C on posite Dynamics in the E as ly Univ es se Luigi Delle Rose 2 - - PowerPoint PPT Presentation

Conposite Dynamics in the Easly Univesse

Luigi Delle Rose

2 Higgs doublets as pseudo Nambu-Goldstone bosons Kei Yagyu

INFN, U. of Florence

Scalars 2017, 2nd Dec, U of Warsaw Collaboration with Stefania De Curtis, Luigi Delle Rose, Stefano Moretti

2 Higgs doublets as pseudo Nambu-Goldstone bosons Kei Yagyu

INFN, U. of Florence

Scalars 2017, 2nd Dec, U of Warsaw Collaboration with Stefania De Curtis, Luigi Delle Rose, Stefano Moretti

• S. De Curtis, LDR, G. Panico, arXiv:1909.07894

Next Frontiers in the Search for Dark Matter GGI, 10/10/2019

Outline

The Standard Model (and beyond) at finite temperature The ElectroWeak Phase Transition Composite Higgs models at finite temperature Gravitational wave spectrum and baryogenesis

100 200 300 400

• 20
• 10

10 20 30 40 50

ϕ [GeV] V(ϕ,T)

T = 0 T = Tc T > Tc

The SM phase transition is a smooth crossover The EW symmetry is restored at T > Tc Different scenario if mh ≲ 70 GeV

The Standard Model at finite temperature

Veff(ϕ, T) = V0(ϕ) + V1(ϕ) + VT

1 (ϕ, T) + VT ring(ϕ, T)

The effective potential at finite temperature

VT

1 (ϕ, T) = ∑ b

nbT4 2π2 JB ( m2

b(ϕ)

T2 ) + ∑

f

nfT4 2π2 JF ( m2

f (ϕ)

T2 ) JB,F(y) = ± ∫

∞

dxx2 log [1 ∓ e−

x2 + y

] JB(y) = − π4 45 + π2 12 y − π 6 y3/2 + … JF(y) = − 7π4 360 + π2 24 y + …

finite temperature one-loop corrections the thermal integrals high-temperature expansion

VT

ring(ϕ, T) = ∑ b

nbT 12π [m3

b(ϕ) − (m2 b(ϕ) + Πb(T))3/2]

resummation of daisy diagrams

New Physics at finite temperature

100 200 300 400 500 600

• 50

50 100 150

ϕ [GeV] V(ϕ,T)

T = Tc T = Tn T < Tn T = T0 T > T0

The EW symmetry is restored at T > T0, below T0 a new (local) minimum appears At a critical Tc the two minima are degenerate and separated by a barrier (two phases coexist) The transition starts at the nucleation temperature Tn < Tc

Bubble nucleation

⟨h⟩ ≠ 0 ⟨h⟩ = 0

B ≠ 0 B ∼ e−⟨h⟩/T

CP

Tree level effects renormalizable terms: new scalars coupling to the Higgs non-renormalizable operators: Thermal effects T = 0 loop effects: large loop corrections from the Coleman-Weinberg potential can generate

A barrier in the effective potential

c|H|6 λhη h2η2

V(h, T) ≃ 1 2(−μ2

h + cT2)h2 + λ

4 h2 − ETh3

E gets contributions from all the bosonic dof coupled to the Higgs E arises from the non-analyticity

• f JB(y) at y = 0

typical BSM scenario realising 1st order EWPhT: light stops in the MSSM

h4 log h2

deviations in the Higgs couplings First order phase transitions Gravitational wave spectrum EW Baryogenesis

New Physics in the Higgs sector

DM candidate

deviations in the Higgs couplings

New Physics in the Higgs sector

Gravitational wave spectrum EW Baryogenesis

• bservables at

future colliders

• bservables at

future interferometers

Collider - cosmology synergy

First order phase transitions DM candidate

Nucleation probability (per unit time and volume) P: Nucleation temperature Tn: Vacuum expectation value in the broken phase at Tn: vn Vacuum energy released in the plasma: Time duration of the phase transition: β/Hn

Bubble wall velocity: vw

key parameters

extracted from the solution

• f the bounce equation

d2ϕ dr2 + 2 r dϕ dr = ∇V(ϕ, T) dϕ/dr|r=0 = 0 ϕ|r=∞ = 0

First order phase transitions

P = T4e−S3/T

∫

∞ Tn

dT T V4

H P ≃ O(1)

α = ϵ/ρrad

β Hn = T d dT S3 T

Tn

for phase transitions at the EW scale S3/Tn ≈ 140 highly non-trivial: requires hydrodynamics modelling of the bubble wall moving in the plasma

single-field equation

V(ϕ,T) ϕ

• V(ϕ,T)

multi-field equation

0.0 0.5 1.0 1.5 0.0 0.5 1.0 1.5

ϕ1 ϕ2

2 4 6 8 0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4

r ϕ1,2

can be solved with the

• vershoot-undershoot method

classical motion analogy: particle at position ɸ moving in time r under the potential -V and a time-dependent friction term trajectory not known: the path is deformed from an initial guess until convergence is reached the bounce is recomputed along each path

