Is there a definitive prediction of mass of new particle by String/CFT, based on which we could approve or discard that theories? Does String/CFT predict experimentally measurable mass of a new particle which could be experimentally discovered by building new accelerator or using existing accelerators, but seeking for specific pattern predicted by these theories?
I am interested in a mass valued in terms of GeV (giga electron volts) or any other standart measuring equipment used by acceleration physics.
The prediction should be definitive to approval or disproval of these theories, on which everybody would agree, i.e. prediction should be both reproducible theoretically and verifiable experimentally. 
There should be no "unknown" variables for "tuning up", the mass should be written definitively and until the end result.
 A: The short answer is no, not really. String theory predicts the existence of many new particles (the higher excited modes of the string), but these only appear at extremely high energies on the order of the string scale. These energies are not supposed to be accessible by experiments, at least not in any naive way. 
It would be important to string theorists if superparticles would show up at the LHC or some other future high-energy experiment. That would at least show that supersymmetry is real, as one would like when doing superstring theory. But technically, finding a superparticle would show nothing more than that supersymmetry is real: still, string theory could be wrong. Conversely, supersymmetry could not be found at all, but this would not necessarily rule out superstring theory, as one could invent scenarios in which supersymmetry is broken at very high energies. 
Currently, the most promising possible connection of string theory to experimental reality to me seems to be not through high-energy colliders, but through the swampland program, which aims to distinguish theories that can be obtained as limits of string theory (the 'landscape') from theories that cannot (the 'swampland'). There is one particularly (in)famous swampland conjecture that states theories in de Sitter space (positive cosmological constant) belong to the swampland; this would mean that mainstream $\Lambda$CDM cosmology cannot be obtained as a limit of string theory. This swampland conjecture thus has implications for cosmology and could result in predictions that can be experimentally verified or falsified in the near future. 
