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Lecture-06 Baryogenesis Ping He ITP.CAS.CN 2006.04.21 http://power.itp.ac.cn/~hep/cosmology.htm 1 6.1 Overview Grand unification (Grand unified theories – GUTs): to unify the strong, weak, and electromagnetic interactions and the quarks and leptons within the framework of a gauge field theory based upon a simple or semi-simple, non-Abelian symmetry group, e.g., SU(5), SO(10), E6. Standard model: SU (3)c SU (2) L U (1)Y GUTs predictions: (1) new interactions violate baryon number B and lepton L conservations, -- instability of the proton proton decay; (2) large amount of superheavy magnetic monopoles. The B-violation interactions are extremely weak today, due to the longevity of proton. GB M 2 1030 GeV 2 , GF 1.1664 105 GeV 2 (Eq-6.1) 2 M: the energy scale of unification M 1014 GeV Baryogenesis, based on these B-violation interactions: (1) can explain how the B-symmetry Universe can evolve into the B-asymmetry Universe; (2) can explain the present baryon-to-photon ratio; (3) can provide a mechanism to unify quarks and leptons. Predictions from baryogenesis based on GUTs conflicts with standard cosmology, that there are too much superheavy monopoles that are not observed. inflation 3 6.2 Evidence for a Baryon Asymmetry Anti-matter is rare on Earth, only in accelerator or cosmic ray. Also rare in the solar system, cosmic ray coming from the galaxy indicates that the galaxy is not anti-matter. On large scales: if matter and anti-matter co-exist, then there are strong gray emission from nucleon-antinucleon annihilation. The absence of such gray flux indicates the asymmetry of matter and anti-matter. In a locally-baryon-symmetric Universe nucleons and antinucleons remain in chemical equilibrium down to T ~ 22 MeV, when nb / s nb / s 7 1020 , In order to avoid the “annihilation catastrophe” a physical mechanism 11 should operate at T > 38 MeV, so that nb / s nb / s 8 10 . 4 The most reasonable conclusion then is that the Universe at early times T>38MeV possessed an asymmetry between baryons and antibaryons which prevented the annihilation catastrophe. At high temperatures T>1GeV, thermal quark-antiquark pairs were present in great numbers, nq ~ nq ~ ng , so that the baryon asymmetry observed today corresponds to a tiny quark-antiquark asymmetry at early times ( t 10 6 s ). nq nq nq 3 108 (Eq-6.2) Baryogenesis scenario provides a very attractive means by which this tiny asymmetry can arise from initially baryon symmetric Universe. 5 6.3 The Basic Picture Three ingredients to generate non-zero baryon number from an initially baryon symmetric state, i.e., Sakharov Criteria: (1) Violation of Baryon number (B) symmetry; (2) Violation of C and CP symmetries; (3) A departure from thermal equilibrium. 1). It’s obviously. If baryon number is conserved in all interactions, the present baryon asymmetry can only reflect asymmetric initial conditions. 2). Without C and CP violation, B-nonconserving interactions will produce baryon and antibaryon excesses at the same rate zero net baryon number. 3). In chemical equilibrium, the chemical potentials associated with all non-conserved quantum numbers vanish, that is, b b 0, by CPT invariance, mb mb , so, f (b) f (b ) [1 exp(( p 2 m2 ) / T )]1 hence nb nb , nB nb nb 0 (Eq-6.3) 6 A toy model: to illustrate the mechanics of baryogenesis. particle final state branching ratio B X qq r 2/3 X ql 1- r -1/3 X qq r -2/3 X ql 1- r 1/3 Since the two final states have different baryon number, B-nonconservation. If C and CP are violated, then r r . symmetric initial conditions X and X bosons. The mean net baryons produced by X is: BX r (2 / 3) (1 r )(1/ 3) If a box containing equal numbers of produced by X : BX r (2 / 3) (1 r )(1/ 3) The mean net baryon number produced by a pair of X and X decay is BX BX r r 0 (C and CP violated) (Eq-6.4) 7 can be treated as indication of the degree of C and CP violation. When T mX , X and X can decay, but can also produce in pair in thermal collision, then: nX nX If always in thermal equilibrium, the process that produces baryon excess balance the one that perishes baryon nb nb when out-of-equilibrium ( H ), due to B, C and CP violation, nb nb (Eq-6.5) The asymmetry can be roughly estimated in the following way nb nb nX A nb nb (Eq-6.6) The correct way to do so should be handled by Boltzmann equation, which may have deviations of several orders of magnitude. 8 6.4 Concluding Remarks (1) Sakharov Three Criteria, but notice the scenario of spontaneous baryogenesis; (2) The precise evolution of the baryon asymmetry is handled by Boltzmann Equation; (3) Lepton-genesis can be treated in a similar way; (4) The current GUTs are not successful. 9 References • E.W. Kolb & M.S. Turner, The Early Universe, Addison-Wesley Publishing Company, 1993 • D. Bailin & A. Love, Cosmology in Gauge Field Theory and String Theory, IoP Publishing, 2004 • 俞允强,热大爆炸宇宙学,北京大学出版 社,2001 • 范祖辉,Course Notes on Physical Cosmology, See this site. 10