You may have come across the concept of “missing energy” in some of the previous posts (Adam’s from June 25, and Monica’s from last year)? What is it? Is it a signature for physics or is that we can’t count properly?
Basically, the idea is the following. When two protons collide, it is actually a part of each one of them that causes the high-energy collision, while the rest of the proton sort of “falls apart” (the latter, aka “the underlying event”, produces lower energy stuff). These two parts (quarks and gluons, generically known as “partons”) have an unknown fraction of the proton energy (or momentum) along the beam direction. However, in a plane perpendicular to this high-energy proton beam these partons have negligible energy; they are essentially moving along the beam direction. Stand in front of a wall and imagine one beam coming out of the wall and the other going into it, and the collision occurs at the surface of the wall. This collision is like a bubbling cauldron (of energy) that spews out particles every which way; hence, they have a momentum component in this transverse plane as well as along the beam direction.
From the principle of energy conservation, since the initial state (two colliding partons) has zero energy in this transverse plane, the final state (a mish-mash of electrons, pions, photons, neutrons, protons, kaons, muons, etc.) should also have zero energy. If we do a vector sum of the energy of all the final state particles in this transverse plane, we should get zero. (For instance, if the collision produces two electrons that are going in opposite directions in this plane, the vector sum of their momentum will add to zero.) If this sum is non-zero, we call it “missing energy”. So what? Does this tell us anything?
Some particles do not produce any detectable signal as they travel through the detector; neutrinos are the most common type. If they have high enough energy, events containing them will have a detectable amount of missing energy. Energetic neutrinos are typically produced in the decay of a W boson or a Top quark; lower energy neutrinos are produced in the decay of Tau leptons or particles containing a Charm or a Bottom quark; even lower energy neutrinos are produced in some decays of pions and kaons. In fact, we are able to use this feature to reconstruct a Top quark.
Most garden-variety events, other than those listed above, typically have very little missing energy. But, what about new phenomena? Well, it turns out that most models of Supersymmetry (see Seth’s post from June 28 ) posit a particle that behaves very much like a neutrino as it travels through the detector, and these can be very heavy (100 to 200 times the mass of a proton). In these models, such particles are produced copiously, thus events containing them will have lots of missing energy, much more than in events mentioned above. In fact, this is one of the unique signatures of these models. Also, there are other new Physics effects for which missing energy is a good discriminant.
However, understanding missing energy is a tricky business; you have to know the dead regions of the detector as well as the noisy ones. Imagine that one part of the detector is not working. Any particle that goes into that region is not measured. If you follow the prescription outlined above, you will get that these events have missing energy; there was stuff there but we didn’t see it. Or, electronic components in one section of the detector are very noisy, so we may think that there is lot of stuff going into that region. Once again, these events will appear to have missing energy. We also have to make a lot of fine corrections to particle energies to determine missing energy accurately. But, if we do it properly, there is a huge payoff in being able to detect new phenomena! Happy hunting.
If we do a vector sum of the energy
Do you mean momentum? Energy is not a vector.. At least not by my high school physics :/
“From the principle of energy conservation . . . .”
Wait, so in particle physics energy is a directional quantity? Or are you really talking about momentum conservation?
Hi,
Apologies for the confusion. We use energy and momentum sort of interchangeably, and it can get confusing for others. We can get away with this because the masses of most of the particles that we detect are much much smaller than their momentum, e.g., an electron has a mass of 0.5 MeV, whereas we mainly deal with ones having a momentum of at least 15,000 MeV. Similarly for the other charged particles.
Imagine an event with two electrons going opposite to each other (in this transverse plane). The part of the detector that finds the electron track measures its momentum, whereas the calorimeter measures its energy. Both will give the same result.
Now the calorimeter is not a monolithic detector; it is made of very small sub-units. So when an electron hits one of these sub-units, we know the exact direction in which it was going, hence we can assign a vector to the energy.
Does this clarify things?
Vivek
Thanks for the clarification, Vivek.