K. Cheung 1. Collider Phenomenology on Supersymmetry

Transcription

1 K. Cheung 1 Collider Phenomenology on Supersymmetry

2 K. Cheung 2 Outline 1. Motivations. 2. A few supersymmetry breaking scenarios, associated phenomena and current experiment limits. 3. Connection with Cosmology (next lecture).

3 K. Cheung 3 Motivations for Supersymmetry Provide an elegant solution to hierarchy problem Gauge coupling unification Dynamical electroweak symmetry breaking Provide a natural dark matter candidate

4 K. Cheung 4 Gauge Hierarchy Problem Two known scales in particle physics: Weak scale M W 100 GeV, Planck scale M Pl GeV. M Pl M W A very large disturbing sensitivity to the Higgs potential.

5 K. Cheung 5 Mass Protection Fermion mass protected by chiral symmetry. Gauge boson mass protected by gauge symmetry. Scalar boson mass?? H f H Two choices: MH 2 = λ [ ( ) ] f 2 2Λ 2 16π 2 UV + 6m 2 ΛUV f ln +... m f 1. Make Λ UV not too large, where some new physics appears. 2. Find some cancellation mechanism to remove Λ 2 UV divergence

6 K. Cheung 6 Suppose there exists a new scalar S M 2 H = The leading term in Λ UV H H λ [ ( S Λ 2 16π 2 UV 2m 2 ΛUV ) ] S ln +... m S will cancel if λ S = λ f 2 and if there are 2 such scalars Such systematic cancellation requires a new symmetry Supersymmetry. Q boson = fermion Q fermion = boson Cancellation OK if SUSY partner mass splitting M W

7 K. Cheung 7 Minimal Supersymmetric Standard model (MSSM) Standard Model ( ) u L Q = d ( L ) ν L L = e L Supersymmetrize ( ) ũ L d ( L ) ν L ll squarks sleptons u c, d c, e c ũ c, dc, ẽ ( ) ( ) c H + u H + u H u = higgsinos H 0 u H ( ) ( 0 u ) H 0 d H 0 d H d = H H d d g g gluino W ±, W 0 W ±, W 0 winos B B bino

8 K. Cheung 8 Neutral higgsinos, winos, and bino mix to form mass eigenstates: H 0 u, H 0 d, W 0, B = neutralinos χ 0 1, χ 0 2, χ 0 3, χ 0 4 Charged higgsinos and winos mix to form mass eigenstates: H + u, H d, W ±, = charginos χ ± 1, χ± 2 The left-handed squark and right-handed squark mix to form mass eigenstates, especially the stop, sbottom, and stau e.g. bl, b R = b 1, b 2

9 K. Cheung 9 Soft supersymmetry breaking L = L susy Based on the underlying gauge symmetries and supersymmetry. So far supersymmetry is not broken. SM particles and SUSY partners are both massless. Gluon, W, Z bosons are massless and so are the gluino, wino, bino before SUSY breaking.

10 K. Cheung 9-a Soft supersymmetry breaking L = L susy +L soft susy break Based on the underlying gauge symmetries and supersymmetry. So far supersymmetry is not broken. SM particles and SUSY partners are both massless. It is broken by L soft susy break. Gluon, W, Z bosons are massless and so are the gluino, wino, bino before SUSY breaking.

11 K. Cheung 9-b Soft supersymmetry breaking L = L susy +L soft susy break Based on the underlying gauge symmetries and supersymmetry. So far supersymmetry is not broken. SM particles and SUSY partners are both massless. It is broken by L soft susy break. Gluon, W, Z bosons are massless and so are the gluino, wino, bino before SUSY breaking. L soft = 1 2 (M 3 g g + M 2 W W + M1 B B) + c.c. gaugino mass give masses to the gluino, wino, bino. Thus, break SUSY.

12 K. Cheung 9-c Soft supersymmetry breaking L = L susy +L soft susy break Based on the underlying gauge symmetries and supersymmetry. So far supersymmetry is not broken. SM particles and SUSY partners are both massless. It is broken by L soft susy break. Gluon, W, Z bosons are massless and so are the gluino, wino, bino before SUSY breaking. L soft = 1 2 (M 3 g g + M 2 W W + M1 B B) + c.c. gaugino mass give masses to the gluino, wino, bino. Thus, break SUSY. Similarly, L soft = Q M 2 Q Q L M 2 L L... scalar mass give masses to the scalar quarks and scalar leptons.

13 K. Cheung 10 dg i dt = g i 16π 2 Gauge Coupling Unification [ ( 3 3 b i g 2 i π 2 j=1 b ij g 2 i g2 j j=1 a ij g 2 i λ2 j )] α α 1 2 α 1 1 α α 1 2 α α α a) Standard Model 10 b) M SUSY =1 TeV µ(gev) µ (GeV) Ellis, Kelly, Nanopoulos; Amaldi, de Hoer, Furstenau; Langacker, Luo (1991).

