}=C/C_{rm M}$, where $C_{rm M}$ is the high-frequency variability derived from XVA. Given the similar shape of power-law dominated X-ray spectra in ULXs and AGN, this can be applied to BH mass estimates of ULXs. We discuss the observed QPO frequencies and BH mass estimates in the Ultra-Luminous X-ray source M82 X-1 and NGC 5408 X-1 and favor ULXs as intermediate mass BH systems (abridged).
