The measurements of the forward-backward asymmetry in Z -> c cbar and Z -> b
bbar decays are among the most precise determinations of sin^2(theta)_W. In
this paper the results obtained by the DELPHI experiment at LEP with three
different analyses are reviewed together with the impact of the combined LEP
result on the global Electroweak fit.Comment: 7 pages, RevTeX, fonts changed in 2 eps file

Migliore, Ernesto

English

arXiv

The measurements of the forward-backward asymmetry in Z -> c cbar and Z -> b bbar decays are among the most precise determinations of sin^2(theta)_W. In this paper the results obtained by the DELPHI experiment at LEP with three different analyses are reviewed together with the impact of the combined LEP result on the global Electroweak fit.The measurements of the forward-backward asymmetry in Z -> c cbar and Z -> b bbar decays are among the most precise determinations of sin^2(theta)_W. In this paper the results obtained by the DELPHI experiment at LEP with three different analyses are reviewed together with the impact of the combined LEP result on the global Electroweak fit

CERN Document Server

Heavy quark asymmetries with DELPHIErnesto MiglioreCERN, CH-1211 Geneva 23, SwitzerlandThe measurements of the forward-backward asymmetry in Z → cc¯ and Z → bb¯ decays areamong the most precise determinations of sin2 θ`W,eff . In this paper the results obtained by theDELPHI experiment at LEP with three different analyses are reviewed together with the impact ofthe combined LEP result on the global Electroweak fit.I. INTRODUCTIONAs a consequence of the parity violating couplings of the Z boson to the fermions, in electron positron annihilationat the Z mass fermions are more likely produced in the forward direction, with respect the incoming electron, than inthe backward. In the Electroweak Standard Model the asymmetry at the Z pole 1 is expressed as:Af,0FB =34AeAfAe and Af are functions of the ratio xf of vector vf and axial af couplings of the Z boson to the fermions:Af = 2xf1 + x2fThe ratio depends on the quantum numbers of the fermion, the charge Qf and the weak isospin I3,f , and on thefundamental parameter of the theory the electroweak mixing angle sin2 θW : xf = 1− 4|Qf | sin2 θW .The dependence of the Born level Af on sin2 θW for different fermion species is shown in fig 1: For sin2 θW ' 0.23the asymmetry for qq¯ final states is from 3 to 5 times larger than for leptonic final states.FIG. 1. Dependence of Born level Af on sin2 θW for leptons, up-type quarks and down-type quarks.As among all the qq¯ final states the decays of the Z boson into cc¯ and bb¯ pairs are the most easily distinguished,the experimental effort was concentrated on the measurement of AcFB and AbFB.Most of the electroweak radiative corrections can be accounted for by introducing in the Born level equations aneffective electroweak mixing angle sin2 θfW,eff defined for each fermion family. On the contrary the sensitivity of thequark asymmetry to the final state couplings is heavily suppressed. This can be understood from the the dependenceof the sensitivity on Qf and xf :1Throughout this paper pseudo-observables defined at the Z pole are indicated with an apex 0 while values measured at theZ peak (√s = 91.26 GeV) without.11Af∂Afsin2 θfW,eff= 4|Qf |1− x2fxf (1 + x2f )The final state c and the b quarks have a smaller charge and a higher value of xf compared with the initial stateleptons. The sensitivity to the quark couplings is reduced of about a factor 50 for the b and 5 for the c asymmetry.The main motivation for a precise measurement of the asymmetry is that mH , the mass of the still undiscoveredHiggs boson, enters in the definition of sin2 θ`W,eff . Table I shows that, even if the dependence is only logarithmic, themeasurement of Ab,0FB sets currently the most stringent limits on mH : A 4 % accuracy in the determination correspondsto values of the mass of the Higgs boson in a range from 70 GeV/c2 to 1000 GeV/c2. On the contrary the ratios ofpartial widths of the Z boson into cc¯ and bb¯ pairs are, in