14 K. Cheung 11 Dynamical Electroweak Symmetry Breaking (Chamseddine, Arnowitt and Nath; Gaume, Polchinski, and Wise; Ellis, Nanopoulos, The Higgs potential Tamvakis ( )) V H = (M 2 H u + µ 2 ) H u 2 + (M 2 H d + µ 2 ) H d 2 + B(ɛ ij H i dh j u + h.c.) (g2 + g 2 ) [ H u 2 H d 2] g2 H i d H i u 2 EWSB occurs when one of the (M 2 H u + µ 2 ), (M 2 H d + µ 2 ) becomes negative. M 2 H u can run to a negative value by the top Yukawa coupling. dm 2 H u dt = 1 ( 3 ) 8π 2 5 g2 1M1 2 3g2M λ 2 t (MQ 2 L + Mt 2 R + MH 2 u + A 2 t )

15 K. Cheung Evolution of sparticle masses 700 M m~ br,q ~ L mass (GeV) m~ tr m 1 M 2 m~ τl m 2 m~ τr \/ m 2 0 µ 2 m + 1/2 100 M 1 m Q (GeV)

16 K. Cheung 13 The lightest SUSY particle (LSP) is a Dark Matter candidate. Imposing the R-parity conservation R = 1 for the SM particles R = 1 for SUSY particles SUSY particles must be pair produced. E.g. p p q q g g The LSP is stable: χ 0 1 SM particles LSP remains since freeze-out in the early universe

17 K. Cheung 14 Some problems of SUSY Too many soft parameters, more than 100. µ problem Proton decay operators Too many sources for FCNC and CP violation No SUSY Particles (NSP) Found So Far

18 K. Cheung 15 Various SUSY scenarios and Associated Phenomenology

19 K. Cheung 16 Gravity mediated SUSY breaking Arnowitt, Chamseddine, Nath MSSM visible sector Mediation Sector SUSY Breaking hidden sector SUSY breaking theory origin is in the hidden sector, and the SUSY breaking effect is transmitted by a mediation sector. Historically, the most popular one is the gravity. Gravitation, suppressed by M Pl couples the hidden sector to the visible. By dimension: M soft F M Pl Naturalness requires M soft O(0.1 1) TeV, implying F GeV Gravitino mass is F/M Pl.

20 K. Cheung 17 Supergravity Lagrangian The hidden sector fields couple to the visible sector via gravity interactions. In the effective Lagrangian, it contains nonrenormalizable terms: L sugra = F X 1 M Pl 2 f aλ a λ a + c.c. F X FX M 2 k i j φ iφ j Pl ( F X α ijk ) M Pl 6 φ iφ j φ k + βij 2 φ iφ j + c.c. where F X is the auxillary field of a chiral superfield X in the hidden sector. When F X develops a VEV, SUSY is broken in the hidden sector and thus communicates to the visible sector. It develops gaugino masses: M a = f a F X /M Pl sfermion masses: (M 2 ) i j = ki j F X 2 /M 2 Pl Trilinear terms: A ijk = α ijk F X /M Pl B term: B ij = β ij F X /M Pl It is not obvious they are flavor-blind.

21 K. Cheung 18 Minimal Supergravity (msugra) Arnowitt, Chamseddine, Nath One solution to flavor problem is to adopt universal boundary conditions. The soft parameters are defined by 5 parameters only: M 0 : universal scalar mass M 1/2 : A 0 : tan β v u /v d : sign(µ) : universal gaugino mass universal A term ratio of VEV of the Higgs fields sign of the µ parameter The LSP is usually the lightest neutralino (the combination of bino, neutral wino and higgsinos). It is the dark matter candidate. Only 5 parameters very predictive. But somehow quite restrictive now by the WMAP data. Relaxing the universality can relieve the suitable parameter space.

22 K. Cheung 19 msugra Spectrum m [GeV] 700 q L q R g b2 t 2 m [GeV] 700 H 0, A 0 H ± g 600 b1 600 χ 0 4 χ 0 3 χ ± 2 q L q R t 2 b2 500 t b 1 ll ν l lr 400 H 0, A 0 H± τ 2 ντ χ χ χ ± τ χ 0 2 χ ± ll ν l l R τ2 ν τ τ 1 χ 0 2 χ ± 1 t h 0 χ h 0 χ SPS 4 SPS 5 0 SPS4: msugra: m 0 = 400 GeV, m 1/2 = 300 GeV, A 0 = 0, tan β = 50, µ > 0. SPS5: msugra: m 0 = 150 GeV, m 1/2 = 300 GeV, A 0 = 1000, tan β = 5, µ > 0.

