Flavoring GMSB - Non-Degenerate Squarks and a Heavy Higgs in Flavored GMSB

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1 Flavoring GMSB - Non-Degenerate Squarks and a Heavy Higgs in Flavored GMSB Iftah Galon Technion - Israel Institute of Technology arxiv: [hep-ph] with: M. Abdullah, Y. Shadmi and Y. Shirman arxiv: [hep-ph] with: G. Perez and Y. Shadmi Nov 7, 2013 Iftah Galon - Technion Nov 7, 2013 UC Irvine 1 / 50

2 Outline 1 Motivation: Flavor SUSY Higgs 2 Messenger - Matter couplings: Flavored Gauge Mediation(FGM) 3 Non-degenerate squarks 4 A heavy Higgs (with interesting spectra) 5 Analytic Continuation into Superspace and soft terms calculation 6 Conclusions and outlook Iftah Galon - Technion Nov 7, 2013 UC Irvine 2 / 50

3 Motivation: SM Flavor Puzzle & New Physics SM Flavor Puzzle m e : m µ : m τ 1 : 200 : 4, 000 m d : m s : m b 1 : 30 : 4, 000 m u : m c : m t 1 : 1, 000 : 200, 000 V CKM = ( 1 λ 2 /2 λ Aλ 3 (ρ iη) λ 1 λ 2 /2 Aλ 2 Aλ 3 (1 ρ iη) Aλ 2 1 ) λ 0.22 A 0.81 ρ 0.13 η 0.35 very non trivial structure How should the new physics flavor structure look like? Theory of flavor for SM = Automatically explains new physics flavor structure (soft terms) Iftah Galon - Technion Nov 7, 2013 UC Irvine 3 / 50

4 Motivation: The Higgs Boson Pretty clear we found a Higgs boson = m h = ± 0.4 GeV (PDG) Data-Bkg Events / GeV Data Sig+Bkg Fit Bkg ATLAS Preliminary pp H γ γ, s = 8 TeV -1 L dt = 20.3 fb N jets = m γγ [GeV] figure from: ATLAS-CONF Iftah Galon - Technion Nov 7, 2013 UC Irvine 4 / 50

5 Motivation: The Higgs Mass in The MSSM In the MSSM at 1-loop ( mh 2 mz 2 cos 2 2β + 3m4 t log 4π 2 v 2 ( M 2 S m 2 t ) + X t (1 2 X )) t 2 MS 2 12MS 2 where M 2 S = m t 1 m t 2 & X t = A t µ cot β Implication for m h 126 GeV large M S or large Xt M S Iftah Galon - Technion Nov 7, 2013 UC Irvine 5 / 50

6 In GMSB For GMSB (and General Gauge Mediation (GGM)) RG = generates A-terms (zero at messenger scale) M g = Running of A-terms and m 2 t To realize m h 126 GeV with GMSB 1 a high messenger scale 2 heavy squarks & heavy gluinos e.g Feng, Surujon & Yu for GGM, Draper, Meade, Reece & Shih In GMSB - no A-terms = Heavy t(all squarks) 8 10 TeV for 3-loops see Feng, Kant, Profumo & Sanford Iftah Galon - Technion Nov 7, 2013 UC Irvine 6 / 50

