is supersymmetry alive? status from theory and experiment · is supersymmetry alive? status from...

Is supersymmetry alive?Status from theory and experiment

A. P. Morais1,2

1Center for Research and Development in Mathematics and Applications (CIDMA)Aveiro University, Aveiro, Portugal

2Theoretical High Energy Physics (THEP)Lund University, Lund, Sweden

September 30, 2015

V NRHEP Network MeetingFederal University of Pará, Belem, Brazil

Morais (L.U. & A.U.) Is supersymmetry alive? Status from theory and experiment September 30, 2015 1 / 43

Suggested Literature

1 S. P. Martin, A Supersymmetry primer , Adv.Ser.Direct.High EnergyPhys. 21 (2010) 1-153, [hep-ph/9709356]

2 D. Bailin and A. Love, Supersymmetric gauge field theory and stringtheory , Bristol, UK: IOP (1994) 322 p. (Graduate student series inphysics)

3 I. J. R. Aitchison, Supersymmetry in Particle Physics. An ElementaryIntroduction, Cambridge, UK: Univ. Pr. (2007) 222 p

4 K. A. Intriligator and N. Seiberg, Lectures on Supersymmetry BreakingClass. Quant. Grav. 24 (2007) S741 [hep-ph/0702069]

5 I. J. R. Aitchison, Supersymmetry and the MSSM: An Elementaryintroduction, [hep-ph/0505105]


Outline

1 IntroductionMotivationThe Minimal Supersymmetric Standard Model - MSSM

2 Experimental resultsExclusion limitsExcesses

3 Theory and PhenomenologyImplications from the Higgs boson massBeyond the MSSM

4 Supersymmetric Trinification with SU(2)F-flavourRevisiting TrinificationDescription of the modelTree-level results

5 Concluding Remarks


Introduction Motivation

Outline








IntroductionMotivations for physics beyond the Standard Model (BSM)

For many years the Standard Model (SM) proved to be the most accuratedescription of Particle Physics, however theoretical and experimentaldisagreements:

The SM does not provide a dark matter (DM) particle

No explanation for the origin of electric and color charges (gauge structureof the SM)

No explanation for fermion masses and mixings and flavour structure

Observation of neutrino oscillations requires mass eigenstates→ notpredicted in the SM

Anomalous magnetic moment of the muon

The SM suffers from the Hierarchy Problem

Hard to reconcile with the theory of General Relativity



Features of supersymmetry (SUSY)

A possible cold dark matter particle

Unification of the gauge couplings (SUSY GUT theories)

Possible solution for the anomalous magnetic moment of the muon

Connection to gravity in the limit of Local SUSY a.k.a supergravity(SUGRA)

Mathematical beauty

However the one really good feature in favour os supersymmetry is

The Hierarchy Problem (Planck scale vs electroweak scale)


Introduction The Minimal Supersymmetric Standard Model - MSSM

Outline








Particle ContentChiral Supermultiplets

Chiral Supermultiplet Fields in the MSSMNames Spin 0 Spin 1/2 SU(3)c× SU(2)L×U(1)y

Squarks, Quarks(× 3) QL (uL, dL) (uL, dL) 3, 2, 1/3

ˆuR ˜uL = u∗R uL = (uR)c 3, 1, -4/3

ˆdR˜dL = d∗R dL = (dR)

c 3, 1, 2/3Sleptons, Leptons

(× 3) LL (νeL, eL) (νeL, eL) 1, 2, -1

ˆeR ˜eL = e∗R eL = (eR)c 1, 1, 2

Higgs, Higgsinos Hu (H+u , H0

u) (H+u , H0

u) 1, 2, 1Hd (H0

d , H−d ) (H0

d , H−d ) 1, 2, -1

Table : Chiral supermultiplet fields in the MSSM. The leftmost column provides theusual designation for the fundamental particles, the two middle ones the spin and therightmost the gauge charges.



Particle ContentGauge Supermultiplets

Gauge Supermultiplet Fields in the MSSMNames Spin 1/2 Spin 1 SU(3)c× SU(2)L×U(1)y

Gluinos, Gluons Ga g g 8, 1, 0Winos, W bosons Wa W±, W0 W±, W0 1, 3, 0

Bino, B Boson B B B 1, 1, 0

Table : Gauge supermultiplet fields in the MSSM. The left column provides the usualdesignation for the gauge fields, the middle one the spin and the right one the gaugecharges.



