What can an e + e - Linear Collider teach us ?

1. P. Grannis Apr. 2000 What can an e+ e- Linear Collider teach us ? The LHC seems assured of discovering new phenomena related to Electroweak Symmetry Breaking. A 500 GeV e+e- linear collider can make precision measurements that considerably extend the LHC studies of EWSB. The e+ e- linear colliders are well developed technically. It is likely that we will need to make decisions on proceeding with a linear collider within the next few years. It is imperative that we understand the physics case as clearly as possible.

2. What are the Physics questions we want to attack? For me, there are to be two fundamental questions before experimental high energy physics at present: • What is the origin of the symmetry breaking observed in the electroweak interaction? • What gives the W/Z (and fermions) their mass? • Is there unification of forces, and at what scale? • Are there new phenomena or new particles associated with the physics responsible for EWSB? • What is the origin of flavors? • Why three generations and the peculiar mass patterns? • Why is there CP violation, and why is it insufficient for the matter/antimatter asymmetry in the universe? • Is there some common origin for fermion masses and Yukawa couplings?

3. How will we make progress on these questions? There is considerable room for intuition on how we will make progress over the next decade or so -- and these lead to different strategies for shaping the long term program. It seems clear to most of us that some evidence for EWSB, mass generation and unification will come in the next round of experiments at LEP2/Tevatron and particularly LHC. I believe that these experiments will not tell us all we want to know -- fundamental questions will remain. Progress can be made through study of very rare processes or precise measurements ( rare K decays, g-2 etc.). These may tell us somethingis out there, but not what. It is preferable to go to the scale of the new phenomena if possible. Further experiments to study flavor are highly interesting and topical -- CKM measurements for quarks, rare K decays, neutrino masses and mixings (and even n CP violation) -- but it seems a long shot to imagine that these are going to give fundamental insights on the basic question of the origin of flavor in the near future. Exploring EWSB mechanism is possible with near term experiments; we should pursue these opportunities vigorously. (the lamppost illuminates the terrain where the clues should be)

4. Plan of this talk • I will review what I think are the primary themes that can justify building a linear e+e- collider -- • The discovery and exploration of the Higgs sector • The discovery and understanding of Supersymmetry, or whatever else is responsible for EWSB; for these, precision EW measurements may play a crucial role. • (there are many other topics -- EW boson studies, top quark processes, new investigations of QCD, search for strong W scattering, etc. that form a part of the linear collider justification, but for me the case is dominated by the two primary issues and I concentrate on these.) • There have been 100’s of original contributions to these subjects -- and this talk is a summary of the work of many others (not me). I apologize for not citing all these works. • The question of what a linear collider can do is inextricably wound with the LHC experiment’s capabilities, so these are worth review. • The Linear Collider projects being discussed are ambitious and expensive; it seems clear that a first step will be made at ECM ~ 500 GeV, so the justification for this step must be convincing.

5. Linear Collider parameters NLC (SLAC/LBL/LLNL/FNAL) Initial Phase: ECM = 500 GeV Dt = 1.4 ns L = 0.5 2 x 1034 cm-2 s-1 Upgrade to 1 TeV ( L = 3 x 1034 ) since May 1999 (Lehman review: $7.9B including contingency, escalation, detectors) some progress: permanent magnets in Linac, reduced # klystrons needed with permanent magnet focus and new modulator, new beam delivery design is much shorter, electronics inside tunnel. Some descope/deferrals possible to control cost further: build Linacs for 500 GeV initially, push-pull detectors? Reduce cost by 1/3 - 1/2 ? ------------------------------------------- TESLA (DESY) (TDR in 2001) Initial phase ECM = 300 - 500 GeV Dt = 340 ns L = 3 x 1034 cm-2 s-1 Upgrade to 800 GeV ------------------------------------------- JLC (KEK) ECM = 300 - 500 GeV Dt = few ns L = presumed the same as NLC if X band gg options are available at 90% of full energy, reduced luminosity (circularly polarized lasers are now available); electron polarization high (>80%); positron polarization possible (present in TESLA)

