Determination of the upper limit on m_nu_tau from LE

a r X i v :h e p -e x /9903062v 2 30 M a r 1999Determination of the upper limit on m ντfrom LEP.

Fabio Cerutti

Laboratori Nazionali dell’INFN Frascati,Via E.Fermi 40,00044Frascati Italy

CERN EP Division,1211Geneva 23,Switzerland

A review of the direct determinations of the upper limit on the tau-neutrino mass from the LEP

experiments is given.The experimental methods,the results and the comparison with non LEP

measurements are also discussed.The study of the systematic errors shows that the LEP results are

statistically limited so that their combination will improve the sensitivity to a massive tau-neutrino.

An uno?cial combination of the ALEPH and OPAL measurements gives a 95%con?dence level

upper limit of 15MeV/c on m ντ.

I.INTRODUCTION:MOTIV ATION AND INDIRECT CONSTRAINTS.The neutrino masses are one of the most puzzling and hot subject of discussion in the high energy physics community.It is believed that the smallness the neutrinos masses can be explained by assuming that they are produced by the mixing between standard Dirac mass terms and large Majorana mass terms;the Majorana masses are related to a new energy scale at which the lepton number conservation is violated.This is the so called see-saw [1]mechanism which is present in many grand-uni?ed models.If the Standard Model mass hierarchy is preserved in the Dirac sector of the neutrino mass matrix the tau-neutrino is expected to be by far the heaviest neutrino.Under this assumption the neutrino mass hierarchy is expected to be of the order m ντ:m νμ:m νe =m 2t :m 2c :m 2u .Cosmology [2]can put strong constraints on the neutrino masses because of their in?uence on the actual density of the universe.An unstable tau-neutrino with a mass of the order of 10-20MeV can survive to the cosmological constraints.Measurements of light nucleus abundances which results from Big Bang Nuleo Synthesis [3]can give information on the neutrino masses.The incompatibility between the BBNS prediction and the measured D and H 3abundances can be solved by and unstable tau-neutrino with a mass of the order of 10-25MeV [4].The claimed superK [5]discovery of atmospheric neutrinos oscillation would constrain m ντto be lighter than about 170KeV (which is the direct limit on the mu-neutrino mass)if what they observe is an oscillation between tau and mu neutrinos.II.THE FIT TO m ντ:2-DIMENSIONAL METHOD The m ντmeasurements at LEP are based on a ?t to the E h ,M h spectrum in hadronic tau decays.This method

has been introduced for the ?rst time by two LEP experiments OPAL [6]and ALEPH [7].The fact that for each

given hadronic mass the hadronic energy is constrained between the two values E max,min h (M h ,m ντ)gives a sizable

improvement in the sensitivity to the tau-neutrino mass with respect to the one obtained by a ?t to the M h spectrum alone,as explained in [8,9].

The two decays used at LEP are τ→5π±ντand τ→3π±ντ.The ?rst decay mode bene?ts of a invariant mass spectrum which extends to large values but is limited by the very small branching which is of the order of 0.08%.The second mode bene?t of a large statistics (BR(τ→3π±ντ)～9%)but the M h spectrum is suppressed at values close to M τbecause of the a 1dominance in 3πtau decays.The two modes have similar sensitivities even though the regions in the M h ,E h plane from which this sensitivity comes are slightly di?erent:for the ?ve-prong mode it comes from few events at very high values of M H and E h while for the three-prong mode events at very high energy and intermediate mass can contribute too.

The value of m ντis obtained by a likelihood ?t to the observed events where the likelihood has the following form:

L (m ν)= events 1

dE h dm h ?G (E beam ,E τ)?R (m h ,E h ,ρ,σm h ,σE h ,...)?ε(m h ,E h )(1)

The d2Γ

using the so called Monte Carlo cloning technique

[7]which allows the determination of these parameters on an event by event basis.

The ?t to the ALEPH events showed in Fig.1gives a limit of m ντ<22.3MeV at 95%con?dence level.The

systematic error is dominated by the knowledge of the parameters of the resolution function.The energy and the mass scales and resolutions have been determined by using the Z →μ+μ?events and the charm decays D 0→K ?π+,D 0→K ?π+π+π?and D +→K ?π+π+.By adding linearly the 0.8MeV systematic error the ?nal 95%C.L.limit is m ντ<23.1MeV.

