Higgs boson mass: the quest for precise predictions in SUSY models

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Higgs boson mass: the quest for precise predictions in SUSY models

Dominik St¨ockinger

TU Dresden

26.1.2017, PSI/Z¨urich, Particle Theory Seminar

based on: [Athron, Park, Steudtner, DS, Voigt ’16] + Kwasnitza

Dominik St¨ockinger 1/32

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M_h^Exp= 125.09±0.24GeV

95 100 105 110 115 120 125

-3 -2 -1 0 1 2 3

Mh / GeV

Xt / MSUSY FlexibleEFTHiggs/MSSM

FlexibleSUSY/MSSM FlexibleSUSY/HSSUSY SOFTSUSY 3.6.2 SARAH/SPheno FeynHiggs 2.12.0 SUSYHD 1.0.2

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Outline

1 Fixed-order, EFT-type, and new combined approach

2 Numerical results

3 Uncertainty estimates

4 Application to non-minimal models, further improvements

Dominik St¨ockinger Introduction 3/32

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Hallmark of SUSY: M

h

predictable!

Standard Model: m_h²=λv²

MSSM: λ↔gauge couplings

HHHH ↔ HHH˜H˜

m²_h= 1 2 h

m_A² +m_Z² −q

(m²_A+m_Z²)²−4m²_Zm²_Ac_2β² i

=v²1

4 g_Y² +g₂²

cos²2β+O 1

m²_A

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Extremely large loop corrections

Σ^leading_h ∝v²y_t⁴ L , X_t² , X_t⁴

, whereL≡lnMSUSY

M_weak Compare: RGE forλhas additive term, allows to predict the large log from simple EFT-arguments

β_λ^SM=−12κ_Ly_t⁴+. . .

In contrast, theXt-terms originate from finite loop corrections

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Plots illustrate qualitative behaviour ∝ X

_t²

, X

_t⁴

95 100 105 110 115 120 125

-3 -2 -1 0 1 2 3

Mh / GeV

X_t / M_SUSY FlexibleEFTHiggs/MSSM

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Plots illustrate qualitative behaviour ∝ L

80 90 100 110 120 130 140

1 10 100

Mh / GeV

MSUSY / TeV 0.2

FlexibleEFTHiggs/MSSM FlexibleSUSY/MSSM FlexibleSUSY/HSSUSY SOFTSUSY 3.6.2 SARAH/SPheno FeynHiggs 2.12.0 SUSYHD 1.0.2

. . . and three types of calculations:

Fixed order (Softsusy [Allanach], SPheno [Porod, Staub],FlexibleSUSY), 2-loop (gaugeless limit)

EFT-type (SUSYHD [Vega,Villadoro],HSSUSY), 2-loop matching/3-loop running

Combined (FeynHiggs [Hahn et al],FlexibleEFTHiggs)

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80 90 100 110 120 130 140

1 10 100

Mh / GeV

MSUSY / TeV 0.2

FlexibleEFTHiggs/MSSM FlexibleSUSY/MSSM FlexibleSUSY/HSSUSY SOFTSUSY 3.6.2 SARAH/SPheno FeynHiggs 2.12.0

SUSYHD 1.0.2 95

100 105 110 115 120 125

-3 -2 -1 0 1 2 3

Mh / GeV

Aims and questions

How/why do the calculations differ?

What is the theory uncertainty?

Present improved method FlexibleEFTHiggs

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Outline

1 Fixed-order, EFT-type, and new combined approach

Dominik St¨ockinger Fixed-order, EFT-type, and new combined approach 8/32

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Overview of M

h

calculations

Two basic approaches

standard P.T. = tree +O(α) +O(α²) +O(α³) +. . . resummed logs = tree +O(αⁿLⁿ) +O(αⁿLⁿ⁻¹) +. . . Resummation via EFT+RGE neglects termsO(1/M_SUSY)

[systematic improvement by orders ofM_weak/M_SUSYpossible with higher-dimensional operators in EFT]

Combined approaches:

resummed logs + full MSUSY-dependence at fixed order

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Overview of Higgs mass calculators

Status of Flexible* and other Higgs mass calculations:

MSSM FS-versions of: non-MSSM, generated FS-original (≈Softsusy) ^{fixed 2L} FS-original ^{fixed 1L}

Spheno ^“

SUSYHD,HSSUSY EFT, 2L matching+3L running

FEFTHiggs EFT, 1L matching+3L running FEFTHiggs

⇒many verifications; can study differences in detail. Note:≥2-loop only in gaugeless limit!

