# Pair production mass

I’ve read other questions on here, but I still don’t have the answer that I need. In pair production, where does the mass come from that’s found in the electron-positron pair? I’m extremely novice and recognize that part of my problem with understanding how mass comes from energy is due to the lack of understanding I have for energy’s relation to mass. If someone could help me understand this, I would greatly appreciate it.

• A lot of information can be found here: en.m.wikipedia.org/wiki/Pair_production Are you familiar with Einstein's mass-energy equivalence principle (i.e. $\ce {E = mc^2}$ ) ? – Tan Yong Boon Mar 5 '20 at 1:56
• @TanYongBoon Yes, I am. I think my problem is equating it to photons turning into things that have mass. – Allex Kramer Mar 5 '20 at 1:59
• Photons have energy $E=h\nu$ even though they are massless. That energy goes to make the electron and positron. – G. Smith Mar 5 '20 at 2:42
• Are you ok with an electron & a positron annihilating each other & producing a couple of photons? – PM 2Ring Mar 5 '20 at 2:54
• I think I am confused as to the photon turns into something that suddenly rest mass? Does it slow down, in layman terms? Is the energy put in a type of box, layman again? – Allex Kramer Mar 5 '20 at 15:18

## 4 Answers

The mass does not "come from" anywhere. You should view the produced electrons as excitations of the electron field. The electron field has the property that the energy $$E$$ and momentum $$p$$ of an excitation must satisfy the relation $$E^2 = p^2 + m^2$$, where $$m$$ is some parameter that we call the mass. Because the photon (or whatever) couples to the electron field, it can produce a pair of these excitations that we identify as electrons/positrons. Given the energy and momenta of the initial particles, the electron and positron are produced with energy and momenta that satisfy the relevant conservation laws and the above relation to the mass parameter of the electron field.

It comes from $$E = mc^2$$. A photon of 1.022 MeV, will decay into an electron (rest mass = .511 MeV) and a positron (rest mass = .511 MeV). This is pair production. The photon ceases to exist. Its energy was converted to mass.

• Photons do not decay. A further body is required here. – my2cts Mar 5 '20 at 5:25

Here is a simple pair production diagram used to calculate crossections to compare with experiment: Special relativity is necessary to understand it, in addition to quantum mechanics. In special relativity all particles are described by four vectors. The energy momentum four vector has a "length" , a quantity invariant under Lorentz transformations and in the case of a particle it is defined as its invariant mass. It is the mass that describes the electron or the positron in the diagram above. When two four vectors are added , as in the diagram, the invariant mass is the "length" of their added four vectors. In order for the reaction to happen, the incoming photon has to have the added energy of the two outgoing particles. That is how energy balances in special relativity.

Note the necessity of the off shell gamma at the lower end. A single gamma cannot "decay" into a pair, as its invariant mass is zero and the invariant mass of the pair is at least two electron masses.

• Thank you for taking the time to answer this. I notice that the wikipedia diagram has the arrow at the top pointing from e+ to the end of the photon line. Can you describe why the diagram is laid out this way? I've noticed that other pair production diagrams do not show the same. – Allex Kramer Mar 5 '20 at 13:53
• @AllexKramer backwards arrows show antiparticle quantum numbers, thus e+ – anna v Mar 5 '20 at 17:37

An isolated photon cannot decay into an electron + positron because that would disobey conservation of momentum. But a high energy photon in the vicinity of a nucleus can decay into an electron + positron because the nucleus can balance out the momentum.

Rest mass is just a form of energy (and in particle physics it is sometimes called rest energy), and there's no problem with converting other forms of energy to rest mass, or vice versa, as long as you obey all the conservation laws. For pair production or annihilation, that means energy, momentum, electric charge and lepton number must be the same before and after the reaction.