OPE leading twist = collinear factorisation

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In summary, the operator product expansion and collinear factorization are related, but the input parton densities used in collinear factorization are defined in terms of local operators while the operator product expansion uses non-local operators.
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CAF123
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The operator product expansion systematically expands QFT interactions in terms of a sum of local operators.

Is the leading twist of this expansion identifiable with collinear factorisation and, if so, how is this reconciled with the fact that the input Parton densities are quantum field theoretically defined in terms of non-local operators?
 
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The leading twist of the operator product expansion is indeed related to collinear factorization, as both describe how a high-energy scattering process can be decomposed into a product of two independent subprocesses. However, the input parton densities that are used in collinear factorization are defined in terms of local operators, rather than non-local operators. This is because the parton densities describe the probability of finding a parton with a particular momentum and flavor in the hadron, which can be expressed as a matrix element of a local operator between the hadron state and the vacuum.
 

Related to OPE leading twist = collinear factorisation

What is OPE leading twist?

OPE (operator product expansion) leading twist is a mathematical concept in quantum field theory that describes the behavior of operators at high energies. It refers to the dominant contribution of a particular operator in the OPE expansion, which becomes more important as the energy of the system increases.

What is collinear factorisation?

Collinear factorisation is a mathematical technique used to simplify the calculation of scattering amplitudes in quantum field theory. It involves separating the calculation into two parts: the collinear part, which describes the behavior of particles moving along the same direction, and the soft part, which describes the behavior of particles with low energy. This allows for a more efficient calculation of scattering amplitudes.

How is OPE leading twist related to collinear factorisation?

OPE leading twist and collinear factorisation are closely related concepts. In fact, collinear factorisation is a consequence of OPE leading twist. This means that the dominant contribution of a particular operator in the OPE expansion can be calculated using collinear factorisation.

Why is OPE leading twist = collinear factorisation important?

OPE leading twist = collinear factorisation is important because it allows for the calculation of scattering amplitudes in quantum field theory to be simplified and made more efficient. This is especially useful when dealing with high energy systems, where traditional methods may be too complex or time-consuming.

What are some applications of OPE leading twist = collinear factorisation?

OPE leading twist = collinear factorisation has many applications in theoretical physics, including in the study of high energy collisions, particle interactions, and the behavior of quantum field theories. It is also used in the development of new theoretical models and in the interpretation of experimental data.

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