Whither SUSY? G. Ross, Birmingham, January 2013

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1 Whither SUSY? G. Ross, Birmingham, 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]

2 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,.. (?)

3 ATLAS LHC tests of SUSY

4 SUSY to what place? Little hierarchy problem MSSM: 105 +(19) Parameters ^ M Z 2 =! a i m! 2 i + M # 2! i +... q ",l " g ",W!,B! m q! > 0.6!1TeV " # > a m" 2 M # Z

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

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

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

8 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

9 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 III. Implications of 125 GeV Higgs

10 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

11 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 = ± 2GeV < 3! WMAP:! Min = 18, m h = ± 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 ) m 2 2 M H u ( P ) + m ( Q3 ( M P ) + m M u 3 ( P )) ) +! + # + " * Q 2 M P 2 2 3y t, $ 4' 2. & ( 1. %. -

12 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 = ± 2GeV < 3! WMAP:! Min = 18, m h = ± 2GeV LHC Nov 2012 LHC Jan 2011

13 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 = ± 2GeV < 3! WMAP:! Min = 18, m h = ± 2GeV LHC Nov 2012 Significant Higgsino LSP component -now excluded by XENON 100 LHC Jan 2011

14 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 = ± 2GeV m H > 125GeV < 3! WMAP:! Min = 18, m h = ± 2GeV! > 300

15 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)

16 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

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

18 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 = " ( 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?

19 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

20 GNMSSM R-symmetry ensures Singlet extensions natural

21 GNMSSM NMSSM spectrum No perturbative μ term Commutes with SO(10) Anomaly cancellation N q 10 q 5 q Hu q Hd q S 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)

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

23 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

24 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

25 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

26 GNMSSM benchmark point

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

28 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 New focus point: cancellation between M 3 and M 2 contributions if M 2 2! M 3 2 at M SUSY M 3 : M 2 : M 1 =! 3 :1:! 1

29 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 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 = ; SO(10) : ( 45 # 45) symm = ! 3 :1:! 1 2.7! 3 :1: 0.5! 1 String: # ( 3 +! GS ) :("1 +! GS ) : " 33 $ % 5 +! & GS ' ( (OII, also mixed moduli anomaly)

30 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

31 Summary CMSSM (and other MSSMs) highly fine tuned

32 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

33 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

34 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

35 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

36 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?...

37 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

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

39

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