Florian Staub | MU Programmtag 2016, 12th December 2016 · Physics beyond the SM Minimal...

KARLSRUHE INSTITUTE OF TECHNOLOGY, ITP & IKP

The generic approach to Higgs mass calculations

Florian Staub | MU Programmtag 2016, 12th December 2016

KIT – Die Forschungsuniversität in der Helmholtz-Gemeinschaft www.kit.edu

Physics beyond the SM

Minimal supersymmetry (MSSM) is the best studied extension

Solves the hierarchy problem

Predicts gauge coupling unification

Provides a dark matter candidate

Relates EWSB and large top mass

Precision calculationsMany calculations to get precise predictions for the Higgs mass, flavourobservables, . . . were mainly done in the context of the MSSM.

Public tools to study SUSYThe tools used so far (SoftSusy, Suspect, Isajet, Superiso, Susy_Flavor, FeynHiggs, NMSSMTools, . . . )

can handle only very few models.

Beyond the SM

Florian Staub – The generic approach to Higgs mass calculations (MU Programmtag, 12.12.16) 2/19

Beyond the SM

The problems of minimalsupersymmetry

The natural MSSM gets currently disfavoured by1 null results at LHC2 rather heavy Higgs mass

Possible solution:1 The SUSY scale is much higher than expected

→ see talk by Emanuele

2 Nature has chosen another (SUSY) model

Golden era of model building?Many more BSM models are studied than before the LHC was turned on

Beyond the SM

Ideas to increase the Higgs mass

Extended Higgs/Gauge sectorFor instance in singlet/triplet extensions, gauge extensions, orR-symmetric models.

F /D-term enhanced tree-level mass

Mixing with lighter scalars

Extended Matter sectorFor instance in vector-like extensions

New loop corrections to Higgs mass

Beyond the SM

Ideas to increase the Higgs mass

Extended Higgs/Gauge sectorFor instance in singlet/triplet extensions, gauge extensions, orR-symmetric models.

F /D-term enhanced tree-level mass

Mixing with lighter scalars

Extended Matter sectorFor instance in vector-like extensions

New loop corrections to Higgs mass

Beyond the SM

Many ideas exist to go beyond the SM(without any claim to completeness)

SUPERSYMMETRY

COMPOSITE MODELSEXTRA DIMENSIONS

STRING THEORY

QUANTUMGRAVITY

SEESAW MODELS

AXION(-LIKE)MODELS

EXTRA GAUGE GROUPS

UNPARTICLES

HIDDEN SECTOR

milli-chargedparticles

VECTOR-LIKEFERMIONS

SINGLET EXTENSIONS

LEPTO-QUARKS

Beyond the SM

Many ideas exist to go beyond the SM(without any claim to completeness)

SUPERSYMMETRY

COMPOSITE MODELSEXTRA DIMENSIONS

STRING THEORY

QUANTUMGRAVITY

SEESAW MODELS

AXION(-LIKE)MODELS

EXTRA GAUGE GROUPS

UNPARTICLES

HIDDEN SECTOR

milli-chargedparticles

VECTOR-LIKEFERMIONS

SINGLET EXTENSIONS

LEPTO-QUARKS

NMSSMGNMSSM

real SSMcomplex SSM

SLQtrilinear

U(1)-LSSM

bilinearRpV

MRSSMDiracNMSSM

SplitSUSYµνSSM

MDGSSM

E6MSSM

M-Theory

F-Theory

Heterotic

Type-IIA&B

Type-I

Type-IType-II

Type-III

Flipped

Lepto-Specific

Type–IType–II

Type–III

inverse S.linear S.

radiativeSeesaw

Randall-Sundrum

Bulk Higgs

B−L Left-Right Pati-S

SO(10)SU(5)

T ′ T ′′B′

E′Q′

Little Higgs

Littlest HiggsTechnicolor

Twin Higgs

Mirror World

Dark Photon

Relaxion

PQ Axion

MajoronFamilons

Beyond the SM

Many BSM models become more and more popular,. . .

. . . , but precision calculations for them rarely exist:

→ uncertainty in Higgs mass prediction usually much bigger than inMSSM

→ A new approach was needed to confront many BSM models withthe Higgs (mass) measurements

Beyond the SM

Many BSM models become more and more popular,. . .. . . , but precision calculations for them rarely exist:

Beyond the SM

Many BSM models become more and more popular,. . .. . . , but precision calculations for them rarely exist:

Beyond the SM

Generic Higgs mass calculations

Thousands of Feynman diagrams are needed to be calculated:

e k e k

u k u k

d k d k

Χ k Χ l

Χ m Χ n

e k e k

Χ k Χ l

Χ m Χ n

e k e k

u k u k

d k d k

u k u k

d k d k

Χ k Χ l

Χ m Χ n

u k d l

→ can be reduced to a small number of generic diagrams

Generic approach

Generic Higgs mass calculations

Thousands of Feynman diagrams are needed to be calculated:→ can be reduced to a small number of generic diagrams

Generic expressions

S1Sout1 Sout2c1c2

Generic expression f (mouti ,mS,mFi ,ci) are

Valid for any model and for any real scalar

→ Disentangle the calculation of . . .

