Warped Passages - Lisa Randall [191]
If Standard Model particles are confined to a brane, extra dimensions can be much larger than physicists previously thought: they can be as large as about a tenth of a millimeter.
Extra dimensions can be so large that they can explain why gravity is so much weaker than the electromagnetic, weak, and strong forces.
If large extra dimensions solve the hierarchy problem, higher-dimensional gravity would become strong at about a TeV.
If higher-dimensional gravity becomes strong at about a TeV, the LHC will produce KK particles at a measurable rate. The KK particles would carry away energy from the collision, so their signature would be events with missing energy.
20
Warped Passage: A Solution to the Hierarchy Problem
What’s so small to you,
Is so large to me.
If it’s the last thing I do,
I’ll make you see.
Suzanne Vega
Athena awoke with a start. She had just revisited her recurring dream, which had again begun with her entering the dreamworld’s rabbit hole. In this episode, when the Rabbit announced, “Next stop, TwoDLand,” Athena ignored him and waited to hear the choices that remained.
At the three-spatial-dimensional stop, the Rabbit announced, “If you lived here, you’d be home by now.” But he refused to open the doors, despite Athena’s pleas that she did indeed live there and very much wanted to return home.
At the next stop, uniformed six-dimensioners tried to enter. But the Rabbit took one look at their inordinately large girth and abruptly closed the doors, saying that they couldn’t possibly fit. They quickly departed once the Rabbit threatened to cut them down to size.*
The elevator continued on its extraordinary journey. When it stopped again, the Rabbit announced “Warped Geometry—a five-dimensional world.”† He gently pushed Athena towards the door, advising her, “Enter the funhouse mirror—it will take you home.” Since the Rabbit had mentioned a fifth dimension, Athena found this highly unlikely. But she didn’t have any choice but to enter and hope the tricky Rabbit was right.
When you learn a language, the words you remember depend on your particular needs or interests. On a bicycle trip in Italy, for example, I learned to ask for water in many different ways—acqua di rubinetto, acqua minerale, acqua (minerale) gassata, acqua (minerale) naturale, etc.* Similarly, when learning about new physical scenarios, each physicist has her own perspective and her own questions, and might therefore notice certain aspects of a system or discover different implications of what is already known. Each of us can hear something different, even when faced with the same words or situation. It makes sense to listen carefully.
Raman and I had each been thinking about the hierarchy problem for years. But we were not searching for a new, better solution to the hierarchy problem when we began our collaboration. We were working on the model of sequestered supersymmetry breaking that I presented in Chapter 17. In the course of that work, we inadvertently discovered a remarkable warped geometry of spacetime (a particular type of curved geometry that we’ll soon explore) that was bounded by two branes. And because Raman and I were concerned with particle physics and the weakness of gravity, we immediately recognized the warped geometry’s potential significance: if the Standard Model of particle physics lies in this spacetime, the hierarchy problem could be solved. I’m not sure that we were the first to study this particular set of Einstein’s equations. But we were definitely the first to recognize this startling implication.
The next few chapters explain this and other remarkable possibilities of curved spacetime and how its consequences sometimes violate our expectations. This chapter focuses on a warped five-dimensional world that could help to explain the vast range of masses that are relevant to particle physics. Whereas in four-dimensional quantum field theory, particles are expected to have roughly the same masses, in a warped higher-dimensional geometry this is no longer the case. Warped geometries