Baryogenesis from Helical Magnetic Fields Through the EW Phase Transition Andrew Long EWPT Workshop at U Mass Amherst based on 1606.08891 (PRD) April 7, 2017 & 1610.03074 (PRD) in collab. w/ Kohei Kamada
Baryogenesis “by-products” Among the outstanding problems in modern cosmology (dark matter, dark energy, inflation, baryogenesis) … the matter / anti-matter asymmetry is uniquely challenging, because we only know one number (n B /s = 10 -10 )! Therefore it is compelling to study models with “secondary predictions” that we can test in the lab (e.g., EWBG tested by collider observables & EDMs). However, the physics of baryogenesis may not within reach of terrestrial experiments. In this case, we may still probe the origin of the matter / anti- matter asymmetry through observations of baryogenesis “by-products”. Baryogenesis requires a departure from thermal equilibrium (Sakharov), and such conditions may create additional cosmological relics (e.g., gravity waves and topological defects) or the OOE conditions may be provided by other relics (e.g., primordial black holes and primordial magnetic fields). If we could observe these other relics, we would gain a new handle on the origin of the matter / anti-matter asymmetry (more numbers) . April 7, 2017 Andrew Long
Primordial Magnetic Fields The creation of long-range, coherent magnetic generation fields in the early universe has been studied extensively (e.g., Turner & Widrow 1987). The evolution of such fields is studied with evolution sophisticated magnetohydrodynamics simulations. There is a natural connection between magnetic helicity and baryogenesis (SM anomalies). this work However, the mapping from B-field to BAU depends sensitively on the nature of the EW phase transition. The PMF will persist in the universe today as an intergalactic magnetic field (IGMF). Currently there detection is no evidence for an IGMF, but it is being probed by observations of the CMB and TeV blazars. April 7, 2017 Andrew Long
(axion Helical Primordial inHlation, Hyper-magnetic Field etc) Standard Model Quantum Anomalies, Magneto- d.j B = YYdual hydrodynamics EW Phase Transition Final BAU depends sensitively on how B Y converts into B em ! Baryon Asymmetry Intergalactic of the Universe Magnetic Field η B (baryogenesis by-product) η B = n B /s ' 10 − 10 B 0 , λ 0 B 0 April 7, 2017 Andrew Long
E.g., field generation via axion inflation Garretson, Field, & Carroll (1992); Anber & Sorbo (2006) For example, a helical magnetic field may Durrer, Hollenstein, Jain (2010) be generated during inflation from a Barnaby, Moxon, Namba, Peloso, Shiu, & Zhou (2012) Fujita, Namba, Tada, Takeda, Tashiro (2015) pseudo-scalar inflaton (or spectator field). Anber & Sabancilar (2015) axion coupled to EM … rolling sources helicity ... opens kinetic instability ξ ≡ d ϕ /dt fH ✓ ∂ 2 F µ ν = d ϕ /dt − L int = ϕ ◆ ∂η 2 + k 2 ± k ξ 4 f F µ ν e A · B + · · · A ± ( η , k ) = 0 2 f η B today ∼ 10 − 13 Gauss λ today ∼ 10 pc �� �� � �� � λ ���� ( � - � ) ( � � ) �� � �� Lattice simulation �� � � ���� of B-field growth � �� �� � during preheating �� � after axion inflation � �� � Adshead, Gilpin, ��� ��� ��� ��� ��� ��� ��� ��� ��� ��� ��� ��� � - ������� ������ � � - ������� ������ � Scully, Sfakianakis (2016) April 7, 2017 Andrew Long
What is a Helical Magnetic Field? April 7, 2017 Andrew Long
What is a helical magnetic field? Statistically isotropic, stochastic magnetic field: h B i ( t, k ) B j ( t, k 0 ) ⇤ i = P ij ( t, k ) (2 π ) 3 δ (3) ( k � k 0 ) ⇣ ⌘ � ij − ˆ k i ˆ P E ( t, k ) − i ✏ ijm ˆ P ij ( t, k ) = k m P H ( t, k ) k j energy spectrum helicity spectrum (1) Helicity means more power in L- or R-circular pol: L i = P H ( t, k ) (2 π ) 3 δ (3) ( k � k 0 ) h B R B ⇤ R i � h B L B ⇤ (2) Helicity means parity violation Z d 3 k (2 π ) 3 2 k P H ( t, k ) e i k · ( x − x 0 ) h B · r ⇥ B i = April 7, 2017 Andrew Long
What is a helical magnetic field? (3) Helicity measures “topology” of linked flux tubes (Gauss linking number) Moffatt (1969); Berger & Field (1984) Z A · B d 3 x H = I I H = Φ 1 A · d l 1 + Φ 2 A · d l 2 = ± 2 Φ 1 Φ 2 H > 0 H < 0 April 7, 2017 Andrew Long
Changing Helicity The pseudoscalar product describes helicity changes h ∂ �i � � � F µ ν = − 4 E · B = 2 F µ ν e A · B + r · φ B + E × A ∂ t Z F µ ν = 2 ∂ H d 3 x F µ ν e ∂ t Z with A · B d 3 x H = April 7, 2017 Andrew Long
