Higgs Alignment from Extended Supersymmetry Sophie Williamson - - PowerPoint PPT Presentation
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
Sophie Williamson
LPTHE, Sorbonne Universit´ e, CNRS Based on work in collaboration with Karim Benakli and Mark Goodsell (arXiv:1801.08849)
LSPC Grenoble, 14th March 2018
Sophie Williamson (LPTHE Paris) Higgs Alignment from N = 2 LSPC Grenoble, 14/03/18 1 / 43
Introduction
Alignment in the MDGSSM
Simplified MRSSM analysis
Sophie Williamson (LPTHE Paris) Higgs Alignment from N = 2 LSPC Grenoble, 14/03/18 2 / 43
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
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
In minimal SUSY: Two complex SU(2) Higgs doublets - Hu, Hd
EWSB
= = = ⇒ 5 physical Higgs bosons: h, H, A, H±. 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
Keep mH 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
Our Model:
Sophie Williamson (LPTHE Paris) Higgs Alignment from N = 2 LSPC Grenoble, 14/03/18 6 / 43
Add N = 1 chiral multiplets S (singlet), T (SU(2) triplet), O (SU(3)
groups. Majorana gauginos (one Weyl fermion) → Dirac Gauginos (Weyl fermion + adjoint chiral fermion)
2Miλiλi + h.c.
− → L ⊃ −miDχiλi + h.c.
New states destroy of gauge coupling unification.
Sophie Williamson (LPTHE Paris) Higgs Alignment from N = 2 LSPC Grenoble, 14/03/18 7 / 43
Two supersymmetry generators: Q1
α, Q2 α.
N = 2 multiplets:
Sophie Williamson (LPTHE Paris) Higgs Alignment from N = 2 LSPC Grenoble, 14/03/18 8 / 43
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
Choose N = 2 conserving superpotential. Modification to the MSSM Higgs sector: WHiggs = µ Hu · Hd + λSS Hu · Hd + 2λT Hd · THu At tree level: N = 2 supersymmetry imposes: λS = g′ √ 2 , λT = g √ 2 ,
Sophie Williamson (LPTHE Paris) Higgs Alignment from N = 2 LSPC Grenoble, 14/03/18 10 / 43
Map the MDGSSM onto the two-Higgs doublet model (THDM) → Integrate out the adjoint scalars. THDM parametrization:
VEW = m2
11Φ† 1Φ1 + m2 22Φ† 2Φ2 − [m2 12Φ† 1Φ2 + h.c] + 1
2 λ1(Φ†
1Φ1)2 + 1
2 λ2(Φ†
2Φ2)2
+λ3(Φ†
1Φ1)(Φ† 2Φ2) + λ4(Φ† 1Φ2)(Φ† 2Φ1)
+ 1 2 λ5(Φ†
1Φ2)2 + [λ6(Φ† 1Φ1) + λ7(Φ† 2Φ2)]Φ† 1Φ2 + h.c
To map the MDGSSM onto this, we make the identifications Φ2 = Hu, Φi
1 = −ǫij(Hj d)∗
In the limit of |mDY | ≪ mS, |mD2| ≪ mT
λ1, λ2 → 1 4 (g2
2 + g2 Y ),
λ3 → 1 4 (g2
2 − g2 Y ) + 2λ2 T ,
λ4 → − 1 2 g2
Y + λ2 S − λ2 T , Sophie Williamson (LPTHE Paris) Higgs Alignment from N = 2 LSPC Grenoble, 14/03/18 11 / 43
Low energy theory: type-II two-Higgs doublet model with an additional Dirac Bino and Wino.
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
Alignment basis: Mass matrices for the CP-even scalars: M2
h =
Z1v2 Z6v2 Z6v2 m2
A + Z5v2
Alignment when Z6 → 0. With N = 2 supersymmetry, at tree level: Z6 = −1 2 sin(2β) cos(2β) (g2
2 + g2 Y )
2 − (λ2
S + λ2 T)
S + λ2 T = g2
2 +g2 Y
2
, the Higgs doublets are automatically aligned!
Sophie Williamson (LPTHE Paris) Higgs Alignment from N = 2 LSPC Grenoble, 14/03/18 13 / 43
The Higgs mass at tree level: Lightest Higgs mass given by the (1,1) component of M2
h
→ m2
h = Z1v2
In terms of λi: Z1v2 =m2
Z + v2
S − g2 Y ) + (2λ2 T − g2 2 )
⇒ In alignment limit, see that m2
h → m2 z.
⇒ When couplings deviate from N = 2 relations, get a tree-level boost to mh.
