Warped Passages - Lisa Randall [132]
The specific mass that a superpartner must exceed to have eluded detection depends on that particular particle’s charge and interactions. Stronger interactions make particles easier to produce. So to avoid being detected, particles with stronger interactions must be heavier than more weakly interacting ones. Current experimental constraints on most models of supersymmetry breaking tell us that, should supersymmetry exist, all superpartners must have a mass of at least a few hundred GeV to have escaped detection. Those superpartners that are subject to the strong force, such as the squarks, must be even heavier—with masses of at least a thousand GeV.
Broken Supersymmetry and the Higgs Particle Mass
As we’ve seen, the quantum contributions to the Higgs particle’s mass are not problematic in supersymmetric theories because supersymmetry guarantees that they add up to zero. However, we have also just seen that supersymmetry must be broken if it is to exist in the real world. Because superpartners don’t have the same mass as their Standard Model counterparts in a model with broken supersymmetry, the quantum contributions to the Higgs particle’s mass are not so rigidly balanced as they are when supersymmetry is exact. So when supersymmetry is broken, virtual contributions no longer cancel exactly.
Nonetheless, so long as the quantum contributions to the Higgs particle’s mass are not too large, the Standard Model can get by without fine-tuning or fudging. Even when supersymmetry is broken—so long as the effect is small—the Standard Model can contain a light Higgs particle. Supersymmetry, even if broken a little bit, is sufficiently powerful to eliminate the huge Planck scale mass contributions from virtual energetic particles. With only a small amount of supersymmetry breaking, no exceptionally unlikely cancellations would be necessary.
We want supersymmetry breaking to be small enough to make the supersymmetry-breaking mass difference between superpartners and Standard Model particles sufficiently small to avoid fudging. It turns out that the quantum contribution to the Higgs particle’s mass from a virtual particle and its superpartner, though nonzero, will never have a magnitude much greater than the supersymmetry-breaking mass difference between the particle and its superpartner. That tells us that the mass differences between all particles and their superpartners should be about the weak scale mass. In that case the quantum contributions to the Higgs particle’s mass would also be about the weak scale mass, which is about the right size for the mass of the Higgs particle.
Because known particles in the Standard Model are light, the mass difference between a superpartner and a Standard Model particle will be comparable to the superpartner’s mass. Therefore, if supersymmetry solves the hierarchy problem, the superpartner masses should not be much greater than the weak scale of about 250 GeV.
If the superpartner masses are about the same as the weak scale mass, the quantum contribution to the Higgs particle’s mass will not be very large. Unlike the non-supersymmetric case, in which quantum contributions to the Higgs particle’s mass were sixteen orders of magnitude too big, so that intolerable fudging was required to maintain a light Higgs particle, a supersymmetric world with supersymmetry-breaking masses of a few hundred GeV would generate no excessively large quantum contributions to the Higgs particle’s mass.
The requirement that the Higgs particle, and therefore the superpartners, not be much heavier than a few hundred GeV (so as not to reintroduce large quantum contributions to the Higgs particle’s mass), coupled with the fact that experiments have already looked for superpartners with masses of about a couple of hundred GeV, tells us that if supersymmetry exists in nature and solves the hierarchy problem, then supersymmetric partners must have masses that are about a few hundred GeV. This is quite exciting because it suggests that experimental evidence of supersymmetry could be just around