Baryogenesis and New Physics How many baryons? The abundances of the primordial elements and the height of the peaks of the CMB power spectrum dependC.E.M. on the ratio Wagner of baryons-to-photons. EFI & KICP , Univ.Strumia of Chicago HEP Division, Argonne National Lab. Fields, Sarkar KICP Colloquium, Univ. of Chicago, February 3rd, 2015 1 Anti-Matter • An inevitable prediction of the marriage of Quantum Mechanics and Special Relativity. Its existence was first postulated by Dirac, in order to make sense of the negative energy states appearing as solutions of the Dirac equation Dirac, 1930 Positrons discovered by C. Anderson in 1932 • Holes of negative energy : Positive energy positrons. • Antiparticles carry the same mass and spin as particles, but opposite charges. Every particle has its antiparticle. Symmetry C (and CP) relates them. Under reasonable assumptions, CPT is a symmetry of nature. • No symmetry prevents the annihilation of matter and anti-matter. So, they don’t coexist easily together. 2 Matter-Antimatter Annihilation 3 The Puzzle of the Matter-Antimatter asymmetry • Anti-matter is governed by the same interactions as matter. • Observable Universe is composed of matter. • Anti-matter is only seen in cosmic rays and particle physics accelerators • The rate observed in cosmic rays consistent with secondary emission of antiprotons n P "10!4 n P 4 Theory vs. Observation Baryons annihilate with anti-baryons via strong interactions mediated by mesons This is a very efficient annihilation channel and the equilibrium density is nB¯ nB 20 = 10− nγ nγ How does this compare to experiment ? First of all, we have the problem of the unobserved antimatter. Secondly, from the analysis of BBN and CMBR, one obtains, consistently 5 BaryonBaryon AbundanceAbundance inin thethe UniverseUniverse ! Information on the baryon abundance comes from two main sources: ! Abundance of primordial elements. When combined with Big Bang Nucleosynthesis tell us n B 421 " = , n! = 3 n! cm ! CMBR, tell us ratio %B !5 2 GeV $#B , %c "10 h 3 %c cm ! There is a simple relation between these two quantities "8 2 # =2.68 10 !Bh 6 How many baryons? The abundances of the primordial elements and the height of the peaks of the CMB power spectrum depend on the ratio of baryons-to-photons. Strumia Fields, Sarkar How to explain the absence of antimatter and the appearance of such a small asymmetry ? 7 SmallMatter Asymmetry and may Anti-Matterbe generated dynamically, at temperaturesEarly belowUniverse the reheating one : Baryogenesis NB=30 000 000 001 NB =30 000 000 000 1,000,000,001 1,000,000,000 t 10−6 s Matter Anti-matter Murayama 54 Assuming the existence of a small primordial asymmetry solves the puzzle. Indeed, matter-antimatter annihilation can now occur efficiently and finally the small asymmetry will lead to observable matter in the Universe 8 8 Matter and Anti-Matter Small Asymmetry may be generated primordially : EarlyBaryogenesis Universe NB=1 NB =0 NB=30 000 000 001 NB =30 000 000 000 1,000,000,001 1,000,000,000 t 10−6 s now Matter Anti-matter Murayama 54 Assuming the existence of a small primordial asymmetry solves the puzzle. Indeed,Now matter-antimatterthe question annihilation is: why can was now there occur efficiently in the and very finally early the small asymmetry will lead to observable matter in the Universe Universe an excess of baryons 9 BaryogenesisBaryogenesisBaryogenesis 9 Baryogenesis ConditionsBaryogenes ifors at Baryogenesisthe weak scale ! Under natural assumptions, there are three conditions, enunciated by Sakharov, that need to be fulfilled for baryogenesis. The SM fulfills them : ! Baryon number violation: Anomalous Processes ! C and CP violation: Quark CKM mixing ! Non-equilibrium: Possible at the electroweak phase transition. 10 Anomalous processes in the SM Non-equivalent Vacua and Static Energy in Field Configuration Space The sphaleron is a static configuration with non-vanishing values of the Higgs and gauge boson fields. Its energy may be identified with the height of the barrier separating vacua with different baryon number The quantity v is the Higgs vacuum expectation value, < H > = v. 8! v E = This quantity provides an order parameter which sph distinguishes the electroweak symmetry gW preserving and violating phases. N &µ j B,L = g Tr( $ µ#!" F F ) µ 32 % 2 µ# !" ∆B =∆L =3 Instanton configuratio∆ns (mBay be rLeg)=0arded as semiclasical configurampationslitudes for tunelling effect− between vacuum states with different baryon number 11 2" Sinst = #%B$0 " exp(!Sinst ) !W Weak interactions: Transition amplitude exponentially small. No observable baryon number violating effects at T = 0 .. At high temperatures,B,L theN barrier can be crossed &µ j = g Tr( $ µ#!" F F ) µ 32 % 2 µ# !" Baryon Number Violation at finite T n AnomalousIns tprocessesanton config uviolaterations mbothay b ebaryon regarde dand as s eleptonmiclasi cnumber,al but configurampationslitudes for tunelling effect between vacuum states with preserve d Biff e–re L.nt bRelevantaryon num forber the explanation of the Universe baryon asymmetry. 