The Super-Natural Supersymmetry - USTC, ICTSicts.ustc.edu.cn/chinese/seminar/transparencies/Tianjun Li/Tian-Jun... · Introduction The SUSY EW Fine-Tuning Problem No-Scale F-SU(5)

IntroductionThe SUSY EW Fine-Tuning Problem

No-Scale F-SU(5)No-Scale MSSM

The Super-Natural Supersymmetry and Its GeneralizationsConclusion

The Super-Natural Supersymmetry

Tianjun Li

Institute of Theoretical Physics, Chinese Academy of Sciences

October 30, 2015

Tianjun Li ITP-CAS




References:

I T. Leggett, T. Li, J. A. Maxin, D. V. Nanopoulos andJ. W. Walker, arXiv:1403.3099 [hep-ph]; Phys. Lett. B 740,66 (2015) [arXiv:1408.4459 [hep-ph]].

I G. Du, T. Li, D. V. Nanopoulos and S. Raza, Phys. Rev. D92, no. 2, 025038 (2015) [arXiv:1502.06893 [hep-ph]].

I R. Ding, T. Li, F. Staub and B. Zhu, arXiv:1510.01328[hep-ph].

I T. Li, S. Raza, X. Wang, 1510.06851.

I Papers in preparations.

Tianjun Li ITP-CAS




Outline

Introduction

The SUSY EW Fine-Tuning Problem

No-Scale F-SU(5)

No-Scale MSSM

The Super-Natural Supersymmetry and Its Generalizations

Conclusion

Tianjun Li ITP-CAS




Outline

Introduction


No-Scale F-SU(5)

No-Scale MSSM


Conclusion

Tianjun Li ITP-CAS




The Standard Model

The Standard Model (SM) is a model that describes theelementary particles in the nature and the fundamentalinteractions between them.

Tianjun Li ITP-CAS




Fundamental Interactions

Interactions Invariant Symmetry Fields Spin

Gravity Diffeomorphism Graviton 2

Strong Gauge SU(3)C Gluon 1

Weak Gauge SU(2)L W±, W 0 1

Hypercharge Gauge U(1)Y B0 1

Tianjun Li ITP-CAS




Properties for the theories

Gauge theory is renormalizable, and described by quantumfield theory which is consistent with both quantummechanics and special relativity. However, gravity theory isnon-renormalizable, and we do not have a correct quantumgravity theory.

Tianjun Li ITP-CAS




Elementary Particles

I Three families of SM fermions:

Quarks : Q1 =

(U U UD D D

)L

, (U U U)R , (D D D)R .

Leptons : L1 =

(νE

)L

, ER .

I One Higgs doublet

H =

(H0

H−

).

Tianjun Li ITP-CAS




Lagrangian

LMSM = − 1

2g2s

TrGµνGµν − 1

2g2TrWµνW

µν

− 1

4g ′2BµνB

µν + iθ

16π2TrGµνG

µν + M2PlR

+|DµH|2 + Qi i 6DQi + Ui i 6DUi + Di i 6DDi

+Li i 6DLi + Ei i 6DEi −λ

2

(H†H − v2

2

)2

−(hijuQiUj H + hijdQiDjH + hijl LiEjH + c .c .

),

where H ≡ iσ2H∗. The SM has 20 parameters (19 without gravity): 3 gauge couplings, 1 Planck scale, 1

strong CP phase, 6 quark masses, 3 charged lepton mass, 3 CKM mixing angles, 1 CKM CP phase, 2 Higgs

parameters.

Tianjun Li ITP-CAS




The Higgs potential is

VHiggs =λ

2

(H†H − v2

2

)2

.

At minimum, Higgs field has a non-zero VEV

〈H0〉 =v√2.

All the gauge symmetries, under which H0 is charged, arebroken after Higgs mechanism.

Tianjun Li ITP-CAS




Symmetry Breaking

I SU(2)L × U(1)Y is broken down to the U(1)EM symmetry.

I W± and Z 0 become massive, and γ is massless

Z 0 = cos θWW 0 − sin θWB0 , γ = sin θWW 0 + cos θWB0 .

I The SM quarks and leptons obtain masses via Yukawacouplings, except the neutrinos.

I Higgs boson with mass around 125.5 GeV.

The SM explains existing experimental data very well,including electroweak precision tests.

Tianjun Li ITP-CAS




The Standard Model

I Fine-tuning problemscosmological constant problem; gauge hierarchy problem;strong CP problem; SM fermion masses and mixings; ...

I Aesthetic problems interaction and fermion unification; gaugecoupling unification; charge quantization; too manyparameters; ...

Tianjun Li ITP-CAS




The Standard Model

I Fine-tuning problemscosmological constant problem; gauge hierarchy problem;strong CP problem; SM fermion masses and mixings; ...

I Aesthetic problems interaction and fermion unification; gaugecoupling unification; charge quantization; too manyparameters; ...

Tianjun Li ITP-CAS




Gauge Hierarchy Problem

−L = λfHf f + λS |H|2|S |2 .

∆m2H = −|λf |

2

8π2Λ2UV +

λS16π2

Λ2UV .

Tianjun Li ITP-CAS




Gauge Hierarchy Problem

Tianjun Li ITP-CAS




Solutions

I Techicolor: the Higgs is a condensation of new fermions.Point: no fundamental scalar.

I Larger extra dimension(s): Arkani-Hamed-Dimopoulos-Dvali(ADD) and Randall-Sundrum (RS). Point: thehigh-dimensional Planck scale is close to the TeV.

I Supersymmetry.

I Little Higgs model, effective theories for compositeness, theanthropic solution, etc.

Tianjun Li ITP-CAS




Supersymmetry

I A supersymmetry transformation turns a bosonic state into afermionic state, and vice versa.

Q|Boson〉 = |Fermion〉, Q|Fermion〉 = |Boson〉.

I Algebra: supersymmetry generator Q is a fermionic operatorwith spin-1/2.

Q,Q† = Pµ,

Q,Q = Q†,Q† = 0,

[Pµ,Q] = [Pµ,Q†] = 0.

I Each supermultiplet contains an equal number of fermion andboson degrees of freedom.

Tianjun Li ITP-CAS




The Supersymmetry Standard Model

I Four-dimesional N = 1 supersymmetry: Kahler potential,superpotential, gauge kinetic function.

