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delta baryon

{{Short description|Family of subatomic particles}}

{{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 = Fermionic

| interaction = Strong, weak, electromagnetic, and gravity

| antiparticle =

| status =

| theorized =

| discovered =

| symbol = {{math|Δ}}

| 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 subatomic particle made of three up or down quarks (u or d quarks), the same constituent quarks that make up the more familiar protons and neutrons.

Properties

Four closely related {{math|Δ}} baryons exist: {{SubatomicParticle|Delta++}} (constituent quarks: uuu), {{Subatomic Particle|Delta+}} (uud), {{SubatomicParticle|Delta0}} (udd), and {{SubatomicParticle|Delta-}} (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}} baryons have a mass of about {{val|1232|u=MeV/c2|fmt=gaps}}; their third component of isospin \; I_3 = \pm\tfrac{1}{2} ~\mathsf{ or }~ \pm\tfrac{3}{2}\;; and they are required to have an intrinsic spin of {{sfrac| 3 |2}} or higher (half-integer units). Ordinary nucleons (symbol N, meaning either a proton or neutron), by contrast, have a mass of about {{val|939|u=MeV/c2}}, and both intrinsic spin and isospin of {{sfrac|1| 2 }}. The {{math|{{SubatomicParticle|Delta+}}}} (uud) and {{math|{{SubatomicParticle|Delta0}}}} (udd) particles are higher-mass spin-excitations of the proton ({{SubatomicParticle|Nucleon+}}, uud) and neutron ({{SubatomicParticle|Nucleon0}}, 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-}}}} (ddd), is not closely related to the antiproton ({{SubatomicParticle|antiproton}}, {{overline|uud}}).

The Delta states discussed here are only the lowest-mass quantum excitations of the proton and neutron. At higher 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 spin {{sfrac| 3 |2}}, {{sfrac| 5 |2}}, {{sfrac| 7 |2}}, ..., {{sfrac| 11 |2}} multiplied by reduced Planck constant. A complete listing of all properties of all these states can be found in Beringer et al. (2013).

There also exist antiparticle Delta states with opposite charges, made up of the corresponding antiquarks.

Discovery

The states were established experimentally at the University of Chicago cyclotron

{{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

}}

{{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

}}

and the Carnegie Institute of Technology synchro-cyclotron

{{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 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

}}

in the mid-1950s using accelerated positive pions on hydrogen targets. The existence of the {{math|{{SubatomicParticle|Delta++}}}}, with its unusual electric charge of {{val|+2|u=e}}, was a crucial clue in the development of the quark model.

Formation and decay

The Delta states are created when a sufficiently energetic probe – such as a photon, electron, neutrino, or pion – impinges upon a proton or neutron, or possibly by the collision of a sufficiently energetic nucleon pair.

All of the Δ baryons with mass near {{val|1232|u=MeV|fmt=gaps}} quickly decay via the strong interaction into a nucleon (proton or neutron) and a pion of appropriate charge. The relative probabilities of allowed final charge states are given by their respective isospin couplings. More rarely, the {{SubatomicParticle|Delta+}} can decay into a proton and a photon and the {{SubatomicParticle|Delta0}} can decay into a neutron and a photon.

List

class="wikitable sortable" style="text-align: center;"

|+Delta baryons

class=unsortable| Particle
name

! Symbol

!class=unsortable| Quark
content

! Mass
(MeV/speed of light2)

! Isospin

! Total angular momentumParity (physics)

! charge (physics)
(elementary charge)

! strangeness

! charm (quantum number)

! bottomness

! topness

! Mean lifetime
(s)

! class=unsortable | Commonly
decays to

style="height:40px"

|align="left"| Delta

{{cite report

|author1=Beringer, J.

|display-authors=etal

|collaboration=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

}}

| {{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}}{{ref|Lifetime|[a]}}

| align="left" | {{nobr| {{SubatomicParticle|link=yes|Proton+}} + {{SubatomicParticle|link=yes|Pion+}} }}

style="height:40px"

|align="left"| Delta

| {{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}}{{ref|Lifetime|[a]}}

|align="left"| {{nobr| {{SubatomicParticle|link=yes|Pion+}} + {{SubatomicParticle|link=yes|Neutron0}}, or}}
{{nobr|{{SubatomicParticle|link=yes|Pion0}} + {{SubatomicParticle|link=yes|Proton+}} }}

style="height:40px"

|align="left"| Delta

| {{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}}{{ref|Lifetime|[a]}}

|align="left"| {{nobr| {{SubatomicParticle|link=yes|Pion0}} + {{SubatomicParticle|link=yes|Neutron0}}, or}}
{{nowrap|{{SubatomicParticle|link=yes|Pion-}} + {{SubatomicParticle|link=yes|Proton+}} }}

style="height:40px"

|align="left"| Delta

| {{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}}{{ref|Lifetime|[a]}}

|align="left"| {{nobr| {{SubatomicParticle|link=yes|Pion-}} + {{SubatomicParticle|link=yes|Neutron0}} }}

[a] {{note|Lifetime2}} PDG reports the resonance width (Γ). Here the conversion \tau = \frac{\hbar}{\Gamma} is given instead.

References

{{reflist|25em}}

= Bibliography =

  • {{cite journal

|author1=Amsler, C.

|display-authors=etal

|collaboration=Particle Data Group

|year=2008

|title=Review of Particle Physics

|journal=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