7 Motivation: SUSY The LHC So far: No light, flavor-blind superpartners ATLAS SUSY Searches* - 95% CL Lower Limits Status: SUSY 2013 ATLAS Preliminary L dt = ( ) fb 1 s = 7, 8 TeV Model e, µ, τ, γ Jets E miss T L dt[fb 1 ] Mass limit Reference Inclusive Searches 3 rd gen. g med. MSUGRA/CMSSM jets Yes 20.3 q, g 1.7 TeV m( q)=m( g) ATLAS-CONF MSUGRA/CMSSM 1 e, µ 3-6 jets Yes 20.3 g 1.2 TeV any m( q) ATLAS-CONF MSUGRA/CMSSM jets Yes 20.3 g 1.1 TeV any m( q) q q, q q χ jets Yes 20.3 q 740 GeV m( χ 0 1)=0 GeV ATLAS-CONF g g, g q q χ jets Yes 20.3 g 1.3 TeV m( χ 0 1)=0 GeV ATLAS-CONF g g, g qq χ ± 1 qqw ± χ0 1 1 e, µ 3-6 jets Yes 20.3 g 1.18 TeV m( χ 0 1)<200 GeV, m( χ ± )=0.5(m( χ 0 1)+m( g)) ATLAS-CONF g g, g qq(ll/lν/νν) χ e, µ 0-3 jets g 1.12 TeV m( χ 0 1)=0 GeV ATLAS-CONF GMSB ( l NLSP) 2 e, µ 2-4 jets Yes 4.7 g 1.24 TeV tanβ< GMSB ( l NLSP) 1-2 τ 0-2 jets Yes 20.7 g 1.4 TeV tanβ >18 ATLAS-CONF GGM (bino NLSP) 2 γ - Yes 4.8 g 1.07 TeV m( χ 0 1)>50 GeV GGM (wino NLSP) 1 e, µ + γ - Yes 4.8 g 619 GeV m( χ 0 1)>50 GeV ATLAS-CONF GGM (higgsino-bino NLSP) γ 1 b Yes 4.8 g 900 GeV m( χ 0 1)>220 GeV GGM (higgsino NLSP) 2 e, µ (Z) 0-3 jets Yes 5.8 g 690 GeV m( H)>200 GeV ATLAS-CONF Gravitino LSP 0 mono-jet Yes 10.5 F 1/2 scale 645 GeV m( g)>10 4 ev ATLAS-CONF g b b χ b Yes 20.1 g 1.2 TeV m( χ 0 1)<600 GeV ATLAS-CONF g t t χ jets Yes 20.3 g 1.1 TeV m( χ 0 1) <350 GeV g t t χ e, µ 3 b Yes 20.1 g 1.34 TeV m( χ 0 1)<400 GeV ATLAS-CONF g b t χ e, µ 1 3 b Yes 20.1 g 1.3 TeV m( χ 0 1)<300 GeV ATLAS-CONF rd gen. squarks direct production EW direct b1 b1, b1 b χ b Yes 20.1 b GeV m( χ 0 1)<90 GeV b1 b1, b1 t χ± 1 2 e, µ (SS) 0-3 b Yes 20.7 b GeV m( χ ± 1 )=2 m( χ 0 1) ATLAS-CONF t1 t1(light), t1 b χ± e, µ 1-2 b Yes 4.7 t GeV m( χ 0 1)=55 GeV , t1 t1(light), t1 Wb χ0 1 2 e, µ 0-2 jets Yes 20.3 t GeV m( χ 0 1) =m( t1)-m(w )-50 GeV, m( t1)<<m( χ ± 1 ) ATLAS-CONF t1 t1(medium), t1 t χ0 1 2 e, µ 2 jets Yes 20.3 t GeV m( χ 0 1)=0 GeV ATLAS-CONF t1 t1(medium), t1 b χ± b Yes 20.1 t GeV m( χ 0 1)<200 GeV, m( χ ± 1 )-m( χ 0 1)=5 GeV t1 t1(heavy), t1 t χ0 1 1 e, µ 1 b Yes 20.7 t GeV m( χ 0 1)=0 GeV ATLAS-CONF t1 t1(heavy), t1 t χ b Yes 20.5 t GeV m( χ 0 1)=0 GeV ATLAS-CONF t1 t1, t1 c χ0 1 0 mono-jet/c-tag Yes 20.3 t GeV m( t1)-m( χ 0 1)<85 GeV ATLAS-CONF t1 t1(natural GMSB) 2 e, µ (Z) 1 b Yes 20.7 t1 500 GeV