B - L

The difference between the baryon number and the lepton number ${\displaystyle B}$ ${\displaystyle L}$ , in short , is a many-particle quantum number in particle physics . Each particle is assigned a baryon number and a lepton number ; At the level of the elementary particles, each lepton receives the lepton number and each quark the baryon number , since a baryon is always made up of three quarks. Antiparticles are given the respective negative quantum number. Both quantities are additive and are independent conservation quantities in the standard model of elementary particle physics described in perturbation theory . In a large unified theory (GUT) as an extension of the Standard Model, neither the number of baryons nor the number of leptons are preserved independently of one another, but their difference is preserved. This enables a baryogenesis with simultaneous leptogenesis to fulfill the Sakharov criteria for the emergence of the asymmetry between matter and antimatter. ${\displaystyle B-L}$ ${\displaystyle L=+1}$ ${\displaystyle B=1/3}$

B - L as the conservation size

The property of the difference between the number of baryons and the number of leptons as a conserved quantity results from the absence of anomalies in a quantum field theory and is related to the weak hypercharge of the particles. The weak hypercharge is the charge of the symmetry group, under which the equations of motion are invariant. With the introduction of an additional symmetry group as an extension of the standard model, only the assignment of the quantum numbers for quarks and for leptons leads to a consistent description (apart from a general normalization factor) . ${\displaystyle U(1)_{Y}}$ ${\displaystyle U(1)}$ ${\displaystyle 1/3}$ ${\displaystyle -1}$

If the symmetry represents a calibration symmetry , a corresponding calibration boson must exist. These hypothetical particles are called leptoquarks because they couple to both leptons and quarks in a vertex. ${\displaystyle U(1)_{B-L}}$

Example: proton decay

The proton decay is a prediction of many GUT variants, so that the final state is a neutral pion and a positron (anti-electron): ${\displaystyle \pi ^{0}}$

${\displaystyle p^{+}\to \pi ^{0}e^{+}}$

The proton is a baryon , the pion is a meson and therefore has and the positron is an antilepton . Therefore neither baryons nor leptons are preserved in this process, but the difference . In the standard model, however, the proton is the lightest baryon and is stable. Since the lower bound on the experimental life is very high proton (about 10 ³³ years, compared to the universe is "only" 10 ¹⁰ years old), has the mass of any -Eichbosons in the order of 10 ¹⁶ GeV are . ${\displaystyle B=1}$ ${\displaystyle B=L=0}$ ${\displaystyle L=-1}$ ${\displaystyle B-L}$ ${\displaystyle U(1)_{B-L}}$ 

See also

• Sphaleron , a non-perturbative process in the Standard Model that receives neither nor , but . ${\displaystyle B}$ ${\displaystyle L}$ ${\displaystyle B-L}$

swell

• Mattew D. Schwartz: Quantum Field Theory and the Standard Model . Cambridge University Press, Cambridge 2014, ISBN 978-1-107-03473-0 (English).