The Superpotential and Soft Lagrangian

The MSSM has the same gauge structure as the SM for the strong andelectroweak interactions

SU(3)c × SU(2)L × U(1)y

Superpotential

WMSSM = εαβ

[(yu)ij uRixQαx

Lj Hβu − (yd)ij dRixQαxLj Hβd − (ye)ij eRiLαLjH

βd + µHαu Hβd

](1)

Soft SUSY-breaking Lagrangian

−Lsoft = m2Hd

|Hd |2 + m2

Hu|Hu|

2 + Q αxLi

(m2

QL

)i

jQ∗ j

Lαx + L αLi

(m2

LL

)i

jL∗ j

Lα

+ u∗ xRi

(m2

uR

)ij u j

Rx + d∗ xRi

(m2

dR

)i

jd j

Rx + e∗Ri

(m2

eR

)ij e j

R

+ εαβ

[auijHαu uRixQβx

Lj − adijHαd dRixQβxLj − aeijHαd eRiL

βLj + bHαd Hβu + h.c.

]+

12[M1B · B + M2Wa · Wa + M3ga · ga + h.c.

], (2)


Experimental results Exclusion limits

Outline








Experimental resultsExclusion limits strong sector

ATLAS searches for the strong sector in the cMSSM/mSUGRA

[GeV]0

m

0 1000 2000 3000 4000 5000 6000

[G

eV

]1

/2m

300

400

500

600

700

800

900

1000

(2400 G

eV

)q ~

(1600 G

eV

)q ~

(1000 GeV)g~

(1400 GeV)g~

h (1

22 G

eV

)

h (1

24 G

eV

)

h (1

26 G

eV

)

> 0µ, 0 = 2m0

) = 30, AβMSUGRA/CMSSM: tan(

ATLAS1 = 8 TeV, L = 20 fbs

τ∼

LSP

All limits at 95% CL.

)expσ1 ±Expected (

)theory

SUSYσ1 ±Observed (

Expected

Observed

Expected

Observed

Expected

Observed

Expected

Observed

Expected

Observed

Expected

Observed

(0+1)lepton combination

miss

T0lepton + 710 jets + E

miss

T0/1lepton + 3 bjets + E

miss

TTaus + jets + E

miss

TSS/3L + jets + E

miss

T1lepton (hard) + 7 jets + E

cMSSM high scale softparameters

Common scalarmass m0

Common trilinearcoupling A0

Common gauginomasss M1/2

cMSSM by itself suffers from several theoretical problems such as vacuumstability, dark matter relic density, lack of high scale motivation and ishighly fine tuned



