General Gauge Mediation @ the EW scale Diego Redigolo GGI, - PowerPoint PPT Presentation

General Gauge Mediation @ the EW scale Diego Redigolo GGI, Florence September 4th based on 1507.04364 & to appear work with S. Knapen and D.Shih �

2+1 problems for BSM physics -1 -1 s = 7 T eV , L = 5.1 fb s = 8 T eV , L = 5.3 fb CM S Events / 3 GeV Events / 3 GeV Data 6 16 K > 0.5 D Z+X 5 Why is the Higgs @ 125 GeV? Z *, ZZ 14 γ 4 m =125 GeV 3 H 12 2 1 10 0 120 140 160 Is the EW scale natural at all? m (GeV) 8 � 4 6 4 2 0 80 100 120 140 160 180 m (GeV) � 4 Summary of CMS SUSY Results* in SMS framework ICHEP 2014 m(mother)-m(LSP)=200 GeV m(LSP)=0 GeV gluino production 0 ~ ∼ SUS 13-019 L=19.5 /fb g → qq χ ~ ∼ 0 SUS-14-011 SUS-13-019 L=19.3 19.5 /fb g → bb χ ~ 0 SUS-13-007 SUS-13-013 L=19.4 19.5 /fb ∼ g → tt χ ~ ~ ∼ 0 g t( t t ) SUS-13-008 SUS-13-013 L=19.5 /fb → → χ x = 0.20 ~ ∼ ∼ 0 SUS-13-013 L=19.5 /fb Where is everybody? ± x = 0.50 g → qq( χ → W χ ) ~ ~ ∼ ± ∼ 0 SUS-13-008 SUS-13-013 L=19.5 /fb g → b( b → t( χ → W χ )) squark ~ 0 SUS-13-019 L=19.5 /fb ∼ q → q χ ~ ∼ 0 SUS-14-011 L=19.5 /fb t t → χ + 0 x = 0.25 ~ ∼ ∼ SUS-13-011 L=19.5 /fb x = 0.50 t → b( χ → W χ ) x = 0.75 stop ~ ∼ 0 ∼ 0 SUS-13-014 L=19.5 /fb t → t b χ ( χ → H G) ~ ~ ∼ 0 SUS-13-024 SUS-13-004 L=19.5 /fb t → ( t → t χ ) Z ~ 2 ~ 1 1 ∼ 0 SUS-13-024 SUS-13-004 L=19.5 /fb t → ( t → t χ ) H 2 1 1 sbottom 0 ~ ∼ SUS-13-018 L=19.4 /fb b → b χ SM & nothing else or ~ ∼ 0 SUS-13-008 SUS-13-013 L=19.5 /fb b → tW χ ~ ∼ 0 SUS-13-008 L=19.5 /fb b bZ → χ x = 0.05 ∼ 0 ∼ ± ∼ 0 ∼ 0 SUS-13-006 L=19.5 /fb x = 0.50 χ χ → lll ν χ χ x = 0.95 EWK gauginos 2 + 0 0 ∼ ∼ - + - ∼ ∼ SUS-13-006 L=19.5 /fb χ χ → l l ν ν χ χ 0 0 0 0 CMS Preliminary ∼ ∼ ∼ ∼ SUS-14-002 L=19.5 /fb χ χ → Z Z χ χ ∼ 2 ∼ 0 2 ∼ 0 ∼ 0 χ ± χ → W Z χ χ SUS-13-006 L=19.5 /fb 2 ∼ 0 ∼ 0 ∼ 0 ∼ 0 SUS-14-002 L=19.5 /fb χ χ → H Z χ χ For decays with intermediate mass, 2 2 ∼ ± ∼ 0 ∼ 0 ∼ 0 SUS-14-002 L=19.5 /fb χ χ → H W χ χ ∼ 0 ∼ 2 ∼ 0 ∼ 0 x = 0.05 m = x ⋅ m +(1-x) ⋅ m ± ll SUS-13-006 L=19.5 /fb x = 0.50 χ χ → τ ν χ χ BSM around the corner? 2 x = 0.95 intermediate mother lsp ∼ 0 ∼ ∼ 0 ∼ 0 ± SUS-13-006 L=19.5 /fb χ χ → τ τ τ ν χ χ slepton 2 0 ~ ∼ SUS-13-006 L=19.5 /fb l → l χ ~ SUS-12-027 L=9.2 /fb g → qll ν λ 122 ~ g → qll ν λ SUS-12-027 L=9.2 /fb ~ 123 g → qll ν λ SUS-12-027 L=9.2 /fb 233 ~ g → qbt µ λ ' SUS-12-027 L=9.2 /fb 231 ~ g → qbt µ λ ' SUS-12-027 L=9.2 /fb ~ 233 EXO-12-049 L=19.5 /fb g → qqb λ '' 113/223 ~ g → qqq λ '' EXO-12-049 L=19.5 /fb ~ 112 g → tbs λ '' SUS-13-013 L=19.5 /fb ~ 323 SUS-12-027 L=9.2 /fb g → qqqq λ '' ~ 112 q qll → ν λ SUS-12-027 L=9.2 /fb 122 ~ RPV SUS-12-027 L=9.2 /fb q → qll ν λ 123 ~ q → qll ν λ SUS-12-027 L=9.2 /fb ~ 233 q qbt ' → µ λ SUS-12-027 L=9.2 /fb 231 ~ SUS-12-027 L=9.2 /fb q → qbt µ λ ' ~ 233 q → qqqq λ '' SUS-12-027 L=9.2 /fb R 112 ~ SUS-13-003 L=19.5 9.2 /fb t → µ e ν t λ R 122 ~ SUS-12-027 L=9.2 /fb t → µ τ ν t λ ~ R 123 t t SUS-13-003 L=19.5 9.2 /fb → µ τ ν λ R 233 ~ SUS-13-003 L=19.5 /fb t → tbt µ λ ' R 233 0 200 400 600 800 1000 1200 1400 1600 1800 *Observed limits, theory uncertainties not included Mass scales [GeV] Only a selection of available mass limits Probe *up to* the quoted mass limit BSM physics vs strong bounds from flavor observables