The bounce equation

The SM + scalar singlet

V(h, η, T) = μ2

h

2 h2 + λh 4 h4 + μ2

η

2 η2 + λη 4 η4 + λhη 2 h2η2 + (ch h2 2 + cη η2 2 ) T2 ch = 1 48 (9g2 + 3g′2 + 12y2

t + 24λh + 2λhη)

cη = 1 12(4λhη + λη)

Higgs + singlet effective potential (Z2 symmetric) in the high-temperature limit thermal masses (count the dof coupled to the scalars) 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, cη < ch and the singlet is destabilised before the Higgs

The SM + scalar singlet

phenomenology

Higgs + singlet (with Z2 symmetry and mη > mh/2) poorly constrained mη < mh/2 excluded by the invisible Higgs decay direct searches very challenging: need for a 100TeV collider. interesting channel: qq -> qq ηη (VBF) indirect searches:

λ3 = m2

h

2v + λ3

hη

24π2 v3 m2

η

+ …

modification to the triple Higgs coupling 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

Curtin, Meade, Yu, 2015

change of notation: η -> s

Nonperturbative λS required for V(v,0) < V(0,w) (tree-level) One-Loop Analysis of EWPT breaks down μS

2> 0

Nonperturbative λS required to avoid negative runaways (tree-level) μS

2< 0

two

• step

EWPT

• ne-step EWPT

μS

2> 0

• []

λ

λ3 modified by more than 10% accessed at FCC-hh with 30/ab with VBF accessed at FCC-hh with 30/ab S/ B > 2 σZh modified by more than 0.6% accessed at FCC-ee PhT param. space shrinks if nucl. prob. is taken into account nightmare scenario

The SM + scalar singlet

Beniwal et al., 2017

change of notation: η -> s

In the Z2 symmetric model, the singlet scalar cannot account for all the DM without any new dark sector

the basic idea: Higgs as Goldstone boson of G/H of a strong sector

EWPhT in Composite Higgs models

G

H SM

EM

f v

PhTs in Composite Higgs models

phase transition G -> H in the strongly coupled sector EW phase transition

multiple peaks in the GW spectrum?

G

H SM

EM

f v

a global symmetry G above f (~ TeV) is spontaneously broken down to a subgroup H the structure of the Higgs sector is determined by the coset G/H H should contain the custodial group the number of NGBs (dim G - dim H) must be larger than (or at least equal to) 4 the symmetry G must be explicitly broken to generate the mass for the (otherwise massless) NGBs

Basic rules for Composite Higgs models

G/H elem. SM

g, y m* mh

E

we borrow the idea from QCD where we observe that the (pseudo) scalars are the lightest states the Higgs could be a kind of pion arising from a new strong sector

̴ TeV ̴ 100 GeV

𝜛 π

E

̴ GeV ̴ 100 MeV

h h h h Higgs mass = +

SM s t r

• n

g s t r

• n

g

Mass spectra

G H NG 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) SO(6) SO(4) × SO(2) 8 4+2 + ¯ 42 = 2 × (2, 2) SO(7) SO(6) 6 6 = 2 × (1, 1) + (2, 2) SO(7) G2 7 7 = (1, 3) + (2, 2) SO(7) SO(5) × SO(2) 10 100 = (3, 1) + (1, 3) + (2, 2) SO(7) [SO(3)]3 12 (2, 2, 3) = 3 × (2, 2) Sp(6) Sp(4) × SU(2) 8 (4, 2) = 2 × (2, 2), (2, 2) + 2 × (2, 1) SU(5) SU(4) × U(1) 8 45 + ¯ 4+5 = 2 × (2, 2) SU(5) SO(5) 14 14 = (3, 3) + (2, 2) + (1, 1)

Symmetry structure of the strong sector

Mrazek et al., 2011

G H NG 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) SO(6) SO(4) × SO(2) 8 4+2 + ¯ 42 = 2 × (2, 2) SO(7) SO(6) 6 6 = 2 × (1, 1) + (2, 2) SO(7) G2 7 7 = (1, 3) + (2, 2) SO(7) SO(5) × SO(2) 10 100 = (3, 1) + (1, 3) + (2, 2) SO(7) [SO(3)]3 12 (2, 2, 3) = 3 × (2, 2) Sp(6) Sp(4) × SU(2) 8 (4, 2) = 2 × (2, 2), (2, 2) + 2 × (2, 1) SU(5) SU(4) × U(1) 8 45 + ¯ 4+5 = 2 × (2, 2) SU(5) SO(5) 14 14 = (3, 3) + (2, 2) + (1, 1) Minimal scenario: SO(5)/SO(4) one Higgs doublet

