P. Grannis – Snowmass Workshop July 1, 2001 Any major new accelerator facility should address the big questions of particle physics research for the next several decades:  What is the origin of symmetry breaking in the electroweak interaction ? W/Z fermion masses, new physics at the TeV scale, force unification?  Where do the quark and lepton flavors come from ? why 3 generations? CP violation? Fermion mass disparities and mixing patterns?  What are the unseen elements of the universe ? dark matter, dark energy, cosmological constant = 0 Snowmass studies should address how the Linear Collider can shed fundamental insights on these overarching questions Linear Collider Physics Studies

TESLA  JLC-C NLC  /JLC-X  L design (10 34 ) E CM (GeV) Gradient (MV/m) RF freq. (GHz)  t bunch (ns) L = 1x10 34 cm -2 s -1 for 10 7 sec. year gives 100 fb -1 /year For 120 GeV Higgs 6000 Higgs from HZ Higgstrahlung 8000 Higgs from WW fusion For 220 GeV charginos, 6000     pairs; 70,000 top pairs For example: E CM = 500 GeV, 1 1x10 34 cm -2 s -1  TESLA TDR DESY (March 2001)  NLC,  US and Japanese X-band R&D cooperation; machine parameters may differhttp://www-project.slac.stanford.edu/lc/wkshp/snowmass2001/ Linear ee Colliders H HZ Hee MHMH  (fb)  qq WW tt  RRRR Zh HA ~~ ~~ E CM E CM =500 GeV E=500 GeV 800 GeV electron polarization ~ 80%; may have positron polarization ~60% Optional  e -  e - e - collisions at reduced luminosity for special physics

Precision measurements in the past decade (LEP, SLC, Tevatron, scattering) indicate the need for something like the Higgs boson below a few 100 GeV. The SM Higgs mechanism is unstable; vacuum polarization contributions from the known particles should drive its mass, and the gauge boson masses, to the force unification scale. We expect some new physics at the TeV scale. Study the `Higgs boson’ (or its surrogate) and measure its characteristics. Find and explore this new physics sector.  Also a rich additional program – top physics, QCD studies, precision EW measurements, etc.) Recent comprehensive physics studies: TESLA TDR, DESY 2001 – 011, (Part III – Physics at an e + e - Linear Collider) LC Physics : Resource Book for Snowmass 2001, ( hep-ex , 056, 057, 058 including: “The Case for a 500 GeV e + e - Linear Collider”, hep-ex/ ) (e.g. if Supersymmetry, a whole set of new sfermions with which to explore Flavor Physics, seek dark matter, etc.) Main themes for the Linear Collider physics program : 3

Measurements tell us Higgs mass is low: (SM) M higgs GeV. Tevatron can discover up to 180 GeV (Only measurements will tell us ! ) Higgs self-coupling diverges Higgs potential has 2nd min. LEP Higgs search – Maximum Likelihood for Higgs signal at m H = GeV with 2.9  significance (4 experiments) If LEP indication is correct, there must be physics beyond the SM before the GUT scale Measurements from past 10 years are telling us that there should be a light Higgs, or something that mimics it. Nature would seem particularly malign to point so clearly to something that is not there !! What is the Higgs ?? W/topZ lineshapeZ asym scat Z BR’s 4

Find a Higgs boson candidate, and measure its mass (or masses of added Higgs states in SM extensions) Measure total width, and couplings to all available fermion pairs and gauge bosons. Are the couplings proportional to mass? Do they conform to the simple SM? to Susy models? Do they saturate the full g HVV coupling ? (are there more Higgs?) Measure the quantum numbers of the Higgs states: for the SM, expect J PC = 0 ++ ; for Susy, both 0 ++ and Explore the Higgs potential. The self-couplings lead to multiple Higgs production. LHC (or Tevatron) should discover Higgs, and measure the mass well (unless Higgs decays dominantly in invisible modes - then the LC finds it). LHC will not do  TOT (or do rather poorly). Ratios of some couplings only to ~20%. Linear Collider can measure  and couplings to ~5%; these are the crucial measurements for establishing the nature of the higgs. LHC will not do; Linear Collider will do easily LHC will not do; LC can do trilinear coupling, with sufficient luminosity LHC should discover a Higgs candidate; LC should discover what it really is. We will likely need both ! Program for Higgs Study 5