Experimental resultsExclusion limits electroweak sector

ATLAS searches for the electroweak sector

) [GeV]2

0χ∼ (=m1

±χ∼ m

100 200 300 400 500 600 700

[GeV

]0 1χ∼

m

0

100

200

300

400

500

600Expected limits

Observed limits

arXiv:1402.7029 3L, , ν∼/ LL~

via 02

χ∼±1

χ∼

arXiv:1403.5294 2l, , ν∼/ LL~

via −1

χ∼ +1

χ∼

arXiv:1402.7029 3L, , τν∼/ Lτ∼ via 02

χ∼±1

χ∼

arXiv:1407.0350, τ2≥ , τν∼/ Lτ∼ via 02

χ∼±1

χ∼

arXiv:1407.0350, τ2≥ , τν∼/ Lτ∼ via −1

χ∼ +1

χ∼

arXiv:1403.5294 2l+3L, via WZ, 02

χ∼±1

χ∼

arXiv:1501.07110 +3L,±l±+lγγlbb+l via Wh, 02

χ∼±1

χ∼

arXiv:1403.52942l, via WW, −1

χ∼ +1

χ∼

All limits at 95% CL

=8 TeV Status: Feb 2015s, -1 Preliminary 20.3 fbATLAS

)2

0χ∼ + m 1

0χ∼ = 0.5(m ν∼/ L

τ∼/ Ll~m

τ/µL = e/

µl = e/

10χ∼

= m

20χ∼m

Z

+ m

10χ∼

= m

20χ∼m

h

+ m

10χ∼

= m

20χ∼m

1

0χ∼ = 2m

2

0χ∼m

A lot to explore in the electroweak sector→ focus have been the strong sector



Experimental resultsExclusion limits electroweak sector

ATLAS searches for the electroweak sector

) [GeV]2

0χ∼ (=m1

±χ∼ m

100 200 300 400 500 600 700

[GeV

]0 1χ∼

m

0

100

200

300

400

500

600Expected limits

Observed limits

arXiv:1402.7029 3L, , ν∼/ LL~

via 02

χ∼±1

χ∼

arXiv:1403.5294 2l, , ν∼/ LL~

via −1

χ∼ +1

χ∼

arXiv:1402.7029 3L, , τν∼/ Lτ∼ via 02

χ∼±1

χ∼

arXiv:1407.0350, τ2≥ , τν∼/ Lτ∼ via 02

χ∼±1

χ∼

arXiv:1407.0350, τ2≥ , τν∼/ Lτ∼ via −1

χ∼ +1

χ∼

arXiv:1403.5294 2l+3L, via WZ, 02

χ∼±1

χ∼

arXiv:1501.07110 +3L,±l±+lγγlbb+l via Wh, 02

χ∼±1

χ∼

arXiv:1403.52942l, via WW, −1

χ∼ +1

χ∼

All limits at 95% CL

=8 TeV Status: Feb 2015s, -1 Preliminary 20.3 fbATLAS

)2

0χ∼ + m 1

0χ∼ = 0.5(m ν∼/ L

τ∼/ Ll~m

τ/µL = e/

µl = e/

10χ∼

= m

20χ∼m

Z

+ m

10χ∼

= m

20χ∼m

h

+ m

10χ∼

= m

20χ∼m

1

0χ∼ = 2m

2

0χ∼m

A lot to explore in the electroweak sector→ focus have been the strong sectorMorais (L.U. & A.U.) Is supersymmetry alive? Status from theory and experiment September 30, 2015 13 / 43


Experimental resultsExclusion limits summary

Model e, µ, τ, γ Jets Emiss

T

∫L dt[fb−1] Mass limit Reference

Inclu

siv

eS

ea

rch

es

3rd

ge

n.

gm

ed

.3rd

gen.

squark

sdir

ect

pro

duction

EW

dir

ect

Lo

ng

-liv

ed

pa

rtic

les

RP

V

Other

MSUGRA/CMSSM 0-3 e, µ /1-2 τ 2-10 jets/3 b Yes 20.3 m(q)=m(g) 1507.055251.8 TeVq, g

qq, q→qχ01 0 2-6 jets Yes 20.3 m(χ

01)=0 GeV, m(1st gen. q)=m(2nd gen. q) 1405.7875850 GeVq

qq, q→qχ01 (compressed) mono-jet 1-3 jets Yes 20.3 m(q)-m(χ

01 )<10 GeV 1507.05525100-440 GeVq

qq, q→q(ℓℓ/ℓν/νν)χ01

2 e, µ (off-Z) 2 jets Yes 20.3 m(χ01)=0 GeV 1503.03290780 GeVq

gg, g→qqχ01 0 2-6 jets Yes 20.3 m(χ

01)=0 GeV 1405.78751.33 TeVg

gg, g→qqχ±1→qqW±χ01 0-1 e, µ 2-6 jets Yes 20 m(χ

01)<300 GeV, m(χ

±)=0.5(m(χ

01)+m(g)) 1507.055251.26 TeVg

gg, g→qq(ℓℓ/ℓν/νν)χ01

2 e, µ 0-3 jets - 20 m(χ01)=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 TeVg

GGM (bino NLSP) 2 γ - Yes 20.3 cτ(NLSP)<0.1 mm 1507.054931.29 TeVg

GGM (higgsino-bino NLSP) γ 1 b Yes 20.3 m(χ01)<900 GeV, cτ(NLSP)<0.1 mm, µ<0 1507.054931.3 TeVg

GGM (higgsino-bino NLSP) γ 2 jets Yes 20.3 m(χ01)<850 GeV, cτ(NLSP)<0.1 mm, µ>0 1507.054931.25 TeVg

GGM (higgsino NLSP) 2 e, µ (Z) 2 jets Yes 20.3 m(NLSP)>430 GeV 1503.03290850 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

gg, g→bbχ01 0 3 b Yes 20.1 m(χ

01)<400 GeV 1407.06001.25 TeVg

gg, g→ttχ01 0 7-10 jets Yes 20.3 m(χ

01) <350 GeV 1308.18411.1 TeVg

gg, g→ttχ01

0-1 e, µ 3 b Yes 20.1 m(χ01)<400 GeV 1407.06001.34 TeVg

gg, g→btχ+1 0-1 e, µ 3 b Yes 20.1 m(χ

01)<300 GeV 1407.06001.3 TeVg

b1b1, b1→bχ01 0 2 b Yes 20.1 m(χ

01)<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(χ

01) 1404.2500275-440 GeVb1

t1 t1, t1→bχ±1 1-2 e, µ 1-2 b Yes 4.7/20.3 m(χ

±1 ) = 2m(χ

01), m(χ

01)=55 GeV 1209.2102, 1407.0583110-167 GeVt1 230-460 GeVt1

t1 t1, t1→Wbχ01 or tχ

01

0-2 e, µ 0-2 jets/1-2 b Yes 20.3 m(χ01)=1 GeV 1506.0861690-191 GeVt1 210-700 GeVt1

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

01 )<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(χ01)=0 GeV 1403.529490-325 GeVℓ

