Warped Passages - Lisa Randall [178]
Figure 74. Kaluza-Klein particles correspond to the waves that oscillate an integer number of times around the curled-up dimension. Waves with more oscillations correspond to heavier particles.
The many successively heavier KK particles resemble the multiple generations of an immigrant family. The members of the youngest generation who were born in the USA fully assimilate American culture, speak English perfectly, and don’t betray their foreign roots at all. That isn’t as true for the previous generation, the parents of this youngest generation: perhaps they speak with a trace of an accent, and occasionally tell a few proverbs from the old country. The generation that is older still would sound even more foreign, and wear clothing and tell stories that originated in their homeland. These earlier generations might be said to add cultural dimensions to what would otherwise be a less colorful, uniform society.
Similarly, the lightest KK particles are indistinguishable from particles in a fundamentally four-dimensional world; only the more massive “older relations” would reveal evidence of extra dimensions. Although the lightest of the KK particles would appear to be four-dimensional, their provenance would become apparent once sufficient energy to produce the more massive “elders” was achieved.
If experimenters discover new heavy particles with the same charges as familiar ones and masses that are similar to one another, those particles will be strong evidence of extra dimensions. If such particles share the same charges and occur at regular intervals of mass, it would very likely mean that a simple curled-up dimension has been discovered.
But more complicated extra-dimensional geometries will yield more complicated patterns of masses. If enough such particles are discovered, the KK particles would then reveal not only the existence of extra dimensions, but also the extra dimensions’ sizes and shapes. No matter what the geometry of the hidden dimensions, the KK particles’ masses would depend on it. In all cases, the KK particles and their masses could tell us quite a lot about extra-dimensional properties.
Experimental Constraints
Until recently, most string theorists assumed that extra dimensions are no bigger than the minuscule Planck scale length. This is because gravity becomes strong at the Planck scale energy, and a theory of quantum gravity, which could be string theory, should take over at that point. But the Planck scale length is far smaller than any length we can study experimentally. The tiny Planck scale length corresponds (according to quantum mechanics and special relativity) to the enormous Planck scale mass (or energy)—ten thousand trillion times the reach of current particle accelerators. Planck-mass KK particles would be so heavy that they would be well out of range of any conceivable experiment.
However, perhaps extra dimensions are bigger and KK particles are lighter. Why not ask instead what experimental tests tell us about an extra dimension’s size? What do we really know, theoretical prejudice aside?
If the world is higher-dimensional and there are no branes, then all familiar particles—the electron, for example—would have KK partners.32 These would be particles that have exactly the same charge as familiar particles, but carry momenta in the additional dimensions. The electron’s KK partners would be negatively charged like the electron, but heavier. If an extra dimension is rolled up into a circle, the mass of the lightest such particle would differ from the electron’s mass by an amount inversely proportional to the extra dimension’s size. That means that, the larger the extra dimension, the smaller the particle’s mass. Because a bigger dimension would give rise to lighter KK particles, none of which have been seen in experiments, the bounds on KK particles’ masses constrain the allowed size of an extra curled-up dimension.
So far there