A number of experiments are reaching a point where we can determine if the Standard Model is right, or if there are physics beyond it. In particular, some of these could falsify many popular versions of Supersymmetry, which is a necessary component of Sting Theory (a.k.a. M-Theroy). What are those experiments?
1. Measure the electric dipole moment of an electron.
The standard model predicts that the electron's electric dipole moment is less than 10^–38 in units of electron charge times centimeters. That's equivalent to separating an electron and a similar charged particle by a distance of 10^–38 centimeters. . . But extensions of the standard model predict the electric dipole moment to be bigger, between 10^–25 and 10^–30. In 2002, [scientists] published the most stringent limit yet: 1.6 × 10–27.
Experiments in progress costing about $10 million, a bargain in the fundamental physics world, should determine if the electron's electric dipole moment is more than 10^-29 by one of a few possible methods in the next few years.
The minimal supersymmetric standard model, or MSSM, is a standard model extension that holds that every elementary particle has a “superpartner.” One of the simplest versions has been ruled out by the current limit.
An electric dipole moment for an electron of less than 10^-30 would rule out most versions of supersymmetry, and hence, most versions of string theory.
2. Fail to find the Higgs boson.
The Higgs boson is predicted by the Standard Model to be the particle that gives other particles mass. Tireless searching with particle accellerators has determined that if it exists it must weigh 114 GeV to 158 Gev (or must be much, much heavier), with the most promising hints that it might exist around 140 GeV or perhaps a bit less. Other not quite statistically significant tests suggest that it might be a little lighter than that. The Large Hadron Collide should be able to determine if there is a previously undiscovered particle of that mass within the next couple of years.
If the Higgs boson isn't there, then the Standard Model and most versions of Supersymmetry (which predicts at least one, but often more than one Higgs boson, and in most cases predicts at least one "light" Higgs boson) are falsified and scientists have to figure out some other way for particles to acquire mass.
A Higgsless Standard Model has been proposed, but supersymmetry could probably not manage without a Higgs.
3. Break the CKM Matrix.
The CKM matrix sets forth the probabilities that quarks will turn into different kinds of quarks in weak force interactions and predicts how often charge parity (CP) violations take place. Experiments with B mesons (two quark particles that include a bottom quark), have shown that CP violations take place in these experiments to an extent that seems to conflict with the Standard Model at its current consensus CKM matrix parameters, and the discrepency may be greater than it is possible to resolve by tweaking the parameters of the CKM within the boundaries of the Standard Model.
Other anomolous CP violations have also turned up, even in neutrinos.
4. Find a new generation of quarks.
There are four main kinds of fermions (particles that are not force carriers). Up and down quarks, electrons, and neutrinos. But, there are three generations of each kind. The second and third generations (for the electron and neutrino they are called the muon and tau, for quarks the second generation consists of the charm and strange and the third generation consists of the top and bottom).
Supersymmetry requires that there be precisely three generations of particles. But, if the CKM matrix lacks entries whos possibilities sum to 100% in all circumstances has entries that fail to sum up to 100% in all circumstances, then the weak interaction can produce particles that aren't in the matrixes in the form of 4th and our higher generation fermions. The heavier a fourth generation particle is the less of an impact it would make on the CKM matrix, because heavier particles are less likely to be produced in weak force interactions.
Alternately, a fourth generation fermion could be observed in an experiment at the Large Hardon Collider if it wasn't too massive. Current experiments strongly disafavor the existence of any new quark of less than 355 GeV.
5. Find a new generation of leptons.
The lepton (electron and neutrino) verision of the CKM matrix is the PMNS matrix, which isn't know nearly as well. A fourth generation could be inferred from neutrino flavor oscillation, since neutrinos constantly cycle from one generation to another, and a fourth generation could be infered from that cycling pattern.
6. Fail to find supersymmetric particles.
Supersymmetry, and by association, string theory, predicts that there will be a "lightest supersymmetric particle" among many undiscovered particles, that has not yet been discovered. Most versions put its mass within the range of what could be discovered by the Large Hardon Collider. If the LHC doesn't find one, this would disfavor supersymmetry and string theory, although it would not rule out either, as "string vacua" with heavier lighest supersymmetric particles can be imagined.
7. Discover something that doesn't fit.
The Standard Model predicts almost nothing other than the Higgs boson that hasn't been observed yet. It is minimal. Supersymmetry and string theory, generally, while more inventive, only include new elements that provide greater theoretical consistency to what has already been observed.
For example, neither predicts CPT symmetry violations, which have never been observed. If it was observed, some significant new physics would have to be devised to explain it.
