Revisiting EW Constraints at a Linear Collider Work done by S. Heinemeyer P. Rowson U. Baer G. Weiglein M. Woods + many others K. Moenig B. Schumm R. Hawkings D. Gerdes G. Wilson L. Orr Lawrence Gibbons Cornell University
Why improve EW parameters? S. Heinemeyer (LC Physics Resource Book) 0.23250 Dominant theory limitations ❚ present theory range 68% CL: M t ❙ 0.23225 LEP/SLC/Tevatron ∆α = α QED (M Z )- α QED (0) ❙ ❚ Three key measurements 0.23200 2 θ eff tt threshold: M t ❙ sin Z pole: sin 2 θ eff ❙ 0.23175 W + W - threshold: M W ❙ 0.23150 0.23125 80.25 80.30 80.35 80.40 80.45 80.50 M W [GeV] 7 Jan 2002 Chicago LC Workshop 2
Why improve EW parameters? S. Heinemeyer (LC Physics Resource Book) 0.23250 Dominant theory limitations ❚ p r e s e n t 68% CL: M t ❙ t h e o 0.23225 r LEP/SLC/Tevatron y r a ∆α = α QED (M Z )- α QED (0) ❙ n g LHC/LC e GigaZ ❚ Three key measurements 0.23200 M H = m t 2 θ eff tt threshold: M t ❙ 180 GeV ∆α sin Z pole: sin 2 θ eff ❙ 0.23175 150 GeV W + W - threshold: M W ❙ 120 GeV 0.23150 Indirect prediction power ❚ M W to ± 4 MeV ❙ 0.23125 M H to +- 8% ❙ 80.25 80.30 80.35 80.40 80.45 80.50 Caveat: must improve ∆α ❚ M W [GeV] 7 Jan 2002 Chicago LC Workshop 3
tt threshold: M t O. Yakovlev (LC Physics Resource Book) 1.75 Kinematic reconstruction ❚ LO 1.5 NLO Hadronic machines ❙ NNLO 1.25 systematics limited 1 R(E) M t to ~ ± 2-3 GeV R 0.75 Measures ~ pole mass ❙ 0.5 Pole mass ill-defined in QCD ❚ 0.25 Nonperturbative ambiguity ❙ 344 346 348 350 352 of O ( Λ QCD ) in definition √ s (GeV) ❙ Eg., poorly-behaved perturbation series for threshold cross-section Want short-distance mass, eg. M t (M t ) ❚ EW constraints, ∆ M B , … ❙ 7 Jan 2002 Chicago LC Workshop 4
tt threshold: M t (LC Physics Resource Book) 1.4 Large Γ t (~1.4 GeV) a boon ❚ LL 1.2 NLL 1.0 NNLL Γ t >> Λ QCD ⇒ no narrow ❙ 0.8 resonances, smooth line R 0.6 shape 0.4 Allows calc. in pert. QCD 0.2 ❙ 0.0 infrared cutoff, smearing R 346 347 348 349 350 351 352 353 354 �� � � √ s � Ge V � 0.8 A few short-distance mass def’s near threshold ❚ m t =170 GeV 0.6 σ eff (pb ) 1S peak position stable to ~200-300 MeV ❙ 0.4 Masses related to MS mass via pert. QCD series ❙ 0.2 1 fb –1 /point Modest luminosity required ❚ 0 332 336 340 344 s (GeV) 10 fb -1 → ± 40 MeV stat. uncertainty ❙ M t to ± 200 MeV M t to ± 200 MeV 7 Jan 2002 Chicago LC Workshop 5
Other top measurements High energy ❚ Threshold ❚ ❙ Yukawa coupling Total top width ❙ e + e - → tth → W + W - bbbb R Peak σ ~ 1/ Γ t R 800 GeV (1000 fb -1 ): ~5.5% R 100 fb -1 → ~2% uncertainty R R 500 GeV: ~4x worse Yukawa coupling ❙ ❙ All neutral and charged current 115 GeV Higgs → 5-8% R couplings increase in threshold σ Measure/limit mostform R 2-3% uncertainty in R factors at 1% level predicted cross section 500 GeV, 100-200 fb -1 • • 14-20% on Yukawa ttZ couplings unique to LC R coupling • production polarization asymm. Sensitivity drops for R ❙ Test QCD, EW radiative corr. increasing Higgs mass σ (e + e - → tt → l ν jjbb) to < 1% R 7 Jan 2002 Chicago LC Workshop 6
