Gravitino
Encyclopedia
The gravitino is the supersymmetric
partner of the graviton
, as predicted by theories combining general relativity
and supersymmetry
; i.e. supergravity
theories. If it exists, it is a fermion
of spin
and therefore obeys the Rarita-Schwinger equation
.
The gravitino field is conventionally written as ψμα with a four-vector
index and a spinor
index.
For one would get negative norm modes, as with every massless particle of spin
1 or higher. These modes are unphysical, and for consistency
there must be a gauge symmetry which cancels these modes: where εα(x) is a spinor
function of spacetime. This gauge symmetry is a local supersymmetry
transformation, and the resulting theory is supergravity
.
Thus the gravitino is the fermion mediating supergravity interactions, just as the photon
is mediating electromagnetism
, and the graviton
is presumably mediating gravitation
. Whenever supersymmetry is broken in supergravity theories, it acquires a mass which is determined by the scale at which supersymmetry is broken
. This varies greatly between different models of supersymmetry breaking, but if supersymmetry is to solve the hierarchy problem
of the Standard Model
, the gravitino cannot be more massive than about 1 TeV
/c
.
, at least naïvely.
One option is that the gravitino is stable. This would be the case if the gravitino is the lightest supersymmetric
particle and R-parity
is conserved (or nearly so). In this case the gravitino is a candidate for dark matter
; as such gravitinos will have been created in the very early universe. However, one may calculate the density of gravitinos and it turns out to be much higher than the observed dark matter
density.
The other option is that the gravitino is unstable. Thus the gravitinos mentioned above would decay and will not contribute to the observed dark matter
density. However, since they decay only through gravitational interactions, their lifetime would be very long, of the order of in natural units
, where Mpl is the Planck mass and m is the mass of a gravitino. For a gravitino mass of the order of TeV this would be , much later than the era of nucleosynthesis
. At least one possible channel of decay must include either a photon
, a charged lepton
or a meson
, each of which would be energetic enough to destroy a nucleus
if it strikes one. One can show that enough such energetic particles will be created in the decay as to destroy almost all the nuclei created in the era of nucleosynthesis
, in contrast with observations. In fact, in such a case the universe would have been made of hydrogen
alone, and star formation
would probably be impossible.
One possible solution to the cosmological gravitino problem is the split supersymmetry
model, where the gravitino mass is much higher than the TeV scale, but other fermionic supersymmetric partners of standard model particles already appear at this scale.
Another solution is that R-parity
is slightly violated and the gravitino is the lightest supersymmetric
particle. This causes almost all supersymmetric
particles in the early Universe to decay into Standard Model particles via R-parity
violating interactions well before the synthesis of primordial nuclei; a small fraction however decay into gravitinos, whose half-life is orders of magnitude greater than the age of the Universe due to the suppression of the decay rate by the Planck scale
and the small R-parity
violating couplings.
Supersymmetry
In particle physics, supersymmetry is a symmetry that relates elementary particles of one spin to other particles that differ by half a unit of spin and are known as superpartners...
partner of the graviton
Graviton
In physics, the graviton is a hypothetical elementary particle that mediates the force of gravitation in the framework of quantum field theory. If it exists, the graviton must be massless and must have a spin of 2...
, as predicted by theories combining general relativity
General relativity
General relativity or the general theory of relativity is the geometric theory of gravitation published by Albert Einstein in 1916. It is the current description of gravitation in modern physics...
and supersymmetry
Supersymmetry
In particle physics, supersymmetry is a symmetry that relates elementary particles of one spin to other particles that differ by half a unit of spin and are known as superpartners...
; i.e. supergravity
Supergravity
In theoretical physics, supergravity is a field theory that combines the principles of supersymmetry and general relativity. Together, these imply that, in supergravity, the supersymmetry is a local symmetry...
theories. If it exists, it is a fermion
Fermion
In particle physics, a fermion is any particle which obeys the Fermi–Dirac statistics . Fermions contrast with bosons which obey Bose–Einstein statistics....
of spin
Spin (physics)
In quantum mechanics and particle physics, spin is a fundamental characteristic property of elementary particles, composite particles , and atomic nuclei.It is worth noting that the intrinsic property of subatomic particles called spin and discussed in this article, is related in some small ways,...
and therefore obeys the Rarita-Schwinger equation
Rarita-Schwinger equation
In theoretical physics, the Rarita–Schwinger equation is therelativistic field equation of spin-3/2 fermions. It is similar to the Dirac equation for spin-1/2 fermions. This equation was first introduced by William Rarita and Julian Schwinger in 1941...
.
The gravitino field is conventionally written as ψμα with a four-vector
Four-vector
In the theory of relativity, a four-vector is a vector in a four-dimensional real vector space, called Minkowski space. It differs from a vector in that it can be transformed by Lorentz transformations. The usage of the four-vector name tacitly assumes that its components refer to a standard basis...
index and a spinor
Spinor
In mathematics and physics, in particular in the theory of the orthogonal groups , spinors are elements of a complex vector space introduced to expand the notion of spatial vector. Unlike tensors, the space of spinors cannot be built up in a unique and natural way from spatial vectors...
index.