More Higgs mass calculations in MSSM:

MSSM, fixed order: H3m, FeynHiggs, Softsusy, Spheno,. . . MSSM, EFT: SUSYHD, HSSUSY

MSSM, combined: FeynHiggs, FlexibleEFTHiggs

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Overview of Higgs mass calculators

Status of Flexible* and other Higgs mass calculations:

MSSM FS-versions of: non-MSSM, generated FS-original (≈Softsusy) ^{fixed 2L} FS-original ^{fixed 1L}

Spheno ^“

SUSYHD,HSSUSY EFT, 2L matching+3L running

FEFTHiggs EFT, 1L matching+3L running FEFTHiggs

⇒many verifications; can study differences in detail. Note:≥2-loop only in gaugeless limit!

More Higgs mass calculations in MSSM:

MSSM, fixed order: H3m, FeynHiggs, Softsusy, Spheno,. . . MSSM, EFT: SUSYHD, HSSUSY

MSSM, combined: FeynHiggs, FlexibleEFTHiggs

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Fixed order DR calculation in detail

1 Find DR parameters ˜gi, ˜yt, ˜m_Z, . . . at the SUSY scale. E.g. ˜yt from m^FS,SPh_t =M_t+ Σ⁽¹⁾_t

M_tFS

˜ m_t_SPh

(FS≈Softsusy)

2 Calculate the Higgs pole mass from the DR parameters.

0 = det h

p²δij −(m²_φ)ij + ˜Σφ,ij(p²) i

( ˜Σ includes tadpole term)

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Example: leading logs in fixed-order calculations

1 Find DR parameters ˜g_i, ˜y_t, ˜m_Z, . . . at the SUSY scale. E.g. ˜y_t from

m^FS_t ^,SPh=Mt+ Σ⁽¹⁾_t

MtFS

m_t_SPh

0 = det h

p²δ_ij −(m²_φ)_ij + ˜Σ_φ,ij(p²) i

M_h² =m²_h+ ˆv²yˆ_t⁴



12Lκ_L−192ˆg₃²L²κ²_L+ 4ˆg₃⁴L³κ³_L







736_EFT

736 9923 FS

3 SPh





 +· · ·





Hence: not fixed order w.r.t. low-energy parameters, induced 3-loop terms different and wrong!

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Example: leading logs in fixed-order calculations

m^FS_t ^,SPh=Mt+ Σ⁽¹⁾_t

MtFS

m_t_SPh

M_h² =m_h²+ ˜v²y˜_t⁴

12Lκ_L+ 192˜g₃²L²κ²_L



12Lκ_L−192ˆg₃²L²κ²_L+ 4ˆg₃⁴L³κ³_L







736_EFT

736 9923 FS

3 SPh





 +· · ·





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Example: leading logs in fixed-order calculations

(in terms of low-energy SM parameters ˆy_t, ˆg₃:)

˜

y_t^FS,SPh= ˆy_t

1−8ˆg₃²Lκ_L+

₉₇₆

10409 FS 9 SPh

ˆ g₃⁴L²κ²_L

+. . .

M_h² =m_h²+ ˜v²y˜_t⁴

12Lκ_L+ 192˜g₃²L²κ²_L



12Lκ_L−192ˆg₃²L²κ²_L+ 4ˆg₃⁴L³κ³_L







736_EFT

736 9923 FS

3 SPh





 +· · ·





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Example: leading logs in fixed-order calculations

(in terms of low-energy SM parameters ˆy_t, ˆg₃:)

˜

y_t^FS,SPh= ˆy_t

1−8ˆg₃²Lκ_L+

₉₇₆

10409 FS 9 SPh

ˆ g₃⁴L²κ²_L

+. . .