m( χ0 1)>150 GeV ATLAS-CONF t2 t2, t2 t1 + Z 3 e, µ (Z) 1 b Yes 20.7 t GeV m( t1)=m( χ0 1)+180 GeV ATLAS-CONF ll,r ll,r, l l χ0 1 2 e, µ 0 Yes 20.3 l GeV m( χ 0 1)=0 GeV ATLAS-CONF χ + 1 χ 1, χ + 1 lν(l ν) 2 e, µ 0 Yes 20.3 χ ± GeV m( χ 0 1)=0 GeV, m( l, ν)=0.5(m( χ ± 1 )+m( χ 0 1 1)) ATLAS-CONF χ + 1 χ 1, χ + 1 τν(τ ν) 2 τ - Yes 20.7 χ ± GeV m( χ 0 1)=0 GeV, m( τ, ν)=0.5(m( χ ± 1 )+m( χ 0 1 1)) ATLAS-CONF χ ± 1 χ0 2 llν lll( νν), l ν lll( νν) 3 e, µ 0 Yes 20.7 χ ± 600 GeV m( χ ± 1 )=m( χ 0 2), m( χ 0 1)=0, m( l, ν)=0.5(m( χ ± 1 )+m( χ 0 1)) ATLAS-CONF , χ0 2 χ ± 1 χ0 2 W χ 0 1Z χ 0 3 e, µ 1 0 Yes 20.7 χ ± m( χ ± 1 )=m( χ 0 2), m( χ 0 1, χ GeV 1)=0, sleptons decoupled ATLAS-CONF χ ± 1 χ0 2 W χ 0 1h χ 0 1 e, µ 1 2 b Yes 20.3 χ ± m( χ ± 1 )=m( χ 0 2), m( χ 0 1, χ GeV 1)=0, sleptons decoupled ATLAS-CONF Long-lived Other RPV particles Direct χ + 1 χ 1 prod., long-lived χ ± 1 Disapp. trk 1 jet Yes 20.3 χ ± m( χ ± 1 )-m( χ 0 1)=160 MeV, τ( χ ± GeV 1 )=0.2 ns ATLAS-CONF Stable, stopped g R-hadron jets Yes 22.9 g 832 GeV m( χ 0 1)=100 GeV, 10 µs<τ( g)<1000 s ATLAS-CONF GMSB, stable τ, χ 0 1 τ(ẽ, µ)+τ(e, µ) 1-2 µ χ GeV 10<tanβ<50 1 ATLAS-CONF GMSB, χ 0 1 γ G, long-lived χ γ - Yes 4.7 χ GeV 0.4<τ( χ 0 1)<2 ns q q, χ 0 1 qqµ (RPV) 1 µ, displ. vtx q 1.0 TeV 1.5 <cτ<156 mm, BR(µ)=1, m( χ 0 1)=108 GeV ATLAS-CONF LFV pp ντ + X, ντ e + µ 2 e, µ ντ 1.61 TeV λ 311 =0.10, λ132= LFV pp ντ + X, ντ e(µ) + τ 1 e, µ + τ ντ 1.1 TeV λ 311 =0.10, λ 1(2)33= Bilinear RPV CMSSM 1 e, µ 7 jets Yes 4.7 q, g 1.2 TeV m( q)=m( g), cτlsp<1 mm ATLAS-CONF χ + 1 χ 1, χ + 1 W χ 0 1, χ 0 1 ee νµ, eµ νe 4 e, µ - Yes 20.7 χ ± m( χ GeV 1)>300 GeV, λ121>0 ATLAS-CONF χ + 1 χ 1, χ + 1 W χ 0 1, χ 0 1 ττ νe, 3 e, µ + τ - eτ ντ Yes 20.7 χ ± m( χ GeV 1)>80 GeV, λ133>0 ATLAS-CONF g qqq jets g 916 GeV BR(t)=BR(b)=BR(c)=0% ATLAS-CONF g t1t, t1 bs 2 e, µ (SS) 0-3 b Yes 20.7 g 880 GeV ATLAS-CONF Scalar gluon pair, sgluon q q 0 4 jets sgluon GeV incl. limit from Scalar gluon pair, sgluon t t 2 e, µ (SS) 1 b Yes 14.3 sgluon 800 GeV ATLAS-CONF WIMP interaction (D5, Dirac χ) 0 mono-jet Yes 10.5 M* scale 704 GeV m(χ)<80 GeV, limit of<687 GeV for D8 ATLAS-CONF s = 7 TeV full data s = 8 TeV partial data s = 8 TeV full data Mass scale [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. Iftah Galon - Technion Nov 7, 2013 UC Irvine 7 / 50

