Lambda baryon

The lambda baryons (Λ) are a family of subatomic hadron particles containing one up quark, one down quark, and a third quark from a higher flavour generation, in a combination where the quantum wave function changes sign upon the flavour of any two quarks being swapped (thus slightly different from a neutral sigma baryon,
Σ⁰
). They are thus baryons, with total isospin of 0, and have either neutral electric charge or the elementary charge +1.

Lambda baryon

Quark structure of the lambda baryon.
Composition	Λ0 : u d s Λ+ c: u d c Λ0 b: u d b
Statistics	Fermionic
Family	Baryons
Interactions	Strong, weak, electromagnetic, and gravity
Types	3
Mass	Λ0 : 1115.683±0.006 MeV/c2[1] Λ+ c: 2286.46±0.14 MeV/c2 Λ0 b: 5619.60±0.17 MeV/c2
Spin	1⁄2
Isospin	0

Overview

The lambda baryon
Λ⁰
was first discovered in October 1950, by V. D. Hopper and S. Biswas of the University of Melbourne, as a neutral V particle with a proton as a decay product, thus correctly distinguishing it as a baryon, rather than a meson,^[2] i.e. different in kind from the K meson discovered in 1947 by Rochester and Butler;^[3] they were produced by cosmic rays and detected in photographic emulsions flown in a balloon at 70,000 feet (21,000 m).^[4] Though the particle was expected to live for ~10⁻²³ s,^[5] it actually survived for ~10⁻¹⁰ s.^[6] The property that caused it to live so long was dubbed strangeness and led to the discovery of the strange quark.^[5] Furthermore, these discoveries led to a principle known as the conservation of strangeness, wherein lightweight particles do not decay as quickly if they exhibit strangeness (because non-weak methods of particle decay must preserve the strangeness of the decaying baryon).^[5] The
Λ⁰
with its uds quark decays via weak force to a nucleon and a pion − either Λ → p + π⁻ or Λ → n + π⁰.

In 1974 and 1975, an international team at the Fermilab that included scientists from Fermilab and seven European laboratories under the leadership of Eric Burhop carried out a search for a new particle, the existence of which Burhop had predicted in 1963. He had suggested that neutrino interactions could create short-lived (perhaps as low as 10⁻¹⁴ s) particles that could be detected with the use of nuclear emulsion. Experiment E247 at Fermilab successfully detected particles with a lifetime of the order of 10⁻¹³ s. A follow-up experiment WA17 with the SPS confirmed the existence of the
Λ⁺
_c (charmed lambda baryon), with a lifetime of (7.3±0.1)×10⁻¹³ s.^[7][8]

In 2011, the international team at JLab used high-resolution spectrometer measurements of the reaction H(e, e′K⁺)X at small Q² (E-05-009) to extract the pole position in the complex-energy plane (primary signature of a resonance) for the Λ(1520) with mass = 1518.8 MeV and width = 17.2 MeV which seem to be smaller than their Breit–Wigner values.^[9] This was the first determination of the pole position for a hyperon.

The lambda baryon has also been observed in atomic nuclei called hypernuclei. These nuclei contain the same number of protons and neutrons as a known nucleus, but also contains one or in rare cases two lambda particles.^[10] In such a scenario, the lambda slides into the center of the nucleus (it is not a proton or a neutron, and thus is not affected by the Pauli exclusion principle), and it binds the nucleus more tightly together due to its interaction via the strong force. In a lithium isotope (⁷
_ΛLi
), it made the nucleus 19% smaller.^[11]

Types of lambda baryons

Lambda baryons are usually represented by the symbols
Λ⁰
,
Λ⁺
_c,
Λ⁰
_b, and
Λ⁺
_t. In this notation, the superscript character indicates whether the particle is electrically neutral (⁰) or carries a positive charge (⁺). The subscript character, or its absence, indicates whether the third quark is a strange quark (
Λ⁰
) (no subscript), a charm quark (
Λ⁺
_c), a bottom quark (
Λ⁰
_b), or a top quark (
Λ⁺
_t). Physicists expect to not observe a lambda baryon with a top quark, because the Standard Model of particle physics predicts that the mean lifetime of top quarks is roughly 5×10⁻²⁵ seconds;^[12] that is about ⁠1/20⁠ of the mean timescale for strong interactions, which indicates that the top quark would decay before a lambda baryon could form a hadron.