I A chiral SM fermion has a complex scalar partner.

I A gauge boson has a spin 1/2 partner.

I A graviton has a spin 3/2 partner.

Tianjun Li ITP-CAS




The Supersymmetry Standard Model

I Two Higgs doublet.

I R symmetry: R = (−1)3B−L+2s .

I The SM particle are even while the supersymmetric particlesare odd.

I Dark matter: neutralino, sneutrino, gravitino, etc.

I Solution to the proton decay problem.

Tianjun Li ITP-CAS




Names spin 0 spin 1/2 SU(3)C , SU(2)L, U(1)Y

squarks Q (uL dL) (uL dL) ( 3, 2 , 16 )

quarks u u∗R u†R ( 3, 1, −23 )

d d∗R d†R ( 3, 1, 13 )

sleptons L (ν eL) (ν eL) ( 1, 2 , −12 )

leptons e e∗R e†R ( 1, 1, 1)

Higgs Hu (H+u H0

u) (H+u H0

u) ( 1, 2 , + 12 )

Higgsinos Hd (H0d H−d ) (H0

d H−d ) ( 1, 2 , −12 )

Table: Chiral supermultiplets in the Minimal Supersymmetric StandardModel. The spin-0 fields are complex scalars, and the spin-1/2 fields areleft-handed two-component Weyl fermions.

Tianjun Li ITP-CAS




Names spin 1/2 spin 1 SU(3)C , SU(2)L, U(1)Y

gluino, gluon g g ( 8, 1 , 0)

winos, W bosons W± W 0 W± W 0 ( 1, 3 , 0)

bino, B boson B0 B0 ( 1, 1 , 0)

Table: Gauge supermultiplets in the Minimal Supersymmetric StandardModel.

Tianjun Li ITP-CAS




Gauge Coupling Unification for the SM and MSSM

Tianjun Li ITP-CAS




The Supersymmetric Standard Models

I Solving the gauge hierarchy problem

I Gauge coupling unification

I Radiatively electroweak symmetry breaking

I Natural dark matter candidates

I Electroweak baryogenesis

I Electroweak precision: R parity

Tianjun Li ITP-CAS




Problems in the MSSM:

I µ problem: µHuHd

I Little hierarchy problem

I CP violation and EDMs

I FCNC

I Dimension-5 proton decays

Tianjun Li ITP-CAS




The Grand Unified Theories: SU(5), and SO(10)

I Unification of the gauge interactions, and unifications of theSM fermions

I Charge quantization

I Gauge coupling unification in the MSSM, and Yukawaunification

I Radiative electroweak symmetry breaking due to the large topquark Yukawa coupling

I Weak mixing angle at weak scale MZ

I Neutrino masses and mixings by seesaw mechanism

Tianjun Li ITP-CAS




Problems:

I Gauge symmetry breaking

I Doublet-triplet splitting problem

I Proton decay problem

I Fermion mass problem: me/mµ = md/ms

Tianjun Li ITP-CAS




String Models:

I Calabi-Yau compactification of heterotic string theory

I Orbifold compactification of heterotic string theoryGrand Unified Theory (GUT) can be realized naturally through the elegant E8 breaking chain:

E8 ⊃ E6 ⊃ SO(10) ⊃ SU(5)

I D-brane models on Type II orientifoldsN stacks of D-branes gives us U(N) gauge symmetry: Pati-Salam Models

I Free fermionic string model builingRealistic models with clean particle spectra can only be constructed at the Kac-Moody level one: the

Standard-like models, Pati-Salam models, and flipped SU(5) models.

Tianjun Li ITP-CAS




F -Theory Model Building:

I The models are constructed locally, and then the gravityshould decoupled, i.e., MGUT/MPl is a small number.

I The SU(5) and SO(10) gauge symmetries can be broken bythe U(1)Y and U(1)X/U(1)B−L fluxes.

I Gauge mediated supersymmetry breaking can be realized viainstanton effects. Gravity mediated supersymmetry breakingpredicts the gaugino mass relation.

I All the SM fermion Yuakwa couplings can be generated in theSU(5) and SO(10) models.

I The doublet-triplet splitting problem, proton decay problem, µproblem as well as the SM fermion masses and mixingproblem can be solved.

Tianjun Li ITP-CAS




Supersymmetry

I The most promising new physics beyond the Standard Model.

I Gauge coupling unification strongly suggests the GrandUnified Theories (GUTs), and the SUSY GUTs can beconstructed from superstring theory.

Supersymmetry is a bridge between the low energyphenomenology and high-energy fundamental physics.

Tianjun Li ITP-CAS




Outline

Introduction


No-Scale F-SU(5)

No-Scale MSSM


Conclusion

Tianjun Li ITP-CAS




Higgs boson mass in the MSSM:

I The SM-like Higgs boson mass is around 126 GeV.

I The tree-level Higgs boson mass is smaller than MZ .

I The Higgs boson mass is enhanced by the top quarks/squarksloop corrections.

I The maximal stop mixing is needed to relax the fine-tuning.

Tianjun Li ITP-CAS




The LHC Supersymmetry Search Contraints:

I The gluino and squark mass low bounds are around 1.7 TeV inthe CMSSM/mSUGRA

I The gluino mass low bound is around 1.3 TeV.

I The stop/sbottom mass low bounds are around 600 GeV.

I If the LSP is heavy enough, all the bounds will be gone.

