# Presentation: 325727

## Linear Collider Physics Studies

- 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

## 	                      TESLA          JLC-C      NLC/JLC-X Ldesign                (1034)          3.4      5.8          0.43             2.0      3.4

- ECM 	           (GeV)          500     800          500            500     1000
- Gradient  (MV/m)           23.4     35             34                   70
- RF freq.           (GHz)             1.3                  5.7                 11.4
- tbunch 	         (ns)        337     176           2.8                  1.4

**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: ECM = 500 GeV,                    1 year @ 1x1034 **cm****-2****s****-1**** **

- TESLA TDR  DESY 2001-011 (March 2001)                                                                    NLC,  _[http://www-project.slac.stanford.edu/lc/wkshp/snowmass2001/](http://www-project.slac.stanford.edu/lc/wkshp/snowmass2001/)_             US and Japanese X-band R&D cooperation; machine parameters may differ

- Linear ee Colliders

- H

- HZ

- Hee

- MH

- (fb)

- (fb)

- qq

- WW

- tt

- 

- RR

- Zh

- HA

- ~

- ~

- ~

- ~

-              ECM

- ECM =500 GeV

- E=500 GeV

- 800 GeV

- 103

- 106

-   1

- 2

- electron polarization ~ 80%;  may have positron polarization ~60%        Optional e- e-e- collisions at reduced luminosity for special physics

## Study the `Higgs boson’ (or its surrogate) and measure its characteristics.

- 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-ex0106055, 056, 057, 058    including:                            	  “The Case for a 500 GeV e+e- Linear Collider”, hep-ex/0007022 )

- (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

## What is the Higgs ??

- Measurements tell us Higgs mass is low:                                                 (SM) Mhiggs < 190 GeV at 90% CL.         LEP2 limit Mhiggs > 113.5 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**** = 115.0 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 !!

- 4

## Program for Higgs Study

- 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 gHVV  coupling ?       (are there more Higgs?)

- Measure the **quantum numbers** of the Higgs states: for the SM, expect JPC = 0++ ; for Susy, both 0++ and 0-+.

- 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 !**

- 5

## TOT  to few%  for M > 110 GeV.  

- BR(H      WW*) = WW / TOT          WW  from  ZH  or  WW fusion.
- Test for unexpected Higgs decays

- TOT  to few%  for M > 110 GeV.

- 100

- 150

-  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.

-  Total width

- 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

## Higgs Couplings

-    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 MA well above ECM.
- 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;  mh < mH );   **A****0** (CP odd);   **H**
- For Susy mass scale < 1 TeV, Mh < 135 GeV .   Higgs sector in MSSM controlled by tan = <> / <>  and  mA .   At large mA,  h0 becomes SM-like and H0,A0,H  become massive and nearly degenerate.    (decoupling limit)

- From likelihood fn’s  using vertex, jet mass, shape information

- (Mh = 120 GeV)

- BR

- MH

- (lose the ff BRs for     MH > 180 GeV, except tt)

- 7

## Higgs spin parity

- = cm production angle;      = fermion decay angle in Z frame

-                                     JP = 0+                       JP = 0
-         	        d/dcos         sin2               (1 - sin2 )
-     	     d/dcossin2              (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 self couplings

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## LC must be able to sort out which is at work. Can imagine cases where LHC sees new phenomena, but misunderstands the source.

-         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

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##    Supersymmetry

- 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 (JP = 1- )

-    Supersymmetry

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## ~

**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 eL+ eL-  and eR+ eR- .  Bkgnd WW suppressed for beam eR- .

- e-

- e-

- e+

- e+

- e+

- e+

- e-

- e-

- ,Z

- 

- e       e  

- eL,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

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## Masses are again determined from end points in reactions like    e+ e-        with decays:

- 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:
-      M2() +M2() =  M22 + 2 M2(W)  + 2
-        M() xM()    = M2 - M2(W) sin(2)

- e+

- e+

- e-

- e-

- 

- 

- 

- 

- Z

- 

- ~

_**e**__**-**__** Polarization is again crucial**_:
**e****R****- ****e****+       **************************   removes the t-channel diagram;  cross section and AFB  give the higgsino/wino content of .    Tests of Susy relations are possible (e.g. measure MW to   ~ 23 MeV from purely Susy quantities.)

- ~

** ****e****L****- ****e****+       ******************************has strong s & t channel interference, sensitive to m( ) to about 2 ECM.

**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

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##   Linear Collider Supersymmetry

- 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

- ~

- ~

-   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 10
- (g-2) result suggests relatively light sfermions or charginos, if Susy is at work.

- ~

- ~

-   Linear Collider Supersymmetry

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**These points need updating**** **

## Susy breaking mechanism

- 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.

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## Precision studies constrain ANY new physics

- sin2 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

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##     Strong Coupling Gauge Models

- 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

- MW=30 MeV, MTop=2 GeV

-     Strong Coupling Gauge Models

- 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****.**

- MH

- Technirho relative signal significance for  **LHC  **and **     ****LC **at **500****,**  **1000**, **1500** GeV

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##     Strong Coupling Gauge Models

-     Strong Coupling Gauge Models

- Expect observable modifications to WW coupling.   For ,Z , LC at 500 GeV has precision 10-20 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

-     error

-      error

- Discovery reach for **Z’ **at** LC500** is better or comparable to** ****LHC **for different models; better for** ****LC1000** by       factor ~2.

- Fields propagating in extra spatial dimensions give observable consequences – e.g. Kaluza Klein excitations, missing ET signatures, modifications to cross sections
- Many possible phenomenologies to distinguish, depending on size of extra dimensions and fields propagating in the bulk.

- 10-2

- 10-4

- 10-2

- 10-4

- 17

- Anomalous top couplings to Z, are expected, only observable at LC.

##    Extra Dimensions

**Large Extra Dimensions****:  **gravity propagates in 4+dimensions.  Modify            ee      Z + unseen GKK or angular distributions in       ee       ff .  **LC500** and **LHC** are comparable in reach for fundamental Planck scale M*;                 ECM 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    Gn)

- =6

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- 3

- 4

- 5

- =2

- 3

- ECM

- 400

- 600

- 800

## Snowmass studies

-    **Scenarios:  **For different scenarios of physics after 1st 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?

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## Summary

- 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.