Dear all,(adsbygoogle = window.adsbygoogle || []).push({});

I am new here and hope that I write this in the right place. ;-)

I am seeking help in deriving Ji's Sum Rule, which tells you that the second moment of the nucleon's GPDs equals the total angular momentum of the quarks. E.g. in Diehl, hep-ph/0307382, Sect. 3.6.

The step where I'm stuck is in the previously mentioned paper, from Eq. (68) to Eq. (69). It seems so easy, though: for $\mu$ different from $\nu$, the terms in $g^{\mu\nu}$ in (68) disappear, while the other term in C disappears in the forward limit p'->p. One thus keeps only the terms in A and B. For the B-term, I immediately use the Gordon identity. This gives me:

\[<p|T^{\mu\nu}|p> = (A(0)+B(0))/2 \bar{u} \frac{p^{\mu}\gamma^{\nu} + p^{\nu}\gamma{\mu}}{2} u - B(0) \bar{u} \frac{p^{\mu}p^{\nu}}{m} u\]

If I then fill in some values for the spinors, I always arrive at (A-B)/2 instead of (A+B)/2. I don't see where it goes wrong, which is so frustrating... Is it due to my spinors? Or to something else? I don't seem to need the fact that the proton is at rest (which is written below Eq. (66)). In fact, I always end up with a term ~ Lz, which turns zero in the limit of a proton in its rest frame.

I hope that someone here can help me... I've read so many papers about it, and still don't find the mistake.

Kind regards,

C

**Physics Forums | Science Articles, Homework Help, Discussion**

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Ji's Sum Rule

Can you offer guidance or do you also need help?

Draft saved
Draft deleted

**Physics Forums | Science Articles, Homework Help, Discussion**