The OPAL experiment has performed a similar measurement by selecting 22τ→5π±ντdecays [6].The selection e?ciency is of 9.3%with a dangerous background of the order of 2.5%.The parameters of the resolution function have been determined,as for ALEPH,with the Monte Carlo cloning technique.In the OPAL paper is proved that this technique is able to spot events with reconstruction problem as shown in Fig.2.

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m 5π(GeV)E 5π(G e V )m 5π(GeV)5πm 5π(GeV)E 5π(G e V )m 5π(GeV)5πFIG.2.The results of the Monte Carlo cloning technique applied to two Monte Carlo events with reconstruction problems are shown in ?gures (a)and (b);the beginning of the arrow shows the generated values of M h and E h ,the end of the arrow shows values of these quantities after the ?rst Monte Carlo reconstruction and the boxes show the distribution of these quantities obtained by applying the Monte Carlo cloning technique to these two events.The result of the same technique applied to the two most sensitive data events is shown in ?gures (c)and (d).

Typical mass and energy resolutions of the OPAL analysis are 20-25MeV and 500MeV respectively.The ?t to the 22OPAL events gives a limit of m ντ<39.6MeV at 95%con?dence level.As for ALEPH the systematic error

is dominated by the knowledge of the resolution function parameters and is of 3.6MeV.By adding linearly this systematics to statistical limit OPAL obtains a 95%C.L.upper limit on m ντof 43.2MeV.

B.Results form τ→3π±ντtau decays

As mentioned in the introduction the three-prong tau decay mode is competitive with the ?ve-prong one in the determination of the tau neutrino mass.The three LEP experiments ALEPH [10],DELPHI [11]and OPAL [12]have used this decay mode to constraint the tau-neutrino mass.

The ALEPH results is based on a ?t to the M h ,E h distribution.Due to the large statistics the ?t has been limited to an high M h ,E h region where 3000τ→3π±ντdecays have been selected.The selection e?ciency in this region is of about 49%with a background from dangerous topologies of less then 0.2%.The high statistics of this channel make the cloning technique not viable.For this reason ALEPH has parameterised the quantities entering in resolution R as a function of the hadronic mass and energy.The typical values of the mass and of the energy resolution are similar to the ones obtained in the ?ve-prong mode.The ?t gives a statistical limit of 21.5MeV on the tau-neutrino mass at 95%con?dence level.The systematic error on this limit is again dominated by the knowledge of the resolution function and ammount to 4.2MeV.This error is larger than the ?ve-prong one mainly because of the non use of the

cloning technique.Adding linearly the systematic error to the?t result a95%C.L.limit of mν

τ<25.7MeV has been

obtained.

The OPAL experiment has tried to increase its sensitivity to the tau neutrino mass by partially reconstructing the tau direction in three-prong versus three-prong tau events.In this kind of events the thrust axes is a good approximation of the tau direction especially for events where the three-prong are very energetic.By a?t to the two variables square missing-mass and missing-energy on a sample of2514events OPAL obtained an upper limit of32.1 MeV at95%C.L.on mντ.The systematic error has been estimated to be of3.2MeV dominated by the knowledge of the resolution function parameters.This gives a?nal limit of mντ<35.3MeV at95%con?dence level.

The DELPHI experiment has selected12538τ→3π±ντdecays with a38%e?ciency and a dangerous background of1.5%.A?t to the M h,E h distribution gives a95%C.L.upper limit of25MeV on the tau-neutrino mass.In the study of the systematics DELPHI has observed a signi?cant disagreement between the three-prong mass spectrum in the data sample and the one obtained with a Monte Carlo based on the K¨u n-Satamaria model[13].This discrepancy is observed in the M h range(1.5-1.9)GeV.The DELPHI collaboration claimed[14]that this excess could be explained if about2.3%of new resonance,the a’(1700)with a mass of1.7GeV and a width of0.3GeV,was added in the three-prong tau decay.The description to the Dalitz plots in the three-prong tau decays also improved by the addition of this resonance.The CLEO experiment has tried to measure the ammount of this resonance in their three-prong tau sample[15](by assuming a massless tau-neutrino)and has obtained(with di?erent models)an a’(1700)fraction of the order of(0.1-0.4)%which is signi?cantly smaller than the2.3%reported by DELPHI.