0.0 0.5 1.0 1.5 2.0 2.5 3.0 0.000 0.005 0.010 0.015 0.020 0.025 0.030

h / f V / f4

0.0 0.1 0.2 0.3 0.4 0.5 0.0000 0.0005 0.0010

T = 0 T = Tc

PhT similar to the SM due to the pheno constraint

ξ = v2/f 2 ≲ 0.1

no 1st order PhT unless one allows for a small tilt

Symmetry structure of the strong sector

Di Luzio et al., 2019

G H NG 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) SO(6) SO(4) × SO(2) 8 4+2 + ¯ 42 = 2 × (2, 2) SO(7) SO(6) 6 6 = 2 × (1, 1) + (2, 2) SO(7) G2 7 7 = (1, 3) + (2, 2) SO(7) SO(5) × SO(2) 10 100 = (3, 1) + (1, 3) + (2, 2) SO(7) [SO(3)]3 12 (2, 2, 3) = 3 × (2, 2) Sp(6) Sp(4) × SU(2) 8 (4, 2) = 2 × (2, 2), (2, 2) + 2 × (2, 1) SU(5) SU(4) × U(1) 8 45 + ¯ 4+5 = 2 × (2, 2) SU(5) SO(5) 14 14 = (3, 3) + (2, 2) + (1, 1) Next to minimal scenario: SO(6)/SO(5)

• ne Higgs doublet

+ a scalar singlet

V (h, ⌘) = µ2

h

2 h2 + h 4 h4 + µ2

η

2 ⌘2 + η 4 ⌘4 + hη 2 h2⌘2

the scalar potential

Symmetry structure of the strong sector

Lint = gJµW µ Lint = yL qL OL + yR tR OR

linear interactions between composite and elementary operators

yL/g* yR/g* g* ytop ≈

L = m∗ ¯ T T + y f ¯ t T

in the IR partial compositeness

4 = (2, 1)+1 (1, 2)1 , 6 = (2, 2)0 (1, 1)+2 (1, 1)2 , 10 = (2, 2)0 (3, 1)+2 (1, 3)2 , 15 = (1, 3)0 (3, 1)0 (1, 1)0 (2, 2)+2 (2, 2)2 , 200 = (3, 3)0 (2, 2)+2 (2, 2)2 (1, 1)+4 (1, 1)4 (1, 1)0 .

SO(6) representation decompositions under

SU(2)L ⊗ SU(2)R ⊗ U(1)η

Partial compositeness

4 — not suitable for the top quark: large ZbLbL coupling 10 — no potential for the scalar singlet η 6, 15, 20’ — viable representations for the top quark (qL, tR) ̴ (6, 6)

typically predicts unless we consider:

(qL, tR) ̴ (15, 6)

λη ≃ 0, λhη ≃ λh/2

large tuning in bottom quark and gauge sectors elementary-composite mixings λqL, λtR, up to the fourth power less-tuned scenario: no need to rely on bottom and gauge but λѱ still at the fourth power large parameter space available without large tuning

(qL, tR) ̴ (6, 20’)

Classification of representations

• ()

() () μη

>

→ η η

Parameter space

Classification of representations

n

• 1

s t

• r

d e r P h T 1st order PhT ?

(qL, tR) ̴ (6, 20’)

Properties of the EWPhT

• =

η =

• /

bubbles fail to nucleate:

the system is trapped in the false metastable vacuum (it may decay to the true EW vacuum at zero temperature)

• the bounce action is

bounded from below

2 step PhT

vn/Tn: strength of the PhT a crucial parameter for EWBG

Properties of the EWPhT

Nucleation and critical temperatures

• =

η =

• β/
• =

η =

• Inverse time

duration of the phase transition

Gravitational waves

fpeak = f* a* a0 ∼ 10−3 mHz ( f* β ) ( β H* ) ( T* 100 GeV) ( g* 100)

1/6

1st order phase transitions are sources of a stochastic background of GW:

bubble collision sound waves in the plasma turbulence in the plasma

f*/β ≡ ( f*/β)(vw) β/H* ≃ 𝒫(102) − 𝒫(103)

• LISA

BBO Ultimate DECIGO DECIGO

• SW

M H D

peak frequencies within the sensitivity reach of future experiments for a significant part of the parameter space GW spectra with non trivial structure

bubble velocity vw taken from

Dorsch, Huber, Konstandin, No, 2017

EW Baryogenesis

η = nB − n ¯

B

nγ ≃ 6 × 10−10

explain matter - antimatter asymmetry baryogenesis at the EW scale is testable (by definition) B violation Out of equilibrium dynamics C and CP violation Sakharov’s conditions

