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Baryon Asymmetry of the Universe

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Baryon Asymmetry of the Universe Baryon asymmetry of the Universe Alexey Boyarsky PPEU 2014 1 Observed matter-antimatter asymmetry Main questions: Why do the Earth, the Solar system and our • galaxy consists of of matter and not of antimatter? Why we do not see any traces of antimatter in the universe except • of those where antiparticles are created in collisions of ordinary particles? This looks really strange, as the properties of matter and antimatter • are very similar. Alexey Boyarsky PPEU 2014 2 Baryon asymmetry of the Universe There are two possibilities: Observed universe is asymmetric and does not contain any • antimatter The universe consists of domains of matter and antimatter • separated by voids to prevent annihilation. The size of these zones should be greater than 1000 Mpc, in order not to contradict observations of the diffuse γ spectrum. The second option, however, contradicts to the large scale isotropy of the cosmic microwave background. Thus, we are facing the question: Why the universe is globally asymmetric? Alexey Boyarsky PPEU 2014 3 γ-rays from antiproton annihilation 100 -1 ] 10 -1 sr -1 10-2 MeV -1 s -2 10-3 10-4 COMPTEL -5 Schönfelder et al. (1980) Flux [photons cm 10 Trombka et al. (1977) White et al. (1977) 10-6 1 10 Photon Energy [MeV] Data and expectations for the diffuse γ-ray spectrum (upper curve d = 20 Mpc, lower curve d = 1000 Mpc) Alexey Boyarsky PPEU 2014 4 Antiprotons in the universe Example: antiproton-to-proton fraction in GeV: 10−7 10−3 − Alexey Boyarsky PPEU 2014 5 Positrons in the universe Example: positron-to-electron fraction in GeV: 0:02 0:2 − Alexey Boyarsky PPEU 2014 6 IF THERE ARE NO ANTI-BARYONS NOW, WHAT KIND OF ASYMMETRY THIS IMPLIES IN THE EARLY UNIVERSE? Alexey Boyarsky PPEU 2014 7 Thermal history of baryon asymmetry nB−nB¯ The baryon asymmetry ∆B = today is very close to 1 • nB+nB¯ How did it evolve? What was its value in the earlier times? • Any quark (actually, any particle) is present in the plasma if T mq, • & because of the annihilation processes q+¯q γ+γ (or q+¯q g+g) n − n B B n + n B B 1 annihilation of symmetric background η B −6 10 s t Alexey Boyarsky PPEU 2014 8 Thermal history of baryon asymmetry At early times for each 1010 quarks there is 1010 1 antiquark. • − Symmetric quark-antiquark background annihilates into photons • and neutrinos while the asymmetric part survives and gives rise to galaxies, stars, planets. Alexey Boyarsky PPEU 2014 9 Sakharov conditions Sakharov: To generate baryon asymmetry of the Universe 3 conditions should be satisfied I. Baryon number should not be conserved II. C-symmetry and CP-symmetry must be broken III. Deviation from thermal equilibrium in the Universe expansion Alexey Boyarsky PPEU 2014 10 Sakharov conditions-I If baryon number is conserved, then in every process • 1 + 2 + χ1 + χ2 + ::: left hand side and right hand side···! contain equal number of (baryons - anti-baryons) Experimentally we see that baryon charge is conserved in particle • physics processes. As a consequence proton (the latest baryon) is stable (proton • lifetime > 6:6 1033 years for decays such as p π0 + e+ or p π0 + µ+.× This bound is 5 1023 times longer than! the age of the! Universe × The conservation of baryon number would mean that the total • baryon charge of the Universe remains constant in the process of evolution. If initial conditions were matter-antimater symmetric – no baryon • asymmetry could have been generated Alexey Boyarsky PPEU 2014 11 Sakharov conditions-I Problem. Taking the lower bound on the proton’s lifetime as its actual lifetime, compute the amount of water one would need to observe 1 proton decay during 10 years. Alexey Boyarsky PPEU 2014 12 New interactions violating baryon number Postulate new interaction mediated but a massive gauge boson (X- • boson), transforming quarks to leptons: X q + ` (similar to W ! boson in electroweak theory where W e +ν ¯e) ! As a consequence, the processes with X-boson exchange violate • the baryon number For example, the protons may decay. • The proton decays mediated by X-boson: p e+ + π0 ) ! + p ν¯e + π ) ! Alexey Boyarsky PPEU 2014 13 New interactions violating baryon number The proton lifetime can be estimated as (similar to muon decay): • 2 2 −1 αX 5 −1 αW 5 τp 2 mp τµ 2 mµ ∼ MX ∼ MW 33 Existing experimental bounds on the proton lifetime: τp & 10 yrs • 16 gives MX & 10 GeV. Yukawa couplings may violate CP (Sakharov conditions). • However, this mechanism requires new physics at