Whither SUSY? G. Ross, RAL, January PDF Free Download

Whither SUSY? G. Ross, RAL, January 2013 whither Archaic or poetic adv 1. to what place? 2. to what end or purpose? conj to whatever place, purpose, etc. [Old English hwider, hwæder; related to Gothic hvadrē; modern English form influenced by HITHER]

Low energy ^ SUSY to what end or purpose? Unification: SU(5), SO(10), The hierarchy problem: M Higgs, M W,Z! M Planck, M GUT,.. (?)

ATLAS LHC tests of SUSY

SUSY to what place? Little hierarchy problem MSSM: M Z 2 =! a i m! 2 i + b i M # 2! i +... q ",l " 105 +(19) Parameters g ",W!,B! m t! > 0.6!1TeV " # > a m" 2 M # 100 2 Z (a! 1 for M X! M GUT, a! 1/10 for M X! TeV )

An exception: Natural SUSY light stop m t!,lhc > 250 GeV FCNC: 1,2 sgenerations heavy Hierarchy problem: 3 rd sgeneration light but realistic models??

The Higgs mass in SUSY? M S 2 = m q3 m U3! ( 900GeV ) 2! 125GeV (LHC) Atlas CMS LHC July 2012 at 5σ significance

SUSY to what place? Little hierarchy problem MSSM:! 105 +(19) Parameters breaking definite SUSY structure ^ M Z 2 =! a i m! 2 i + b i M # 2! i +... q ",l " g ",W!,B! m q! > 0.6!1TeV " # > a m" 2 M # 100 2 Z! Correlations between SUSY breaking parameters and/or additional low-scale states

SUSY searches - significance SUSY parameters Likelihood % %! v 0 " " m2 (# i )( ' & ' $(# i ) ) * & 1/2 ( * ) Ghilencea, GGr! q = % ' & i $ " i M Z #M Z #" i 2 ( * ) 1/2 Ellis, Enquist, Nanopoulos, Zwirner Barbieri, Giudice Fine tuning measure! q = 100, "# 2! 9, "# 2 / d.o.f.! 1

Outline I. II. The CMSSM Scalar focus point Reduced fine tuning (G)NMSSM Gaugino focus point Natural SUSY R-parity breaking Supersoft SUSY breaking Compressed spectrum } Hidden SUSY III. Implications of 125 GeV Higgs

I. The CMSSM µ 0,m 0, m 1/ 2, A 0, B 0 assume correlation between SUSY breaking parameters v 2 = m2! Couplings and masses evaluated to two loop (leading log) order enhanced sensitivity due to small tree-level! = 1 8 g 2 2 ( 1 + g 2 )cos 2 2" Cassel, Ghilencea, GGR c.f. earlier work : Dimopoulos, Giudice Chankowski, Ellis, Olechowski, Pokorski

e.g. CMSSM! i " µ 0,m 0, m 1/2, A 0, B 0 Pre-LHC Relic density restricted 1 h 0 resonant annihilation 2 h! t-channel exchange 3! co-annihilation 4 t! co-annihilation 5 A 0 / H 0 resonant annihilation Within 3! WMAP:! Min = 15, m h = 114.7 ± 2GeV < 3! WMAP:! Min = 18, m h = 115.9 ± 2GeV λ increases with m H v 2 = m2! Limit of RGE focus point -natural cancellation of terms for m HU (M X ) = m t! R (M X ) = m t! L (M X ) = m 0 Cassel, Ghilencea, GGR 2 m Hu ( Q ) 2 2 = m Hu 2 ( M P ) + 1 2 m 2 2 M H u ( P ) + m 2 2 2 2 ( Q3 ( M P ) + m M u 3 ( P )) ) +! + # + " * Q 2 M P 2 2 3y t, $ 4' 2. & ( 1. %. -

e.g. CMSSM! i " µ 0,m 0, m 1/2, A 0, B 0 Direct SUSY searches: 1 h 0 resonant annihilation 2 h! t-channel exchange 3! co-annihilation 4 t! co-annihilation 5 Relic density restricted A 0 / H 0 resonant annihilation Within 3! WMAP:! Min = 15, m h = 114.7 ± 2GeV < 3! WMAP:! Min = 18, m h = 115.9 ± 2GeV LHC Nov 2012 LHC Jan 2011

e.g. CMSSM! i " µ 0,m 0, m 1/2, A 0, B 0 1 h 0 resonant annihilation 2 h! t-channel exchange 3! co-annihilation 4 t! co-annihilation 5 Relic density restricted A 0 / H 0 resonant annihilation Within 3! WMAP:! Min = 15, m h = 114.7 ± 2GeV m H > 125GeV < 3! WMAP:! Min = 18, m h = 115.9 ± 2GeV! > 300

