Phase transitions in cosmology Thomas Konstandin FujiYoshida, August 31, 2017
Electroweak phase transition gravitational waves baryogenesis
Outline Introduction MSSM Composite Higgs
Baryogenesis [Sakharov '69] Baryogenesis aims at explaining the observed asymmetry between matter and antimatter abundances. The main ingredients for viable baryogenesis are stated by the celebrated Sakharov conditions: Bnumber violation (baryonnumber) C and CP violation (charge/parity) outofequilibrium
Baryogenesis [Sakharov '69] Baryogenesis aims at explaining the observed asymmetry between matter and antimatter abundances. C and CP violation (charge/parity) outofequilibrium Bnumber violation (baryonnumber) The main ingredients for viable baryogenesis are stated by the celebrated Sakharov conditions:
Baryogenesis [Sakharov '69] Baryogenesis aims at explaining the observed asymmetry between matter and antimatter abundances. outofequilibrium C and CP violation (charge/parity) Bnumber violation (baryonnumber) The main ingredients for viable baryogenesis are stated by the celebrated Sakharov conditions:
Baryogenesis [Sakharov '69] Baryogenesis aims at explaining the observed asymmetry between matter and antimatter abundances. outofequilibrium C and CP violation (charge/parity) Bnumber violation (baryonnumber) The main ingredients for viable baryogenesis are stated by the celebrated Sakharov conditions:
Baryogenesis [Sakharov '69] Baryogenesis aims at explaining the observed asymmetry between matter and antimatter abundances. C and CP violation (charge/parity) outofequilibrium Bnumber violation (baryonnumber) The main ingredients for viable baryogenesis are stated by the celebrated Sakharov conditions:
Baryogenesis [Sakharov '69] Baryogenesis aims at explaining the observed asymmetry between matter and antimatter abundances. SM @ EW temp C B BL anomaly CP Jarlskog invariant eq expansion slow EW PT? sphaleron beyond the SM physics essential
eq Firstorder phase transition The free energy (as a function of the Higgs vev) decides the nature of the phase transition: secondorder crossover firstorder
eq Firstorder phase transitions firstorder phase transitions proceed by bubble nucleations in case of the electroweak phase transition, the Higgs bubble wall separates the symmetric from the broken phase this is a violent process ( ) that drives the plasma outofequilibrium bosons that are strongly coupled to the Higgs tend to make the phase transition stronger
Electroweak baryogenesis [Kuzmin, Rubakov, Shaposhnikov '85] [Cohen, Kaplan, Nelson '93] B i diffus eq CP on C
Electroweak baryogenesis [Kuzmin, Rubakov, Shaposhnikov '85] [Cohen, Kaplan, Nelson '93] CP ion s u f f i d
Electroweak baryogenesis [Kuzmin, Rubakov, Shaposhnikov '85] [Cohen, Kaplan, Nelson '93] B C CP ion s u f f i d
Electroweak baryogenesis [Kuzmin, Rubakov, Shaposhnikov '85] [Cohen, Kaplan, Nelson '93] B C CP e e ion s u f f i d
Electroweak baryogenesis [Kuzmin, Rubakov, Shaposhnikov '85] [Cohen, Kaplan, Nelson '93] B avoid washout: e CP e ion s u f f i d B
Why is this interesting? The hierarchy problem indicates that there is some BSM physics at EW scales Electroweak baryogenesis involves only physics at the electroweak scale that is accessible to collider experiments Electroweak baryogenesis leads naturally to the observed baryon asymmetry beyond SM?
What are the challenges? [Kuzmin, Rubakov, Shaposhnikov '85] [Cohen, Kaplan, Nelson '93] sphaleron (EW anomaly) B i diffus on CP quantum mechanics statistical physics
Detour
Semiclassical reflection Many particles change their mass when passing into the Higgs bubble wall frame and reflection when
Transport equations In case of a statistical system with particle distribution function the change in momentum and translates into or flow term force transport equation of Boltzmann type CP?
Inin formalism Usually in QFT, we integrate time from negative infinity to positive infinity
Inin formalism At finite temperature, one has to integrate into the imaginary direction to obtain the Euclidean Lagrangian
Inin formalism For out of equilibrium, one has to integrate along a closed time path. This can be expressed through an additional 2x2 matrix structure.