6. Higgs self-coupling diverges Higgs potential develops 2nd min. L is the scale for new physics to appear to avoid SM Higgs inconsistencies Where is the Higgs In the context of the SM, we have an indirect upper bound on the Higgs mass of about 190 GeV from precision EW measurements at LEP1, LEP2, SLC, Tevatron, and the direct LEP2 lower bound of 108 GeV. Region I:108<mH<130 in allowed Susy range; needs L< Mplanck Region II: 130<mH<180 FNAL range; can have L= Mplanck Region III: 180<mH<230in SM allowed range; need LHC. L< Mplanck

7. Where is the Higgs But we cannot take the SM (MSSM) Higgs as completely foolproof. The possibility that EWSB involves no fundamental Higgs or other new particles at O (100’s) GeV has been explored: present constraints do not rule out new strong scales up to 3 TeV although no realizable models are known. Models of EWSB must obey the recent precision data from LEP/SLC/Tevatron/n scattering. For almost all, the claim is made that models are constrained to have a Higgs-like particle below 500 GeV, or to show other observable phenomena. S&T are independent self energy corrections arising from possible extensions of the SM. Precision measurements constrain DS, DT to < ~0.1, and severely limit new models in which the Higgs-like object occurs at m > 500 GeV. Different models give different DS, DT. EW corrections firmly required: from LEP measurements (SU(2) x U(1) S=T = 0) Without EW corrections

8. Program for Higgs Study • Find a Higgs boson candidate, and measure its mass (or masses of added Higgs states in SM extensions) • Measure its total width, and branching fractions (couplings) to all fermion pairs and gauge bosons. Are the couplings proportional to mass? Do they conform to the simple SM, or to Susy models? Do the couplings saturate the full EWSB needs (are there more Higgs?) • Measure the quantum numbers of the Higgs states: for the SM, expect JP = 0+ ; for Susy, both 0+ and 0-. • Explore the Higgs potential. The self-couplings lead to multiple Higgs production. • The experimental needs, for Higgs of differing masses and couplings, vary quite widely. A broadband approach may be necessary to fill in the whole picture.

9. SM Higgs production at LHC SM Higgs Branching ratios SM Higgs range from EW fits Susy (h) mass range

10. SM Higgs discovery reach at LHC ATLAS CMS 100 fb-1 is obtained in 1 std year (107 s) at full LHC Luminosity

11. LHC SM Higgs precision dmH / mH ~ few 10-3 Higgs width is sensitive to presence of additional decays; LHC width determination to ~ 10% Only sense GH for mass above SM window

12. SM Higgs Couplings/Quantum No’s -- LHC BR(WH gg) / BR(WH bb) to 30% BR(H gg) / BR(H ZZ*) to 15% (ttH gg/bb) / (WH gg/bb ) g2Htt/g2HWW to 25% (H WW*) / (H ZZ* ) g2HWW/g2HZZ to 30% Some ability to constrain H f f/ H bb by distinguishing gg H and WW fusion processes. ~ 25% on coupling ratios (MH dependent) • JPC difficult at LHC: • If observe H gg J 1 • H Z Z (4 l ) gives some ability to distinguish J=0 and J=1 • ttH study can distinguish CP=+ and - for low mass Higgs, if both tops reconstructed (will be tough).

13. Minimal Supersymmetric Model Higgs Sector 2 complex Higgs doublets f1and f2: after mass generation for W, Z get : h0 , H0 (CP even; mh < mH ) A0 (CP odd) H If Susy mass scale is < 1 TeV, the lighter h0 mass is below 150 GeV Higgs sector in MSSM controlled by two parameters:tan b = <f1> / <f2>and mA As mA , h0 becomes SM-like and H0,A0,H become massive and nearly degenerate. (decoupling limit)

14. LHC MSSM Higgs search Both experiments, 3 years at high luminosity needed to fully close all regions of parameter space. For large mA, distinguishing H and A is difficult. For mA > 500 GeV, discovery of H, A restricted to large tanb.

15. LHC MSSM mass, widths, parameters, couplings • h0 mass to 0.1% to 3%, depending on channel observed; s x BR to 7 - 20%. Region (3<tan b <10) and (mA ~ 150) is hard. h bb would help. • error on tan b ~10-20% for tan b > 10, where H/A tt /mm; difficult at low tan b, or where H/A are not observed. • Won’t measure Gh;can begin to measure GH/A above 250 GeV if states observable. • Some sensitivity to H/A neutralinos for intermediate tan b and mA • MSSM in decoupling limit (large mH, mA); can distinguish from SM in some regions using A/H tt or from rate for h gg . Tough to do for mA > 500 GeV.

