The Search for Supersymmetry

Transcription

1 Th Sarch for Suprsymmtry Introduction th Standard Modl of Particl Physics Introduction to Collidr Physics Succsss of th Standard Modl What th Standard Modl Dos Not Do Physics Byond th Standard Modl Introduction to Suprsymmtry Sarching for Suprsymmtry Dark Mattr Sarchs Futur Prospcts Othr Scnarios Summary Ptr Krigr, Carlton Univrsity, August

2 Forc Unifications magntism Maxwll lctromagntism Standard Modl dos NOT account for gravitational intractions lctricity lctrowak wak intractions strong intractions S T A N D A R D M O D E L GUT TOE Planck Scal (or Planck Mass) is dfind as th nrgy scal at which gravitational intractions bcom of th sam strngth as SM intractions clstial movmnt Nwton gravitation trrstrial movmnt M EW M GUT M planck

3 Th Standard Modl Dscribs th FUNDAMENTAL PARTICLES and thir INTERACTIONS All known FORCES ar mdiatd by PARTICLE EXCHANGE a a α X α a a Effctiv strngth of an intraction dpnds on th coupling strngth at th vrtx th mass of th xchangd particl M X Forc Effctiv Strngth Procss Strong Nuclar binding Elctromagntic - Elctron-nuclus binding Wak -5 Radioactiv β dcay

4 Th Standard Modl SPIN-½ MATTER PARTICLES intract via th xchang of SPIN- BOSONS MATTER PARTICLES thr gnrations of quarks and lptons ν u d µ ν τ µ ν τ c s t b Q 3 3 m < m µ < m τ = m ν Each quark coms in thr colour changs Mass incrass with gnration: M u,d.3 GV M t 7 GV GAUGE BOSONS mdiat th intraction of th fundamntal frmions γ W ±, Z g 3 8 Gaug particl of lctromagntism (carris no lctric charg) Gaug particls of th wak intraction (ach carris wak charg) Gaug particls of th strong intraction (ach gluon carris a colour and an anti-colour charg charg) All Standard Modl frmions and gaug bosons hav bn xprimntally obsrvd Thr is on mor particl in th SM th Higgs Boson. This is vital to th SM but rmains xprimntally undtctd

5 Spontanous Symmtry Braking Initial Attmpts to unify th wak and lctromagntic intractions faild bcaus whil M( γ ) =, th rlativ strngth of th wak intraction rquirs M(wak gaug boson) GV Th SM is formulatd in trms of MASSLESS particls Introduction of xplicit mass trms dstroys a vital proprty of th thory In th SM, masss for th wak intraction gaug bosons ar gnratd via SPONTANEOUS SYMMETRY BREAKING SSB may occur in systms whr th quations dscribing th systm hav a SYMMETRY which is NOT OBEYED by th GROUND STATE (T-T c )> (T-T c )< Considr a frromagnt at tmpraturs abov and blow th Curi point: Spins randomly orintd Rotational Symmtry Spins alignd Rotational symmtry brokn

6 Elctrowak Unification In th Standard Modl SSB is introducd by hand by introducing nw filds (4 dgrs of frdom) V( µ, λ) And and intraction potntial with µ analogous to T-T c Choosing µ < Spontanous Symmtry Braking Th 4 dgrs of frdom thr masss (on ach for W, W -, Z ) On physical spin- (scalar) particl (th Higgs Boson) Th mass of th Higgs boson is NOT prdictd by th thory Th masss of th W and Z ar rlatd by th wak-mixing angl sin ϑ W M = M Th W and Z bosons wr both discovrd at CERN in 984 (at th prdictd masss)! Z W Dsign and construction of th Larg Elctron Positron Collidr at CERN

7 Th LEP Collidr at CERN LAKE GENEVA POINT 8. GENEVA CERN Prévssin CERN POINT. Two phas xprimntal program plannd: POINT 6. POINT 4. DELPHI L3 SPS - Elctron Positron OPAL ALEPH LEP R. Lwi jan. 99 s Phas - prcision masurmnts of th Z (E cm = M Z ) compltd Phas prcision masurmnts of th W (E cm > M W ) nds soon (Spt/) Most rcnt running has bn at nrgis up to 9 GV