LC can produce Higgs in association with Z allowing study of its decays without bias -- even invisible decays of Higgs are possible using the recoil Z (in ee, , qq modes). BR(H WW * ) =  WW /  TOT  WW from  ZH or WW fusion. Test for unexpected Higgs decays  TOT to few% for M > 110 GeV Higgs Z/W couplings Higgs studies -- Discovery & Mass ZH brems Fitted dijet mass Measuring the lightest Higgs coupling in ZH production tests whether there are additional higher mass Higgs. WW fusion ZHWW Total width Fitted recoil mass from Z WW/ZZ fusion dominates at mass, energy -- measures VV couplings. Can distinguish from ZH using jet tags and missing mass. 6 Z recoil mass fitted Higgs mass Missing mass

500 fb -1 for 300 GeV LC H bb 2.4% H cc 8.3% H gg 5.5 % H  6.0% H WW 5.4% Measurement of BR’s is powerful indicator of new physics, and senses M A well above E CM. MSSM Higgs BR’s must agree with MSSM parameters from many other measurements. SM value (decoupling limit) approx. errors We need to determine experimentally that Higgs couplings are indeed proportional to mass. BR’s In Susy, 2 complex Higgs doublets    and  . After mass generation for W, Z get : h 0, H 0 (CP even; m h < m H ); A 0 (CP odd) ; H For Susy mass scale / and m A. At large m A, h 0 becomes SM-like and H 0,A 0,H become massive and nearly degenerate. (decoupling limit) From likelihood fn’s using vertex, jet mass, shape information Higgs Couplings (M h = 120 GeV) BR MHMH (lose the ff BRs for M H > 180 GeV, except tt) 7

 = cm production angle;  = fermion decay angle in Z frame J P = 0 + J P = 0  d  /dcos  sin 2  (1 - sin 2  ) d  /dcos  sin 2  (1 +/- cos  ) 2  and angular dependences near threshold permit unambiguous determination of spin-parity Can produce CP even and odd states separately using polarized  collisions.  H or A  (can reach higher masses than e + e - ) Measures Higgs potential shape  independent of Higgs mass meas. Study ZHH production and decay to 6 jets (4 b’s). Cross section is small; premium on very good jet energy resolution. Can enhance XS with positron polarization.  error 36% 18% Higgs spin parity Higgs self couplings 8

The defects of the SM are widely known: No gauge interaction unification occurs Higgs mass is unstable to loop corrections Can’t explain baryon asymmetry in universe … Many possible new theories are proposed to cure these ills and embed the SM in a larger framework. Supersymmetry Susy models come in many variants, with different scales of Susy breaking (supergravity, gauge mediation, anomaly mediation … ) Each has a different spectrum of particles, underlying parameters. A new gauge interaction like QCD with `mesons’ at larger masses. (Technicolor/topcolor) These interactions avoid introducing a fundamental scalar. `technipions’ play the role of Higgs; new particles to be observed, and modifications to WW scattering. String-inspired models with some extra dimensions compactified at millimeter to femtometer scales. LC must be able to sort out which is at work. Can imagine cases where LHC sees new phenomena, but misunderstands the source. Something different? Physics beyond the Standard Model 9

If Susy is to stabilize the Higgs & gauge boson masses (and give grand unification) it is ‘natural’ to believe that some Supersymmetric particles will appear at a 500 GeV LC. The main goal is to measure the underlying model parameters and deduce the character of the supersymmetry, energy scale for Susy breaking. There are ~ 105 unknown MSSM parameters, all of which should be measured, and used to fix models. This can be done through measurement of the masses, quantum numbers, branching ratios, asymmetries, CP phases -- and in particular the pattern of mixing of states with similar quantum numbers -- the 2 stops, sbottoms, staus, and the 2 chargino and 4 neutralino states (partners of the  /Z/W and supersymmetric Higgs states). Susy may well be the next frontier for flavor physics – FCNC, CP violation for sparticles, generational patterns, etc. Susy can provide a dark matter candidate. The LHC will discover Susy if it exists. But disentangling the information on the full mass spectrum, particle quantum no’s/couplings and the mixings will be difficult at LHC. The LC can make these crucial measurements, (e.g. sparticle masses to 0.1 – few % level) benefitting from -- Polarization of electron (positron?) beam Known partonic cm energy Known initial state (J P = 1 - ) Supersymmetry 10

