In this article I will review the measurements of the b quark mass performed
by ALEPH and DELPHI and presented at the HEP99 Conference in Tampere. Very
clean effects of the mass running are observed, even if a wide spread in the
results and large systematic errors due to hadronization corrections prevent to
extract an average value of the running b quark mass.Comment: 3 pages, 1 figure

Palla, Fabrizio

English

arXiv

In this article I will review the measurements of the b quark mass performed by ALEPH and DELPHI and presented at the HEP99 Conference in Tampere. Very clean effects of the mass running are observed, even if a wide spread in the results and large systematic errors due to hadronization corrections prevent to extract an average value of the running b quark mass.In this article I will review the measurements of the b quark mass performed by ALEPH and DELPHI and presented at the HEP99 Conference in Tampere. Very clean effects of the mass running are observed, even if a wide spread in the results and large systematic errors due to hadronization corrections prevent to extract an average value of the running b quark mass

CERN Document Server

arXiv:hep-ex/9910044v1  20 Oct 1999An investigation on the b-quark massFabrizio Palla1†1 Istituto Nazionale di Fisica NucleareSezione di Pisa, Via Livornese 1291I-56010 San Piero a Grado (PI) ItalyAbstractIn this article I will review the measurements of the b quark mass performed byALEPH and DELPHI. A large set of observables has been used together withdetailed studies on jet algorithms. Very clear effects due to the b quark massrunning are observed , even if a wide spread in the results and the large systematicerrors coming from hadronization corrections prevents to extract an average valueof the running b quark mass.1. IntroductionThe b quark mass is one of the fundamentalparameters of the QCD Lagrangian. However,due to confinement, quarks do not appear as freeparticles and therefore the definition of their massis ambiguous. In fact, quark masses can be eitherdefined as for free particles (such as the leptons) asthe position of the pole of the propagator, or theycan be interpreted as running coupling constants inthe Lagrangian. In the former definition the massis called “pole mass” and does not run with energy;in the latter the mass is called “running mass” andit can run if measured at different scales.Most of the b quark mass determinations havebeen performed at rather low scales [1]. It istherefore interesting to measure this parameter athigher scales such as the one offered by LEP.At LEP, the possibility to test the runningof the b quark mass within the framework ofthe perturbative QCD has been not considereduntil very recently. The reason is that theeffects of the mass become rapidly very small withincreasing energy for many observables, since theyare proportional to m2b/M2Z (O (0.1%)) for instanceas in the total cross section. For other specificquantities, such as jet rates, the effects are of theorder of few percent due to the fact that the energyscale is lowered to ycut ×M2Z , where ycut ≈ 0.01 isthe jet resolution parameter.The measurements are performed by measuringthe ratio of observables in b and uds induced events.In this article I will review the measurementsdone by ALEPH[2] using a large set of event shapeobservables and by DELPHI[3, 4] using the three-jet† E-mail: Fabrizio.Palla@cern.chrate. The different sensitivity to the hadronizationcorrections and next-to-leading order correctionscan be used to investigate the interpretation of theresults.2. Analysis MethodThe method to extract the b quark mass is basedon measuring the ratio R of any infrared safeobservableO computed for b and uds induced eventsand assuming αS universality:Rb/uds =ObOuds. (1)As observables the following variables have beenstudied by ALEPH:• The rate of the three-jet events, where jetsare reconstructed using the Durham clusteringalgorithm using ycut = 0.02.