Axial Fermion-Number Generation in QED in the Presence of a Helical Magnetic Field April 7, 2017 Andrew Long
Massless Electrodynamics Let’s think about massless electrodynamics. There are four kinds of particles, classified by their quantum numbers under two charges. chiral charge == helicity ( h = S . p ) electric charge Interactions between these particles and the photons leave the two charges conserved. April 7, 2017 Andrew Long
Bring System to Finite Temperature and Density We are interested in how the various particle densities evolve. (Analogous to baryon number in the Standard Model.) We describe the evolution with a system of Boltzmann equations. (schematic!) These terms account for particle - changing processes like annihilations : These equations encode the electric & chiral charge conservation : April 7, 2017 Andrew Long
Including Quantum Effects When quantum effects are taken into account, the chiral charge is not conserved. This is the well-known chiral (or axial) anomaly of QED [Adler, Bell, Jackiw, ’69] How does this affect our Boltzmann equations? In the presence of a mag. field… The anomaly violates the conservation of chiral charge where the source term is April 7, 2017 Andrew Long
Semi-Classical Understanding (“ quantum effects ”) E - field wants B - field wants p align with qE µ ∼ qS align with B S p p good for both E & B good for both E & B E B April 7, 2017 Andrew Long
Semi-Classical Understanding (“ quantum effects ”) E - field wants B - field wants p align with qE µ ∼ qS align with B S p p good for both E & B good for both E & B E B April 7, 2017 Andrew Long
Diagrammatic Representation E · B > 0 E · B < 0 April 7, 2017 Andrew Long
The Chiral Magnetic Effect In a medium with a chiral asymmetry (nonzero net chiral charge) a magnetic field induces a current in electric charge. Also well-known, [Vilenkin, ’80 … Fukushima, Kharzeev, & Warringa, ’08]. B - field wants electric µ ∼ qS align with B current chiral mag . effect Ohm ’ s law B April 7, 2017 Andrew Long
The Chiral Magnetic Effect In a medium with a chiral asymmetry (nonzero net chiral charge) a magnetic field induces a current in electric charge. Also well-known, [Vilenkin, ’80 … Fukushima, Kharzeev, & Warringa, ’08]. B - field wants electric µ ∼ qS align with B current chiral mag . effect Ohm ’ s law B April 7, 2017 Andrew Long
QED at Finite Density in a Magnetic Field Source term is a pseudo - scalar . electron - positron annihilation Arises in presence of a helical via interactions with photons magnetic field . chiral magnetic effect tends to spin - flip reactions that erase any chiral asymmetry . violate chiral charge conservation , induced Recent applications to early universe: Frohlich & Pedrini, ‘00; by the electron mass Boyarsky, Frohlich, & Ruchaiskiy, ‘12; Pavlovic, Leite, & Sigl, ‘16 April 7, 2017 Andrew Long
QED at Finite Density in a Magnetic Field source washout changing magnetic helicity wants to grow the chiral asymmetry spin - flip and CME want to washout the asymmetry April 7, 2017 Andrew Long
Generation of Baryon- and Lepton-Number from Helical Hypermagnetic Field April 7, 2017 Andrew Long
SM Global Anomalies - Sphaleron Quantum anomalies in the Standard Model relate topology of gauge fields to global charge non-conservation. ‘t Hooft (1976) baryon & lepton number U (1) Y gauge field SU (2) L gauge field The SU(2) L term arises from thermal fluctuations of the SU(2) L gauge fields (EW sphaleron), and it plays a key role in many models of baryogenesis. c R ¯ u L c L t L ¯ t R ¯ W f u R W > 0 ¯ d R ¯ ¯ b R e L µ L τ L s R The EW sphaleron (along with the Yukawa interactions) tend to wash out the baryon-number. Kuzmin, Rubakov, Shaposhnikov (1985) � � n L = − Γ w . o . n B = ˙ ˙ n B + n L April 7, 2017 Andrew Long
SM Global Anomalies – Helicity Quantum anomalies in the Standard Model relate topology of gauge fields to global charge non-conservation. ‘t Hooft (1976) baryon & lepton number U (1) Y gauge field SU (2) L gauge field The U(1) Y source term arises from changing magnetic helicity ν e L , ν µ L , ν τ L × y 2 e R , µ R , τ R × y 2 L e L , µ L , τ L × y 2 e R Y e u R , c R , t R × y 2 L Y > 0 u L , c L , t L × y 2 u R Q d R , s R , b R × y 2 d L , s L , b L × y 2 d R Q Helicity decays because of ohmic losses h Y µ ν ˜ Y µ ν i = � 4 h B Y · r ⇥ B Y i / σ Y b/c E Y = j Y / σ Y ≈ r × B Y / σ Y � � σ Y ∼ 100 T April 7, 2017 Andrew Long
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