In the book 'Particle Dark Matter: Observations, Models and Searches' by Gianfranco Bertone I came across the following statement:
'...the sea quarks and gluons do not contribute to the vector current. Only valence quarks contribute...'
What is the reason?
Because sea quarks and gluons are virtual particles i.e quantum fluctuations that contribute nothing on average.
What exactly is meant by vector current in the context of that statement?
In some deep inelastic scattering experiments nucleons are probed with virtual photons, which in my book is a vector current. One cannot detect gluons this way, since gluons carry no electric charge. But I see no reason why they should not react with sea quarks in an observable manner.
Added: The book is really a collection of individual contributions, edited by Gianfranco Bertone. Which chapter of that book are you referring to?
@Kåre
p.380
spin independent contribution to WIMP-nucleon
"The vector coupling (which is present, for example, in the case of a Dirac
fermion but vanishes for Majorana particles) gives rise to an extra contribu-
tion. Interestingly, the sea quarks and gluons do not contribute to the vector
current. Only valence quarks contribute"
> p.380
Which should mean the article of Ch 18: Annual modulation signature with large mass ... by Rita Bernabei and Pierluigi Belli? I find nothing there.
If the vector current is the electromagnetic current, then the gluons don't couple, because they don't carry electric charge and the sea quarks contribute in (oppositely charge) pairs, so the net contribution cancels.
However this doesn't have anything to do with dark matter, that doesn't carry either electric or color charge and may carry weak charge.
I found the quote in Ch. 17: Direct detection of WIMPS, by Cerdeno and Green (p. 351). They earlier say that "Since the WIMP–nucleon relative speed is of order 100 km−1 s−1 [sic], the elastic scattering occurs in the extreme non-relativistic limit"
It is for this reason that only average quantities contribute (I don't understand why they feel a need to label this by interestingly), contrary to the case of deep inelastic scattering.
Since the weak current is a (vector) current for the weak charge, in fact the same comments apply to it, save for the different way of describing ``opposite charge'', since the group is non-abelian. Gluons don't carry weak charge and sea quarks contribute in ways that cancel out, on average, since they contribute in pairs.
The WI in WIMPs refers to the weak interactions of the Standard Model, not to the strength of the interaction itself.
Thank you for the answers but I guess I have an explanation. The vector current essentially counts the number of quarks minus number of anti-quarks (by number operator) which practically leaves only the valence quarks.
Basabendu> The vector current essentially counts the number of quarks minus number of anti-quarks
Yes, but with some flavour dependent weight factors. As Stam says, the current of relevance is the weak neutral current. There is a more detailed discussion of it in f.i. Eur Phys J A (2005) 24, s1, 115–118 ("The weak neutral current of the nucleon", see the link). For the case at hand, it should be sufficient to consider the form factors discussed there at zero momentum transfer, which reduces the problem to number counting, as you say.
http://link.springer.com/article/10.1140%2Fepjad%2Fs2005-05-020-0
Yes indeed Kåre Olaussen, as I have already mentioned, I am concerned about the zero momentu transfer (which is the case for direct detection of dark matter) scenario. Thank you for the reference.
It always is about number counting-but the point is what is the appropriate number operator. That is the operator that counts the degrees of freedom that carry the-net-charge under discussion. (And if the degrees of freedom are confined, they don't contribute either.)
Once more, if one's interested in dark matter, since dark matter particles don't carry color charge, they don't couple to gluons. If they have weak charge-which is the object of direct dark matter searches-they will couple directly to the valence quarks of hadrons, assuming they have the momentum transfer to resolve the quarks. The coupling to the sea quarks, in any event, can only be probed by charge polarization effects, since sea quarks contribute in pairs. At low momentum transfer, when the quark structure of hadrons isn't relevant, however, they will couple to the weak charge of the hadrons themselves and it doesn't make sense talking about quarks, whether valence or sea, or of gluons, at all, in that case.
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