We discuss a scenario in which the diphoton enhancement at Mγγ = 750 GeV, observed by the ATLAS and CMS Collaborations, is a neutral
technipion π~0. We consider two distinct minimal models for the
dynamical electroweak symmetry breaking. In a first one, two-flavor vector-like
technicolor (VTC) model, we assume that the two-photon fusion is a dominant
production mechanism. We include γγ→π~0 and
production of technipion associated with one or two jets. All the considered
mechanisms give similar contributions. With the strong Yukawa
(technipion-techniquark) coupling gTC = 10 - 20 we obtain the measured
cross section of the "signal". With such values of gTC we get a relatively
small Γtot. In a second approach, one-family walking technicolor
(WTC) model, the isoscalar technipion is produced dominantly via the
gluon-gluon fusion. We also discuss the size of the signal at lower energies
(LHC, Tevatron) for γγ (VTC) and jet-jet (WTC) final states and
check consistency with the existing experimental data. We predict a measurable
cross section for π~0 production associated with one or two soft
jets. The technipion signal in both models is compared with the SM background
diphoton contributions. We observe the dominance of inelastic-inelastic
processes for γγ induced processes. In the VTC scenario, we
predict the signal cross section for purely exclusive pp→ppγγ processes at s = 13 TeV to be about 0.2 fb. Such a cross
section would be, however, difficult to measure with the planned integrated
luminosity. In all considered cases the signal is below the background or/and
below the threshold set by statistics.Comment: 26 pages, 16 figures, 1 tabl