DELPHI Collaboration DELPHI 96-167 PHYS 656 2 December, 1996 Measurement of mass dierence between? and + and mass of -neutrino from three-prong -decays M.Chapkin V.Obraztsov IHEP, Protvino Abstract The mass dierenece of the -lepton and its antiparticle is measured from an analysis of three-prong -decays collected by the DELPHI detector during 1991-1994. It is equal to m(? )?m( + ) =?2:3:2MeV=c 2. The square of the -neutrino mass is measured to be m 2 =?:12 :14(GeV=c 2 ) 2 and 95% condence level upper limit for m is m 45MeV=c 2.
1 Introduction The usual eld theory of microscopic process is invariant under the product of charge conjugations (C), space reection (P) and time reversal (T). For this reason a test of CPT invariance is really a test of correctness of the description of the microscopic phenomena in terms of existing eld theory. CPT violation would mean an existence of unknown properties of the elds and their interactions which are outside the standard eld theory. The best known consequence of CPT invariance is the equality of masses and lifetimes of a particle and its antiparticle. The most impressive limit on mass dierence between particle and its antiparicle was obtained for the system (K ; K ). In the literature [1], the reader can meet the estimate j(m K? mk )=m K j < 9 1?19, but it does not mean that the parameters describing CPT violation are extremely small too. The extraordinary smallness of this ratio originates from the factor 2(m KL? m KS )=m K 1:4 1?14 which has nothing to do with CPT violation and the ratio is also not independent of some approximations and theoretical assumptions ( see also ref. [2]). It is more natural to look for CPT vialation in the processes in which one of the invariances C, P, or T is violated. Such are the processes initiated by weak interaction, in particular, the decays of -leptons. Up to now there is no data on the mass dierence of? and +. In this paper we measure the masses of? and + separately and determine their mass dierence which is practically not sensitive to the systematic errors because they shift the mass value in the same way both for? and for +. We analyse the 3-prong decays of -leptons using the method developed by ARGUS [3] for measurement the mass of -lepton. It consists of the construction of the variable which is smaller than or equal to mass of the and analysing its behaviour near the boundary of physically allowed region. We also apply the same idea for -neutrino mass measurement and construct the variable which is greater than or equal to the mass of invisible or unmeasured particles. The best upper limit for -neutrino mass was obtained by the ALEPH collaboration[4] from the analysis of the two-dimensional distribution m had? E had. The method which was used in this work has smaller dependance on the shape of theoretical distributions of the decay products of -lepton and dierent systematics. The data used were collected by the DELPHI experiment at LEP in the years 1991 to 1994 at centre-of-mass energies around 91.2 GeV. 2 The method of mass measurement Let us consider the decay! 3. The square of the -neutrino mass is equal to : m 2 = m2 + m2 3? 2E E 3 + 2p p 3 cos( 3 ); (1) where m and m 3 is the mass of tau and 3 pion system respectively, E 3 and p 3 is the energy and absolute value of the momentum of 3 pions, 3 is angle between the direction of -lepton and momentum of the 3 pions, and E and p is the energy and absolute value of momentum of the -lepton ( we assume here that E is known and equal to the beam energy). We increase the right side of equation (1) if we take cos( 3 ) equal to 1. We can analyse the variable m 2 max = m2 + m2 3? 2E E 3 + 2p p 3 ; (2) 1
which is greater than or equal to m 2 and on the other hand smaller than or equal to (m?m 3 ) 2. This means that the variable is more powerful than the commonly used m 3 value. KORALZ[5] Monte Carlo shows that distribution on m 2 max when the Initial State Radiation (ISR) is switched o has form dn=dm 2 max = (a1 + a2 m 2 max) (m 2 max? m 2 ) (3) in a wide range of variation of m 2 max (for the analysis we consider m 2 max less than :15(GeV=c 2 ) 2 ). It is illustrated by g.1 which shows the m 2 max distributions for two Monte Carlo samples with m = and 5 MeV=c 2 as input parameters. The shape of the distribution of m 2 max is not changed with changes in the shape of m 3 distribution. For example instead of the?!?? + decay mode we can consider together the two decay modes?!?? + and?!?? + assuming that is lost. This change the parameters a1 and a2 of the equation (3) but does not change the threshold behaviour of the distribution. This fact makes our analysis free of the assumption on the d?=dm 3 de 3 distribution which is important in the ALEPH analysis of (m 3 ; E 3 ) distribution. In an analogous way we may construct a variable which is smaller than the mass. Assuming the mass of -neutrino equal to zero, that is E = p, where E and p is the neutrino energy and the absolute value of momentum, E = E? E 3, we have m 2 = m 2 3 + 2E 3 (E? E 3 )? 