Natural SUSY and the LHC

Natural SUSY and the LHC Clifford Cheung University of California, Berkeley Lawrence Berkeley National Lab N = 4 SYM @ 35 yrs

I will address two questions in this talk. What is the LHC telling us about weak scale supersymmetry? Given what we now know, what can we expect from LHC in the future?

I will address two questions in this talk. What is the LHC telling us about weak scale supersymmetry? (a lot) Given what we now know, what can we expect from LHC in the future? (depends)

Supersymmetry has yielded many successes. mathematical beauty gauge coupling unification dark matter naturalness

unification SM

unification MSSM

dark matter Supersymmetry has all ingredients needed of the WIMP miracle: neutralino + R-parity Ωh 2 1pb σv Caveat emptor: SUSY DM far from perfect!

naturalness puzzle And of course, SUSY resolves the hierarchy problem of the SM. f H

Unification does not require new physics at LHC accessible energies. 10 TeV unifons 1 TeV SM

Unification does not require new physics at LHC accessible energies. 10 TeV unifons (too heavy) 1 TeV SM

Dark matter does not require new physics that is produced en mass at LHC. 10 TeV 1 TeV WIMPs SM

Dark matter does not require new physics that is produced en mass at LHC. 10 TeV 1 TeV WIMPs (too weakly interacting) SM

Only naturalness requires new, colored states accessible to the LHC. 10 TeV squarks 1 TeV etc. SM

Only naturalness requires new, colored states accessible to the LHC. 10 TeV 1 TeV squarks etc. (LHC signals!) SM

naturalness is...... a poorly defined concept. However, formal definitions are adopted for standardization, for some ultraviolet parameter, c.

naturalness in SUSY Define the vev direction in the MSSM to be H cos β H d +sinβ H u The symmetry breaking potential takes form: V = λ H 4 + m 2 H 2

two faces of the little hierarchy V = λ H 4 + m 2 H 2 i) EWSB ii) higgs mass v = 246 GeV m h 125 GeV? little hierarchy = naturalness vs. exp t

i) EWSB + LHC

EWSB For instance, at large tan beta where the soft mass gets 1-loop corrected,

EWSB For instance, at large tan beta where the soft mass gets 1-loop corrected,

Natural EWSB: some but not all states are required to be light. M 1 TeV g 500 GeV µ h 0 2 h + h 0 1 t 2 bl t 1 Closeness to Higgs (fig. by L.J. Hall)

Limits on colored sparticles @ ATLAS, 5/fb. [GeV] m 1/2 700 600 MSUGRA/CMSSM: tan% = 10, A = 0, µ>0 0 q ~ (1800) ATLAS $ -1 L dt = 4.71 fb, Combined CL s CL s Preliminary s=7 TeV observed 95% C.L. limit median expected limit 500 400 ~ q (1000) ~ q (1400) ATLAS EPS 2011 &# LSP LEP Chargino ~ No EWSB g (1200) ~ g (1000) 300 ~ g (800) 200 ~ q (600) ~ g (600) 500 1000 1500 2000 2500 3000 3500 4000 m 0 [GeV] 17 / 48

Limits on colored sparticles @ CMS, 5/fb.

! )*' [GeV] m 1/2 700 600 Caveat: M T2 limit is a combination 500 of M T2 (low m 0 ) and M T2 b (high m 0 ) 400 MSUGRA/CMSSM: tan% = 10, A = 0, µ>0 0 ~ q (1000) ~ q (1400) q ~ (1800) ATLAS Preliminary -1 $ L dt = 4.71 fb, Combined s=7 TeV observed 95% C.L. limit CL s median expected limit CL s ATLAS EPS 2011 &# LSP LEP Chargino ~ No EWSB g (1200) ~ g (1000) 300 ~ g (800) 200 q ~ (600) ~ g (600) 500 1000 1500 2000 2500 3000 3500 4000 [GeV] m 0 17 / 48!! (*41$1*5!6789 4:4;*&012#<0&*')*=0-&>?!6*1-*@?4*A*!"#$%&'()'*+,-../ bottom line: gluinos > 900 GeV squarks * > 1.4 TeV * Limit on first + second generation squarks only.