χ+1χ−1 , χ

+1→ℓν(ℓν) 2 e, µ 0 Yes 20.3 m(χ

01)=0 GeV, m(ℓ, ν)=0.5(m(χ

±1 )+m(χ

01)) 1403.5294140-465 GeVχ±

1

χ+1χ−1 , χ

+1→τν(τν) 2 τ - Yes 20.3 m(χ

01)=0 GeV, m(τ, ν)=0.5(m(χ

±1 )+m(χ

01)) 1407.0350100-350 GeVχ±

1

χ±1χ02→ℓLνℓLℓ(νν), ℓνℓLℓ(νν) 3 e, µ 0 Yes 20.3 m(χ

±1 )=m(χ

02), m(χ

01)=0, m(ℓ, ν)=0.5(m(χ

±1 )+m(χ

01)) 1402.7029700 GeVχ±

1, χ

0

2

χ±1χ02→Wχ

01Zχ

01

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

02), m(χ

01)=0, sleptons decoupled 1403.5294, 1402.7029420 GeVχ±

1, χ

0

2

χ±1χ02→Wχ

01h χ

01, h→bb/WW/ττ/γγ e, µ, γ 0-2 b Yes 20.3 m(χ

±1 )=m(χ

02), m(χ

01)=0, sleptons decoupled 1501.07110250 GeVχ±

1, χ

0

2

χ02χ03, χ

02,3 →ℓRℓ 4 e, µ 0 Yes 20.3 m(χ

02)=m(χ

03), m(χ

01)=0, m(ℓ, ν)=0.5(m(χ

02)+m(χ

01)) 1405.5086620 GeVχ0

2,3

GGM (wino NLSP) weak prod. 1 e, µ + γ - Yes 20.3 cτ<1 mm 1507.05493124-361 GeVW

Direct χ+1χ−1 prod., long-lived χ

±1 Disapp. trk 1 jet Yes 20.3 m(χ

±1 )-m(χ

01)∼160 MeV, τ(χ

±1 )=0.2 ns 1310.3675270 GeVχ±

1

Direct χ+1χ−1 prod., long-lived χ

±1 dE/dx trk - Yes 18.4 m(χ

±1 )-m(χ

01)∼160 MeV, τ(χ

±1 )<15 ns 1506.05332482 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 χ

01

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

1

gg, χ01→eeν/eµν/µµν displ. ee/eµ/µµ - - 20.3 7 <cτ(χ

01)< 740 mm, m(g)=1.3 TeV 1504.051621.0 TeVχ0

1

GGM gg, χ01→ZG displ. vtx + jets - - 20.3 6 <cτ(χ

01)< 480 mm, m(g)=1.1 TeV 1504.051621.0 TeVχ0

1

LFV pp→ντ + X, ντ→eµ/eτ/µτ eµ,eτ,µτ - - 20.3 λ′311

=0.11, λ132/133/233=0.07 1503.044301.7 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, g

χ+1χ−1 , χ

+1→Wχ

01, χ

01→eeνµ, eµνe 4 e, µ - Yes 20.3 m(χ

01)>0.2×m(χ

±1 ), λ121,0 1405.5086750 GeVχ±

1

χ+1χ−1 , χ

+1→Wχ

01, χ

01→ττνe, eτντ 3 e, µ + τ - Yes 20.3 m(χ

01)>0.2×m(χ

±1 ), λ133,0 1405.5086450 GeVχ±

1

gg, g→qqq 0 6-7 jets - 20.3 BR(t)=BR(b)=BR(c)=0% 1502.05686917 GeVg

gg, g→qχ01, χ

01 → qqq 0 6-7 jets - 20.3 m(χ

01)=600 GeV 1502.05686870 GeVg

gg, g→t1t, t1→bs 2 e, µ (SS) 0-3 b Yes 20.3 1404.250850 GeVg

t1 t1, t1→bs 0 2 jets + 2 b - 20.3 ATLAS-CONF-2015-026100-308 GeVt1

t1 t1, t1→bℓ 2 e, µ 2 b - 20.3 BR(t1→be/µ)>20% ATLAS-CONF-2015-0150.4-1.0 TeVt1

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

01)<200 GeV 1501.01325490 GeVc

Mass scale [TeV]10−1 1

√s = 7 TeV

√s = 8 TeV

ATLAS SUSY Searches* - 95% CL Lower LimitsStatus: July 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.


