View source for Gravitino

{{short description|Hypothetical superpartner to the graviton}}
{{infobox Particle
| bgcolour =
| name = Gravitino
| image =
| caption =
| num_types =
| composition = [[elementary particle]]
| statistics = [[fermion]]ic
| group = [[fermion]]
| generation =
| interaction = [[gravitation]]
| particle =
| antiparticle = self
| status = hypothetical
| theorized = 
| discovered = 
| symbol = {{subatomic particle|gravitino}}
| mass = 
| mean_lifetime = 
| decay_particle =
| electric_charge = 0&nbsp;[[elementary charge|''e'']]
| color_charge =
| spin = {{sfrac|3|2}}&nbsp;[[reduced Planck constant|''ħ'']]
}}
In [[supergravity]] theories combining [[general relativity]] and [[supersymmetry]], the '''gravitino''' ({{subatomic particle|gravitino}}) is the gauge fermion [[supersymmetry|supersymmetric]] partner of the hypothesized [[graviton]].  It has been suggested as a candidate for [[dark matter]].

If it exists, it is a [[fermion]] of [[Spin (physics)|spin]] {{sfrac|3|2}}&nbsp;''ħ'' and therefore obeys the [[Rarita–Schwinger equation]]. The gravitino field is conventionally written as ''ψ<sub>μα</sub>'' with {{nowrap|1=''μ'' = 0, 1, 2, 3}} a [[four-vector]] index and {{nowrap|1=''α'' = 1, 2}} a [[spinor]] index.
For {{nowrap|1=''μ'' = 0}} one would get negative norm modes, as with every massless particle of [[Spin (physics)|spin]] 1&nbsp;''ħ'' or higher. These modes are unphysical, and for [[unitarity (physics)|consistency]] there must be a [[gauge symmetry]] which cancels these modes: {{nowrap|1=''δψ<sub>μα</sub>'' = ∂''<sub>μ</sub>ε<sub>α</sub>''}}, where ''ε<sub>α</sub>''(''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 [[Supersymmetry breaking|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&nbsp;[[TeV]]/''c''<sup>2</sup>.

== History ==

[[Murray Gell-Mann]] and [[Peter van Nieuwenhuizen]] intended the spin-3/2 particle associated with supergravity to be called the 'hemitrion', meaning 'half-3', however the editors of ''[[Physical Review]]'' were not keen on the name and instead suggested 'massless Rarita–Schwinger particle' for their 1977 publication.<ref>{{cite speech |last=van Nieuwenhuizen |first=P. |author-link=Peter van Nieuwenhuizen |title=Some personal recollections about the discovery of supergravity |event=Dirac medal lecture |date=1993 |location= |language=English |publisher=International Atomic Energy Agency (IAEA) |url=https://ncatlab.org/nlab/files/vanNieuwenhuizen1993.pdf }}</ref><ref>{{cite journal |last1=Grisaru |first1=M.T. |last2=Pendleton |first2=H.N. |last3=van Nieuwenhuizen |first3=P. |date=1977 |title=Supergravity and the S Matrix |url= |journal=Phys. Rev. D |volume=15 |issue=4 |pages=996–1006 |doi=10.1103/PhysRevD.15.996 |pmid=|arxiv= |bibcode=1977PhRvD..15..996G  |s2cid= }}</ref> The current name of gravitino was instead suggested by [[Sidney Coleman]] and [[Heinz Pagels]],<ref>{{cite journal |last1=de Wit |first1=B. |author-link1=Bernard de Wit |last2=Freedman |first2=D.Z. |author-link2=Daniel Z. Freedman |date=1977 |title=On SO(8) Extended Supergravity |url= |journal=Nucl. Phys. B |volume=130 |issue=1 |page=106 |doi=10.1016/0550-3213(77)90395-9 |pmid= |arxiv= |bibcode=1977NuPhB.130..105D |s2cid= }}</ref> although this term was originally coined in 1954 by [[Felix Pirani]] to describe a class of negative energy excitations with zero rest mass.<ref>{{cite journal |last1=Pirani |first1=F.A.E. |author-link1=Felix Pirani |date=1955 |title=On the energy-momentum tensor and the creation of matter in relativistic cosmology |journal=Proc. R. Soc. Lond. |volume=228 |issue=1175 |pages=455–462 |doi=10.1098/rspa.1955.0061 |pmid= |arxiv= |bibcode=1955RSPSA.228..455P |s2cid=122814633 }}</ref>