Limits on 3rd gen. @ ATLAS, 5/fb. [GeV] m χ 0 1 350 300 250 stop pair in GMSB Natural model ATLAS Preliminary L dt = 2.05 fb -1 Reference points, s = 7 TeV CL s CL s observed limit (95% C.L.) expected limit (95% C.L.) Expected CL s limit ±1σ 200 150 t m~ 1 + < m b +m χ 1 100 m χ 0 1 < m Z 50 100 150 200 250 300 350 400 m~ t 1 [GeV]

What are the remedies for tuned EWSB?

i) R-parity violation Perhaps with no MET, weaker limits? leptonic RPV baryonic RPV Not so simple...

leptonic RPV: In general, still have MET from neutrino. Exception: sneutrino LSP, flavor games. Also, beware of ruining neutrino masses.

baryonic RPV: The cost of baryonic RPV: Must avoid constraints from B violation ( displaced vertices). No baryogenesis above weak scale. No SUSY dark matter.

ii) squashed spectra Reduce MET by flattening the spectrum. Compressed SUSY : degenerate, by fiat 1104.4304 1111.6897

Squashed spectra somewhat ad hoc. In some cases there is a dynamical reason. Stealth SUSY : degenerate, by SUSY high mult. final states }possible 1105.5135 1201.4875

iii) split families Split 3rd from 1st + 2nd generation squarks. geography conformal dynamics flavor symmetries...stay tuned for Lisa s talk. 1201.1293 1202.6339 1203.0572 1203.1622...

ii) Higgs + LHC

Higgs mass MSSM higgs is typically too light at tree. tree: m h m Z cos 2β At loop, MSSM higgs is corrected. loop:

Bottom line: without funny business, some tweaking needed to get mh correct. no mixing: stop squark > 1.2 TeV max mixing: stop squark > 250 GeV However, LHC tells us even more...

ATLAS Higgs

CMS Higgs

What are the remedies for tuned Higgs?

i) large A-terms MSSM Higgs Mass mh GeV 140 130 120 110 m h 124126 GeV 100 X t 0 Suspect FeynHiggs 90 200 300 500 700 1000 1500 2000 3000 m t1 X t GeV 6 m t 1112.2703

ii) MSSM + new states A heavier Higgs requires a larger quartic: non-decoupling F-terms non-decoupling D-terms These are quartics from soft SUSY breaking arising from additional new states.

MSSM + S Add a singlet chiral superfield coupled via which generates a quartic for the Higgs, so λ<0.7 for GUT pert. low tan β hep-ph/0607332

MSSM + U(1)X Add a U(1)X gauge symmetry under which the Higgs is charged. For X = a Y + b (B - L), the Higgs mass is hep-ph/0309149 hep-ph/0409127

For given stop mass, min value of gx is fixed. 0.70 0.65 0.60 g 0.55 0.50 ming X 0.45 0.40 0.35 0.30 g' 500 1000 1500 2000 m t GeV Anomaly free U(1)X boson decays to leptons.

effects on Higgs physics Modifications of the MSSM Higgs sector can also mean modifications of Higgs decays. For mh = 125 GeV the BRs are: bb : 58% WW : 22% Easiest way to change Higgs properties is via bb. ZZ : 3%

Higgs EFT of MSSM = 2HDM The quartic structure of the MSSM is less constrained w/ non-decoupling contribs. U(1)X + MSSM S + MSSM + 1 2 λ 1(Φ 1 Φ 1) 2 + 1 2 λ 2(Φ 2 Φ 2) 2 + λ 3 (Φ 1 Φ 1)(Φ 2 Φ 2)+λ 4 (Φ 1 Φ 2)(Φ 2 Φ 1) { 1 + 2 λ 5(Φ 1 Φ 2) 2 + [ λ 6 (Φ 1 Φ 1)+λ 7 (Φ 2 Φ 2) ] } Φ 1 Φ 2 +h.c..

S + MSSM can boost h to γγ. m A GeV 500 450 400 350 0.8 Λ 1.2 1.4 1.6 1.8 m A GeV 500 450 400 350 BRhΓΓBR SM hγγ 1 1.2 1.8 2.2 2.6 1.6 2.4 2 300 1 1 2 3 4 5 6 7 tan Β 300 1.4 1 2 3 4 5 6 7 tan Β

U(1)X + MSSM can deplete h to γγ (note: is charge dependent). 1000 1 g X 1000 BRhΓΓBR SM hγγ 900 9000.95 m A GeV 800 700 600 1.2 500 1.4 400 0.8 3001.6 2 3 4 5 6 tan Β m A GeV 800 700 600 0.9 5000.85 0.8 400 0.75 0.7 300 0.65 2 3 4 5 6 tan Β

conclusions

LHC results reveal an immense amount about natural, weak-scale SUSY. squark/gluino limits Higgs limits EWSB tuning? Higgs tuning?

