Bayesian Naturalness and NMSSM Focus...
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The2ndIBS-KIASJointWorkshop@High111thJan2018
Bayesian Naturalness and NMSSM Focus Points
Doyoun Kim IBS-CTPU
arXiv:1709.07895 [hep-ph] JHEP 1710 (2017) 160
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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.
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Focus Point Scenario
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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:
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
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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.
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
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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
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�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]
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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
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Result
• Reexamined the Focus Point features
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LargeAterm
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Result
• Minimum fine-tuning measures found in the scans
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Result
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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.
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