Single top observation - when ? June 9, 2006
Posted by dorigo in physics, science.trackback
Following Michael's suggestion (see previous post), I will venture to make a prediction for the next important measurement CDF will make within the timescale of the winter 2007 conferences. But let me make a preamble here.
The top quark was observed in 1995, when its pair-production was seen in CDF and D0 data. However, 11 years after that success, we are not through with the study of top production mechanisms at a proton-antiproton collider: we have not observed the production of a single top quark yet.
Top quarks have a quantum number nobody really cares about: it is T, for "top"ness. Every quark possesses a similar quantum number - the first to be discovered was strangeness, in the fifties. I will post about the discovery of strangeness later. For now, let's note that strong interaction, the one responsible for keeping quarks together inside protons and neutrons, and thus guaranteeing the stability of baryonic matter - nuclei, that is - conserves these quantum numbers.
So, strong force obliges the rule of conservation of T. What that means is that with a strong interaction you will never be able to create a single top quark, if you had none to begin with: the carrier of strong force, the gluon, is unable to do the trick of changing a given quark into one of a different kind. You can, however, create a pair: a top-antitop pair will have net T=0, because top has T=+1 and antitop has T=-1. That is how pair production of top quarks occurs.
How, then, can you produce a single top quark ? Via the weak interaction, of course: weak interactions do not oblige to quark quantum numbers conservation. Weak interactions are in fact solely responsible for the decay of a heavy quark into a lighter one. W bosons couple different quarks together, and allow transitions between them.
With weak interactions at work you are able to create a single top quark from a proton-antiproton collision. The diagrams above show how this can happen. On the left, a gluon from a proton splits into a b anti-b pair, and the b quark interacts with a u or a anti-d quark through the weak inteaction carrier, the W boson; a top quark is thus created, and the standard decay to a W-b pair follows. On the right, a simpler mechanism is at work: a W boson is created at high virtuality: that is, with much more rest energy than the nominal W mass; that allows that "off-shell" W to decay to a top anti-b quark pair, something on-shell W's don't usually do - their mass is half what is needed for the process to occur.
However, weak interactions have a problem - they are, indeed, weak. A process mediated by weak interaction will be much less frequent that one mediated by strong interaction because of the smaller value of the relative coupling constant.
Despite of the weak coupling constant, the fact that you only need to produce one heavy object instead than two makes it comparatively less rare: the less energy a process needs, the more frequent it will be.
In the end, the two mentioned effects balance each other, and at the Tevatron the production of a single top quark is only half as frequent as pair production. Not so rare then: we have already hundreds of top pair production events in our bags… Unfortunately, single top produces a much less distinct signature. Backgrounds are much higher, and signal extraction becomes really hard.
So far, CDF and D0 have only been able to put an upper limit to the production rate of single top quarks at the Tevatron. But we are close to make an observation for this elusive process.
I am optimistic by nature, and I am willing put some money on the fact that CDF or D0 will produce a first evidence for single top production in time for the 2007 winter conferences. Anybody willing to take a 1 dollar bet with me ?
Tomaso,
I’ve read, “The law of the conservation of baryon number states that the total number of baryons must be the same before and after any subatomic event.” Is this a supersymmetrical condition “thus guaranteeing the stability of baryonic matter?”
Thanks for your patience, Fred
Hi Fred,
no, no supersymmetry at work here.
In the Standard Model, Baryon number violation is actually allowed, although with extremely low probability and at very low energy.
Baryon number violating processes in the SM are associated with a quantum-mechanical effect called “tunnelling”, whereby an exponentially decaying spatial amplitude for a wave function maintains a non-zero value through an energy barrier, and - if the barrier is narrow enough and not high enough to make the wave function really vanishing - the wave function has a chance to “pop out” of the barrier, tunnelling away from the trap.
Not clear enough, huh ? Ok. Imagine a quantum well. It is a region of space where the potential energy of a particle is smaller than its total energy. Thus, the particle has some kinetic energy left, and it propagates within the region. Now, if you take the quantum-mechanical description of the particle as a wave propagating in the well, this is a wave function. A function that describe the “amplitude” for the particle to be in any particular spatial point within the well.
Within, and outside of it. In fact, if the height of the “walls” is not infinite, the wave function “leaks” outside of the well and inside the walls, with an exponentially vanishing amplitude. It is as if the particle has a extremely small, but non zero, chance of being found inside of the walls.
Now, if the walls are not thick enough, this exponential tail of the wave function will extend past the wall. Past it, the particle described by that tiny amplitude that has leaked out of the wall will have again a positive kinetic energy, and it will be perfectly legal for it to propagate there. The particle has “tunneled” inside of the wall and out of the well.
I think I will post about this effect in my blog… Just allow me some time to recover from tonight’s soccer game - I’m exhausted!
Cheers
Tommaso
Hmm, and if a single top is not seen… how many time will be take to have “new physics at five-sigma deviations” for this particular reaction? I am thinking on the models where symmetry breaking comes from a composite of top+bottom or top+newcolouredthing. The b-t-W vertex should be affected by this new physics.
Good question… If you ask how long it will take CDF and D0 to exclude single top production, I think it will take a couple more years of running to say it for sure (95% cl exclusion limits below the SM prediction mean nothing to me - once in twenty times they are wrong!). It would be puzzling… and fun!
Cheers,
T.
Hi Tommaso,
I’ll bet that you’re right, and CDF & D0 find the first evidence for single-top production at the Tevatron. As you point out, this is quite difficult for experimental reasons, and requires a lot of data. One question I have, though: why would you, personally, find a positive result for this interesting? There are theoretical and experimental reasons, but what is the most relevant, in your opinion?
Michael
I think single top production has the potential of yielding a measurement of Vtb of some significance only at the LHC, and even there, not terribly so.
In the SM these processes occur by force and it is not too interesting to find them. More interesting would be not to find them! As Alejandro points out, a whole set of theories would take the stage.
So, as experimentalists, we should finish the job with the top quark, and show it behaves as we expect it does.
Cheers,
T.