Natural SUSY now requires add l struct. EWSB tuning Higgs tuning R-parity violation or squashed spectra big A-terms or MSSM++ or split families

Meso-tuned SUSY may be in our future, i.e. revise your naturalness criteria. 10 TeV scalars MSSM w/ heavy scalars: 1 TeV gauginos SM

thanks!

naturalness, quantified m 2 t (400 GeV)2 1 1+A 2 t /2m 2 t 20% 1 3 log Λ/m t mhiggs 120 GeV 2 µ 2 (200 GeV) 2 20% 1 mhiggs 120 GeV 2 M 2 3 (700 GeV) 2 1 1 A t /2M 3 20% 1 3 log Λ/m t 2 mhiggs 120 GeV 2

Simplified Model limits @ ATLAS, 5/fb. squark mass [GeV] 2000 1800 1600 1400 Squark-gluino-neutralino model, m(" # 0 ) = 0 GeV 1 ATLAS Combined CL s CL s $ Preliminary observed 95% C.L. limit median expected limit Expected limit ±1! ATLAS EPS 2011-1 L dt = 4.71 fb,! SUSY s=7 TeV = 1 fb MSUGRA/C 1200 1000! SUSY = 10 fb ~ q (1000) 800! SUSY = 100 fb ~ q (600) 600 600 800 1000 1200 1400 1600 1800 2000 gluino mass [GeV]

gluino-mediated stop @ ATLAS, 5/fb. [GeV] t 1 m~ 650 600 550 500 450 400 ~ g - ~ g production, ATLAS ~ ~ g" t 1 +t, 2-lepton SS, 4 jets 0 = 60 GeV m # $ m$ # 1 ± 1 m~ q 1,2 & 2 m # $ 0 1 >> m~ g ~ t $ 1 "b+# ~ ~ g" ± 1 t 1 t forbidden % -1 L dt = 2.05 fb, s=7 TeV Obs. CL s 95% C.L. limit Exp. CL 95% C.L. limit s Expected limit ±1! 1 lepton plus b-jets 2.05 fb -1 350 300 250 200 400 450 500 550 600 650 700 750 800 [GeV] m~ g

1/fb Susy, pre-moriond Limits depend strongly on LSP mass. squark mass [GeV] 2000 1750 1500 1250 1000 750 Squark-gluino-neutralino model Tevatron, Run I CDF, Run II D0, Run II ATLAS Preliminary 0 lepton 2011 combined -1, L dt = 1.04 fb s=7 TeV Obs. m LSP = 0 GeV Exp. m = 0 GeV LSP Obs. m LSP = 195 GeV Exp. m = 195 GeV LSP Obs. m LSP = 395 GeV Exp. m = 395 GeV LSP σ SUSY σ SUSY = 0.01 pb = 0.1 pb 500 σ SUSY σ SUSY = 1 pb = 10 pb 250 LEP2 ~ q 0 0 250 500 750 1000 1250 1500 1750 2000 gluino mass [GeV]

high-scale + split SUSY HighScale Supersymmetry Split Supersymmetry 200 180 0.5 3 10 Nonp urbati 200 180 0.5 3 10 Nonpert urbative Higgs mass m h in GeV 160 140 0.3 0.2 HighScale SUSY 0.1 0.05 0 2 1 Higgs mass m h in GeV 160 140 0.2 0.3 SplitSUSY Metastable 2 1 120 Metastable 0.0 120 0.1 Unstable 100 10 4 10 6 10 8 10 10 10 12 10 14 10 16 10 18 Supersymmetry breaking scale in GeV Unstable 100 10 4 10 6 10 8 10 10 10 12 10 14 10 16 10 18 Supersymmetry breaking scale in GeV 1108.6077 Figure 1: Contour plot of the Higgs quartic coupling renormalized at the supersymmetry breaking