Sophie Williamson (LPTHE Paris) Higgs Alignment from N = 2 LSPC Grenoble, 14/03/18 14 / 43
Heavy CP-even neutral scalar does not take part in EWSB. The model shows alignment for any value of tan β:
h
= mZ , mN=2
H
= mA
H±
= m2
A + 2m2 W − m2 Z .
⇒ First demonstrated by Antoniadis, Benakli, Delgado and Quir´
the context of gauge mediation arXiv:hep-ph/0610265. ⇒ Phenomenological study done by Ellis, Quevillon, Sanz taking MN =2 = Q arXiv:1607.05541.
Sophie Williamson (LPTHE Paris) Higgs Alignment from N = 2 LSPC Grenoble, 14/03/18 15 / 43
Radiative Corrections: Chiral Matter Chiral fields present at the N = 2 scale. Splitting of λS, λT from their N = 2 scale values during running: Z6(MSUSY ) =1 4s2βc2β
S − g2 Y ) + (2λ2 T − g2 2 )
Can find an approximate magnitude of the splitting by integrating
S − g′2 MSUSY
= − 2g′2 16π2
log MN =2 MSUSY
T − g2 MSUSY
= − 2g2 16π2
log MN =2 MSUSY
⇒ Estimate e.g. |Z6(MSUSY )| O(0.1).
Sophie Williamson (LPTHE Paris) Higgs Alignment from N = 2 LSPC Grenoble, 14/03/18 16 / 43
Radiative Corrections: Mass splitting Mass splitting between the fermionic/bosonic components of the superpartners: Z6(v) ≃ Z6(MSUSY ) + s3
βcβ × 3y4 t
8π2 log m2
˜ t
m2
t
Less misalignment than in the MSSM:
→ O( 1
2) for tan β = 2 because of:
Sophie Williamson (LPTHE Paris) Higgs Alignment from N = 2 LSPC Grenoble, 14/03/18 17 / 43
Q → MSUSY 1l matching Yukawas to SM values + 2l strong corrections to yt. 1l gauge threshold corrections. 2l corrections to mh. Running: 2l Low energy THDM + Dirac electroweakinos in SARAH. MSUSY → MN=2 Tree-level corrections from DG-masses and 1l corrections to λi. Conversion of MS → DS gauge + Yukawa couplings. Running: 2l MDGSSM in SARAH. Assumptions Q = 400 GeV. MSUSY : Stop masses; other MSSM particles → vary to obtain mh = 125.15 GeV at 2l.
Sophie Williamson (LPTHE Paris) Higgs Alignment from N = 2 LSPC Grenoble, 14/03/18 18 / 43
The precision study implemented scans over tan β, MSUSY and MN=2 and defined Mscalars (heavier S, T scalars) = 5 TeV. (mDY , mD2, µ) = (400, 500, 600) GeV. mtree
A
= 600 GeV.
A
∼ mH ∼ mH± because of small mixing.
A
.
Sophie Williamson (LPTHE Paris) Higgs Alignment from N = 2 LSPC Grenoble, 14/03/18 19 / 43
Dependence of the couplings on the N = 2 scale:
Find gY ∼ 0.37 and g2 ∼ 0.64 both at Q and MSUSY , with little dependence on MN =2. Ratios show stronger dependence on MN =2.
1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0
tanβ
0.7 0.8 0.9 1.0 1.1 1.2 1.3
p
2λS/T/gY,2(MSUSY)
p
2λT/g2,MN =2 =1010 GeV
p
2 λ
S
/ g
Y
, M
N = 2
= 1
1
G e V
p
2λS/gY,MN =2 =1016 GeV MN =2 =MSUSY
10 15 20 25 30
p
2λT/g2,MN =2 =1016 GeV
→ Enhancement of mh due to λT splitting.
Sophie Williamson (LPTHE Paris) Higgs Alignment from N = 2 LSPC Grenoble, 14/03/18 20 / 43
Tree level mh before running MSUSY → Q.
1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0
tanβ
75 77 79 81 83 85 87 89 91 93 95 97 99
v ×
q
Z1(MSUSY) (GeV)
MN =2 =1010 GeV MN =2 =MSUSY
10 15 20 25 30
MN =2 =1016 GeV
Increasing MN=2 increases mh. MSSM: mtree
h
goes like mZ| cos β| → drops off for small tan β.