8 One common assumption in SUSY searches The superpartner spectrum is flavor-blind Iftah Galon - Technion Nov 7, 2013 UC Irvine 8 / 50

9 Flavor Issues Low-E observables constrain the SUSY flavor structure c g ũ i uũ j ū g c = δ ij ( m2 ) ij K ij m 2 Degeneracy Alignment Decoupling In many SUSY models Minimal Flavor Violation m 2 I + #YY Iftah Galon - Technion Nov 7, 2013 UC Irvine 9 / 50

10 Motivation - MFV Vs. Non-MFV In theories which are MFV: m 2 I + #YY degenerate 1st & 2nd generations no mixing Most SUSY searches - tuned for an MFV spectrum Simplest searches: Jets + /E T Rough bounds: m g, m q 1.7 TeV(CMSSM) Iftah Galon - Technion Nov 7, 2013 UC Irvine 10 / 50

11 Flavor in SUSY searches But in fact MFV is over constraining sfermions can have mass splittings and/or mixing K ij bounds on δ ij = ( m2 ) ij allow: small mixing large splitting m 2 Iftah Galon - Technion Nov 7, 2013 UC Irvine 11 / 50

12 Flavor Effects If the flavor structure of superpartners is non-trivial previously unavailable channels might lead to new signals techniques designed to find the signatures of flavor-blind spectra may become inefficient Iftah Galon - Technion Nov 7, 2013 UC Irvine 12 / 50

13 Example 1: χ 0 2 l ± l j χ 0 1 l j l ± i χ 0 2 l j l ± l ± i Di-lepton endpoint m 2 ll endpoint = (m2 χ 0 2 Galon & Shadmi arxiv: [hep-ph] m2 l )(m2 l m 2 l m 2 χ 0 1) χ 0 1 No Flavor degeneracy mẽ = m µ no mixing signal in ee, µµ distribution No signal in eµ distribution No Flavor For ee, µµ Iftah Galon - Technion Nov 7, 2013 UC Irvine 13 / 50

14 Example 1: χ 0 2 l ± l j With Flavor Mixing ) ( ) (ẽ ) ( l1 cos θ sin θ = l 2 sin θ cos θ µ Splitting m 2 = m 1 + m With Flavor χ 0 1 l j l ± i In the flavored case Cannot use Flavor Subtraction : ee + µµ eµ µe Cannot enhance the slepton signal see Eckel, Shepherd & Su Iftah Galon - Technion Nov 7, 2013 UC Irvine 14 / 50

15 Example 2: Squark Mass Bounds Simplified Models (and the resulting bounds) assume 8-fold squark degeneracy non-mfv Squarks at LHC searches Production: X-sections affected by non-degenerate 1 st 2 nd gen squarks - mainly sensitive to u, d PDFs (for non-decoupled gluinos) Detection: lighter squarks: efficiency reduced (e.g light c R ) Mahbubani, Papucci, Perez, Ruderman & Weiler mixings affect detection (especially for t, b, c) Blanke, Giudice, Paradisi, Perez & Zupan, Agrawal & Frugiuele Iftah Galon - Technion Nov 7, 2013 UC Irvine 15 / 50

16 Extend: GMSB Flavored GMSB (FGM) = Iftah Galon - Technion Nov 7, 2013 UC Irvine 16 / 50

17 Gauge Mediated SUSY Breaking (GMSB) The (minimal) GMSB superpotential Dine, Nelson & Shirman Dine, Nelson, Nir & Shirman W = X φ φ + Y u QH u u c + Y d QH d d c + Y l LH d e c where X = M + θ 2 F parametrizes SUSY and φ, φ - vector like pair of SU(5) Main Features ( m 2 soft ) i,j = δ i,j m 2, A u,d,l i,j = 0 at µ = M Evolving down with RGEs Minimally Flavor Violating (MFV) Theory Iftah Galon - Technion Nov 7, 2013 UC Irvine 17 / 50

18 Coupling to Messengers of SU(5) messengers ( T D) φ i = ( ) T φ i = D In general Messenger can couple to visible fields in various ways D H d, L, D Hu, need a mechanism (symmetry, 5d construction) to prevent them from coupling to matter Dine, Nir & Shirman Dvali, Giudice & Pomarol Chacko & Ponton Iftah Galon - Technion Nov 7, 2013 UC Irvine 18 / 50

19 Schematics Yukawa-like messenger-matter couplings ( T D) φ i = ( ) T φ i = D = W FGM y u Q Du c, y d QDd c Upshot flavor dependent 1 new scalar soft-mass contributions non-degenerate squarks 2 non-zero A-terms a heavy higgs (& light squarks) Iftah Galon - Technion Nov 7, 2013 UC Irvine 19 / 50

20 FGM: Model Symmetries Superfield R-parity Z 3 X even 1 D 1 even 0 D 1 even 1 D 2 even 1 D 2 even 0 T I, T I, D I >2, D I >2 even 1 q, u c, d c, l, e c odd 0 H U, H D even 0 Shadmi & Szabo N 5 2 for: y U and y D, y L W = X ( T i T i + D i Di ) + Y u QH u u c + Y d QH d d c + Y l LH d e c + y u Q D 1 u c + y d QD 2 d c + y l LD 2 e c Iftah Galon - Technion Nov 7, 2013 UC Irvine 20 / 50

21 Soft Terms At µ = M: non-zero A-terms A 1 (4π) Yy 2 F 2 M soft masses 2 loop : m 2 1 ( g 4 g 2 y 2 + y 4 ± Y 2 y 2) F (4π) 4 M soft masses 1 loop : (for M < 10 7 GeV) m 2 y 2 (4π) 2 F 4 M 6 2 Iftah Galon - Technion Nov 7, 2013 UC Irvine 21 / 50

