  [Abridged] We consider extensions of the standard model based on open strings
ending on D-branes. Assuming that the fundamental string mass scale M_s is in
the TeV range and that the theory is weakly coupled, we discuss possible
signals of string physics at the upcoming HL-LHC run (3000 fb^{-1}) with
\sqrt{s} = 14 TeV, and at potential future pp colliders, HE-LHC and VLHC,
operating at \sqrt{s} = 33 and 100 TeV, respectively. In such D-brane
constructions, the dominant contributions to full-fledged string amplitudes for
all the common QCD parton subprocesses leading to dijets and \gamma + jet are
completely independent of the details of compactification, and can be evaluated
in a parameter-free manner. We make use of these amplitudes evaluated near the
first (n=1) and second (n=2) resonant poles to determine the discovery
potential for Regge excitations of the quark, the gluon, and the color singlet
living on the QCD stack. We show that for string scales as large as 7.1 TeV
(6.1 TeV), lowest massive Regge excitations are open to discovery at 5\sigma in
dijet (\gamma + jet) HL-LHC data. We also show that for n=1, the dijet
discovery potential at HE-LHC and VLHC exceedingly improves: up to 15 TeV and
41 TeV, respectively. To compute the signal-to-noise ratio for n=2 resonances,
we first carry out a complete calculation of all relevant decay widths of the
second massive level string states. We demonstrate that for string scales M_s
<~ 10.5 TeV (M_s <~ 28 TeV), detection of n=2 Regge recurrences at HE-LHC
(VLHC) would become the smoking gun for D-brane string compactifications. Our
calculations have been performed using a semi-analytic parton model approach
which is cross checked against an original software package. The string event
generator interfaces with HERWIG and Pythia through BlackMax. The source code
is publically available in the hepforge repository.
