What is the Contribution of Heavy Quarks to Proton Structure?

[ChrisVer]

I am looking at the structure of protons, and in my script, when they define the Parton Distribution Functions of all parton species they say that the integral over PDFs of all parton species yields a total momentum fraction of:

$\sum_i \int_{0}^{1} f_{i}(x) x dx =1$
where $i$ denots the species:
$g,u,d,s,c,\bar{u},\bar{d},\bar{s},\bar{c}$
Then it says that b or t quarks are not included due to their high mass...
However isn't the $c$ quark pretty massive (1.29GeV >1 GeV) for the proton (~1 GeV)?

 

[e.bar.goum]

I'm profoundly not an expert in this, but there may be some charm quark component in the proton thanks to perturbative QCD. This paper http://arxiv.org/abs/0901.0739 suggests the existence of some intrinsic charmness to a proton. This blog post http://muon.wordpress.com/2009/01/18/does-the-proton-contain-charm-quarks/ talks about the paper.

 

[kurros]

They are off-shell quarks, so they don't have to have their on-shell masses. Also those masses are defined in a tricky way since you cannot actually isolate a quark to measure its mass.

 

[ChrisVer]

They are off-shell quarks, so they don't have to have their on-shell masses. Also those masses are defined in a tricky way since you cannot actually isolate a quark to measure its mass.

that works fine for me... but if I accept the existence of off-shell quarks, wouldn't the same reasoning work for b or t quarks?

 

[kurros]

that works fine for me... but if I accept the existence of off-shell quarks, wouldn't the same reasoning work for b or t quarks?

Yep, pretty sure. Theoretically virtual b and t quarks contribute, but I think they are just negligible so people ignore them.

 

[Vanadium 50]

There are 5 flavor PDFs. There are not 6 flavor ones because the top contributions are unmeasurably small.

 

[mfb]

The b contribution is there (you can measure it via single-top production in proton/proton collisions), but its contribution to the total momentum is quite small. The charm contribution is a bit larger. If you include those two (or just 1) depends on the precision you want. Including the top is pointless because its contribution is tiny compared to the uncertainties from the light quarks.

 

[RGevo]

Note that the Parton distributions functions are required to describe the evolution of patrons before an interaction.

The point is that quark content arises due to the evolution of patrons. So, by evolving the patrons to high virtuality (q^2), the c, b, or t quarks can effectively contribute to an interaction.

At a 100tev hadron collider, the t quark distribution will have to be studied theoretically and experimentally.

 

[Vanadium 50]

The b-contribution is also there in four-flavor PDF's. There it comes from the gluon splitting to bbar.

There is no physical distinction between starting with u, d and g PDFs and letting them evolve and starting with 4 or 5 flavor PDFs. It's a question of ease of calculation and ease of comparison with data.

 

[RGevo]

The b contribution in the 4 flavour scheme is present in the gluon splitting *only in the matrix element*.

It is neglected from the PDF to allow the b quarks to be treated as massive quarks in the matrix element. This improves the accuracy of the prediction for the b quark in the final state... At a consequence of losing the resummation of b quark contributions in the PDF which are ignored.

The treatment is only the same if you can calculate the full interaction (all orders in the matrix element), which is not and will not be possible.