. . . loop amplitudes (difficult) and masses & couplings (easy)

Generic approach

Fully automatised two-loop calculations

The combination SARAH/SPheno provides a fully automatised two-loopcalculation of the Higgs mass in SUSY models.

Approach[Goodsell,Nickel,FS,1411.0675,1503.03098]

Generic one- and two-loop calculations which are matched onconcrete models.

Auto-generated Fortran code for numerical evaluation

Approximations @2-loop: gaugeless limit (g1 = g2 = 0), p2 = 0:

similar precision as most public tools provide for MSSM

All available (DR) two-loop results (MSSM, NMSSM) are exactlyreproduced!

CP violation possible [Goodsell,FS,1604.05335]

Generic approach

The setup

Mathematica Code(Analytical calculations)

Masses &Verticesin model

Generic exp. formasses &vertices

Generic loopexpressions

Expressions forHiggs mass

Fortran Code(Numerical calc.)

NumericalRoutines

LoopIntegrals

Higgs mass

User defined model

Generic approach

New results for the Higgs mass

The setup was used to calculate many new two-loop results:

Contributions from trilinear RpV [Dreiner,Nickel,FS,1411.3731]

Missing corrections in the NMSSM [Goodsell,Nickel,FS,1411.4665 ]

CP violating NMSSM beyond O(αsαt) [Goodsell,FS, 1604.05335 ]

Contributions from non-holomorphic soft-terms[Ün, Tanyildizi,Kerman Solmaz,1412.1440]

MRSSM [Diessner,Kalinoswki,Kotlarski,Stöckinger,1504.05386]

Contributions from vectorlike (s)tops [Nickel,FS,1505.06077]

Other vector-like states [Basirnia, Macaluso, Shih, 1605.08442]

The MSSM beyond MFV [Goodsell,Nickel,FS,1511.01904]

The Higgs mass in non-minimal SUSY models

The MSSM beyond MFV

The soft-breaking Lagrangian provides in general many new couplings

LSB = ·· ·+T iju u∗

i qjHu +T ijd d∗

i qjHd +T ije e∗i ljHd +h.c.

T 32u and T 23

u hardly constrained by flavour observables

→ can be huge

→ known impact on the Higgs mass at one-loop: up to 60 GeV![Arana-Catania,Heinemeyer,Penaranda,1109.6232]

The MSSM beyond MFV

i qjHu +T ijd d∗

T 32u and T 23

→ can be huge

The MSSM beyond MFV

i qjHu +T ijd d∗

T 32u and T 23

→ can be huge

The MSSM beyond MFV

i qjHu +T ijd d∗

T 32u and T 23

→ can be huge

What happens at two-loop?

The MSSM beyond MFV

i qjHu +T ijd d∗

T 32u and T 23

→ can be huge

What happens at two-loop?

When are the two-loop effects large?

[Goodsell,Nickel,FS,1511.01904]

Important effects of several GeV in case of . . .. . . specific ratios of T-terms

. . . hierarchy between soft masses

Bounds from Vacuum stability and flavour constraints inlcudedThe Higgs mass in non-minimal SUSY models

When are the two-loop effects large?

[Goodsell,Nickel,FS,1511.01904]

Important effects of several GeV in case of . . .. . . specific ratios of T-terms. . . hierarchy between soft masses

Bounds from Vacuum stability and flavour constraints inlcudedThe Higgs mass in non-minimal SUSY models

Two-loop corrections in the NMSSM

αS(αb +αt) (known before)

f ′j

MSSM-likefi

f ′j

NMSSM-specific(available for first time!)

χ′j

φ′k

φ′j

NMSSM results I: heavy singlet & large λ[Goodsell,Nickel,FS,1411.4665]

κ= 1.6 tanβ= 3 Tλ = 600 GeV Tκ =−2650 GeV µeff = 614 GeV

m2f= 2 ·106 GeV2 Ti = 0 M1 = 200 GeV M2 = 400 GeV M3 = 2000 GeV

1.0 1.1 1.2 1.3 1.4 1.5 1.6

1.54 1.56 1.58 1.60 1.62

1–loop / αS(αb +αt ) / full / MSSM approx.

