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All known leptons are listed in the table given above. There are only six leptons (and their antiparticles), and they seem to be fundamental in that they have no apparent underlying structure. Leptons have no discernible size other than their wavelength, so that we know they are pointlike down to about 10 18 m size 12{"10" rSup { size 8{ - "18"} } m} {} . The leptons fall into three families, implying three conservation laws for three quantum numbers. One of these was known from β size 12{β} {} decay, where the existence of the electron's neutrino implied that a new quantum number, called the electron family number     L e size 12{L rSub { size 8{e} } } {} is conserved. Thus, in β size 12{β} {} decay, an antielectron's neutrino v - e size 12{ { bar {v}} rSub { size 8{e} } } {} must be created with L e = 1 size 12{L rSub { size 8{e} } = - 1} {} when an electron with L e =+ 1 size 12{L rSub { size 8{e} } "=+"1} {} is created, so that the total remains 0 as it was before decay.

Once the muon was discovered in cosmic rays, its decay mode was found to be

μ e + v - e + v μ , size 12{μ rSup { size 8{ - {}} } rightarrow e rSup { size 8{ - {}} } + { bar {v}} rSub { size 8{e} } +v rSub { size 8{μ} } ","} {}

which implied another “family” and associated conservation principle. The particle v μ size 12{L rSub { size 8{μ} } } {} is a muon's neutrino, and it is created to conserve muon family number     L μ size 12{L rSub { size 8{μ} } } {} . So muons are leptons with a family of their own, and conservation of total L μ size 12{L rSub { size 8{μ} } } {} also seems to be obeyed in many experiments.

More recently, a third lepton family was discovered when τ size 12{τ} {} particles were created and observed to decay in a manner similar to muons. One principal decay mode is

τ μ + v - μ + v τ . size 12{τ rSup { size 8{ - {}} } rightarrow μ rSup { size 8{ - {}} } + { bar {v}} rSub { size 8{u} } +v rSub { size 8{τ} } "."} {}

Conservation of total L τ size 12{L rSub { size 8{μ} } } {} seems to be another law obeyed in many experiments. In fact, particle experiments have found that lepton family number is not universally conserved, due to neutrino “oscillations,” or transformations of neutrinos from one family type to another.

Mesons and baryons

Now, note that the hadrons in the table given above are divided into two subgroups, called mesons (originally for medium mass) and baryons (the name originally meaning large mass). The division between mesons and baryons is actually based on their observed decay modes and is not strictly associated with their masses. Mesons are hadrons that can decay to leptons and leave no hadrons, which implies that mesons are not conserved in number. Baryons are hadrons that always decay to another baryon. A new physical quantity called baryon number     B size 12{B} {} seems to always be conserved in nature and is listed for the various particles in the table given above. Mesons and leptons have B = 0 size 12{B=0} {} so that they can decay to other particles with B = 0 size 12{B=0} {} . But baryons have B =+ 1 size 12{B"=+"1} {} if they are matter, and B = 1 size 12{B= - 1} {} if they are antimatter. The conservation of total baryon number    is a more general rule than first noted in nuclear physics, where it was observed that the total number of nucleons was always conserved in nuclear reactions and decays. That rule in nuclear physics is just one consequence of the conservation of the total baryon number.

Forces, reactions, and reaction rates

The forces that act between particles regulate how they interact with other particles. For example, pions feel the strong force and do not penetrate as far in matter as do muons, which do not feel the strong force. (This was the way those who discovered the muon knew it could not be the particle that carries the strong force—its penetration or range was too great for it to be feeling the strong force.) Similarly, reactions that create other particles, like cosmic rays interacting with nuclei in the atmosphere, have greater probability if they are caused by the strong force than if they are caused by the weak force. Such knowledge has been useful to physicists while analyzing the particles produced by various accelerators.

Questions & Answers

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Suppose a 0.250-kg ball is thrown at 15.0 m/s to a motionless person standing on ice who catches it with an outstretched arm as shown in [link] . (b) What is his angular velocity if each arm is 5.00 kg? You may treat the ball as a point mass and treat the person's arms as uniform rods (each has a length of 0.900 m) and the rest of his body as a uniform cylinder of radius 0.180 m. Neglect the effect of the ball on his center of mass so that his center of mass remains in his geometrical center.
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