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 •Put the electron on the other side •Put the neutrino on the other side •All thee processes convert neutrons to protons and vice versa

n 0 n 0 +

e +

n 0 +



p + + p +

e -

+ p + + +



e -



Neutron/Proton Freezeout

•Weak interactions interconvert protons/neutrons •These are slow processes, so they fall out of equilibrium fairly early •At

k B T

= 0.71 MeV, the process stops •What is ratio of protons to neutrons at this temperature?

•Non-relativistic, •Ratio is:

E

=

mc

2 .

P n P p

  exp exp    

m c n m c p

2 2

k T B k T B

     exp

n n n p

 exp exp    

n

2

m c k T m c p

2

k T B

   exp    

mc

2

k T B

   exp  1.294 MeV 0.71 MeV  0.162

 

n n n n



n p

 0.162

1.162

 0.139

•This happens at about:

t

 g eff 

k T B

  2  2.42 s 10.75

MeV 0.71 MeV 2  1.5 s 

The Deuterium Bottleneck

•The next step in making more complex elements is to make 2 H, deuterium: •This releases about 2.24 MeV of energy

p

•Naively: this process will go ahead as soon as

+

k B T

+ n 0 p + n 0

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 neutrons are gone due to decay

t

 g eff 

k T B

  2  2.42 s 3.36

MeV 0.1 MeV 2  130 s  

n n n n



n p

  132 s   

n n n n



n p

  1.5 s exp  130 886  0.120

•Ratio depends weakly on density of protons/neutrons – more makes it happen sooner

Making Helium

•Once we make deuterium, we continue quickly to continue to helium:

p + n 0 + n 0 n 0 p + n 0 p + n 0 + p + p + n 0 p + n 0 p + n 0 + p + n 0 p + n 0 p + p + n 0 p + + n 0 n 0 p + n 0 p +

Y P

•For every two neutrons, there will be two protons that combine to make 4 He •Mass fraction of 4 He is twice that of neutron fraction     total   2

n n n B

 0.24

• 4 He 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,

Y P

increases weakly:

Y P

  6 10  10  

n B n



Making Other elements

•When you run out of neutrons, 3 He can still be turned into 4 He via

p + n 0 p + + p + n 0 p + n 0 p + n 0 p + + p + + p +

•The last few •As  2 H, 3 He, and •There will be small amount of each of these isotopes left •The more baryons there are, the easier it is to find a partner increases, 2 H, 3 3 H nuclei will have trouble finding partners He, and 3 H all decrease •There are other rare processes that produce a couple of other isotopes : • 7 Li and 7 Be are produced •I don’t understand how they depend on  •Within a few hundred seconds, the baryons are all in 1 H, 2 H, 3 H, 3 He, 4 He, 7 Be and 7 Li

p + n 0 p + n 0 p + n 0 + + n 0 p + n 0 p + n 0 p + n 0 p + p + n 0 p + n p + p n 0 0 + n p + 0 n 0 p + n 0 p + n 0

Anything we missed?

•Two of these isotopes are unstable: •Add 3 H to 3 He and 7 Be to 7 Li 7 Be  3 H

e

   3 He 7 Li   

e



e

 

e

•The process whereby stars make heavier elements do

not

•Density is too low for unstable 8 Be to find  another 4 He to react with 4 He work in the early universe 4 He 4 He  8 Be *   8 Be * 12 C •In the end, we should be able to predict abundance (compared to hydrogen) of 2 H, 3 He, 4 He, 7 Li •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 with predictions •A very strong test of Big Bang theory  

n n B

     10  10

The results

     10  10 •Predictions for 4 He, 2 H and 3 He all work very well •Prediction for 7 Li seems to be off •The Lithium problem •Overall, success for the model

Summary of Events:

Event Neutrinos Decouple Neutron/Proton freezeout 0.7 MeV Electron/Positron Annihilate 170 keV Primordial Nucleosynthesis

k B T

or 1 MeV

T

80 keV Time 0.4 s 1.5 s 30 s 200 s Matter/Radiation Equality Recombination 0.76 eV 0.26 eV 57 kyr 380 kyr Structure formation Now 30 K 2.725 K 500 Myr 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?

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

k B T

• Pions, mass 135-139 MeV, at about

k B T

• At a temperature of about

k B T

= 35 MeV (

g

= 45 MeV (

g

= 4 fermions) = 3 bosons) = 100 MeV, we have quark deconfinement

Quark Confinement

• There are a group of particles called

baryons

• Proton and neutron are examples that have

strong

interactions • 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”

d u

• At low temperatures quarks are

confined

into these packets • •

u

Estimated

k B T

= 150 MeV

u

t

 g eff 

k T B

  2  2.42 s 61.75

MeV 150 MeV 2   5 1.4 10 s

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

k B T

= 50 GeV

t

 g eff 

k T B

  2  2.42 s 100   MeV 50, 000 MeV   2  10  10 s

• Above the electroweak phase transition, all known particles of the standard model should exist with thermal densities

g

eff  28  7 8

The Standard Model

 106.75

• From here on, we will be speculating on the physics • Cosmology sometimes indicates we are guessing right • Goal: Learn physics from cosmology Particle Electron Electron neutrino Up quark Down quark Muon Muon neutrino Charm quark Strange quark Tau Tau neutrino Top quark Bottom quark symbols spin

e



e

½ ½

u u u

½

d d d

  

c c c s s s

  

t t t b b b

½ ½ ½ ½ ½ ½ ½ ½ ½ Photon Gluon W-boson Z-boson 

g g g g g g g g W Z

1 1 1 1 Higgs

H

0 12 4 2 12 12

g

4 2 12 12 4 2 12 2 16 6 3 1

mc

2 (GeV) 0.0005

~0 ~0.005

~0.010

0.1057

~0 1.27

~0.10

1.777

~0 173 4.7

0 0 80.4

91.2

115–285

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 a problem called the

hierarchy problem

• But only if it doesn’t happen at too high an energy • If supersymmetry is right, then scale of supersymmetry breaking probably around

k B T

• If this is right, the LHC should discover it • In most versions of supersymmetry, the lightest super partner (LSP) should be

t

 g eff 

k T B

= 500 GeV or so.

  2  2.42 s 100 MeV  5 absolutely stable Could this be dark matter?

2  10  12 s

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 energy of about 10 16 GeV, the three forces are equal in strength • At

k B T

= 10 16 GeV, there will be another phase transition – the Grand Unification transition

t

 2.42 s 210 MeV 19 10 MeV 2  10  39 s No Supersymmtery With Supersymmtery Baryogenesis might occur at this scale Scale could be right for inflation

Summary of Events:

Event Grand Unification Supersymmetry Scale Electroweak Scale Quark Confinement

k B T

10 16 or

T

GeV 500 GeV 50 GeV 150 MeV Time 10 -39 s 10 -12 s 10 -10 s 1.4

 10 -5 s Neutrinos Decouple Neutron/Proton freezeout 1 MeV 0.7 MeV Electron/Positron Annihilate 170 keV Primordial Nucleosynthesis 80 keV 0.4 s 1.5 s 30 s 200 s Matter/Radiation Equality Recombination 0.76 eV 0.26 eV Structure formation Now 30 K 2.725 K 57 kyr 380 kyr 500 Myr 13.75 Gyr