16. Linear Collider SM Higgs ZH production WW/ZZ fusion Dominant at lower s Dominant at higher s ZH production 103 events/year at L=1034 WW/ZZ fusion

17. LC SM Higgs Linear Collider Higgs signal is low background ee ZH (Z qq ; H bb) several low mass Higgs masses. s = 300 GeV, 30 fb-1 similar resolution/bknd for other channels H W W; MH = 500 GeV; s = 1 TeV ; 60 fb-1 Clean signal even for high mass Higgs; SM WW background can be varied with electron polarization. SM Higgs mass resolution dmH /mH ~ 10-3 independent of LC energy (low mass Higgs) Measure recoil mass against Z (missing mass -- dm/m ~ 1.2x10-3)Hinvisible also seen this way 500 GeV LC finds Higgs up to 350 GeV with L = 50 fb-1

18. LC: SM Higgs Width Measure BR: G(H gg) / GTOT and s( gg H) ~ G(H gg) GTOT (~15%) (requires gg operation) OR: Use H WW* : BR(H WW*) = GWW / GTOT Get GWW from : sZH and assume universality (W/Z) orWW fusion to get GWW Few % measurement of GTOT for mass < 150 GeV; if GTOT GSM , have evidence for new physics. S g2(h VV)i = (MVgV)2 V= W or Z Measuring the first Higgs coupling tests whether there are any additional higher mass Higgs.

19. Quantum No’s We want to do a model independent determination of Higgs quantum numbers (assume not J=1 if LHC sees H gg ) Suppose the data looks like this. (Would expect JP = 0+ to look like this for Z angular distribution in ee Z h) cos qZ e t-channel production of bump would give strong forward backward Z peak -- ruled out clearly. s-channel radiation: ALR tells us that it is the Z that radiates; demonstrates that the Higgs couples to mass. Above distribution for JP = 0+ is distinct from ~ cos2qZ from JP = 0- .. Z e “H” Z,g e Z e H Higgs ZZ/WW couplings can be deduced from ZH and WWH production to determine whether the observed Higgs is the only Higgs-like particle -- can do these to few %. Here is a place where gg (polarized) could help: form H through W loop; suppress QCD background -- measure Ggg and probe CP properties of Higgs.

20. The crucial measurement in Higgs sector Higgs Couplings at the LC Use SLD-like vertex algorithms to give probabilities for jets to be b, c, light quarks. Based on probability for track to be primary/ secondary vertex; no. displaced tracks; invariant mass; pT of leptons; probability of one secondary vertex. Tau ID based on number of jets, charged multiplicity, Thrust, visible energy, impact parameter. (Likelihood functions) (Battaglia) b likelihood c likelihood uds likelihood Each event plotted in b, c, uds likelihood; fit with constraint of ( Pb+ Pc + Puds) =1 to get the individual BR’s

21. Higgs Couplings Theory errors (bands) from mb, mc, mt, aS uncertainties. gg = light quarks 1000 fb-1 for 500 GeV Linear Collider: H bb 2.4% H cc 8.3% H light quarks 5.5 % H t t 6.0% H WW 5.4% dBR/BR (Mh = 120 GeV) Experimental errors ~ 1/ N; theory errors from b,c masses will come down

22. Higgs Couplings, cont’d Measurement of BR’s is powerful indicator of new physics (MSSM or other). Want to check that couplings are indeed proportional to mass. BR approx. errors Find MSSM parameters giving right mh, and agreement with BR ratios : bb/hadrons cc/hadrons uds/hadrons bb/WW* SM value (decoupling limit) tanb Express region of good fit in terms of limit on mA -- limit up to about 700 GeV with a 500 GeV collider. Limit on mA scales between N1/4 and N0 ( N=no. evnts); not a huge premium on luminosity (needs recheck) dMA ~ 80 GeV for MA = 500 30 90% CL 10 600 mA