The ALEPH and the OPAL experiments has observed the same problem as DELPHI in describing theτ→3π±ντDalitz plots however the do not observe any excess with respect to the Kh¨u n and Santamaria model in the hadronic mass spectrum.The ALEPH experiment has checked the e?ect of such a large ammount of a’(1700)on its limit: if a2.5%of a’(1700)with the parameters suggested by DELPHI is added in the three-prong?t the limit on mντis worsened by about6MeV.This implies a variation on the combined three-and?ve-prong ALEPH upper limit, reported in the following,of about1MeV.

As DELPHI correctly states that a simultaneous?t of the a’(1700)properties and of mντin three-prong tau decays is not possible.In view of the CLEO results and of the ALEPH check is unlikely that the limit on the tau neutrino mass can be deteriorated by the presence of this new resonance.More inputs from theorists is welcome.

https://www.sodocs.net/doc/3611207481.html,bination of the ALEPH and OPAL results

The ALEPH and the OPAL collaborations have combined[10,6](separately)their three-and?ve-prong upper limits on the tau-neutrino masses.The method used to combine these results is based on the likelihood product. In doing the combination the correlation between the systematic errors of the two decay modes has been properly taken into account as described in[10,6].The limit obtained by the OPAL and by the ALEPH collaborations are respectively of mντ<27.6MeV and of mντ<18.2MeV at95%con?dence level,including systematic e?ects.

The results from the di?erent LEP experiments and from the di?erent tau decay modes are limited by statistics. Moreover the dominant systematics(resolution function parameters)are mainly uncorrelated between the di?erent LEP experiments.For this reason a combination of the LEP results would improve the sensitivity to the tau-neutrino mass.I have done this exercise in order to get an estimate of what this combined limit would be.I have used the ?ve-and three-prong likelihoods published by the ALEPH and by the OPAL experiments(the DELPHI results have not yet been published).The method is the same as the one used in the ALEPH and OPAL publications:

L COMB(mν)=L3πOP AL(mν)×L5πOP AL(mν)×L5πALEP H(mν)×L3πALEP H(mν)(2)

the combined likelihood is shown in Fig.3.

From this likelihood a95%C.L.limit mντ<13.6MeV can be derived by requiring ln(L(m95ν))=ln(L MAX)?1.92 (this method is almost equivalent to the one based on the integration of the likelihood,used for example by CLEO, when the likelihood shape is fairly Gaussian as in this case).

To estimate the systematic error all the modi?ed likelihoods containing the e?ect of the di?erent systematic sources would be needed.Since they are not published a rough estimate of the systematics have been obtained by multi-plying each likelihood by a constant factor which brings,for each channel,the limit on mντto be equal to the ones which includes the systematics.The total systematics has been obtained as followed:the systematic error for each combined mode is obtained by subtracting to the limit derived with the modi?ed likelihoods the one obtained with-out systematics;all these errors are added in quadrature(in this way the possible correlations between the di?erent systematic errors are not taken into account)giving a total systematics of1.4MeV.By adding linearly this error the the statistical result a combined ALEPH+OPAL95%C.L upper limit of15MeV on mντis obtained.I want to stress that this combination is uno?cial and approximated.The aim is to give an idea of the gain which could be achieved with the combination of the LEP results and to push the ALEPH,DELPHI and OPAL collaboration to produce an o?cial combined mντlimit.

FIG.3.The ALEPH and OPAL combined likelihood as a function of mντobtained from?ve-and three-prong published results.This likelihood does not include systematic e?ects.

https://www.sodocs.net/doc/3611207481.html,PARISON WITH CLEO RESULTS

The CLEO experiment has collected a huge statistics of tau decays at a centre-of-mass energy close to theΥ(4s) resonance and is expected to have a sensitivity to mντlarger than that of the LEP experiments.The performance of the CLEO[16],ALEPH[7]and OPAL[6]5πanalyses are compared in table I.The CLEO limits are worse than the ALEPH one even though the CLEO statistics is a factor of?ve larger.This brings to the question:is CLEO unlucky or the are LEP results lucky?It would be nice to evaluate for each experiment the expected limit on mντ. Its comparison with the actual one will tell us who is lucky and who is unlucky.Unfortunately the unknown hadronic dynamics doesn’t allow the evaluation of the a priori sensitivity of an experiment.The ALEPH experiment claims that the probability to get such a lucky distribution in the M h,E h plane is at the level of15%if a model of the dynamics driven byππa1is assumed in5πtau decays.At the same time CLEO claims that the probability to get a limit on mντsuch a bad or worse than what they have obtained is at the level of23%if a softer mass spectrum is assumed in the?ve-prong tau decays.So the puzzle stays unsolved.What can be done is to compare data with data in the region where they are more sensitive to the tau-neutrino mass.This exercise is shown in Fig.4where the number of5πevents are plotted in slices of iso-mντin the M h,E h plane;in order to have more statistics the ALEPH and the OPAL events have been summed up in this comparison.