8 Th OPAL Dtctor at LEP Run : vn t 493 : Dat 9357 T im 76 Ctrk(N= 39 Sump= 73.3) Ecal (N= 5 SumE= 3.6) Hcal (N= SumE=.6) Elctromagntic calorimtrs Muon dtctors Ebam Evis 99.9 Emiss -8.6 Vtx ( -.7,.6, -.8) Muon(N= ) Sc Vtx(N= 3) Fdt(N= SumE=.) Bz=4. 35 Thrus t = Ap l an=. 7 Ob l a t =. 48 Sphr=. 73 Hadron calorimtrs and rturn yok Jt chambr Vrtx dtctor Microvrtx dtctor y Y z θ ϕ x Prsamplrs Solnoid and Prssur Vssl Z chambrs Z Cn t r o f sc rn i s (.,.,. ) X. cm. 5 5 GV Original forward dtctor Tim of flight dtctor Silicon-tungstn forward dtctor Z qq hadron jts

9 Som Basic Collidr Physics How dos on calculat th rat for som physics procss at a collidr? M = sum of all contributing procsss (diagrams) hr for W W - W - - W - - W - γ Z ν... W W W Dfin CROSS-SECTION σ M (units of lngth ) Dfin LUMINOSITY L f n bunch N A N cross-sctional siz of th bams Instantanous production rat N = L σ L Siz of data sampls typically quotd in (pb - ) Numbr of vnts in data sampl givn by dt N = σ L dt

10 Standard Modl Elctrowak Summary Th Standard Modl is vry halthy (unfortunatly?) m W [GV] LEP, SLD, νn Data LEP, pp Data 68% CL χ 6 4 thory uncrtainty α (5) had =.84± ±.6 Higgs mass from EW fit M SMfit Higgs < 7 CL LEP dirct sarch limit m H [GV] 3 3 Prliminary m t [GV] Excludd Prliminary 3 m H [GV] M SM Higgs > 3.3 CL Elctrowak quantitis affctd by virtual particl loops - Z t Z t - - f (M t /M W ) f - Z Z Z H ln(m H /M W ) f - f sin ϑ W = M M Z W

11 Som xampls: Th SM Dos Not Do Evrything Quarks and lptons ar unrlatd fundamntal frmions, yt thir lctric chargs ar rlatd by simpl ratios. Why should this b th cas? particl ν d u Q 3 3 What causs th hirarchy in th frmion masss? (ths ar fr paramtrs in th SM) M u,d.3 GV M t 7 GV What causs lctrowak symmtry braking? (Higgs mchanism for SSB put in by hand) GRAND UNIFIED THEORIES attmpt to provid answrs by postulating that th strong and lctrowak forcs unify to a singl forc at som high nrgy scal (M GUT ) thr is a singl forc with coupling quarks and lptons ar rlatd ν instad of w gt Colour indics: rd, grn, blu α GUT ν dr dg db Th structur of th thory rquirs that th charg in this multiplt sum to Q( ν ) Q( ) 3Q( d) = SUCCESS! But thr ar problms too

12 Running of Coupling Strngths Imagin masuring th lctromagtic coupling strngth via scattring α α f f q = f f... f f Charg Scrning th obsrvd charg dpnds on th nrgy scal lctromagntic intraction (charg scrning) f γ γ f α quark confinmnt Asymptotic frdom strong coupling wak coupling lctromagntic coupling - - γ momntum transfr Q distanc scal Q strong intraction(colour anti-scrning) q g g q g g g g momntum transfr q

13 Som GUT Problms α = = α α For a singl forc with a singl coupling at M GUT xpct 3 ( ) α µ - Invrs coupling constant α ( µ ) - α ( µ ) - α ( µ ) 3 U() E.M. Forc SU() Wak Forc SU(3) Strong Forc Grand Unifid# (GUT) Scal No Suprsymmtry Enrgy Scal, µ [GV] u u d τ ( p π u ( othr diagrams) ) π Quark-lpton rlationship proton dcay Simplst modls prdict π 8 τ ( p ) 3 yars Inconsistnt with xprimntal rsults π τ ( p ) > 4.4 ( from SuprKamiokand) 33 9%CL