has far reaching implications for SUSY m h = 125 GeV minimal: consistent UV completions BUT issues with fine-tuning non-minimal: hard UV completions BUT better fine-tuning Run I hints at an heavier scale for SUSY states minimal: no light states at Run I are expected once the Higgs mass is imposed non-minimal: LHC bounds are LHC bound dominating the tuning non-minimal: minimal

Maybe in minimal SUSY the Higgs mass is already telling us that SUSY was not expected at Run I? What about Run II? LHC bound Have we learn everything we can from Run I? We will try to answer these questions for ALL the possible gauge mediation models with the MSSM @ low energy

Why gauge mediation? Gauge mediation In the MSSM, automatically gives SUSY-breaking terms flavor bind SUSY-breaking are problematic for flavor Visible Hidden N = 1 vector multiplet Sector Sector g 2 F i √ m soft ' ( g 1 , g 2 , g 3 ) of G SM M, F (4 π ) 2 M SM gauge interactions are flavor blind! It also provides a COMPLETE theory of SUSY breaking It is consistent up to the Planck scale It accommodates unification of gauge couplings

General Gauge Mediation (GGM) gives a model independent definition of “pure” gauge mediation (Meade, Seiberg, Shih 2008) C 1 / 2 C 1 C 0 sfermion + { m 2 Q , m 2 U , m 2 L } masses: + gaugino { M 1 , M 2 , M 3 } B 1 / 2 masses: µ + “by-hand” All the other (non-zero) soft masses are fixed by UV sum-rules/flavor universality M mess ex: m 2 H u = m 2 H d = m 2 L 8 PARAMETERS E = 3 m 2 m 2 U − m 2 Q + m 2 � � CALCULABLE parameter space: � L 2 i.e. realizable in terms of weakly coupled models (Buican, Meade, Seiberg, Shih 2008) B µ ≈ 0 CAVEAT: extensions of the pure GGM will destroy the sum-rules and in some cases even flavor universality: A-terms ≈ 0 Ex: D-tadpoles, MSSM-messenger-messenger, MSSM-MSSM-messenger couplings…