• The first and the second moments of the eventshape variables Thrust T, C-parameter C, y3,Total and Wide Jet Broadening, BT and BW .DELPHI has used the three and the four jetevents rate.Firstly events are tagged as to originate from bor uds quarks. Both ALEPH and DELPHI use a btag based on lifetime and mass information [5]. Inorder to tag uds events ALEPH uses a dedicatedtag using lifetime as well as kinematic informationcombined to a discriminant variable. DELPHI usesinstead a different region of the lifetime tag wherethe majority of the events are coming from uds.Typical b quark purities for the b enriched sampleare of the order of about 85% and efficiencies ofabout 85% for ALEPH and 50% for DELPHI. The2uds purity is about 80% with 60% efficiency forboth.The ratio is then corrected for hadronization,detector and tag biases.The b quark mass is extracted by comparingthe corrected measured ratio RPb/uds with thepredictions for each observable.The general form of the NLO prediction forRPb/uds as a function of the b quark mass is of theformRPb/uds = 1 +m2bM2Z[b0(mb) +αS2pib1(mb)](2)The coefficient functions b0 and b1 have beencomputed for the three and four jet rate ratio [6, 7].The three jet rate ratio allows a NLO prediction,while for the four jet rate only a LO predictionis available. For the other variables used byALEPH the predictions have been obtained usingthe MC generators ZBB4[7] and EVENT[8] whichare correct to NLO. The hadronization correctionshave been evaluated for all variables by computingthe relevant observables at parton and at hadronlevel.3. ALEPH AnalysisAs shown in table 1 for the majority ofthe observables the hadronization corrections aresizeable. Therefore it has been decided to extractthe b quark mass from the ones which receivecorrections smaller than 10%: these are the threejet rate ratio and the second moment of the WideJet Broadening BW2. The first two moments ofthe y3 variable being very much correlated to thethree jet rate have not been used for the final result.Nonetheless the mass has been computed for allvariables. The results are given in table 1, wherethe error is statistical only. As it can be seen thereis a large scatter in the results. It is worth noticingthat the result extracted from the first moment ofthe y3 are quite different from the one extractedfrom the three jet rate ratio, despite of the fact thatthe two variables are very much correlated. Thismight indicate that there are still large uncontrolledbiases from hadronization and/or that the NNLOcorrections are sizeable.Systematic uncertainties can be divided in threecategories: the ones coming from uncertainties onthe tagging biases, from the hadronization and fromthe missing higher order corrections. The first onesare evaluated by varying the gluon splitting ratewhich influences the purity of the lifetime tag andby varying the cut variables so that the effect ofthe tag corrections are twice the effect of the masson a given variable. This results in varying thetag purities by about 5%. The uncertainty comingfrom hadronization correction has been evaluatedmainly varying the Q0 Jetset parameter from 1 to4 GeV and taking half of the difference betweenJetset and Herwig predictions. The uncertaintydue to missing higher orders has been evaluated byvarying the scale from 0.1 MZ to 2 MZ and by thedifference in the result in the value of the running bquark mass directly extracted and the one extractedfrom the following procedure: from the pole massmeasurement one translates it to a running mass atthe scale of the b quark mass mb(mb) and finally tothe Z mass scale m¯b(Mz).The results for the running b quark mass asextracted using the three jet rate ratio and thesecond moment of the Wide Jet Broadening arerespectively:mb(MZ) = 3.04+0.37−0.34(stat)+0.44−0.39(syst)+0.72−0.59(hadr)+0.20−0.42(theo)GeV/c2. (3)mb(MZ) = 3.78± 0.14(stat)± 0.17(syst)±0.10(hadr)+0.12−0.13(theo)GeV/c2. (4)O Hb/l mb(MZ)T1 1.142 4.48± 0.09T2 1.139 4.84± 0.20C1 1.175 4.41± 0.06C2 1.181 4.69± 0.12y31 1.029 3.89± 0.28y32 0.990 3.51+1.50−0.95BT1 1.302 3.94± 0.03BT2 1.333 3.57± 0.06BW1 1.142 4.74± 0.05BW2 1.093 3.78± 0.14RDur3j (0.02) 0.989 3.04+0.37−0.34Table 1. Table of the ratio of hadronization correctionsHb/l, and the extracted running b-quark mass mb(MZ).The errors are statistical only.4. DELPHI AnalysisThe first measurement of the running b quarkmass at scales of the Z mass has been performedby DELPHI, using 1992 to 1994 data and threejet rate ratio using the Durham algorithm for jetclustering.