M_h² =m_h²+ ˜v²y˜_t⁴

12Lκ_L+ 192˜g₃²L²κ²_L



12Lκ_L−192ˆg₃²L²κ²_L+ 4ˆg₃⁴L³κ³_L







736EFT 736 9923 FS

3 SPh





 +· · ·





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EFT-type calculation in detail

assume SUSY masses atM_SUSY∼Q_matchM_weak∼Q assume SM = correct low-energy EFT belowQ_match Then: setup for correct terms of orderαⁿLⁿ, αⁿLⁿ⁻¹

1 atµ=Q_match: integrate out SUSY, match to SM need 1-loop δp_i p_i^SM(µ) =p^SUSY_i (µ) +δp_i

2 between Q_match> µ >Q: run in SM need 2-loopβ_p^SM_i dp_i^SM(µ)

d lnµ =β_p^SM_i (µ)

3 atµ=Q: compute Higgs mass in SM, match toMt,α^Exps . . . need 1-loop SM ˆΣ_h M_h²=λ^SM(Mweak)v²+ ˆΣh

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Example: leading logs in EFT-type calculations

1 atµ=Q_match: integrate out SUSY, match to SM

λ≡λ^SM(Q_match) = m_h^MSSM v²

2 between Qmatch> µ >Q: run in SM

ˆλ=λ+ ˆy_t⁴

12LκL−192ˆg₃²L²κ²_L+ 4ˆg₃⁴L³κ³_L(736) +. . .

3 atµ=Q: compute Higgs mass in SM, match toM_t,α^Exps . . .

M_h² = ˆλˆv²



12LκL−192ˆg₃²L²κ²_L+ 4ˆg₃⁴L³κ³_L







736_EFT

736 9923 FS

3 SPh





 +· · ·





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Example: leading logs in EFT-type calculations

1 atµ=Q_match: integrate out SUSY, match to SM λ≡λ^SM(Q_match) = m_h^MSSM

v²

2 between Qmatch> µ >Q: run in SM

ˆλ=λ+ ˆy_t⁴

12LκL−192ˆg₃²L²κ²_L+ 4ˆg₃⁴L³κ³_L(736) +. . .

M_h² = ˆλˆv²



12LκL−192ˆg₃²L²κ²_L+ 4ˆg₃⁴L³κ³_L







736_EFT

736 9923 FS

3 SPh





 +· · ·





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Example: leading logs in EFT-type calculations

v²

2 between Qmatch> µ >Q: run in SM λˆ =λ+ ˆy_t⁴

12LκL−192ˆg₃²L²κ²_L+ 4ˆg₃⁴L³κ³_L(736) +. . .

M_h² = ˆλˆv²



12LκL−192ˆg₃²L²κ²_L+ 4ˆg₃⁴L³κ³_L







736_EFT

736 9923 FS

3 SPh





 +· · ·





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Example: leading logs in EFT-type calculations

v²

2 between Qmatch> µ >Q: run in SM λˆ =λ+ ˆy_t⁴

12LκL−192ˆg₃²L²κ²_L+ 4ˆg₃⁴L³κ³_L(736) +. . .

3 atµ=Q: compute Higgs mass in SM, match toM_t,α^Exps . . . M_h² = ˆλˆv²



12LκL−192ˆg₃²L²κ²_L+ 4ˆg₃⁴L³κ³_L







736_EFT

736 9923 FS

3 SPh





 +· · ·





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EFT-type calculation in detail: matching at SUSY scale

“pure EFT” (SUSYHD, HSSUSY):

require Γ^full(p = 0) = Γ^EFT(p = 0) in limitM_SUSY → ∞ λ= 1

4 g_Y² +g₂²

cos²2β+ ∆λ⁽¹⁾+ ∆λ⁽²⁾ Pro: clean expansion in well-defined orders

Con: neglects 1/M_SUSY-terms already at tree-level!