sin 2 θ W status LEPEWWG: summer 2001 At Z pole: dominated by ❚ Preliminary 0,l A 0.23099 ± 0.00053 LEP b quark A b ❙ fb FB A l (P τ ) 0.23159 ± 0.00041 SLD A LR ❙ A l (SLD) 0.23098 ± 0.00026 A b 0,b ❙ FB : not in best agreement A 0.23226 ± 0.00031 fb 0,c A 0.23272 ± 0.00079 w/ SM fb < Q fb > 0.2324 ± 0.0012 Lower energy scales ❚ Average 0.23152 ± 0.00017 χ 2 /d.o.f.: 12.8 / 5 Recent NUTEV result ❙ 10 3 m H [ GeV ] “3 σ high” ❘ atomic parity violation ❙ ∆α (5) ∆α had = 0.02761 ± 0.00036 10 2 ~2 σ low ❘ m Z = 91.1875 ± 0.0021 GeV m t = 174.3 ± 5.1 GeV 0.23 0.232 0.234 lept sin 2 θ eff 7 Jan 2002 Chicago LC Workshop 7
Giga-Z ❚ Revisit Z pole with a linear collider Expect L ~ 5 x 10 33 cm -2 s -1 ❙ 10 9 Z decays in ~ 10 7 s ❙ Could contemplate interruption of high energy program R 10 10 Z decays: 3-5 year program ❙ Would need simultaneous low energy/high energy running R Mainly heavy flavor program benefits R Polarization ❙ 80% electron polarization a given R R positron polarization an enormous boon: achievable? • 60% polarization desirable 7 Jan 2002 Chicago LC Workshop 8
Z pole scan ❚ Measured ❚ Extracted M Z M Z : ± 2 MeV → LC E scale ❙ ❙ ❙ Γ Z 2 ): ± 0.0027 → ± 0.0009 α S (M Z ❙ → 2 σ 0 ∝ Γ had Γ ll/ Γ Z ❙ ρ l : ± 0.001 → ± 0.0005 ❙ R l = Γ had / Γ ll ❙ N ν : ± 0.008 → ± 0.0004 ❙ Current measurements systematics limited ❚ 2x improvement on eff. syst. (no th’y improvement for L ) ❙ R 4x R l , 30% σ 0 improvements δ E beam / E beam : potentially 10 -5 w/ Moller spectrometer? ❙ 2x Γ Z improvement R Energy spread: beamstrahlung to O (2%): further study needed ❙ Γ Z , ρ l limited otherwise R R monitor with Bhabha acolinearity? 5 point scan? 7 Jan 2002 Chicago LC Workshop 9
A LR → sin 2 θ W 20 18 P - =0.8 A LR the most sensitive ❚ 16 variable to sin 2 θ W 14 ∆ A LR x10 5 12 1 − 4sin 2 θ W eff A LR = 1 N L − N R 10 = A e = 2 2 P N L + N R 1 + 1 − 4sin 2 θ W eff ( ) 8 − 6 GigaZ = 2000x SLD ❙ 4 2 SLD: A LR =0.1514 ± 0.0022 ❘ 0 e + polarization: 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 ❚ P + ❙ None: δ P - /P - dominates uncertainty: 0.25% (optimistically) feasible ∆ A LR to 4x10 -4 ❘ With: use Blondel scheme (combine N LL ,N RR ,N LR ,N RL ) ❙ ❘ 60% P + ↔ effective 95% polarization, don’t need absolute polarization ⇒ ∆ A LR to 10 -4 ❘ 7 Jan 2002 Chicago LC Workshop 10
A LR → sin 2 θ W : experimental issues ❚ polarization Blondel scheme: need relative L,R polarizations to 10^ -4 ❙ Appears feasible ❘ Systematics: polarimeters after IP? ❙ • Difficult w/o crossing angle Can positron helicity be switched rapidly enough relative to ❙ beam stability? ❘ What is the relevant time scale? 7 Jan 2002 Chicago LC Workshop 11