Experimental results Excesses

Outline








Experimental resultsJets plus dilepton extracted signal (1502.06031)

Opposite-sign same flavour leptonsare looked for (e+e−, µ+µ−)

Fit to data is not explained with justDrell-Yan and flavour-symmetricbackground

Extracted signal componentneeded to justify data

Typical kinematical edge SUSYsignature



Experimental resultsDiboson excess (1506.00962)

1.5 2 2.5 3 3.5

Eve

nts

/ 100

GeV

1−10

1

10

210

310

410DataBackground model1.5 TeV EGM W', c = 12.0 TeV EGM W', c = 12.5 TeV EGM W', c = 1Significance (stat)Significance (stat + syst)

ATLAS-1 = 8 TeV, 20.3 fbs

WZ Selection

[TeV]jjm1.5 2 2.5 3 3.5

Sig

nific

ance

2−1−0123

Signal not directly interpreted in thecontext of SUSY

Interpreted as a W ′ candidate froma new SU(2)R gauge symmetry

[TeV]W' m1.4 1.6 1.8 2 2.2 2.4 2.6 2.8 3

WZ

) [fb

]→

BR

(W'

× W

') →

(pp

σ

1−10

1

10

210

310

410 Observed 95% CL

Expected 95% CL

uncertaintyσ 1±

unceirtaintyσ 2±

EGM W', c = 1

ATLAS-1 = 8 TeV, 20.3 fbs

No signal from semi-leptonic channelsW → jj, lνl

Z → jj, l+l−, νν

Possible to accommodate in SUSY models with Left-Right (LR) symmetry


Theory and Phenomenology Implications from the Higgs boson mass

Outline








Theory and PhenomenologyImplications from the Higgs boson mass

The Higgs boson discovery gave us the effective self interaction term λ in theStandard Model with accuracy better than 1%

V(H†H

)= m2H†H + λ(H†H)2

Minimization −→ 〈H〉 = m√2λ≡ v√

2

H =1√2

(G+

v + h + iG0

), v = 246 GeV

Radial oscillations around vacuum generate a bare Higgs mass term

Lmass,h =12(2m2

)︸︷︷︸m2

h

h2 and λ =m2

h

2v2 = 0.126

This value for λ seems to be a success for electroweak scale supersymmetry as itstrongly agrees with theoretical predictions within the MSSM




However mh = 125 GeV suggests heavier superpartners within the MSSM(heavy stops or highly mixed)

Mass scale of the Higgs potential becomeslarger which is claimed to be problematic dueto the little hierarchy problemm2

Z = −2(|µ|

2+ m2

Hu

)+ higher order terms

1. µ is the Higgsino mass parameter2. mHu is the supersymmetric version of m,

and is typically negative3. mZ = 91 GeV is the Z-boson mass4. µ is a SUSY preserving parameter and

mHu is a SUSY breaking parameter

It is often claimed that if there are no light Higgsinos, natural SUSY is dead!




Taking this at face value one needs small µ and small mHu , where, in terms of highscale parameters {Pi} (leading contributions)

m2Hu

(Pi) = 1.82M23 − 0.21M2

2 + 0.16M3M2 − 0.64m2Hu

+ 0.36m2Q3

+ 0.28m2u3+ · · ·

m2Z (Pi) ≈ −2

(|µ|

2+ m2

Hu(Pi)

)

If gluinos are heavy

1 M3 is large2 then m2

Huis also large

3 which requires large µ⇔ heavy higgsinos4 fine-tuning



Theory and Phenomenologym2

Hu= 1.82M2

3 − 0.21M22 + 0.16M3M2 − 0.64m2

Hu+ 0.36m2

Q3+ 0.28m2

u3+ · · ·

Choose parameters in order to arrange for natural cancellations

Phenomenological Minimal Supersymmetric Standard Model→ pMSSM#

# is the number of independent parametersvery popular/main-stream within phenomenologists

I personally don’t like it as there is no UV motivation (embeddingsymmetry)

Non-Universal Higgs Mass→ NUHM m2Hu6= m0 = m2

Q3= m2

u3+ · · ·

compatible with SO(10)-GUTs

Non universal gaugino masses, in particular M3 = 0.3M2

a) Is there any objective measure of fine-tuning/naturalness?b) µ and mHu have completely different origins... why combing them in this

measure?c) Regard fine-tuning as an indication that the model is not complete

Need to go beyond the MSSM




Hu= 1.82M2

3 − 0.21M22 + 0.16M3M2 − 0.64m2

Hu+ 0.36m2

Q3+ 0.28m2

u3+ · · ·



# is the number of independent parametersvery popular/main-stream within phenomenologistsI personally don’t like it as there is no UV motivation (embeddingsymmetry)


Q3= m2

u3+ · · ·





Need to go beyond the MSSM




Hu= 1.82M2

3 − 0.21M22 + 0.16M3M2 − 0.64m2

Hu+ 0.36m2

Q3+ 0.28m2

u3+ · · ·



# is the number of independent parametersvery popular/main-stream within phenomenologistsI personally don’t like it as there is no UV motivation (embeddingsymmetry)


Q3= m2

u3+ · · ·





Need to go beyond the MSSMMorais (L.U. & A.U.) Is supersymmetry alive? Status from theory and experiment September 30, 2015 22 / 43

Theory and Phenomenology Beyond the MSSM

Outline








Theory and PhenomenologyBeyond the MSSM

One of the problems of the MSSM is the origin of the Higgsino mass term µHuHd

Singlet superfield extension λSHuHd → Next-to-Minimal SSM (NMSSM)µ parameter generated by an electroweak scale vacuum expectation value(vev) of the singlet scalar component λ〈S〉HuHd

Gauginos are commonly described by Majorana spinors ΨM = Ψ†M

Origin of µ-parameter(s) can also be explained in Dirac-gaugino models

Scenario not yet realized in any UV completion!!