Possible improvements: EFT+non-renormalizable operators

FeynHiggs: combined approach, add resummed logs onto fixed-order calculation without double counting

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EFT-type calculation in detail: matching at SUSY scale

FlexibleEFTHiggs: pole mass matching:

requireM_h^pole,full=M_h^pole,EFT λ= 1

v² h

(M_h^MSSM)²+ ˜Σ^SM_h ((M_h^SM)²) i

y_t,m_Z, . . .similar

Pro: exact at tree-level and 1-loop (2-loop can/will be included)

Pro: easier to automate for non-minimal SUSY

Con: can contain superfluous 2-loop terms, e.g. ∝∆y_t⁴∗L

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Further details and discussion

“pure EFT”

λ= 1 4

g_Y²+g₂²

cos²2β+ 1 (4π)²





 3(y_t^SM)⁴



ln m_Q²

3 Q²



+

6(y_t^SM)⁴X_t²ln m2

Q3 m2

U3 m²_Q

3−m²_U 3





 +. . .

pole mass matching

λ= 1 v² h

(m^MSSM_h )²−Σ˜^MSSM_h ((M_h^MSSM)²,y_t^MSSM, . . .) + ˜Σ^SM_h ((M_h^SM)²,y_t^SM, . . .)i

Equivalence at one-loop up toO(M_weak² /M_SUSY² ) [Athron,Park,Steudtner,DS,Voigt]

Equivalence at two-loop [Kwasnitza, Voigt]

“superfluous” 2-loop terms in one-loop matching

form of terms: lnQ²-dependent/independent! How to estimate missing higher-order terms?

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Outline

2 Numerical results

Verify expected similarities, differences between calculations

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Verification: step-by-step comparison to SUSYHD

X_t= 0, so ∆λ⁽²⁾≈0

80 90 100 110 120 130

1 10 100

Mh / GeV

M_SUSY / TeV 0.2

SUSYHD λ⁽²⁾, y_t NNNLO SUSYHD λ⁽¹⁾, y_t NNNLO SUSYHD λ⁽¹⁾, y_t NNLO FlexibleEFTHiggs/MSSM λ⁽²⁾, y_t NNNLO FlexibleEFTHiggs/MSSM λ⁽¹⁾, y_t NNNLO FlexibleEFTHiggs/MSSM w/ y_t⁽⁰⁾, y_t NNNLO FlexibleEFTHiggs/MSSM w/ y_t⁽⁰⁾, y_t NNLO FlexibleEFTHiggs/MSSM w/ y_t⁽¹⁾, y_t NNLO

agreement with replica of SUSYHD, two-loop matching here unimportant (commonM_SUSY,Xt= 0) FlexibleEFTHiggs-like matching: drastic change at lowM_SUSY uncertainty of SUSYHD changes ofytat matching/low scales higher-order effect, numerically sizeable

Dominik St¨ockinger Numerical results 18/32

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Verification: step-by-step comparison to SUSYHD

X_t= 0, so ∆λ⁽²⁾≈0

-2.5 -2 -1.5 -1 -0.5 0 0.5 1 1.5

1 10 100

(Mh - MhFlexibleEFTHiggs/MSSM) / GeV

M_SUSY / TeV 0.2

SUSYHD λ⁽²⁾, y_t NNNLO SUSYHD λ⁽¹⁾, y_t NNNLO SUSYHD λ⁽¹⁾, y_t NNLO FlexibleEFTHiggs/MSSM λ⁽²⁾, y_t NNNLO FlexibleEFTHiggs/MSSM λ⁽¹⁾, y_t NNNLO FlexibleEFTHiggs/MSSM w/ y_t⁽⁰⁾, y_t NNNLO FlexibleEFTHiggs/MSSM w/ y_t⁽⁰⁾, y_t NNLO FlexibleEFTHiggs/MSSM w/ y_t⁽¹⁾, y_t NNLO

agreement with replica of SUSYHD, two-loop matching here unimportant (commonM_SUSY,Xt= 0) FlexibleEFTHiggs-like matching: drastic change at lowM_SUSY uncertainty of SUSYHD changes ofy_tat matching/low scales higher-order effect, numerically sizeable

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Comparison fixed-order and EFT results

