B − L
In this article we will explore B − L in depth, a topic that has sparked great interest and debate in recent years. From its origins to its relevance today, B − L has captured the attention of various spheres of society. Through an exhaustive analysis, we will examine the different edges that make up B − L, as well as their implications in different contexts. In addition, we will emphasize the evolution of B − L over time, highlighting its impact in different areas and its influence on decision making. By weighing the various points of view on B − L, we seek to provide a comprehensive perspective that enriches the understanding of this topic that is so relevant today.
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In particle physics, B − L (pronounced "bee minus ell") is a quantum number which is the difference between the baryon number (B) and the lepton number (L) of a quantum system.
Details
This quantum number is the charge of a global/gauge U(1) symmetry in some Grand Unified Theory models, called U(1)B−L. Unlike baryon number alone or lepton number alone, this hypothetical symmetry would not be broken by chiral anomalies or gravitational anomalies, as long as this symmetry is global, which is why this symmetry is often invoked.
If B – L exists as a symmetry, then for the seesaw mechanism to work B – L has to be spontaneously broken to give the neutrinos a nonzero mass.
The anomalies that would break baryon number conservation and lepton number conservation individually cancel in such a way that B – L is always conserved. One hypothetical example is proton decay where a proton (B = 1, L = 0) would decay into a pion (B = 0, L = 0) and positron (B = 0, L = –1).
The weak hypercharge YW is related to B – L via
where X charge (not to be confused with the X boson) is the conserved quantum number associated with the global U(1) symmetry Grand Unified Theory.
See also
References
- ^ Wilczek, Frank; Zee, A. (1979). "Operator analysis of nucleon decay". Physical Review Letters. 43 (21): 1571–1573. Bibcode:1979PhRvL..43.1571W. doi:10.1103/PhysRevLett.43.1571.
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