14 Th Naturalnss Problm Masss in SM gt radiativ corrctions M physical = M δm Naturalnss (asthtic critrion) rquirs O( M physical ) O( M) O( δm) i.. no fin tuning This is not tru for fundamntal scalars (Higgs) for which whr Λ is th highst nrgy to which th thory rmains valid ( δm) Λ So for M H < TV (SM bias) rquir ithr Λ TV i.. SM braks down at TV, OR Som symmtry xists which can producs Such a symmtry xists O( δm) O( M H ) indpndnt of Λ Suprsymmtry

15 Suprsymmtry Each SM boson (frmion) has a frmionic (bosonic) suprsymmtric partnr with IDENTICAL MASS and Standard Modl COUPLINGS γ γ Z Z W W ± ± b t s c d u b t s c d u τ µ τ µ ν τ ν µ ν ν τ ν µ ν lptons slptons quarks squarks gauginos ± ± H H A A H H h h higgsinos g g gluinos Mass ignstats ar mixturs of gauginos and higgsinos This dfins th particl contnt of th Minimal Suprsymmtric Standard Modl or MSSM ± =, χ i Charginos 4 Nutralinos,4 χ j=

16 Suprsymmtry is a Brokn Symmtry Suprsymmtry rquirs a doubling of th particl spctrum. Is this cost xcssiv? It has bn succssful bfor (anti-mattr) BUT M = M M M W do not s suprsymmtric mattr mad of snuclons and slctrons Suprsymmtry is a BROKEN SYMMETRY But. If suprsymmtry is to solv th NATURALNESS PROBLEM, w rquir M TV SUSY This is oftn rfrrd to as WEAK-SCALE SUPERSYMMETRY

17 R-parity R-Parity is a quantum numbr which distinguishs SM and suprsymmtric particls R = ( ) 3( B L) S Most suprsymmtric modls assum R-Parity Consrvation This has two important consquncs: Suprsymmtric particls must b producd in pairs Thr must b som Lightst Suprsymmtric Particl or LSP This LSP is usually th lightst nutralino and is a good Cold Dark Mattr candidat or WIMP (Wakly Intracting Massiv Particl) χ

18 Coupling Constant Evolution - SUSY Forc unification rvisitd (now with MSSM particl contnt) ( ) α µ - Invrs coupling constant α ( µ ) - α ( µ ) - α ( µ ) 3 in SUSY GUTs U() E.M. Forc SU() Wak Forc SU(3) Strong Forc 5 7 τ ( p 9 π ) = Grand Unifid# (GUT) Scal With Suprsymmtry Enrgy Scal, µ [GV] 38±? yars u u d p K ν W still hav a quark-lpton rlationship and thrfor proton dcay. Dominant mod in SUSY GUTs is p K ν u s ν K Modl prdictions vary: τ ( p K ) yars ν ν Exprimntal limits τ ( p K ) >.9 95% CL (Supr K) Supr Kamiokand dtctor will prob liftims up to 34 yars

19 Suprsymmtric Modl Paramtrs MSSM has 5 fr paramtrs ( in addition to th 9 fr paramtrs of th SM)!!! masss couplings mixing angls othr paramtrs arising from suprsymmtry braking Frquntly rsults of suprsymmtric particl sarchs ar intrprtd within th framwork of th Constraind MSSM which assums that many fr paramtrs of th MSSM unify at th GUT scal 5 paramtr Constraind MSSM

20 Othr Faturs of Suprsymmtric GUTS Unification of fr paramtrs at th GUT scal (as for th couplings) ϑ W Can provid a corrct prdiction of sin (xprimntally.98 /-.) Mchanismm for Elctrowak symmtry braking: µ positiv at th GUT scal but runs ngativ at th EW scal Mass prdiction for th lightst higgs! M(h ) < 3 GV (MSSM) M(h ) < 5 GV (Suprsymmtry in gnral) May allow for unification with gravity: Most string thoris ar suprsymmtric