The symbols encountered in this list are: I (isospin), J (total angular momentum quantum number), P (parity), Q (charge), S (strangeness), C (charmness), B′ (bottomness), T (topness), u (up quark), d (down quark), s (strange quark), c (charm quark), b (bottom quark), t (top quark), as well as other subatomic particles.

Antiparticles are not listed in the table; however, they simply would have all quarks changed to antiquarks, and Q, B, S, C, B′, T, would be of opposite signs. I, J, and P values in red have not been firmly established by experiments, but are predicted by the quark model and are consistent with the measurements.^[13][14] The top lambda (
Λ⁺
_t) is listed for comparison, but is expected to never be observed, because top quarks decay before they have time to form hadrons.^[15]

Lambda baryons

Particle name	Symbol	Quark content	Rest mass (MeV/c²)	I	JP	Q (e)	S	C	B′	T	Mean lifetime (s)	Commonly decays to
Lambda[6]	Λ0	u d s	1115.683±0.006	0	⁠1/2⁠+	0	−1	0	0	0	(2.631±0.020)×10−10	p+ + π− or n0 + π0
charmed lambda[16]	Λ+ c	u d c	2286.46±0.14	0	⁠1/2⁠+	+1	0	+1	0	0	(2.00±0.06)×10−13	decay modes[17]
bottom lambda[18]	Λ0 b	u d b	5620.2±1.6	0	⁠1/2⁠+	0	0	0	−1	0	1.409+0.055 −0.054×10−12	Decay modes[19]
top lambda‡	Λ+ t	u d t	—	0	⁠1/2⁠+	+1	0	0	0	+1	—	‡

‡ ^ Particle unobserved, because the top-quark decays before it has sufficient time to bind into a hadron ("hadronizes").

The following table compares the nearly-identical Lambda and neutral Sigma baryons:

Neutral strange baryons

Particle name	Symbol	Quark content	Rest mass (MeV/c²)	I	JP	Q (e)	S	C	B′	T	Mean lifetime (s)	Commonly decays to
Lambda[6]	Λ0	u d s	1115.683±0.006	0	⁠1/2⁠+	0	−1	0	0	0	(2.631±0.020)×10−10	p+ + π− or n0 + π0
Sigma[20]	Σ0	u d s	1,192.642 ± 0.024	1	⁠1/2⁠+	0	−1	0	0	0	7.4 ± 0.7 × 10−20	Λ0 + γ (100%)