practice, not sensitive to mH at all. The current precisionon Ab,0FB is smaller than this value and the prediction on the Higgs boson mass is spoiled mainly by the uncertaintyon αQED(M2Z).TABLE I. Dependence of the electroweak pseudo observables in the heavy flavours sector on radiative correction (from [1] ).mt = 175 GeV/c2 ±6 GeV/c2mH = 300 GeV/c2 +700−230 GeV/c21/αQED(M2Z) = 128.896 ±0.090Ab,0FB0.0998 ±0.0010 −0.0037+0.0042 ∓0.0013Ac,0FB0.0711 ±0.0008 −0.0028+0.0032 ∓0.0010R0b 0.2158 ∓0.0002 0 0R0c 0.1722 ±0.0001 0 0II. EXPERIMENTAL TECHNIQUES.All the analyses of the asymmetry follow three steps: The tag of the flavour of the decay of the Z boson, thedetermination of the direction of the primary quark and the separation of quark and antiquark hemispheres. Theanalyses described [2] differ on how the tag is performed: Exploiting the long flight distance of the heavy flavouredhadron, the presence of a high momentum lepton or finally a reconstructed D meson in the final state 2. This choicedetermines also how the assignment of quark-antiquark hemispheres is done: Using the charge flow in the event orthe charge of the identified lepton or the charge state of the D meson. Common to the analyses is the determinationof the direction of the initial qq¯ pair done with the thrust axis of the event conventionally oriented to form an angleθT < 90◦ with the direction of the incoming electron beam. The observed asymmetry is finally extracted from a χ2 fitto the differential asymmetryN+i−N−iN+i+N−iwhere N+i (N−i ) is the number of forward (backward) events in bin i of cos θT .A. Ab,0FBusing jet charge technique.Methods exploiting the long fly distance of b-hadrons (γβcτb ∼ 2 mm) and the accurate resolution on secondaryvertex reconstruction of silicon vertex detectors provide the most efficient way to select a sample of bb¯ events. In orderto maximize the efficiency versus purity performance the b-tag algorithm used in the DELPHI experiment combinesthe informations from the reconstructed secondary vertex (its effective mass, the rapidity of the tracks associated toit and the fraction of the jet energy carried by them) with the lifetime information.2If not explicitly mentioned charge conjugate states are implicitly included.200.10.20.30.40.50.60 1 2 3 4 5 6 7 8 9btag variable 1/N dN/d btagdatalight quarksc quarksb quarksFIG. 2. Distributions of the b-tag variable in data and simulation for 1994 data.In the measurement of Ab,0FB the fraction Pb(cut) of bb¯ events in the sample after a cut in the b-tag variable isdetermined from the data themselves using the relation:Pb(cut) =F (cut)−Rc × εc(cut)− (1−Rc −Rb)× εuds(cut)F (cut)where F (cut) is the fraction of the data after the cut, εuds(cut) and εc(cut) the efficiencies for light (q = u, d, s) andcharm quark taken from the simulation and Rc and Rb the partial widths of the Z into cc¯ and bb¯ pairs from theStandard Model. Fig. 2 shows the distribution of the b-tag variable in data and in simulation. The value of the tagchosen for the analysis corresponds to εb = 75% and Pb = 92%.The separation of b from b¯ quark relies on the hemisphere charge Qhem defined as the sum of the charges qi of thetracks in each hemisphere, as defined by the thrust axis ~T , weighted by the projection of their momenta ~pi along ~Titself, to some power κ:Qhem =∑i qi|~pi · ~T |κ∑i |~pi · ~T |κThis estimator is based on the fact that, due to the electric charge conservation, the particles produced in thehadronization of the primary quark retain some information of its charge. In the analysis done by DELPHI κ = 0.8.This choice minimizes the total statistical and systematic error.In each event the total charge QTOT = QF + QB and the charge flow QFB = QF −QB are measured. A part fromreinteractions 〈QTOT 〉 ' 0, while the average charge flow is directly related to the asymmetries:〈QFB〉 =∑PqηqδqAqFB (1)Pq is the fraction of events of flavour q in the sample, ηq is an acceptance correction factor and δq = 〈Qq − Qq¯〉 isthe charge separation: It would be twice the charge of the quark if quarks would be