Next Frontiers in the Search for Dark Matter GGI, 10/10/2019 C on posite Dynamics in the E as ly Univ es se Luigi Delle Rose 2 Higgs doublets as 2 Higgs doublets as pseudo Nambu-Goldstone bosons pseudo Nambu-Goldstone bosons S. De Curtis, LDR, G. Panico, arXiv:1909.07894 Kei Yagyu Kei Yagyu INFN, U. of Florence INFN, U. of Florence Collaboration with Collaboration with Stefania De Curtis, Luigi Delle Rose, Stefano Moretti Stefania De Curtis, Luigi Delle Rose, Stefano Moretti Scalars 2017, 2 nd Dec, U of Warsaw Scalars 2017, 2 nd Dec, U of Warsaw
Outline The Standard Model (and beyond) at finite temperature The ElectroWeak Phase Transition Composite Higgs models at finite temperature Gravitational wave spectrum and baryogenesis
The Standard Model at finite temperature 50 40 T > T c T = T c 30 V ( ϕ ,T ) T = 0 20 10 0 - 10 - 20 0 100 200 300 400 ϕ [ GeV ] The SM phase transition is a smooth crossover The EW symmetry is restored at T > T c Different scenario if m h ≲ 70 GeV
The effective potential at finite temperature V eff ( ϕ , T ) = V 0 ( ϕ ) + V 1 ( ϕ ) + V T 1 ( ϕ , T ) + V T ring ( ϕ , T ) finite temperature one-loop corrections 2 π 2 J B ( 2 π 2 J F ( ) + ∑ ) n f T 4 m 2 n b T 4 m 2 f ( ϕ ) 1 ( ϕ , T ) = ∑ b ( ϕ ) V T T 2 T 2 b f J B , F ( y ) = ± ∫ dxx 2 log [ 1 ∓ e − ∞ ] x 2 + y the thermal integrals 0 resummation of daisy diagrams ring ( ϕ , T ) = ∑ n b T 12 π [ m 3 b ( ϕ ) − ( m 2 b ( ϕ ) + Π b ( T )) 3/2 ] V T b J B ( y ) = − π 4 45 + π 2 12 y − π 6 y 3/2 + … high-temperature expansion J F ( y ) = − 7 π 4 360 + π 2 24 y + …
New Physics at finite temperature 150 T > T 0 T = T 0 100 V ( ϕ ,T ) 50 T = T c 0 T = T n T < T n - 50 0 100 200 300 400 500 600 ϕ [ GeV ] The EW symmetry is restored at T > T 0 , below T 0 a new (local) minimum appears At a critical T c the two minima are degenerate and separated by a barrier (two phases coexist) The transition starts at the nucleation temperature T n < T c
Bubble nucleation ⟨ h ⟩ = 0 ⟨ h ⟩ ≠ 0 B ≠ 0 CP B ∼ e −⟨ h ⟩ / T
A barrier in the effective potential Tree level effects renormalizable terms: new scalars coupling to the Higgs λ h η h 2 η 2 non-renormalizable operators: c | H | 6 Thermal effects E gets contributions from all the bosonic dof coupled to the Higgs V ( h , T ) ≃ 1 h + cT 2 ) h 2 + λ 4 h 2 − ETh 3 2( − μ 2 E arises from the non-analyticity of J B (y) at y = 0 typical BSM scenario realising 1 st order EWPhT: light stops in the MSSM T = 0 loop effects: large loop corrections from the Coleman-Weinberg potential can h 4 log h 2 generate
New Physics in the Higgs sector DM candidate First order phase transitions Gravitational wave deviations in the spectrum Higgs couplings EW Baryogenesis
New Physics in the Higgs sector DM candidate First order phase transitions Collider - cosmology synergy Gravitational wave deviations in the spectrum Higgs couplings observables at observables at future interferometers future colliders EW Baryogenesis
