1. Energy and Luminosity reach Our charge asks for evaluation of a baseline machine of 500 GeV with energy upgrade to about 1 TeV. (the “about” came about due to the specific proposals from Tesla and X-band of 800 and 1000 GeV, and desire of parameters group not to prejudge the eventual choice). The context of the energy and luminosity tradeoff is PHYSICS reach. The LC is blessed with a set of questions, some of which have relatively well specified energy reach (Higgs, top, precision Z and WW production) and some that are indicative of rich payoff in the subTeV region but are not specific as to energy and mass scale – Susy, models with expanded gauge symmetries, extra dimensions… Grannis 1

2. In the Susy case, a successful program requires that certain states – the partners of the leptons, gauge bosons and higgs – be seen and measured reasonably accurately. In particular, getting enough information to understand the kind of Susy that Nature chooses, and to extrapolate to the Susy-breaking scale, requires that we see at least the low lying gauginos (   ,   ,     and the sleptons. Failure to get above the appropriate thresholds for these severely restricts the physics, so the premium is upon having sufficient energy. Since we don’t know now what the scale is, the ability to raise the energy when the need arises is very important. 2

3. Point 1 2 3 4 5 6 GeV GeV GeV GeV GeV GeV        336 336 90 160 244 92       494 489 142 228 355 233       650 642 192 294 464 304       1089 858 368 462 750 459 e e/  920 922 422 1620 396 470  860 850 412 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 1276 364 q q 1882 1896 630 1828 1352 1010 ~ ~~ ~ ~~ reaction ~~        336 336 90 160 244 92       494 489 142 228 355 233       650 642 192 294 464 304       1089 858 368 462 750 459 e e/  920 922 422 1620 396 470  860 850 412 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 1276 364 q q 1882 1896 630 1828 1352 1010 ~ ~~ ~ ~~ ~~ RED: reactions accessible at 500 GeV BLUE: reactions accessible at 1000 GeV LHC Susy benchmark points. Susy particles are pair produced – thresholds at sum of two masses 3

4. For Strong Coupling models, little Higgs models, the new states (vector quarks, techni-rho, new gauge bosons, etc.) are likely somewhat heavier than 1 TeV, so evidence for these models will come from deviations in WW scattering, modifications to gauge boson trilinear couplings, top quark form factors etc. Here the advantage in higher energy is in magnifying these ‘loop effects’. The energy needed is thus not as clearly defined, but is nevertheless real. M  = 1240 GeV M  =2500 GeV significance  Z Z error Significance for technirho at LHC and LC at 500, 1000, 1500 GeV. (factor 6 gain in significance going from 500 → 1000 GeV.) Error on anomalous trilinear gauge coupling at LHC, LC at 500, 1000, 1500 GeV. (error reduced by >2 going from 500 → 1000 GeV. Note: scale of  in strong coupling models is 10 -3 – 10 -4.) 4

5. A similar response to energy occurs for extra dimensions – the effects such as mono-photons, modifications to cross sections etc. will vary rather smoothly with energy. Production of mini black holes probably has a well defined energy threshold. Linear collider Seeing Kaluza Klein states (Z’) requires energy sufficient to produce. Raising energy magnifies the difference between # extra dimensions. Gain going from 800 → 1000 GeV increases cross section by ~2.5 (D=8). Much more benefit from energy than luminosity. 5

6. The important factor for precision is integrated luminosity, so peak luminosity and the fraction of time the collider is producing collisions for physics are equally important. The gain in precision goes as √N (√ ∫Ldt )to a good approximation (providing that systematic errors are data driven and setup time for special runs don’t dominate, which we don’t think they will). Knowing results to higher precision is good, but for many physics studies, a factor of 2 in ∫Ldt does not seem to make a large difference. Gaugino mass extrapolation Here the main issue as I see it is in the risk factor for actually attaining reasonable ∫Ldt (Round table II) e.g. for gaugino mass unification at higher scale, the LHC errors already dominate those at LC. 6 Width of bands are errors LHC LC

7. SM value (decoupling limit) approx. errors Susy Higgs couplings to fermions, WW (ZZ) differ from SM as Susy parameters change. Precision BR measurements → new physics Susy couplings Integrated luminosity does translate into crucial precision for Higgs BRs, and these in turn dictate the precision with which one can infer new non-SM physics such as M A in MSSM. Expected precision with 500 fb -1 should give indirect M A up to about 600 GeV. 7

8. So – more energy is good and more luminosity is good, but my reading is that getting higher energy is more important than higher luminosity. The LC will likely explore terrain where there are new particle thresholds. Sensitivity via loop effects to new phenemona at higher mass is improved through E increase faster than luminosity increase. What does this mean?  I am not advocating that we aim at energies substantially above 1 TeV (another panel, another time). The prospect for superb physics at TeV scale is excellent.  I do regard the ability to go above the nominal top energy by 20-30%, even with lower luminosity, as an important advantage for physics.  Setting the stage for some future multi-TeV e + e - collider would be nice, but not crucial: our understanding of physics beyond the TeV scale is very unclear at this time and it may well be that the appropriate next step is a much higher energy hadron collider, 3 TeV CLIC, a very powerful proton- driver for neutrino physics, a 10 TeV lepton collider … We don’t have enough understanding to predict the right next step yet. 8