An example: production of selectron pairs -- have two diagrams; typically the t-channel    exchange  dominates and allows measurement of neutralino couplings (gaugino vs. higgsino) to lepton/slepton. s-channel  /Z process only for e L + e L - and e R + e R -. Bkgnd WW suppressed for beam e R -. e-e- e-e- e+e+ e+e+ e+e+ ~ e+e+ ~ e-e- ~ e-e- ~ ,Z  e e    ~ e L,R e    ~ Supersymmetry studies at the Linear Collider ~ ~ ~~ Decay: Upper & lower end points of decay electron energy distribution from gives masses of left and right handed selectrons and neutralino. Angular distributions of decay electrons, using both polarization states of beam e -, tell us about quantum numbers, coupling of exchanged neutralino and give information on neutralino mixing, hence the underlying Susy mass parameters. e distributions for both e - polarizations 11

Masses are again determined from end points in reactions like e + e -        with decays:        W + /     l  /     q ’ q as for previous case (few %). The mass values of        constrain the mass mixing parameters: M 2 (    ) +  M 2 (    ) = M M 2 (W) +  2 M(    ) x  M(    ) =  M 2 - M 2 (W) sin(2  ) e+e+ e+e+ e-e- e-e-      Z ~ e - Polarization is again crucial: e R - e +       removes the t-channel diagram; cross section and A FB give the higgsino/wino content of   . Tests of Susy relations are possible (e.g. measure M W to ~ 23 MeV from purely Susy quantities.) ~ e L - e +        has strong s & t channel interference, sensitive to m( ) to about 2 E CM. e L - e +       allows test of SUSY coupling relation g(   e) = g(W + e ) ~ ~~~ Similar studies for neutralino, t, , production lead to independent measures of similar parameters and should enable a constrained fit to Susy model. Chargino studies 12

The Linear Collider can determine the Susy model, and make progress to understand the higher energy supersymmetry breaking scale. To do this, one would like to see the full spectrum of sleptons, gaugino/higgsino states. Point GeV GeV GeV GeV GeV GeV                          e e/   Z h Z H/A H + H q q ~ ~~ ~ ~~ reaction ~~ Thresholds for selected sparticle pair productions -- at LHC mSUGRA model points. It is likely that, in the case that supersymmetry exists, one will want upgrades of energy to at least 1 TeV. RED: Accessible at 500 GeV BLUE: added at 1 TeV Operation in e  mode can increase mass reach: e -  e  1 0 (g-2) result suggests relatively light sfermions or charginos, if Susy is at work. ~~ Linear Collider Supersymmetry 13 These points need updating. New data rules some pts out, but message is still similar

The LC complements the LHC. LHC will see those particles coupling to color, some Higgs & sleptons, lighter gauginos only if present in cascade decays of squarks and gluinos. LC will do sleptons, sneutrinos, gauginos well. Electron polarization is essential for disentangling states and processes at LC. We really want understand the origin of Susy -- determine the 105 soft parameters from experiment without assuming the model (mSUGRA, GMSB, anomaly, gaugino … ) mediation. We want to understand Susy breaking, gain insight into the unification scale and illuminate string theory. Detailed patterns of mass spectra give indications of the model class. LC mass, cross sect. as input to RGE evolution of mass parameters, couplings reveal the model class without assumptions. This study for ~ 1000 fb -1 LC operation and LHC meas. of gluinos and squarks show dramatically distinct mass parameter patterns for mSUGRA and GMSB. Susy breaking mechanism 14

sin 2  W S & T measure effect on W/Z vacuum polarization amplitudes. S for weak isoscalar and T for isotriplet All EW observables are linear functions of S & T and are presently measured to 0.01 to be in agreement with SM with a light Higgs. Giga-Z samples at LC (20 fb -1 ) would improve sin 2  W by x10 (requires e + polarization), WW threshold run improves  M W to 6 MeV, etc. Factor 8 improvement on S,T. LC will measure top mass to 200 MeV. The chevron shows the change in S & T as the Higgs mass increases from 100 to 1000 GeV, given the current top mass constraint. If the Higgs is heavy (> 200 GeV), need some compensating effects from new physics. Need a positive  T or negative  S. Several classes of models to do this, but it is difficult to evade observable consequences at LC. The precision measurement of S&T at a linear collider could be crucial to understand the nature of the new physics, if no Susy. Present 68% S,T limits 68% S,T limits at LC; location of precision ellipse gives model info. Precision studies constrain ANY new physics 15