X_t= 0, ∆λ⁽²⁾≈0

80 90 100 110 120 130 140

1 10 100

Mh / GeV

MSUSY / TeV 0.2

FEFTHiggs agrees with pure EFT for large masses

and agrees with fixed-order calculations for masses “interpolates”

fixed-order calculations differ strongly at highM_SUSY theory uncertainty

Dominik St¨ockinger Numerical results 19/32

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Comparison fixed-order and EFT results

Xt6= 0, ∆λ⁽²⁾6= 0

95 100 105 110 115 120 125 130 135 140

1 10 100

Mh / GeV

MSUSY / TeV 0.3

95 100 105 110 115 120 125

-3 -2 -1 0 1 2 3

Mh / GeV

non-log shift between FEFTHiggs and SUSYHD from missing 2-loop matching fixed-order calculations differ strongly at highM_SUSY theory uncertainty

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Outline

3 Uncertainty estimates

Find comprehensive estimates for fixed-order and EFT

Dominik St¨ockinger Uncertainty estimates 20/32

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Uncertainties of fixed-order calculations

Source:

missing ≥3 loop terms (∝L³,L²,L,1) Estimates:

1 Estimate using known MSSM higher-order results

2 Estimate from generating motivated higher-order terms

1 top-mass definition (sensitive toL³)

2 renormalization scale (sensitive to≤L²)

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Illustrate fixed-order uncertainty estimates

80 90 100 110 120 130 140

1 10 100

Mh / GeV

MSUSY / TeV 0.2

FlexibleSUSY/MSSM yt(MZ) SARAH/SPheno yt(MZ) FlexibleSUSY/MSSM yt(MS) SARAH/SPheno yt(MS) uncertainty from varying C1 ΔMh(Q)

Estimate using known MSSM higher-order results: change m^FS_t ^,SPh =M_t+ Σ⁽¹⁾_t (. . .)±∆m_t^(2),known induces leading 3-loop change inM_h

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Illustrate fixed-order uncertainty estimates

80 90 100 110 120 130 140

1 10 100

Mh / GeV

MSUSY / TeV 0.2

Estimate from generating motivated higher-order terms:

m^FS_t ^,SPh=M_t+ Σ⁽¹⁾_t

MtFS

m_t_SPh

at

M_SUSY or M_weak

four options also induce leading 3-loop changes in Mh

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Illustrate fixed-order uncertainty estimates

80 90 100 110 120 130 140

1 10 100

Mh / GeV

MSUSY / TeV 0.2

renormalization scale Q varied by factor 2 induces change in M_h of

O(3-loop×L²×ln(2)) andO(2-loop, non-gaugeless×L×ln(2)) scale variation by itselfnot sufficient!

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Uncertainties of fixed-order calculations

Source:

missing ≥3 loop terms (∝L³,L²,L,1) Estimates:

1 top-mass definition (sensitive toL³)

2 renormalization scale (sensitive to≤L²)

Comments: method can be applied to non-minimal models. Could be an underestimate of the uncertainty: missing estimates for 3LL terms governed by not y_t, non-divergent 3NLL terms.

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Summary of fixed-order uncertainty estimates

-6 -4 -2 0 2 4 6

1 10 100

ΔMh / GeV

MSUSY / TeV 0.3

ΔM_h^{(4 x y}t) ΔMh(Q)

-4 -2 0 2 4

-3 -2 -1 0 1 2 3

ΔMh / GeV

X_t / M_SUSY ΔM_h^{(4 x y}t)

ΔMh(Q)

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Uncertainties of new EFT calculation

Sources:

high-scale uncertainty: missing≥2 loop matching corrections

low-scale uncertainty: missing ≥2 loop terms in low-scale Higgs pole mass calculation

EFT-uncertainty (in SUSYHD/HSSUSY): from missing 1/M_SUSY-suppressed terms

Estimate high-scale uncertainty:

1 top-mass matching either at tree-level or 1-loop (∆y_t^1L∼X_t,m_gluino)

2 matching scale (sensitive to divergent terms, not toX_t)

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Illustrate FlexibleEFTHiggs uncertainty estimates

-4 -2 0 2 4

-3 -2 -1 0 1 2 3

ΔMh / GeV

Xt / MSUSY uncertainty from varying C2 and C3

ΔMh(y_t 0L vs. 1L) ΔMh(Q_match) ΔMh(Q)

