## Top quark: a short history – part III November 23, 2007

Posted by dorigo in physics, science.

4 -Searches for the top quark: the techniques

I left the discussion of top quark history in the last post of this series by mentioning that among the three basic strategies for producing new massive particles – and thus search for the top quark, the massive isospin partner of the bottom quark found by Lederman and collaborators in 1977 – the one that was going to win the house was soon recognized to be the same one that had bagged the W and Z boson discoveries at CERN: colliding a intense, high energy proton beam against a beam of antiprotons traveling in the opposite direction within the same vacuum chamber, and bent and kicked by the same electromagnetic field.

That does not mean that electron-positron colliders did not attempt at producing pairs of top quarks: they did, in fact, but only were able to report the failure to observe the production of two heavy quarks, which would produce an increase in the R ratio (see the discussion in the former post of this series), some spectacular resonances, and a more spherical distribution of hadrons in the detector. The latter signature is due to the large mass of the produced quark, which can impart high energy to all the bodies it decays into – and thus allow them to deviate from the original flying direction of the parent particle.

And in fact, the UA1 and UA2 experiments at CERN 546 GeV (later 630 GeV) proton-antiproton collider took the challenge quite seriously: not satiated with the weak bosons – which would soon fruit Carlo Rubbia and Simon Van der Meer a Nobel prize – they wanted to put their hands on the top quark. And they indeed could have, had the top mass been lower.

What happens if the top quark has a mass of, say, 50 GeV ? At a proton-antiproton collider you can produce top quarks in pairs by strong interactions – and that is exactly how it is done at the Tevatron these days, roughly once every hour during data taking- but if the sum of top and bottom quark masses are lower than 80 GeV, an enticing new possibility arises: electroweak production of a W boson, followed by a decay into a top-antibottom pair. The energy balance allows the W to decay into top quarks, and in subatomic physics everything that is not forbidden is compulsory, as I mentioned earlier.

In the plot on the right – a vintage one, in fact – you can see the then still fairly uncertainty prediction for the top quark cross section at the Tevatron (top curves) and at the SppS collider (bottom curves) as a function of the top quark mass. The sudden decrease as the 80 GeV mass is reached is due to the strong suppression of electroweak single top production by W decay at about that mass value. The lower of each two sets for top masses below 80 GeV represents the contribution to the cross section of the pair production process alone.

So what would the CERN experiments expect to see from a 50 GeV top? Well, typically a lepton, missing transverse energy from an escaping neutrino, and two hadronic jets from the two remaining b-quarks: something like $p \bar p \to WX \to t \bar b X \to e \nu b \bar b$ , where we assumed the top decayed semileptonically, and X denotes whatever else the two incoming hadrons fragmented into. A signature like that is sought nowadays at the Tevatron in the study of single top production, in fact: a single top is produced by electroweak interaction.

The UA1 experiment in fact did see the above signature, and from the observed 12 events claimed discovery of the top quark in 1984! They had predicted to see 3.5 events in their dataset due to background sources (mainly due to W production accompanied by QCD radiation), and 12 events looked like a signal: from it they could also measure a top quark mass of $40 \pm 10 GeV$! Unfortunately, the roads of particle physics are paved with tombstones of 3-sigma effects, fluctuations, unexplained effets. These invariably go away after more data is collected, and so it happened with UA1. UA2, the competitor experiment, could not confirm the discovery, and a few years later, it set the highest lower limit on top mass at 69 GeV (1990).

What had happened to UA1 then ? It so happened that QCD, the theory of strong interactions, dictating the phenomenology of interactions between quarks and gluons, was already a well-tested, mature theory, but its description by Monte Carlo simulations and models was not perfect yet. Physicists need simulations of the subatomic processes  in their detectors, in order to estimate backgrounds when searching for a signal – and that was the weak link of the chain of deductions that had led UA1 to broadcast the false claim. W production occurred way more often in association with hadronic jets than predicted by simulations, and so it had been heavily underestimated.

The top mass was soon realized to be higher than 77 (1990) and then 91 GeV (1992) when the CDF experiment published their analysis of the first 4 inverse picobarns of collisions collected between1988 and 1989. That simply meant that the top quark could not be produced copiously by W decay. That process was kinematically forbidden unless the W was strongly “off-mass-shell”, that is if it was produced with an unusually large mass. The business of discovering a top quark was harder than earlier thought, because not only the quark was heavy – and thus more rarely produced in the collisions (the cross section dependence on the mass has been shown in the plot above)- but it was to be produced in pairs, and so with a doubled effort. A task to be left to the upgraded CDF detector and its competitor, D0, in the run foreseen for 1992….

A final candy: the plot below shows a very interesting feature of W decay. The W boson has a total width of about 2.1 GeV. That means it decays “quite quickly” – in a trillionth of a trillionth of a second, more or less. More interesting is to note that the W is “democratic” in its decay: it generates an electron-electron neutrino pair once every nine times, and with the same frequency a $\mu \nu_\mu$ pair or a $\tau \nu_\tau$ pair; the other six out of nine decays are shared evenly between the three $u \bar d$ and the three $c \bar s$ quark pairs (remember, quarks are colored and they come in three colors!). So physicists talk about the “partial width” of W decay into one specific final state. Now, in the presence of a light top quark, the latter would claim its right to be generated in W decays as well, and each of the possible pairs would then have to be content with a 12th of the total share, there being now three more quark pairs allowed, the $t \bar b$ ones. By measuring the partial width of W decay into leptons, one can thus determine if the W does also decay to top quarks!

This exceptionally simple result was however obtained only later, when a very precise determination of the partial widths of W decay were possible with the large Tevatron data. The plot shows the ratio between total W width and partial width to electron-neutrino pairs (the black curve  turning down to a constant) as a function of the top quark mass. The CDF measurement (bottom horizontal line with hatched 1-sigma region) implies that the W width is shared in nine equal parts, and the top must be heavier than about 62 GeV at 95% confidence level. (Also note the curved structure of the dependence of the inverse partial width in the standard model, due to the “turning off” of the $t \bar b$ decay which becomes progressively kinematically forbidden as the top mass becomes closer to the W mass).

[To be continued…]

1. helen soderberg - November 23, 2007

Well it is still November 22nd,in Naperville,so have you dicovered time travel ? If not ,I have and will tell you the secre ,maybe, one day.

2. dorigo - November 23, 2007

That’s right helen, this blog runs on Greenwich time apparently. You should be familiar with it…

Cheers,
T.

3. Matteo Martini - November 24, 2007

Tommaso,
just a question.
Where do you find the time to write all the posts every single day?
How long does it take?

Regards,

Matteo

4. dorigo - November 24, 2007

Hi Matteo,

I take the time to write the blog from the time I used to spend playing chess online 😉
Seriously, it takes about one hour per day of my time, if I write something meaningful as the post above is meant to be.
Of course, speed of writing improves with practice…

Cheers,
T.

5. Paolo - November 26, 2007

Hi Tommaso… and thanks for the nice series about the Top quark: in 1995 I was in Pisa, almost completely absorbed by electrical engineering things, but the excitement was very high and with some friends we all listened to Giorgio Bellettini and his coworkers announcing the evidence and then the discovery. Nice recollections… I would really prefer reading your history off-line, take my time to fully enjoy it: are you considering making it available also as a pdf, or a ps, or something similar? Thanks again.

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