23 K. Cheung 20 Collider Phenomenology of SUGRA The neutral LSP will not leave any tracks in the detector, ie, it gives to missing energies. Smoking gun signatures: 1. Multi-leptons plus E T 2. Multi-lepton multi-jets plus E T pp χ + 1 χ 1 l + l ν ν χ 0 1 χ 0 1 pp χ ± 1 χ 0 2 l ± l + l ν χ 0 1 χ 0 1 pp g g, q q, g q Gluino is majorana that can decay into leptons of either charges same-sign dilepton + E T signal. 3. Gluino can decay into b b 1 b b χ 0 1 4b+ E T signal.

24 K. Cheung 21 χ ~o 1 χ ~o 1 W u d + χ χ ~ ~ o Z e µ µ ν ν ~ + + e * Tri-lepton + E T signal χ ~o 1 ~ g ~ g χ ~o 1 q q g q q q q q q * ~ ~ Multi-jet + E T

25 K. Cheung 22 CDF search for gluino decays g b b In the gluino pair production p p g g ( b b/ b b) ( b b/ b b) 4b + 2 χ 0 1 The signal is defined by a E T > 80 GeV plus b tags. Thus, no evidence for gluino pair production with squential decay into sbottom-bottom is observed.

26 K. Cheung 23 Gluino-sbottom 95% exclusion pb] Cross Section [ Gluino b ~ 1b, 95% C.L. Cross Section Limit CDF Run II Preliminary, 156pb PROSPINO, NLO 2 Q Scale Uncertainty m(q ~ ) = 500 GeV /c 2 m(g ~,b ~ 1 ) = 60 GeV /c 2 0 m(χ 1) = 60 GeV /c 2 Excl. Single B-Tag Incl. Double B-Tag Mass of the Gluino [ GeV/c 2 ] GeV/c 2 ] Sbottom mass [ Gluino b ~ 1b, 95% C.L. Exclusion Limit, 156pb CDF Run II Preliminary BR(g ~ b b ~ 1 )=100% 0 )=60GeV /c 2 m(χ 1 m(q ~ ) = 500 GeV /c 2 g ~ bb ~ 1kinematically forbidden (excl. single tag) CDF Run I excluded (incl. double tag) Gluino mass [ GeV/c 2 ] -1

27 K. Cheung 24 CDF Tri-lepton search for chargino-neutralino production Tri-lepton signal comes from the associated chargino-neutralino production p p χ ± 1 χ 0 2 l+ l lν χ 0 1 χ 0 1 Search for χ ± χ µ e + µ/e N events / 5 GeV CDF Run II Preliminary 0.7 fb Data Drell-Yan+γ W(Z/γ*),ZZ tt Drell-Yan+jets ± 0 msugra: χ 1 χ Missing transverse E T of trilepton events (GeV) With L = 745 pb 1 the µ + ll final state only found one event, consistent with the SM background of 0.64 event.

28 K. Cheung 25 DØ Tri-lepton search for chargino-neutralino production (325 pb 1 ) ) BR(3l) (pb) 0 2 ± χ 1 σ(χ Search for χ ± M(χ1 ) 0 M(χ2 ) 0 ± 0 1 χ 2 3l+X 2M(χ1 ); M(slepton) > M(χ tanβ = 3, µ > 0, no slepton mixing heavy-squarks 3l-max 0 2 ) -1 DØ, 320 pb Preliminary Expected Limit (no τ) Observed Limit Expected Limit LEP Chargino Searches large-m Chargino Mass (GeV) Heavy squarks: no negative interference in the production. 3l-max: leptonic BR is enhanced maximally for > m l m χ 0. Large m 0 : gives small leptonic BR. 2

29 K. Cheung 26 LEP 2 limits At LEP2 e e + collider, it can produce many sparticle pairs: e e + l + l, χ + 1 χ 1, χ 0 1 χ 0 2, χ 0 2 χ 0 2, q q There are limits on slepton masses, chargino masses, as they can readily produced at LEP if they exist. The exclusion is almost up to half of the s if the mass difference from the LSP is large enough. Another constraint comes from SM Higgs mass bound: m h > GeV Most of the SUSY parameter space yields a SM-like Higgs boson, therefore the Higgs mass bound is applicable.