E MX ... • ∼ Can we generate baryon number at lower energies? YES! Alexey Boyarsky PPEU 2014 14 Quantum anomalies (violation of classical symmetries at quantum level) Alexey Boyarsky PPEU 2014 15 Chiral symmetry Massless fermions can be left and right-chiral (left and right • moving): 0 ! ¨¨* ¨m i(@ + ~σ ~ ) µ ¨¨H ¨ t L (iγ @µ ¨mH) = − ·0r = 0 ¨¨* − i(@t ~σ ~ ) ¨m R − · r ¨− where γ5 R;L = R;L and γ5 = iγ0γ1γ2γ3 ± iα iβ Two global symmetries: L e L and R e R • ! ! According to the Nother¨ theorem, one can define two independently • conserved charges that we call the number of left-movers NL = R 3 y R 3 y d x L L and the number of right-movers NR = d x R R. Linear combinations of these charges are known as fermion number NL + NR ¯ µ µ (current γ ) and axial fermion number NL −NR (current ¯γ γ5 ). Again, both are conserved independently in the free theory Alexey Boyarsky PPEU 2014 16 Axial anomaly Gauge interactions respects chirality (Dµ = @µ + eAµ). • ! 0 i(Dt + ~σ D~ ) L · = 0 i(Dt ~σ D~ ) 0 R − · The symmetry ! eiα(x) is gauged, but the Lagrangian seemingly still iα iβ preserves both global symmetries: L ! e L and R ! e R . but the difference of left and right-movers is not conserved • anymore: Z 2 Z d(NL NR) 3 5 e 3 − = d ~x @µj = d ~x E~ B~ = 0 dt µ 2π2 · 6 . if one takes into account quantum corrections Alexey Boyarsky PPEU 2014 17 Reminder: Landau levels Recall: particle in the uniform magnetic field , parallel to z axis: • B~ = (0; 0;B) Take Dirac equation coupled to the gauge potential A~ = (0; Bx; 0) • Conserved quantities: energy, momenta py; pz • Take the square of the Dirac equation to get: • 2 d 2 2 2 + (eBx py) 2eBsz φ = (E p )φ (1) −dx2 − − − z 1 Spin projection sz = ±2 The l.h.s. of (1) is just a Schodinger¨ equation for the harmonic • oscillator with the frequency ! = 2eB, whose origin is shifted by eB ± 1 The energy levels of harmonic oscillators n = !(n + ), n 0 • 2 ≥ Alexey Boyarsky PPEU 2014 18 Reminder: Landau levels Therefore, the spectrum of Eq. (1) is given by • 2 2 E p = eB(2n + 1) + 2szeB (2) n − z Spectrum has three quantum numbers: • B n = 0; 1; 2 ::: B pz + −∞ ≤ 1 ≤ 1 sz = B ±2 1 Consider n = 0. For sz = the spectrum (2) becomes • −2 2 2 E = pz massless 1-dimensional fermion (3) 1 for sz = +2 there is no massless mode For n > 0 there is no cancellation between eB(2n + 1) and 2szeB • term Alexey Boyarsky PPEU 2014 19 Chiral anomaly Right particle with electric charge eR in magnetic field B Landau energy levels Asymmetric branch on n=0 Landau level E(p )= cp Chiral anomaly explained z z Ε(pz) Consider Landau levels: • n=2 2 2 ~ E = pz + eB(2n + 1) + 2eB ~s · n=1 Particles with B~ ~s < 0 have • · n=0 massless branches: pz e R pz move down along z-axis E = − pz move up along z-axis Dirac vacuum all states E < 0 • are filled: $ B E = pz < 0 ~p ~s< 0 – left n=-1 particles− ) · B E = pz < 0 ~p ~s> 0 – right n=-2 particles ) · Particles creation from vacuum Alexey Boyarsky PPEU 2014 20 left particles can In applied electric field E : compensate the effect • if pz = eRE left-right symmetry is exact Particles from negative energy levels of Dirac vacuum are pushed into positive energy levels of matter • n π2 2 2 = (1 / 4 ) [(eR) - (eL) ] E•B MACIEJ KOCH-JANUSZ AND ZOHAR RINGEL PHYSICAL REVIEW B 89,075137(2014) vanishing of the partition function Eq. (5), exactly as in the 2D many-body system, depicted in Fig. 1(d) as a function of flux, case. exhibits a level crossing at π flux. The presence of a crossing in the spectrum as a function of flux is a robust feature of the many-body spectrum, even III. ROBUSTNESS OF THE Z2 CHIRAL ANOMALY in the presence of interactions. Indeed, provided that TRS TO INTERACTIONS is not explicitly broken and that edges remain decoupled, In this section, we show that the Z2 anomaly is robust to the Karmer’s degeneracy point at π flux cannot be removed. electron-electron interactions provided that (i) the bulk gap Thus, provided that the flux insertion is carried at a rate much remains open and (ii) there is no direct coupling between slower than the splitting at φ 0, a level crossing occurs and = the gapless boundaries. Specifically, the orthogonality relation the ground state evolves into an excited state. Notably, this implied by Eqs. (6)and(7)holdsalsoforinteractingTIs. argument holds also in the presence of a spontaneous TRS Another way to phrase it is to say that the boundary of an breaking on the edge—in this case, the two states which cross interacting TI always supports a low-lying state which can be will be the two symmetry-related ground states.
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