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Feynman diagram in QCD 
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#1
Feb2314, 02:34 AM

P: 9

the number stand for the index of particles (quarks and gluons) [itex]M=\bar{v}(p_2) ig_sT_{12}\gamma^\mu(12)u(p_1)\frac{i}{p_7^2}\bar{u}(p_5) ig_sT_{56}\gamma_\mu(56)\bar{v}(p_6)\frac{i}{m\gamma^\mu p_{9\mu}}\bar{v}(p_3) ig_sT_{34}\gamma^\mu(34)u(p_4)\frac{i}{p_8^2}\bar{u}(p_5)ig_sT_{56}\gamma_\mu(56)\bar{v}(p_6)[/itex] [itex]u(p_i)[/itex] and [itex]v(p_i)[/itex] stand for the wave function of quark and antiquark, respectively. [itex]p_i[/itex] stand for the four momentum I am studying the QCD right now. Do I write the amplitude above right? Someone recommend me a textbook by T.Muta. But I make some confusion when I confront complex diagrams like above. Which book or paper can tell me about this? Thank you! 


#2
Feb2314, 05:20 AM

PF Gold
P: 472

I like to structure it more as to not make mistakes:
##\def\lts#1{\kern+0.1em /\kern0.45em #1} \bar{u}_6 (i g_s \gamma_{\mu} T^a) \frac{i}{\lts{p}_9  m}(i g_s \gamma_{\nu} T^b) u_5## ##\times \left(\bar{u}_4 (i g_s \gamma_{\alpha} T^c) u_3\right)## ##\times \left(\bar{u}_2 (i g_s \gamma_{\beta} T^d) u_1\right)## ##\times \left( i \frac{g^{\mu \alpha} \delta^{ac}}{p_8^2} \right) \times \left( i \frac{g^{\nu \beta} \delta^{bd}}{p_7^2} \right) ## My convention is to always start with outgoing, working AGAINST the arrows (particle flow), and for fermion propagators write the momentum such that it goes WITH the arrow, and use ##\def\lts#1{\kern+0.1em /\kern0.45em #1} i \frac{\lts{p}+m}{p^2m^2}## which will be right. You have a couple small errors I think. Also, I assumed those gauge bosons were gluons, though normally that would be the springy/curly line, not the wavy one. Wavy is reserved for basically all spin1 bosons (gamma, w z) except the gluon. 


#3
Feb2314, 07:19 AM

P: 9

Yes, the gauge bosons were gluons. I will take care next time,thanks!



#4
Feb2314, 07:36 AM

Thanks
P: 1,948

Feynman diagram in QCD



#5
Feb2314, 07:58 AM

Thanks
P: 1,948

@ Hepth: Shouldn't you have used u's and v's instead of all u's for the external legs? I think Thor Shen had that right.



#6
Feb2314, 08:07 AM

P: 9




#7
Feb2314, 08:43 AM

PF Gold
P: 472

I guess it might make the most sense as a strong decay of some meson from the top down now that Im thinking about it deeper than a diagram. I always go from left to right as in to out states. 


#8
Feb2314, 10:06 AM

P: 9

The diagram is from the protonantiproton annihilation into two mesons.



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