I am confused too right now. I think that plot is either wrong (for instance it assumed zero Z mass to plot the pseudorapidity instead than the rapidity) or it is showing only some of the sea-sea interactions.

The total Z production _rapidity_ distribution should not have a dip at zero, any more than that of its decay products; please note that in this post above we are discussing the rapidity of muons from the Z, while in the other post we were discussing the Z rapidity itself.

All I can find in my archives about the studies I produced for the Z rapidity is the plot you can find here , which I think is the correct one (it has the total distribution, as well as the one for each quark type -I think ddbar is in red, uubar is in blue, ssbar in green, ccbar in yellow and bbbar in magenta).

Cheers,
T.

the Z rapidity also has two bumps …
I don’t understand why Z is ok but not this one. I’m confused.

I am an undergraduate student at the University of Kansas doing research with the physics department. My research is looking into Feynman’s limiting fragmentation. I see that the histogram of the rapidity distribution is done in ROOT. I was wondering if there is anyway I could get a copy of the ROOT file of this distribution as I am trying to find a function, some curve, to fit these plots with. I think it would give me a good start at and a basis for checking my goodness of fit for my curves. Thanks for your time.

Best,

Michael Stingo

sure. Just make a question and I will try to answer it. As for your initial one: the rapidity distribution of particles created in a proton-proton collision is important for several reasons.

1) we construct our detector around the collision point in a way that allows us to “see” as many as possible of the particles created in the interaction. The rapidity distribution is basically a distribution of the angle that the emitted bodies make with the proton beams. The fact that the distribution peaks at zero rapidity, and falls off rapidly at larger absolute values, implies that we can construct our detector as a cylinder, instrumenting best the zones which particles emitted at large angle from the beam will hit. A much flatter rapidity distribution would force us to build our detectors as a hour-glass, with two lobes covering best the forward- and backward- going regions, close to the beam axes.

2) a particle rapidity tells us a lot about the production mechanism. By studying it in detail we can figure out details about the interaction which produced it. For instance, by studying the rapidity distribution of muons emitted from a W boson decay (), we can determine the asymmetry with which the W boson was created, and infer information on the distribution of quarks in the proton.

3) Rapidity is one of the angular quantities we measure for each particle, from which we determine the particle energy and direction with good precision. These quantities are crucial to reconstruct the possible origin of the particles we detect, such as, for instance, if a heavy particle has been produced and decayed to those we detect. Take for instance a Higgs boson: . It can decay to four muon tracks, and if we measure their energies and momenta well, we can then determine the Higgs boson mass.

Cheers,
T.

the plot is indeed at generation level. As for a real demonstration from first principles on the fact that at zero rapidity there should be a maximum, given monotonous PDF functions, I am unable to provide one, although my intuition tells me it is a correct statement. Maybe there is somebody willing to fiddle with it around ?

The problem can be stated as follows:
Given f(x) a continuous function in [0,1] such that , and the function , show that in y=0 one has , .

This is my conjecture

Cheers,
T.

yes, ignoring the mass is a good idea – unless one deals with W or Z bosons (it did happen to me once to produce a screwed Z rapidity distribution by using the massless approximation, lol).

As for muons, they are the result of decays from light hadrons. To produce one, you have to provide some Q^2 to the interaction. This is in effect a cutoff on the rapidity of the center of momentum.

For an example, take . This makes a hard interaction with , which is close to the minimum value which will produce mesons. For such a system the rapidity is …
And this totally neglects the fact that the plot above might have been constructed by asking for a minimal requirement on the transverse momentum to the muons!

Ciao,
T.

thanks for the explanation about the cutoff!

Concerning proton rapidity in the beam – your argument using the angle shows that you are an experimentalist, equating pseudo-rapidity and rapidity! In the heavy-ion simulation codes I have worked with, one has of course easy access to energy and longitudinal momentum and can use the formula you have given in the post, or y = arcosh γ.

Now plugging in γ = 7000/0.94 for the protons in the beam yields y = 9.6, or 19.2 for the rapidity interval between the colliding protons… Which makes me wonder, why is the muon distribution not much wider? Why are there no muons closer to beam rapidity? Can they not be measured with the CMS detector, which may be just OK for the purpose of the experiment? Or is the plot for a lower beam energy?

Cheers, Stefan

the plot shows the rapidity of muons that did not fire the trigger (or so I believe – one never knows with a plot crafted by somebody else until it is verified etc.). The trigger collects muons with Pt>20 GeV, but the lower-Pt muons have a fat chance to be mismeasured at trigger level, and so they may trigger even if they have 5, or 10 GeV. The momenta of muons from interesting physics processes is larger than these values, fortunately – so we can keep thresholds higher and still collect interesting stuff. In any case, for W and Z bosons decaying to muons, the typical Pt remains of the order of M/2, i.e. 30-40 GeV, because most bosons are produced at low transverse momentum themselves, providing no additional boost.

For the proton beams, the crossing angle of the two beams is very, very small – I think it is 96 microradians. That means a rapidity of 14 if I’m not screwing something up.

Cheers,
T.

So the plot shows the rapidity distribution of all those muons with transverse momentum below a certain cutoff? What was this cutoff momentum, just to get an impression of the momenta involved at the LHC?

And since I am too lazy right now to check it out for myself, what is the rapidity of the incoming proton beams of the LHC? Seems it is something around +/- 6?

Cheers, Stefan

I assume that’s a generator-level plot, but if it were reconstruction then page 10 of the following paper (“Effect of Magnetif Field”) would shed some light on the situation…

http://home.fnal.gov/~sceno/jpg/results/Minbi.pdf