A LR → sin 2 θ W : experimental issues ❚ Z- γ interference: A LR changes rapidly away from pole Control δ E/E to 10 -5 ❙ Control of beamstrahlung (effective √ s shift) ❙ Ignore: A LR shift of 9x10 -4 at TESLA, much worse at NLC ❘ E scale from Z pole scan + LEP M Z . Same beam parameters? ❘ Trade L for reduced beamstrahlung ❘ • NLC:125 → 18 MeV E shift for factor 5 L penalty ❚ If beam issues controlled: sin 2 θ W to ± 0.000013 sin 2 θ W to ± 0.000013 7 Jan 2002 Chicago LC Workshop 12
Zbb vertex 0.94 A b : 2.5–3.5 σ discrepancy w/ SM ❚ + SM LEP/SLD persists Giga-Z 68% c.l. Stat’s dominated measurement ❙ 0.92 Complementary sensitivity to ❚ “new physics” than S,T,U A b R b = Γ bb / Γ had 0.9 ❚ Measure corrections to Zbb vtx ❙ R EW prop., QCD corr. cancel 0.88 5x improvement from b-tagging ❙ ❚ A b (=3/4 A FB,LR ) P + =60%: 15x improvement ❙ 0.215 0.216 0.217 0.218 0.219 P + =0: 6x improvement ❙ R b 7 Jan 2002 Chicago LC Workshop 13
b physics at Giga-Z? 4 ❚ Great potential P - =+0.8 P + = -0.6 P - = -0.8 P + =+0.6 P - =+0.8 P + =+0.6 3 ❙ Production flavor tagging P - = -0.8 P + = -0.6 d σ /dcos θ ε D 2 ~0.6 vs 0.1-0.25 R 2 R D=1-2P(mistag) 1 Large boost ❙ 0 R b’s well-separated -1 -0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8 1 b quark cos θ Excellent b tagging R 0.5 ❙ Well-defined initial state: 0.4 mistag fraction ” ν -reconstruction” R 0.3 Stiff competition ❚ 0.2 Mainly cross checks others on ❙ 0.1 “standards” 0 -1 -0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8 1 R CKM unitarity angles event thrust axis cos θ ∆ m s R 7 Jan 2002 Chicago LC Workshop 14
Some unique b physics B s → Xl ν rate ❚ Constrain uncontrolled uncertainty in OPE from quark-hadron ❙ duality violations Polarized Λ b decays (G. Hiller) ❚ Probe b R → q L γ (SM) vs b L → q R γ (new physics) ❙ 10 9 Z’s gives interesting reach in θ (spin,p γ ) asymmetry R B → X s νν ❚ Emiss constraints + well-separated b decays allow access ❙ Non-SM physics affects X s νν , X s l + l - differently ❙ ❙ reach? B →τν bkg? Production flavor tagged B →π 0 π 0 ❚ 7 Jan 2002 Chicago LC Workshop 15
W + W - threshold: M W ❚ Potential indirect precision: δ M W ~ ± 4 MeV Tevatron/LHC: expect 15-20 MeV precision (syst. limited) ❙ ❚ EW constraints: can LC approach indirect precision? E beam , beamstrahlung appear to be most serious issues ❙ high energies: direct reconstruction needs E beam constraint R • E scale likely to be pinned via M Z ⇒ explore threshold region • Beamstrahlung scales as (E beam ) 2 Threshold needs: ❙ E beam to 10 -5 : potentially e + e - → γ Z, Z → µµ ,ee? R • Stat’s for √ s vs time? Beamstrahlung: control shape distortion to 0.12% ↔ ± 2 MeV R • Bhabha acolinearity? Theory: cross section shape to 0.12% R 7 Jan 2002 Chicago LC Workshop 16
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