23. Summary of Higgs Issues • LHC should discover SM or MSSM Higgs if LEP2/Tevatron do not. For some regions of MSSM parameters, considerable luminosity is required. LC seems assured of effective study of MSSM h and SM Higgs in the prescribed mass range. • If SM Higgs is in low mass region, LHC confined to low statistics gg with little confirmation of the character of the state. LC can make it copiously and demonstrate its quantum numbers and couplings to mass. • LC should make an order of magnitude improvement on Higgs width over LHC -- can measure it for low masses. • MSSM higgs; neither will do H/A/H well over full parameter space. (LC would benefit from EEM = 1 TeV) • LHC will do only rough measurements of some Branching Ratios (~25% in favorable cases); LC should do precise measure of bb, cc, qq, tt, WW BR’s, and thus be able to cleanly distinguish MSSM and SM. These couplings play a role similar to precision EW measurements for the Higgs sector -- and form a strong justification for the LC. They tell us that Higgs couples proportional to mass.

24. Supersymmetry Studies • Susy postulates partners of opposite statistics for all SM fermions and bosons. • In the absence of new particles, the SM Higgs mass is quadratically divergent and requires exquisite fine tuning to be O (100 GeV)/ O (MPlanck) . Spectrum of superpartners stabilizes the Higgs mass (and enables unification of Strong/EW couplings). • Mass scale of Susy (e.g. lesser mass of gluino/squark) should be O (1 TeV) to avoid additional fine tuning. • Higgs sector is enlarged to two complex doublets with 5 surviving Higgs (h, H, A, H ). Lightest Higgs (h) has mass < 150 GeV. • Simplest models conserve Rparity (+1 for SM particles, -1 for sparticles). In this case, the lightest Susy particle (LSP) is stable (and neutral, weakly interacting), typically it is the lightest superpartner of (g, Z, h, H). LSP is dark matter candidate. • In general, > 100 new parameters, as the Lagrangian can have arbitrary sparticle mass parameters etc. (MSSM). (If require unification at GUT scale and universal scalar masses, get 13 parameters)

25. ~ ~ ~ G G G ~ t Susy Models • Necessary to break Susy (as we know there is no scalar electron at 0.511 MeV). Not possible using only the MSSM fields, thus need a hidden sector to break Susy with some fields to communicate symmetry breaking to observable particles. • Supergravity (SUGRA) : gravity is the messenger from the Planck scale. Minimal SUGRA has only 5 parameters (unified scalar and spin 1/2 masses, tanb = ratio of Higgs doublet vev’s, A = universal higgs couplings to sfermions, and m = higgs mass parameter. • Gauge Mediated (GMSB) : Susy breaking at scales much lower than Planck scale, and transmitted to sparticles by gauge interactions (e.g. SU(5) ). Now LSP is Gravitino ( ), and NLSP decays: g or t can be sought (NLSP can be quasi-stable). Use 5 parameters. • Anomaly Mediated (AMSB) : no supergravity couplings; related to `large’ extra compactified dimensions. Running SM couplings generate Susy masses. First chargino and LSP neutralino nearly degenerate. • Other schemes may arise! And R parity violation can be grafted on to any scheme. c10

26. Chargino and Neutralino States The two superpartners of the underlying ordinary charged bosons (w +, H+ ) are the Wino and (charged ) Higgsino (w, h+ ) . These mix to form mass eigenstates ( c1+ , c2+ ). In the wino/ higgsino basis (relevant for the couplings) the mass matrix is: ~ ~ M2 2 MW sinb 2 MW cosbm M2 is wino mass m is higgsino mass The neutral underlying ordinary bosons (b, w 0, h10 , h20 ) have Susy partners (b, w 0, h10 , h20 ) which also mix to give the neutralinos ( c10 , c20 , c30 , c40 ), with a 4X4 mass mixing matrix depending on M1 (bino mass), M2 , and m (and qW , b ) In the case that m >> M2 , c1+ , c10 , c20 are dominantly Gaugino (wino/zino/bino) and couple more strongly to the (W,Z, g ). In the complementary case, the lighter chargino and neutralino couple more to the Higgs states. Measuring the chargino and neutralino mass patterns permits understanding of the bino, wino & higgsino masses and hence tells us the character of the Susy model. (all the LHC mSUGRA points have m >> M2 and thus gaugino type couplings). AMSB has m <M2 and c10 and c1+ nearly degenerate. ~ ~ ~ ~

