FlexibleSUSY: an attempt towards automated BSM physicsstudies
Jae-hyeon Park
KIAS Quantum Universe Center
Beyond the BSM(The 4th Kavli IPMU-Durham IPPP-KEK-KIAS workshop)
HOTEL 天坊 伊⾹保町, 02.10.2018
Refs.
Athron, JhP, Stöckinger, Voigt, CPC190(2015)139
Athron, JhP, Stöckinger, Voigt, NPPP273(2016)2424
A,P,S,V, Steudtner, JHEP01(2017)079
A,P,S,V, Bach, Harries, Kwasnitza, Ziebell, CPC230(2018)145
JhP, 1809.07774

FlexibleSUSY: an attempt towards automated BSM physics studies

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FlexibleSUSY: an attempt towards automated BSM physics studies

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2 / 29Public spectrum calculators
ModelSpectrum calculators

MSSM

ISASUSY, Softsusy, SPheno,
SuSeFlav, SuSpectNMSSM
NMSPEC, Softsusy
User-defined SARAH Staub , FlexibleSUSY
SARAH
generates code inFlexibleSUSY

FORTRAN C++11reuses code fromSPheno
symbolic calculation
doneof β-functions etc.

Softsusy
invokes SARAH

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How FlexibleSUSY works
FlexibleSUSY model file

SARAH model file
SARAH

FlexibleSUSY
meta-codetree-level masses
interaction vertices
self-energies
tadpolesβ-functions

compiler
C++11 class library

spectrum calculator
executable

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Tower of effective field theories
Typical example: LFV from SUSY see-saw
RGFlowMSSMRHN_high_scale_constraintMX

MSSMD5O_MSSMRHN_matching

Mν

MSSMD5O_susy_scale_constraintMS

MSSMD5O_low_scale_constraint

MZ

MSSMRHNMSSMD5O

Other configurations of interest:▸ GUT [SU(5), SO(10), E ] → MSSM
6▸ Split-SUSY, high-scale SUSY
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Boundary value problem

Constrain m2H , m̃2 , Ma , Afenergy
scale

MSSM example

MXImpose EWSB condition
Calculate pole masses

MSConstrain ga , yf

MZ

RGE:dga= β ga
d ln μRGE:

dv= βvd ln μFlexibleSUSY: an attempt towards automated BSM physics studies

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Boundary conditions at MX
CMSSM(m2f )ij (MX ) = m20 δij
Afij (MX ) = A0
Mi (MX ) = M1/2
NUHMSSMSame as above exceptHiggs soft masses ≠ m0
something elseFlexibleSUSY: an attempt towards automated BSM physics studies

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8 / 29Pole mass spectrum

Find p such that0 = det [p2 1 − mtree − Σ(p2 )]By default, self energy Σ is calculated to 1-loop
In (N)MSSM, FlexibleSUSY calls external FORTRAN routines toevaluate 2-loop Higgs mass corrections
SlavichFlexibleSUSY: an attempt towards automated BSM physics studies

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Higgs mass in MSSM
Okada, Yamaguchi, Yanagida; Ellis, Ridolfi, Zwirner; Haber, Hempfling(m2h )0 = m2Z cos2 2β
M2SUSY
3g224m ln ()8π 2 m2W tm2t⎡
⎢ 4 2g22 Nc
X2t
2⎢(Δmh )1,mix ≃)2m X (1 −16π 2 m2W M2SUSY ⎢⎢ t t
12M2SUSY⎣⎤⎥
X2b4 2⎥+ 2mb Xb (1 −)12M2SUSY ⎥⎥⎦(Δm2h )1,log ≃Xt ≡ At − μ cotβ,Xb ≡ Ab − μ tanβFlexibleSUSY: an attempt towards automated BSM physics studies

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Automated Higgs mass calculation
Categories of multi-loop Higgs mass calculation:
1
Fixed-order:
1
Diagrammatic approachHempfling, Hoang, Heinemeyer, Hollik, Weiglein
2