First order phase transitions key parameters P = T 4 e − S 3 / T Nucleation probability (per unit time and volume) P : Nucleation temperature T n : ∞ for phase transitions at the EW scale ∫ dT T V 4 H P ≃ O (1) S 3 /T n ≈ 140 T n Vacuum expectation value in the broken phase at T n : v n Vacuum energy released in the plasma: α = ϵ / ρ rad Time duration of the phase transition: β /H n S 3 β = T d extracted from the solution H n dT T of the bounce equation T n d 2 ϕ Bubble wall velocity: v w dr 2 + 2 d ϕ dr = ∇ V ( ϕ , T ) r highly non-trivial: requires hydrodynamics modelling of the bubble wall moving in the plasma d ϕ / dr | r =0 = 0 ϕ | r = ∞ = 0
The bounce equation single-field equation V ( ϕ ,T ) can be solved with the overshoot-undershoot method classical motion analogy: - V ( ϕ ,T ) particle at position ɸ moving in time r under the potential -V and a time-dependent friction term ϕ multi-field equation 1.5 trajectory not known: the path is deformed from an initial guess until convergence is reached 1.0 1.4 1.2 ϕ 2 1.0 the bounce is 0.5 0.8 recomputed ϕ 1,2 0.6 along each path 0.4 0.2 0.0 0.0 0.0 0.5 1.0 1.5 0 2 4 6 8 r ϕ 1
The SM + scalar singlet Higgs + singlet effective potential (Z 2 symmetric) in the high-temperature limit 2 h 2 η 2 + ( c h 2 ) T 2 μ 2 V ( h , η , T ) = μ 2 λ η λ h η h 2 η 2 2 h 2 + λ h η 4 h 4 + 2 η 2 + 4 η 4 + h 2 + c η thermal masses (count the dof coupled to the scalars) c h = 1 c η = 1 48 (9 g 2 + 3 g ′ � 2 + 12 y 2 t + 24 λ h + 2 λ h η ) 12(4 λ h η + λ η ) EW symmetry restored at very high T: <h, η > = (0,0) two interesting patterns of symmetry breaking (as the Universe cools down) 1. (0,0) -> (v,0) 1-step PhT 2. (0,0) -> (0,w) -> (v, 0) 2-step PhT 2-step more natural as, typically, c η < c h and the singlet is destabilised before the Higgs
The SM + scalar singlet phenomenology Higgs + singlet (with Z 2 symmetry and m η > m h /2) poorly constrained m η < m h /2 excluded by the invisible Higgs decay direct searches very challenging: need for a 100TeV collider. interesting channel: qq -> qq ηη (VBF) indirect searches: λ 3 λ 3 = m 2 v 3 h η modification to the triple Higgs coupling h 2 v + + … 24 π 2 m 2 η corrections to the Zh cross section at lepton colliders dark matter direct detection the singlet can be a DM candidate constraints are very model dependent. the cosmological history depends on the hidden sector
The SM + scalar singlet nightmare scenario � One - Loop Nonperturbative λ S required Analysis of EWPT for V ( v,0 ) < V ( 0,w ) breaks down ( tree - level ) � with VBF S / B > 2 change of notation: η -> s EWPT one - step EWPT accessed at FCC-hh with 30/ab � - step two σ Zh modified by more than 0.6% λ �� 2 > 0 2 > 0 � μ S μ S accessed at FCC-ee 2 < 0 μ S � λ 3 modified by more than 10% PhT param. space Nonperturbative λ S required to avoid accessed at FCC-hh with 30/ab shrinks if nucl. prob. - � negative runaways ( tree - level ) is taken into account - � ��� ��� ��� ��� ���� � � [ ��� ] Curtin, Meade, Yu, 2015
The SM + scalar singlet change of notation: η -> s In the Z 2 symmetric model, the singlet scalar cannot account for all the DM without any new dark sector Beniwal et al., 2017
EWPhT in Composite Higgs models the basic idea: Higgs as Goldstone boson of G/H of a strong sector
PhTs in Composite Higgs models G phase transition G -> H in the strongly f coupled sector H SM v EW phase transition EM multiple peaks in the GW spectrum?
