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Can the diphoton enhancement at 750 GeV be due to a neutral technipion?

We discuss a scenario in which the diphoton enhancement at $M_{γγ}$ = 750 GeV, observed by the ATLAS and CMS Collaborations, is a neutral technipion $\tildeπ^0$. 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 $γγ\to {\tilde π}^0$ and production of technipion associated with one or two jets. All the considered mechanisms give similar contributions. With the strong Yukawa (technipion-techniquark) coupling $g_{TC}$ = 10 - 20 we obtain the measured cross section of the "signal". With such values of $g_{TC}$ we get a relatively small $Γ_{\rm tot}$. 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 ${\tilde π}^0$ 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 $p p \to p p γγ$ processes at $\sqrt{s}$ = 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.