Effective potential
Brignole, Dedes, Degrassi, Slavich, Zwirner, Martin

2Resummation via EFT
Casas, Espinosa, Quirós, Riotto, Carena, Wagner

SARAH performs 1 2 for user-defined models
Goodsell, Nickel, Staub

FlexibleEFTHiggs is a variant of 2 implemented in
FlexibleSUSY
Athron, JhP, Stöckinger, Voigt, Steudtner
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11 / 29FlexibleEFTHiggs
A variant of EFT approach
Assume SM as EFT
High-scale matching condition:
2SUSY 2(MSM)h ) = (Mhinstead of λ-matching

Automatizable using only pole masses (available from SARAH)
Not a full SMEFT, works only for mh calculation
Current accuracy: 1-loop matching + 3-loop runningWork on 2-loop matching is underway

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MSSM, varying MSUSY
140130Mh / GeV

120110FlexibleEFTHiggs/MSSM
FlexibleSUSY/MSSM
FlexibleSUSY/HSSUSYSOFTSUSY 3.6.2
SARAH/SPheno
FeynHiggs 2.12.0
SUSYHD 1.0.2

10090800.2110100

MSUSY / TeV

tanβ = 5,Xt = 0
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MSSM theory uncertainties, Xt = 0135130

Xt = 0125120
Mh / GeV

115110105
10095

FlexibleEFTHiggs/MSSM
FlexibleSUSY/MSSM
ΔMhFlexibleSUSY
ΔMhFlexibleEFTHiggs

9085800.2110100

MSUSY / TeV

tanβ = 5
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NMSSM, varying MSUSY
150
FlexibleEFTHiggs/NMSSM
FlexibleSUSY/NMSSMSOFTSUSY 3.6.2
SARAH/SPheno
NMSSMTools 4.8.2
SARAH/SPheno FS-likeΔMhFlexibleSUSY
ΔMhFlexibleEFTHiggs

140130Mh / GeV

120110100908070
60

0.2

110MSUSY / TeV

tanβ = 5,Xt = 0,

λ = κ = 0.4

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E6 SSM
150140Mh / GeV

130120110FlexibleEFTHiggs/E6SSM
FlexibleSUSY/E6SSM
SARAH/SPheno
SARAH/SPheno FS-likeΔMhFlexibleSUSY
ΔMhFlexibleEFTHiggs

10090800.2

110MSUSY / TeV

tanβ = 5,

Xt = 0,λ = 0.1

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MRSSM
140130120

Mh / GeV

110
1009080
FlexibleEFTHiggs/MRSSM
FlexibleSUSY/MRSSM 1L
SARAH/SPheno 2L
SARAH/SPheno 2L FS-likeΔMhFlexibleSUSY
ΔMhFlexibleEFTHiggs

706050400.2

110100MSUSY / TeV

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FlexibleAMU for aμ ≡ (gμ − 2)/2Calculates aBSMat 1-loop level
μGeneric diagrams
γFFSγ

SS
Fµµµµ
All possible BSM diagrams are auto-generated
Renormalization scale is set to running mass of lightest charged
BSM particle in loop
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FlexibleCPV
Allows for complex-valued parameters
Calculates lepton EDMs at 1-loop level
de in CP-violating MSSM
0.40.004

−

φM1/2

0.002

0.

−0.002

0.

1−87

0.2

−0.287de /(10−28 ecm)
bounds on de0
φµ0.002

0.004

μAe > 0FlexibleSUSY: an attempt towards automated BSM physics studies

0.

0.

−

187

5000.

5

−0.004 −0.002−500−0.004

0.

1

φAe

−0.