2" Sinst = #%B$0 " exp(!Sinst 2) !W n At zero T baryon number violating processes highly suppressed Weak interactions: Transition amplitude exponentially small. No observable baryon number violating effects at T = 0 n At finite T, only Boltzman suppression 4MW T<TEW − T>T EW Tet AtAt largelarge temperatures,temperatures,Klinkhamer and Manton transitionstransitions ’85, Arnold and Mc violatingviolating Lerran ’88 B+LB+L (and(and preservingpreserving B-L)B-L) occuroccur veryvery often.often. 12 SPHALERONS Just toRelevance summarize: of Sphaleron Processes: In SU(5) there existSU(5) gauge Example bosons Xµ whose SU(3), SU(2) and U(1)y quantum numbers are (3, 2,−5/6 ), as well as Higgs• In bosons SU(5) GrandY with Unification quantum Theories,numbers there(3, 1, are 1/3 24 ), and whosegauge couplings bosons, are only similar 12 of to which those belong of the to vectors the SM. Taken from arXiv:hep-ph/0609145 17 13 Baryon number is violated If C and CP are violated, Mean net baryon number produced in the decay of X Mean net antibaryon number produced in the decay of X The resulting baryon asymmetry is: BX ++BX¯ =(r r¯) − 14 Lepton Number In order for this baryon asymmetry to be preserved, there must be departure from thermal equilibrium. Otherwise Γ(X Y )=Γ(Y X) ! ! No baryon asymmetry will be generated Thermal equilibrium broken due to the expansion of the universe, at temperatures below the heavy gauge boson masses Net baryon number will be generated What about lepton number ? L = (1 r),L¯ =(1 r¯) X − − X − L = L + L ¯ =(r r¯) X X − 15 Sphaleron erasure of B Sphaleron processes are in thermal equilibrium at high energies. Since they violate B + L, the sphaleron processes will suppress this quantity But since we started from an initial condition with B - L = 0, and this is preserved, then B + L =0=2B = B =0 ) Generated baryon number is erased ! GUT baryogenesis in SU(5) or other B-L preserving GUT theory doesn’t work. 16 Leptogenesis Baryon asymmetry could be generated if the generated asymmetry carries non-zero B-L charge Sphaleron could be used to our advantage, and we could generate a non-zero baryon charge starting from a net lepton number charge at high energies. Lepton number violation is naturally associated with heavy Majorana right-handed neutrinos. Such particles can a) Explain the smallness of the observed neutrino masses b) Lead to the necessary generation of lepton number via the decay of the Majorana neutrinos. Sphaleron processes convert this lepton number into Baryon number ! 17 Type I see-saw mechanism: Introduce heavy right-handed neutrinos (at least two). it!! See-sawThat 'mechanisms TheAs itmost is well general known, Lagrangian after adding compatible the right-handed with the neutrinos Standard to theModel SM gaugemodel, symmetry one is allowed is: to write Majorana mass terms for these particles Minkowski’77, Yanagida’80, Gell-Man, Ramond, Slansky’80 Naturally small due to the suppression For Yukawa couplings of order one, by smallness the large ofright-handed neutrino massesneutrino may masses be explained by large values of M 18 Lepton number generation 1- Generation of the lepton asymmetry Fukugita, Yanagida’86 At tree level, the total decay rate is: c c The rate for N1 lH and N1 l H are identical. No CP asymmetry: 19 1- Generation of the lepton asymmetry 1- Generation of the lepton asymmetry 1- GenerationAt one of theloop ,lepton new diagrams asymmetry contribute to the decay rate: Generation of a lepton Asymmetry At one loop, new diagrams contribute to the decay rate: At one loop, new diagrams contribute to the decay rate: Interference with the wave-function correction Interference with the vertex correction Tricky! Calculable only when Mi -M1 Gi-G1 Enhanced,Enhancement when of massesthe CP asymmetry are when the closeright-handed (resonant neutrinos leptogenesis) are almost degenerate A lepton (and therefore a B-L) asymmetry is generated by the heavy Majorana neutrino decays. Complex phases necessary 20 Baryon number generation • Several relevant processes in equilibrium at high temperatures, including weak sphalerons (essential), strong sphalerons, gauge and Yukawa processes • The condition of equilibrium leads to a relation between the chemical potential of the Higgs, quark and lepton species 8N +4 Harvey, Turner’90 B = f (B L)in 22Nf + 13 − 14N +9 L = f (B L)in −22Nf + 13 − • Then, for three families of quark and leptons one gets (B L)in nB 2 B − 10− ✏1 ' 3 nγ ' 21 A global fit to neutrino oscillation data Neutrino Masses and Mixing Forero, Tortola, Valle (2014) 22 Parametrization of the “lost” parameters: Work in the basis where the right-handed neutrino mass matrix is diagonal: Relation with Neutrino Phenomenology The most general Yukawa coupling which solves this equation is: Fermion Mass Spectrum Casas,Casas, AI Ibarra’01 Right-handed “Fixed” by neutrino masses experiments 3 real parameters 3 real parameters and 3 phases Ulep 23 1- Upper bound on the CP asymmetry 1- Upper boundConsider on the the scenario CP asymmetry with hierarchical right-handed neutrinos.