The Composite Twin Higgs Davide Greco EPFL Higgs Hunting, Paris - - PowerPoint PPT Presentation

The Composite Twin Higgs Davide Greco EPFL Higgs Hunting, Paris - 02/09/2016

The hierarchy problem ◮ After LHC run I, the Higgs boson has been discovered, marking an important step in the understanding of EWSB. ◮ However, in the SM any elementary scalar is unstable under radiative corrections, so the Higgs should be as heavy as the Planck scale. ◮ We may solve the tension between naturalness and the actual Higgs mass by lowering the SM cut-off to a few TeV. ◮ A new dynamics should exist at that scale, endowed with a symmetry protection mechanism that keeps the Higgs mass light.

The Composite Higgs

The composite Higgs potential ◮ The Higgs potential is generated at one-loop due to the Composite-Elementary mixing: q L U Ψ + y R f ¯ L mix = gW α µ J µ α + y L f ¯ t R U Ψ ◮ The biggest contribution comes from the top sector: � �� � y L � 2 � h � � y L � 4 � h V ( h ) ∼ N C 16 π 2 M 4 + b a F 2 F 4 Ψ g ∗ f g ∗ f ◮ The Higgs mass is highly sensitive to the fermionic scale so a light Higgs requires light coloured top partners: H ∼ N C y 2 m 2 8 π 2 M 2 L Ψ

The Twin Higgs

The Twin Higgs potential ◮ The gauging breaks the global symmetry and generates a potential for the Higgs at 1-loop: ∆ V = 9 g 2 Λ 2 64 π 2 H † H + 9 � g 2 Λ 2 H † � 64 π 2 � H . ◮ Imposing the Z 2 symmetry g = � g and the Higgs mass vanishes: � � ∆ V = 9 g 2 Λ 2 H † � H † H + � H . 64 π 2 ◮ At order O ( g 4 ), there are contributions breaking SU (4) and generating a non-vanishing potential: � Λ � g 4 ( H 4 + � H 4 ) . ∆ V = 16 π 2 log gf

The Composite Twin Higgs - Gauge sector

The Composite Twin Higgs potential - Gauge sector ◮ The gauge contribution to the Higgs potential cancels in the Z 2 symmetric limit: � � V ( h ) g 2 = 9 g 2 ∗ f 4 2 sin 2 h 2 cos 2 h g 2 g 2 f + � . 512 π 2 f ◮ The cancellation can be proven by spurion analysis: invariant operators = ( H invariants) - ( G invariants) . ◮ Since for SO (8) / SO (7), 28 = 21 ⊕ 7 , only one operator can appear. ◮ For the original SU (4) / SU (3), 15 = 8 ⊕ 3 ⊕ ¯ 3 ⊕ 1 , there are two invariants and the protection of the Higgs mass is not guaranteed.

The Composite Twin Higgs - Top Sector

The Composite Twin Higgs potential - Top Sector ◮ The Twin mechanism ensures the cancellation of the Higgs potential at order O ( y 2 L ), when y L = � y L . ◮ The relevant terms in the potential arise at order O ( y L ) 4 : ◮ The first is an IR effect corresponding to the running of the Higgs quartic down from the scale m ∗ � � m 2 m 2 V IR ( h ) = N C m t ( h ) 4 log t ( h ) 4 log ∗ ∗ m t ( h ) 2 + m � 16 π 2 t ( h ) 2 m � ◮ The second is pure y 4 L contribution not enhanced by IR logs: � � V y 4 ( H ) ∼ N C L sin 4 h L cos 4 h y 4 y 4 f + � . 16 π 2 f

The full potential ◮ The gauge plus top potential can be rewritten as: � � s 4 log a s 2 + c 4 log a V ( h ) = f 4 β , c 2 y 4 64 π 2 , log a = log 2 µ 2 3 y 4 with β = t f 2 + t F 1 . t L y 2 y 4 ◮ This potential is not realistic: either it does not have tunable minima or a small fine tuning requires an unacceptably large f . ◮ We need to turn on Twin Parity breaking sources; one possibility is not to gauge the Twin Hypercharge.

Realistic EWSB

A light Higgs without colored top partners ◮ We can obtain a naturally light Higgs for � log a ∼ 6 + log ξ. ◮ A realistic value of ξ = 0 . 1 requires a ∼ 5, which can be easily reproduced for g ∗ ∼ 4 π . ◮ Minimal tuning also implies log Λ UV ≥ 50 bB , m ∗ which means a large separation of the two scales.