30 K. Cheung 27 LEP2 slepton and squark mass limits M χ (GeV/c 2 ) s = GeV + - ẽ RẽR + - µ Rµ R + τ Rτ - R M l < M χ R ADLO squark mass (GeV/c 2 ) UA1 & UA2 M q = M g D0 CDF ADLO LEP Observed Expected Excluded at 95% CL (µ=-200 GeV/c 2, tanβ=1.5) M l (GeV/c 2 ) R 100 LEP 1 M q < M χ gluino mass (GeV/c 2 )

31 K. Cheung 28 LEP2 chargino mass limits 105 tanβ=2 µ= -200 GeV ADLO preliminary Gaugino - Mν ~ > 500 GeV ADLO s > GeV expected limit 103 Mχ ~ 1 + (GeV) 102 M (GeV) Excluded at 95% C.L Mν ~ (GeV) Mχ ~ + 1(GeV) 10-1

32 K. Cheung 29 Gauge mediated SUSY breaking Dine, Nelson, Shirman; Dimopoulos, Dine, Raby, Thomas This is a very simple idea to use the gauge interactions to communicate the SUSY breaking from the hidden sector to the visible sector. It is flavor-blind. It could just be the SU(3) C SU(2) L U(1) Y Typical soft masses are of order M soft α 4π F X M mess symmetry. where F X is the auxillary field of a chiral superfield in the hidden sector, M mess is the mass scale of the messenger sector. Both F X and M mess can be as low as 10 TeV. The gravition mass M 3/2 F X /M Pl M soft can be as low as sub-ev.

33 K. Cheung 30 A minimal GMSB model Suppose the messenger sector contains q, q c, l, l c that transform under SU(3) SU(2) L U(1) Y as q (3, 1, 1/3), q c ( 3, 1, 1/3), l (1, 2, 1/2), l c (1, 2, 1/2) which contain the fermionic and scalar parts. They couple to a gauge singlet chiral superfield of the hidden sector W mess = y 2 Sll c + y 3 Sqq c Suppose F S develops a VEV by some dynamical SUSY breaking mechanisms, and we assume the scalar part of S develops a VEV too: S. The effect of SUSY breaking is then transmitted to the messenger sector: l, l c : M 2 ferm = y 2 S 2, M 2 scal = y 2 S 2 ± y 2 F S q, q c : M 2 ferm = y 3 S 2, M 2 scal = y 3 S 2 ± y 3 F S

34 K. Cheung 31 The SUSY breaking is then transmitted to MSSM gauginos via 1 loop diagram: λ N λ M a (M mess ) = α a 4π Λ where Λ = F S S

35 K. Cheung 31-a The SUSY breaking is then transmitted to MSSM gauginos via 1 loop diagram: λ N λ M a (M mess ) = α a 4π Λ where Λ = F S S MSSM scalars receive mass from 2 loop diagrams: φ N φ M 2 i (M mess) = 2Λ 2 [( α3 4π ) 2 ( ) 2 C i 3 + α2 C i 2 4π ( α1 4π ) 2 ] C i 1 where C 3,2,1 = 0 for gauge singlets, and otherwise C 3,2,1 = 4/3, 3/4, (Y/2) 2 for fundamental representation of SU(3), SU(2) L, U(1) Y, respectively.

36 K. Cheung 31-b The SUSY breaking is then transmitted to MSSM gauginos via 1 loop diagram: λ N λ M a (M mess ) = α a 4π Λ where Λ = F S S MSSM scalars receive mass from 2 loop diagrams: φ N φ M 2 i (M mess) = 2Λ 2 [( α3 4π ) 2 ( ) 2 C i 3 + α2 C i 2 4π ( α1 4π ) 2 ] C i 1 where C 3,2,1 = 0 for gauge singlets, and otherwise C 3,2,1 = 4/3, 3/4, (Y/2) 2 for fundamental representation of SU(3), SU(2) L, U(1) Y, respectively. The minimal messenger sector can be generalized to N copies, then M a (M mess ) = N α a 4π Λ M 2 i (M mess) = 2N Λ 2 [( α3 4π ) 2 ( ) 2 C i 3 + α2 C i 2 4π ( α1 4π ) 2 ] C i 1

37 K. Cheung 32 Phenomenology Trilinear terms are further suppressed by α a /4π relative to gaugino mass.

38 K. Cheung 32-a Phenomenology Trilinear terms are further suppressed by α a /4π relative to gaugino mass. The LSP is always the gravitino (sub-ev).

39 K. Cheung 32-b Phenomenology Trilinear terms are further suppressed by α a /4π relative to gaugino mass. The LSP is always the gravitino (sub-ev). Gaugino and scalars have comparable mass M a, M i α a 4π Λ

40 K. Cheung 32-c Phenomenology Trilinear terms are further suppressed by α a /4π relative to gaugino mass. The LSP is always the gravitino (sub-ev). Gaugino and scalars have comparable mass M a, M i α a 4π Λ Note that the gaugino mass increases as N, but scalar mass increases as N. For N = 1 bino is the NLSP while for N 2 the stau is the NLSP.