−

0.
1587

de /(10−28 ecm)
bounds on de

−0.4
−0.4

−0.20
φµ0.2

0.4

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FlexibleCPVCP-violating CMSSM
111.502000(T u )33 / GeV

Mh / GeV

111.00110.50−200−400Re(T u )33 FlexibleSUSY 2.0110.00
FlexibleSUSY 2.0SPheno 4.0.2

109.50−π0φµIm(T u )33 FlexibleSUSY 2.0−600Re(T u )33 SPheno 4.0.2
Im(T u )33 SPheno 4.0.2

π−800104106108 1010 1012
Q / GeV10141016

1-loop lightest Higgs pole mass
2-loop RG running of stop trilinear coupling
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20 / 29FlexibleMWCalculates muon decay constant GF at 1-loop level
Can determine g1 and g2 from GF and MZGeneric diagrams
ffνei eieiWWνei µf1

f3

f2

All possible BSM diagrams are auto-generated

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EFT picture of bounds on MSUSY0.10
3Σ bands in
Mt = 173.3 ± 0.8 GeV HgrayL
Α3 HMZ L = 0.1184 ± 0.0007HredL
Mh = 125.1 ± 0.2 GeV HblueLHiggs quartic coupling Λ0.08
0.06
0.04Matching condition of λ atMSUSY
1
λ = (g22 + g2Y ) cos2 2β+4threshold corrections

0.02
Mt = 171.1 GeV

0.00

Αs HMZ L = 0.1205-0.02

Αs HMZ L = 0.1163
Mt = 175.6 GeV

-0.04
102

104

106

108 1010 1012 1014 1016 1018 1020
RGE scale Μ in GeV

Buttazzo, Degrassi, Giardino, Giudice, Sala, Salvio,Strumia (2013)
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Trilinears for fitting Higgs mass̃ b̃cSupersymmetric trilinear ΔLSUSY = yb μ H∗u QSoft SUSY breaking trilinears
̃ t̃c − Tb Hd Q̃ b̃c
ΔLsoft = Tt Hu Qhenhance e.g. h-b̃L -b̃R vertices in(Tt ≡ yt At , Tb ≡ yb Ab )b̃Lhhb̃Rb̃Lb̃RhUse FlexibleSUSY-2.2.0 to calculate Higgs mass in high-scale(split) MSSM in EFT approach
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Vacuum metastability constraintRequire (Γ/V)T4 < 1 where T is age of Universe andΓ/V = A exp (−S [ϕ])with “bounce” ϕBounce of ϕ = {h, H, b̃L , b̃R , t̃L , t̃R } within tree-level scalar potential
is numerically obtained using CosmoTransitions
Wainwright (2012)

Estimate A ≈ M4SUSY↝ S ≳ 400 is safe if MSUSY ≈ 100 GeVClaudson, Hall, Hinchliffe (1983)↝S ≳ 560

if MSUSY = MPlanck
For 1-loop calculation of A, see Endo, Moroi, Nojiri, Shoji

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Metastability constraint does not decouple
Consider action
11S = ∫ dx4 [ (∂ϕ)2 + m2 ϕ2 + Aϕ3 ]22
whose bounce is ϕ(x)ϕ′ (x) ≡ aϕ(ax) is then a bounce of
11S′ = ∫ dx4 [ (∂ϕ)2 + (am)2 ϕ2 + (aA)ϕ3 ]22withS[ϕ] = S′ [ϕ′ ] = S(A/m)

modulo scale anomaly
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Xt reproducing correct mh
5.0
4.5|Xt / MSUSY|

4.0
3.5
3.0

Δmt = +0σ

2.52.01081010

101210141016

MSUSY / GeV

High-scale SUSYμ > 0, Tt < 0tanβ = 1, Xb = Xτ = 0
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Xt reproducing correct mh
5.0
4.5|Xt / MSUSY|

4.0
3.5
3.0

Δmt = +1σΔmt = +0σΔmt = -1σ2.5

2.0108101010121014

1016

MSUSY / GeV

High-scale SUSY
μ > 0, Tt < 0tanβ = 1, Xb = Xτ = 0
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Xt reproducing correct mh5.04.5|Xt / MSUSY|