For one would get negative norm modes, as with every massless particle of spin
Spin (physics)
In quantum mechanics and particle physics, spin is a fundamental characteristic property of elementary particles, composite particles , and atomic nuclei.It is worth noting that the intrinsic property of subatomic particles called spin and discussed in this article, is related in some small ways,...
1 or higher. These modes are unphysical, and for consistency
Unitarity (physics)
In quantum physics, unitarity is a restriction on the allowed evolution of quantum systems that insures the sum of probabilities of all possible outcomes of any event is always 1....
there must be a gauge symmetry which cancels these modes: where εα(x) is a spinor
Spinor
In mathematics and physics, in particular in the theory of the orthogonal groups , spinors are elements of a complex vector space introduced to expand the notion of spatial vector. Unlike tensors, the space of spinors cannot be built up in a unique and natural way from spatial vectors...
function of spacetime. This gauge symmetry is a local supersymmetry
Supersymmetry
In particle physics, supersymmetry is a symmetry that relates elementary particles of one spin to other particles that differ by half a unit of spin and are known as superpartners...
transformation, and the resulting theory is supergravity
Supergravity
In theoretical physics, supergravity is a field theory that combines the principles of supersymmetry and general relativity. Together, these imply that, in supergravity, the supersymmetry is a local symmetry...
.
Thus the gravitino is the fermion mediating supergravity interactions, just as the photon
Photon
In physics, a photon is an elementary particle, the quantum of the electromagnetic interaction and the basic unit of light and all other forms of electromagnetic radiation. It is also the force carrier for the electromagnetic force...
is mediating electromagnetism
Electromagnetism
Electromagnetism is one of the four fundamental interactions in nature. The other three are the strong interaction, the weak interaction and gravitation...
, and the graviton
Graviton
In physics, the graviton is a hypothetical elementary particle that mediates the force of gravitation in the framework of quantum field theory. If it exists, the graviton must be massless and must have a spin of 2...
is presumably mediating gravitation
Gravitation
Gravitation, or gravity, is a natural phenomenon by which physical bodies attract with a force proportional to their mass. Gravitation is most familiar as the agent that gives weight to objects with mass and causes them to fall to the ground when dropped...
. Whenever supersymmetry is broken in supergravity theories, it acquires a mass which is determined by the scale at which supersymmetry is broken
Supersymmetry breaking
In particle physics, supersymmetry breaking is the process to obtain a seemingly non-supersymmetric physics from a supersymmetric theory which is a necessary step to reconcile supersymmetry with actual experiments. It is an example of spontaneous symmetry breaking...
. This varies greatly between different models of supersymmetry breaking, but if supersymmetry is to solve the hierarchy problem
Hierarchy problem
In theoretical physics, a hierarchy problem occurs when the fundamental parameters of some Lagrangian are vastly different than the parameters measured by experiment. This can happen because measured parameters are related to the fundamental parameters by a prescription known as renormalization...
of the Standard Model
Standard Model
The Standard Model of particle physics is a theory concerning the electromagnetic, weak, and strong nuclear interactions, which mediate the dynamics of the known subatomic particles. Developed throughout the mid to late 20th century, the current formulation was finalized in the mid 1970s upon...
, the gravitino cannot be more massive than about 1 TeV
TEV
TEV may refer to:* TeV, or teraelectronvolt, a measure of energy* Total Enterprise Value, a financial measure* Total Economic Value, an economic measure* Tobacco etch virus, a plant pathogenic virus of the family Potyviridae....
/c
.Gravitino cosmological problem
If the gravitino indeed has a mass of the order of TeV, then it creates a problem in the standard model of cosmologyCosmology
Cosmology is the discipline that deals with the nature of the Universe as a whole. Cosmologists seek to understand the origin, evolution, structure, and ultimate fate of the Universe at large, as well as the natural laws that keep it in order...
, at least naïvely.
One option is that the gravitino is stable. This would be the case if the gravitino is the lightest supersymmetric
Supersymmetry
In particle physics, supersymmetry is a symmetry that relates elementary particles of one spin to other particles that differ by half a unit of spin and are known as superpartners...
particle and R-parity
R-parity
R-parity is a concept in particle physics. In the supersymmetric extension of the Standard Model, baryon number and lepton number are no longer conserved by all of the renormalizable couplings...
is conserved (or nearly so). In this case the gravitino is a candidate for dark matter
Dark matter
In astronomy and cosmology, dark matter is matter that neither emits nor scatters light or other electromagnetic radiation, and so cannot be directly detected via optical or radio astronomy...
