Higgs Alignment from Extended Supersymmetry Sophie Williamson LPTHE, Sorbonne Universit´ e, CNRS Based on work in collaboration with Karim Benakli and Mark Goodsell (arXiv:1801.08849) LSPC Grenoble, 14 th March 2018 Sophie Williamson (LPTHE Paris) Higgs Alignment from N = 2 LSPC Grenoble, 14/03/18 1 / 43
A la carte Introduction • Higgs alignment • Dirac Gaugino models • N = 2 supersymmetry Alignment in the MDGSSM • Low energy Two-Higgs Doublet Model limit • Causes of misalignment • Precision Study and results • Experimental Constraints Simplified MRSSM analysis Sophie Williamson (LPTHE Paris) Higgs Alignment from N = 2 LSPC Grenoble, 14/03/18 2 / 43
Motivation Absence of strongly-coupled particles at the LHC → interest in new electroweak-coupling particles. Is the Higgs boson part of a larger scalar sector? Strong LHC constraints imply the heavy Higgs should be aligned with or decoupled from the SM-like one. Interested in theories where alignment is untuned. Could finding a second Higgs doublet unveil a full SUSY theory? If SUSY is discovered, is R-symmetry conserved? Sophie Williamson (LPTHE Paris) Higgs Alignment from N = 2 LSPC Grenoble, 14/03/18 3 / 43
Higgs Alignment In minimal SUSY: Two complex SU (2) Higgs doublets - H u , EWSB ⇒ 5 physical Higgs bosons: h , H , A , H ± . H d = = = However: strong contraints on Higgs couplings from experiment. Higgs Alignment : Mass eigenstates align with the VEV → SM-like Higgs. Sophie Williamson (LPTHE Paris) Higgs Alignment from N = 2 LSPC Grenoble, 14/03/18 4 / 43
Alignment without decoupling Keep m H light (possible LHC detection). Choosing masses/quartic couplings from the bottom-up → alignment is not generic. Interested in deriving the THDM couplings from the top-down → Find cases where Higgs alignment arises naturally. Higgs alignment can be realised from N = 2 supersymmetry. Minimal Dirac Gaugino Supersymmetric Standard Model (MDGSSM) Sophie Williamson (LPTHE Paris) Higgs Alignment from N = 2 LSPC Grenoble, 14/03/18 5 / 43
Effective Field Theory Approach Our Model: Sophie Williamson (LPTHE Paris) Higgs Alignment from N = 2 LSPC Grenoble, 14/03/18 6 / 43
Minimal Dirac Gaugino Supersymmetric Standard Model Add N = 1 chiral multiplets S (singlet), T ( SU (2) triplet), O ( SU (3) octet) in the adjoint representation of the corresponding gauge groups. Majorana gauginos (one Weyl fermion) → Dirac Gauginos (Weyl fermion + adjoint chiral fermion) • L ⊃ − 1 − → L ⊃ − m iD χ i λ i + h . c . 2 M i λ i λ i + h . c . • Dirac masses preserve R-symmetry. New states destroy of gauge coupling unification. • Can add vector-like lepton fields to restore the property. Sophie Williamson (LPTHE Paris) Higgs Alignment from N = 2 LSPC Grenoble, 14/03/18 7 / 43
N = 2 Supersymmetry Two supersymmetry generators: Q 1 α , Q 2 α . N = 2 multiplets: • N = 2 vector multiplet: • N = 2 hypermultiplet: Sophie Williamson (LPTHE Paris) Higgs Alignment from N = 2 LSPC Grenoble, 14/03/18 8 / 43
