PRECISION&MEASUREMENTS&

Transcription

1 PRECISION&MEASUREMENTS& AT&Z&RESONANCE Z&Lineshape&and&number&of&neutrinos Lecture'2 Shahram&Rahatlou Fisica&delle&Par,celle&Elementari,&Anno&Accademico&

2 EVENT&SELECTION e + e - pairs reconstructed in electromagnetic calorimeter ALEPH μ + μ - pairs in muon chambers typically in the outer layer quarks produce jets with multiple tracks and energy deposits in both electromagnetic and hadronic calorimeters τ + τ - events have missing energy and multiple topologies 1 prong decays with 1 e/mu/pi 3 prong decays require visible energy to be below total center-of-mass energy 1 E 8 6 (GeV) ch N ch 1 Figure 2.1: Experimental separation of the final states using onlytwovariables,th the track momenta, E ch,andthetrackmultiplicity,n ch,inthecentraldetectorofthe experiment. 22

3 SOURCES&OF&BACKGROUND Non-resonant ee ϒϒ q anti-q interaction uniform cross section across spectrum Data driven method to estimate background in signal sample Lower momentum spectrum compared to signal Event not balanced along the beam line Negligible machine background τ + τ - nisi FNSN II 8-29 because of missing neutrino energy can mimic ee/μμ final states selection based on total visible energy helps reducing mis-identification Mode Fraction (Γ i /Γ) Co Modes with one charged particle Γ 1 particle neutrals K ν τ ( 1-prong ) (85.35±.7) % Γ 2 particle neutrals K L ν τ (84.72±.7) % Γ 3 µ ν µ ν τ [a] (17.36±.6) % Γ 4 µ ν µ ν τ γ [b] ( 3.6 ±.4 ) 1 3 Γ 5 e ν e ν τ [a] (17.84±.6) % Γ 6 e ν e ν τ γ [b] ( 1.75±.18) % Γ 7 h K L ν τ (12.3±.11) % Γ 8 h ν τ (11.75±.11) % Γ 9 π ν τ [a] (11.6±.11) % Γ 1 K ν τ [a] ( 6.86±.23) 1 3 Γ 11 h 1 neutralsν τ (36.92±.14) % Γ 12 h π ν τ (25.87±.13) % Γ 13 π π ν τ [a] (25.41±.13) % Γ 14 π π non-ρ(77)ν τ ( 3. ±3.2 ) 1 3 Γ 15 K π ν τ [a] ( 4.54±.27) 1 3 Γ 16 h 2π ν τ (1.76±.15) % Γ 17 h 2π ν τ ( 9.39±.14) % Γ 18 h 2π ν τ (ex.k ) ( 9.23±.14) % Γ 19 π 2π ν τ (ex.k ) [a] ( 9.17±.14) % Γ 2 π 2π ν τ (ex.k ), < scalar Γ 21 π 2π ν τ (ex.k ), vector < Γ 22 K 2π ν τ (ex.k ) [a] ( 5.8 ±2.3 ) 1 4 Γ 23 h 3π ν τ ( 1.37±.11) % Γ 24 h 3π ν τ ( 1.21±.1) % Γ 25 π 3π ν τ (ex.k ) [a] ( 1.8±.1) % 23

4 SAMPLE&PURITY ALEPH DELPHI L3 OPAL qq finalstate acceptance s /s >.1 s /s >.1 s /s >.1 s /s >.1 efficiency [%] background [%] e + e final state acceptance.9 < cos θ <.7 cos θ <.72 cos θ <.72 cos θ <.7 s > 4m 2 τ η < 1 η < 25 η < 1 efficiency [%] background [%] µ + µ final state acceptance cos θ <.9 cos θ <.94 cos θ <.8 cos θ <.95 s > 4m 2 τ η < 2 η < 9 m 2 /s >.1 ff efficiency [%] background [%] τ + τ final state acceptance cos θ <.9.35 < cos θ <.94 cos θ <.92 cos θ <.9 s > 4m 2 τ s > 4m 2 τ η < 1 m 2 /s >.1 ff efficiency [%] background [%] Monte Carlo simulations used to estimate detector acceptance and signal efficiency Reject initial state radiation with s /s requirement 24

5 CROSS&SECTION&MEASUREMENT Nsel: selected number of events σ = N sel N bg ɛ sel L Nbg: estimated background very small at LEP and well measured efficiency & acceptance: well under control through detailed detector simulation Luminosity:.5% uncertainty Very precise measurement of luminosity with bhabha scattering cross section known exactly biggest limitation: detector acceptance at very small angles (2-6 mrad) 25