Tianjun Li ITP-CAS




Model e, µ, τ, γ Jets EmissT

∫L dt[fb−1] Mass limit Reference

Incl

usiv

eS

earc

hes

3rdge

n.g

med

.3rd

gen.

squa

rks

dire

ctpr

oduc

tion

EW

dire

ctLo

ng-li

ved

part

icle

sR

PV

Other

MSUGRA/CMSSM 0 2-6 jets Yes 20.3 m(q)=m(g) 1405.78751.7 TeVq, g

qq, q→qχ01 0 2-6 jets Yes 20.3 m(χ0

1)=0 GeV, m(1st gen. q)=m(2nd gen. q) 1405.7875850 GeVq

qqγ, q→qχ01 (compressed) 1 γ 0-1 jet Yes 20.3 m(q)-m(χ0

1 ) = m(c) 1411.1559250 GeVq

gg, g→qqχ01 0 2-6 jets Yes 20.3 m(χ0

1)=0 GeV 1405.78751.33 TeVg

gg, g→qqχ±1→qqW±χ01 1 e, µ 3-6 jets Yes 20 m(χ0

1)<300 GeV, m(χ±)=0.5(m(χ01)+m(g)) 1501.035551.2 TeVg

gg, g→qq(ℓℓ/ℓν/νν)χ01 2 e, µ 0-3 jets - 20 m(χ0

1)=0 GeV 1501.035551.32 TeVg

GMSB (ℓ NLSP) 1-2 τ + 0-1 ℓ 0-2 jets Yes 20.3 tanβ >20 1407.06031.6 TeVgGGM (bino NLSP) 2 γ - Yes 20.3 m(χ0

1)>50 GeV ATLAS-CONF-2014-0011.28 TeVgGGM (wino NLSP) 1 e, µ + γ - Yes 4.8 m(χ0

1)>50 GeV ATLAS-CONF-2012-144619 GeVgGGM (higgsino-bino NLSP) γ 1 b Yes 4.8 m(χ0

1)>220 GeV 1211.1167900 GeVgGGM (higgsino NLSP) 2 e, µ (Z) 0-3 jets Yes 5.8 m(NLSP)>200 GeV ATLAS-CONF-2012-152690 GeVg

Gravitino LSP 0 mono-jet Yes 20.3 m(G)>1.8 × 10−4 eV, m(g)=m(q)=1.5 TeV 1502.01518865 GeVF1/2 scale

g→bbχ01 0 3 b Yes 20.1 m(χ0

1)<400 GeV 1407.06001.25 TeVg

g→ttχ01 0 7-10 jets Yes 20.3 m(χ0

1) <350 GeV 1308.18411.1 TeVg

g→ttχ01 0-1 e, µ 3 b Yes 20.1 m(χ0

1)<400 GeV 1407.06001.34 TeVg

g→btχ+1 0-1 e, µ 3 b Yes 20.1 m(χ01)<300 GeV 1407.06001.3 TeVg

b1b1, b1→bχ01 0 2 b Yes 20.1 m(χ0

1)<90 GeV 1308.2631100-620 GeVb1

b1b1, b1→tχ±1 2 e, µ (SS) 0-3 b Yes 20.3 m(χ±1 )=2 m(χ01) 1404.2500275-440 GeVb1

t1 t1, t1→bχ±1 1-2 e, µ 1-2 b Yes 4.7 m(χ±1 ) = 2m(χ01), m(χ0

1)=55 GeV 1209.2102, 1407.0583110-167 GeVt1 230-460 GeVt1

t1 t1, t1→Wbχ01 or tχ0

1 2 e, µ 0-2 jets Yes 20.3 m(χ01)=1 GeV 1403.4853, 1412.474290-191 GeVt1 215-530 GeVt1

t1 t1, t1→tχ01 0-1 e, µ 1-2 b Yes 20 m(χ0

1)=1 GeV 1407.0583,1406.1122210-640 GeVt1

t1 t1, t1→cχ01 0 mono-jet/c-tag Yes 20.3 m(t1)-m(χ0

1 )<85 GeV 1407.060890-240 GeVt1

t1 t1(natural GMSB) 2 e, µ (Z) 1 b Yes 20.3 m(χ01)>150 GeV 1403.5222150-580 GeVt1

t2 t2, t2→t1 + Z 3 e, µ (Z) 1 b Yes 20.3 m(χ01)<200 GeV 1403.5222290-600 GeVt2

ℓL,R ℓL,R, ℓ→ℓχ01 2 e, µ 0 Yes 20.3 m(χ0

1)=0 GeV 1403.529490-325 GeVℓ

χ+1 χ−1 , χ+1→ℓν(ℓν) 2 e, µ 0 Yes 20.3 m(χ0

1)=0 GeV, m(ℓ, ν)=0.5(m(χ±1 )+m(χ01)) 1403.5294140-465 GeVχ±

1χ+1 χ

−1 , χ+1→τν(τν) 2 τ - Yes 20.3 m(χ0

1)=0 GeV, m(τ, ν)=0.5(m(χ±1 )+m(χ01)) 1407.0350100-350 GeVχ±

1χ±1 χ

02→ℓLνℓLℓ(νν), ℓνℓLℓ(νν) 3 e, µ 0 Yes 20.3 m(χ±1 )=m(χ0

2), m(χ01)=0, m(ℓ, ν)=0.5(m(χ±1 )+m(χ0

1)) 1402.7029700 GeVχ±1 , χ

02

χ±1 χ02→Wχ0

1Zχ01 2-3 e, µ 0-2 jets Yes 20.3 m(χ±1 )=m(χ0

2), m(χ01)=0, sleptons decoupled 1403.5294, 1402.7029420 GeVχ±

1 , χ02

χ±1 χ02→Wχ0

1h χ01, h→bb/WW/ττ/γγ e, µ, γ 0-2 b Yes 20.3 m(χ±1 )=m(χ0

2), m(χ01)=0, sleptons decoupled 1501.07110250 GeVχ±

1 , χ02

χ02χ

03, χ0

2,3 →ℓRℓ 4 e, µ 0 Yes 20.3 m(χ02)=m(χ0

3), m(χ01)=0, m(ℓ, ν)=0.5(m(χ0

2)+m(χ01)) 1405.5086620 GeVχ0

2,3

Direct χ+1 χ−1 prod., long-lived χ±1 Disapp. trk 1 jet Yes 20.3 m(χ±1 )-m(χ0

1)=160 MeV, τ(χ±1 )=0.2 ns 1310.3675270 GeVχ±1

Stable, stopped g R-hadron 0 1-5 jets Yes 27.9 m(χ01)=100 GeV, 10 µs<τ(g)<1000 s 1310.6584832 GeVg