N = 2 Supersymmetry in a Dirac Gaugino model A fully N = 2 supersymmetric lagrangian only permits gauge interactions. But isn’t the matter sector fundamentally chiral and therefore N = 1? → Assume N = 2 supersymmetry in the Higgs/gauge sector only. 2 Higgs doublets of MSSM naturally sit in an N = 2 hypermultiplet. New chiral superfields → N = 2 extended gauge sector. Sophie Williamson (LPTHE Paris) Higgs Alignment from N = 2 LSPC Grenoble, 14/03/18 9 / 43
Modifications to the Higgs sector Choose N = 2 conserving superpotential. Modification to the MSSM Higgs sector: W Higgs = µ H u · H d + λ S S H u · H d + 2 λ T H d · TH u At tree level: N = 2 supersymmetry imposes: λ S = g ′ λ T = g √ , √ , 2 2 Sophie Williamson (LPTHE Paris) Higgs Alignment from N = 2 LSPC Grenoble, 14/03/18 10 / 43
The Two-Higgs Doublet Model Limit: I Map the MDGSSM onto the two-Higgs doublet model (THDM) → Integrate out the adjoint scalars. THDM parametrization: 1 Φ 2 + h.c] + 1 1 Φ 1 ) 2 + 1 11 Φ † 22 Φ † 12 Φ † 2 λ 1 (Φ † 2 λ 2 (Φ † m 2 1 Φ 1 + m 2 2 Φ 2 − [ m 2 2 Φ 2 ) 2 V EW = + λ 3 (Φ † 1 Φ 1 )(Φ † 2 Φ 2 ) + λ 4 (Φ † 1 Φ 2 )(Φ † 2 Φ 1 ) � 1 � 1 Φ 2 ) 2 + [ λ 6 (Φ † 2 λ 5 (Φ † 1 Φ 1 ) + λ 7 (Φ † 2 Φ 2 )]Φ † + 1 Φ 2 + h.c , To map the MDGSSM onto this, we make the identifications Φ 2 = H u , 1 = − ǫ ij ( H j d ) ∗ Φ i In the limit of | m DY | ≪ m S , | m D 2 | ≪ m T λ 1 , λ 2 → 1 λ 3 → 1 λ 4 → − 1 4 ( g 2 2 + g 2 4 ( g 2 2 − g 2 Y ) + 2 λ 2 2 g 2 Y + λ 2 S − λ 2 Y ) , T , T , Sophie Williamson (LPTHE Paris) Higgs Alignment from N = 2 LSPC Grenoble, 14/03/18 11 / 43
The Two-Higgs Doublet Model Limit: II Low energy theory: type-II two-Higgs doublet model with an additional Dirac Bino and Wino. • Mass of electroweakinos ≪ m S , m T . • The gluino remains heavy: LHC constraints → O (2 TeV). Running: Fix the boundary conditions at high energies, and run down. Sophie Williamson (LPTHE Paris) Higgs Alignment from N = 2 LSPC Grenoble, 14/03/18 12 / 43
Tree Level Alignment: I Alignment basis: Mass matrices for the CP-even scalars: � Z 1 v 2 Z 6 v 2 � M 2 h = with Z i = Z i ( λ i ) . Z 6 v 2 m 2 A + Z 5 v 2 Alignment when Z 6 → 0. With N = 2 supersymmetry, at tree level: � ( g 2 2 + g 2 Z 6 = − 1 Y ) � − ( λ 2 S + λ 2 2 sin(2 β ) cos(2 β ) T ) 2 T = g 2 2 + g 2 ⇒ when the couplings take their N = 2 values λ 2 S + λ 2 Y , the 2 Higgs doublets are automatically aligned! Sophie Williamson (LPTHE Paris) Higgs Alignment from N = 2 LSPC Grenoble, 14/03/18 13 / 43
Tree Level Alignment: II The Higgs mass at tree level: Lightest Higgs mass given by the (1,1) component of M 2 h → m 2 h = Z 1 v 2 In terms of λ i : � � Z 1 v 2 = m 2 sin( β ) 2 cos( β ) 2 Z + v 2 (2 λ 2 S − g 2 Y ) + (2 λ 2 T − g 2 2 ) ⇒ In alignment limit, see that m 2 h → m 2 z . ⇒ When couplings deviate from N = 2 relations, get a tree-level boost to m h . Sophie Williamson (LPTHE Paris) Higgs Alignment from N = 2 LSPC Grenoble, 14/03/18 14 / 43
