A. Zee, Quantum Field Theory in a Nutshell · Problem VII.6.3

The key insight is that $B - L$ (baryon minus lepton number) is a global $U(1)$ symmetry that emerges independently of the gauge structure—it's not imposed by $SU(5)$, but rather a consequence of how quarks and leptons must transform to keep the theory anomaly-free. To show conservation, verify that all $SU(5)$ representations assign consistent $B - L$ values to their components. For the challenge, you'll need to introduce new particles or interactions (like right-handed neutrinos with Majorana masses, or leptoquarks) that explicitly mix baryon and lepton quantum numbers, breaking this accidental symmetry while preserving $SU(5)$ gauge invariance.

The key insight is that $B - L$ (baryon minus lepton number) is a global $U(1)$ symmetry that emerges independently of the gauge structure—it's not imposed by $SU(5)$, but rather a consequence of how quarks and leptons must transform to keep the theory anomaly-free. To show conservation, verify that all $SU(5)$ representations assign consistent $B - L$ values to their components. For the challenge, you'll need to introduce new particles or interactions (like right-handed neutrinos with Majorana masses, or leptoquarks) that explicitly mix baryon and lepton quantum numbers, breaking this accidental symmetry while preserving $SU(5)$ gauge invariance.