Unitarity Method: A fresh new look at our understanding of Feynman Diagrams and Supergravity
To develop a fully consistent picture of the universe, we MUST find a way to incorporate gravity into a quantum-mechanical edifice. If gravity acts like other forces of nature, it should be transmitted by graviton particles. Gravitons should collide and scatter just like other particles, thus we should be able to draw Feynman Diagrams for them.
In the 1980’s, attempts were made to describe graviton scattering by quantizing Einstein’s theory in the simplest possible way. This approach lead to infinities, or nonsensical predictions (which would make it wrong). These calculations should clearly be finite, and infinities can arise at intermediate stages of calculations but are eventually cancelled out in the Standard Model. For gravity, no such cancellations appear. Thus, according to a phrase coined by John Wheeler, “spacetime foam” due to quantum fluctuations with virtual particles, would spiral out of control.
At first physicists tried to explain this by “undiscovered particles” that existed in the quantum effects that reined in this so-called Supergravity Theory. This was eventually discarded because indirect arguments suggested nonsensical infinities should still arise from three or more virtual-particle loops.
Virtual particles are a quintessential feature of quantum theory. They are represented by loops on Richard Feynman’s tree diagrams. They are not directly observable, but have a measurable effect on forces and are ephemeral. They add enormous complexity to Feynman Tree Diagrams. For example, in quantum chromodynamics (QCD, a coupling of the strong nuclear force) if you had the audacity and time to calculate a collision of two incoming and eight outgoing gluons, you would need to write out a staggering 10 million diagrams.
This suggested they were using the wrong tool for the job and the idea was discarded, eventually later leading to Supersymmetry and then String Theory.
In the mid 1990’s, Stephen Hawking advocated giving Supergravity another look. He pointed out the 1980’s era studies had taken serious shortcuts that made their conclusions questionable. He was unable to convince anyone to reopen the case though because the reasons that people took these shortcuts was that the mathematics was simply TOO complex for anyone to solve.
The key to the triumphs of the Unitarity Method is that it avoids the direct use of virtual particles and it summarizes all the possible (however unlikely) paths a particle can take. And since these loops eventually cancel each other out, you can get rid of the excess mathematical baggage by simplifying formulas.
They found that gravity DOES work and it does look like other forces, albeit in an abstract way. It behaves like a double-copy of a gluon of the strong nuclear force, a gluon stitched on top of itself! For example, three gravitons interact just like two copies of three interacting gluons. This double-copy property persists no matter how many particles are scattering or how many virtual particle loops are involved. Figuratively speaking, gravity is the square of the strong subnuclear force interaction.
If this concept seems strange, don’t worry; it is. Experts are not sure and don’t have a good mental image of what that means but, nonetheless, the precision of its mathematical calculations seems to “hold water” using the Unitarity approach to rule out infinities for up to 4-loop calculations of the theoretical graviton.
Normally, without Unitarity, to see if three virtual-graviton loops produced infinite quantities, one would need to evaluate 10^20 terms. A 5-loop diagram creates 10^30 terms: enormously hard to do. But using the Unitarity approach, they were able to use formulas to simplify it and find out four virtual-graviton loops DO NOT produce infinities, which is profound theoretical work.
Physicists are now using this approach to tackle previously thought-to-be impossible calculations inside the particle jets of the large hadron collider (LHC).
Joe Incandela of U.C. Santa Barbara, the spokesperson for the 2000+ physicist CMS experiment at the LHC, came to the advocates of the Unitarity Method with a proposition. They wanted to see if the LHC was making dark matter. Any of these particles the LHC possibly produced would elude the detector, leaving the impression that some of the energy had gone missing.
The problem is that the LHC frequently produces an ordinary particle called the Z boson, and 20% of the time it decays into two neutrinos. These rarely interact, and escape the detector also. This too would show the missing energy signature.
To solve this, Incandela and his group proposed a solution. Take the number of photons the CMS detector records, extrapolate the number of events involving neutrinos using Unitarity and see whether or not they fully explain the apparent energy loss. If not, the LHC might be indirectly creating dark matter.
This would ONLY work if the Unitarity method was precise enough. Professor Zvi Bern, Lance J. Dixon and David A. Kosower were eventually able to prove just that, and work is still being done in the regard to the hunt for dark matter in particle jets.
They have since taken on more ambitious projects with more colleagues making extremely accurate predictions about other collisions with neutrinos—some that would have taken teams of physicists decades—solved in time frames of about a year.
There is still a lot of work to be done before making such bold claims as “Unitarity being a quantum theory of gravity” but perhaps after success with 7-loop tree diagram problems (where quantum effects should grow strong enough to produce infinities) the team will effectively quash all of the skeptics if sensible, finite results appear.
Even if the Supergravity and Unitarity Method are self-consistent, it would not capture other kinds of effects that are too tiny to see in the loop-by-loop approach the team was following. Those effects may still require an even deeper theory, like string theory. It will take the team a long time to translate the mathematics into physical insight and check to see if it is true under ALL conditions.
For now, the crucial point is that gravity may not be so different from all the other forces of nature.
-Tyson (via Quarks and Quasars)
Further reading on Unitarity
The article this topic was based on from Scientific American (which you can purchase here)
The Scientific American article is based on papers:
“Supergravity- finite after all” by Kellogg Stelle in Nature physics, Vol. 3 pages 448-450; July 2007
"Lovely as a tree amplitude: hidden structures underlie Feynman diagrams" by Steve K. Blau in Physics today vol. 57 No.7, page 19; July 2004
"Cancellations beyond finiteness in N-8 Supergravity at Three loops" by Z. Bern, J. J. Carrasco, L. J. Dixon, Hjohansson, D.a. Kosower and R. Rioban in Physical Review Letters, vol. 98; No. 16; April 20, 2007
"Pulling QCD Predictions out of a (black) hat" by Daniel Maitre in SLAC Today; August 7, 2008