Stable g R-hadron trk - - 19.1 1411.67951.27 TeVg

GMSB, stable τ, χ01→τ(e, µ)+τ(e, µ) 1-2 µ - - 19.1 10<tanβ<50 1411.6795537 GeVχ0

1

GMSB, χ01→γG, long-lived χ0

1 2 γ - Yes 20.3 2<τ(χ01)<3 ns, SPS8 model 1409.5542435 GeVχ0

1

qq, χ01→qqµ (RPV) 1 µ, displ. vtx - - 20.3 1.5 <cτ<156 mm, BR(µ)=1, m(χ0

1)=108 GeV ATLAS-CONF-2013-0921.0 TeVq

LFV pp→ντ + X, ντ→e + µ 2 e, µ - - 4.6 λ′311=0.10, λ132=0.05 1212.12721.61 TeVντ

LFV pp→ντ + X, ντ→e(µ) + τ 1 e, µ + τ - - 4.6 λ′311=0.10, λ1(2)33=0.05 1212.12721.1 TeVντ

Bilinear RPV CMSSM 2 e, µ (SS) 0-3 b Yes 20.3 m(q)=m(g), cτLS P<1 mm 1404.25001.35 TeVq, gχ+1 χ

−1 , χ+1→Wχ0

1, χ01→eeνµ, eµνe 4 e, µ - Yes 20.3 m(χ0

1)>0.2×m(χ±1 ), λ121,0 1405.5086750 GeVχ±1

χ+1 χ−1 , χ+1→Wχ0

1, χ01→ττνe, eτντ 3 e, µ + τ - Yes 20.3 m(χ0

1)>0.2×m(χ±1 ), λ133,0 1405.5086450 GeVχ±1

g→qqq 0 6-7 jets - 20.3 BR(t)=BR(b)=BR(c)=0% ATLAS-CONF-2013-091916 GeVgg→t1t, t1→bs 2 e, µ (SS) 0-3 b Yes 20.3 1404.250850 GeVg

Scalar charm, c→cχ01 0 2 c Yes 20.3 m(χ0

1)<200 GeV 1501.01325490 GeVc

Mass scale [TeV]10−1 1√

s = 7 TeVfull data

√s = 8 TeV

partial data

√s = 8 TeV

full data

ATLAS SUSY Searches* - 95% CL Lower LimitsStatus: Feb 2015

ATLAS Preliminary√s = 7, 8 TeV

*Only a selection of the available mass limits on new states or phenomena is shown. All limits quoted are observed minus 1σ theoretical signal cross section uncertainty.

Tianjun Li ITP-CAS




Mass scales [GeV]0 200 400 600 800 1000 1200 1400

0χ∼ l → l

~

0

χ∼ 0

χ∼ν τττ → ±χ∼ 2

0χ∼

0

χ∼ 0

χ∼ν τ ll→ ±χ∼ 2

0χ∼

0χ∼

0χ∼ H W →

2

0χ∼ ±χ∼

0χ∼

0χ∼ W Z →

2

0χ∼ ±χ∼

0χ∼0χ∼νν-l+ l→ -χ∼+χ∼

0χ∼

0χ∼ν lll → ±χ∼

2

0χ∼

0χ∼ bZ → b

~0

χ∼ tW → b~

0χ∼ b → b

~

H G)→ 0χ∼(0χ∼ t b → t~)0χ∼ W → ±χ∼ b (→ t~)0χ∼ W→ +χ∼ b(→ t~0χ∼ t → t~0χ∼ t → t~

0χ∼ q → q~

0χ∼ q → q~

))0

χ∼ W→ ±χ∼ t(→ b~

b(→ g~)

0χ∼γ →

2

0χ∼ qq(→ g~

)0

χ∼ W→±χ∼|0

χ∼γ→2

0χ∼ qq(→ g~

)0χ∼ W→±χ∼ qq(→ g~)

0χ∼ Z →

2

0χ∼ qq (→ g~

)0χ∼ ν± l→ ±χ∼ qq(→ g~)0χ∼ t→ t~ t(→ g~)0χ∼ |0χ∼ W→±χ∼ qq(→ g~)

0χ∼ |

0χ∼ τ τ →

2

0χ∼ qq(→ g~

)0

χ∼-

l+

l→2

0χ∼ qq (→ g~

0χ∼ tt → g~

0χ∼ bb → g~

0χ∼ qq → g~

0χ∼ qq → g~

SUS-13-006 L=19.5 /fb

SUS-13-008 SUS-13-013 L=19.5 /fb

SUS-13-011 L=19.5 /fbx = 0.25

x = 0.50x = 0.75

SUS-13-008 L=19.5 /fb

SUS-12-001 L=4.93 /fb

SUS-11-010 L=4.98 /fb

SUS-13-006 L=19.5 /fbx = 0.05

x = 0.50x = 0.95

SUS-13-006 L=19.5 /fb

SUS-13-012 SUS-12-028 L=19.5 11.7 /fb

SUS-12-005 SUS-11-024 L=4.7 /fb

SUS-12-028 L=11.7 /fb

SUS-13-008 SUS-13-013 L=19.5 /fb

SUS-13-014 L=19.5 /fb

SUS-13-004 SUS-13-007 SUS-13-008 SUS-13-013 L=19.4 19.5 /fb

SUS-13-013 L=19.5 /fbx = 0.20

x = 0.50

SUS-13-004 SUS-12-024 SUS-12-028 L=19.3 19.4 /fb

SUS-12-001 L=4.93 /fb

SUS-13-012 SUS-12-028 L=19.5 11.7 /fb

SUS-12-010 L=4.98 /fb x = 0.25x = 0.50x = 0.75

SUS-12-005 SUS-11-024 L=4.7 /fb

SUS-13-008 SUS-13-013 L=19.5 /fb

SUS-13-017 L=19.5 /fb

SUS-12-004 L=4.98 /fb

SUS-13-006 L=19.5 /fb

SUS-11-011 L=4.98 /fb

SUS-13-011 SUS-13-004 L=19.5 19.3 /fb left-handed topunpolarized top

right-handed top

SUS-11-024 SUS-12-005 L=4.7 /fb

SUS-11-021 SUS-12-002 L=4.98 4.73 /fbx = 0.25

x = 0.50x = 0.75

SUS-13-006 L=19.5 /fb x = 0.05x = 0.50

x = 0.95

SUS-13-006 L=19.5 /fb

SUS-11-030 L=4.98 /fb

glui

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rodu

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sbot

tom

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ton

Summary of CMS SUSY Results* in SMS framework

CMS Preliminary

m(mother)-m(LSP)=200 GeV m(LSP)=0 GeVSUSY 2013

= 7 TeVs

= 8 TeVs

lspm⋅-(1-x)

motherm⋅ = xintermediatem

For decays with intermediate mass,

Only a selection of available mass limits*Observed limits, theory uncertainties not included