== Gravitino cosmological problem ==
If the gravitino indeed has a mass of the order of 1&nbsp;TeV/''c''{{sup|2}}, then it creates a problem in the [[Lambda-CDM model|standard model of cosmology]], at least naïvely.<ref>{{cite journal | last1=Moroi | first1=T. | last2=Murayama | first2=H. | last3=Yamaguchi | first3=Masahiro | title=Cosmological constraints on the light stable gravitino | journal=Physics Letters B | volume=303 | issue=3–4 | year=1993 | issn=0370-2693 | doi=10.1016/0370-2693(93)91434-o | pages=289–294| bibcode=1993PhLB..303..289M }}</ref><ref>{{cite journal | last1=Okada | first1=Nobuchika | last2=Seto | first2=Osamu | title=Brane world cosmological solution to the gravitino problem | journal=Physical Review D | volume=71 | issue=2 | date=2005-01-19 | issn=1550-7998 | doi=10.1103/physrevd.71.023517 | article-number=023517|arxiv=hep-ph/0407235| bibcode=2005PhRvD..71b3517O | s2cid=119391278 }}</ref><ref>{{cite journal | last1=de Gouvêa | first1=André | last2=Moroi | first2=Takeo | last3=Murayama | first3=Hitoshi | title=Cosmology of supersymmetric models with low-energy gauge mediation | journal=Physical Review D | volume=56 | issue=2 | date=1997-07-15 | issn=0556-2821 | doi=10.1103/physrevd.56.1281 | pages=1281–1299|arxiv=hep-ph/9701244| bibcode=1997PhRvD..56.1281D | s2cid=15935292 }}</ref><ref>M. Endo [http://susy06.physics.uci.edu/talks/5/endo.pdf Moduli Stabilization and Moduli-Induced Gravitino Problem] {{webarchive |url=https://web.archive.org/web/20110724084240/http://susy06.physics.uci.edu/talks/5/endo.pdf |date=2011-07-24 }} talk given at SUSY'06, 12 June 2006</ref>

One option is that the gravitino is stable. This would be the case if the gravitino is the [[Lightest Supersymmetric Particle|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 [[Mean lifetime|lifetime]] would be very long, of the order of {{nowrap|{{SubSup|''M''|pl|2}}/''m''{{sup|3}}}}, where ''M''<sub>pl</sub> is the [[Planck mass]] and ''m'' is the mass of a gravitino. For a gravitino mass of the order of 1&nbsp;TeV/''c''{{sup|2}} this would be {{val|e=5|u=s}}, much later than the [[Big Bang nucleosynthesis|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 [[Atomic nucleus|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 [[Big Bang nucleosynthesis|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 [[supersymmetry|supersymmetric]] particle. This causes almost all [[supersymmetry|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.<ref>{{cite journal | last1=Takayama | first1=Fumihiro | last2=Yamaguchi | first2=Masahiro | title=Gravitino dark matter without R-parity | journal=Physics Letters B | volume=485 | issue=4 | year=2000 | issn=0370-2693 | doi=10.1016/s0370-2693(00)00726-7 | pages=388–392|arxiv=hep-ph/0005214| bibcode=2000PhLB..485..388T | s2cid=17469058 }}</ref>

== See also ==
{{div col|colwidth=30em}}
* [[Dual graviton]]
* [[Graviton]]
* [[Gravity]]
* [[Supersymmetry]]
{{div col end}}

== References ==
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[[Category:Fermions]]
[[Category:Quantum gravity]]
[[Category:Supersymmetry]]
[[Category:Hypothetical elementary particles]]