View source for Physics:Delta baryon

{{Infobox Particle
| name = Delta baryon
| num_types = 4
| composition = {{plainlist|
*{{SubatomicParticle|Delta++}}: {{SubatomicParticle|Up quark}}{{SubatomicParticle|Up quark}}{{SubatomicParticle|Up quark}}
*{{SubatomicParticle|Delta+}}: {{SubatomicParticle|Up quark}}{{SubatomicParticle|Up quark}}{{SubatomicParticle|Down quark}}
*{{SubatomicParticle|Delta0}}: {{SubatomicParticle|Up quark}}{{SubatomicParticle|Down quark}}{{SubatomicParticle|Down quark}}
*{{SubatomicParticle|Delta-}}: {{SubatomicParticle|Down quark}}{{SubatomicParticle|Down quark}}{{SubatomicParticle|Down quark}}}}
| statistics = [[Physics:Fermion|Fermion]]ic
<!-- template objects / docs say "group=" is okay ---
| group = [[Physics:Baryon|Baryon]]s
 -->
| interaction = [[Physics:Strong interaction|Strong]], [[Physics:Weak interaction|weak]], [[Physics:Electromagnetic interaction|electromagnetic]], and [[Physics:Gravity|gravity]]
| antiparticle = 
| status = 
| theorized = 
| discovered = 
| symbol = {{math|&Delta;}}
| mass = {{val|1232|2|ul=MeV/c2|fmt=gaps}}
| mean_lifetime = 
| width = 
| decay_particle = 
| electric_charge = 
| charge_radius = 
| electric_dipole_moment = 
| electric_polarizability = 
| magnetic_moment = 
| magnetic_polarizability = 
| color_charge = 
| spin = {{sfrac| 3 |2}}, {{sfrac| 5 |2}}, {{sfrac| 7 |2}} ...
| num_spin_states = 
| baryon_number = 
| strangeness = 0
| charm = 0
| bottomness = 0
| topness = 0
| isospin = {{sfrac| 3 |2}}
| weak_isospin = 
| weak_isospin_3 = 
| hypercharge = 
| weak_hypercharge = 
| chirality = 
| B-L =
| X_charge =
| parity = 
| g_parity = 
| c_parity = 
| r_parity = 
| condensed_symmetries =
}}

The '''Delta baryons''' (or '''{{math|Δ}} baryons''', also called '''Delta resonances''') are a family of [[Physics:Subatomic particle|subatomic particle]] made of three [[Physics:Up quark|up]] or [[Physics:Down quark|down]] [[Physics:Quark|quark]]s (u or d quarks), the same constituent quarks that make up the more familiar protons and neutrons.

== Properties ==
Four closely related {{math|Δ}} [[Physics:Baryon|baryon]]s exist: {{SubatomicParticle|Delta++}}&nbsp;(constituent quarks: uuu), {{Subatomic Particle|Delta+}}&nbsp;(uud), {{SubatomicParticle|Delta0}}&nbsp;(udd), and {{SubatomicParticle|Delta-}}&nbsp;(ddd), which respectively carry an electric charge of {{val|+2|ul=e}}, {{val|+1|u=e}}, {{val|0|u=e}}, and {{val|-1|u=e}}.

The {{math|Δ}}&nbsp;baryons have a mass of about {{val|1232|u=MeV/c2|fmt=gaps}}; their third component of [[Physics:Isospin|isospin]] <math>\; I_3 = \pm\tfrac{1}{2} ~\mathsf{ or }~ \pm\tfrac{3}{2}\;;</math> and they are required to have an intrinsic [[Physics:Spin|spin]] of {{sfrac| 3 |2}} or higher (half-integer units). Ordinary [[Physics:Nucleon|nucleon]]s (symbol N, meaning either a [[Physics:Proton|proton]] or [[Physics:Neutron|neutron]]), by contrast, have a mass of about {{val|939|u=MeV/c2}}, and both intrinsic [[Physics:Spin|spin]] and [[Physics:Isospin|isospin]] of {{sfrac|1| 2 }}. The {{math|{{SubatomicParticle|Delta+}}}}&nbsp;(uud) and {{math|{{SubatomicParticle|Delta0}}}}&nbsp;(udd) particles are higher-mass spin-excitations of the [[Physics:Proton|proton]] ({{SubatomicParticle|Nucleon+}},&nbsp;uud) and [[Physics:Neutron|neutron]] ({{SubatomicParticle|Nucleon0}},&nbsp;udd), respectively.

The {{math|{{SubatomicParticle|Delta++}}}} and {{math|{{SubatomicParticle|Delta-}}}}, however, have no direct nucleon analogues: For example, even though their charges are identical and their masses are similar, the {{math|{{SubatomicParticle|Delta-}}}}&nbsp;(ddd), is not closely related to the [[Physics:Antiproton|antiproton]] ({{SubatomicParticle|antiproton}},&nbsp;{{overline|uud}}).