The new forces and particles that string theory predicts are very well defined. For example, the superpartners of fermions in supersymmetry "have the same color charge, weak isospin charge, and hypercharge (and consequently electric charge)" as their orinary fermion partners and are bosons (i.e. integer spin particles). The discovery, for example, of a particle like looks in all other respects like a superpartner of an up quark, with an electric charge of +3/4 would send string theory to the dust bin and leave physicists scatching their heads.
There are lots of proposals for supersymmetry particles that could account for dark matter. There are also many experiments that are trying to determine directly the properties of dark matter particles that aren't ordinary matter. If the dark matter particles we find have properties that aren't a good fit for anything that supersymmmetry proposes exists, this would present a "beyond String Theory" problem.
One of the strongest possibilities for this kind of discovery is an apparent inconsistency between measurements of hydrogen atoms with ordinary electrons and measurements of hydrogen atoms in which muons are present instead of electrons. The Standard Model and all common extensions of it expected these measurements to be consistent. But, the measured results were five standard deviations apart, and if the discrepency can't be explained by experimental error there is no ready explanation for why the measurements should differ.
Unlikely Sources Of Evidence
1. Rule out extra dimensions.
Experimental efforts to detect extra dimensions rule out dimensions greater than three micrometers (about 10,000 times the size of an atom), but the expected scale of extra dimensions in string theory are many orders of magnitude smaller than that, so the experiments are unlikely to provide much experimental proof or disproof of string theory.
2. Find evidence to support a non-stringy quantum gravity.
One of the reasons that String Theory requires so many extra dimensions and particles is to allow it to incorporate a quatum field theory of gravity similar to that for the other three fundamental forces of physics, mediated by a spin two graviton. If evidence could be found to experimentally verify that this is not how gravity works, and that some other model of quantum gravity, like loop quantum gravity, was actually the correct model, then a far less complex theory would be needed to integrate the other three forces and know particles.
But, there have been no experiments indicating any deviation from general relativity, and despite general relativity's inconsistency with quatum mechanics, the circumstances where that discrepency exists involve situations like the big bang and black holes that lead to singularities in general relativity, that are difficult to measure in the pertinent ways from our solar system, the gravitational fields of individual particles that are hopelessly drowned by their surroundings, and issues related to how time works.
Experimentally, evidence regarding the nature of quantum gravity could come from the search for gravity waves, from more precise cosmic background radiation maps, from astronomy observations of black holes, or from the discovery of discrepencies between general relativity and experiment in very strong or very weak gravitational fields.
3. Show that the fundamental forces don't unify.
One of the main theoretical of supersymmetry is to unify, at least, the three fundamental forces in such a way that at a certain energy scale, their coupling constants merge them into a single force. If it was possible to determine empirically that these constants do not in fact merge at that energy scale (about 1000 GeV), as the Standard Model implies, then supersymmetry would be invalidated. But, as with quantum gravity, no one has devised practicable ways to measure the physics in question at that energy scale.
4. Find proton decay or magnetic monopoles.
Many early efforts to go beyond the Standard Model in physics predicted proton decay and magnetic monopoles. But, neither has ever been observed. The shortest possible proton decay half-life that cannot be ruled out be experiment 1.01×10^34 years. By comparison, the estimated age of the universe is a little less than 14 billion years (i.e. 10^11 years), and the half life of a neutron is about 614 seconds.
The lack of such events places a limit on the number of monopoles of about one monopole per 10^29 nucleons. . . experiments suggest that monopoles with masses below 600 GeV/c2 do not exist, while upper limits on their mass due to the very existence of the universe - which would have collapsed by now if they were too heavy - are about 10^17 GeV/c2.
Models that predict them at any detectable level have fallen into disfavor. The discovery of either would reinvigorate those models which have been largely discarded in favor of more mainstream versions of supersymmetry and string theory.
String theory predicts magnetic monopoles ought to be around the Plank mass, which is far beyond the range of experiments to detect.
5. Find evidence for some other theory that naturally explains the Strong CP problem.
While CP violations are greater than expected in a number of weak force interactions, "there are natural terms in the [quantum chromodynamics] QCD Lagrangian [that governs the strong nuclear force] that are able to break the CP symmetry. . . For a nonzero choice of the θ angle and the chiral quark mass phase θ′ one expects the CP symmetry to be violated." Yet, in what is called the Strong CP problem, "Experiments do not indicate any CP violation in the QCD sector. For example, a generic CP violation in the strongly interacting sector would create the electric dipole moment of the neutron which would be comparable to 10−18 e·m while the experimental upper bound is roughly a trillion times smaller."
Discovering some very low level of strong CP violation is probably beyond the realm of possibility. But, coming up with a sound theoretical reason why the terms of the QCD Langrangian that a zero theta angle and zero chiral quark mass phase remove from the QCD Lagrangian is within the realm of possiblity, and there might be some other experimentally testable implication of that theory that can be tested.