6 HADRONIC&CROSS&SECTION $ had [nb] 4 3 ALEPH DELPHI L3 OPAL $ 2 % Z 1 measurements (error bars increased by factor 1) $ from fit QED corrected.4 M Z E cm [GeV] Similar energy dependence for muon and tau cross sections 26

7 INVISIBLE&WIDTH&AND&#&OF&NEUTRINOS Largest uncertainty due to luminosity: ~.46 on Nν Γ inv = Γ Z (Γ had + Γ ee + Γ µµ + Γ ττ ) R inv = N ν ( Γνν Γ ll R inv = ( 12πR l σ had m2 Z ) SM ) 1 2 R l (3 + δ τ ) Parameter Average Correlations [MeV] Γ ff Without Lepton Universality Γ had Γ ee Γ µµ Γ ττ Γ bb Γ cc Γ inv Γ had ± Γ ee ± Γ µµ ± Γ ττ 84.8 ± Γ bb ± Lepton& Universality! Γ cc 3.5 ± Γ inv ± $ had [nb] ALEPH DELPHI L3 OPAL average measurements, error bars increased by factor 1 2& 3& 4& E cm [GeV] N ν = ±.82 δn ν 1.5 δn had n had 3. δn lep n lep 7.5 δl L 27

8 DIRECT&MEASUREMENT&OF&#&NEUTRINOS Nucl.Phys.Proc.Suppl.85:67-71,2 d 2 σ de γ d cos θ γ = H(E γ, cos θ γ,s)σ (s ) Experimental signature: empty detector with 1 photon only! Main background: radiative Bhabha scattering electron and positrons lost in the beam line Requirements σ (s) = 12π M 2 Z sγ e N ν Γ ν (s M 2 Z )2 + s 2 Γ 2 Z /M 2 Z Good trigger capability for low energy photons s = s(1 2E γ / s). n by: Good hermiticity at very low angles to discriminate background +W terms( few % of dominant term at Z pole 28

9 RESULTS&OF&DIRECT&MEASUREMENT LEP1 results on N ν with the neutrino counting method Acceptance Y ear L dt Ndata N back Γ inv N ν N ν E γ in GeV pb 1 in MeV Aleph cosθ < E γ > 1.5 ±34 ± 34 ±.2 ±.2 Delphi cosθ < E γ > 3. ±.32 ±.19 L3 cosθ < E γ > 1. ±12 ± 12 ±.7 ±.7 Opal cosθ < E γ > 1.75 ±26 ± 17 ±.16 ±.1 N ν =2.98 ±.7(stat) ±.7(syst) number of events / (.5 GeV) Data $$% signal ee% backgr. %%%+2% backgr. L3 ' (pb) L N $ =4 N $ =3 N $ =2 data E % (GeV) &s (GeV) 29

10 WHY&TWO&METHODS? Different statistics indirect method relies on radiative corrections --> low statistics If New Physics exists we should measure same value with both methods Remember: indirect method measures what we DO NOT see If particle X exists indirect method would measure N < 3 exotic Z decays to undetectable particles accounted for as invisible Direct method measures explicitly decays to neutrinos Two distinctive signatures in direct method photon energy spectrum cross section vs s: peak cross section at slightly higher energy than Z mass New exotic particles could result in peaks beyond Z 3

11 ASYMMETRIES Lineshape measurements allowed the determination of total Z width partial Z width in hadrons and leptons Z mass total of 6 parameters Several observable asymmetries sensitive to fundamental parameters of Standard Model angular distribution to spin 1 of Z boson different couplings for left and right handed fermions possibly use polarization of initial state electrons 31

12 FORWARD8BACKWARD&ASYMMETRY Terms proportional to cos θw provide test of parity violation 2s π 1 N f c dσ ew dcos θ (e+ e ff) = α(s)q f 2 (1 + cos 2 θ) }{{} σ γ 8R { α (s)q f χ(s) [ G Ve G Vf (1 + cos 2 θ)+2g Ae G Af cos θ ]} }{{} γ Z interference +16 χ(s) 2 [( G Ve 2 + G Ae 2 )( G Vf 2 + G Af 2 )(1 + cos 2 θ) } +8R {G Ve G Ae } R {G Vf G Af } cos θ] {{ } σ Z Electron direction assumed as positive hemisphere Asymmetry has dependency on s Contribute only to asymmetry: canceled if integrated over solid angle Contribute only to total cross section and Z width Discrimination of fermions and anti-fermions charge for leptons A FB = N F N B, for quarks look at all info: tagging with leptons N F + N B and displaced vertices for b and c quarks (flavor tagging) e -, f + f, e + 32

