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Baryon number violation in the SM *June 10, 2006*

*Posted by dorigo in mathematics, physics, science.*

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Fred asks me whether the Standard Model accommodates baryon number violation….

I am not too sure of the answer I gave in the post – I think I read something about it some time ago, but information leaks away from my neurons very quickly these days…

So I will expose here my ignorance, and if anybody corrects me I will be more than happy to learn something (over again).

Also, if anybody can point me to a graph showing the wave function in a quantum well and the exponential decay due to tunneling, I'd be grateful.

Here is Fred's question and my (poor) answer follows.

“The law of the conservation of baryon number states that the total number of baryons must be the same before and after any subatomic event.” Is this a supersymmetrical condition “thus guaranteeing the stability of baryonic matter?”

No, no supersymmetry at work here.

In the Standard Model, Baryon number violation is actually allowed, although with extremely low probability and at very low energy.

Baryon number violating processes in the SM are associated with a quantum-mechanical effect called “tunnelling”, whereby an exponentially decaying spatial amplitude for a wave function maintains a non-zero value through an energy barrier, and – if the barrier is narrow enough and not high enough to make the wave function really vanishing – the wave function has a chance to “pop out” of the barrier, tunnelling away from the trap.

Not clear enough, huh ? Ok. Imagine a quantum well. It is a region of space where the potential energy of a particle is smaller than its total energy. Thus, the particle has some kinetic energy left, and it propagates within the region. Now, if you take the quantum-mechanical description of the particle as a wave propagating in the well, this is a wave function. A function that describe the “amplitude” for the particle to be in any particular spatial point within the well.

Within, and outside of it. In fact, if the height of the “walls” is not infinite, the wave function “leaks” outside of the well and inside the walls, with an exponentially vanishing amplitude. It is as if the particle has a extremely small, but non zero, chance of being found inside of the walls.

Now, if the walls are not thick enough, this exponential tail of the wave function will extend past the wall. Past it, the particle described by that tiny amplitude that has leaked out of the wall will have again a positive kinetic energy, and it will be perfectly legal for it to propagate there. The particle has “tunneled” inside of the wall and out of the well.

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I want to know about simple experiments which can be performed at home and not such difficult and hard ones which we don’t even know about.