2p 3 (E? E 3 )cos( 3 ); (4) where 3 is the angle between the momentum of the 3 pions and the neutrino. If we take cos( 3 ) = 1 we get the expression q m 2 min = m 2 3 + 2(E? E 3 )(E 3? p 3 ); (5) which is smaller or equal to m 2 and greater than m2 3. So we will analyse the variable m min = m 2 min. The distribution on m min has also the form (3), where intead of m 2 we should put m. If the ISR is switched on the threshold behaviour of distribution (3) becomes smeared and a tail appears in unphysical region as it is shown on g.2 where m 2 max distribution with ISR and with no ISR are compared. The experimental resolution in measuring of charged decay products smears the distribution (3) in the same way as ISR. To describe real distributions of m min and m 2 max we should take into account the initial state radiation, photon conversion and Dalitz decays of leading to missidentication of electrons as pions, energy distribution of electrons inside the beam around the average value of beam energy, momentum resolution of charged decay products of -leptons. We also account for contamination to the selected? + sample from hadronic decays of Z-bozon, interactions, Z!? + n and Z! e? e + n. 3 Experiment and data selection A detailed description of the DELPHI detector can be found elsewhere [6]. In the analysis only charged particles were used but some cuts on neutrals were done in the selection criteria for? + selection. The momenta of charged particles were measured in the 1.23 T solenoidal magnetic eld by the following tracking detectors: the Micro Vertex Detector, 2
the Inner Detector, the Time Projection Chamber (TPC, the principal tracking device of DELPHI), the Outer Detector and the Forward Chambers A and B. A charged particle was required to satisfy the following criteria : { momentum, p, between.5 GeV=c and 55 GeV=c; { p=p < 1; { polar angle,, with respect to the beam between 25 and 155 ; { measured track length in the TPC greater than 3 cm; { impact parameter with respect to the nominal beam crossing point within.5 cm in the transverse xy plane and 3 cm along the beam direction (z-axis).? + events were then selected if { there were at 4 or 6 charged particles with net charge equal to zero; { the total energy of charged particles (assuming a pion mass) in each of the two hemispheres dened with respect to the beam direction exceeded 3 GeV; { the total energy of all charged particles was greater than 15 GeV; { each hemisphere dened with respect to the thrust axis has 3 or 1 particle with net charge equal to 1 or -1; { angle between any two tracks from dierent hemispheres with respect to thrust axes greater than 16 ; { no identied electrons using de/dx or HPC in hemisphere with 3 tracks; { no photon conversion in the hemisphere with 3 tracks; { no identied photon or with E > 1:5GeV in the hemisphere with 3 tracks; { the tting of the 3 tracks in the hemisphere to the secondary vertex should give P ( 2 ) > :1. A total of 1535 events satised these cuts. The main contamination to the 3-3 topology is from hadronic decays of the Z-boson (about 1:7%), and to 3-1 topology hadronic events, dimuon events, events and bhabha events give a contribution with total value about :7%. Using KORALZ events passed through the full detector simulation with the program DELSIM[7] and after that through the same reconstruction programs as the experimental data we found that resolution functions for the m 2 min and m 2 max can be approximately described by a Breit-Wigner function as shown on g.3. The central values of the resolution functions both for m 2 max and for m 2 min are slightly shifted. Their positions are at?:8(gev=c 2 ) 2 and +1MeV=c 2 for m 2 max and m min respectively. The convolution of a -function with a Breit-Wigner function is an arctangent function. The experimental distributions of m min and m 2 max were tted by the form dn=dx = (a1 + a2 x) arctg((x? a3)=a4) + a5 + a6 x + a7 x 2 ; (6) 3
where x stands for m min or m 2 max and a1-a7 are tted parameters. We assume that parameters a1-a7 take into account all sources of background and detector imperfections mentioned above. After the t we correct the value of parameter a3 due to non-zero central value of of resolution functions. The distribution of m min both for negative and positive is shown on g.4 with the result of the t with (6). It also have to be remarked that for mass distributions the bin width variation does not change the conclusions of our analysis. The value of m obtained from the t is m = 1778:42:5MeV=c 2 and after taking into account the resolution shift we get m = 1777:4 2:5MeV=c 2 ; (7) which is in good agreement with PDG[1] data. Using this fact we can x the value of the average mass of the at the PDG value 1777MeV=c 2 and t both distributions for negative and positive