Estimate using known MSSM higher-order results: change λ→λ±∆λ^(2),known

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Illustrate FlexibleEFTHiggs uncertainty estimates

-4 -2 0 2 4

-3 -2 -1 0 1 2 3

ΔMh / GeV

Estimate from generating motivated higher-order terms yt-matching either at tree-level or 1-loop

matching-scale variation

induce 2-loop changes in λ-matching

(41)

Illustrate FlexibleEFTHiggs uncertainty estimates

-4 -2 0 2 4

-3 -2 -1 0 1 2 3

ΔMh / GeV

Low-scale uncertainty: missing SM higher orders

However: non-linear behaviour, different definitions possible ^109.5₁₀₉

110 110.5 111 111.5 112 112.5 113 113.5

100 150 200 250 300

Mh / GeV

Q / GeV ΔMh(Q) Mh(Q)

Mh = 111.22 GeV

(42)

Summary of fixed-order and FlexibleEFTHiggs uncertainty estimates

-6 -4 -2 0 2 4 6

1 10 100

ΔMh / GeV

MSUSY / TeV 0.3

ΔMh(4 x yt) ΔMh(Q)

-6 -4 -2 0 2 4 6

1 10 100

ΔMh / GeV

MSUSY / TeV 0.3

uncertainty from varying C2 and C3 ΔMh(yt 0L vs. 1L) ΔMh(Qmatch) ΔMh(Q)

-4 -2 0 2 4

-3 -2 -1 0 1 2 3

ΔMh / GeV

Xt / MSUSY ΔMh(4 x yt)

ΔMh(Q) -4

-2 0 2 4

-3 -2 -1 0 1 2 3

ΔMh / GeV

ΔMh(yt 0L vs. 1L) ΔMh(Qmatch) ΔMh(Q)

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Combined uncertainty estimates

fixed-order: combine quadratically

∆M_h^(4×y^t⁾,∆M_h^(Q⁾ (1) EFT: combine quadratically

maxh

∆M_h^(y^t ^{0L vs. 1L)},∆M_h^(Q^match⁾i

,∆M_h^(Q) (2)

(44)

80 85 90 95 100 105 110 115 120 125 130 135

1 10 100

Mh / GeV

MSUSY / TeV Xt = 0

0.2

FlexibleEFTHiggs/MSSM FlexibleSUSY/MSSM ΔMhFlexibleSUSY ΔMhFlexibleEFTHiggs

95 100 105 110 115 120 125 130

-3 -2 -1 0 1 2 3

Mh / GeV

Xt / MSUSY MSUSY = 2 TeV

FlexibleEFTHiggs/MSSM FlexibleSUSY/MSSM ΔMhFlexibleSUSY ΔMhFlexibleEFTHiggs

110 115 120 125 130 135 140

-3 -2 -1 0 1 2 3

Mh / GeV

X_t / M_SUSY MSUSY = 30 TeV

FlexibleEFTHiggs/MSSM FlexibleSUSY/MSSM ΔM_hFlexibleSUSY ΔMhFlexibleEFTHiggs

FlexibleEFTHiggs more precise than fixed order above∼2 TeV reliable at low and highM_SUSY

uncertainty estimates are conservative and overlap consistently

(45)

Outline

4 Application to non-minimal models, further improvements

Dominik St¨ockinger Application to non-minimal models, further improvements 29/32

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NMSSM

λ=κ= 0.2 λ=κ= 0.4

80 90 100 110 120 130

1 10

Mh / GeV

MSUSY / TeV 0.2

FlexibleEFTHiggs/NMSSM FlexibleSUSY/NMSSM SOFTSUSY 3.6.2 SARAH/SPheno NMSSMTools 4.8.2 SARAH/SPheno FS-like ΔMhFlexibleSUSY ΔMhFlexibleEFTHiggs

60 70 80 90 100 110 120 130 140 150

1 10

Mh / GeV

MSUSY / TeV 0.2

FlexibleEFTHiggs/NMSSM FlexibleSUSY/NMSSM SOFTSUSY 3.6.2 SARAH/SPheno NMSSMTools 4.8.2 SARAH/SPheno FS-like ΔMhFlexibleSUSY ΔMhFlexibleEFTHiggs