FIG.4.The LEP(ALEPH+OPAL)?ve-prong events compared with the CLEO ones in terms of mντslices in the M h,E h plane after requiring M h>1.65GeV and E h/E b>0.9.The red dots represents the LEP events.The dark-blue histogram shows the CLEO events normalised to the number of LEP events in this sensitive region.The green histogram shows the CLEO events normalised to the total number of LEP selected events.The ligh-blue histogram shows the expected events obtained by using aππa1model for the?ve-prong tau decay.

Only the events in a sensitive region which corresponds to M h>1.65GeV and E h/E b>0.9are shown.The selection e?ciency is assumed to be?at in the full M h,E h plane.It?nds out from this plot that the shapes of the LEP and CLEO data are compatible.This is shown by the comparison between the dark-blue line and the red dots of Fig.4;the CLEO events in the sensitive region have been normalised the number of ALEPH+OPAL events in the same region.

For what concerns the fraction of5πevents selected in this region with respect to the total number of selected5πevents the compatibility is less good as can be observed by comparing the green line in Fig.4with the red dots;the ALEPH and the OPAL experiments select a total of16events in this sensitive region which should be compared with about7which is the number of events observed by CLEO in this sensitive region rescaled to the ALEPH+OPAL5πstatistics.These two numbers are barely compatible.The number of expected events normalised to the ALEPH plus OPAL statistics is of about18with theππa1dynamics(this is showed by the light-blue line of Fig.4)and of about 9with a softer dynamics similar to phase-space.

Even more intriguing is the fact that the likelihood shown by the CLEO experiment at the TAU98workshop[17] shows a peak at mντ～18MeV.This likelihood is preliminary and doesn’t include the systematic errors.If the ALEPH method described above is applied to this likelihood the value of mντ=0is excluded at more than90% con?dence level.This could mean that CLEO is on the verge of a very interesting result or that(more probably but less interesting)there is in the CLEO likelihood a bias towards large neutrino masses.This bias would make the CLEO limit more conservative(explaining why their limit is so unlucky)and is therefore not warring in terms of the validity of their mντupper limit.One should remember that most of the systematics determined by the di?erent experiments are studied in terms of bias towards a massless tau-neutrino while less attention is played to possible sources which can mimic a massive neutrinos.A typical example is the fact that all the experiments reduce the dangerous background(the one which can mimic a massless tau-neutrino)at the1-2%level while backgrounds as high as10%from higher decay multiplicities(like a3π±π0reconstructed as a3π±tau decays)which can mimic a massive neutrino are accepted.The CLEO experiment as still a large fraction of its statistics to analyse so I think that this intriguing situation will be clari?ed soon.

TABLE https://www.sodocs.net/doc/3611207481.html,parison between the performance of LEP and CLEO5πanalyses.For the di?erent analyses the mass resolution in Mev,the energy resolution divided by the beam energy,the number of selected events,the e?ciency in per cent and the95%upper limit,statistical only,on mντin MeV are reported.

σ(M h)GeVσ(E h)/E beam N evts E?ciency%m95νMeV

OPAL5π±20-250.5/45.622939.6 CLEO5π±150.025/10.266331.0 CLEO3π±2π0250.05/10.2070.433.0

V.CONCLUSIONS AND ACKNOWLEDGEMENTS

The LEP experiments have put constraints on mντby?tting the M h,E h distribution in three-and?ve-prong tau decays.The best results obtained by a single experiment is given by ALEPH which obtains mντ<18.2MeV at95% con?dence level by combining the three-and?ve-prong results.

An uno?cial combination of the ALEPH and OPAL results shows that LEP can exclude at95%C.L.values of mντhigher than15MeV.In my personal opinion the CLEO experiment has the statistical power to go below this limit.

I want to thank Ronan McNulty from DELPHI,Achim Stahl from OPAL and Jean Duboscq from CLEO for the help that I received in preparing this talk.A special thank goes to my ALEPH colleague(and friend)Luca Passalacqua who shared with me three years of mντmeasurements with the ALEPH detector.I also want to thank the organisers of this very nice conference.