Suppose a new particle is discovered how will it be assigned a lepton and baryon number? Moreover, what difference would it make if the electron had +1 lepton number and a positron -1? The same question goes for any particle-antiparticle pair like neutron and anti-neutron pair.
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$\begingroup$ to get a clear picture of leptons hyperphysics.phy-astr.gsu.edu/hbase/Particles/lepton.html . each type of lepton has its own lepton number. antileptons have the negative one so in annihilation the specific lepton number is zero $\endgroup$– anna vCommented Jun 8, 2019 at 5:34
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$\begingroup$ @annav, I am always wondering whether there is a physics-savvy AI answering SE questions in an impeccable way. Well, of course, you are carbon-based, I assume. $\endgroup$– MadMaxCommented Jun 10, 2019 at 14:10
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The sign of lepton number(s) and baryon number is arbitrary. $n$ and $\overline n$ must have opposite baryon numbers, but whether we call these +1 and -1 or -1 and +1 does not matter, provided we are consistent. (Of course expressions like the Gell-Mann Nishijima formula, $Q=I_3+{1 \over 2}(S+B)$, would need to be adjusted appropriately.)
When a new particle is discovered its Baryon and Lepton numbers are established from the total B and L either of the particles that produce it, or of the particles into which it decays. It's good to have both available as if it decays into neutrinos, or other undetected particles, you don't know what quantum numbers they carry, and likewise if the production is inclusive (i,e. other particles are produced in the collision) you don't know what they are.
answered Jun 8, 2019 at 8:50