13 CROSS&SECTION&DEPENDENCY&ON&POLARIZATION gl gr gl tree = ρ (T3 f Q f sin 2 θw tree ) gr tree = ρ Q f sin 2 θw tree, dσ Ll dcosθ dσ Rr dcosθ dσ Lr dcosθ dσ Rl dcosθ gle 2 g2 Lf (1 + cos θ)2 gre 2 g2 Rf (1 + cos θ)2 gle 2 g2 Rf (1 cos θ)2 g 2 Re g2 Lf (1 cos θ)2. L, R: polarization of initial state electron typically sum over possible polarizations At SLC polarized electron beam l, r: polarization of final state fermion Since coupling constants are different --> very different cross sections to measure 33

14 MIXING&ANGLE&FROM&ASYMMETRY&MEASUREMENT A f = g2 Lf g 2 Rf g 2 Lf + g2 Rf A = 2g Vfg Af g 2 Vf + g2 Af g Vf /g Af =2 1+(g Vf /g Af ) 2 g Vf g Af = 1 2Q f T f 3 sin 2 θ f eff = 1 4 Q f sin 2 θ f eff asymmetry very sensitive to mixing angle fermion charge plays important role in terms of power of measurement leptons: Q 2 = 1 up quarks: Q 2 = (2/3) 2 =.44 down quarks: Q 2 = (1/3) 2 =.11 A f 1.5 ν e e u d L Al Family T T 3 Q ν µ µ Ac L ν τ τ L Ab 1/2 +1/2 1/2 1 ν er ν µr ν τr e R µ R τ R 1 L c s L t b L 1/2 +1/2 1/2 +2/3 1/3 u R c R t R +2/3 d R s R b R 1/3 Less sensitive when smaller factor in front of sin θ sin 2 θ f eff 34

15 Utilize lifetime of decay products: larger for b and c quarks data MC uds MC udsc MC all In addition can use mass of final 1-2 state to separate b and c quarks V No. of Hemispheres uds c LIFETIME&TAGGING DELPHI b s rate rate Data MC Mass (GeV/c 2 ) No. of Hemispheres 35 3 OPAL data Monte 2 Carlo b Monte Carlo c Monte Carlo uds uds decay 3 length 4 significance 5 L/$ 6 L V c Data MC Mass (GeV/c 2 ) Figure 5.4: Reconstructed vertex mass from SLD for data and simulation tagging variable B b ALEPH DELPHI L3 OPAL SLD bpurity[%] befficiency [%] Table 5.2: b-tagging 1-6 performance of the different experiments at the cut where the are performed. The lifetime tagging is combined with other information (see text). tag is an OR of a secondary vertex and a lepton tag. 35

16 LEPTON&FLAVOR&TAGGING Γ 3 Exploit semi-leptonic b and c decays Distinctive spectrum for leptons in final states depending on flavor of original fermion Charge of leptons correlated with parent fermion Higher momentum for leptons from b quark because of higher mass Γ 1 B + ( 4.1 ± 1.3 ) % Γ 2 B ( 4.1 ± 1.3 ) % B s ( 11.3 ± 1.3 ) % Γ 4 b -baryon ( 8.5 ± 2.2 ) % Γ 5 B c DECAY MODES Semileptonic and leptonic modes Γ 6 ν anything ( 23.1 ± 1.5 ) % Γ 7 l + ν l anything [a] ( 1.69±.22) % Γ 8 e + ν e anything ( 1.86±.35) % Γ 9 µ + ν µ anything ( )% Γ 1 D l + ν l anything [a] ( 2.2 ±.4 ) % S=1.8 Γ 11 D π + l + ν l anything ( 4.9 ± 1.9 ) 1 3 Γ 12 D π l + ν l anything ( 2.6 ± 1.6 ) 1 3 Γ 13 D l + ν l anything [a] ( 6.84±.35) % Γ 14 D π l + ν l anything ( 1.7±.27) % Γ 15 D π + l + ν l anything ( 2.3 ± 1.6 ) 1 3 Γ 16 D l + ν l anything [a] ( 2.75±.19) % Γ 17 D π l + ν l anything ( 6 ± 7 ) 1 4 Γ 18 D π + l + ν l anything ( 4.8 ± 1. ) 1 3 Γ 19 D j l+ ν l anything [a,b] ( 2.6 ±.9 ) 1 3 B(D j D + π ) B mesons L3 6 L3 Page 4 Created: 7/3/21 16:47 Number of muons Data uds c fake l b#l b#c#l Number of muons 4 2 Data uds c fake l b#l b#c#l Muon momentum (GeV/c) Muon transverse momentum (GeV/c) 36