CMSSM summary: Minimises MSSM fine tuning (focus point) (c.f. gauge mediation! >>! CMSSM ) Max [! EW,! " ] = 15(29), m h = 114(116) ± 2GeV Complementary DM & LHC searches DM LHC! " 100 Sensitivity # (10 $100) ( Full region LHC 14TeV 10 fb!1 ) (Now achieved!) BUT! > 300 for m H = 126GeV (If give up on unification of soft parameters fine tuning reduced by factor! 10)

II. Reduced fine tuning : more correlations between parameters later beyond the MSSM e.g. singlet extensions the NMSSM additional quartic interaction!v = "H u H d 2 increases m h

Fine tuning in the NMSSM (! " 0.7 ) Higgs not lightest scalar (! ht not included) Kowalska, Munir, Roszkowski, Sessolo, Trojanowski, Tsai

Fine tuning in the NMSSM (! " 0.7 ) Higgs not lightest scalar Focus-point; DM exclusion (! ht not included) Kowalska, Munir, Roszkowski, Sessolo, Trojanowski, Tsai

Reduced fine tuning : BMSSM - General Operator analysis ( )( ) 2, S = m 0 ""! L = # d 2 " 1 µ 0 + c 0 S H 1 H 2 M * Dimension 5!V = " ( 2 2 1 h 1 + h 2 )h 1 h 2 + " 2 h 1 h 2 ( ) 2 ; " 1 = µ 0 M *, " 2 = c 0 m 0 M *!! Cassel, Ghilencea, GGR Casas, Espinosa, Hidalgo Dine, Seiberg, Thomas Batra, Delgardo, Tait Kaplan, m h MSSM m h + dim 5 operators effect mainly comes from! 1 h 1 2 h 1 h 2 term origin?

Reduced fine tuning : singlet extensions GNMSSM µ S >> m 3/2 c.f. NMSSM W GNMSSM eff = ( H u H d ) 2 / µ s + µh u H d µ 2 2 H u + H d µ S ( )H u H d v 2 =! m2 " Reduced fine tuning mainly for GNMSSM CMSSM CGNMSSM CNMSSM (Higgs not universal) LHC constraints applied LHC +DM constraints applied GGR, Schmidt-Hoberg, Staub c.f. Hall, Pinner, Ruderman

GNMSSM R-symmetry ensures Singlet extensions natural

GNMSSM NMSSM spectrum No perturbative μ term Commutes with SO(10) Anomaly cancellation N q 10 q 5 q Hu q Hd q S 4 1 1 0 0 2 8 1 5 0 4 6 D=5 operators SUSY breaking up and down Yukawas allowed 1 M QQQL 3q 10 + q 5 + q Hu + q Hd = 4 Mod N! 3q 10 + q 5 = 0 Mod N!! R-symmetry ensures singlets light 1 M LLH u H u Weinberg operator W,!! R=2 non=perturbative breaking Z R 4,8! Z 2 R R " parity Domain walls and tadpoles safe Abel µ! m 3/2, O( m 3/2 M 2 QQQL) W = W MSSM +!SH u H d +"S 3 + #W!W R Z4! m 3/2 H u H d + m 2 3/2 S + m 3/2 S 2!W R Z8! m 2 3/2 S μ term and mass terms natural GNMSSM (c.f. NMSSM) Lee, Raby, Ratz, GGR, Schieren, Schmidt Hoberg, Vaudrevange

Dark Matter structure (! LSP "! DM ) (! LSP "! DM ) Xenon1T Stau co-annihilation DM searches insensitive

Higgs structure ( h u, h d, s) µ s! µ MSSM SUSY structure with heavy Higgs µ s, m s, b s! µ h 1! H u,d +!S, h 2 = S "!H u,d... h 2 may be lighter than LEP bound m h1 v/s! for the case m h2 < m h1

Higgs structure ( h u, h d, s) µ s! µ MSSM SUSY structure with heavy Higgs µ s, m s, b s! µ h 1! H u,d +!S, h 2 = S "!H u,d... h 2 may be lighter than LEP bound... h 1 may have enhanced!! rate H! ± u,d Schmidt- Hoberg, Staub