observed directly. As for Pb, thecharge separation for b quark is measured directly in the data. The principle of the method is sketched in fig. 3: Fora pure b sample the charge separation leads to an increase of the spread σFB of the distribution of QFB comparedto σTOT from the distribution of QTOT so that δ2b ' σ2FB − σ2TOT . As for the sample composition δu,d,s,c are takenfrom the simulation, carefully tuned in order to reproduce the measured distributions of hadronic event shapes andcharged particle inclusive quantities. -2 0 200.51-2 0 2  dN/dQ TOT  sumquark backwardquark forward QTOTσfσf00.51dN/dQ FB  <QFB>QFBδfσfσfσFB-2 0 2FIG. 3. Sketch of the principle of the 〈QFB〉 and the δf measurement for a single (down type) flavour f.3The observable 〈QFB〉 in data and simulation as a function of increasing b-purity of the sample is shown in fig 4: Theobserved difference is due to different values of both δb and the input asymmetry between data and simulation.-0.02-0.0170. 75. 80. 85. 90. 95. 100.MCDATA κ = 0.8b purity (Pb) [%]< Q FB >FIG. 4. 〈QFB〉 as obtained from data and simulation for κ = 0.8 and for 1994 data.To exploit the angular dependence of the asymmetry itself, AbFB is extracted from a χ2 fit of equation 1 to 〈QFB〉distribution in 4 bins of cos θT , the acceptance being limited to θT > 35◦ by the actual angular coverage of the vertexdetector.The results for the Z peak asymmetry for 1992-95 sample is AbFB = 0.0982± 0.0047 (stat). The main contributionsto the systematic error are listed in the top part of table II. The largest contribution (±0.0011) comes from thehemisphere-hemisphere charge correlation which is due to charge conservation, the common thrust axis and theparticle crossovers between hemispheres. This correlation is checked between data and simulation by means of thevariable H defined such that differences in the description of the secondary interactions mostly cancel out: H =〈QF QB〉 − 〈QTOT 〉2/4. The systematic error accounts for 20 % discrepancy between data and simulation found inthe distribution of H .Effects related to the description of the physical processes which could effect the b-tag performance (gluon splittinginto cc¯ and bb¯, K0 and Λ content in light quark events, lifetimes, spectra and production fraction of D mesons) aresmaller than ±0.0003 each.TABLE II. Main contributions, in units of 10−3, to the systematic error to AcFB and AbFB for Z peak data.δAcFB δAbFBJet Charge tag R0c ± 5% ± 0.4H charge correlation ± 1.1Detector resolution ± 0.7total ± 1.6leptons tag c decay model ∓ 1.8 ± 1.4b → c¯ → ` ± 1.9 p⊥ and jet reconstruction ± 1.3bgd asymmetry ± 4.7 B0B¯0 mixing ± 1.1total ± 6.3 ± 2.7D mesons tag MC stat ± 2.5 ± 3.5fit method ± 1.7 ∓ 2.8bgd asymmetry (b, c quark) ∓ 1.3 ∓ 3.6χeff ± 5.8total ± 3.5 ∓ 8.5B. Ac,0FBand Ab,0FBusing prompt leptons.Electrons and muons are produced in the decay of heavy flavoured hadrons mainly by 3 processes with a branchingratio of about 10 % each:• primary semileptonic b decays, b → `−• weak cascades of b hadrons, b¯ → c¯ → `−• primary semileptonic c decays, c¯ → `−4These leptons can be used to select on statistical basis cc¯ or bb¯ events as they have momentum (p) spectrum harderthan fragmentation particles, 〈xE〉c ∼ 0.5 and 〈xE〉b ∼ 0.7, and high transverse momentum (p⊥) with respect thedirection of the jet 3, because of the high mass of the parent hadron.The correlation between the charge of the lepton and the one of the quark is exploited to determine the quarkhemisphere. The correlation is different in the three classes, resulting in a dilution of the measured asymmetry:AobsFB = (1− 2χ)(fb − fbc)AbFB − fcAcFB + fbgdAbgdFB (2)where the fi’s are the composition of the sample, (1− 2χ) is the dilution factor due to the B0B¯0 mixing and the lastterm accounts for a non zero asymmetry of the misidentified hadrons (mainly punch through hadrons and photonconversions) and non prompt leptons from K and pi decays.DELPHI has recently introduced in the analysis of the data collected in 1994-95 the use of lifetime based b-tagvariable which is used