In conventional SUSY models there is a Z2 symmetry, R-parity, implying that inany SUSY interaction one has to have an even number of sparticles

lightest susy particle (LSP) kinematically forbidden to decay (stable)→dark matter candidate.



Theory and PhenomenologyBeyond the MSSM

One of the problems of the MSSM is the origin of the Higgsino mass term µHuHd

Singlet superfield extension λSHuHd → Next-to-Minimal SSM (NMSSM)µ parameter generated by an electroweak scale vacuum expectation value(vev) of the singlet scalar component λ〈S〉HuHd

Gauginos are commonly described by Majorana spinors ΨM = Ψ†M

Origin of µ-parameter(s) can also be explained in Dirac-gaugino modelsScenario not yet realized in any UV completion!!

In conventional SUSY models there is a Z2 symmetry, R-parity, implying that inany SUSY interaction one has to have an even number of sparticles

lightest susy particle (LSP) kinematically forbidden to decay (stable)→dark matter candidate.



SO(10) GUT with dark matterImpose SO(10) symmetry among the free parameters of the MSSM+νR (MSSM extendedwith right-handed neutrinos)

1. Fermions and sfermions in 16 irreps of SO(10)2. Higgs and Higgsinos in 10⊕ 126 irreps of SO(10)3. Gauge and gauginos (binos and winos) in 45 adjoint irreps of SO(10)

Recall that µ and mHu have completely different originLet us try to stabilize just mHu upon infinitesimal fluctuations of input parameters

∆i = 2

∣∣∣∣∣Pi

m2Z

∂m2Hu

∂Pi

∣∣∣∣∣∆ = max{∆i}

Pi → theoryparameters

(1) Dark green points: Preferred DM and∆ < 10

(2) Light green points: Preferred DM and10 < ∆ < 100

(3) Dark blue points: little DM and ∆ < 10

(4) Light blue points: little DM and10 < ∆ < 100



Red points: Higgsino dark matter

Green points: Wino dark matter

Filled squares: Chargino NLSP

Diamonds: Neutralino NLSP

Circles: Stau NLSP

Observations

1. Considered non-universal gaugino masses

2. mHu and all SUSY breaking sector becomes natural (small fine-tuning)

3. compatible with large SUSY scale, Msusy ∼ 4 TeV for 125 GeV Higgs bosonmass

4. µ is fine-tuned→ interpret this as an indication that the origin of thisparameter is not understood

5. Considered R-Parity, which is an ad hoc symmetry. Is it really there?



Supersymmetry can well be hiding from detection in various ways:

It can be just heavy, beyond LHC14 reach

It can be completely decoupled from the (few)-TeV scale (split SUSY)

If R-parity is violated we lose the missing energy typical signatures to detectSUSY, becoming challenging for accelerators

Dirac gaugino models predict heavy gluinos and squark pair-production is highlysuppressed

So far SUSY is the best surviving theory explaining the hierarchy betweenweak and Planck scales

Most of its competitors are now dead or at least as challenged as SUSY byLHC data (E.g. Technicolor, Higgsless models)


Supersymmetric Trinification with SU(2)F -flavour Revisiting Trinification

Outline








Trinification (Glashow, Georgi and De Rujula 1984)J. E. Camargo-Molina, R. Pasechnik, M. O. P. Sampaio, J. Wessen

Why trinification?

SU(3)L ⊗ SU(3)R ⊗ SU(3)C with Z3 → gauge unification

All matter can be arranged elegantly in bi-fundamental representations.

No Adjoint Higgses needed to break the symmetry down to the SM.

Gauge symmetry preserves baryon number→ Proton decay through gaugeboson exchange is suppressed.(Achiman and Stech, 1978) (Glashow and Kang 1984)

The model can be motivated as low energy versions of E8 ⊗ E8 heterotic stringtheory (Gross et al. 1985), E6 orbifold (Braam et al. 2010) and N = 8supergravity(Cremmer et al. 1979).

Trinification models can account for baryon-antibaryon assymetry through heavyHiggs decays at one-loop(He and Pakvasa, 1986).

The model can accomodate any quark and lepton masses and mixing angles(Sayre et al. 2006)



Revisiting Trinification

Issues of this class of models

Unmotivated Hierarchy between the breaking of trinification to the SM gaugegroup and Electroweak Symmetry Breaking.