27. Particle spectra in different Susy models The Sparticle spectra in the various classes of Susy tend to differ. Thus as complete a study of the particles of Susy will be important for understanding the basic model type. These spectra for mSUGRA, GMSB and AMSB are only generic --effects of mixing, specific parameter choices will modify them. But the elevation of squark masses in GMSB and AMSB is generic, as are the relations among the gauginos. Left and right-handed ordinary fermions have separate Susy partners: these can mix to give mass eigenstates (e.g. t1 t2, t1 t2 , b1 b2 expected to be mixed L and R). These mixings also discriminate Susy models. ~ ~ ~ ~ ~ ~

28. Program for Susy Study • Discover the presence of Susy through excess of events over SM backgrounds. • Measure the masses and identity of the Susy spectrum (the squark, gluino, sleptons, lighter gauginos are of particular interest). • Determine the quantum numbers, branching ratios of the accessible states. • Determine the mixing parameters for charginos, neutralinos, stau, stop … . Is there CP violation? • Figure out the type of Susy model that is operative, and the underlying parameters of that model. • Try to understand the mechanism for supersymmetry breaking -- where is the unification scale (is there unification?); what is the messenger sector?

29. ~ g ~ q Susy at the LHC Atlas has studied a dozen models that try to span the Susy space -- 6 mSUGRA models, 4 GMSB models, and R parity violating. Define effective mass from in multijet events from jet ET and missing ET: Meff is a good indicator of Susy scale (lower of squark and gluino masses). LHC should discover Susy if it exists (e.g. need ~30 fb-1 to find squark/gluinos up to 2.5 TeV). copiously produced; other sparticles tend to come from decay chains. Main backgrounds to Susy are from other Susy particles.

30. Point 1 2 3 4 5 6 LHC mSUGRA points m0 (GeV) 400 400 200 800 100 200 m1/2 (GeV) 400 400 100 200 300 200 A (GeV) 0 0 0 0 300 0 tanb 2 10 2 10 2.1 45 sgn(m) + + - + + - • Points 1 & 2 (differing only in tanb ) have as large squark/gluino mass as sensible (~1 TeV) • Point 3, with low mass scale, with rich low mass spectrum of sparticles • Point 4 is near the boundary where EWSB can work, large m0 • Point 5 has dark matter candidate, light sleptons • Point 6 chosen for large tanb and mainly stau decays of gauginos • All of these points have the lower chargino/ neutralino states mainly wino/zino; heavier gauginos are mainly higgsino.

31. Point 1 2 3 4 5 6 LHC mSUGRA point MASSES (GeV) ~ g 1004 1009 298 582 767 540 c10 168 168 45 80 122 81 c20 326 321 97 148 233 152 c1+ 325 321 96 147 232 152 c2+ 764 537 272 315 518 307 <uL,uR>941 948 315 914 676 505 b1 854 871 278 774 633 390 t1 643 710 264 594 489 365 < , >460 461 211 810 198 235 430 425 206 797 157 132 486 485 207 810 230 237 h 95 116 69 112 93 112 H 1046 737 379 858 638 157 A 1044 737 371 859 634 157 1046 741 378 862 638 182 ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ mL/mR 1.14 1.14 1.04 1.01 1.52 1.14 l l L R ~ t1 ~ n H

32. ~ q ~ l Susy masses at LHC Mass determinations dependent upon the specific Susy model point -- decay chain dependent. e.g. : c20q, c20c10l l c20 c10 h c10 b b l or bb mass bump discovers Higgs; (input mh = 93 GeV) In this case, can measure mass distribution of dilepton, lepton + jet, b b +jet, and the lower and higher dilepton + jet mass: mbb From these distributions, can determine squark, selectron, c10and c20 masses to O (10%).(this is a particularly favorable model point (5) -- two nice decay modes)