22 Flavor Structure Y u, Y d, Y l SM flavor structure {me mµ mτ } {m d m s m b } {m u m c m t}, V CKM Messenger flavor structure y u, y d, y l Add a flavor theory Explain SM mass hierarchies & mixings within the flavor theory Automatically same flavor theory controls new couplings Iftah Galon - Technion Nov 7, 2013 UC Irvine 22 / 50

23 non-degenerate squarks IG, G. Perez and Y. Shadmi arxiv: [hep-ph] = Iftah Galon - Technion Nov 7, 2013 UC Irvine 23 / 50

24 Flavor Symmetry Flavor symmetry (say U(1)) is broken by a spurion λ( 1) λ 0.2 Higher-dim operators and n, n = sum of charges W CQH u u c (λ) n + C Q Du c (λ) n +... Froggatt-Nielsen Y { Cλ n n 0 0 n < 0 = y = C λ n n = n = Y y MFV n > n = Y > y suppressed n < n = Y < y interesting Iftah Galon - Technion Nov 7, 2013 UC Irvine 24 / 50

25 Flavor Symmetry Flavor symmetry U(1) U(1) with spurions S 1 ( 1, 0), S 2 (0, 1) Charges, borrowing from Leurer-Nir-Seiberg Q 1 (6, 3), Q 2 (2, 0), Q 3 (0, 0) u1 c( 6, 9), uc 2 ( 2, 3), uc 3 (0, 0) H u (0, 0), H d (0, 0) d1 c( 6, 9), d 2 c(2, 0), d 3 c(2, 0) produce quark masses and V CKM Y U λ6 λ λ 3 λ 2, Y D λ λ 4 λ λ 2 λ 2 (up to O(1) coefficients) Iftah Galon - Technion Nov 7, 2013 UC Irvine 25 / 50

26 Flavor Symmetry Assigning messenger charges D(m, n), D( m, n) determines the pattern of y u = m u 2 y u y u y u y u, y u YY y u, Y y u y u Y, g 2 y u y u,... we will choose n, m such that Y s and m q,u,d 2 are approximately diagonal in the same basis m 2 exhibits large splitting & small mixing Iftah Galon - Technion Nov 7, 2013 UC Irvine 26 / 50

27 Alignment Usual Alignment Nir & Seiberg aligned soft terms - above the flavor symmetry scale = must be high scale SUSY RGE: mild splittings Iftah Galon - Technion Nov 7, 2013 UC Irvine 27 / 50

28 Supersymmetric Alignment Supersymmetric Alignment Shadmi & Szabo aligned superpotential couplings can be low-scale SUSY soft-terms inherit structure RGE: large splittings Iftah Galon - Technion Nov 7, 2013 UC Irvine 28 / 50

29 Non-Degenerate Squarks IG, Perez & Shadmi, arxiv: [hep-ph] Choose (m, n) such that (y u ) ij yδ i2 δ j2 = Then ( m 2 q) 22 = 1 2 ( m2 u) 22 δm 2 For r m 2 = δm2 m 2 GMSB (N 5 = 1) r m 2 M M 10 5 GeV M 10 6 GeV M 10 8 GeV y Iftah Galon - Technion Nov 7, 2013 UC Irvine 29 / 50

30 Phenomenology Light charm- and strange-squarks λ D( 1, 3), D(1, 3) = y u 0 c 22 λ 0 = (δ m QL, δ m UR ) Heavy up- and down-squarks D(0, 6), D(0, 6) = yu = (δ m QL, δ m UR ) Notice the Holomorphic zeros Iftah Galon - Technion Nov 7, 2013 UC Irvine 30 / 50

31 Non-Degenerate Squarks - Running Effects For low scale models r m 2 can be large for relatively small y s less running less (RG) degeneracy Examples: (N 5 = 1 (light gluino), tan β = 5) - Massless c R 1 M = 500 TeV, F /M = 200 TeV µ = M m q 2 TeV, m g 1.5TeV, c R 870 GeV 2 M = 400 TeV, F /M = 150 TeV m q 1.6 TeV, m g 1.2TeV, c R 670 GeV Iftah Galon - Technion Nov 7, 2013 UC Irvine 31 / 50

32 A heavy Higgs Abdullah, IG, Shadmi & Shirman, arxiv: [hep-ph] Evans, Ibe & Yanagida Kang, Li, Liu, Tong & Yang Craig, Knapen, Shih & Zhao Albaid & Babu Craig, Knapen & Shih Evans & Shih... = Iftah Galon - Technion Nov 7, 2013 UC Irvine 32 / 50