Probe *up to* the quoted mass limit

Tianjun Li ITP-CAS




[GeV]0m0 1000 2000 3000 4000 5000 6000

[GeV

]1/

2m

300

400

500

600

700

800

900

1000

(2400 GeV

)q ~

(1600 GeV

)q ~

(1000 GeV)g~

(1400 GeV)g~

h (122 GeV

)

h (124 GeV

)

h (126 GeV

)

Expected

ObservedExpected

ObservedExpected

ObservedExpected

ObservedExpected

ObservedExpected

Observed

> 0µ, 0 = -2m0

) = 30, AβMSUGRA/CMSSM: tan( Status: SUSY 2013

ATLAS Preliminary = 8 TeVs,

-1 L dt = 20.1 - 20.7 fb∫

τ∼

LSP not included.theory

SUSYσ95% CL limits.

0-lepton, 2-6 jets

0-lepton, 7-10 jets

0-1 lepton, 3 b-jets

1-lepton + jets + MET

1-2 taus + jets + MET

3 b-jets≥2-SS-leptons, 0 -

ATLAS-CONF-2013-047

arXiv: 1308.1841

ATLAS-CONF-2013-061

ATLAS-CONF-2013-062

ATLAS-CONF-2013-026

ATLAS-CONF-2013-007

Tianjun Li ITP-CAS




[GeV]g~m600 700 800 900 1000 1100 1200 1300 1400 1500 1600

[GeV

]10 r¾

m

200

400

600

800

1000

1200

forbidden

10r¾t t

Ag~

= 8 TeVs), g~) >> m(q~, m(10

r¾t tAg~ production, g~g~ Lepton & Photon 2013

ATLASPreliminary

ExpectedObservedExpectedObservedExpectedObservedExpectedObserved

10 jets*0-lepton, 7 -

3 b-jets*0-1 lepton,

4 jets*3-leptons,

3 b-jets*2-SS-leptons, 0 -

ATLAS-CONF-2013-054

ATLAS-CONF-2013-061

ATLAS-CONF-2012-151

ATLAS-CONF-2013-007

]-1 = 20.3 fbint

[L

]-1 = 20.1 fbint

[L

]-1 = 12.8 fbint

[L

]-1 = 20.7 fbint

[L

not included.theorySUSYm95% CL limits.

[GeV]1t

~m

100 200 300 400 500 600 700

10

χ∼+mt

< m

1t~m

10

χ∼

+ m

W

+ m

b

< m

1t~m

10

χ∼

+ m

c

< m

1t~m

200 300 400 500 600

)1

0χ∼ m×

= 2

1

±χ∼ ( m

1

±χ∼+m

b < m1t~m

< 106 GeV 1

±χ∼ m

( = 150 GeV)1

±χ∼ > m1

0χ∼

m

+5 G

eV)

10χ∼

= m

1±χ∼

( m

1±χ∼

+mb

< m

1t~m

< 103.5 GeV1

±χ∼m

[GeV

]10 χ∼

m

0

100

200

300

400

500

600

Observed limits

Expected limits

All limits at 95% CL

[1203.4171]-1CDF 2.6 fb

ATLAS Preliminary

production1t~1t

~Status: Moriond 2014

=8 TeVs -1 = 20 - 21 fbintL =7 TeVs -1 = 4.7 fbintL

0L ATLAS-CONF-2013-024

1L ATLAS-CONF-2013-037

2L [1403.4853]

2L [1403.4853]

0L mono-jet/c-tag, CONF-2013-068

0L [1308.2631]

2L [1403.4853]

1L CONF-2013-037, 0L [1308.2631]

2L [1403.4853]

1L CONF-2013-037, 2L [1403.4853]

0L [1208.1447]

1L [1208.2590]

2L [1209.4186]

-

-

-

2L [1208.4305], 1-2L [1209.2102]

-

-

1-2L [1209.2102]

1

0χ∼ (*) W→

1

±χ∼, 1

±χ∼ b → 1t~

1

0χ∼ t →1t~

/ 1

0χ∼ W b →1t~

/ 1

0χ∼ c →1t~

0L,

1L,

2L,

2L,0L,

0L,

1-2L,

1L,

2L,1-2L,

1

0χ∼ t →1t~

1

0χ∼ t →1t~

1

0χ∼ t →1t~

1

0χ∼ W b →1t~

1

0χ∼ c →1t~ mono-jet/c-tag,

+ 5 GeV1

0χ∼ = m±

1χ m

= 106 GeV±1

χ, m

1

±χ∼ b → 1t~

= 150 GeV±1

χ, m

1

±χ∼ b → 1t~

- 10 GeV1t~ = m±

1χ

, m1

±χ∼ b → 1t~

1

0χ∼ m× = 2 ±1

χ, m

1

±χ∼ b → 1t~

Tianjun Li ITP-CAS




gluino mass [GeV]

600 700 800 900 1000 1100 1200 1300 1400 1500

LSP

mas

s [G

eV]

0

100

200

300

400

500

600

700

800

900

ObservedSUSYtheoryσObserved -1

Expected

m(g

luin

o) - m

(LSP) =

2 m

(top)

Moriond 2014 = 8 TeVs

CMS Preliminary1

0χ∼ t t →g~ production, g~-g~

-1) 19.5 fbT+HTESUS-13-012 0-lep (-1SUS-13-004 0+1-lep (razor) 19.3 fb

-1 6) 19.3 fb≥jets

SUS-13-007 1-lep (n-1SUS-13-016 2-lep (OS+b) 19.7 fb-1SUS-13-013 2-lep (SS+b) 19.5 fb

-1SUS-13-008 3-lep (3l+b) 19.5 fb

stop mass [GeV]

100 200 300 400 500 600 700 800

LSP

mas

s [G

eV]

0

50

100

150

200

250

300

350

400

450

500

W

=m1

0χ∼

-mt~

m

t

=m1

0χ∼

-mt~

m

SUSY 2013 = 8 TeVs

CMS Preliminary

productiont~-t

~

)1

0χ∼ t →t~ (-1SUS-13-004 0-lep+1-lep (Razor) 19.3 fb

)1

0χ∼ t →t~ (-1SUS-13-011 1-lep (leptonic stop)19.5 fb

, x=0.25)1

+χ∼ b →t~ (-1SUS-13-011 1-lep (leptonic stop)19.5 fb

Observed

Expected

W

=m1

0χ∼

-m1

±χ∼m

Tianjun Li ITP-CAS




Fine-Tuning Definition I:

I Electroweak symmetry breaking condition

µ2 +1

2M2

Z =m2

Hd−m2

Hutan2 β

tan2 β − 1.

