# 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, Σ$^0$ ). They are thus baryons, with total isospin of 0, and have either neutral electric charge or the elementary charge +1.

## Overview

The lambda baryon Λ$^0$ 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, i.e. different in kind from the K meson discovered in 1947 by Rochester and Butler; they were produced by cosmic rays and detected in photographic emulsions flown in a balloon at 70,000 feet (21,000 m). Though the particle was expected to live for ~10$^{−23}$ s, it actually survived for ~10$^{−10}$ s. The property that caused it to live so long was dubbed strangeness and led to the discovery of the strange quark. 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). The Λ$^0$ with its uds quark decays via weak force to a nucleon and a pion − either Λ → p + π$^−$ or Λ → n + π$^0$.
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.
In 2011, the international team at JLab used high-resolution spectrometer measurements of the reaction H(e, e′K$^+$)X at small Q$^2$ (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. 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. 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 ($^7$ $_Λ$Li ), it made the nucleus 19% smaller.

## Types of lambda baryons

Lambda baryons are usually represented by the symbols Λ$^0$ , Λ$^+$ $_c$, Λ$^0$ $_b$, 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 ( Λ$^0$ ) (no subscript), a charm quark ( Λ$^+$ $_c$), a bottom quark ( Λ$^0$ $_b$), 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; 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. 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.
Lambda baryons :
| Particle name | Symbol | Quark content | Rest mass (MeV/c²) | I | J | Q (e) | S | C | B′ | T | Mean lifetime (s) | Commonly decays to |
| Lambda | Λ$^0$ | u d s | 1115.683±0.006 | 0 | ⁠1/2⁠$^+$ | 0 | −1 | 0 | 0 | 0 | (2.631±0.020)×10$^{−10}$ | p$^+$ + π$^−$ or n$^0$ + π$^0$ |
| charmed lambda | 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 |
| bottom lambda | Λ$^0$ $_b$ | 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 |
| 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 | J | Q (e) | S | C | B′ | T | Mean lifetime (s) | Commonly decays to |
| Lambda | Λ$^0$ | u d s | 1115.683±0.006 | 0 | ⁠1/2⁠$^+$ | 0 | −1 | 0 | 0 | 0 | (2.631±0.020)×10$^{−10}$ | p$^+$ + π$^−$ or n$^0$ + π$^0$ |
| Sigma | Σ$^0$ | u d s | 1,192.642 ± 0.024 | 1 | ⁠1/2⁠$^+$ | 0 | −1 | 0 | 0 | 0 | 7.4 ± 0.7 × 10$^{−20}$ | Λ$^0$ + γ (100%) |