33 MFV-like FGM so for m h 126 GeV need access to stop sector: A t, m 2 q 3, m 2 t Simplest example: MFV-like D, H u : same flavor charges y u Y u Iftah Galon - Technion Nov 7, 2013 UC Irvine 33 / 50

34 Main Features W = X ( T i T i + D i D i ) + Y u QH u u c + Y d QH d d c + Y l LH d e c At µ = M: + yq 3 Dt c non-zero A-terms A 1 (4π) Yy 2 F 2 M soft masses 2 loop : m 2 1 ( g 4 g 2 y 2 + y 4 ± Y 2 y 2) F (4π) 4 M soft masses 1 loop : (for M < 10 7 GeV) m 2 y 2 (4π) 2 F 4 M 6 Iftah Galon - Technion Nov 7, 2013 UC Irvine 34 / 50 2

35 Higgs mass Two possibilities for Higgs mass mostly stop A-terms, LL, RR ± contributions cancel (1-loop: mainly low scales): light spectra. enhanced by the large LL,RR stop masses - heavy stops Iftah Galon - Technion Nov 7, 2013 UC Irvine 35 / 50

36 MFV-like: Heavy Higgs & TeV Spectra A 33, m 2 33 = M = 400 TeV, tan β = 10 Iftah Galon - Technion Nov 7, 2013 UC Irvine 36 / 50

37 Example Spectrum masses GeV g Χ o Χ o Χ u R d R u L d L c R s R c L s L t 2 b t 2 1 b 1 M = 400 TeV Λ = 165 TeV tan β = 10 y t = 1.2 m χ 0 = 233 GeV m q 1.7 TeV 1000 m g 1.3 TeV 500 h o Χ Χ o Χ e R Ν e e L Μ R Ν ΜΜ L Τ 1 Ν Τ Τ 2 m t 1 2 TeV Iftah Galon - Technion Nov 7, 2013 UC Irvine 37 / 50

38 MFV-like: Heavy Higgs & TeV Spectra A 33, m 2 33 = M = TeV, tan β = 10 No tachyonic stops (negative 1-loop is negligible) y t 1.2 tachyonic staus, EWSB problems Need Λ large heavy spectrum Iftah Galon - Technion Nov 7, 2013 UC Irvine 38 / 50

39 Example Spectrum 7000 Χ o Χ o Χ t 2 masses GeV g e R u R d R u L d L Μ R c R s R c L s L Τ 2 b 1 b 2 t 1 M = GeV Λ = 355 TeV tan β = 10 y t = 1.14 m τl = 390 GeV mũr = 2401 GeV m g = 2540 GeV 1000 Χ o Χ Χ o Ν e L Ν ΜΜ L Τ 1 Ν Τ h whereas in mgmsb m t 1 8 TeV heavy split stops affect the RG evolution: can lead to interesting spectra Iftah Galon - Technion Nov 7, 2013 UC Irvine 39 / 50

40 A Heavy Higgs & Non-Degenerate Squarks Choose flavor charges D( 2, 3), D(2, 3) Then λ y u 0 λ 2 0 = 0 y 0 Soft masses: (δ m ur ) 22, (δ m ur ) 33, (δ m QL ) 33 A-terms: A t 1 16π 2 y 2 Y t A non-degenerate squarks, and a heavy Higgs and new stop mass contributions. Iftah Galon - Technion Nov 7, 2013 UC Irvine 40 / 50

41 Analytic Continuation into Superspace and calculation of soft terms = Iftah Galon - Technion Nov 7, 2013 UC Irvine 41 / 50

42 Calculation of Soft Terms Analytic Continuation into superspace SUSY enters through Z(X, X, µ) Z X =M+θ 2 F = Z + Z X θ2 F + Z X θ2 F 2 Z X X θ4 F F Expanding d 4 θφ Zφ = m 2 φ = 2 ln Z (ln X ) (ln X ) F F M M Giudice & Rattazzi Arkani-Hamed, Giudice, Luty & Rattazzi The key: identify M = X X m 2 φ = 1 2 ln Z F 2 4 (ln M) 2 M Iftah Galon - Technion Nov 7, 2013 UC Irvine 42 / 50

43 Calculation of Soft Terms Schematically Analytic Continuation Integrate out messenger leading F /M soft terms Running d ln Z = γ(λ), d ln µ dλ = β d ln µ Iftah Galon - Technion Nov 7, 2013 UC Irvine 43 / 50