41 K. Cheung 32-d Phenomenology Trilinear terms are further suppressed by α a /4π relative to gaugino mass. The LSP is always the gravitino (sub-ev). Gaugino and scalars have comparable mass M a, M i α a 4π Λ Note that the gaugino mass increases as N, but scalar mass increases as N. For N = 1 bino is the NLSP while for N 2 the stau is the NLSP. Collider signature depends on which is the NLSP: χ 0 1 G + (γ, Z, h), τ G + τ One is the multi-photon while another is multi-tau-lepton in the final state. Typical decay length if the NLSP is ( F L (10 km) βγ 10 7 GeV ) 4 ( 100 GeV M NLSP ) 5

42 K. Cheung 33 Typical GMSB spectrum m [GeV] g q L q R t 2 b2 b1 t 1 m [GeV] q L q R t 2 b1 b2 t g H 0, A 0 H± χ 0 4 χ 0 3 χ ± H 0, A 0 H± ll νl τ 2 χ 0 χ χ ± 2 ll ν l τ 2 χ 0 2 χ ± h 0 lr τ 1 χ h 0 lr τ 1 χ 0 2 χ 0 1 χ ± 1 0 SPS 7 SPS 8 0 SPS7: GMSB with τ NLSP: Λ = 40 TeV, M mess = 80 TeV, N = 3, tan β = 15, µ > 0. SPS8: GMSB with χ 0 1 NLSP: Λ = 100 TeV, M mess = 200 TeV, N = 1, tan β = 15, µ > 0.

43 K. Cheung 34 Combined CDF and DØ limit on GMSB diphoton plus E T events ) 2 Neutralino Mass (GeV/c (pb) 2 σ BR (γ+x) CDF 202 pb DØ 263 pb -1-1 expected limit observed limit GMSB γγ+e/ T M=2Λ, N=1, tanβ=15, µ>0 PROSPINO NLO QCD Uncertainty Chargino Mass (GeV/c )

44 K. Cheung 35 DØ Search for GMSB diphoton plus E T events Using 760 pb 1 data, search for events with 2γ E T > 25 GeV and η < 1.1 E T > 45 GeV 4 events with an estimated background of 2.1 ± 0.7 events.

45 K. Cheung 36 DØ GMSB limit using 760 pb 1 Expected limit on chargino mass > 215 GeV.

46 K. Cheung 37 LEP2 GMSB limits σ LIMIT at s = 208 GeV (pb) ALEPH DELPHI L3 OPAL 130 s 209 GeV Observed Expected m(e ~ ) = 2.0m(χ ~ o 1 ) m(e ~ ) = 1.1m(χ ~ o 1 ) (σ excl. *BR 2 ) max (pb) τ (τ NLSP) σ exp., s =208GeV excluded at 95% CL for all lifetimes ADLO Preliminary s = GeV 86.9 GeV/c χ ~ o 1 mass (GeV/c 2 ) Search using acoplanar diphoton plus E T, and di-taus plus E T. m(τ ) (GeV/c 2 )

47 K. Cheung 38 Anomaly mediated SUSY breaking Randall, Sundrum; Giudice, Luty, Murayama, Rattazzi In 4D, gravity mediation between hidden and visible sectors is always present. In extra dimensions, one can separate the two sectors geometrically. The hidden and visible sectors on separate branes. Only the gravity in the bulk communicate in between. Almost all SUSY breaking effects are suppressed. The conformal anomaly generates loop-suppressed soft SUSY breaking. These contributions are always present. Gauginos and scalars acquire M a = β a g a m 3/2, (M 2 ) j i = 1 2 dγ j i d(ln Q) m2 3/2 where m 3/2 is the gravitino mass, β a = b a g 3 a, and b a = ( 33/5, 1, 3), and γ j i anomalous dimensions. are The slepton masses are tachyonic.

48 K. Cheung 39 Phenomenology Need some means to give positive slepton mass squared.

49 K. Cheung 39-a Phenomenology Need some means to give positive slepton mass squared. The most special feature of the model is the gaugino mass pattern. Wino is the lightest particle.

50 K. Cheung 39-b Phenomenology Need some means to give positive slepton mass squared. The most special feature of the model is the gaugino mass pattern. Wino is the lightest particle. Note that the gravitino mass m 3/2 needs to be in O(100) TeV in order to give acceptable gaugino masses.

51 K. Cheung 39-c Phenomenology Need some means to give positive slepton mass squared. The most special feature of the model is the gaugino mass pattern. Wino is the lightest particle. Note that the gravitino mass m 3/2 needs to be in O(100) TeV in order to give acceptable gaugino masses. In this wino-lsp scenario, the charged wino forming the lightest chargino is very close in mass to the LSP: χ + 1 χ (π + or l + ν)

52 K. Cheung 40 Typical AMSB spectrum 1400 m [GeV] 1200 g q b H 0, A 0 H ± χ 0 4, χ0 3 χ ± 2 t 2 b1 t χ ll τ2 ν l ν lr τ τ h 0 χ 0 1 χ ± 1 0 SPS 9 SPS9: AMSB : m 0 = 450 GeV, m 3/2 = 60 TeV, tan β = 10, µ > 0.

