What does next to next leading order calculations mean?

In summary, next to next leading order calculations in the standard model refer to the two loop corrections to the lowest order diagram for a given process. This is achieved by considering all diagrams with two extra loops compared to the leading order diagram. However, this only applies in the context of infrared effects and the number of vertices or loops must be specified when discussing the "order" of a diagram.
  • #1
lavster
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me again... what are next to next leading order calculations in the standard model?
 
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  • #2
lavster said:
me again... what are next to next leading order calculations in the standard model?

That just means the two loops corrections to the lowest order diagram you can draw for a given process. So you consider a certain process and draw the diagram with the fewest number of loops possible; this is your leading order diagram (this leading order diagram could be a tree level diagram but it may also contain loops since some processes are only possible with loops). Then you consider all the diagrams containing two extra loops relative to the leading order diagram. These are the next to next leading order corrections.
 
  • #3
It depends if you count loop-order L or coupling-constant-order N. You can add vertices increasing N keeping L fixed.
 
  • #4
tom.stoer said:
It depends if you count loop-order L or coupling-constant-order N. You can add vertices increasing N keeping L fixed.

Good point. But this possibility arises only in the context of infrared effects, where we do not observe the low energy particles (for example photons). Otherwise, having a differenr number of coupling constant does not give the same diagram as the lowest order diagram (the asymptotic particle content is different).
 
  • #5
Yes, I agree.

All what I say is that talking about "the order" is ambiguous unless you specify whether it is the number of verices or the number of loops.
 
  • #6
It's right that if you count loop-order L or coupling-constant-order N.
 

Related to What does next to next leading order calculations mean?

1. What is meant by "next to next leading order calculations" in science?

Next to next leading order calculations, also known as NNL, refer to a method used in theoretical physics to improve the accuracy of predictions by taking into account the next order of corrections after the leading order. This method is particularly important in particle physics, where high precision is required to test theoretical models against experimental data.

2. How do NNL calculations improve upon leading order calculations?

NNL calculations take into account higher order corrections, which are often neglected in leading order calculations. These higher order corrections can significantly impact the accuracy of predictions, especially in complex systems. By including these corrections, NNL calculations provide a more precise and reliable result.

3. What are the limitations of NNL calculations?

One of the main limitations of NNL calculations is that they can become increasingly complex and time-consuming as more orders of corrections are included. This can make it challenging to perform calculations for systems with a large number of particles or interactions. Additionally, NNL calculations may not provide accurate results in extreme conditions, such as high energies or strong interactions.

4. How are NNL calculations used in practical applications?

NNL calculations are used in a wide range of scientific fields, including particle physics, cosmology, and condensed matter physics. They are essential in making precise predictions and testing theoretical models against experimental data. NNL calculations are also used to improve the accuracy of simulations and computer models.

5. What is the difference between NNL calculations and other methods, such as perturbation theory?

While both NNL calculations and perturbation theory involve calculating corrections to the leading order, they differ in their approach. Perturbation theory uses a series expansion to approximate the solution, while NNL calculations take into account specific higher order corrections. This makes NNL calculations more accurate and reliable, but also more complex and computationally demanding.

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