44 Calculation of Soft Terms see Chacko & Ponton ln M ln Z φ (µ < M) = γ > d(ln µ ) + ln Λ d ln Z φ d(ln M) = γ(m) µ=m d 2 ln Z φ d(ln M) 2 = d γ(m) µ=m d(ln M) dγ< (µ) d(ln M) ln µ ln M µ=m γ < d(ln µ ) λ(µ < M) = λ(λ) + ln M ln Λ β> d(ln µ ) + ln µ ln M β< d(ln µ ) [ ] m 2 φ γ φ = λ β> λ γ< φ λ β F λ M λ Iftah Galon - Technion Nov 7, 2013 UC Irvine 44 / 50 2

45 Calculation of Soft Terms Must be done carefully: multiple fields dz d ln µ = Z 1/2 γz 1/2 Kinetic mixing at 1-loop = m 2 2 loop Iftah Galon - Technion Nov 7, 2013 UC Irvine 45 / 50

46 Calculation of Soft Terms Simplified Model - High-E theory Superpotential W = X DD + Y 0 Hle + y 0 Dle Kinetic terms d 4 θ ( ( D H ) Z DD Z DH Z HD Z HH and assume Z i,j (µ = Λ) = δ i,j ) ( ) D = H d 4 θ φ i Z i,jφ j Simplified Model - Low-E theory Kinetic term, d 4 θ h Z h h, Superpotential W = Y 0 h hle Iftah Galon - Technion Nov 7, 2013 UC Irvine 46 / 50

47 Calculation of Soft Terms Things to note: Calculating m 2 loop 2 - must account for 1-loop effects. physical 1-loop? associated physical coupling ỹ j? RG running: γ >, γ <, γ? Need to match theories at the boundary M 1 loop Iftah Galon - Technion Nov 7, 2013 UC Irvine 47 / 50

48 Calculation of Soft Terms Match couplings at boundary Implications Z h = Z 22 (1-loop) Determines RG at low-e modifications γ 12 Bottom line γ < l ỹ 2 2 and γ l = ỹ 2 1 γ < h ỹ 2 2 and γ h 0 Higgs: unchanged Matter: receive yy 2 Iftah Galon - Technion Nov 7, 2013 UC Irvine 48 / 50

49 Conclusions and Outlook Flavored Gauge Mediation (FGM) allows viable non-mfv models with some degree of mass splitting and mixings with low scale supersymmetric alignment you can get large mass splitting (unlike high-scale) non-zero A-terms at µ = M can contribute to 126 GeV Higgs mass with superpartners accessible at the LHC FGM models lead to interesting squark and slepton masses Flavorful spectra - need new LHC search strategies Iftah Galon - Technion Nov 7, 2013 UC Irvine 49 / 50

50 Thank You Iftah Galon - Technion Nov 7, 2013 UC Irvine 50 / 50

51 Backup Slides Iftah Galon - Technion Nov 7, 2013 UC Irvine 51 / 50

52 Formula for mass splitting where δm 2 1 (4π) y 2 F 4 M (4π) 4 ( 6 y 2 G y ) y 2 F 2 M 2, G y 16 3 g g g 2 1. Iftah Galon - Technion Nov 7, 2013 UC Irvine 52 / 50

53 Bounds On δs (δ q ij ) MM = m2 q j q i m 2 q (K q M ) ij(k q M ) jj, where m 2 q j q i = m 2 q j m 2 q i, and m 2 q q ij (δ q ij ) MM Im(δ q ij )2 MM Im((δ q ij ) LL(δ q ij ) RR) d u d Table: The upper bounds on (δ q ij ) MM, taken from Isidori, Nir & Perez, but assuming order-one phases, for m q = 1 TeV and m g /m q = 1. Iftah Galon - Technion Nov 7, 2013 UC Irvine 53 / 50

54 MFV-like: Heavy Higgs & TeV Spectra A 33, m 2 33 = M = 900 TeV, tan β = 10 Iftah Galon - Technion Nov 7, 2013 UC Irvine 54 / 50

55 Higgs Mass M = 900 TeV, tan β = 10 x t = Xt M S edge large close to Iftah Galon - Technion Nov 7, 2013 UC Irvine 55 / 50

56 Higgs Mass - y t and y b Λ = 230 TeV M = 10 8 GeV tan β = 10 large y b Tachyonic l Iftah Galon - Technion Nov 7, 2013 UC Irvine 56 / 50

57 A-terms 3rd-generation limit and also A U 3,3 = Y t [ ] 3y 2 16π 2 t + yb 2 F M A D 3,3 = Y b [ ] 3y 2 16π 2 b + yt 2 F M A L 3,3 = 3Y τy 2 τ 16π 2 F M δa U 33 = 1 16π 2 y 2 t F 3 M 5. Iftah Galon - Technion Nov 7, 2013 UC Irvine 57 / 50