I Fine-tuning Definition I 1: the quantitative measure ∆FT forfine-tuning is the maximum of the logarithmic derivative ofMZ with respect to all the fundamental parameters ai at theGUT scale

∆FT = Max∆GUTi , ∆GUT

i =

∣∣∣∣ ∂ln(MZ )

∂ln(aGUTi )

∣∣∣∣ .1

J. R. Ellis, K. Enqvist, D. V. Nanopoulos and F. Zwirner, Mod. Phys. Lett. A 1, 57 (1986); R. Barbieri andG. F. Giudice, Nucl. Phys. B 306, 63 (1988).

Tianjun Li ITP-CAS




Fine-Tuning Definition II

I Higgs potential:

V = m2h|h|2 +

λh4|h|4 .

I Higgs boson mass

m2h = −2m2

h , m2h ' |µ|2 + m2

Hu|tree + m2

Hu|rad .

I The fine-tuning measure 2:

∆FT ≡2δm2

h

m2h

.

2R. Kitano and Y. Nomura, Phys. Lett. B 631, 58 (2005) [hep-ph/0509039]; Phys. Rev. D 73, 095004 (2006)

[hep-ph/0602096].

Tianjun Li ITP-CAS




Fine-Tuning Definition II

I The µ term or effective µ term is smaller than 400 GeV.

I The squar root Mt ≡√

m2t1

+ m2t2

of the sum of the two stop

mass squares is smaller than 1.2 TeV.

I The gluino mass is lighter than 1.5 TeV.

Tianjun Li ITP-CAS




Fine-Tuning Definition III

I The minimization condition for electroweak symmetrybreaking

M2Z

2=

m2Hd

+ Σdd − (m2

Hu+ Σu

u) tan2 β

tan2 β − 1− µ2 .

I The fine-tuning measure 3

∆FT ≡ Max2Ci

M2Z

.

3H. Baer, V. Barger, P. Huang, D. Mickelson, A. Mustafayev and X. Tata, Phys. Rev. D 87, no. 11, 115028

(2013) [arXiv:1212.2655 [hep-ph]].

Tianjun Li ITP-CAS




Comments on Fine-Tuning

I Fine-Tuning Definition III is weak.

I Fine-Tuning Definition II is medium.

I Fine-Tuning Definition I is strong.

Tianjun Li ITP-CAS




Supersymmetric SMs:

I Natural supersymmetry 4.

I Supersymmetric models with a TeV-scale squarks that canescape/relax the missing energy constraints: R parityviolation 5; compressed supersymmetry 6 ; stealthsupersymmetry 7; etc.

4S. Dimopoulos and G. F. Giudice, Phys. Lett. B 357, 573 (1995) [hep-ph/9507282]; A. G. Cohen,

D. B. Kaplan and A. E. Nelson, Phys. Lett. B 388, 588 (1996) [hep-ph/9607394].5

R. Barbier, C. Berat, M. Besancon, M. Chemtob, A. Deandrea, E. Dudas, P. Fayet and S. Lavignac et al.,Phys. Rept. 420, 1 (2005) [hep-ph/0406039].

6T. J. LeCompte and S. P. Martin, Phys. Rev. D 84, 015004 (2011) [arXiv:1105.4304 [hep-ph]]; Phys. Rev. D

85, 035023 (2012) [arXiv:1111.6897 [hep-ph]].7

J. Fan, M. Reece and J. T. Ruderman, JHEP 1111, 012 (2011) [arXiv:1105.5135 [hep-ph]]; arXiv:1201.4875[hep-ph].

Tianjun Li ITP-CAS




Supersymmetric SMs:

I Supersymmetric models with sub-TeV squarks that decreasethe cross sections: supersoft supersymmetry 8.

I Displaced Supersymmetry 9.

I Double Invisible Supersymmetry 10.

8G. D. Kribs and A. Martin, arXiv:1203.4821 [hep-ph], and references therein.

9P. W. Graham, D. E. Kaplan, S. Rajendran and P. Saraswat, JHEP 1207, 149 (2012) [arXiv:1204.6038

[hep-ph]].10

J. Guo, Z. Kang, J. Li, T. Li and Y. Liu, arXiv:1312.2821 [hep-ph]; D. S. M. Alves, J. Liu and N. Weiner,arXiv:1312.4965 [hep-ph].

Tianjun Li ITP-CAS




Outline

Introduction


No-Scale F-SU(5)

No-Scale MSSM


Conclusion

Tianjun Li ITP-CAS




Flipped SU(5)× U(1)X Models: 13

I Doublet-triplet splitting via missing partner mechanism 11.

I No dimension-five proton decay problem.

I Little hierarchy problem in string models:MString ∼ 20×MGUT

MString = gString × 5.27× 1017 GeV .

I Testable flipped SU(5)× U(1)X models: TeV-scale vector-likeparticles 12.

11I. Antoniadis, J. R. Ellis, J. S. Hagelin and D. V. Nanopoulos, Phys. Lett. B 194, 231 (1987).

12J. Jiang, T. Li and D. V. Nanopoulos, Nucl. Phys. B 772, 49 (2007).

13S. M. Barr, Phys. Lett. B 112, 219 (1982); J. P. Derendinger, J. E. Kim and D. V. Nanopoulos, Phys. Lett.

B 139, 170 (1984).

Tianjun Li ITP-CAS




Flipped SU(5)× U(1)X Models:

I Free-fermionic string construction 14.

I F-theory model building 15.

I Heterotic String Constructions: Calabi-Yau 16; Orbifold 17.

I Orbifold GUTs 18.