simultaneousely with one free parameter m? + instead of two parameters m? and m +. The t with m? and m + as free parameters yelds the value of the m? + consistent with the value when the average mass was xed. 4 Results The distributions of m min for negative and positive are shown on Fig.5 together with the result of the t both distributions simultaneousely. The t of mass dierence between? and + gives m?? m + =?2: 3:2MeV=c 2 (8) The t for the square of -neutrino mass gives m 2 =?:2 :13(GeV=c 2 ) 2. The distribution of the m 2 max was also built for the Monte-Carlo events with zero neutrino mass as input. The tted parameters of both for data and Monte-Carlo events are listed in Table 1 and Fig.6 shows the distributions of the data and Monte-Carlo together with the result of the t. Table 1 Results of the t with the Form (6) for data and Monte-Carlo. Parameters Data Monte-Carlo a1 -.2.13 -.14.17 a2.25.28.15.33 a3 5.18 1.17 9.4 1.33 a4-15 37 13.9 13.3 a5 12.1 1.3 1.4.76 a6 26.1 3.4-19.8 21.5 a7 241 567 36 13 2 /NDF 1.23 1.18 After adding to the tted experimental value of neutrino mass the value of resolution shift we get m 2 =?:12 :13(GeV=c2 ) 2 (9) 4
The main systematic error comes from the resolution shift. The peak position of the resolution function varies with variation of the selection criteria within :4(GeV=c 2 ) 2. Some additional uncertainty comes from the choice of t range and the form of tting function (we tried a Fermi function instead an arctangent and polinomial of dierenet power). The total systematic error is estimated to be :5(GeV=c 2 ) 2. Combining the errors qudratically we get m 2 =?:12 :139(GeV=c2 ) (1) To get an upper limit on -neutrino mass we use the Bayes' approach as proposed in PDG[1] where the fact that m 2 can not take negative values is taken into account. We renormalize the gaussian distribution centered at -.12 with = :139 to be equal to unity for m 2 and obtain that m 2 with 95% probability lies in the region between and :22(GeV=c 2 ) 2. That is Extracting the square root from this value we can say 5 Summary m 2 :22(GeV=c 2 ) 2 : (11) m < 45MeV=c 2 at CL = 95% (12) From an analysis of the three-prong -decays the mass dierence of -lepton and its antiparticle is measured: m?? m + =?2: 3:2MeV=c 2 : The the square of -neutrino mass is measured to be: m 2 =?:12 :13(GeV=c 2 ) 2 : The 95% condence level upper limit for the -neutrino mass is m 45MeV=c 2 : At the present level of statistics no evidence for a mass dierence between? and + or a non-zero -neutrino mass is observed. Acknowledgements We thank A. Tomaradze for his interest in and discussions about this work. References [1] Particle Data Group, Phys. Rev. D54 (1996) 1. [2] Rev. Mod. Phys. 51 (1979) 237. 5
[3] Phys. Lett. B292 (1992) 221. [4] CERN{PPE/95{3 An upper limit for the neutrino mass from! 5( ) decays D. Buskulic et al. 13 January 1995 Phys. Lett. B349 (1995) 585. [5] S. Jadach and Z. Was, Comp. Phys. Commun. 36 (1985) 191; S. Jadach, B.F.L. Ward and Z. Was, Comp. Phys. Commun. 66 (1991) 276. [6] CERN{PPE/95{194 Performance of the DELPHI Detector P. Abreu et al. 21 December 1995 Nucl. Instr. and Meth. A378 (1996) 57. [7] DELPHI Collaboration, DELSIM User's Guide, DELPHI Note 89-67 PROG 142. 6
Entries/.25(GeV/c 2 ) 2 12 1 8 6 4 2 -.15 -.1 -.5.5.1.15.2.25 m ν 2 max (GeV/c 2 ) 2 Entries/.25(GeV/c 2 ) 2 12 1 8 6 4 2 -.15 -.1 -.5.5.1.15.2.25 m ν 2 max (GeV/c 2 ) 2 Figure 1: KORALZ distributions of m 2 max with input parameter of m 5MeV=c 2 and with switched o ISR equal to and 7
Entries/.25(GeV/c 2 ) 2 14 12 1 8 6 4 2 -.1 -.5.5.1.15 m ν 2 max (GeV/c 2 ) 2 Entries/.25(GeV/c 2 ) 2 14 12 1 8 6 4 2 -.1 -.5.5.1.15 m ν 2 max (GeV/c 2 ) 2 Figure 2: KORALZ distributions of m 2 max switched on when the ISR is switched o and when it is 8
6 5 4 3 2 1 -.6 -.4 -.2.2.4.6 Resolution of m ν 2 max (GeV/c 2 ) 2 25 2 15 1 5 -.6 -.4 -.2.2.4.6 Resolution of m τmin (GeV/c 2 ) Figure 3: Resolution functions of m 2 max and m min obtained from the Monte Carlo. The curves are the result of the t with Breit-Wigner function 9
Entries/5Mev/c 2 6 5 4 3 2 1 1.55 1.6 1.65 1.7 1.75 1.8 1.85 m τmin (GeV/c 2 ) Figure 4: Experimental distribution of m min both for negative and positive. The curve is the rusult of the t with form (6) 1
Entries/5MeV/c 2 35 3 25 2 15 1 5 1.55 1.6 1.65 1.7 1.75 1.8 1.85 m τmin (GeV/c 2 ) Entries/5MeV/c 2 3 25 2 15 1 5 1.55 1.6 1.65 1.7 1.75 1.8 1.85 m τmin (GeV/c 2 ) Figure 5: Experimental distributions of m min for negative and positive separately. The curves are the rusult of the t with form (6) of both distributions simultaneousely 11
Entries/.25(GeV/c 2 ) 2 45 4 35 3 25 2 15 1 5 -.6 -.4 -.2.2.4.6.8.1.12 m ν 2 max (GeV/c 2 ) 2 Figure 6: Experimental and Monte-Carlo distributions of m 2 max. The points with bars are the data and histogram is the Monte-Carlo. The solid curve is the result of the t with form (6) of the data and the dashed one is of the Monte-Carlo distribution 12