Tree Level Alignment: Summary Heavy CP-even neutral scalar does not take part in EWSB. The model shows alignment for any value of tan β : • m N =2 m N =2 = m Z , = m A h H • m 2 , N =2 = m 2 A + 2 m 2 W − m 2 Z . H ± ⇒ First demonstrated by Antoniadis, Benakli, Delgado and Quir´ os in the context of gauge mediation arXiv:hep-ph/0610265. ⇒ Phenomenological study done by Ellis, Quevillon, Sanz taking M N =2 = Q arXiv:1607.05541. Sophie Williamson (LPTHE Paris) Higgs Alignment from N = 2 LSPC Grenoble, 14/03/18 15 / 43
Misalignment: N = 2 to N = 1 SUSY Radiative Corrections: Chiral Matter Chiral fields present at the N = 2 scale. Splitting of λ S , λ T from their N = 2 scale values during running: Z 6 ( M SUSY ) =1 � � (2 λ 2 S − g 2 Y ) + (2 λ 2 T − g 2 2 ) + threshold corrections . 4 s 2 β c 2 β Can find an approximate magnitude of the splitting by integrating over the difference in β λ S and β λ T : � M N =2 − 2 g ′ 2 � 3 | y t | 2 + 3 | y b | 2 + | y τ | 2 − 10 g ′ 2 � 2 λ 2 S − g ′ 2 � � � = log , M SUSY 16 π 2 M SUSY � M N =2 − 2 g 2 � 3 | y t | 2 + 3 | y b | 2 + | y τ | 2 − 6 g 2 � 2 λ 2 T − g 2 � � = � log . M SUSY 16 π 2 M SUSY ⇒ Estimate e.g. | Z 6 ( M SUSY ) | � O (0 . 1). Sophie Williamson (LPTHE Paris) Higgs Alignment from N = 2 LSPC Grenoble, 14/03/18 16 / 43
Misalignment: N = 1 to N = 0 Radiative Corrections: Mass splitting Mass splitting between the fermionic/bosonic components of the superpartners: 8 π 2 log m 2 β c β × 3 y 4 ˜ Z 6 ( v ) ≃ Z 6 ( M SUSY ) + s 3 t t m 2 t Less misalignment than in the MSSM: • No tree-level contribution to Z 6 . • Stop correction to m h smaller in the MDGSSM. → O ( 1 2 ) for tan β = 2 because of: • Tree-level boost to m h (so smaller stop contributions required) • Only small stop mixing is possible Sophie Williamson (LPTHE Paris) Higgs Alignment from N = 2 LSPC Grenoble, 14/03/18 17 / 43
Precision Study: Implementation Q → M SUSY 1l matching Yukawas to SM values + 2l strong corrections to y t . 1l gauge threshold corrections. 2l corrections to m h . Running: 2l Low energy THDM + Dirac electroweakinos in SARAH . M SUSY → M N =2 Tree-level corrections from DG-masses and 1l corrections to λ i . Conversion of MS → DS gauge + Yukawa couplings. Running: 2l MDGSSM in SARAH . Assumptions Q = 400 GeV. M SUSY : Stop masses; other MSSM particles → vary to obtain m h = 125 . 15 GeV at 2l. Sophie Williamson (LPTHE Paris) Higgs Alignment from N = 2 LSPC Grenoble, 14/03/18 18 / 43
Other Inputs: Numerical values The precision study implemented scans over tan β , M SUSY and M N =2 and defined M scalars (heavier S , T scalars) = 5 TeV. ( m DY , m D 2 , µ ) = (400 , 500 , 600) GeV. m tree = 600 GeV. A • In the scans we see that m tree ∼ m H ∼ m H ± because of small mixing. A • ⇒ results not particularly sensitive to m tree . A Sophie Williamson (LPTHE Paris) Higgs Alignment from N = 2 LSPC Grenoble, 14/03/18 19 / 43
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