Neutron decay and interconversion

1.   Primordial Nucleosynthesis Neutron decay and interconversion • Particle processes are a lot like equations • You can turn them around and they still work • You can move particles to the other side by “subtracting them” • This means replacing them with anti-particles • The neutron (in isolation) is an unstable particle • Decays to proton + electron + anti-neutrino • Mean lifetime: 886 seconds + + n0 p+ e- • Put the electron on the other side + + n0 p+ e+ • Put the neutrino on the other side • All thee processes convert neutrons to protons and vice versa + + p+ e- n0 

2. Neutron/Proton Freezeout • Weak interactions interconvert protons/neutrons • These are slow processes, so they fall out of equilibrium fairly early • At kBT = 0.71 MeV, the process stops • What is ratio of protons to neutrons at this temperature? • Non-relativistic, E = mc2. • Ratio is: • This happens at about:

3. The Deuterium Bottleneck • The next step in making more complex elements is to make 2H, deuterium: • This releases about 2.24 MeV of energy • Naively: this process will go ahead as soon as kBT drops below 2.24 MeV • Actually, much lower temperature is required because of very low density of nucleons • Actual temperature is about factor of 20 lower: 0.1 MeV • Age of universe at this time: • At this point, some neutronsare gone due to decay + p+ p+ n0 n0 • Ratio depends weakly on density of protons/neutrons – more makes it happen sooner

4. Making Helium • Once we make deuterium, we continue quickly to continue to helium: + + n0 p+ n0 p+ p+ p+ p+ p+ p+ p+ n0 n0 n0 + + n0 n0 p+ n0 n0 n0 n0 p+ p+ p+ p+ p+ • For every two neutrons, there will be two protons that combine to make 4He • Mass fraction of 4He is twice that of neutron fraction • 4He is extremely stable – once formed it won’t go back. • The sooner it happens, the more neutrons are left over • Define  as the current ratio of baryons (protons + neutrons) to photons • As  increases, YP increases weakly: n0 n0 n0

5. Making Other elements • When you run out of neutrons, 3He can still be turned into 4He via • The last few 2H, 3He, and 3H nuclei will have trouble finding partners • There will be small amount of each of these isotopes left • The more baryons there are, the easier it is to find a partner • As  increases, 2H, 3He, and 3H all decrease • There are other rare processes that produce a couple of other isotopes: • 7Li and 7Be are produced • I don’t understand how theydepend on  • Within a few hundred seconds, thebaryons are all in 1H, 2H, 3H, 3He, 4He, 7Be and 7Li + + + p+ p+ n0 p+ p+ p+ p+ p+ p+ p+ n0 n0 n0 n0 n0 n0 n0 p+ p+ p+ p+ p+ p+ n0 n0 n0 p+ n0 + n0 p+ p+ p+ n0 p+ n0 + n0 p+ n0 p+ n0

6. Anything we missed? • Two of these isotopes are unstable: • Add 3H to 3He and 7Be to 7Li • The process whereby stars make heavier elements do not work in the early universe • Density is too low for unstable 8Be to findanother 4He to react with • In the end, we should be able to predict abundance (compared to hydrogen) of2H, 3He, 4He, 7Li • These have all been measured, mostly by studying light from quasars • Back in the good old days (the 90s), this was how we estimated  • Now we have an independent way of estimating it (later lecture) • We should be able to compare the results withpredictions • A very strong test of Big Bang theory

7. The results • Predictions for 4He, 2H and 3He all work very well • Prediction for 7Li seems to be off • The Lithium problem • Overall, success for the model

8. Summary of Events: EventkBT or TTime Neutrinos Decouple 1 MeV 0.4 s Neutron/Proton freezeout 0.7 MeV 1.5 s Electron/Positron Annihilate 170 keV 30 s Primordial Nucleosynthesis 80 keV 200 s Matter/Radiation Equality 0.76 eV 57 kyr Recombination 0.26 eV 380 kyr Structure formation 30 K 500 Myr Now 2.725 K 13.75 Gyr • Lots of unsolved problems: • What is the nature of dark matter? • Why is the universe flat (or nearly so)? • Where did all the structure come from? • What is the nature of dark energy?