[3] A new analysis has been performedon 1994 and 1995 data using both Durham andCambridge jet algorithms, in addition to a better b-tag algorithm. The Cambridge algorithm has beenproven to have smaller NLO corrections as well as3a reasonable stable hadronization correction as afunction of ycut down to very low values.The same systematic sources have beenconsidered as ALEPH. Some differences arise in theway they are evaluated. The ones coming formthe tags have been evaluated by changing the tagpurities by 1% and taking the difference betweenthe new and old tag. The hadronization correctionshave been evaluated by changing the fragmentationtuning of the Monte Carlo by 2 sigma and bycomparing Jetset with Herwig. The theoreticaluncertainty due to missing higher orders has beenevaluated by changing the scale from 0.5 MZ to2 MZ and by comparing the results obtained byrunning the pole b mass to m¯b(MZ) as explainedbefore. The analysis performed using the Durhamalgorithm gives consistent results with the old dataanalysis. The values of the three jet rate ratio usingthe Cambridge algorithm are shown in figure 1. Thedata are not compatible with the prediction usinga pole mass of 4.6 GeV/c2.The result obtained with the Cambridgealgorithm at ycut = 0.005 for the three jet rate ratioismb(MZ) = 2.61± 0.18(stat)+0.45−0.49(hadr)±0.04(tag)± 0.07(theo)GeV/c2. (5)where the average between the direct extraction ofthe running mass mb(MZ) and the one extractedfrom the running of the pole mass m¯b(MZ).Despite of the small dependence of the measuredmass from the value of the jet resolution parameterycut (changing ycut from 0.005 to 0.025 the value ofmb(MZ) changes by 0.15 GeV/c2), the result stillsuffers from large hadronization corrections.Effects of the running of the b quark mass havealso been measured in the four jet rate ratio asreported by [9].5. ConclusionsALEPH has studied a large set of observablesto extract the running b quark mass. A verynice agreement has been with the DELPHI resultsusing a three jet rate ratio. A wide spread inthe b quark masses extracted from all the variousobservables might indicate uncontrolled biases fromhadronization and/or NNLO corrections.DELPHI has measured the running b quarkmass using the Cambridge jet clustering algorithmfinding a very good agreement with NLOcalculations and small theoretical errors, but stillsuffers from large hadronization systematics.Due to these findings the interpretation of theresults have to be taken with care and do not allowto extract an average of the running b quark massfrom different observables.0.90.920.940.960.9810 0.005 0.01 0.015 0.02 0.025 0.03 0.035 0.04 0.045PRELIMINARYDELPHICambridgeDatamb(MZ) = 2.8 GeV/c2Mb = 4.6 GeV/c2LO - mb(MZ)NLO - mb(MZ)NLO - MbLO - MbycR3blFigure 1. Corrected data values for the three jet ratioRbl3 using the Cambridge algorithm as a function of theycut compared with the theoretical predictions at LOand NLO in terms of the pole mass Mb (dashed lines)and in terms of the running mass mb(solid lines).References[1] C. Caso et al., Particle Data Group, Eur. Phys.J. C 3 (1998) 1.[2] The ALEPH Collaboration, EPS-HEP99 1-384,ALEPH Conference note 99-034[3] P. Abreu et al., DELPHI Collab., Phys. Lett.B418 (1998) 430.[4] The DELPHI Collaboration, EPS-HEP991-223, DELPHI Conference paper 308[5] R. Barate et al., ALEPH Collab., Phys. Lett.B401 (1997) 150.P. Abreu et al., DELPHI Collab., Eur. Phys. J.C 10, (1999) 415.[6] G Rodrigo, QCD96 Montpellier,hep-ph/9609213 and Nucl. Phys. Proc. Suppl.54A (1997) 60.G Rodrigo, M. Bilenky, A. Santamaria, Phys.Rev. Lett. 79 (1997) 193.[7] P. Nason, C. Oleari, Phys. Lett. B407 (1997)57.[8] Z. Kunszt, P. Nason, private communication.G. Altarelli, R. Kleiss, C. Verzegnassi, ZPhysics at LEP1, CERN Yellow Report 89-08,vol.1, p.373.[9] S. Mart´ı i Garc´ıa, these proceedings.

An investigation on the b quark mass

Abstract

Similar works

Full text

Available Versions

CERN Document Server