The Delta states discussed here are only the lowest-mass quantum excitations of the proton and neutron. At higher [[Physics:Spin|spins]], additional higher mass Delta states appear, all defined by having constant {{sfrac| 3 |2}} or {{sfrac| 1 |2}} isospin (depending on charge), but with [[Physics:Spin|spin]] {{sfrac| 3 |2}}, {{sfrac| 5 |2}}, {{sfrac| 7 |2}}, ..., {{sfrac| 11 |2}} multiplied by [[Physics:Reduced Planck constant|{{mvar|ħ}}]]. A complete listing of all properties of all these states can be found in Beringer ''et al''. (2013).<ref name=PDGDelta/>

There also exist [[Physics:Antiparticle|antiparticle]] Delta states with opposite charges, made up of the corresponding antiquarks.

== Discovery ==

The states were established experimentally at the [[Organization:University of Chicago|University of Chicago]] [[Physics:Cyclotron|cyclotron]]<ref>
{{cite journal
 |last1=Anderson |first1=H. L.          |last2=Fermi |first2=E.
 |last3=Long     |first3=E. A.          |last4=Nagle |first4=D. E.
 |date=1 March 1952
 |title=Total cross-sections of positive pions in hydrogen
 |journal=Physical Review
 |volume=85 |issue=5 |pages=936
 |doi=10.1103/PhysRev.85.936
 |bibcode=1952PhRv...85..936A
}}
</ref><ref>
{{cite journal
 |last1=Hahn    |first1=T. M.        |last2=Snyder  |first2=C. W.
 |last3=Willard |first3=H. B.        |last4=Bair    |first4=J. K.
 |last5=Klema   |first5=E. D.        |last6=Kington |first6=J. D.
 |last7=Green   |first7=F. P.
 |date=1 March 1952
 |title=Neutrons and gamma-rays from the proton bombardment of beryllium 
 |journal=Physical Review
 |volume=85 |issue=5 |pages=934
 |doi=10.1103/PhysRev.85.934
 |bibcode=1952PhRv...85..934H
}}
</ref>
and the Carnegie Institute of Technology synchro-cyclotron<ref>
{{cite journal
 |last1=Ashkin |first1=J.      |last2=Blaser |first2=J. P.
 |last3=Feiner |first3=F.      |last4=Stern  |first4=M. O.
 |date=1 February 1956
 |title=Pion-proton scattering at 150 and 170&nbsp;Mev
 |journal=Physical Review
 |volume=101 |issue=3 |pages=1149–1158
 |doi=10.1103/PhysRev.101.1149
 |bibcode=1956PhRv..101.1149A
 |hdl=2027/mdp.39015095214600 |hdl-access=free
 |url=https://cds.cern.ch/record/1241674
}}
</ref>
in the mid-1950s using accelerated positive pions on hydrogen targets. The existence of the {{math|{{SubatomicParticle|Delta++}}}}, with its unusual [[Physics:Electric charge|electric charge]] of {{val|+2|u=e}}, was a crucial clue in the development of the [[Physics:Quark|quark model]].

== Formation and decay ==
The Delta states are created when a sufficiently energetic probe – such as a [[Physics:Photon|photon]], [[Physics:Electron|electron]], [[Physics:Neutrino|neutrino]], or [[Physics:Pion|pion]] – impinges upon a proton or neutron, or possibly by the collision of a sufficiently energetic nucleon pair.

All of the Δ&nbsp;baryons with mass near {{val|1232|u=MeV|fmt=gaps}} quickly decay via the [[Physics:Strong interaction|strong interaction]] into a [[Physics:Nucleon|nucleon]] ([[Physics:Proton|proton]] or [[Physics:Neutron|neutron]]) and a [[Physics:Pion|pion]] of appropriate charge. The relative probabilities of allowed final charge states are given by their respective [[Physics:Clebsch–Gordan coefficients|isospin couplings]]. More rarely and more slowly, the {{SubatomicParticle|Delta+}} can decay into a [[Physics:Proton|proton]] and a [[Physics:Photon|photon]] and the {{SubatomicParticle|Delta0}} can decay into a [[Physics:Neutron|neutron]] and a [[Physics:Photon|photon]].

