# Sea-valance quarks of protons

1. Aug 14, 2014

### 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)?

2. Aug 15, 2014

### e.bar.goum

3. Aug 15, 2014

### 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.

4. Aug 15, 2014

### ChrisVer

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?

5. Aug 15, 2014

### kurros

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

6. Aug 15, 2014

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

7. Aug 16, 2014

### Staff: Mentor

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.

8. Aug 16, 2014

### 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.

9. Aug 16, 2014

Staff Emeritus
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.

10. Aug 16, 2014

### 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.