Soft and ultrasoft gluons in QCD

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In summary, the terms "soft gluons" and "ultrasoft gluons" are frequently used in factorization in QCD, with their definitions based on power counting. Soft gluons have an offshellness of \lambda^2 while ultrasoft gluons have an offshellness of \lambda^4. Their distinction is important in exclusive or semi-inclusive processes, as seen in the work of Bauer, Pirjol, and Stewart.
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petergreat
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I'm reading about factorization in QCD. The terms "soft gluons" and "ultrasoft gluons" are frequently referred to. I know how they are defined in terms of power counting, but don't understand their physical significance. In which QCD processes are soft gluons important, and in which are ultrasoft gluons significant?
 
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It depends a great deal on what it is you are looking at, and to some extent it is just semantics. But as a rule, if [itex]\lambda[/itex] is your (IR) power counting parameter, then in terms of light cone momenta (and setting the hard scale to 1):

[tex](p^+,p^-,p_\perp)\sim (\lambda,\lambda,\lambda)\Rightarrow{\rm soft}[/tex]
[tex](p^+,p^-,p_\perp)\sim (\lambda^2,\lambda^2,\lambda^2)\Rightarrow{\rm ultrasoft}[/tex]

So that the "offshellness" of a soft mode is [itex]\lambda^2[/itex] while the usoft mode is [itex]\lambda^4[/itex].

When dealing with fully inclusive processes this distinction is irrelevant. The trouble comes in when you have exclusive or semi-inclusive processes. Then you have to distinguish soft from usoft.

See, for instance, Bauer, Pirjol, Stewart, hep-ph/0109045
 

1. What are soft and ultrasoft gluons in QCD?

Soft and ultrasoft gluons are particles that carry the strong nuclear force in quantum chromodynamics (QCD). They are the exchange particles responsible for binding quarks together to form protons, neutrons, and other particles. Soft gluons have low energies and are responsible for long-range interactions, while ultrasoft gluons have even lower energies and are responsible for short-range interactions.

2. How are soft and ultrasoft gluons different from each other?

The main difference between soft and ultrasoft gluons is their energy levels. Soft gluons typically have energies on the order of a few hundred MeV, while ultrasoft gluons have energies on the order of a few MeV. This difference in energy levels leads to different behaviors and effects in QCD processes.

3. What role do soft and ultrasoft gluons play in QCD interactions?

Soft and ultrasoft gluons play a crucial role in QCD interactions by mediating the strong nuclear force between quarks. This force is responsible for binding quarks together to form hadrons, such as protons and neutrons. Soft gluons are responsible for long-range interactions, while ultrasoft gluons contribute to short-range interactions.

4. How do scientists study soft and ultrasoft gluons in QCD?

Scientists study soft and ultrasoft gluons in QCD through a variety of experimental and theoretical methods. Experimental techniques, such as particle colliders, allow scientists to observe and measure the properties of these particles. Theoretical calculations, using techniques such as perturbation theory and lattice QCD, help to understand the behavior of soft and ultrasoft gluons in different QCD processes.

5. What are the implications of studying soft and ultrasoft gluons in QCD?

Studying soft and ultrasoft gluons in QCD has important implications for our understanding of the strong nuclear force and the structure of matter. By studying these particles, scientists can gain insight into the behavior of quarks and the dynamics of QCD processes. This knowledge can also have practical applications, such as in the development of new technologies and materials.

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