Sophie Williamson (LPTHE Paris) Higgs Alignment from N = 2 LSPC Grenoble, 14/03/18 21 / 43
Alignment in the Dirac Gaugino Model: Z6(MSUSY )
Recall: Z6(MSUSY ) = 1 4 s2βc2β
S − g2 Y ) + (2λ2 T − g2 2 )
1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0
tanβ
0.025 0.020 0.015 0.010 0.005 0.000 0.005 0.010
Z6 (MSUSY)
MN =2 =1010 GeV MN =2 =1016 GeV MN =2 =MSUSY
10 15 20 25 30
Sophie Williamson (LPTHE Paris) Higgs Alignment from N = 2 LSPC Grenoble, 14/03/18 22 / 43
Interpret corrections δλi as effect of integrating out supersymmetric particles at Q
Effect of running from λS, λT non-negligible. Take mA large with respect to mh and mZ, then ⇒ Z6 ≈
0.12 tβ − 1 2 tβ 1+t2
β
S − g2 Y ) + (2λ2 T − g2 2 )
(LPTHE Paris) Higgs Alignment from N = 2 LSPC Grenoble, 14/03/18 23 / 43
Alignment in the Dirac Gaugino Model: Z6(Q)
1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0
tanβ
0.02 0.00 0.02 0.04 0.06 0.08 0.10 0.12
Z6(Q) MN =2 =1010 GeV MN =2 =1016 GeV MN =2 =MSUSY
10 15 20 25 30
Independent of mA, mh is very SM-like for tan β ≥ 3.
Sophie Williamson (LPTHE Paris) Higgs Alignment from N = 2 LSPC Grenoble, 14/03/18 24 / 43
Reasonable fit of Z6(Q) with approximate formula Squark corrections enhance mh but also misalignment This misalignment is compensated for by the running of λS and λT. ⇒ Partial or total cancellation of misalignment contributions!
Sophie Williamson (LPTHE Paris) Higgs Alignment from N = 2 LSPC Grenoble, 14/03/18 25 / 43
Effects of loop corrections in the low-energy theory on mh.
5 10 15 20 25 30
tanβ
116 118 120 122 124 126 128
mh (GeV)
Tree level, 1016 GeV Tree level, MSUSY 1-loop, 1016 GeV 1-loop, MSUSY
→ Loop effects from tops, heavy Higgses and electroweakinos boost mh by ∼ 5 GeV.
Sophie Williamson (LPTHE Paris) Higgs Alignment from N = 2 LSPC Grenoble, 14/03/18 26 / 43
Higgs mass bounds on the SUSY scale
3000 4000 5000 6000 7000 8000 10 15 20 25 30
MN =2 =MSUSY
3000 4000 5000 6000 7000 8000
MSUSY [GeV]
1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0
tanβ M
N = 2
= 1
1
G e V MN =2 =1016 GeV
105 106 1.5 2.0 2.5 3.0 3.5 4.0 4.5 104 105 1 5 10 15 20 25 30
Minimum for MSUSY around tan β ∈ (2, 3).
Sophie Williamson (LPTHE Paris) Higgs Alignment from N = 2 LSPC Grenoble, 14/03/18 27 / 43
Uncertainty on the Higgs mass bounds very difficult to estimate. Expect contributions not included to be small. ⇒ Expect ∆mh ≤ GeV in comparison with the MSSM. Expect smaller errors at lower MSUSY .
Sophie Williamson (LPTHE Paris) Higgs Alignment from N = 2 LSPC Grenoble, 14/03/18 28 / 43
Higgs couplings Model realises excellent alignment → no significant constraint from Higgs couplings. Electroweak precision corrections Current bound: ∆ρ = (3.7 ± 2.3) × 10−4 → central value restricts mT+ > 2 TeV. → Always well within experimental bounds.
5 10 15 20 25 30
tanβ
∆ρ/(10−4 )
1016 GeV 1010 GeV 108 GeV 106 GeV 104 GeV MSUSY Sophie Williamson (LPTHE Paris) Higgs Alignment from N = 2 LSPC Grenoble, 14/03/18 29 / 43
Strongest constraints come from flavour searches:
300 400 500 600 700 800 900
MA (GeV)
2 4 6 8 10 12
tanβ B →sγ
Dirac gaugino model hMSSM
Bounds mH± > 580 GeV
Sophie Williamson (LPTHE Paris) Higgs Alignment from N = 2 LSPC Grenoble, 14/03/18 30 / 43
Sophie Williamson (LPTHE Paris) Higgs Alignment from N = 2 LSPC Grenoble, 14/03/18 31 / 43
Preserve exact continuous R-symmetry by including two R-Higgs doublet superfields. Superpotential becomes: W MRSSM
Higgs
= µu Ru · Hu + µd Rd · Hd + λSuS Ru · Hu + λSdS Rd · Hd +2λTu Ru · THu + 2λTd Rd · THd . N = 2 supersymmetry must be imposed: λSu = gY √ 2 , λSd = − gY √ 2 , λTu = λTd = g2 √ 2 . Can treat (Ru, Hu) and (Rd, Hd) as hypermultiplets.