9. The Early Universe What we know and what we don’t: • Up to now, everything we have discussed is based on pretty well understood physics • And the experimental results match it well! • As we move earlier, we reach higher temperatures/energies, and therefore things become more uncertain • For a while, we can assume we understand the physics and apply it, but we don’t have any good tests at these scales • New particles appear as temperature rises: • Muons, mass 105.7 MeV, at about kBT = 35 MeV (g = 4 fermions) • Pions, mass 135-139 MeV, at about kBT = 45 MeV (g = 3 bosons) • At a temperature of about kBT = 100 MeV, we have quark deconfinement

10. Quark Confinement • There are a group of particles called baryons that have strong interactions • Proton and neutron are examples • There are also anti-baryons and other strong particles called mesons • In all experiments we have done, the baryon number is conserved • Baryon number = baryons minus anti-baryons • All strongly interacting particle contain quarks or anti-quarks or both • The quarks are held together by particles called “gluons” u u g • At low temperatures quarks are confined into these packets • At high temperatures, these quarks become free (deconfined) • Estimated kBT= 150 MeV d u u

11. Electroweak Phase Transition • There are three forces that particle physicist understand: • Strong, electromagnetic, and weak • Electromagnetic and weak forces affected by a field called the Higgs field • The shape of the Higgs potential is interesting: • Sometimes called a Mexican Hat potential • At low temperatures (us), one direction is easy to move (EM forces) and one is very hard (weak forces) • At high temperatures, (early universe) you naturally move to the middle of the potential • All directions are created equal • Electroweak unification becomes apparent at perhaps kBT = 50 GeV

12. The Standard Model Particlesymbolsspingmc2 (GeV)Electrone ½ 4 0.0005Electron neutrino e ½ 2 ~0Up quark uuu ½ 12 ~0.005Down quark ddd ½ 12 ~0.010Muon ½ 4 0.1057Muon neutrino  ½ 2 ~0Charm quark ccc ½ 12 1.27Strange quark sss ½ 12 ~0.10Tau  ½ 4 1.777Tau neutrino  ½ 2 ~0Top quark ttt ½ 12 173Bottom quark bbb ½ 12 4.7 Photon 1 2 0Gluon gggggggg1 16 0W-boson W 1 6 80.4Z-boson Z 1 3 91.2 Higgs H 0 1 115–285 • Above the electroweak phase transition, all known particles of the standard model should exist with thermal densities • From here on, we will be speculating on the physics • Cosmology sometimes indicates we are guessing right • Goal: Learn physics from cosmology

13. Supersymmetry • In conventional particle physics, fermions and bosons are fundamentally different • And never the twain shall meet • In a hypothesis called supersymmetry, fermions and bosons are interrelated • There must be a superpartner for every particle: • Supersymmetry also helps solve aproblem called the hierarchy problem • But only if it doesn’t happen attoo high an energy • If supersymmetry is right, then scale ofsupersymmetry breaking probably around kBT = 500 GeV or so. • If this is right, the LHC should discover it • In most versions of supersymmetry, the lightest super partner (LSP) should be absolutely stable Could this be dark matter?

14. Grand Unification Theories (GUT’s) • In the standard model, there are three fundamental forces, and three corresponding coupling constants • These have rather different values • But their strength changes as you change the energy of the experiment, theortically • How much they change depends on whether supersymmetry is right or not • If supersymmetry is right, then at an energyof about 1016GeV, the three forces areequal in strength • At kBT = 1016GeV, there will be anotherphase transition – the Grand Unificationtransition With Supersymmtery No Supersymmtery Baryogenesis might occur at this scale Scale could be right for inflation

15. Summary of Events: EventkBT or TTime Grand Unification 1016GeV 10-39 s Supersymmetry Scale 500 GeV 10-12 s Electroweak Scale 50 GeV 10-10 s Quark Confinement 150 MeV 1.410-5 s Neutrinos Decouple 1 MeV 0.4 s Neutron/Proton freezeout 0.7 MeV 1.5 s Electron/Positron Annihilate 170 keV 30 s Primordial Nucleosynthesis 80 keV 200 s Matter/Radiation Equality 0.76 eV 57 kyr Recombination 0.26 eV 380 kyr Structure formation 30 K 500 Myr Now 2.725 K 13.75 Gyr