21 Snsitivity to Nw-Particl Production REQUIREMENTS for DIRECT OBSERVATION of a particl X with mass M X X production (som procss) must b kinmatically accssibl th production procss must hav XX σ ( XX) =. pb for instanc for σ > ( L dt) if rquir } E ( CM L > M dt) > X pb NON-OBSERVATION of a PROCESS implis only that th CROSS-SECTION is lowr than th snsitivity of th data sampl On can EXCLUDE A MODEL if it prdicts a cross-sction that is xcludd On can EXCLUDE THE EXISTENCE OF PARTICLE X only if th cross-sction (at a givn nrgy) is a function of th mass only or if othr rlvant paramtrs ar scannd CROSS-SECTION LIMITS ar typically modl indpndnt (masurmnts) MASS LIMITS ar typically modl dpndnt (intrprtations of masurmnts)

22 Suprsymmtric Particl Sarchs at LEP LEP is an lctrowak machin Bst candidats for SUSY sarchs ar th lowst mass charginos and nutralinos χ χ invisibl Bst discovry channl at LEP χ χ - χ - - χ - σ( - W W - ) γ,z ν σ( - χ χ - ) (pb) - - OPAL snsitivity M ν > 45 GV M ν > GV (minimum σ) χ ± mass [GV] χ χ procsss intrfr dstructivly E cm = 83 GV

23 Chargino Dcays Exprimntal Signaturs Dcay Mod l, q χ ± W ν, q χ ± l,ν l,ν χ (missing nrgy) χ ± q q χ (missing nrgy) χ (missing nrgy) ν,l q Exprimntal Signatur lpton missing nrgy hadron jts missing nrgy lpton missing nrgy hadron jts missing nrgy χ is massiv and intracts only wakly with mattr (i.. th dtctor) carris off missing (undtctd) nrgy So for χ χ xprimntal signaturs ar: Exprimntal Signatur jts missing nrgy jts lptons missing nrgy lptons missing nrgy SM background ZZ ( qq)( νν ) W W Missing nrgy is carrid off by nutrinos W W ( qq )( lν ) ( lν )( l ν )

24 Exprimntal Signaturs Cont d So what do ths vnts look lik in th dtctor? jts missing nrgy jt lpton missing nrgy lptons missing nrgy Look for an xcss of such vnts ovr xpctd SM background

25 A Chargino Candidat Evnt Run: 7445 Dat: Bam Enrgy: 8.5 GV Evnt : 89 Tim: 4:56. 4 h y Sid viw - plan of Thrust axis Ph i =83. jts missing nrgy channl Ph i = 93. z Also consistnt with coming from a SM procss: x z Sid viw - plan prp. to Thrust miss x-y viw miss miss / M = ( E P ) M Missing nrgy carrid off by nutrinos? Z - ν Z * Z q q ν ν

26 Cross-sction Limits Signal for nw physics is an xcss of vnts abov th SM backgrounds But. N vnts (slctd) consistnt with N vnts (xpctd from SM procsss) OPAL Plac limits on σ χ χ ( ) ( M ) ± M( χ ) χ in plan of vs m(χ ) [GV] (a) [. pb,.4 pb] [. pb,. pb] ± m(χ ) [GV] [.9 pb,. pb] [.75 pb,.9 pb] [.68 pb,.75 pb] [.9 pb,. pb] [. pb,. pb] [. pb,.4 pb] [.4 pb,.75 pb] [.75 pb,.37 pb] Ths rsults ar at E cm = 89 GV

27 Mass Limits for Suprsymmtric Particls Modl dpndnt mass limits can b st by scanning th CMSSM paramtr spac and comparing prdictd cross-sctions with xprimntal limits Exprimntal σ Limits σ( - χ χ ) - σ( - χ χ ) tc MSSM Paramtr spac 5 Fr paramtrs Vary som or all MSSM paramtrs All masss, BRs, σ tc fully dtrmind Paramtr st xcludd? [GV] m(χ ) Mass limit for MSSS Cold Dark Mattr Candidat OPAL 3.6 GV Excludd at 95% CL tan β last scan paramtr χ mass limit M(χ ) (for instanc) Excludd for all paramtrs? M ( χ ) > 3.6 CL

28 Dark Mattr Mattr whos xistnc has bn infrrd only via its gravitational ffcts Thr is xtnsiv vidnc that much of this is non-baryonic wakly intracting particls Wakly Intracting Massiv Particls S hot dark mattr (rlativistic).g. nutrinos cold dark mattr (non-rlativistic) } is χ an xcllnt CDM candidat in most of th MSSM paramtr spac Strong vidnc coms from th rotation curvs of spiral galaxis Expct v( r) Obsrv v(r) indpndnt of r r This FLAT ROATATION CURVE implis that M r This is th xpctd mass profil of a slf gravitating ball of idal gas at a uniform tmpratur

