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Lepton versus hadron collisions October 31, 2006

Posted by dorigo in physics, science.

My former post triggered two interesting questions by Gabriel:

“a little off topic, but i would like to make a question. i want to understand whats the difference betwen a pp and a ee collision, in a specific sense. first lets forget the syncroton energy loss issue and lets assume that the CM energy of the ee is 3 times the pp (naive, for taking into acount the 3 quarks). in this case i have the same “potential” of observing new physics? put in other way, how will change the menu of produced particles?

A little bit confusing to me, still in the topic but a different thing, is why they had to make pp collision to first observe the W.”

Protons and electrons are both particles, but they are as different as whales and ducks are different animals. Just as the latter can both float, but they obey different physics laws in order to do so, so protons and electrons can both collide and produce new states of matter, but they do so in a very different way, exploiting different elementary forces.

When protons collide, as you say, it is actually their constituent quarks that do. So, dividing by three is a good first guess idea of the effective energy released in the collision. Things are more complicated, though, because each quark in the proton can carry any value of the total proton energy from zero to the maximum, and the probability to find it with a given energy fraction is given by a distribution that has to be determined by experiment.

Anyway, let’s get to the core of your first question. Proton-antiproton collisions have a different menu of possible final states that get produced with respect to electron-positron collisions. The reason is that the overwhelming majority of the collisions of protons is mediated by the strong force: one that could not care less about the fact that both quarks and electrons have electric charge. Instead, the strong force sees the colour charge of the quarks, and ignores electrons as if they were not there.

The opposite, though, is not true: the electromagnetic force responsible for electron-positron interactions also can scatter quarks off one another, or annihilate them with the production of a photon. So in a way, with a proton-antiproton collision you can do what you can do with an electron-positron collision, plus more.

Let’s say there is a Higgs boson out there. How would you discover it ? You can smash electrons and positrons, producing a ZH final state through electroweak interaction. That is what LEP II has tried to do until a few years ago. But you can also smash protons and antiprotons together, hoping for an electroweak interaction of the incoming quarks, that will yield the same final state. That is because both proton constituents and electrons “feel” the electroweak interaction.

If instead you were after production of a massive strongly-interacting electrically neutral particle, you would need strongly interacting projectiles. But only in practice. In theory, you could annihilate electron-positron pairs and sometimes the high-energy photon produced would materialize into quarks, and the latter still produce the odd particle.

So it is not so much a matter of energy, but of the relative frequency with which you can produce a certain process with a given projectile.

As for the W discovery: W’s are charged, so a neutral electron-positron initial state is not the best way to produce them. To do it, you need provide enough energy to make a W together with something else carrying away a unit of charge, and the best chance is then another W. But you need lots of energy and the process is very rare (was done in LEP II, but only 15 years after the W discovery). Instead, of course electron-positron collisions are ideal to produce Z bosons. But synchrotron radiation prevented that in 1983, so Z bosons were indeed produced in electroweak processes with protons as projectiles.

Mind you, it is quite hard to separate the very rare electroweak processes amidst the huge rate of strong interactions when you smash protons. That required quite some skills by the UA1 and Ua2 collaborations….



1. gabriel - November 1, 2006

Hello Dorigo, thanks for your insightful answer.
So, its not a matter of energy only, we surely have to look at the fundamental possible diagrams. Its much more probable to make a W from a d-bar + u -> W than from a e+e- or even a p+p+ collision.
More, in the case of e+e- you can in low order produce only 2 real W, while in p+p- W goes as a virtual particle, off-shell, so more aesy to create. In this way, the menu is basically the lowest order process plus rare higher order… Is that the idea?

I was trying to figure out whats the motivation of ILC being a ee collider!


2. dorigo - November 1, 2006

Hi Gabriel,
yes, you got everything right, except that e+e- as you say cannot produce a W alone, as much as p+p- cannot, but the quarks inside the protons can… This works for on-shell particles. Off-shell we do not really talk about “W bosons”, for instance when we talk about a neutron beta decay the W is there, but it is off-shell and we prefer to forget it mediated the process.

ILC will be an electron machine because lepton collisions are way cleaner. For instance, they provide the top quark mass to be measured by threshold scans, when you vary the beam energy and get the mass by checking the collision rate.

However, the ILC will live only if the LHC finds something to study… I believe that if the LHC only found the Higgs, and no Supersymmetry or other exotic phenomenon, it would be very hard to motivate a large expense of money…

3. Tobias Persson - April 26, 2009

Thanks for a very interesting article. In an article i recently read it was stated that the lepton collider could probe new physics at cm-energy 1/10 to that of the hadronic collider with same energy. Is that true?

4. dorigo - April 26, 2009

Hi Tobias,

well, yes and no. It depends on how much data these machine can collect. Take the Tevatron (2 TeV, proton-antiproton) versus LEP II (up to 209 GeV, e+e-): the LEP II collider obtained a limit on the Higgs at 115 GeV which has only been improved by the Tevatron this year, after several years of data taking. However, the LEP II collider would have never found particles with mass above 200 GeV, while the Tevatron has put bounds on SUSY particles with masses above 300 GeV, and on other particular states up to 800-900 GeV.

The rule of thumb is that one tenth the energy of a hadron collider allows to study interesting physics, and probably do precision measurements that rival those of the hadron machines; but I would not assign too much significance to this order-of-magnitude assessment. For sure, a 1 TeV lepton collider would be a great machine to build, but it will only make sense if the LHC proves that there is new physics to study with precision. If the LHC (10-14 TeV) does not find NP, then a leptonic collider is simply useless.


5. dorigo - April 26, 2009

Oh, and – this site has moved to http://www.scientificblogging.com, please check out my new blog there: http://www.scientificblogging.com/quantum_diaries_survivor . Thanks!

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