Strong coupling Observables at LC: Bound states of new fermions should occur on the TeV scale. Since the longitudinal components of W/Z are primordial higgs particles, WW (ZZ) scattering is modified: a broad resonance is seen at LHC; LC sees modification to ee WW cross section. For many, fundamental scalars are unnatural. We have a theory (QCD) in which pseudoscalars (pions) arise as bound states of fundamental TT  M W =30 MeV,  M Top =2 GeV Strong Coupling Gauge Models M  = 1240 GeV ; =2500 GeV significance fermions. A new Strong Interaction could provide the Higgs mechanism and generate EWSB. At LC, strong coupling composite ‘higgs’ should be constrained to < 500 GeV with Giga Z. MHMH Technirho relative signal significance for LHC and LC at 500, 1000, 1500 GeV 16

Strong Coupling Gauge Models Expect observable modifications to WW  coupling. For  ,Z, LC at 500 GeV has precision times better than LHC – in the range expected in Strong Coupling models.  WW gives orthogonal information of comparable precision. Errors on WW  / WWZ coupling for LHC and LC at 500, 1000, 1500 GeV   ZZ Z error Discovery reach for Z’ at LC500 is better or comparable to LHC for different models; better for LC1000 by factor ~2. Extra Dimensions Fields propagating in extra spatial dimensions give observable consequences – e.g. Kaluza Klein excitations, missing E T signatures, modifications to cross sections Many possible phenomenologies to distinguish, depending on size of extra dimensions and fields propagating in the bulk Anomalous top couplings to Z,  are expected, only observable at LC.

~ Large Extra Dimensions : gravity propagates in 4+  dimensions. Modify ee  Z + unseen G KK or angular distributions in ee ff. LC500 and LHC are comparable in reach for fundamental Planck scale M * ; E CM dependence at LC gives   Polarized  WW process has larger sensitivity to graviton exchange for large ED than e + e - or LHC. If supersymmetry in the bulk, KK tower of gravitinos modifies ee ee, sensitive to M * = 12 TeV for  = 6 at LC500 using polarized e -. ~ Warped ED/localized gravity: Sensitivity to KK resonances at LC500 is comparable to LHC; LC1000 exceeds LHC. There are many phenomenological models of Extra Dimensions; LC500 sensitivity is roughly comparable to LHC, but gives complementary information needed to unscramble the character of the model. Extra Dimensions  (ee  G n )  =  =2 3 E CM

LC Resource Book gives several topics for further study:  Scenarios: For different scenarios of physics after 1 st years of LHC, what is the optimum LC program ?  Options: What is the need for , e , e - e - operation for different physics scenarios? Benefit from positron polarization?  IR configuration: NLC has low-energy and extendible high energy IR in baseline. TESLA has optional second HE IR. What is the optimal IR strategy, and how is it physics dependent?  Detector issues: Detector cost driver is energy flow calorimetry; quantify the benefit, and seek optimizations. What benefits from fully silicon strip tracking?  Fixed target: What unique physics can done with fixed target experiments using LC beam ? and …  Physics questions: For each sector of LC physics, studies remain to be done (see Resource Book). A few examples:  Fully simulated study of Higgs branching ratios vs. mass  How well can we profile a 200 GeV Higgs ?  Measure top Yukawa coupling at tt threshold ?  How measure the full chargino /neutralino mixing matrices? Can one determine all 105 MSSM parameters?  How well can CP violation in Susy be measured? What limits can be set on lepton flavor violation?  How can LC measurements illuminate Susy breaking mechanism?  How well can one characterize Strong Coupling models ?  Role of , e , e - e - for extra dimensions studies ?  Cases where LC unscrambles LHC confusion on new physics? Snowmass studies 19

A Linear Collider, starting at 500 GeV and expanding to higher energy, will bring crucial understanding of the main questions before our field, significantly beyond that obtained at LHC. I believe that the US community should embrace a LC proposal in the US, but prepare to strongly engage in the LC wherever it can be built. This workshop offers a timely opportunity for us to assess the capability of the LC, and to guide the future of our field. Summary LC can only be achieved through international cooperation and requires global consensus.