33. ~ g ~ q LHC Susy measurements • For some model parameters, independent masses can be measured; often get combinations of masses. If assume mSUGRA can fit for parameters: (squark/gluino masses to few %) m0 to 2 - 25% m1/2 to 1 - 5% tan b to 3 - 20% for model points studied • Similar precision for most GMSB and R parity violating models studied, if one can guess the model type we are in. In some cases (long lived NLSP or no missing ET) this is possible). • LHC will : • Discover Susy if it has to do with EWSB • Determine squark/gluino masses, sleptons if in decays • Sometimes understand the Susy model type • LHC will not : • Find sleptons unless found in decays • Find heavier gauginos or Higgs states • Determine quantum numbers or mixing angles for most cases; CP violation seems very hard

34. Susy Studies at the LC • Linear Collider offers some strong advantages for the study of Susy: • One has two body final states, through (g, Z) s-channel or sparticle t-channel. Fixed initial state. Final state is the CM, so production angular distributions are known. Know the final state energies and quantum numbers (Beamsstralung loss ~ 10%, correctable using Bhabha’s) • Controllable partonic cm energy -- tune for the process to study (at expense of multiple run conditions) • Vary polarization of at least the electron (Pe- ~ 90%) (maybe positron?). This allows controllable contribution from both background (WW ) and some Susy processes. • Cross sections depend on Susy model; typically sparticle-antisparticle cross sections in the range 30 - 300 fb-1 (0.1 - 1 R) at ECM = 500 GeV. • These advantages yield more incisive and extensive Susy studies at a LC than the LHC.

35. LC cross sections Typical cross section variation with ECM for selected SM and Susy processes. Peak cross sections roughly 50 -100 GeV over the threshold for the reaction. 103 evnts/yr at L = 1034 for s = 10 fb Variation of cross sections at 500 GeV (LHC point 3) with electron polarization -- for SM processes, and for Susy processes. ~ ~ eR eR PL(e-)

36. LC Reaction Thresholds for LHC points Point 1 2 3 (s) 4 5 6 GeV GeV GeV(fb)GeV GeV GeV reaction c10 c10 336 336 90(250)160 244 92 c10 c20 494 489 142 (130) 228 355 233 c1+ c1- 650 642192(400)294 464 304 c1+ c2- 1089 858368(10)462 750 459 e e/ m m 920 922422(125)1620396 470 t t 860 850412 1594 314 264 Z h 186 207 160 (60) 203 184 203 Z H/A 1137 828 466 950 727 248 H+ H - 2092 1482 756 1724 1276364 q q 1882 1896 630 1828 1352 1010 ~ ~ ~ ~ ~ ~ ~ ~ Thresholds in bold red for allowed reactions at ECM = 500 GeV Thresholds in blue are inacessible at 500 GeV Cross sections in green for LHC point 3

37. LC reaction accessibility vs. ECM Point 1 2 3 4 5 6 GeV GeV GeV GeV GeV GeV reaction c10 c10 336 336 90160 244 92 c10 c20 494 489 142 228 355 233 c1+ c1- 650 642192294 464 304 c1+ c2- 1089 858368462 750 459 e e/ m m 920 9224221620396 470 t t 860 850412 1594 314 264 Z h 186 207 160 203 184 203 Z H/A 1137 828 466 950 727 248 H+ H - 2092 1482 756 1724 1276364 q q 1882 1896 630 1828 1352 1010 RED: Accessible at 500 GeV ~ ~ ~ ~ ~ ~ ~ ~ c10 c10 336 336 90160 244 92 c10 c20 494 489 142 228 355 233 c1+ c1- 650 642192294 464 304 c1+ c2- 1089 858 368 462 750459 e e/ m m 920 9224221620396 470 t t 860 850412 1594 314 264 Z h 186 207 160 203 184 203 Z H/A 1137 828 466 950 727 248 H+ H - 2092 1482 756 1724 1276364 q q 1882 1896 630 1828 1352 1010 RED: Accessible at 1000 GeV ~ ~ ~ ~ ~ ~ ~ ~ If Susy exists, will want to upgrade energy (probably true if EWSB is non-SM in some other way too).