KadanoffBaym equations [Kadanoff, Baym '61] The KadanoffBaym equations are a statistical generalisation of the SchwingerDyson equations of QFT (SchwingerKeldysh formalism) Formally the equation looks like SD, but The 2point function depends on x and y seperately X and p in Fourier (Wigner) space There is an additional 2x2 structure from the ininformalism
KadanoffBaym equations In Wigner space this leads to the Moyal star product With One of the Green functions (Wightman function) encodes the particle distribution function and is in equilibrium given by and
One fermion flavor For one fermion flavor with a spacetime dependent mass, the KadanoffBaym equation reads In order to do progress analytically, one typically uses several approximations/techniques: 1) Neglect most interactions: 2) Planar approximation (z): 3) Gradient expansion: [Kainulainen, Prokopec, Schmidt, Weinstock '02]
One fermion flavor For one fermion flavor with a spacetime dependent mass, an expansion in gradients leads to the equations and with and spins s forces CP [Cline, Joyce, Kainulainen '00] [Kainulainen, Prokopec, Schmidt, Weinstock '02] decays scatterings
Detour
Ingredients 1 2 eq CP Strong firstorder electroweak phase transition Some fermion species that changes its mass in a CP violating way during the electroweak phase transition (and prefereably charged under )
Summary i diffus B CP on B
Outline Introduction MSSM Composite Higgs
MSSM CP In the minimal supersymmetric standard model, the leading CP violation comes from the mass matrix of the charginos eq The strength of the electroweak phase transition is reduced by larger Higgs masses is enhanced by bosonic degrees of freedom that couple strongly to the Higgs stops important
CP Several flavours In the most prominent case (MSSM), CP violation results from mixing effects between different flavors. [Careno, Moreno, Quiros, Seco, Wagner '00] In this case, new CPviolating sources occur but also additional complications arise due to flavor oscillations gradient expansion? [TK, Prokopec, Schmidt '05]
MSSM Assuming a strong firstorder phase transition, the baryon assymetry depends mostly on the chargino mass and the CP violation in the chargino sector [TK, Prokopec, Schmidt, Seco '05]
MSSM In the minimal supersymmetric standard model, the leading CP violation comes from the mass matrix of the charginos Flavor mixing? Resonances? Higgs resummation? 10 1 08/11 05/05 04/12 02/08 00/06 Higgs transport? 100 00/01 Flavor oscillations? for maximal CPV
Electric dipole moments Even if all sfermions are heavy, there are twoloop (BarrZee) contributions from the chargino to the EDM of the electron and the neutron [Chang, Chang, Keung '02]
EDMs Even if all sfermions are heavy, there are twoloop (BarrZee) contributions from the chargino to the EDM of the electron and the neutron 8.8% 7.5% 6.6% 5.8% 5.3% 4.7% 4.4% [Hudson et al. '11] 4.3% [Chang, Chang, Keung '02]
MSSM baryogenesis [Hudson et al. '11] The EDM constraints translate into 100 10 1 08/11 05/05 04/12 02/08 00/06 00/01
Chargino driven MSSM baryogenesis ruled out [Baron et al. '13] The EDM constraints translate into 100 10 1 08/11 05/05 04/12 02/08 00/06 00/01 Caveat: EDM bounds avoided by using binos [Li, Profumo, RamseyMusolf '08]
eq Phase transition MSSM phase transition after LEP: very heavy lefthanded stop required no color breaking [Carena, Nardini, Quiros, Wagner '08]
eq Phase transition no color breaking [Carena, Nardini, Quiros, Wagner '08] you are here! MSSM phase transition after LEP: very heavy lefthanded stop required and hide righthanded stop from LHC
Conclusions MSSM Electroweak baryogenesis in MSSM is ruled out, since it relied on Light (< 200 GeV) and almost mass degenerate charginos or binos CP violation for charginos that in the most optimistic cases in conflict with EDM measurements (caveat: binos) very light stops required for a strong firstorder phase transition (extended Higgs sector?)
Outline Introduction MSSM Composite Higgs
Composite Higgs models The Higgs could be a PseudoGoldstone boson of a broken global symmetry QCD: The broken symmetry will determine the light degrees of freedom and their quantum numbers but also [Kaplan, Georgi '84]
Holographic techniques in composite Higgs models Lately, this old idea underwent a renaissance due to holographic models to determine some quantity of the strongly coupled theory (like the Higgs potential) in a 5D setup. [Contino, Nomura, Pomarol '03] [Agashe, Contino, Pomarol '04] 5D GIM mechanism for flavor problems oblique parameters better than in technicolor many parameters and a certain arbitrariness in the scalar sector
Ingredients Two ingredients of baryogenesis are missing in the Standard Model. These are provided in models that have an additional singlet in the low energy effective description eq Strong firstorder electroweak phase transition CP CP violation from dimensionfive operators
eq Phase transition The construction of a potential barrier and hence firstorder phase transitions are easily achieved in extended scalar sectors: For example consider deformations of the symmetric supermexicanhat that has a phase transition
CP CP violation During the phase transition this leads to a top mass of the form So, the complex phase during the phase transition behaves as This is a one flavor system and the BAU can be reliably determined with the semiclassical force approach.
Baryogenesis strength of CP violation strength of the phase transition [Espinosa, Gripaios, TK, Riva '11]
Signals Higgssinglet mixing ~ CP violation singlet mass [Espinosa, Gripaios, TK, Riva '11]
Conclusions composite Higgs Baryogenesis in composite Higgs models is generically possible if the sector of pseudogoldstone bosons is nonminimal. In the case of a scalar extension of the low energy theory, this leads to rich phenomenology traces of CP violation in terms of EDMs no (Higgssinglet mixing; singlet is not DM)
Conclusions Electroweak baryognesis is still a compelling framework to explain the observed baryon asymmetry. Higgs found No EDMs No minimal SUSY
End of lecture 1 Credits: Gojipedia, the Godzilla Wiki