-8 -6 -4 -2 0 2 4 6 8

1 10

ΔMh / GeV

MSUSY / TeV λ = 0.4

0.2 ΔMh(4 x yt)

ΔM_h^(Q)

-8 -6 -4 -2 0 2 4 6 8

1 10

ΔMh / GeV

MSUSY / TeV

λ = 0.4

0.2

ΔM_h^(Q) ΔMh(Qmatch) ΔM_h^(yt 0L vs. 1L)

Only SPheno has complete 2-loop IR catastrophe, result unreliable for highM_SUSY

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MRSSM

40 50 60 70 80 90 100 110 120 130 140

1 10 100

Mh / GeV

M_SUSY / TeV 0.2

FlexibleEFTHiggs/MRSSM FlexibleSUSY/MRSSM 1L SARAH/SPheno 2L SARAH/SPheno 2L FS-like ΔM_hFlexibleSUSY ΔMhFlexibleEFTHiggs

Point SPheno SPheno SPheno SPheno FlexibleSUSY FlexibleEFT-

1L 2L 1L, (5) 2L, (5) 1L Higgs 1L

BM1⁰ 120.4 125.6±1.3 120.0 125.1±1.3 120.6 122.1±1.7 BM2⁰ 120.8 126.0±1.1 120.4 125.6±1.1 120.2 121.7±1.8 BM3⁰ 121.0 125.7±1.3 120.5 125.2±1.3 120.4 121.9±1.9

points from Diessner, Kalinowski, Kotlarski, DS

-10 -5 0 5 10

1 10 100

ΔMh / GeV

MSUSY / TeV 0.2

-10 -5 0 5 10

1 10 100

ΔMh / GeV

MSUSY / TeV 0.2

ΔMh(yt 0L vs. 1L) ΔMh(Qmatch) ΔMh(Q)

Complementary to/more precise than Sarah/SPheno (FO 2-loop), but uncertainty probably still underestimated

Dominik St¨ockinger Application to non-minimal models, further improvements 31/32

(48)

Improvements

1 1-loop matching → 2-loop matching

2 remove superfluous 2-loop terms induced in 1-loop matching

-4 -2 0 2 4 6 8 10

1 10 100

0.2 (Mh - MhFlexibleEFTHiggs/MSSM 2L) / GeV

MS / TeV

FlexibleEFTHiggs/MSSM 2L FlexibleEFTHiggs/MSSM 1L FlexibleSUSY/MSSM 2L FlexibleSUSY/HSSUSY 2L FlexibleSUSY/HSSUSY 1L SOFTSUSY 3.6.2 SARAH/SPheno FeynHiggs 2.12.2 SUSYHD 1.0.3 FlexibleEFTHiggs/MSSM 1L*

Alexander Voigt + Thomas Kwasnitza, preliminary

(49)

Conclusions

New approach combines FO + EFT

I understand differences, pros and cons

80 90 100 110 120 130 140

1 10 100

Mh / GeV

MSUSY / TeV 0.2

Comprehensive uncertainty estimates

I for fixed-order and EFT

I y_t-change and scale variation

-6 -4 -2 0 2 4 6

1 10 100

ΔMh / GeV

MSUSY / TeV 0.3

-6 -4 -2 0 2 4 6

1 10 100

ΔMh / GeV

MSUSY / TeV 0.3

uncertainty from varying CΔMh(yt2 0L vs. 1L) and C3 ΔMh(Qmatch) ΔMh(Q)

Applicable to non-minimal models

I NMSSM, MRSSM, . . .

I complementary to Sarah/SPheno

40 50 60 70 80 90 100 110 120 130 140

1 10 100

Mh / GeV

MSUSY / TeV 0.2

FlexibleEFTHiggs/MRSSM FlexibleSUSY/MRSSM 1L SARAH/SPheno 2L SARAH/SPheno 2L FS-like ΔMhFlexibleSUSY ΔMhFlexibleEFTHiggs

Dominik St¨ockinger Conclusions 33/32