Initial energy density of p+p collisions at the LHC

Accelerating, exact, explicit and simple solutions of relativistic hydrodynamics allow for a simple description of highly relativistic p+p collisions. These solutions yield a finite rapidity distribution, thus they lead to an advanced estimate of the initial energy density of high energy collisions. We show that such an advanced estimate yields an initial energy density in $\sqrt{s}=7$ and 8 TeV p+p collisions at LHC around or above the critical energy density from lattice QCD, and a corresponding initial temperature above the critical temperature from QCD and the Hagedorn temperature. We also show, that several times the critical energy density may have been reached in high multiplicity events, hinting at a non-hadronic medium created in high multiplicity $\sqrt{s}=7$ and 8 TeV p+p collisions.