Difficult to avoid TeV-scale lepton masses without higher-dimensional operatorsor large Higgs representations within minimal SUSY trinification. (Cauet et al.2011)

Poses a problem for proton decay and adds a lot of free parametersFine tuning (in order to suppress large masses)

Due to the high number of particles, loop calculations are cumbersome. One-loopscalar spectrum has not been calculated.

Vacuum stability not studied (technically challenging)



Revisiting Trinification

We propose several ways of addressing the issues present in trinification models.

Features

We add a global SU(2)flavour symmetry inspired by SU(3)flavour (not unique).

The potentials are engineered so that it allows a tree level local-minima with onenon-zero VEV −→ trinification symmetry broken down to Left-Rightsymmetry

Higgs sector shares gauge and flavour quantum numbers with the lepton sector−→ Higgs-lepton unification.

A possibility to EWSB at the quantum level.

In this talk we will only report on the tree level breaking


Supersymmetric Trinification with SU(2)F -flavour Description of the model

Outline








Supersymmetric trinificationDescription of the model

Left-Right-Color gauge symmetry augmented by global flavour and adiscrete permutation group

G3 = [SU(3)C ⊗ SU(3)L ⊗ SU(3)R]⊗ SU(3)F n Z3 .

Unification of gauge couplings due to Z3 (permutes the gauge fields)

The superpotential

W3=λ3εαβγQ l,αx Q

x,βr L r,γ

l

λ3 → Universal Yukawa couplingα, β and γ→ flavour indicesx, l and r → colour, left-chirality and right-chirality respectively

L r,γl =

H0u H−

d νH+

u H0∗d e

νc ec φ

γ , Qx,β

r =

uc1 uc

2 uc3

dc1 dc

2 dc3

Dc1 Dc

2 Dc3

β , Q l,αx =

u1 d1 D1u2 d2 D2u3 d3 D3

α ,

Higgs-Lepton unification in L r,γl



Charges of the supermultiplets

Chiral Supermultiplet FieldsSuperfield SU(3)C SU(3)L SU(3)R SU(3)F

Lepton L r,γl 1 3l 3r 3γ

Left-Quark Q l,αx 3x 3l 1 3α

Right-Quark Qx,β

r 3x 1 3r 3β

Gauge Supermultiplet FieldsSuperfield SU(3)C SU(3)L SU(3)R SU(3)F

Gluon Caµ, λa

3 8 x2x1

1 1 1Left-Gluon Aa

µ, λaL 1 8 l2

l11 1

Right-Gluon Baµ, λa

R 1 1 8 r2r1

1

All together we have 162 real scalars, 81 chiral fermions + 24 gauginosand 24 gauge bosons



Tree-level potential for the model with SU(3)F does not allow for any stableminimum

Explicitly break SU(3)F → SU(2)F and add soft SUSY breaking terms withparameters inspired by the original SU(3)F model

first and second generations form SU(2)F doublets

third generation is a singlet under SU(2)F

Superpotential with SU(2)F flavour

W2 = λ3εαβ

(Q l,α

x Qx,β

r L rl + Q

x,α

r L r,βl Q l

x + L r,αl Q l,β

x Qx

r

)+ λ2Q l

x Qx

r L rl

+λQ

3!εl1l2l3ε

x1x2x3 Q l1x1

Q l2x2

Q l3x3+λQ

3!εx1x2x3ε

r1r2r3 Qx1

r1Q

x2r2

Qx3

r3

+λL

3!εr1r2r3ε

l1l2l3 L r1l1

L r2l2

L r3l3

For the SU(3)F model only D-terms contributed to the vacuum of the scalarpotential

With reduced flavour we also allow F-term contributions coming from thelast term of W2



As SUSY is protected against quantum corrections one has to softly break it atleading order

Vsoft = m20

{α′L r,α

l L†lr,α + α3L rl L†lr

}+ A0εr1r2r3ε

l1l2l3 L r1l1

L r2l2

L r3l3

+ h.c.

+ m20

{β′Q

x,α

r Q†rx,α + β3Q

x

r Q†rx

}+ B0εx1x2x3ε

r1r2r3 Qx1

r1Q

x2

r2Q

x3

r3+ h.c.

+ m20

{γ′Q l,α

x Q†xl,α + γ3Q l,3x Q†xl,3

}+ C0εl1l2l3ε

x1x2x3 Q l1x1

Q l2x2

Q l3x3+ h.c.

with the first line contributing to the vacuum of the tree-level potential.