The low energy theory for GGM is the MSSM: m tree ≤ m Z h How do we get m h = 125 GeV ? m 2 is radiatively sensitive to 3 soft parameters h Q 3 | 2 + m 2 U 3 | 2 + ( A t H u ˜ Q 3 | ˜ U 3 | ˜ Q 3 ˜ − L soft ⊃ m 2 U 3 + c.c. ) m Q 3 ≈ m U 3 to keep it simple Tuning Lightest Stop Mass 3000 3000 2500 2500 2500 pect Suspect 2000 iggs FeynHiggs zero 2000 2000 multi-TeV eV D é @ GeV D A-terms 1500 1500 1500 A-terms M S m t 1000 1000 1000 500 750 (Hall, Pinner, (Draper, Meade, 500 500 D 100 300 m t 1 é Ruderman, Reece, Shih 2011) 2011) 0 0 - 4 - 2 0 2 4 - 4 - 2 0 2 4 A t ê m é X t ê m t é M S Maximal Mixing delivers light stops Heavy stops: High-scale SUSY, Split-SUSY (possibly accessible at LHC)

in (pure) GGM A t = 0 extensions of the pure GGM can generate large UV A-terms but destroy sum-rules/flavor universality Can we generate large A-terms in pure GGM? What is the min stop mass after m h = 125 GeV is imposed? An intuitive picture I: m Q ≈ m U 4 16 π 2 d U 3 ) + 2 | A t | 2 + · · · M 3 dtm 2 H u = 2 | y t | 2 ( m 2 Q 3 + m 2 2 large A-terms from tension with EWSB: � heavy gluino m H u signed value H TeV L tachyonic stops pull m Hu up 16 π 2 d 32 3 g 2 dtA t = y t 3 M 3 + · · · 0 16 π 2 d Q = − 32 3 | M 3 | 2 + · · · dtm 2 3 g 2 m L 3 A t - 2 m u m Q m 2 H u = m 2 H d = m 2 stops tachyonic L GGM sum-rule to get them light L slepton tachyon � in the IR in the IR - 4 4 6 8 10 12 Log 10 Q ê GeV

Splitting the stops soft masses 6 m u m U � m Q M 3 4 m L 3 signed value H TeV L 2 m H u light 0 left-handed stop A t - 2 m Q - 4 4 6 8 10 12 Log 10 Q ê GeV 6 m U ⌧ m Q m Q M 3 4 m L 3 light signed value H TeV L 2 m H u right-handed stop 0 A t m u GGM sum-rule - 2 E slepton tachyon � E = 3 m E 3 in the IR m 2 m 2 U − m 2 Q + m 2 � � - 4 L 2 4 6 8 10 12 Log 10 Q ê GeV

We expect boundaries @ low stop masses to be produced by the convergence of the tensions discussed The main technical difficulty to get a complete picture is that � • EWSB+Higgs constraints are imposed @ EW scale • GGM boundary conditions are defined @ M mess A systematic approach: We completely characterize GGM with m h = 125 GeV We understand its features in a simple analytical approximation We can use these results to study the LHC coverage on GGM after Higgs Similar techniques can possibly be used in other frameworks

Key ingredient to handle the RG evolution � • Transfer matrix (TM) method: RGE’s are bilinear in soft masses A IR = T � � A UV (common in high-scale scenarios) T 0 � A UV + T 00 � IR = � A UV � m 2 m 2 � UV   µ   B µ A t m 2    H u    .  m 2  �   m 2 = T T 0 T 00 depend on M mess , M S , tan β ONLY . A = �  H d  .    m 2    M 3  Q 3        . . . . . . We trade UV parameters for IR ones once and for all! From GGM UV b.c. Ex: A t ( M mess ) = 0 M 3 ≈ p 0 A t + q 0 M 2 we get relations among IR quantities

parameter counting M 1 , M 2 , A t , m 2 Q 3 , m 2 U 3 , m 2 GGM in the IR : L 3 , µ and M mess all the rest of the spectrum is fixed by 8 parameters IR relations @ the weak scale -2 parameters M mess = 10 15 , 10 11 , 10 7 GeV “high”, “medium”, “low” ∼ g 2 has little impact on the RGEs M 1 = 1 TeV 1 -3 parameters IR constraints: m 2 Z = − 2( m 2 H u + | µ | 2 ) + · · · { 3 parameters 2 EWSB conditions 2 B µ (tan β = 20) + · · · sin 2 β = m 2 Q 3 , m 2 2 | µ | 2 + m 2 H u + m 2 U 3 , M 2 H d m h = 123 GeV (accounting conservatively for + sign µ theory error Allanach & co. 2004)