SM

EW sphaleron processes violate B+L EWPhT not first order 𝜀CKM not enough

SO(6)/SO(5)

as in the SM, η is a gauge singlet EWPhT can be 1st order and sufficiently strong CP violation in the coupling

η¯ tt

CP violation from the scalar singlet

an additional source of CPV is present in CHMs due to the non-linear dynamics of the GBs: dim-5 operator can have a complex coefficient

details depend on the fermion embeddings, for instance in the (qL, tR) ̴ (6, 6) case

A phase in the quark mass is generated. The phase becomes physical during the EW phase transition at T ≠ 0, when η changes its vev this is realised in the two-step phase transition (0,0) -> (0,w) -> (v, 0)

yt 2 h ¯ t cos θ 1 − h2 f 2 − η2 f 2 + i sin θ η f γ5 t

a phase in the top mass is generated

• nly when η gets a vev

Ot = yt ✓ 1 + i b f η ◆ h √ 2 ¯ tLtR + h.c.

EW Baryogenesis

• =

η =

• / [-]
• b/f ~ phase in the top mass needed to

guarantee the amount of CPV for EWBG b/f ≲ TeV-1 is enough to reproduce the

• bserved baryon asymmetry

there is a region where EWBG and an observable GW spectrum can be achieved simultaneously

this crucially depends on the bubble wall velocity

caution: if Z2 is broken (w ≠ 0) at T = 0 constrains on the EDM can challenge EWBG

s h t t t e e e

Some future developments

G H NG 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) SO(6) SO(4) × SO(2) 8 4+2 + ¯ 42 = 2 × (2, 2) SO(7) SO(6) 6 6 = 2 × (1, 1) + (2, 2) SO(7) G2 7 7 = (1, 3) + (2, 2) SO(7) SO(5) × SO(2) 10 100 = (3, 1) + (1, 3) + (2, 2) SO(7) [SO(3)]3 12 (2, 2, 3) = 3 × (2, 2) Sp(6) Sp(4) × SU(2) 8 (4, 2) = 2 × (2, 2), (2, 2) + 2 × (2, 1) SU(5) SU(4) × U(1) 8 45 + ¯ 4+5 = 2 × (2, 2) SU(5) SO(5) 14 14 = (3, 3) + (2, 2) + (1, 1) Next to minimal scenario: SO(6)/SO(4)xSO(2) 2 Higgs doublets Composite 2HDM

ˆ T / 16 ⇥ v2 f2 ⇥ Im[hH1i†hH2i]2 (|hH1i|2 + |hH2i|2)2 .

The predicted leading order correction to the T parameter arises from the non-linearity of the GB Lagrangian. In the SO(6)/SO(4)xSO(2) model is possible solutions: CP (assumed here) C2: ( H1 → H1, H2 → -H2 ) which forbids H2 to acquire a vev

no freedom in the coefficient, fixed by the coset

Custodial symmetry Higgs-mediated FCNCs

FCNCs can be removed by

• 1. assuming C2 in the strong sector and in the mixings
• 2. requiring (flavour) alignment in the Yukawa couplings

Y IJ

1

∝ Y IJ

2

inert C2HDM

⊃ Y ij

u Qiuj

a1uH1 + a2uH2) + Y ij

d Qidj

a1dH1 + a2dH2) + Y ij

e Liej

a1eH1 + a2eH2) + h.c. the ratio a1/a2 is predicted by the strong dynamics

(not considered here)

need to be relaxed for EWBG

C2HDM - the scalar potential

the entire effective potential is fixed by the parameters of the strong sector and the scalar spectrum is entirely predicted by the strong dynamics

yL,R yL,R

V = m2

1H† 1H1 + m2 2H† 2H2 −

h m2

3H† 1H2 + h.c.

i + λ1 2 (H†

1H1)2 + λ2

2 (H†

2H2)2 + λ3(H† 1H1)(H† 2H2) + λ4(H† 1H2)(H† 2H1)

+ λ5 2 (H†

1H2)2 + λ6(H† 1H1)(H† 1H2) + λ7(H† 2H2)(H† 1H2) + h.c.

C2 breaking in the strong sector induces:

m2

3 6= 0, λ6 6= 0, λ7 6= 0

λ6 = λ7 = 5

3 m2

3

f2

it is not possible to realise a 2HDM-like scenario with a softly broken Z2 the potential up to the fourth order in the Higgs fields: very strong correlations among several parameters

Conclusions

Higgs as a pseudo Nambu-Goldstone Boson is a compelling possibility for stabilising the EW scale Non-minimal CHMs can link the dynamics of a strong first order EWPhT to the structure of GW spectrum and the possibility to realise EW Baryogenesis Future collider and space-based gravitational interferometry experiments can provide complementary ways to test the Higgs sector