14J. L. Lopez, D. V. Nanopoulos and K. j. Yuan, Nucl. Phys. B 399, 654 (1993).

15C. Beasley, J. J. Heckman and C. Vafa, JHEP 0901, 059 (2009); J. Jiang, T. Li, D. V. Nanopoulos and

D. Xie, Phys. Lett. B 677, 322 (2009); Nucl. Phys. B 830, 195 (2010).16

A. E. Faraggi, R. S. Garavuso and J. M. Isidro, Nucl. Phys. B 641, 111 (2002)17

J. E. Kim and B. Kyae, Nucl. Phys. B 770, 47 (2007).18

S. M. Barr and I. Dorsner, Phys. Rev. D 66, 065013 (2002).

Tianjun Li ITP-CAS




F -SU(5) Models

I The gauge group SU(5)× U(1)X can be embedded intoSO(10) model.

I Generator U(1)Y ′ in SU(5)

TU(1)Y′= diag

(−1

3,−1

3,−1

3,

1

2,

1

2

).

I Hypercharge

QY =1

5(QX − QY ′) .

Tianjun Li ITP-CAS




I SM fermions

Fi = (10, 1), fi = (5,−3), li = (1, 5) ,

Fi = (Qi ,Dci ,N

ci ), f i = (Uc

i , Li ), l i = E ci .

I Higgs particles:

H = (10, 1), H = (10,−1), h = (5,−2), h = (5, 2) ,

H = (QH ,DcH ,N

cH) , H = (QH ,D

cH ,N

cH) ,

h = (Dh,Dh,Dh,Hd) , h = (Dh,Dh,Dh,Hu) .

I Flip

U ↔ D , N ↔ E , Hd ↔ Hu .

Tianjun Li ITP-CAS




Symmetry breaking:

I Superpotential

WGUT = λ1HHh + λ2HHh + Φ(HH −M2H) .

I There is only one F-flat and D-flat direction along the NcH and

NcH directions: < Nc

H >=< NcH >= MH.

I The doublet-triplet splitting due to the missing partnermechanism

I No dimension-5 proton decay problem.

Tianjun Li ITP-CAS




F -SU(5) Models

I To achieve the string scale gauge coupling unification, weintroduce sets of vector-like particles in completeSU(5)× U(1)X multiplets, whose contributions to theone-loop beta functions of the U(1)Y , SU(2)L and SU(3)Cgauge symmetries, ∆b1, ∆b2 and ∆b3 respectively, satisfy∆b1 < ∆b2 = ∆b3.

I To avoid the Landau pole problem for the gauge couplings, wecan only introduce the following two sets of vector-likeparticles around the TeV scale, which could be observed atthe LHC

Z1 : XF = (10, 1) ≡ (XQ, XDc , XNc) , XF = (10,−1) ;

Z2 : XF , XF , Xl = (1,−5) , Xl = (1, 5) ≡ XE c .

Tianjun Li ITP-CAS




0

20

40

60

103

107

1011

1015

Model IA

MV

= 1000 GeV

MS = 800 GeV

α-1

3

α-1

2

α-1

1

α′-1

1

α-1

5

µ (GeV)

α-1

Figure: Gauge coupling unification in the Type IA model.

Tianjun Li ITP-CAS




No-Scale Supergravity 19:

I The vacuum energy vanishes automatically due to the suitableKahler potential.

I At the minimum of the scalar potential, there are flatdirections which leave the gravitino mass M3/2 undertermined.

I The super-trace quantity StrM2 is zero at the minimum.

K = −3ln(T + T −∑i

ΦiΦi ) .

19E. Cremmer, S. Ferrara, C. Kounnas and D. V. Nanopoulos, Phys. Lett. B 133, 61 (1983); A. B. Lahanas

and D. V. Nanopoulos, Phys. Rept. 145, 1 (1987).

Tianjun Li ITP-CAS




No-Scale Supergravity:

I mSUGRA/CMSSM: M1/2, M0, A, tanβ, sign(µ).

I No-scale boundary condition: M1/2 6= 0, M0 = A = Bµ = 0

I Natural solution to CP violation and FCNC problem.

I Disfavored by phenomenology: M0 = 0 at traditional GUTscale.

I No-scale F-SU(5)

No-scale supergravity can be realized in the compactification of theweakly coupled heterotic string theory 20 and the compactificationof M-theory on S1/Z2 at the leading order 21.

20E. Witten, Phys. Lett. B 155, 151 (1985).

21T. Li, J. L. Lopez and D. V. Nanopoulos, Phys. Rev. D 56, 2602 (1997).

Tianjun Li ITP-CAS




F -SU(5)

I These models can be realized in heterotic string constructions,free fermionic string constructions, and F-theory modelbuilding.

I These models may be tested in the next LHC run.

I The Higgs boson mass can be around 126 GeV.

I The proton decay p → e+π0 from the heavy gauge bosonexchange is within the reach of the future DUSEL andHyper-Kamiokande experiments for a majority of the mostplausible parameter space.

I The dark matter is within the reach of the XENON1Texperiment.

Tianjun Li ITP-CAS




Miracle of Vector-Like Particles

I String scale gauge coupling unification.

I Dimension-six proton decay.

I Lifting the lightest CP-even Higgs boson mass.

I Special sparticle spectra.

Tianjun Li ITP-CAS




Question: Super-Natural Supersymmetry

Can we propose the Super-Natural Supersymmetric SMs whoseEENZ or BG fine-tuning measure will be automatically 1 or order 1(O(1))?

Tianjun Li ITP-CAS




No-Scale Supergravity

I Scalar Potential

V = eK(

(K−1)ijDiWD jW − 3|W |2

).

where (K−1)ij

is the inverse of the Kahler metric

K ji = ∂2K/∂Φi∂Φj , and DiW = Wi + KiW .

I Automatically vanishing scalar potential

K = −3ln(T + T −∑i

ΦiΦi ) .

Tianjun Li ITP-CAS




Natural Solution to the Fine-Tuning Problem

I Fine-Tuning Definition:

∆FT = Max∆GUTi , ∆GUT

i =

∣∣∣∣ ∂ln(MZ )

∂ln(aGUTi )

∣∣∣∣ .I Natural Solution:

MnZ = fn

(MZ

M1/2

)Mn

1/2 .