Higgs structure ( h u, h d, s) µ s! µ MSSM SUSY structure with heavy Higgs µ s, m s, b s! µ h 1! H u,d +!S, h 2 = S "!H u,d... h 2 may be lighter than LEP bound... h 1 may have enhanced!! rate... h 1 may have enhanced LSP annihilation rate to photons..?! Fermi 135GeV line :!," # 1, m A1! 240 $ 280GeV Schmidt- Hoberg, Staub, Winkler

GNMSSM benchmark point

GNMSSM benchmark point Stau co-annihilation limits SUSY masses nearly excluded by LHC

Stau co-annihilation limits SUSY masses nearly excluded by LHC but LSP nature sensitive to gaugino spectrum GNMSSM benchmark point

Reduced fine tuning : nonuniversal gaugino masses 16! d 2 dt m 2 =3( 2 y H u t 2 2 (m Hu + m 2 Q3 + m 2 ) + 2 a u 3 t 2 ) " 6g 2 2 M 2 2 " 6 5 g 2 M 1 1 2 New focus point: cancellation between M 3 and M 2 contributions if M 2 2! M 3 2 at M SUSY Natural ratios? e.g.: GUT: SU(5) :! N " ( 24 # 24) symm = 1 + 24 + 75 + 200; SO(10) : ( 45 # 45) symm = 1+ 54 + 210 + 770! 3 :1:! 1 2.7! 3 :1: 0.5! 1 String: # ( 3 +! GS ) :("1 +! GS ) : " 33 $ % 5 +! & GS ' ( (OII, also mixed moduli anomaly)

Gaugino focus point - Phenomenology Gaugino mass ratios. gauginos can be very heavy Light neutralino and 2 charginos nearly degenerate + for M 1 < µ, Bino or Higgsino LSP candidate

Non-universal gaugino masses in the C MSSM m h = 125.3 ± 0.6 ± 3 GeV Antusch, Calibbi, Maurer, Monaco, Spinrath

Summary CMSSM (and other MSSMs) highly fine tuned

Summary CMSSM (and other MSSMs) highly fine tuned BCMSSM: more correlations or BMSSM -(G) NMSSM Reduced!! GNMSSM! SUSY states can be (slightly)heavier m h! 130GeV Z 4 R, Z 8 R LHC bounds already severe with conventional cosmology

Summary CMSSM (and other MSSMs) highly fine tuned BCMSSM: more correlations or BMSSM -GNMSSM + gaugino focus point; SUSY states heavier Still room for natural SUSY!

Summary CMSSM (and other MSSMs) highly fine tuned BCMSSM: more correlations or BMSSM -GNMSSM + gaugino focus point; SUSY states heavier Still room for natural SUSY! Indirect hints.g-2, h! " ", Fermi

Muon g-2 a µ theory! a µ expt =!(28.7 ± 8.0) "10!10 Theory error from hadronic contribution:! a µ e + e " = 3.6 #! a µ " = 2.4 # SUSY a theory expt ( µ! a µ ) "10!11 $ 100GeV! a SUSY µ = "13#10 "10 % & M SUSY ' ( ) 2 tan* Needs light sleptons anomaly/mirage spectrum? With slepton universality h! " " plausibly correct! Giudice et al

h! " " enhancement in the NMSSM tan! small " #! contribution small Dominant contribution t! 1 A t = 0(1), suppression (enhancement) Singlet mixing - suppressed bb - enhanced!! and WW.. King et al

Summary CMSSM (and other MSSMs) highly fine tuned BCMSSM: more correlations or BMSSM -GNMSSM + gaugino focus point; SUSY states heavier Still room for natural SUSY! Indirect hints.g-2, h! " ", Fermi Hidden SUSY Natural SUSY R-parity breaking Supersoft SUSY breaking Compressed spectrum

Summary CMSSM (and other MSSMs) highly fine tuned BCMSSM: more correlations or BMSSM -GNMSSM + gaugino focus point; SUSY states heavier Still room for natural SUSY! Indirect hints.g-2, h! " ", Fermi Hidden SUSY Intriguing implications of 125GeV pure SM Higgs IRFP?, Higgs inflation?...

III. Implications of 125 GeV Higgs Landau pole <M Planck Vacuum instability RGE - just the Standard Model Higgs coupling small Hambye, Riesselmann

Implications of 125 GeV Higgs vacuum instability V(H ) =! 1 2 M 2 H H 2 + " 4 H 4 Tunneling probability: Isidori, Ridolfi, Strumia! 2! away from stability De Grassi et al

! Higgs mass? (!2" ) 16! 2 " # = 12(# 2 $ h t 4 + #h t 2 )!(3g' 2 + 9g 2 )" + 9 4 ( 1 3 g' 4 + 2 3 g' 2 g 2 + g 4 )