53 K. Cheung 41 Chargino Decay and detection in wino-lsp scenario The decay of χ + 1 χ0 1 W + depends critically on M M χ + 1 M χ 0 1. M < m π : The only available modes are e + ν e and µ + ν µ. The chargino will travel 1 m or so before decay, so appears as heavily charged tracks. Background free. m π < M < 1 GeV: The most difficult region that depends on how many layers of silicon that the chargino can travel before decays, and the momentum resolution to tell the non-pointing pion. 1 2 GeV < M: The decay is prompt. If M is large enough to have energetic leptons and jets, it is easy for detection. If the decay products are too soft, have to rely on other methods. E.g. e + e χ + 1 χ 1 γ M > a few GeV: charged lepton and jets are detectable. Chen, Gunion, Drees.

54 K. Cheung 42 DØ search for metastable charginos Signatures for stable charged tracks, reconstructed as muons, but with speed and mass inconsistent with beam-produced muons. Events/ D Run II Preliminary 100 GeV Staus GeV Higgsino-like Charginos 100 GeV Gaugino-like Charginos Speed (units of c) If m χ + 1 m χ 0 1 < m π, chargino may have a long decay.

55 43 K. Cheung σ(e e χ χ )(pb) LEP2 limits on stable charginos ADLO s= GeV Preliminary excluded 95% CL m χ±(gev/c ) 0.2 0

56 K. Cheung 44 Split Supersymmetry (Arkani, Dimopoulos 2004) The magic word: Landscape!! In the vast number of vacua, there is a good chance to find some with high SUSY breaking scales. In reality, Why Not!! These scenarios are not impossible All scalars are super heavy, except for a light SM-like Higgs boson m GeV Gauginos and Higgsinos are O(TeV).

57 K. Cheung 45 Split Supersymmetry Gauge coupling unification Light SM-like Higgs boson Properties: Super heavy scalars safe FCNC, CP-violation, EDM, but there is still one possible source Relatively light gauginos, Higgsinos, µ parameter Dark Matter Stable gluino, gluinonium signature

58 K. Cheung 46 Gauge Coupling Unification ( 1 α i (MX 2 ) = 1 α i (MZ 2 ) β i M 2 ) 4π ln X MZ 2 SM : (β) = SUSY : (β) SUSY = Split SUSY : (β) split < m = F + F + F NH NH

59 K. Cheung 47 Gauge Coupling Unification SM Weak Scale SUSY Split SUSY α α 1 3 α 1 2 α 1 1 α α 1 3 α 1 2 α a) Standard Model 10 b) M SUSY =1 TeV µ (GeV) µ(gev) Ellis, Kelly, Nanopoulos (1991); Arkani, Dimopoulos 2004

60 K. Cheung 48 Proton decay Consider split SUSY with SU(5) unification. Dim-5 operator is highly suppressed d ~ W ~ u ν O 5 QQ Q Q M Pl u ~ d s Dim-6 operators: p e + π 0 with exchanges of M X,Y bosons. Proton decay rate depends on M GUT and α GUT. Additional matter in complete SU(5) added to the intermediate scale will increase α GUT.

61 K. Cheung 49 Gluino Signature Decay of gluino has to go through a squark: ~ g q ~ q q m GeV > τ g s Gluino is stable within particle detectors. ~ χ o

62 K. Cheung 50 Stable gluino-hadron Hadronize into a massive stable particle. Electrically either neutral or charged, depending on the mass spectrum. The heavy neutral particle will go through the detector unnoticed, very small energy loss. Charged particles also undergo ionization energy loss, via which it can be detected. It happens in central vertex detector and also in muon chamber. (Kilian et al., Hewett et al., KC and Keung)

63 K. Cheung 51 Experimentally, the massive stable charged particle will produce a track in the central tracking and/or silicon vertex system, where de/dx and p can be measured. β γ = p E E M = p M < 0.85 The particle is required to penetrate to the outer muon chamber < β γ c.f. CDF Coll. used a criteria: < βγ < particle of mass of GeV only. 0.86, but it is for a

64 K. Cheung 52 Cross sections at the LHC. σ 1MCP, σ 2MCP denote requiring the detection of 1, 2 massive stable charged particles (MCP) in the final state. m g (TeV) σ 1MCP (fb) σ 2MCP σ 1MCP σ 1MCP σ 1MCP P = 0.5 P = 0.5 P = 0.5 P = 0.1 P = P probability that g fragments into charged R-hadron

65 K. Cheung 53 Problems with R-hadron detection The probability that g charged hadrons depends crucially on the bound state spectrum. The detected cross section depends strongly on P : σ(m g = 1.5TeV) = fb forp = More complications occur when frequent swapping between neutral and charged R-hadron states. E.g., ( gu d) ( gd d) Need an unambiguous signature.

