Recent content by Jan Eysermans

Indeed, including the distributions for x2 are needed.. I have implemented the method of Vanadium 50 and the results are more or less ok! Thanks everyone.

Your explanation was for improving the error on handling the PDFs at q = M_z, right? What I mean is the difference between selecting x1 out of the quark-distributions or the antiquark-distributions. To make things clear, let say we want to produce an on-shell Z boson from u and d quarks (and...

I indeed interchanged the x1 and x2 labels, but still, if I sample only from the u-PDF, there is a difference when I sample only from the anti-u PDF. From this, it is not correct to sample only from the u-PDFs I guess. Is there any statistical procedure to incorporate all the distributions...

What do you mean by symmetry? When I compare the u-PDF generating x1 values with the antiu-PDFs, I notice a slightly difference (not a statistical one because the difference is "reproducible"). The other quarks are incorporated by weighting over all the PDFs.

Yes, indeed. Thank you for the answers! Jan

Yes indeed, that is exactly the result here from my program. One last question about the randomness. Now, I sample always from the u-PDF distribution. But, off course, it is also possible to sample from the anti-u PDFs. I guess it is important to incorporate both PDFs?

Yes, p = 4000 GeV, or LHC collisions. Here is an image of the u-PDF, randomly chosen over 1E6 times: http://postimg.org/image/zc6xga97n It is most likely to produce an x1 value smaller then 10E-1, 1E-2. The correspondig x2 values are then always > 1. Maybe I have to force x2 to be smaller...

I have a set of PDFs from the PDF4LHC program (see http://arxiv.org/abs/0802.0007). My program is written in ROOT, where I load the PDFs (for u,d anti-u and anti-d quarks), and then select a random value between 0 and 1 according to this distribution (thus non uniform). I'll give you an...

Thank you for the explanation! I've implemented in my code, but the results are, as expected, very strange. Suppose, I generate an x1 value from the up-quark PDF. This PDF increases as x decreases, and the generated x1 value is always very very small (order of 10^-4 - 10^-6). The corresponding...

Thanks for your reply. It makes the problem a little more clear to me. Now, I understand why on-shell production implies the fact that the com-energy must be equal to the Z boson mass. But this implies, as get it correct, that the x-values must satisfy the condition: s^2 = (p_1 + p_2)^2 =...

I understand the limitations of the model, that there are no jets are produced and the problem is 1D. I do not understand your argumentation I think. If you say that the invariant mass is just the Z boson, do you mean the rest mass, or the total energy of the boson? As I understand it...

I'm still confused with the center-of-mass (com) energy I think.. The com-energy is the total energy available to create new particles. If the Z boson is created, the com-energy equals the total boson energy: \sqrt{s}=\sqrt{4x_1x_2p^2} = \sqrt{p_z^2+m_Z^2} (assume c=1). This is correct...

Yes indeed, I understand now! In principle, the first constraint must be written as: x_1 + x_2 \geq \frac{E_Z}{p} = \frac{\sqrt{p_Z^2c^2+m_Z^2c^2}}{p} = \frac{\sqrt{(x_1-x_2)^2p^2c^2+m_Z^2c^2}}{p} After rewriting this equation, the second constraint is obtained: \sqrt{x_1x_2} \geq...

Can you explain why this equation is not sufficient? I do not see it immediately..

Thanks for your reply. But why do I require in the first condition that the Z boson must be at rest? The only constraint I apply is that the energy of both partons must be at least the mass of the Z boson. It doesn't matter is x1 or x2 are equal or not.