The2ndIBS-KIASJointWorkshop@High111thJan2018

Bayesian Naturalness and NMSSM Focus Points

Doyoun Kim IBS-CTPU

arXiv:1709.07895 [hep-ph] JHEP 1710 (2017) 160

1

Introduction

• History of endeavor to seek beautiful and well-performing theory recently raised Naturalness problem.

• For three decades, the problem of the physical Higgs mass has been rephrased as ‘Hierarchy’, ‘Naturalness’, and ‘Fine-tuning’ prob. etc.

• Various mechanisms (models) are found to solve the ‘Big Hierarchy’ prob. that stabilizes the EWSB scale from the radiative corrections.

• However, it may require another fine-tuning even for such models in order to reproduce the observed world.

• Here, the supersymmetric (SUSY) examples will be discussed.But the extension to other models are straight forward.

The2ndIBS-KIASJointWorkshop@High111thJan2018

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Focus Point Scenario

3

Focus Point Scenario

• In SUSY models, electroweak symmetry breaking (EWSB) condition relates the low energy observables (Mz, tanb) to the model parameters:

The2ndIBS-KIASJointWorkshop@High111thJan2018

M2Z

2= �

m̄2Hu

tan2 � � m̄2Hd

tan2 � � 1� |µ|2 � 1

2Re⇧T

ZZ

Zpolemass Tree+Coleman-Weinberg TransversepartofZbosonselfenergy

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Focus Point Scenario

• In SUSY models, electroweak symmetry breaking (EWSB) condition relates the low energy observables (Mz, tanb) to the model parameters:

• Fine-tuning problem asks how the new physics: 1. Satisfies EWSB at a proper energy scale. (Little hierarchy prob.) 2. Stability of 1.

The2ndIBS-KIASJointWorkshop@High111thJan2018

M2Z

2= �

m̄2Hu

tan2 � � m̄2Hd

tan2 � � 1� |µ|2 � 1

2Re⇧T

ZZ

Zpolemass Tree+Coleman-Weinberg TransversepartofZbosonselfenergy

5

Focus Point Scenario

• In SUSY models, electroweak symmetry breaking (EWSB) condition relates the low energy observables (Mz, tanb) to the model parameters: and

• Fine-tuning problem asks how the new physics: 1. Satisfies EWSB (Little hierarchy prob.) 2. Stability of 1.

The2ndIBS-KIASJointWorkshop@High111thJan2018

��M2Z

2

t�1⇡ �m̄2Hu

+ � |µ|2�M2Z

2

t�1⇡ m̄2Hu

+ |µ|2

µ �|µ|2Sincetermisnatural,iswell-controlled.

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Focus Point Scenario

• In SUSY models, electroweak symmetry breaking (EWSB) condition relates the low energy observables (Mz, tanb) to the model parameters: and

• Fine-tuning problem asks how the new physics: 1. Satisfies EWSB (Little hierarchy prob.) 2. Stability of 1.

• Fine-tuning in SUSY is how is stabilized around the EW scale.

The2ndIBS-KIASJointWorkshop@High111thJan2018

��M2Z

2

t�1⇡ �m̄2Hu

+ � |µ|2�M2Z

2

t�1⇡ m̄2Hu

+ |µ|2

µ �|µ|2Sincetermisnatural,iswell-controlled.

m̄2Hu

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Focus Point Scenario

• Fortunately, we have a large set of such examples.

The2ndIBS-KIASJointWorkshop@High111thJan2018

tanb=50 tanb=5

m0=7TeV

m0=4.5TeV

m0=2TeV

3.5TeV1.1TeV

m1/2/g0=2.3TeV,A0=0

DKandB.Kyae,PRD92(2015)0750525,[arXiv:1507.07611]

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Focus Point Scenario

• Fortunately, we have a large set of such examples.

The2ndIBS-KIASJointWorkshop@High111thJan2018

tanb=50 tanb=5

m0=7TeV

m0=4.5TeV

m0=2TeV

3.5TeV1.1TeV

m1/2/g0=2.3TeV,A0=0

FOCUS

POINT

DKandB.Kyae,PRD92(2015)0750525,[arXiv:1507.07611]

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Focus Point Scenario in CMSSM

The2ndIBS-KIASJointWorkshop@High111thJan2018

DK,P.Athron,C.Balazs,B.Farmer,E.Hutchison,PRD90(2014)055008[arXiv:1312.4150]

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Focus Point Scenario in CNMSSM

The2ndIBS-KIASJointWorkshop@High111thJan2018

DK,P.Athron,C.Balazs,B.Farmer,E.Hutchison,PRD90(2014)055008[arXiv:1312.4150]

