What is the non-local interaction in HQET?

In summary, the conversation discusses the Heavy Quark Effective Theory and a specific Lagrangian that is non-local due to the presence of the operator \frac{1}{iD\cdot v+2m_Q}. This operator implies an integration over all x or can be expanded in a power series to include derivatives of all orders.
  • #1
Einj
470
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Hi everyone. I have been studying the Heavy Quark Effective Theory and at a certain point we have a Lagrangian like:
$$
\mathcal{L}=\bar h_v iD\cdot v h_v+\bar h_vi\gamma_\mu D^\mu_\perp\frac{1}{iD\cdot v+2m_Q}i\gamma_\nu D_\perp^\nu h_v.
$$
[itex]h_v[/itex] is the field representing the heavy quark, [itex] v[/itex] is the velocity of the heavy quark and [itex]D_\mu[/itex] is the usual covariant derivative.

I read that this Lagrangian is non-local but I can't understand why. Do you have any idea?
 
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  • #2
Is it because you're choosing what the momentum "v" is? Therefor things are no longer technically lorentz invariant, as the theory only holds in the limit that v is "stationary". Basically you're choosing a specific POV to choose the problem.
 
  • #3
Einj said:
$$
\mathcal{L}=\bar h_v iD\cdot v h_v+\bar h_vi\gamma_\mu D^\mu_\perp\frac{1}{iD\cdot v+2m_Q}i\gamma_\nu D_\perp^\nu h_v.
$$

I read that this Lagrangian is non-local but I can't understand why. Do you have any idea?
It's because of the operator [itex]\frac{1}{iD\cdot v+2m_Q}[/itex], which implies an integration over all x. Or you can expand it in a power series and get derivatives of all orders.
 
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  • #4
Great, thanks!
 

1. What is non-local interaction in HQET?

Non-local interaction in HQET (Heavy Quark Effective Theory) refers to a theoretical framework used in particle physics to study the properties and behavior of heavy quarks. It takes into account the effects of the strong interaction between quarks in a non-local manner, meaning that the interactions can occur at a distance rather than at a single point.

2. How is non-local interaction different from local interaction?

In local interactions, the effects of the strong interaction between quarks are only considered at a single point in space and time. Non-local interactions, on the other hand, take into account the possibility of interactions occurring over a distance, allowing for a more accurate description of heavy quark behavior.

3. What are the advantages of using non-local interaction in HQET?

Non-local interaction in HQET allows for a more comprehensive understanding of the properties and behavior of heavy quarks, as it takes into account the effects of the strong interaction over a distance. This can lead to more accurate predictions and interpretations of experimental data.

4. What types of experiments are used to study non-local interaction in HQET?

Experiments that involve the study of heavy quarks, such as those conducted at particle accelerators like the Large Hadron Collider, can provide valuable data for studying non-local interaction in HQET. Other techniques, such as lattice QCD calculations, can also be used to investigate non-local interactions.

5. How does non-local interaction in HQET impact our understanding of the Standard Model of particle physics?

The use of non-local interaction in HQET has contributed to our understanding of the Standard Model by providing a more accurate description of the behavior of heavy quarks. This has allowed for more precise predictions and interpretations of experimental data, helping to further validate the Standard Model.

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