to remove the decays of the Z into light quarks final states. This allows an estimation of thebackground level less dependent on the momentum of the lepton compared to the previous procedure. This consistedfirst in the selection of a high (p, p⊥) region, highly pure in the lepton content, which fixed the lepton identificationefficiency and then in the evaluation of the background level in a low (p, p⊥) region. Moreover the use of the b-tagenriches the sample in cc¯ events increasing the sensitivity of the measurement to AcFB. On the contrary the reductionof the statistical error for the b asymmetry is smaller. This is because the useful sample is limited to the region ofpT > 1 GeV/c as the lower pT region is equally populated of primary b and cascade leptons giving opposite signcontributions to the observed asymmetry: The b-tag variable has little effect in separating these two classes of events.The results for the Z peak asymmetry for 1991-95 statistics are AcFB = 0.0770± 0.0113 (stat) and AbFB = 0.0998±0.0065 (stat). The main contributions to the systematic error are listed in the central part of table II. The variouscontributions can be separated into two categories: The terms arising from the model actually used to simulate thesemileptonic decay processes and the ones related to the description of detector effects. In case of the b asymmetrythey both amount at about ±0.002 the largest effect coming from the description of the c decay (±0.0014).C. Ac,0FBand Ab,0FBusing reconstructed D mesons.A reconstructed D meson uniquely tags a hadronic decay of the Z boson into a heavy flavour qq¯ pair as it can beproduced only in the hadronization of a primarily produced cc¯ pair or in the decay of a b-hadron in a bb¯ event. Thecharge state of the reconstructed D meson is correlated with the charge of the parent quark. Therefore the values ofAc,0FB and Ab,0FB are extracted form a χ2 fit to the distribution of cos θT in D meson events.The analysis done by DELPHI is based on the investigation of 8 decays channels:D∗+ → D0pi+sl→ (K−pi+)pi+sl→ (K−pi+pi−pi+)pi+sl→ (K−pi+(pi0))pi+sl→ (K−µ+ν¯µ)pi+sl→ (K−e+ν¯e)pi+slD0 → K−pi+D0 → K−pi+(pi0)D+ → (K−pi+)pi+The first step in the analysis is the reconstruction of D0 and D+ mesons. In case of D0 a low momentum pion pisl(p∗ = 40 MeV/c) with the correct charge correlation with the meson is searched for the D∗+ reconstruction. The mostrelevant characteristics of the DELPHI detector for this part of the analysis are the particle identification providedby the RICH and the specific energy loss dE/dx measured by the TPC [3]. These informations are combined into a3The axis of the jet is defined excluding the lepton momentum.5pion veto used in the D0/+ channels to reduce the combinatorial background which mainly consists of misidentifiedpions.Further reduction of the background is achieved with cuts in the helicity angle of the kaon candidate with respectthe D0/+ flight direction and in the 3D decay length of the meson. These cuts are applied in function of the scaledenergy of the meson XE(D) = 2ED/√s to account for the energy spectrum of charged particles in hadronic Z decays,peaked at low momentum. Finally candidates are selected either in a ∆m = mD∗ −mD0 region for D∗+ channels, orin a mass interval for a D0/+ decay. The range of ∆m values goes from 160 MeV/c2 to 250 MeV/c2 accordingly tothe invisible energy in the final state, while for D+/0 channel a mass region ±200 MeV/c2 around the nominal massis selected. The reconstructed mass spectra for two channels are shown in fig. 502505007501000125015001750200022500.135 0.14 0.145 0.15 0.155 0.16DELPHI 92-95D*+ → (K-pi+)pi+dataD decaysreflections pisl + Xbackground∆m [GeV/c2]events per  0.50 MeV/c2050010001500200025000.14 0.15 0.16 0.17DELPHI 92-95D*+ → (K-pi+(pio))pi+dataD decaysreflections pisl + Xbackground∆m [GeV/c2]events per  0.80 MeV/c2FIG. 5. The mass difference ∆m spectra for D∗+ → (K−pi+)pi+sland D∗+ → (K−pi+(pi0))pi+sldecay modes for data andsimulation.To extract Ac,0FB and Ab,0FB the contributions of D mesons from cc¯ and bb¯ events should be separated. This is achievedfitting together Ac,0FB and Ab,0FB in bins of cos θT , scaled momentum XE(D) and b-tag variable Pev (fig. 6).0501001502002503003504000.2 0.4 0.6 0.8 1XEeventsdatac → Db → Dbackground(a)D*+ → (K-pi+)pi+0501001502002503003504004500 0.2 0.4 0.6 0.8 1tr(Pev)eventsdatac → Db → Dbackground(b)D*+ → (K-pi+)pi+FIG. 6. The distributions of XE(D) and b-tag probability for the signal region for D∗+ → (K−pi+)pi+sl decay for data andsimulation.In fig. 5 one can notice that, in addition to the pure combinatorial background, in the signal region there are twoother components: Partially reconstructed D∗+ mesons and reflections from other decays mode. Because of the chargecorrelation with the primary quark, these two categories have to be treated like signal in the fit.Finally in case of bb¯ events an effective mixing is introduced to take into account the B0B¯0 mixing for B → Dproduced mesons and the so-called “upper vertex” production of the charm in b → DD¯ decays. This was computed6from data collected at the Υ(4s) resonance by the CLEO and the ARGUS collaborations. The values obtained areχeff = 0.222± 0.033 for D+ and D∗+ modes and χeff = 0.170± 0.030 for the D0 channels, both different from theaverage χ = 0.1214± 0.0043 measured at LEP for b-hadrons.At the Z peak about 62 × 103 D decays were reconstructed and the corresponding value of the asymmetries areAcFB = 0.0659± 0.0094 (stat) and AbFB = 0.0762± 0.0194 (stat). The main contributions to the systematic error arelisted in the bottom part of table II. Besides the limited MC statistics the main contributions are related to the fitmethod itself and to the residual asymmetry of D mesons from pure combinatorial background in cc¯ and bb¯ events.III. LEP COMBINED RESULTS.The currently available determinations of Ac,0FB and Ab,0FB from LEP experiments are shown in figure 7. The precisionon the measurement of Ac,0FB is currently 7 % and the average is dominated by the measurements performed with theD meson tag. On the contrary, it should be noted that the most precise single determination comes from the leptonanalysis tag from OPAL. This indicates that some improvements in the measurement of AcFB can still be achieved.The precision on the measurement of AbFB is currently 2 % with equal weights from jet charge and lepton tag analyses.The impact of these measurements on the determination of sin2 θ`W,eff issin2 θ`W,eff = 0.2322± 0.0010 for Ac,0FBsin2 θ`W,eff = 0.23225± 0.00038 for Ab,0FBAb,0FB provides together ALR from SLD the most precise value available at the moment. On the contrary the twomeasurements are more than 2 sigmas apart from each other. AFBcc_ at √s ≈ mZLEPSummer 980.0709 ± 0.0044OPAL D*   +1990-950.0630 ± 0.0120 ± 0.0055DELPHI D*   -1991-950.0658 ± 0.0093 ± 0.0042ALEPH D*   -1991-950.063  ± 0.009  ± 0.0030OPAL leptons   -1990-950.0595 ± 0.0059 ± 0.0053L3 leptons   +1990-910.0784 ± 0.0370 ± 0.0250DELPHI leptons   -1991-950.0770 ± 0.0113 ± 0.0071Include Total  Sys 0.0022With Common Sys 0.0011 AFBbb_ at √s ≈ mZLEPSummer 980.0990 – 0.0021OPAL jet-ch   +1991-950.1004 – 0.0052 – 0.0044L3 jet-ch   -19940.0855 – 0.0118 – 0.0056DELPHI jet-ch   -1991-950.0979 – 0.0047 – 0.0021ALEPH jet-ch   -1991-950.1040 – 0.0040 – 0.0032OPAL leptons   -1990-950.0910 – 0.0044 – 0.0020L3 leptons   -1990-950.0963 – 0.0065 – 0.0035DELPHI leptons   -1991-950.0998 – 0.0065 – 0.0029ALEPH leptons   +1990-950.0965 – 0.0044 – 0.0026Include Total  Sys 0.0010With Common Sys 0.0007FIG. 7. Results for Ac,0FBand Ab,0FBshown at the ICHEP 98 Vancouver Conference.[1] K. Mo¨nig, Rep. Prog. Phys. 61, 999-1043 (1998).[2] DELPHI Collaboration, P. Abreu et al., CERN EP/98-189 subm. to Eur. Phys. J. C ;DELPHI Collaboration, P. Abreu et al., DELPHI 98-143 CONF 204, contr. paper to ICHEP98, ICHEP’98 # 124, ;DELPHI Collaboration, P. Abreu et al., CERN EP/99-07 subm. to Eur. Phys. J. C.[3] DELPHI Collaboration, P. Abreu et al., Nucl. Inst. Meth. A378 (1996) 57.7

Heavy quark asymmetries with DELPHI

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