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Focus Point Scenario

• In this scenario, is small and dominates

• Thus the stability of EW scale can be measured by defining the fine-tuning as

• This is another derivation of Barbieri-Giudice(-Ellis-Nanopoulos)’s fine-tuning measure, proposed in 1988 (1986):

• Note: Focus Point scenario was found 10 years later. Chan, Chattopadhyay, and Nath, PRD 58, 096004 (1998) Feng, Matchev and Moroi, PRD 61 (2000) 075005

The2ndIBS-KIASJointWorkshop@High111thJan2018

��M2Z

2

t�1⇡ �m̄2Hu

+ � |µ|2�m̄2

Hu�|µ|2

µ2

M2Z

�M2Z

�µ2

�BG = maxi

����@ lnM2

Z

@ ln pi

����

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Fine-tuning Measure

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• Measures perturbative sensitivity of a low energy observable as the model parameters’ fluctuation.

The2ndIBS-KIASJointWorkshop@High111thJan2018

�BG

�BG =X

i

����@ lnM2

Z

@ ln pi

���� ⇠ maxi

����@ lnM2

Z

@ ln pi

���� ⇠����µ2

M2Z

@M2Z

@µ2

���� =µ2

M2Z

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• Generalization: Encapsulates the correlation among the observables.

• Note: Correlations among the high scale model parameters may reduce the fine-tuning at the EW scale.

The2ndIBS-KIASJointWorkshop@High111thJan2018

�J

�J =

����

����@ lnOi

@ ln pj

����

���� ⇠�VO

�Vp

JlogMz

Jlog t

Jlogmt

⇠

H.Baer,V.Barger,D.Mickelson[arXiv:1309.2984]

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• Interestingly, this measure is systematically embedded in the program of Bayesian analysis for the new physics search, in form of the effective prior.

• DISCLAIMER: There is a controversy in model comparison due to the irreducible prior prob. dependency.Therefore, we focus on the param. estimation in a given model even though we present the evidence estimation for each model

The2ndIBS-KIASJointWorkshop@High111thJan2018

�J

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Bayesian Analysis

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Bayesian Naturalness [arXiv:1312.4150]

• In Bayesian Analysis, fine-tuning nature of the Jacobian factor penalizes unnatural parameter regions.

• For example, in CMSSMM. E. Cabrera, J. A. Casas and R. Ruiz de Austri, JHEP 1005, 043 (2010) [arXiv:0911.4686]

The2ndIBS-KIASJointWorkshop@High111thJan2018

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Bayesian Analysis: Jacobian Effective Prior

• In Bayesian Analysis

• For CMSSM (a specific model)

The2ndIBS-KIASJointWorkshop@High111thJan2018

Posterior Evidence Likelihood Prior

Fine-tuningsensitivityofphysicaldatatothemodelparameters

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Bayesian Naturalness [arXiv:1312.4150]

• For CMSSM

• For CNMSSM

The2ndIBS-KIASJointWorkshop@High111thJan2018

JlogMz

Jlog t

Jlogmt

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The2ndIBS-KIASJointWorkshop@High111thJan2018

Bayesian Analysis: Jacobian Effective Prior

•

• are set released

Observable Experimental value

⌦DMh20.1187± 0.0017

mh 125.9± 0.4 GeV

BR (Bs ! µ+µ�) (2.9± 1.1)⇥ 10

�9

BR (b ! s�) (343± 21± 7)⇥ 10�6

BR (B ! ⌧⌫) (114± 22)⇥ 10�6

m�̃01

> 46 GeV

m�̃±1

> 94 GeV if m�̃±1�m�̃0

1> 3 GeV

mq̃ > 1.43 TeV

mg̃ > 1.36 TeV

A0 = �2.5 TeV, tan� = 10

A�, A

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Result

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Result

• Reexamined the Focus Point features

The2ndIBS-KIASJointWorkshop@High111thJan2018

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Result

• Reexamined the Focus Point features

The2ndIBS-KIASJointWorkshop@High111thJan2018

LargeAterm

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Result

• Minimum fine-tuning measures found in the scans

The2ndIBS-KIASJointWorkshop@High111thJan2018

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Result

The2ndIBS-KIASJointWorkshop@High111thJan2018

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Future prospect

• Strong Correlations are found among model parameters.

The2ndIBS-KIASJointWorkshop@High111thJan2018

MSSM

NMSSM

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Summary

• Physical consideration to find natural model parameters such as the Focus Point scenario, can be understood in terms of the Fine-tuning measure which is developed independently.

• Generalized fine-tuning measure is well accommodated with Bayesian approach through the effective prior probability.

• Two categories of benchmark points are well separated physically, and are interesting to study further.

The2ndIBS-KIASJointWorkshop@High111thJan2018

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