Beta Decayu

d

e

d

eu

Probability Scattering ~

E

 100 GeV 2

W

→ MW 80 GeV

Just as the unitarity violation in beta decay “told” us that there was new Weak physics at about 100 GeV …

I. What is the natural scale for LC physics?

WW Scattering

WL

WL

WL

WL

WLWL

WLWL

?

M 1000 GeV

Probability Scattering ~

E

 1000 GeV 2

So also does the unitarity violation in WW scattering “tell” us that there is new physics at the TeV scale.

I. What is the natural scale for LC physics?

II. Several known SM physics topics benefit from energy:

WWh vertex

ZZH vertex

Cross section for Higgs production through WW fusion grows with energy. The WWh coupling is a key parameter.

Yukawa coupling of top quark (ttH coupling) benefits strongly from increased energy.

(Mh = 120 GeV)

BR

MH

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%

To be sure, some measurements require high luminosity at moderate energies; Higgs branching ratios (for mH < 150 GeV) are important to determine nature of beyond-SM physics (e.g. predict higher Susy Higgs masses).

As far as we know, the errors on the Higgs branching ratios scale as √N . But if there is Susy, these BRs will tell us the mass of the higher mass pseudoscalar Higgs (A) that we will want to find. MA is likely to be large (hundreds of GeV), requiring higher energy reach. (And may dictate high energy operation of collider to access spin-parity measurement.)

II. SM physics topics:

Measuring the Higgs self-coupling is likely to require both large luminosity and high energy (and very powerful detectors).

III. New physics benefits from energy (we confidently expect beyond-the-SM physics at the TeV scale) :

IIIa) Supersymmetry:

Supersymmetry is widely expected to have its sparticle states in the 500 – 1500 GeV range. The pattern and scale depend on the mechanism of Susy breaking and details of parameters. The partners of leptons and gauge bosons (very difficult for LHC) tend to be lower in mass than the squarks and gluinos (copiously produced by strong interactions at LHC).

We need the LC to determine the sleptons, sneutrinos and gauginos.

336 336 160 244 92

494 489 228 355 233

650 642 294 464 304

1089 858 462 750 459

e e/920 922 1620 396 470

860 850 1594 314 264

Z h 186 207 203 184 203

Z H/A 1137 828 950 727 248

H+ H - 2092 1482 1724 1276 364

q q 1882 1896 1828 1352 1010

~

~ ~

~

~~

reaction

~ ~

Thresholds for selected sparticle pair productions -- at allowed LHC mSUGRA model points.

Recall that the Susy particles are produced in pairs. Table shows pair thresholds in five variants of gravity mediated models (whose mass spectrum is somewhat below that of some other model classes).

RED: Accessible at 500 GeV

BLUE: added at 1 TeV

Point 1 2 3 4 5 GeV GeV GeV GeV GeV

The point is that if there is Susy, it is very likely that raising the energy of the LC will give substantial benefit.

IIIa) Supersymmetry:

Don’t take these thresholds literally! Strong variation with underlying Susy parameters.

The most accurate mass information comes from threshold scans – providing one has enough energy to see the pairs of particles.

IIIa) Supersymmetry:

Threshold scans give high precision, providing one has the energy required.

Measuring the masses of Susy particles is a key to understanding what breaks supersymmetry; LHC measures the gluino mass (M3); Linear collider is essential to obtain the weak counterparts (M1 and M2) through the measurement of the lowest pair of neutral and lowest charged partners to the (Z,,higgs).

In the end, these determinations of the Susy breaking sector are the most important in the LC Susy program.

If you don’t make the sleptons and gauginos, you can’t make these extrapolations.

IIIa) Supersymmetry:

Width of bands are due to errors in LHC or LC measurements. This case is for mSUGRA, where the extrapolation of gaugino or sparticle masses to common values is indicative of the Susy symmetry breaking mechanism.

Gaugino mass extrapolation

sfermion mass extrapolation

IIIb) Strong Coupling (Technicolor etc.):

It is possible that electroweak symmetry breaking is generated by new strongly coupled states whose mass spectrum should be in the range of 1 – 10 TeV. There excited states of Z. The effects of these states are seen at lower energies through precision measurements whose sensitivity depends strongly on energy.

M= 1240 GeV M=2500 GeV

signifi

cance

Signal significance for techni-rho observation for LHC and LC at 500, 1000, 1500 GeV. (note logarithmic scale)

Z Z

Errors on WWZ couplings for LHC and LC at 500 , 1000 , 1500 GeV. Discovery reach for Z’ at LC500 is better or comparable to LHC for different models; better for LC1000 by factor ~2. (note logarithmic scale)

err

or

10-2

10-

4

IIIc) Large extra dimensions:

It is possible that electroweak symmetry breaking is generated by large extra spatial dimensions, effectively reducing the Planck mass to the 1-1000 TeV scale.

Linear collider

LC measurement of the energy dependence of ‘mono-photons’ due to gravitons escaping into the extra dimensional ‘bulk’ tells us the number of large extra dimensions. (LHC cannot do this.) Increasing the energy wins over adding luminosity for this measurement.

IIIc) Large extra dimensions:.

Other extra dimension models predict towers of Kaluza Klein states (similar to excited Z bosons). Increasing the energy reach gives more opportunity to observe.

IV: Summary

The LEP, SLC, Tevatron, HERA measurements tell us that the scale for new phenomena is around 1 TeV, hence the target of a TeV scale LC

The Standard Model is flawed, and we expect new physics at the TeV scale

The known implementations of Electroweak symmetry breaking and new physics are not precise enough to pinpoint the ‘right’ maximum energy. The new particle spectra, or the incisiveness of precision measurements in inferring new physics, give a premium on the ability to raise the energy.

High luminosity is needed, but in many cases, having sufficient energy is the key to seeing the new physics.