Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

I Dominant Feynman diagram for ##b \to s ~l^+ l^−##

  1. Feb 4, 2017 #1
    Hi all,

    It's written in QFT books, see for instance George_W._S. book "Flavor Physics and the TeV Scale" that the following Feynman diagram (1)
    1.png

    is the dominant Feynman diagram for ## b \to s ~l^+l^− ## decay. Actually I compare this diagram via another possible diagram (2)

    2.png

    Both (1) and (2) are proportional to## G_F^2##, so they are on equal coupling order, also (1) proportional to

    \begin{align}
    \Big(\frac{1}{k\!\!/ - m_t}\Big)^2 ~ \frac{1}{k^2 - m_w^2},
    \end{align}

    while (2) proportional to

    \begin{align}
    \frac{1}{k\!\!/ - m_t} ~ \Big(\frac{1}{k^2 - m_w^2}\Big)^2 ,
    \end{align}

    I mean (1) has two heavy propagtors in the loop, while (2) has only one heavy propagator, so for the first sight, it seems (2) is the dominant diagram, but this is not the fact .. so any one can explain why (1) is dominant one ?
     

    Attached Files:

    • 1.png
      1.png
      File size:
      3.6 KB
      Views:
      18
    • 1.png
      1.png
      File size:
      3.6 KB
      Views:
      21
  2. jcsd
  3. Feb 4, 2017 #2
    Why do you assume the loop contains top quarks?
     
  4. Feb 4, 2017 #3
    because ## \mathcal {M} \propto V_{ib} V_{is} ##, so in the best cases the ##V_{CKM}## matrix elements are ## V_{tb} V_{ts}## or ##V_{cb} V_{cs}## . the first choice is the best because ## \mathcal {M} ## also proportional to ## m_i ##
     
  5. Feb 4, 2017 #4

    ChrisVer

    User Avatar
    Gold Member

    aren't you supposed to add them (each individual flavor within the loop)?
     
  6. Feb 4, 2017 #5
    Hi,

    If you asking about ##Z u_b \bar{u }_c## vertex, there is ##\delta_{bc} ##, i.e., Z couples to the same quark flavor.
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?
Draft saved Draft deleted