# CP破坏的物理(physics of CP violation)part

Physics of CP Violation (V)
Special Lecture at Tsinghua Univiersity, Beijing, China 21-25 March 2011 Tatsuya Nakada
?cole Polytechnique Fédéale de Lausanne (EPFL)

8) Baryogenesis and CP violation
What do we know? We see no anti-nucleus in the cosmic ray. We se no γ rays from pp annihilation in space. Conclusion No evidence of anti-matter in our domain of universe. 8 (~20 Mps ≈10 light-years) Can our universe be “inverse” Emmental Cheese? matter antimatter Unlikely!! Most likely, no anti matter in our universe. 10 (~3000 Mps ≈10 light-years) Void

Two key numbers

stars, gas etc. ≈ 5×10
10

Number of baryons (nB) Number of photons (nγ)

cosmic microwave background radiation Number of baryons now ≈ 0 but ≠ 0 nγ ≈ (NB + NB)/2 nB = NB NB NB NB
10
_ _

NB(B) initial number of (anti)baryons

NB + NB

≈ 10

10

1 baryon out of 10 did not annihilate and survived.

How can we generate NB NB from NB
_ _

NB + NB _ NB = 0 (initial condition for Big Bang at t = 0)?

≈ 10

10

Necessary conditions: 1) Baryon number violations: initial and ?nal baryon numbers are different. 2) C and CP violation: partial decay widths are different. 3) Out of equilibrium: no reversing reaction installing the initial state.
(A.Sakharov, 1967)

Baryon genesis at very high energy (~1019GeV): a la GUT Universe is expanding very rapidly = out of equilibrium X particles: B non-conserving decays __ X→qq: Γqq, _ X→q : _ q Γ q: quark B=1/3 _ _ X→qq: Γqq, X→q : Γq : lepton B=0 _ _ CPT: Γqq + Γq = Γqq + Γq ≡ Γtot _ CP and C: Γq ≠ Γq =0 ≠0 _ _ _ NB ∝ (2Γqq + Γq )/3 _ _ NB NB = 2(Γtot Γtot )/3 + (Γq Γq ) ≠ 0 _ NB ∝ (2Γqq + Γq )/3 NL NL = (Γq Γq ) = NB NB ≠ 0

+ Simple to explain.
Generated at very early time of universe; B = L asymmetry would have been diluted in the evolution.

Baryon genesis at “low” energy (~102GeV): Physics at electroweak scale: the Standard Model + possibly SUSY, L-R, TC etc. + No asymmetry dilution possible afterwards. + Physics is accessible with the accelerators, Dif?cult to explain.

Baryon genesis at “low” energy (~102GeV): Physics at electroweak scale: the Standard Model + possibly SUSY, L-R, TC etc. + No asymmetry dilution possible afterwards. + Physics is accessible with the accelerators, Dif?cult to explain. In the Standard Model ?? Baryon number violation due to “SU(2) anomaly” → transitions to different vacuum states: ΔL = ΔB
(change in baryon number = change in lepton number)

?? CP violation through the KM phase ?? Out of equilibrium through the ?rst-order phase transition

free energy

L=B=2
ΔL = ΔB = 2

L=B=0
vacua

Fermion number

Boiling Water
phase transition at boiling temperature

water

vapour bubble

Electroweak phase transition

mass-less particles
Symmetric Universe Symmetry broken spontaneously (massive particles)

massive particles

Symmetric Vacuum: <φ> = 0 particles are mass-less High temperature ΔB ≠ 0 process active Thermal equilibrium NB = NB q q NB < NB

Broken symmetry particles are massive Low temperature ΔB = 0 Thermal equilibrium NB > NB q

CP
q

Out of equilibrium

Two problems with the minimal Standard Model: 1) Too heavy Higgs mass In order to have the ?rst-order phase transition: mH < 70 GeV/c2 ~ LEP results: > mH ~ 100 GeV/c2 2) Too small CP violation With KM phase: NB NB
_ _

? 4×1010
20

NB + NB

<

JCKM
12 Tc

≈ 10

Required from N(B)/N(γ) 10 ≈ 10

JCKM ≈ (mt2 mc2)(mt2 mu2)(mc2 mu2) ×(mb2 ms2)(mb2 md2)(ms2 md2) × s1s2s3 sinδ Tc ≈ 100 GeV ? 10
5
skip

T ?rst order phase transition vapour ice

continuous transition water

P critical point T symmetric phase (massless particles) Higgs phase (massive particles) mH

They can be overcome by some “minor” extension of the Standard Model: ??Super Symmetry ??Multi Higgs doublet ??etc... which should appear in “electroweak” energy scale.

Search for new particles, unexpected effects in CP violation and rare decays.

Baryogenesis through leptogenesis Recent results indicate; Neutrinos have masses and mix each other, like quarks. One of the most favoured pictures: Neutrinos are Majorana particles (no experimental evidence) neutrino = anti-neutrino There exists very heavy leptons Heavy right handed Majorana neutrino NR: mR ≈ 1010- 1011 GeV Decays into light leptons are CP violating Γ(NR→L) < Γ(NR→L)

Once the temperature of the universe becomes T < 10 GeV, ~ all the NR decay away: NL < NL lepton number generated; L = NL NL < 0 The Standard Model “SU(2) anomaly” process: L+B → 0: i.e. ΔL > 0 Since ΔL = ΔB, this generates Baryon number B > 0 No electroweak phase transition!!! + elegant + measurable parameters at our energy have no relation to what happens at very high energies. NB: CP violation in ν oscillations cannot make this effect Prob(νi νj) ≠ Prob(νi νj) but ∑i N(νi) = ∑i N(νi)

10

free energy

L = 4, B = 0
ΔL = ΔB = 2

L = 2, B = 2
Fermion number

vacua

Search for new physics via CP violation
(Biased?) Conclusion: A good chance that there exists new sources of CP. What do we look for? Deviation from the Standard Model predictions. Where do we look for? 1) Deviation could be large. example: neutron electric dipole moment 2) The Standard Model predictions are precise. K0 → π0νν Many decay modes in the B meson system

We still need to understand why we did not have disappeared!

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