58 Soft Squared Masses 3rd-generation limit { m H 2 U = 1 128π 4 3 ( 3 2 Y t 2 (3yt 2 + yb 2 ) + N 4 g )} 20 g 1 4 F 2 M { m H 2 D = 1 128π Y b 2 (3y b 2 + y t 2 ) 3 ( 3 2 Y τ 2 y τ 2 + N 4 g )} 20 g 1 4 F 2 M { ( ( m q) 2 33 = 1 128π 4 yt 2 + 3yb 2 + 3Y b y τ g g ) yb 2 ( + 3yt 2 + 3Y t g g g 1 2 ) yt 2 + Y by b Y τ y τ 30 g 1 2 ( 4 +N 3 g g ) } 60 g 1 4 F 2 M {( ( m u 2 c ) 33 = 1 128π 4 6yt 2 + y b 2 + Y b 2 + 6Y t g 3 2 3g ( 4 + N 3 g )} 15 g 1 4 F 2 M 15 g 2 1 ) y 2 t Y 2 t y 2 b Iftah Galon - Technion Nov 7, 2013 UC Irvine 58 / 50

59 Soft Squared Masses 3rd-generation limit ( m 2 d c ) 33 = 1 128π 4 ( m 2 l ) 33 = 1 128π 4 { ( 6yb 2 + y τ 2 + yt 2 + Yt 2 + 6Yb g 3 2 3g ) 15 g 1 2 yb 2 ( ) } 4 yt 2 Y b 2 + 2Y F 2 by b Y τ y τ + N, { ( 3 2 y b 2 + 2y τ g g 1 2 ( 3 +N 4 g ) } 20 g 1 4 F 2 M 3 g g 1 4 M ) yτ 2 + ( Yτ 2 y τ 2 + 3Y ) by b Y τ y τ ( m e 2 c ) 33 = {(3y π 4 b + 4y τ 2 3g ) 5 g 1 2 yτ 2 + ( } 2Yτ 2 y τ 2 + 6Y ) 3 by b Y τ y τ + 5 Ng 1 4 F M 2. Iftah Galon - Technion Nov 7, 2013 UC Irvine 59 / 50

60 1-Loop Soft Squared Masses δmq 2 L = 1 1 ( ) F y (4π) 2 u y u + y d y 4 d 6 M 6 ( ) y F 4 u y u δm 2 u R = 1 (4π) δm 2 d R = 1 (4π) δm 2 l = 1 (4π) δm 2 e c = 1 (4π) ( y d y d ( y l y l ( y l y l M 6 ) F 4 M 6 ) F 4 M 6 ) F 4 M 6. Iftah Galon - Technion Nov 7, 2013 UC Irvine 60 / 50

61 A-terms A-term are the coefficients in L (A u ) i,j q Li ũ RjH U + (A d ) i,j q Li d RjH d + (A l ) i,j L Li ẽ RjH d A u = 1 16π 2 [( A d = 1 16π 2 [( A l = 1 16π 2 [( ) ( ) ] y u y u + y d y d Y u + 2Y u y F u y u M ) ( )] F y u y u + y d y d Y d + 2Y d y d y d M ) ( )] F y l y l Y l + 2Y l y l y l M Iftah Galon - Technion Nov 7, 2013 UC Irvine 61 / 50

62 Soft Mass - y u only δ m q 2 = 1 1 ( ) F (4π) 2 y uy u 4 6 M 6 h(x) { ( 3Tr + 1 (4π) 4 δ m u 2 R = 1 1 (4π) 2 3 { + 1 (4π) 4 (y u y u ) 16 3 g 2 3 3g g 2 1 ) y uy u + 3y uy u y uy u + 2y uy u Y uy u 2Y uy u y uy u ( ) ( ) + y uy u Tr 3y u Yu + Y uy u Tr 3Y u yu (y u yu ) F 4 ( 2 3Tr M 6 h(x) (y u yu ) 16 3 g 2 3 3g g 2 1 ) y u yu } F 2 M, + 6y u y uy u y u + 2y u Y uy u y u + 2y u Y d Y d yu 2Y u y uy u Y u } ( ) ( ) + 2y u YuTr 3Y u yu + 2Y u yutr 3y u F 2 Yu M, δ m d 2 R = 1 (4π) 4 2Y d yuy u Y F 2 d M. Iftah Galon - Technion Nov 7, 2013 UC Irvine 62 / 50