38. Measuring Susy particle masses In many cases, the sparticles decay via two-body modes: A B C , with C a known SM particle and A,B Susy particles. In this case, the isotropic decay in the A rest frame is a flat distribution in the CM frame: dN dEC EC E- E+ E = 1/2 (1 b ) (1 - mB2/mA2) ; b = (s/4mA2 - 1) Measure E+ , E- determine mA and mB And quantum numbers from angular distributions ~ ~ ~ ~ For m m, t t -- sin2q for scalar particles (s-channel production). For ee , a mixture of sin2q (s-channel g/Z) and 1/sin4q /2 (t-channel c0) , depending on polarization and selectron handedness. ~ ~ Pe = +0.6 Pe = -0.6

39. R L ~ ~ ~ ~ l l l l ~ ~ ~ m m m ~ t Slepton measurements ~ ~ + - Reaction is e+e- , = or ; H = L or R l l H H c0 l + ( Similar for squark pair production if allowed ) m( ) = (1 - 2) X m( ) c10 Measure mass of and to ~ 1% from end points. Angular distribution of ‘s inferred from masses and measured m momenta (two fold ambiguity -- wrong solution is flat in cosq and can be subtracted). Verify scalar character of ~ l Both solutions plotted Subtract the flat background and see the sin2q behavior

40. ~ ~ ~ tR tR tR- ~ ~ ~ ~ ~ ~ t2 tL t1 t1 t1 tL ~ ~ t t Special measurements with Stau Mass from endpoints as before; using c10 mass from other measurements, get dm/m ~ 1.5% from the t with t r n (one prongs) The states mix to c10 ~ t2 cosqtsinqt -sinqtcosqt = Cross sections with polarized e- and mass of allow determination of sinqt to within 0.03 (100 fb-1) Polarization of t can be determined to ~ 7% from the decay asymmetry; This yields information on the and mixing (and also yields info on tanb) tR-+ Gaugino tL-+ Higgsino A valuable tool for independent study of gaugino mixing c10 ~ tL-

41. Mass determination of ~ ~ using end points eL , eR Selectron studies Now have two diagrams; typically t-channel dominates and allows measurement of neutralino couplings to lepton/slepton. ~ ~ e e c10 e+ e+ e+ ~ e+ c0 g,Z ~ e- e- ~ e- e- Angular distribution determines the spin of neutralino

42. In the typical case, c1+is lighter than e and chargino production dominates, with the s-channel (g, Z) and t-channel (n) production diagrams interfering. ~ Gaugino studies e+ c+ c+ g, Z e+ ~ n e- c- ~ c- e- Masses are determined from end points in reactions like e+ e- c1+ c1- , with decays: c1+ c10W+ / c10 n / c10q q as for previous cases (few %). The mass values of c1+ , c2+constrain the mass mixing model: M2(c1+) +M2(c2+) = M22 + 2 MW2 + m2 M(c1+) xM(c2+) = M2 m - MW2 sin(2b) l Polarization is again important: eR- e+ c1+ c1-removes the t-channel diagram; cross section and AFB tell us about the higgsino content of c1+ and relative mixing of positive and negative gauginos. Tests of Susy relations are possible (measure d (MW ) ~ 23 MeV from purely Susy quantities.) eL- e+ c1+ c1-allows test of SUSY coupling g(c+ ne) = g(W+ne ) ~ e- e+ c1+ c1- has strong s-, t-channel interference sensitive to m( n) to about 2 ECM ~

43. Determining Gaugino properties If we know we are in the gaugino regime, can use c0 exchange in selectron production to test the Susy relations geeb = 2 g’ and the equivalent with c+ exchange for the e nw coupling. Accuracy with 100 fb-1 is about 1% ~ ~ ~ ~ ~ ~ n e+ e+ e+ c+ c0 ~ n ~ e- e- e- The polarization of the beam electrons is also key here (positron polarization would be nice). Scattering to selectrons, from polarized electrons (L and R) on positrons and on polarized electrons, give independent measures of the gaugino/higgsino nature of c10 , wino/bino mass. Getting from gaugino/sleptons to Susy breaking: Measurement of the chargino/neutralino mixing and the slepton masses to the 1% level allow extraction of GUT scale character of model -- Susy breaking, messenger scale, compactification scale. Gaining information about the Susy breaking should be seen as the most important general goal of the Susy portion of the LC program!