Basic rules for Composite Higgs models a global symmetry G above f (~ TeV) is spontaneously broken down to a subgroup H G the structure of the Higgs sector is determined f by the coset G/H H H should contain the custodial group SM v the number of NGBs (dim G - dim H) must be larger than (or at least equal to) 4 EM the symmetry G must be explicitly broken to generate the mass for the (otherwise massless) NGBs
Mass spectra g, y elem. G/H SM we borrow the idea from QCD the Higgs could be a kind of pion where we observe that the arising from a new strong sector (pseudo) scalars are the lightest states E E m * ̴ TeV ̴ GeV 𝜛 m h ̴ 100 GeV ̴ 100 MeV π SM g g n n h h h h Higgs mass = + o o r r t t s s
Symmetry structure of the strong sector G H N G NGBs rep.[ H ] = rep.[SU(2) × SU(2)] SO(5) SO(4) 4 4 = ( 2 , 2 ) SO(6) SO(5) 5 5 = ( 1 , 1 ) + ( 2 , 2 ) 4 + 2 + ¯ SO(6) SO(4) × SO(2) 8 4 � 2 = 2 × ( 2 , 2 ) SO(7) SO(6) 6 6 = 2 × ( 1 , 1 ) + ( 2 , 2 ) SO(7) G 2 7 7 = ( 1 , 3 ) + ( 2 , 2 ) SO(7) SO(5) × SO(2) 10 10 0 = ( 3 , 1 ) + ( 1 , 3 ) + ( 2 , 2 ) [SO(3)] 3 SO(7) 12 ( 2 , 2 , 3 ) = 3 × ( 2 , 2 ) Sp(6) Sp(4) × SU(2) 8 ( 4 , 2 ) = 2 × ( 2 , 2 ) , ( 2 , 2 ) + 2 × ( 2 , 1 ) 4 � 5 + ¯ SU(5) SU(4) × U(1) 8 4 + 5 = 2 × ( 2 , 2 ) SU(5) SO(5) 14 14 = ( 3 , 3 ) + ( 2 , 2 ) + ( 1 , 1 ) Mrazek et al., 2011
Symmetry structure of the strong sector Minimal scenario: SO(5)/SO(4) one Higgs doublet G H N G NGBs rep.[ H ] = rep.[SU(2) × SU(2)] SO(5) SO(4) 4 4 = ( 2 , 2 ) SO(6) SO(5) 5 5 = ( 1 , 1 ) + ( 2 , 2 ) 4 + 2 + ¯ SO(6) SO(4) × SO(2) 8 4 � 2 = 2 × ( 2 , 2 ) 0.030 SO(7) SO(6) 6 6 = 2 × ( 1 , 1 ) + ( 2 , 2 ) SO(7) G 2 7 7 = ( 1 , 3 ) + ( 2 , 2 ) 0.025 SO(7) SO(5) × SO(2) 10 10 0 = ( 3 , 1 ) + ( 1 , 3 ) + ( 2 , 2 ) [SO(3)] 3 SO(7) 12 ( 2 , 2 , 3 ) = 3 × ( 2 , 2 ) 0.020 0.0010 Sp(6) Sp(4) × SU(2) 8 ( 4 , 2 ) = 2 × ( 2 , 2 ) , ( 2 , 2 ) + 2 × ( 2 , 1 ) V / f 4 0.015 4 � 5 + ¯ SU(5) SU(4) × U(1) 8 4 + 5 = 2 × ( 2 , 2 ) T = Tc 0.0005 SU(5) SO(5) 14 14 = ( 3 , 3 ) + ( 2 , 2 ) + ( 1 , 1 ) 0.010 0.0000 PhT similar to the SM T = 0 due to the pheno constraint 0.005 0.0 0.1 0.2 0.3 0.4 0.5 ξ = v 2 / f 2 ≲ 0.1 no 1 st order PhT 0.000 unless one allows for a small tilt 0.0 0.5 1.0 1.5 2.0 2.5 3.0 h / f Di Luzio et al., 2019
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