∂ln(MnZ )

∂ln(Mn1/2)

'Mn

1/2

MnZ

∂MnZ

∂Mn1/2

' 1

fnfn ' O(1) .

Tianjun Li ITP-CAS




No-Scale F -SU(5)

I µ problem 22:

µ ∝ M1/2 ∝ M3/2 .

I All the mass parameters are proportional to M1/2

I Natural solution 23

µ ' M1/2 .

22G. F. Giudice and A. Masiero, Phys. Lett. B 206, 480 (1988).

23T. Leggett, T. Li, J. A. Maxin, D. V. Nanopoulos and J. W. Walker, arXiv:1403.3099 [hep-ph].

Tianjun Li ITP-CAS




400 600 800 1000 1200 1400 1600400

600

800

1000

1200

1400

1600

= M 1/2

(MF)

(MF) [GeV

]

Gaugino Mass M1/2 [GeV]

0

10

20

30

40

50

60

70

80

90

100

EENZ

EENZ

Tianjun Li ITP-CAS




Tianjun Li ITP-CAS




Tianjun Li ITP-CAS




Tianjun Li ITP-CAS




Figure: The Z -boson mass is shown as a function of the dimensionlessparameter c for seven different values of M1/2.

Tianjun Li ITP-CAS




Figure: Depiction of the correlation between the Z -boson mass MZ , topquark mass mt , Higgs boson mass mh, and gluino mass mg , as a functionof c , for M1/2 = 1.2 TeV. Tianjun Li ITP-CAS




Outline

Introduction


No-Scale F-SU(5)

No-Scale MSSM


Conclusion

Tianjun Li ITP-CAS




I In the F-SU(5), there is a mass parameter: vector-likeparticle mass MV .

I The MSSM with no-scale supergravity and Giudice-Masieromechanism.

I Problem: the light stau is the lightest supersymmetric particle(LSP).

I Solution: axino as the LSP.

Tianjun Li ITP-CAS




500 1000 1500 2000

0.

500.

1000.

1500.

2000.

0.

0.25

0.5

0.75

1.

1.25

1.5

1.75

M1 2@GeV D

ΜHG

UT

L@GeV

D

FT

Figure: µ(GUT ) (left-vertical axis) and EWFT measure ∆EENZ

(right-vertical axis) versus M1/2.

Tianjun Li ITP-CAS




85 90 95 100MZ

5

10

15

20

25

30

35

tanΒ

Figure: Plot in the tanβ-MZ plane.

Tianjun Li ITP-CAS




Figure: The green, purple, orange and black points represent mg , mt1,

mu1 and mb1, respectively.

Tianjun Li ITP-CAS




Figure: The dark green, blue, red, and brown lines represent mχ±1

, mχ01,

mτ1 , me1 , respectively.

Tianjun Li ITP-CAS




Figure: The viable parameter spaces in M1/2 − tanβ plane.

Tianjun Li ITP-CAS




Figure: The viable parameter spaces in M1/2 − tanβ plane.

Tianjun Li ITP-CAS




Figure: mτ1 versus Ωh2.

Tianjun Li ITP-CAS




Point 1 Point 2 Point 3

M1/2 1865.849 2725.144 4588.77m0 0.0 0.0 0.0A0 0.0 0.0 0.0

tanβ 28.129 30.594 33.822

B0(GUT) 0.599 0.251 -0.716µ(GUT) 1991 2788 4431B0(EWSB) 92 118 4292µ(EWSB) 1970 2735 166

mh 123 125 127mH 2054 2816 4321mA 2054 2815 4321mH± 2056 2816 4322

Tianjun Li ITP-CAS




Point 1 Point 2 Point 3

mχ01,2

820, 1520 1219, 2238 2100, 3802

mχ03,4

1978, 1985 2747, 2753 4310, 4317

mχ±1,21520, 1985 2238, 2753 3802, 4317

mg 3895 5546 9030

muL,R 3505, 3358 4968, 4746 8035, 7604mt1,2

2786, 3225 3957, 4554 6411, 7343

mdL,R3506, 3356 4968, 4717 8035, 7604

mb1,23205, 3247 4530, 4574 7268, 7364

mν1,2 1199 1737 2889mν3 1177 1701 2819

meL,R 1202, 679 1739, 987 2890, 1653mτ1,2 587,1184 841, 1705 1374, 2822

Tianjun Li ITP-CAS




Outline

Introduction


No-Scale F-SU(5)

No-Scale MSSM


Conclusion

Tianjun Li ITP-CAS





I The Kahler potential and superpotential can be calculated inprinciple or at least inspired from a fundamental theory suchas string theory with suitable compactifications. In otherwords, one cannot add arbitrary high-dimensional terms in theKahler potential and superpotential.

I There is one and only one chiral superfield or modulus whoseF-term breaks supersymmetry. And all the supersymmetrybreaking soft terms are obtained from the above Kahlerpotential and superpotential.

I All the other mass parameters, if there exist such as the µterm in the MSSM, must arise from supersymmetry breaking.

Tianjun Li ITP-CAS





I The EW Symmetry Breaking and Determination of M∗ fromZ Boson Mass.

I New µ Problem in the MSSM and F-SU(5) Model. Solution:M-theory inspired NMSSM.

I Symmetry for Super-Natural Supersymmetry: scale symmetry.

I Multi F-Term SUSY Breakings.

I Effective Super-Natural SUSY.

Tianjun Li ITP-CAS




Outline

Introduction


No-Scale F-SU(5)

No-Scale MSSM


Conclusion

Tianjun Li ITP-CAS




The Super-Natural Supersymmetry

I The EENZ or BG fine-tuning measure is automatically O(1).

I The MSSM and F-SU(5) Model with no-scale supergravityand Giudice mechanism.

I The NMSSM with M-theory inspired supergravity.

I Gauge mediations.

Tianjun Li ITP-CAS




Thank You Very Muchfor Your Attention!

Tianjun Li ITP-CAS

Documents

The Super-Natural Supersymmetry - USTC, ICTSicts.ustc.edu.cn/chinese/seminar/transparencies/Tianjun Li/Tian-Jun... · Introduction The SUSY EW Fine-Tuning Problem No-Scale F-SU(5)