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According to https://en.wikipedia.org/wiki/Up_quark the up quark can decay into a down quark plus a positron plus an electron neutrino. The problem is that the mass of the by-products is greater than the original particle. This would violate conservation of mass/energy unless some source of energy or mass was put into the system to trigger the decay.

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The most common example of this is beta plus decay. In this process one of the up quarks in a proton decays into a down quark and a $W^+$, and the $W^+$ then decays into a positron and electron neutrino. As a result of the decay the proton converts to a neutron.

As you say, the process violates conservation of energy and that means it cannot occur unless energy can be supplied from some other source. An isolated proton cannot undergo beta plus decay to a neutron. However in a nucleus the rearrangement of the nucleons following the decay of the proton to a neutron can supply the required energy, and some nuclei can undergo this type of decay.

So you are quite correct that the decay violates conservation of energy, and therefore it can only happen when that missing energy required can be supplied from elsewhere.

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  • $\begingroup$ I'm still not completely clear where the energy comes from? Is it the drop in electric potential energy due to less repulsion between nucleons? $\endgroup$ – Derek Seabrooke Jun 26 at 17:31
  • $\begingroup$ Nuclei are many body systems because all the nucleons have roughly the same mass. That makes computing their energy levels vastly more complicated than for atoms. The energy that allows beta plus decay obviously comes from a rearrangement of the energy levels in the nucleus - after all there is no other place it can come from - but it's impossible to explain how this happens in simple terms. There will be a contribution from the reduced proton-proton repulsion but also from the changes in the strong nuclear force interaction energy. $\endgroup$ – John Rennie Jun 26 at 17:49
  • $\begingroup$ Why would strong nuclear force be involved? The strong force I thought was quenched inside the nucleus as everything is at the ideal distance. $\endgroup$ – Derek Seabrooke Jun 27 at 13:34
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    $\begingroup$ @DerekSeabrooke it is the residual strong force that is interesting here, governing the interactions between the nucleons, at longer distances. The strong force itself acts inside the nucleons at shorter distances. $\endgroup$ – Árpád Szendrei Jun 27 at 16:26
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Quarks can never be observed isolated, since they only exist in confinement. What you are asking about is basically the conversion of a proton into a neutron. Even then, the proton cannot decay in isolation (except if there is a incident antineutrino with sufficient energy), and there are basically two main types of cases where the proton can do this transformation into a neutron, one of them is covered in John Rennie's answer, where the proton exist inside a nucleus, together with other nucleons, and the extra energy you are asking about is supplied by the changes in the involved EM and residual strong forces.

The other case is electron capture, where the proton rich nucleus of an EM neutral atom absorbs an inner atomic electron. In most cases (except Auger effect) the atom stays EM neutral, the proton converts to a neutron, and all the decay energy is released in form of a neutrino. Contrary to popular belief, the electron is not from an external atom, but from inside the current atomic system. This electron supplies the extra energy you are asking about.

https://en.wikipedia.org/wiki/Electron_capture

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  • $\begingroup$ I agree, however I think the statement in made by Wikipedia that the up quark decays is misleading. It doesn't decay, it is converted by a chain reaction. It kinda like saying a nuclear bomb explodes because of decay and not because someone did something to set it off. $\endgroup$ – Derek Seabrooke Jun 27 at 13:32
  • $\begingroup$ @DerekSeabrooke correct, but it is the proton that decays, but the proton cannot decay in isolation. However, if you are trying to find a reason what triggers this transformation, you will see there is no such trigger, it is just QM. physics.stackexchange.com/questions/164665/… $\endgroup$ – Árpád Szendrei Jun 27 at 16:40
  • $\begingroup$ And an interesting answer perhaps physics.stackexchange.com/questions/220164/… $\endgroup$ – HolgerFiedler Jul 5 at 16:41
  • $\begingroup$ @HolgerFiedler thank you I edited. $\endgroup$ – Árpád Szendrei Jul 5 at 16:45
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A bare single up-quark could not decay into a down-quark, as this would indeed voilate energy-mass conservation. A transition to a down-quark could happen within some interaction with another particle.

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  • $\begingroup$ Indeed, but what interaction? Is this truly decay then if it requires energy input to happen? $\endgroup$ – Derek Seabrooke Jun 26 at 15:04
  • $\begingroup$ The interaction is via weak force, a $W^+$ is needed in this case. The thing is it happens due to other factors, not the up quark decaying all on its own. You'll have to remember that the quarks are part of a complicated composite system with other quarks in an atomic nucleus. $\endgroup$ – Triatticus Jun 26 at 16:53
  • $\begingroup$ The wikipedia article I cited states Stable or Down quark + Positron + Electron neutrino there is no mention here of any W+ is the article wrong? $\endgroup$ – Derek Seabrooke Jun 27 at 13:30
  • $\begingroup$ @Derek Please see en.wikipedia.org/wiki/Beta_decay which has Feynman diagrams of the various types of beta decay. The weak interaction changes the flavor of quarks and leptons, that interaction is mediated by W & Z bosons. $\endgroup$ – PM 2Ring Jun 27 at 16:51

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