Advanced : HQET Derivative manipulation

In summary, the conversation is about simplifying currents in the context of HQET and constructing currents using D operators. The topic is complex and there is no easy way to simplify the expressions. A recommended resource is the Matthias Neubert's "Heavy-quark symmetry" review, which may provide complementary information to the book "HQET" by Manohar and Wise.
  • #1
Hepth
Gold Member
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This is a semi-advanced question for anyone with HQET experience.

When you expand out the Lagrangian, as well as the wave functions, you get things like the equation of motion that are expressed in terms of the covariant derivative and the heavy quark velocity :
[tex]
\def\lts#1{\kern+0.1em /\kern-0.65em #1}
i (v\cdot D) h_v = \left(\frac{1}{2 m_Q} \lts{D}^2_{\perp} - \frac{i}{4 m_Q^2} \lts{D}_{\perp} (v \cdot D) \lts{D}_{\perp} + ...\right)h_v
[/tex]

So when constructing currents you have some really long products of these D operators. Is there a standard strategy to simplification? Such as moving all (v.D)'s to the left or right. I can come up with the commutation relations so that I can write a simple mathematica script that can rearrange them however I see fit, also getting me the sigma.G term.

I'm just wondering if anyone out there has done anything where they could say "oh yeah, the fastest way is to just reqwrite it all in terms of etc etc then do etc.)

As it stands now depending on the order I expand to its quite a long expression.

(Also any direction to books or articles may be useful, though in articles it always seem they avoid including any code or tricks, and the only real books are like HQP Manohar/Wise.
 
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  • #2
In my opinion there no easy way to simplify currents. The HQET is a fairly complicated theory, but I can be wrong. Have you ever tried Neubert review? I don't know if it contains what you are looking for but it's a fairly good reference. Sometimes it can be complementary to Wise's book. The full title is: Matthias Neubert - Heavy-quark symmetry
 

FAQ: Advanced : HQET Derivative manipulation

1. What is HQET and how is it useful?

HQET (Heavy Quark Effective Theory) is a theoretical framework used in particle physics to study the behavior of heavy quarks within hadrons. It allows for the simplification and manipulation of equations, making calculations more manageable. HQET is useful in understanding the properties of heavy quarks and their interactions with other particles.

2. Can HQET be applied to all heavy quarks?

Yes, HQET can be applied to all types of heavy quarks, including the bottom, charm, and top quarks. However, it is most commonly used for bottom and charm quarks due to their relatively low masses.

3. What is the role of derivatives in HQET?

Derivatives play a crucial role in HQET as they allow for the calculation of physical quantities such as masses, decay rates, and cross sections. They also help to simplify equations and make them more manageable.

4. How does HQET differ from other theoretical frameworks?

HQET differs from other theoretical frameworks in that it specifically focuses on the behavior of heavy quarks within hadrons. It is a non-relativistic effective theory that allows for the separation of the heavy quark's mass from its momentum, simplifying calculations. Other frameworks, such as QCD, do not make this separation and are more complex.

5. Are there any limitations to using HQET?

Like any theoretical framework, there are limitations to using HQET. It is most effective for heavy quarks with low velocities, and its accuracy decreases for heavier masses. It also does not account for all interactions and must be combined with other theories, such as QCD, for a more complete understanding.

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