Additional corrections crucial for (very) large λ

Using MSSM results not a good approximation anymore

NMSSM results II: light singlet[Goodsell,Nickel,FS,1411.4665]

κ= 0.596 Tλ =−27 GeV Tκ =−240 GeV µeff = 130 GeV

Tt =−3050 GeV Tb = Tτ =−1000 GeV m2tL

= 9.0 ·105 GeV2 m2tR

= 1.05 ·106 GeV2

0.55 0.56 0.57 0.58 0.59 0.60

1–loop / αS(αb +αt ) / full

Corrections can be larger than the ones ∼αS

Again, MSSM approximations fail

Vectorlike top partners[Nickel,FS,1505.06077]

MSSM with vectorlike top partners

W = WMSSM +Y it′QiT

′Hu +MT ′T ′T ′+mit′UiT

→ Only 1-loop eff. pot results available before

Impact of additional corrections:

0.0 0.2 0.4 0.6 0.8 1.0

eV] BT ′ = 0 (dashed), BT ′ = (1.5 TeV)2 (full), tanβ =

3, MT ′ = 1.0 TeV

shifts by momentum dependence, one-loopthresholds to Ytop, two-loop corrections

Vectorlike top partners[Nickel,FS,1505.06077]

MSSM with vectorlike top partners

W = WMSSM +Y it′QiT

′Hu +MT ′T ′T ′+mit′UiT

→ Only 1-loop eff. pot results available before

Impact of additional corrections:

0.0 0.2 0.4 0.6 0.8 1.0

eV] BT ′ = 0 (dashed), BT ′ = (1.5 TeV)2 (full), tanβ =

3, MT ′ = 1.0 TeV

shifts by momentum dependence, one-loopthresholds to Ytop, two-loop corrections

Models with Dirac gauginos

Models with Dirac gauginos have nice features:

Suppressed flavour constraints

Suppressed production of coloured SUSY states at the LHC

Running of m2Hu

independent of gluino mass

The effects on the Higgs mass are very different compared to the MSSM:

Tree-level Higgs mass is usually suppressed

No A-terms: stop corrections are suppressed

New sgluon corrections at two-loop

Other, potentially large couplings (depending on the model)

Models with Dirac gauginos

Models with Dirac gauginos have nice features:

Suppressed flavour constraints

Suppressed production of coloured SUSY states at the LHC

Running of m2Hu

independent of gluino mass

The effects on the Higgs mass are very different compared to the MSSM:

Tree-level Higgs mass is usually suppressed

No A-terms: stop corrections are suppressed

New sgluon corrections at two-loop

Other, potentially large couplings (depending on the model)

MRSSMW = WY +µD RdHd +µU RuHu + S(λd RdHd +λu RuHu)+Λd RdT Hd +Λu RuT Hu .

New superpotential terms to increase Higgs mass

New coloured corrections

[Diessner,Kalinoswki,Kotlarski,Stöckinger,1504.05386]

2.0 1.5 1.0 0.5 0.0 0.5 1.0 1.5 2.0

4.55.05.56.06.57.07.58.0

m2L−m

eV] 60

2.0 1.5 1.0 0.5 0.0 0.5 1.0 1.5 2.0

456789

101112

m2L−m

MRSSMW = WY +µD RdHd +µU RuHu + S(λd RdHd +λu RuHu)+Λd RdT Hd +Λu RuT Hu .

New superpotential terms to increase Higgs mass

New coloured corrections

[Diessner,Kalinoswki,Kotlarski,Stöckinger,1504.05386]

500 1000 1500 2000 2500 3000

MDO [GeV]

m2L−m

all contributionsno sgluonand no gluinoand no gluon

and no α 2t , αtαb

500 1000 1500 2000 2500 3000 3500 4000 4500

MDO [GeV]

m2L−m

MRSSM, mO =2 TeV

MRSSM, mO =10 TeV

MRSSM, no sgluon contrb.MSSM, no tree-level stop mixingMSSM, strong stop mixing

Summary

There is still plenty of space to discover new physics at the LHC orsomewhere else . . .

. . . but the probability is increasing that it is not minimal SUSY

Need for generic Higgs mass calculationsMost extensions of the SM or MSSM have a large impact on the Higgssector:

→ Generic calculations are needed to confront many models with theHiggs measurements

The combination SARAH/SPheno are the only available tools to gettwo-loop Higgs masses for many different models

Summary and outlook

Summary

Summary and outlook

Summary

Summary and outlook

Summary

Summary and outlook

Florian Staub | MU Programmtag 2016, 12th December 2016 · Physics beyond the SM Minimal...

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