== List ==

{| class="wikitable sortable" style="text-align: center;"
|+Delta baryons
|-
!class=unsortable| Particle<br/>name
! Symbol
!class=unsortable| Quark<br/>content
! [[Physics:Mass|Mass]]<br>(MeV/[[Physics:Speed of light|{{mvar|c}}]]<sup>2</sup>)
! [[Physics:Isospin|{{mvar|I}}{{sub|3}}]]
! [[Physics:Total angular momentum|{{mvar|J}}]]<sup>[[Physics:Parity|{{mvar|P}}]]</sup>
! [[Physics:Charge|{{mvar|Q}}]] <br/>([[Physics:Elementary charge|{{mvar|e}}]])
! [[Physics:Strangeness|{{mvar|S}}]]
! [[Physics:Charm (quantum number)|{{mvar|C}}]]
! [[Physics:Bottomness|{{mvar|B′}}]]
! [[Physics:Topness|{{mvar|T}}]]
! Mean lifetime<br/>([[Second|s]])
! class=unsortable | Commonly<br/>decays to
|- style="height:40px"
|align="left"| Delta<ref name=PDGDelta>
{{cite report
 |author1=Beringer, J.
 |display-authors=0
 |collaboration=[[Physics:Particle Data Group|Particle Data Group]]
 |year=2013
 |title={{SubatomicParticle|Delta}}(1 232)
 |series=Particle listings
 |url=http://pdg.lbl.gov/2013/listings/rpp2013-list-Delta-1232.pdf
}}
</ref>
| {{math|{{SubatomicParticle|Delta++}}}}(1 232)
| {{SubatomicParticle|link=yes|Up quark}}{{SubatomicParticle|link=yes|Up quark}}{{SubatomicParticle|link=yes|Up quark}}
| {{val|1232|2|fmt=gaps}}
| +{{sfrac| 3 |2}}
| {{sfrac| 3 |2}}{{sup|+}}
| +2
| 0
| 0
| 0
| 0
| {{val|5.63|0.14|e=-24}}<sup>{{ref|Lifetime|[a]}}</sup>
| align="left" | {{nobr| {{SubatomicParticle|link=yes|Proton+}} + {{SubatomicParticle|link=yes|Pion+}} }}
|- style="height:40px"
|align="left"| Delta<ref name=PDGDelta/>
| {{math|{{SubatomicParticle|Delta+}}}}(1 232)
| {{SubatomicParticle|link=yes|Up quark}}{{SubatomicParticle|link=yes|Up quark}}{{SubatomicParticle|link=yes|Down quark}}
| {{val|1232|2|fmt=gaps}}
| +{{sfrac|1| 2 }}
| {{sfrac| 3 |2}}{{sup|+}}
| +1
| 0
| 0
| 0
| 0
| {{val|5.63|0.14|e=-24}}<sup>{{ref|Lifetime|[a]}}</sup>
|align="left"| {{nobr| {{SubatomicParticle|link=yes|Pion+}} + {{SubatomicParticle|link=yes|Neutron0}}, or}} <br/>{{nobr|{{SubatomicParticle|link=yes|Pion0}} + {{SubatomicParticle|link=yes|Proton+}} }}
|- style="height:40px"
|align="left"| Delta<ref name=PDGDelta/>
| {{math|{{SubatomicParticle|Delta0}}}}(1 232)
| {{SubatomicParticle|link=yes|Up quark}}{{SubatomicParticle|link=yes|Down quark}}{{SubatomicParticle|link=yes|Down quark}}
| {{val|1232|2|fmt=gaps}}
| {{sfrac|−|1| 2 }}
| {{sfrac| 3 |2}}{{sup|+}}
| 0
| 0
| 0
| 0
| 0
| {{val|5.63|0.14|e=-24}}<sup>{{ref|Lifetime|[a]}}</sup>
|align="left"| {{nobr| {{SubatomicParticle|link=yes|Pion0}} + {{SubatomicParticle|link=yes|Neutron0}}, or}} <br/> {{nowrap|{{SubatomicParticle|link=yes|Pion-}} + {{SubatomicParticle|link=yes|Proton+}} }}
|- style="height:40px"
|align="left"| Delta<ref name=PDGDelta/>
| {{math|{{SubatomicParticle|Delta-}}}}(1 232)
| {{SubatomicParticle|link=yes|Down quark}}{{SubatomicParticle|link=yes|Down quark}}{{SubatomicParticle|link=yes|Down quark}}
| {{val|1232|2|fmt=gaps}}
| {{sfrac|−| 3 |2}}
| {{sfrac| 3 |2}}{{sup|+}}
| −1
| 0
| 0
| 0
| 0
| {{val|5.63|0.14|e=-24}}<sup>{{ref|Lifetime|[a]}}</sup>
|align="left"| {{nobr| {{SubatomicParticle|link=yes|Pion-}} + {{SubatomicParticle|link=yes|Neutron0}} }}
|}
<sup>[a]</sup> {{note|Lifetime2}} PDG reports the [[Physics:Resonance width|resonance width]] (Γ). Here the conversion <math display="inline">\tau = \frac{\hbar}{\Gamma}</math> is given instead.

== References ==
{{reflist|25em}}

=== Bibliography ===

* {{cite journal
 |author1=Amsler, C.
 |display-authors=0
 |collaboration=[[Physics:Particle Data Group|Particle Data Group]]
 |year=2008
 |title=Review of Particle Physics
 |journal=[[Physics:Physics Letters B|Physics Letters B]]
 |volume=667
 |issue=1
 |pages=1–6
 |doi=10.1016/j.physletb.2008.07.018
 |bibcode=2008PhLB..667....1A
 |hdl=1854/LU-685594
 |s2cid=227119789
 |hdl-access=free
 |url=https://www.zora.uzh.ch/id/eprint/11249/2/scalarsV.pdf
 |access-date=2019-12-11
 |archive-date=2020-09-07
 |archive-url=https://web.archive.org/web/20200907211544/https://www.zora.uzh.ch/id/eprint/11249/2/scalarsV.pdf
 |url-status=dead
 }}

{{Particles}}

{{DEFAULTSORT:Delta Baryon}}
[[Category:Baryons]]

{{Sourceattribution|Delta baryon}}