4.0
3.5
3.0

Δmt = +2σΔmt = +1σΔmt = +0σΔmt = -1σΔmt = -2σ2.52.01081010

101210141016

MSUSY / GeV

High-scale SUSY
μ > 0, Tt < 0tanβ = 1, Xb = Xτ = 0
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Xt reproducing correct mh
5.0
4.5|Xt / MSUSY|

4.0
3.5
3.0

Δmt = +2σΔmt = +1σΔmt = +0σΔmt = -1σΔmt = -2σ

2.5
CCB limit2.01081010101210141016

MSUSY / GeV

High-scale SUSY
μ > 0, Tt < 0tanβ = 1, Xb = Xτ = 0
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Xt reproducing correct mh
5.0
4.5|Xt / MSUSY|

4.0
3.5
3.0

2.5

Δmt = +2σΔmt = +1σΔmt = +0σΔmt = -1σΔmt = -2σΓvac limit
CCB limit

2.01081010

101210141016

MSUSY / GeV

High-scale SUSY
μ > 0, Tt < 0tanβ = 1, Xb = Xτ = 0FlexibleSUSY: an attempt towards automated BSM physics studies

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Xt reproducing correct mh
75.0

64.5

53.5
3.0

2.5

Δmt = +2σΔmt = +1σΔmt = +0σΔmt = -1σΔmt = -2σΓvac limit
CCB limit

2.01081010

10121014

1016|Xt / MSUSY||Xt / MSUSY|

4.0

Δmt = +2σΔmt = +1σΔmt = +0σΔmt = -1σΔmt = -2σΓvac limit
CCB limit

432106MSUSY / GeV1081010

101210141016

MSUSY / GeVHigh-scale SUSY
Split SUSY
μ > 0, Tt < 0m1/2 = μ = 1 TeVtanβ = 1, Xb = Xτ = 0FlexibleSUSY: an attempt towards automated BSM physics studies

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Tb reproducing correct mh
3.0
4.0
3.5

2.0

3.0

1.5

2.5

1.0

Δmt = +2σΔmt = +0σ
Γvac limit

0.51081010|Tb / MSUSY||Tb / MSUSY|

2.5+1σ-1σΔmt = +2σΔmt = +1σΔmt = +0σΔmt = -1σΔmt = -2σΓvac limit

2.0

1.5-2σ1012

101410161.0106

MSUSY / GeV

1081010101210141016

MSUSY / GeV

High-scale SUSY
Split SUSY
μ > 0, Tb < 0m1/2 = μ = 1 TeVtanβ = 1, Xt = Xτ = 0FlexibleSUSY: an attempt towards automated BSM physics studies

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Very high tanβ reproducing correct mh
Pardo Vega, Villadoro (2015)
400

★

★

350
300

Δmt = +2σΔmt = +1σΔmt = +0σΔmt = -1σΔmt = -2σΓvac limit
CCB limit

tanβ50105250tanβ100

Δmt = +2σΔmt = +1σΔmt = +0σ
Δmt = -1σΔmt = -2σΓvac limit
CCB limit

2001501001104

106

108

1010 1012 1014 1016

1041061081010 1012 1014 1016
MSUSY / GeV

MSUSY / GeV

High-scale SUSY
μ < 0, Tb = 0, Xt = Xτ = 0
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SummaryFlexibleSUSY auto-generates high-quality spectrum calculator
codes for user-defined (non-)supersymmetric models
New features of FlexibleSUSY 2 include:▸ FlexibleEFTHiggs for resummed mh calculation at NLO +NLL
▸ FlexibleAMU for (gμ − 2)
▸ FlexibleCPV for complex parameters and lepton EDMs
▸ FlexibleMW for θ
W from GFDevelopments underway: decays, LFV, QFV, 2-loop matching
onto SM, 1-loop matching onto 2HDMs
Metastability makes it difficult to reconcile arbitrarily high MSUSY
with mh using trilinear couplings unless mt is lowered by 2σ
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