Quantum number; the difference between the baryon and lepton numbers
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 Y W is related to B – L via
X
+
2
Y
W
=
5
(
B
− − -->
L
)
,
{\displaystyle X+2\,Y_{\text{W}}=5\,(B-L),}
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 .[ 1]
See also
References
Operating Retired Proposed See also