Sophie Williamson (LPTHE Paris) Higgs Alignment from N = 2 LSPC Grenoble, 14/03/18 32 / 43
Tree-level THDM model parameters: In the limit of |mDY | ≪ mS, |mD2| ≪ mT Recall for the MDGSSM:
λ1, λ2 → 1 4 (g2
2 + g2 Y ),
λ3 → 1 4 (g2
2 − g2 Y ) + 2λ2 T ,
λ4 → − 1 2 g2
Y + λ2 S − λ2 T ,
For the MRSSM: λMRSSM
i
→ λMSSM
i
and so
λMSSM
i
, λMSSM
2
→ 1 4 (g2
2 + g2 Y ),
λMSSM
3
→ 1 4 (g2
2 − g2 Y ),
λMSSM
4
→ − 1 2 g2
Y . Sophie Williamson (LPTHE Paris) Higgs Alignment from N = 2 LSPC Grenoble, 14/03/18 33 / 43
No automatic alignment. For mS, mT large: THDM parameters λi → λMSSM
i
With radiative corrections: for non-zero λTu,d, λSu,d
t
Alignment never as good as in MDGSSM because of tree-level contribution to misalignment.
Sophie Williamson (LPTHE Paris) Higgs Alignment from N = 2 LSPC Grenoble, 14/03/18 34 / 43
Alignment only different from MSSM when mS, mT very large
threshold corrections.
⇒ Simplified model:
Sophie Williamson (LPTHE Paris) Higgs Alignment from N = 2 LSPC Grenoble, 14/03/18 35 / 43
Iterative method to converge λi and λS,Tu,d couplings, before mapping back onto the Higgs quartic, λ. mtop → Q 2l matching Yukawas, gauge and Higgs quartic couplings to SM values. Running: 2l SM in SARAH. Q → MSUSY Iterative process to determine λi. Running: 2l Low energy THDM in SARAH. MSUSY → MN=2 1l threshold corrections to S, T. Running: 2l MRSSM in SARAH. Assumptions
Neglect all loop-level thresholds other than those from S and T. Q = 600 GeV. Degenerate adjoint scalar masses, MΣ.
Sophie Williamson (LPTHE Paris) Higgs Alignment from N = 2 LSPC Grenoble, 14/03/18 36 / 43
Dependence of λTu,d/g2 on the N = 2 scale
MSUSY = 10 TeV MΣ = 10 MSUSY
Sophie Williamson (LPTHE Paris) Higgs Alignment from N = 2 LSPC Grenoble, 14/03/18 37 / 43
“Tree level” Higgs mass at MSUSY Extremely boosted value for extreme MΣ and MN=2 due to almost non perturbative λT couplings
Sophie Williamson (LPTHE Paris) Higgs Alignment from N = 2 LSPC Grenoble, 14/03/18 38 / 43
Alignment at Q Little deviation in Z6, regardless of MΣ and MN=2.
Sophie Williamson (LPTHE Paris) Higgs Alignment from N = 2 LSPC Grenoble, 14/03/18 39 / 43
Z6(Q) similar to in the MSSM case. Adjoint scalars never give a large boost to the Higgs quartic. When very high MN=2 and heavy MΣ, the couplings are considerably enhanced ⇒ Worse alignment.
Sophie Williamson (LPTHE Paris) Higgs Alignment from N = 2 LSPC Grenoble, 14/03/18 40 / 43
Approximate Higgs mass bounds on MSUSY in the MRSSM For tan β < 4, MSUSY ≥ 20 TeV. Potentially unreliable results for large MΣ and MSUSY .
Sophie Williamson (LPTHE Paris) Higgs Alignment from N = 2 LSPC Grenoble, 14/03/18 41 / 43
S, T give very small boost to mh but see noticeable effects in MSUSY . Errors Here we take mh = 125 ± 0.5 GeV. Error on MSUSY grows as MSUSY increases:
Recall corrections to parameters ∝ y 4
t log m2
˜ t
m2
t
As MSUSY ↑, yt ↓ ⇒ Require bigger shift in MSUSY to get mh Results at lower MSUSY more accurate.
EFT approach is less accurate when MSUSY ≤ TeV.
Sophie Williamson (LPTHE Paris) Higgs Alignment from N = 2 LSPC Grenoble, 14/03/18 42 / 43
In the MDGSSM: Alignment is realised naturally in Mh, and preserved by quantum corrections. The splitting of λS and λT from the N = 2 relations
MSUSY could be as low as 3 TeV. In the MRSSM: Enforced N = 2 can increase alignment with respect to the MSSM, in the limit of large adjoint scalar masses
Sophie Williamson (LPTHE Paris) Higgs Alignment from N = 2 LSPC Grenoble, 14/03/18 43 / 43