Vtot = VF + VD + Vsoft

1 Yukawa interactions VF (F-terms) come from the superpotential

VF =

∣∣∣∣∂W∂Φ

∣∣∣∣22 VD are scalar interactions of the form

VD =12

∑G

∑a

g2GTr

[Φ†Ta

GΦ]2


Supersymmetric Trinification with SU(2)F -flavour Tree-level results

Outline








Tree-level results

Only the splepton sector contributes to the vacuum of the scalar potential attree-level

1. Choose a vacuum that breaks SU(3)L ⊗ SU(3)R → SU(2)L ⊗ SU(2)R ⊗ U(1)x

〈L〉 rl =

0 0 00 0 00 0 v√

2

2. Calculate minimum conditions with gU the unified gauge coupling of [SU(3)]3

α3 = −g2

Uv2

3m20

3. Calculate the Hessian matrix and apply minimum conditions

4. Calculate eigenvalues



Tree-level results

After requiring the eigenvalues of the Hessian matrix to be positive semi-definite (minimum) oneobtains the conditions

α′ >g2

U v2

6m20∧

{(0 < gU < λL ∧

(g2U−λ2)v

6√

26 A0 6

(−g2U+λ2)v

6√

2

)∨ (λL = gU ∧ A0 = 0)

}General slepton mass spectrum

# of real d.o.f.’s (mass)2 Scalar components9 0 νc,3, ec,3, ν3, e3, Im

[φ3]

1 2g2U v2

3Re[φ3]

4 12

(6√

2A0v − g2uv2 + v2λL

)H3

u, H3d

4 12

(−6√

2A0v − g2uv2 + v2λL

)H3

u, H3d

16 16

(6α′m2

0 − g2Uv2)

H(1,2)u , H(1,2)

d16 1

12

(12α′m2

0 + g2Uv2)

νc,(1,2), ec,(1,2), ν(1,2), e(1,2)

4 13

(3α′m2

0 + g2Uv2)

φ(1,2)

H0u H−

d ν

H+u H0∗

d eνc ec φ

γ 9 Goldstone bosons→ longitudinal modes of new (heavy) gauge bosons

Possible runaway directions reside in the Higgs sector

α′ and λL crucial for vacuum stability→ absent in SU(3)F



Tree-level resultsFor the particular solution with gauge-lepton Yukawa unification

α′ > g2U v2

6m20∧ λL = gU ∧ A0 = 0

Slepton mass spectrum# of real d.o.f.’s (mass)2 Scalar components

9 0 νc,3, ec,3, ν3, e3, Im[φ3]

1 2g2U v2

3Re[φ3]

4 0 H3u, H3

d4 0 H3

u, H3d

16 16

(6α′m2

0 − g2Uv2)

H(1,2)u , H(1,2)

d16 1

12

(12α′m2

0 + g2Uv2)

νc,(1,2), ec,(1,2), ν(1,2), e(1,2)

4 13

(3α′m2

0 + g2Uv2)

φ(1,2)

Furthermore in the limit α′= g2Uv2

6m20

, first and second generation Higgses becomemassless at tree-level

Quantum corrections will (re)generate masses for the Higgs sector



Tree-level results

Our vacuum choice is the only single one allowing for a stable tree-levelminimum with spontaneous gauge symmetry breaking

Good motivation for L-R models

Squarks acquire tree-level (heavy) masses which is compatible with lack of SUSYobservation at the LHC

SM fermions are massless at tree-level and their masses will only be generatedonce the Higgs fields develop vevs by means of Coleman-Weinberg dimensionaltransmutation [Phys. Rev. D 7, 1888 (1973), Phys. Rev. D 13, 12, (1976)]

> Quantum effects generate exponentially suppressed mass scale

〈H0,(1,2,3)u 〉 ∼ 〈H0,(1,2,3)

d 〉 . 〈νc,(1,2)〉 � v

Radiative see-saw mechanism may be naturally present in the model due toheavy R-H neutrinos

Compatible with LHC diboson excess?


Concluding Remarks

Concluding Remarks

Part I

SUSY searches at the LHC are putting significant constraints on the stronginteracting sector but weak sector is still widely unexplored

Recently reported excesses, are tantalizing hints towards BSM models such asSUSY

The often claimed death of natural SUSY (and MSSM) may instead mean that,before putting SUSY to grave, we need to deepen our understanding, developnovel approaches and come up with new ideas!

The LHC has just started exploring a new world and, so far, supersymmetryis by no means excluded


Concluding Remarks

Concluding Remarks

Part II

Considered a trinification model with two main features

(1) Higgs-lepton unification (same supermultiplet)(2) Global flavour SU(2) symmetry

We have obtained a stable minimum at tree-level with one single vev

Only allowed vacuum setting (up to rotations in flavour space)Spontaneously break trinification down to a SU(2)L ⊗ SU(2)R ⊗ U(1)x model

Electroweak scale generated by dimensional transmutation (work inprogress)


is supersymmetry alive? status from theory and experiment · is supersymmetry alive? status from...

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