Penguin diagrams and CP violation

In summary, the discussion was about the contribution of strong penguin diagrams and electro-weak penguins to the amplitude of K to (ππ)I=0. It was explained that gluonic penguin operators do not differentiate between final states with different isospin, so they only contribute to final states with I=0. On the other hand, electroweak penguins contribute to both I=0 and I=2 final states. The ΔI=1/2 selection rule for I=0 final states is an experimental data and there is no clear explanation for it. Additionally, the action of isospin operators on the quark fields was discussed to show that the gluonic penguin operator is
  • #1
Einj
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Hi everyone. I have been studying CP violation in kaon systems. I would like to know is someone can explain why, to leading order, strong penguin diagrams (i.e. involving a gluon) only contribute to the [itex]K\to (\pi\pi)_{I=0}[/itex] amplitude, while the isospin 2 amplitude is given by the electro-weak penguins (i.e. involving a photon or a Z boson).

Thank you very much

Edit: I can add more information to the question. Take the gluon penguin diagram. It contains a [itex](\bar ds)[/itex] current which is an SU(3) octet and another current which is a flavor singlet. Therefore, it transform as an [itex](8_L,1_R)[/itex] representation of [itex]SU(3)_L\times SU(3)_R[/itex]. In many books I've found that this implies that it can only carry a change in isospin [itex]\Delta I=1/2[/itex]. Can anyone explain why?
 
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  • #2
Gluonic penguin operators do not differentiate between a final state uu- and final state dd-,so they only contribute to final states of zero isospin.Those electroweak contribute for both.And that ΔI=1/2 selection rule has it's origin in nonperturbative hadronic physics,and I don't think there is any good explanation for it.It is rather an experimental data to fit the small value of I=2 to I=0.
 
  • #3
Thank you very much for the answer! Could you explain a little bit further why they don't differential between the two final states and why this means that they only contribute to I=0 final states? Thank you very much
 
  • #4
The gluonic penguin operators contain factor like ∑(q-q)V+/-A,Which contribute equally to uu- and dd-,while the electroweak part brings in factors like ∑eq(q-q)V+/-A.Eletroweak penguins with different final states acquire different factors like eq=2/3 for q=u and eq=-1/3 for q=d.You can show now that gluonic ones only contributes to I=0 case.
 
  • #5
I'm sorry to bother you but that's exactly what I can't show.

Edit: I found the following properties on Donoghue's book. Could you tell me if I'm doing correctly? The action of the isospin rising and lowering operators on the quark fields are:
$$
I_+d=u,\;\; I_+\bar u=-\bar d,\;\;I_-u=d,\;\;I_-\bar d=-\bar u,
$$
all the others are zero. Therefore, we have, in the case of QCD penguins:
$$
I_+(\bar u u+\bar d d)=(I_+\bar u)u+\bar u(I_+u)+(I_+\bar d)d+\bar d(I_+d)=\bar d u-\bar d u=0
$$
and
$$
I_-(\bar u u+\bar d d)=(I_-\bar u)u+\bar u(I_-u)+(I_-\bar d)d+\bar d(I_-d)=-\bar u d+\bar u d=0.
$$

Therefore, since both the lowering and rising operators give zero it must be an I=0 operator. Is that correct?
 
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  • #6
You can use ladder operators,but see simply that quark and antiquark pair can have isospin of 0 or 1,and the 1 case is already ruled out as per symmetry requirement.The state symmetric in interchange of u and d is indeed isospin zero state.
 
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  • #7
Got it! Thanks
 

1. What are Penguin diagrams?

Penguin diagrams are a type of Feynman diagram used in particle physics to represent the interactions between particles. They are named after their shape, which resembles a penguin with flippers. These diagrams are particularly useful for studying the effects of the weak nuclear force.

2. How do Penguin diagrams relate to CP violation?

CP violation is a phenomenon in particle physics where the laws of physics are not symmetrical under the combination of charge (C) and parity (P) transformations. Penguin diagrams are often used to study CP violation because they involve particles with different CP properties, allowing for a deeper understanding of this asymmetry.

3. What is CP violation and why is it important?

CP violation is a violation of the CP symmetry in particle physics. This symmetry states that the laws of physics should be the same under the combination of charge (C) and parity (P) transformations. Its importance lies in the fact that it can help explain why there is more matter than antimatter in the universe, a fundamental question in physics.

4. How do scientists study CP violation using Penguin diagrams?

Scientists study CP violation using Penguin diagrams by examining the interactions between particles with different CP properties. This allows them to observe how CP symmetry is broken and gain a better understanding of this phenomenon. They can also use these diagrams to make predictions and test them through experiments.

5. What are some applications of Penguin diagrams and CP violation?

Penguin diagrams and CP violation have many applications in particle physics, including helping scientists understand the origin of matter in the universe and testing the Standard Model of particle physics. They are also used in the search for new physics beyond the Standard Model, such as the existence of new particles or interactions. Additionally, studying CP violation can have practical applications in areas such as quantum computing and cryptography.

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