66 K. Cheung 54 Gluinonium Gluinos are stable, exchange gluons to form a bound state. ~ ~ g g Color : 8 8 = S + 8 A S-wave, Spin : 1 S 0 (antisymmetric), 3 S 1 (symmetric) Possible configurations: 1 S 0 (1), 1 S 0 (8 S ), and 3 S 1 (8 A )

67 K. Cheung 55 Production of Gluinonium Replace the spinor combination u(p/2) v(p/2) by 1 S 0 (1) : u(p/2) v(p/2) 1 2 R 1 (0) 2 4πM 1 S 0 (8 S ) : u(p/2) v(p/2) 1 R 8 (0) 2 2 4πM 3 S 1 (8 A ) : u(p/2) v(p/2) 1 R 8 (0) 2 2 4πM 1 8 δ ab γ 5 ( P + M) 3 5 dhab γ 5 ( P + M) 1 3 f hab ɛ(p ) ( P + M) Color factors: 1 : 8 S : 8 A : 1 δ ab dhab 1 3 f hab

68 K. Cheung 56 Production of Gluinonium... The values of the color octet and singlet wave functions at the origin are given by the coulombic potential between the gluinos, with one-gluon approximation R 8 (0) 2 = 27α3 s(m)m R 1 (0) 2 = 27α3 s(m)m 3 16 There is an additional factor of 1/ 2 because of the identical gluinos in the wave function of the gluinonium.

69 K. Cheung 57 Hadronic Production of Gluinonium 3 S 1 (8 A ) The lowest order process for 3 S 1 (8 A ) q q 3 S 1 (8 A ) The next order include q q 3 S 1 (8 A ) + g qg 3 S 1 (8 A ) + q gg 3 S 1 (8 A ) + g g g~ 3 S 1 (8 A ) g~ q ~ 3 g S 1 (8 A ) q g~ 3 S 1 (8 A ) g~ g g~ g~ 3 S 1 (8 A ) q ~ g q g g g

70 K. Cheung 58 Hadronic Production of Gluinonium 3 S 1 (8 A )... ˆσ = 16π2 α 2 s 3 R 8 (0) 2 M 4 δ( ŝ M). After folding with the parton distribution functions: σ = 32π2 αs 2 R 8 (0) 2 3s M 3 f q/p (x)f q/p (M 2 /sx) dx x, Decay width into uū, d d, s s, c c, b b, t t: Γ (3 S 1 (8 A ) ) = Q=u,d,s,c,b,t α 2 s R 8 (0) 2 M 4 (M 2 + 2m 2 Q) 1 4m 2 Q /M 2 Each mode 1 6 for heavy gluinonium.

71 K. Cheung 59 Hadronic Production of Gluinonium S1 (8 A ) S1 (8 A ) Total cross section (pb) (a) Tevatron 1 S0 (1)+ 1 S 0 (8 S ) Total cross section (pb) (b) LHC 1 S0 (1)+ 1 S 0 (8 S ) Gluinonium mass M (GeV) Gluinonium mass M (GeV)

72 K. Cheung 60 Detection & Background analysis 1 S 0 (1, 8 S ) gg 3 S 1 (8 A ) q q buried under huge QCD background. 3 S 1 (8 A ) t t, b b have the potential feasibility for observation. Irreducible background comes from QCD t t or b b

73 K. Cheung 61 Detection & Background analysis... Gluinonium annihilates into t and t with a large p T We impose p T O(M g ) p T (t), p T ( t) > 3 4 m g for M 1 TeV p T (t), p T ( t) > 100 GeV for M < 1 TeV Invariant mass M t t forms a peak right at gluinonium mass, width determined by experimental resolution. δe/e = 50%/ E We can then calculate the SM background right under the peak.

74 K. Cheung 62 Detection & Background analysis... Cross sections at the LHC for the gluinonium signal into t t with mass M and the continuum t t background between M 50 GeV and M + 50 GeV. M = 2m g σ( 3 S 1 (8 A )) t t bkgd (fb) S/ B (TeV) (fb) (fb) for L = 100 fb Including b b would increase S/ B by 2.

75 K. Cheung 63 DØ search for stopped Gluinos The long-lived gluino can hadronize into charged R-hadron. It may lose all its K.E. by ionization and stopped inside the detector. Then after a while it decays into a gluon and LSP. The signaure is a jet plus E T. Backgrounds: Cosmic muons that fake the signal by initiating a high-energy shower within the detector (identified by a muon in or out of the muon system). Beam-halo muons are those traveling parallel to the beam, very narrow in φ. A gluino-induced shower would be wide and contain no muon.

76 K. Cheung 64 DØ results for stopped gluinos A simulated signal of m g = 400 GeV. 95% C.L. upper limits on σ( g) B( g j+ E T ) for 3 LSP masses of 50, 90, 200 GeV.