See also

• Physics portal

• List of baryons

References

1. Zyla, P. A.; et al. (Particle Data Group) (2020). "Review of Particle Physics". Progress of Theoretical and Experimental Physics. 2020 (8): 083C01. Bibcode:2020PTEP.2020h3C01P. doi:10.1093/ptep/ptaa104. hdl:11585/772320.
2. Hopper, V.D.; Biswas, S. (1950). "Evidence Concerning the Existence of the New Unstable Elementary Neutral Particle". Phys. Rev. 80 (6): 1099. Bibcode:1950PhRv...80.1099H. doi:10.1103/physrev.80.1099.
3. Rochester, G. D.; Butler, C. C. (1947). "Evidence for the Existence of New Unstable Elementary Particles". Nature. 160 (4077): 855–7. Bibcode:1947Natur.160..855R. doi:10.1038/160855a0. PMID 18917296. S2CID 33881752.
4. Pais, Abraham (1986). Inward Bound. Oxford University Press. pp. 21, 511–517. ISBN 978-0-19-851971-3.
5. The Strange Quark
6. Amsler, C.; et al. (Particle Data Group) (2008). "
   Λ
   " (PDF). Particle listings. Lawrence Berkeley Laboratory.
7. Massey, Harrie; Davis, D. H. (November 1981). "Eric Henry Stoneley Burhop 31 January 1911 – 22 January 1980". Biographical Memoirs of Fellows of the Royal Society. 27: 131–152. doi:10.1098/rsbm.1981.0006. JSTOR 769868. S2CID 123018692.
8. Burhop, Eric (1933). The Band Spectra of Diatomic Molecules (MSc). University of Melbourne.
9. Qiang, Y.; et al. (2010). "Properties of the Lambda(1520) resonance from high-precision electroproduction data". Physics Letters B. 694 (2): 123–128. arXiv:1003.5612. Bibcode:2010PhLB..694..123Q. doi:10.1016/j.physletb.2010.09.052. S2CID 119290870.
10. "Media Advisory: The Heaviest Known Antimatter". bnl.gov. Archived from the original on 2017-02-11. Retrieved 2013-03-10.
11. Brumfiel, Geoff (1 March 2001). "The Incredible Shrinking Nucleus". Physical Review Focus. Vol. 7, no. 11.
12. Quadt, A. (2006). "Top quark physics at hadron colliders" (PDF). European Physical Journal C. 48 (3): 835–1000. Bibcode:2006EPJC...48..835Q. doi:10.1140/epjc/s2006-02631-6. S2CID 121887478.
13. Amsler, C.; et al. (Particle Data Group) (2008). "Baryons" (PDF). Particle summary tables. Lawrence Berkeley Laboratory.
14. Körner, J.G.; Krämer, M.; Pirjol, D. (1994). "Heavy Baryons". Progress in Particle and Nuclear Physics. 33: 787–868. arXiv:hep-ph/9406359. Bibcode:1994PrPNP..33..787K. doi:10.1016/0146-6410(94)90053-1. S2CID 118931787.
15. Ho-Kim, Quang; Pham, Xuan Yem (1998). "Quarks and SU(3) Symmetry". Elementary Particles and their Interactions: Concepts and phenomena. Berlin: Springer-Verlag. p. 262. ISBN 978-3-540-63667-0. OCLC 38965994. Because the top quark decays before it can be hadronized, there are no bound ${\displaystyle t{\bar {t}}}$ states and no top-flavored mesons or baryons ... .
16. Amsler, C.; et al. (Particle Data Group) (2008). "
    Λ
    _c" (PDF). Particle listings. Lawrence Berkeley Laboratory.
17. Amsler, C.; et al. (Particle Data Group) (2008). "
    Λ⁺
    _c" (PDF). Decay modes. Lawrence Berkeley Laboratory.
18. Amsler, C.; et al. (Particle Data Group) (2008). "
    Λ
    _b" (PDF). Particle listings. Lawrence Berkeley Laboratory.
19. Amsler, C.; et al. (Particle Data Group) (2008). "
    Λ⁰
    _b" (PDF). Decay modes. Lawrence Berkeley Laboratory.
20. Zyla, P.A.; et al. (Particle Data Group) (2020-08-14). "Review of Particle Physics". Progress of Theoretical and Experimental Physics. 2020 (8): 083C01. Bibcode:2020PTEP.2020h3C01P. doi:10.1093/ptep/ptaa104. hdl:10481/66389.

Further reading

• Amsler, C.; et al. (2008). "Review of Particle Physics" (PDF). Physics Letters B. 667 (1–5): 1–6. Bibcode:2008PhLB..667....1A. doi:10.1016/j.physletb.2008.07.018. hdl:1854/LU-685594. S2CID 227119789.
• Caso, C.; et al. (1998). "Review of Particle Physics". European Physical Journal C. 3 (1–4): 1–783. Bibcode:1998EPJC....3....1P. doi:10.1007/s10052-998-0104-x. S2CID 195314526.
• Nave, R. (12 April 2005). "The Lambda baryon". HyperPhysics. Retrieved 14 July 2010.