; as such gravitinos will have been created in the very early universe. However, one may calculate the density of gravitinos and it turns out to be much higher than the observed dark matter
Dark matter
In astronomy and cosmology, dark matter is matter that neither emits nor scatters light or other electromagnetic radiation, and so cannot be directly detected via optical or radio astronomy...
density.
The other option is that the gravitino is unstable. Thus the gravitinos mentioned above would decay and will not contribute to the observed dark matter
Dark matter
In astronomy and cosmology, dark matter is matter that neither emits nor scatters light or other electromagnetic radiation, and so cannot be directly detected via optical or radio astronomy...
density. However, since they decay only through gravitational interactions, their lifetime would be very long, of the order of in natural units
Natural units
In physics, natural units are physical units of measurement based only on universal physical constants. For example the elementary charge e is a natural unit of electric charge, or the speed of light c is a natural unit of speed...
, where Mpl is the Planck mass and m is the mass of a gravitino. For a gravitino mass of the order of TeV this would be , much later than the era of nucleosynthesis
Big Bang nucleosynthesis
In physical cosmology, Big Bang nucleosynthesis refers to the production of nuclei other than those of H-1 during the early phases of the universe...
. At least one possible channel of decay must include either a photon
Photon
In physics, a photon is an elementary particle, the quantum of the electromagnetic interaction and the basic unit of light and all other forms of electromagnetic radiation. It is also the force carrier for the electromagnetic force...
, a charged lepton
Lepton
A lepton is an elementary particle and a fundamental constituent of matter. The best known of all leptons is the electron which governs nearly all of chemistry as it is found in atoms and is directly tied to all chemical properties. Two main classes of leptons exist: charged leptons , and neutral...
or a meson
Meson
In particle physics, mesons are subatomic particles composed of one quark and one antiquark, bound together by the strong interaction. Because mesons are composed of sub-particles, they have a physical size, with a radius roughly one femtometer: 10−15 m, which is about the size of a proton...
, each of which would be energetic enough to destroy a nucleus
Atomic nucleus
The nucleus is the very dense region consisting of protons and neutrons at the center of an atom. It was discovered in 1911, as a result of Ernest Rutherford's interpretation of the famous 1909 Rutherford experiment performed by Hans Geiger and Ernest Marsden, under the direction of Rutherford. The...
if it strikes one. One can show that enough such energetic particles will be created in the decay as to destroy almost all the nuclei created in the era of nucleosynthesis
Big Bang nucleosynthesis
In physical cosmology, Big Bang nucleosynthesis refers to the production of nuclei other than those of H-1 during the early phases of the universe...
, in contrast with observations. In fact, in such a case the universe would have been made of hydrogen
Hydrogen
Hydrogen is the chemical element with atomic number 1. It is represented by the symbol H. With an average atomic weight of , hydrogen is the lightest and most abundant chemical element, constituting roughly 75% of the Universe's chemical elemental mass. Stars in the main sequence are mainly...
alone, and star formation
Star formation
Star formation is the process by which dense parts of molecular clouds collapse into a ball of plasma to form a star. As a branch of astronomy star formation includes the study of the interstellar medium and giant molecular clouds as precursors to the star formation process and the study of young...
would probably be impossible.
One possible solution to the cosmological gravitino problem is the split supersymmetry
Split supersymmetry
In particle physics, split supersymmetry is a recent proposal for new physics beyond the Standard Model. It was proposed separately in three papers. The first by James Wells in June 2003 in a more modest form that mildly relaxed the assumption about naturalness in the Higgs potential...
model, where the gravitino mass is much higher than the TeV scale, but other fermionic supersymmetric partners of standard model particles already appear at this scale.
Another solution is that R-parity
R-parity
R-parity is a concept in particle physics. In the supersymmetric extension of the Standard Model, baryon number and lepton number are no longer conserved by all of the renormalizable couplings...
is slightly violated and the gravitino is the lightest supersymmetric
Supersymmetry
In particle physics, supersymmetry is a symmetry that relates elementary particles of one spin to other particles that differ by half a unit of spin and are known as superpartners...
particle. This causes almost all supersymmetric
Supersymmetry
In particle physics, supersymmetry is a symmetry that relates elementary particles of one spin to other particles that differ by half a unit of spin and are known as superpartners...
particles in the early Universe to decay into Standard Model particles via R-parity
R-parity
R-parity is a concept in particle physics. In the supersymmetric extension of the Standard Model, baryon number and lepton number are no longer conserved by all of the renormalizable couplings...
violating interactions well before the synthesis of primordial nuclei; a small fraction however decay into gravitinos, whose half-life is orders of magnitude greater than the age of the Universe due to the suppression of the decay rate by the Planck scale
Planck scale
In particle physics and physical cosmology, the Planck scale is an energy scale around 1.22 × 1019 GeV at which quantum effects of gravity become strong...
and the small R-parity
R-parity
R-parity is a concept in particle physics. In the supersymmetric extension of the Standard Model, baryon number and lepton number are no longer conserved by all of the renormalizable couplings...
violating couplings.