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Anxiously waiting for Mia’s results November 10, 2006

Posted by dorigo in mathematics, personal, physics, science.
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This evening the results of yesterday’s written exam of PhD student candidates will be posted in the entrance hall of our Physics Department in Padova. There are about 10 grants (I do not know the exact number!) to cover three years of PhD studies, to be assigned to the best candidates among 42 who participated in the selection… And Mia is among them.

Mia graduated with me a few months ago (see https://dorigo.wordpress.com/2006/07/31/mias-graduation-pictures/ for her graduation pics) and wants to continue working with me in the CMS group. She is a brilliant student, but recently her mind was a bit too distracted by family matters, and I was worried that she would not be able to fully concentrate on the exam… Tonight we will know whether she has passed the written part, the oral part will follow and should not be a problem, but in the written score there is a threshold of 7/10. So we await the results with trepidation.

To me, it means deciding what will be my main research activity in the next few years. Of course, I do not need Mia to do my job, but having a PhD student or being alone are two totally different worlds.

The exam consisted in a written composition on a topic to be chosen among two possibilities (either a discussion of interaction of radiation with matter and applications to a detector of choice of the candidate, or a discussion of symmetries in physics), plus two problems to solve in a set of four.

The problems were simple, but in the little time allotted (2.5 hours for both composition and problems) anybody can make mistakes. And I think Mia did one or two mistakes indeed. But from what I have heard I believe her exam is overall good enough to pass the threshold.

Here I will give one of the problems, a simple kinematical quiz. You have a 700 GeV proton hitting a proton at rest, and you are asked whether you have a chance of producing a real Z boson, and why.

The formula for the center-of-mass energy of the collision is simple, and it yields  s=M^2+M^2+2*M*E, where s is the square of the available energy, M is the proton mass, and E is 700 GeV. The total energy available to produce new states is thus sqrt(1402) GeV, or about 37.5 GeV, which is not nearly enough for a Z (mass=91.2 GeV). Furthermore, one cannot really consider the protons as the interacting bodies, but rather the quarks they are composed of, that have a much smaller total energy available to produce new states.

The answer is then that you cannot produce Z bosons with that little energy in the center-of-mass system. It is for that very reason that to first produce these bodies Carlo Rubbia had to use a collider (the first one), a machine where collisions occurred between protons and antiprotons traveling with the same energy in opposed directions. In fact, when you collide a 700 GeV proton with another particle of the same mass and energy (the antiproton), you get that the total available energy simply sums: 700+700=1400 GeV, plenty for the Z boson.

Rubbia obtained the Nobel prize in Physics for that endeavour, together with Simen Van der Meer. In 1983 the UA1 and UA2 experiments discovered both the W and the Z bosons with the 546 GeV interactions provided by the SppS collider. There, the beam energy was little more than a third of the 700 GeV of the problem above, but the head-on collisions were much more suitable for the discovery of massive objects. The wonders of relativistic kinematics!

Comments

1. Fred - November 11, 2006

Hello Tommaso,

1. I thank the stars that you weren’t my teacher a long time ago as I would now probably be in some lab smashing things up instead of relaxing on the golf course. I was even able to understand ‘a simple kinematical quiz’ from your explanation. Thank you again.

2. How does your wife refrain from becoming jealous of the obviously talented students you get to work with?


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