44. Summary of Susy Issues • LHC will not fail to find Susy if it exists. The energy should be high enough to produce squarks and gluinos copiously. Signatures for mSUGRA, GMSB, R-violating Susy all seem robust. LHC will measure those sparticle masses (mass differences) that arise in cascade decays (O (10%)). Sleptons, higher Higgs states and the higher gauginos are problematic. Quantum numbers, mixing parameters will be poorly measured, if at all. • The LC will make incisive studies of Susy properties of those states produced -- masses to 1% precision, the chargino and neutralino compositions and mixings, branching ratios. The question for the LC is whether the energy is sufficient to see enough of the spectrum. ECM = 500 GeV should give the first charginos, maybe the sleptons. 1000 GeV seems safe for getting most of the lower mass states. • LHC can do a reasonable job in determining Susy parameters if the model is specified; in some cases can distinguish model types. • LC can do model independent tests and fully explore the Susy parameters.. It seems the LC can explore the nature of the Susy breaking and messenger sectors; this important possibility needs more work !

45. What if it’s not Susy? Supersymmetry is many people’s guess for new physics -- it stabilizes the Higgs mass; allows unification of strong and EW, provides a dark matter candidate. It is motivated by string theory, but not in the phenomenological form used for EWSB. But there is no experimental evidence for Susy, and it does introduce theoretical questions. • Other suggestions exist: • Technicolor (a new SU(3) like QCD with high mass scale; pseudo Goldstone bosons = ‘Higgs’ • See-saw top condensate models; higgs mechanism from top condensates • Large extra dimensions; gauge bosons or gravity live in extra dimensions with SM fermions stuck to 3+1 domains. Higgs mechanism involves mixing in 3+1 and higher dimensions ... Any model must obey the precision EW constraints (S,T), so is limited. This implies that the‘Higgs’ or new phenomena must be found in the < 500 GeV regime.

46. Importance of Z pole and Precision Measurements A sample of 108 Z bosons can be obtained in a few month run. This can permit very accurate determination of the precision measurements (sin2qW, lineshape, etc.) With 90% electron polarization and 50% positron polarization (0.5% precision as SLC), one has effective polarization of 95 0.1%. Then ALR permits determination of sin2qW to 0.00002 -- indirect measurement of mH to 5%. To use this precision, need dmt = 0.6 GeV (doable at LC) and improvement in daS by a factor of about 4 (thought to be doable at LC). Such precision on EW corrections is sensitive to Susy loops and allows very sensitive confrontation of observables with any new models of EWSB such as strong coupling, extra dimensions, new Z’/W’ etc. Large samples of Z’s also give important samples of bb from which Rb, AFB(bb) can be determined. Also rare b decays (b s g, Bsy f). (This possibility requires more like 1010 Z’s) Precision t studies with 109 Z’s (tm g)

47. Other LC measurements There are many other topics that form part of a justification for a linear collider that I did not discuss: Precision study of EW bosons -- the trilinear couplings can be measured to O (10-3). W mass to 6 MeV (statistical) but theory errors need to be reduced. The top quark mass can be measured to about 0.2 GeV; evidence for the first unbound tt state; top width. Top anomalous couplings should be accessible. Rare top decays. QCD studies with Z pole and gg scattering. Can get aS to 1% from ee 3 jets Search for evidence of strong symmetry breaking -- WW scattering resonances, anomalous couplings, excited W/Z. Will need 1 TeV or higher. Signatures for new space dimensions at the mm scale These can buttress the LC case, but do not drive it

48. Conclusions LEP/Tevatron/LHC will discover the Higgs, but will not tell us what we want to know about quantum numbers and couplings. A 500 GeV Linear Collider will measure these to good accuracy and pin down the EWSB model. LHC will find Susy if it exists, and map out some of the spectrum of sparticles. Linear Collider will make accurate measurements of quantum numbers, branching ratios, mixings that should enable some understanding of the Susy breaking scale. Upgrade of LC to 1-1.5 TeV is probably needed to explore the sparticle spectrum fully. Other extensions of the SM should have observable effects at a linear collider; these, in conjunction with precision measurements at the Z pole, top, & W properties should be able to delineate these models. The decision to proceed with the Linear Collider will be needed in the next few years. Work to understand and document the physics case is needed now.