29 Dirct Dark Mattr Sarchs hp-x/ Sp 997 In th arly univrs For T>>T X XX XX Production Annihilation WIMP numbr dnsity in quilibrium with,, γ For T < T X th WIMP numbr dnsity drops until th man fr path for annihilation xcds th siz of th univrs RELIC ABUNDANCE Cross-sction for lastic scattring of a WIMP off a nuclus calculabl with spcific modls Can do dirct sarchs for WIMPS g LiF NTD thrmistor Au wir Cold fingr WIMP Apparatus at mk Rquirs propr shilding Cu ribbon Spring contact cm Collimator bolomtr

30 Dark Mattr Exprimntal Summary Tokyo(LiF) surfac EDELWEISS(sapphir) 48m.w.. Tokyo LiF dtctor will rach WIMP-p cross-sction of.pb WIMP-p cross sction[pb]. Excludd by OPAL at 95% CL (havy sfrmions, m = GV) BPRS(CaF(Eu)) 35m.w.. UKDMC(NaI(Tl)) 36m.w.. UPDATE: Lots of xprimnts, including Canadian xprimnt PICASSO. MSSM OPAL limit indicatd is somwhat datd. WIMP Mass[GV]

31 Th LHC pp Collidr at CERN 4 TV pp collidr to b installd in th xisting LEP ring First collisions schduld for 5 Two gnral purpos dtctors approvd for LHC ATLAS ( Canada) and CMS Main objctivs: Discovr th nw TV scal physics Discovry of th Higgs Discovr of Wak-Scal SUSY or fully xclud it Th LHC is a strong-intraction machin SUSY production rats will b highst for q and g LHC Low-luminosity running 4 pb - / yar (3 yars) LHC High-luminosity running 5 pb - / yar (3 yars) cross-sctions for suprsymmtric particl production can b normous! 3 pb (rcall N = σ L dt )

32 Nw Particl Sarchs at Hadron Collidrs Hadon Collidrs can achiv highr cntr-of-mass nrgis than lctron-positron machins.. BUT E CM of constitunt collision Ebam proton rmnant E bam p p E bam p u d u p p q q g q q 3 valnc quarks sa quarks gluons proton rmnant d u d s u momntum fraction x Gluons carry 5% of th protons momntum Collision is btwn two particls ach carrying som fraction x of th protons momntum ffctiv < x < < E CM < E bam

33 Suprsymmtric Particl Production at LHC p p q q g q q q q LHC will discovr (with pb - ): g and q up to TV ± l, χ, χ ovr a mor rstrictd rang j i p σ(pb) pp collisions at E cm = 4 TV p q g q g q q g M q =M g M q =M g sum(qq qg gg) p p g g g g g g g χ χ - gluino mass M g [GV]

34 Conclusions Gnral argumnts NEED FOR PHYSICS BEYOND THE SM Som of ths argumnts NEW PHYSICS AT THE TV SCALE SUPERSYMMETRY is a srious candidat for th dscription of this nw physics WEAK SCALE SUPERSYMMETRY (rlvant to th naturalnss problm) might b accssibl at currnt collidrs. If not, it will b DISCOVERED OR EXCLUDED by th LHC xprimnts

35 Th Latst Thortical Vogu: Larg Extra Dimnsions Hirarchy problm: M EW / M planck Postulat M planck ffctiv nrgy scal, not fundamntal Assum n compact spatial dimnsions of (compactifid) radius R m m M D r ( r) = n n V (r << R) V rlativ strngth ( r) mm n M D = n R r Short-rang gravity with Larg Compact Extra Dimnsions n = 4 n = 3 n = n = 7 Effctiv 4-dimnsional M planck thn givn by Rquiring M D M EW R (3/n)-7 cm (r >> R) n= R 3 cm - xcludd by /r tsts of gravity n= R.-mm - limitd to vry high M D by SN987 data /r distanc (cm) Thr ar othr modls with infinit sizd xtra dimnsions (non-factorizabl spactim gomtry) for which n= is not xcludd