Soft-collinear effective theory
Encyclopedia
In quantum field theory
, soft-collinear effective theory
(or SCET) is a theoretical framework for doing calculations in quantum chromodynamics
(QCD) that involve interacting particles carrying widely different energies.
The motivation for developing SCET was to control the infrared divergence
s that occur in QCD calculations that involve particles that are soft -- carrying much lower energy or momentum than other particles in the process -- or collinear -- traveling in the same direction as another particle in the process. SCET is an effective theory for highly energetic quark
s interacting with collinear and/or soft gluon
s. It has been used for calculations of the decays of B meson
s (quark-antiquark bound states involving a bottom quark
) and the properties of jets
(sprays of hadrons that emerge from particle collisions when a quark or gluon is produced).
The new feature of SCET is its ability to handle more than one soft energy scale. For example, processes involving quarks carrying a high energy Q interacting with gluons have two soft scales: the transverse momentum pT of the collinear particles, plus the even softer scale pT2/Q. SCET provides a power-counting formalism for doing perturbation theory
in the small parameter ΛQCD/Q in a sensible way.
Quantum field theory
Quantum field theory provides a theoretical framework for constructing quantum mechanical models of systems classically parametrized by an infinite number of dynamical degrees of freedom, that is, fields and many-body systems. It is the natural and quantitative language of particle physics and...
, soft-collinear effective theory
Effective theory
-Effective Theory:An Effective Theory is a theory based on reasonable assumption, if not actual evidence, for the purpose of moving on in an area of study. An effective theory provides a framework to explain certain effects, without the claim that the theory correctly models the underlying ...
(or SCET) is a theoretical framework for doing calculations in quantum chromodynamics
Quantum chromodynamics
In theoretical physics, quantum chromodynamics is a theory of the strong interaction , a fundamental force describing the interactions of the quarks and gluons making up hadrons . It is the study of the SU Yang–Mills theory of color-charged fermions...
(QCD) that involve interacting particles carrying widely different energies.
The motivation for developing SCET was to control the infrared divergence
Infrared divergence
In physics, an infrared divergence or infrared catastrophe is a situation in which an integral, for example a Feynman diagram, diverges because of contributions of objects with very small energy approaching zero, or, equivalently, because of physical phenomena at very long distances.The infrared ...
s that occur in QCD calculations that involve particles that are soft -- carrying much lower energy or momentum than other particles in the process -- or collinear -- traveling in the same direction as another particle in the process. SCET is an effective theory for highly energetic quark
Quark
A quark is an elementary particle and a fundamental constituent of matter. Quarks combine to form composite particles called hadrons, the most stable of which are protons and neutrons, the components of atomic nuclei. Due to a phenomenon known as color confinement, quarks are never directly...
s interacting with collinear and/or soft gluon
Gluon
Gluons are elementary particles which act as the exchange particles for the color force between quarks, analogous to the exchange of photons in the electromagnetic force between two charged particles....
s. It has been used for calculations of the decays of B meson
B meson
B mesons are mesons composed of a bottom quark or bottom antiquark and either an up , down , strange or charm quark . The combination of a bottom antiquark and a top quark is not thought to be possible because of the top quark's short lifetime...
s (quark-antiquark bound states involving a bottom quark
Bottom quark
The bottom quark, also known as the beauty quark, is a third-generation quark with a charge of − e. Although all quarks are described in a similar way by the quantum chromodynamics, the bottom quark's large bare mass , combined with low values of the CKM matrix elements Vub and Vcb, gives it a...
) and the properties of jets
Jet (particle physics)
A jet is a narrow cone of hadrons and other particles produced by the hadronization of a quark or gluon in a particle physics or heavy ion experiment. Because of QCD confinement, particles carrying a color charge, such as quarks, cannot exist in free form. Therefore they fragment into hadrons...
(sprays of hadrons that emerge from particle collisions when a quark or gluon is produced).
The new feature of SCET is its ability to handle more than one soft energy scale. For example, processes involving quarks carrying a high energy Q interacting with gluons have two soft scales: the transverse momentum pT of the collinear particles, plus the even softer scale pT2/Q. SCET provides a power-counting formalism for doing perturbation theory
Perturbation theory
Perturbation theory comprises mathematical methods that are used to find an approximate solution to a problem which cannot be solved exactly, by starting from the exact solution of a related problem...
in the small parameter ΛQCD/Q in a sensible way.
External links
Original papers:- C.W. Bauer, S. Fleming, M. Luke, "Summing Sudakov logarithms in
in effective field theory", Phys. Rev. D63, 014006 (2000), arXiv:hep-ph/0005275. - C.W. Bauer, S. Fleming, D. Pirjol, and I.W. Stewart, "An effective field theory for collinear and soft gluons: heavy to light decays", Phys. Rev. D63, 114020 (2001), arXiv:hep-ph/0011336.
- C.W. Bauer, I.W. Stewart, "Invariant Operators in Collinear Effective Theory", Phys. Lett. B516 (2001), 134-142, arXiv:hep-ph/0107001.
- C.W. Bauer, D. Pirjol, and I.W. Stewart, "Soft-collinear factorization in effective field theory", Phys. Rev. D65, 054022 (2002), arXiv:hep-ph/0109045.
- C.W. Bauer, D. Pirjol, and I.W. Stewart, "Power counting in the soft-collinear effective theory", Phys. Rev. D66, 054005 (2002), arXiv:hep-ph/0205289.