77 K. Cheung 65 Neutralinos and Charginos (KC and J. Song, hep-ph/ ) Production and decay via intermediate f disappear. Direct production via Drell-Yan-like processes (γ, Z, W ). Neutralino decays via χ 0 j χ 0 i Z χ 0 i f f χ 0 j χ ± i W χ 0 i f f χ 0 j χ 0 i h χ 0 i b b χ 0 j χ + W loop χ 0 i γ Chargino decays via χ + j χ0 i W χ 0 i f f

78 K. Cheung 66 Decays of Neutralinos ~ χ o j χ ~ o i ~ χ o j χ ~ o i ~ + χ j Z f h b f b ~ χ o j W χ ~ oi Aim: to enhance the χ 0 j χ0 i + γ by suppressing the Z χ0 j χ0 i couplings: O L ij = O R ij = 1 2 (N i4n j4 N i3n j3 ) It is possible but needs fine tuned relation between µ and M 1. Specifically, need M 1 µ Potentially, observe mono-photon plus missing energy signature at hadron colliders.

79 K. Cheung χ o 2 -> χo 1 f - f 10-4 χ o 2 -> χo 1 f - f Partial Widths (GeV) χ o 2 -> χ+- 1 f - f χ o 2 -> χo 1 γ Partial Widths (GeV) χ o 2 -> χ+- 1 f - f χ o 2 -> χo 1 γ µ (GeV) µ (GeV) χ 0 2 decay widths, M 1 = 200 GeV

80 K. Cheung χ o 3-> χ+- 1 f - f 10-4 χ o 3 -> χo 2 f - f χ o 3-> χ+- 1 f - f Partial Widths (GeV) χ o 3 -> χo 1 f - f χ o 3 -> χo 2 f - f χ o 3 -> χo 1 γ Partial Widths (GeV) χ o 3 -> χo 1 γ χ o 3 -> χo 1 f - f µ (GeV) χ o 3 -> χo 2 γ χ o 3 -> χo 2 γ χ o 3 -> χo 1 h µ (GeV) χ 0 3 decay widths, M 1 = 200 GeV

81 K. Cheung Radiative Decay Branching ratio χ o 3 -> χo 1 γ Radiative Decay Branching ratio χ o 3 -> χo 1 γ χ o 2 -> χo 1 γ 0 χ o 3 -> χo 2 γ µ (GeV) χ o 2 -> χo 1 γ µ (GeV) χ 0 3,2 radiative decay branching ratios

82 K. Cheung 70 Production of Neutralinos and Charginos q + q q + q q + q e e + e e + Z χ 0 i + χ 0 j γ,z χ i + χ + j W χ ± i + χ 0 j γ,z χ + i + χ j Z χ 0 i + χ 0 j (Zhu; Kilian et al.; KC and Song)

83 K. Cheung χ + 1 χo 3 χ - 1 χo χ + 1 χo 3 χ - 1 χo 3 Cross Section (pb) χ o 2 χo 3 χ o 1 χo 3 LHC M 1 =200 GeV tanβ=10 Cross Section (pb) χ o 2 χo 3 χ o 1 χo 3 LHC M 1 =200 GeV tanβ= µ (GeV) µ (GeV) χ 0 3 production, M 1 = 200 GeV

84 K. Cheung 72 Production at 0.5 TeV e + e ILC E CM = 0.5 TeV χ + 1 χ χ + 1 χ- 1 Cross Sections (pb) M 1 = 200 GeV, tanβ=10 χ 0 1 χ0 2 Cross Sections (pb) χ 0 1 χ χ 0 1 χ0 3 χ 0 2 χ χ 0 2 χ0 3 χ 0 1 χ µ (GeV) µ (GeV) M 1 = 200 GeV, M 2 = 400 GeV, tan β = 10

85 K. Cheung 73 Production at 1 TeV e + e ILC E CM = 1 TeV Cross Sections (pb) M 1 = 200 GeV, tanβ=10 χ + 1 χ- 1 Cross Sections (pb) χ + 1 χ- 1 χ 0 1 χ0 2 χ 0 1 χ χ 0 1 χ0 3 χ 0 2 χ χ 0 2 χ0 3 χ 0 1 χ µ (GeV) µ (GeV) M 1 = 200 GeV, M 2 = 400 GeV, tan β = 10

86 K. Cheung 74 Topics that cannot be covered in this lecture but equally interesting Mixed Moduli-anomaly SUSY breaking (Choi, hep-ph/ ). Gaugino mediated SUSY breaking (Kaplan et al. hep-ph/ , Chacko et al. hep-ph/ ). SUSY breaking by 5d boundary conditions (Scherk-Schwarz SUSY breaking). Gluino LSP scenarios (Baer et al. hep-ph/ ). Next-to-minimal supersymmetric model (NMSSM).