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Neutrino counting in the upsilon system
Volume 201, number 2
PHYSICS LETTERSB
4 February 1988
N E U T R I N O C O U N T I N G IN THE U P S I L O N SYSTEM Lars BERGSTROM Department of TheoreticalPhysics, Universityof Stockholm, Vanadisvdgen 9, S-113 46 Stockholm, Sweden
and Hector RUBINSTEIN Physikalisches Institut, Universityof Bonn, Nussallee 12, D-5300Bonn I, Fed. Rep. Germany
Received 29 October 1987
The rare decay Y(2S)~rc~v9 is suggestedas an unambiguousprobe of the number of light neutrino species. It is argued that the upgraded Cornell facilities and in particular the recently proposed B meson factory may provide the adequate number of )?(2S) particles to enable a definite distinction between the possibilities of Nv = 3, 4, or 5. The systematicerrors are arguedto be smaller than in methods based on measuring the width of the Z°. The radiative transition "f(3S)--.~v9is also considered.
The number of neutrino species is of greatest importance in particle physics. Besides its fundamental role in the evolution of the early universe, the number of neutrino species may also give a hint as to whether there exist more than three generations of quarks and leptons. Indeed, counting of neutrino species based on the width of the Z ° boson or the photon peak in e÷e - --'7 +missing energy is considered as a matter of highest priority at LEP and SLC. Already, there are indications from the CERN p~ collider data that the number of neutrino flavours is 5 or less [ I ]. There is also indirect astrophysical evidence that the number is in fact 4 or less [ 2]. Settling this question will be a difficult task at the new e+e coUiders [ 3 ]. In particular, there are many sources of systematic errors the size of which will be difficult to estimate. In view of this, it would certainly be important to establish this important number through an independent method. Up to now, the only realistic rare decay method has been thought to be the rare kaon decay K +-,re ÷ vg. However, this has the serious drawback that the hadronic matrix elements and weak mixing angles involved are largely unknown and On leave of absence from the WeizmannInstitute, 76100 Rehovot, Israel. 0370-2693/88/$ 03.50 © Elsevier Science Publishers B.V. (North-Holland Physics Publishing Division)
therefore the theoretical prediction is uncertain by a factor of around eight [4]. This is clearly not good enough to establish the number of neutrino species unambiguously. In this letter, we will show that a much better method is provided by studying the decay chain "f(2S)~Y(1S)nn --, vvnn, and also (although an order of magnitude less favourable) Y(3S) ~X~(2P)7 ~ v ~ . We shall see that the rate for the former process is large enough for a dedicated measurement of this decay at the upgraded Cornell facility CESR to give an unambiguous result for Nv, the number of neutrino species. At the proposed B meson factory [ 5 ], the measurement should be quite simple. In this method, there is the experimentally very appealing possibility to normalize the measured result to the corresponding decay with the neutrino pair replaced by an e+e - or ~t+~t- pair, which has identical kinematics and angular distributions, and which can be calculated unambiguously. This will cancel many systematic errors and provide a useful check of the apparatus, making this a very clean method of determining Nv. The decay Y( 1S)--. v9 proceeds through the vector part of the weak neutral current. Defining the vector coupling constantfv by 283
Volume 201, number 2
(015?~blY) =ifvm?ceu(2),
PHYSICS LETTERS B
(1)
where mr is the mass of'I'(1S) and eU(2) its polarization vector, we find the decay width for T(1S) / ' v =N~G~(48n) -) (sign (eQ) -- 4eQ sin 20w ) 2 m~.f2v × [(1 --mZ/m~) 2 + ( F z / m z ) 2] -'
(2)
Here ( ) denotes an average over the quarks in the wave function; in our case T consists of pure bb, so this factor is - 1 + ~ sin20w (we will use the value sinZ0w = 0.227 [6] in our numerical calculations). The correction from the Z propagator is only a two percent effect and is very insensitive to the Z width F z which we take to be 2.8 GeV; Mz is put at 93 GeV. The vector decay constant fv is related to the value of the wave function at the origin; however, we will take advantage of the fact that it is actually measured in Y--.e+e - or IX+Ix- decays so that we can make the model independent prediction for the ratio R between the two decay modes:
R =I"(~-,vg)/F(~;-.IX+IX -) = NvG~m~c/(64n2a 2) (sign(eQ)--4eQ sinZ0w) 2 X (eQ) - 2 C ( m r / m z ) ,
(3)
where the correction factor C includes the Z - 7 interference and Z propagator effects and is given by
C ( m r / m z ) -l = (1 _ff2)2 +p2 +if4 (UQ)2(/)2 +aZ)/(eQ )2
+ 2pZ(1--pZ)(VQ)Vo/(eQ).
(4)
Here p=rnr/mz, ~ =Fz/mz, vf= [ sign(er) 4efsin20w]/(4 sin 0w cos 0~) and af= - s i g n ( e r ) / ( 4 × sin 0w cos 0w). In our case, we find C ~ 1.02. Electromagnetic radiative corrections should be incorporated in the standard way for the final IX+IX- pair [7]. An approximative version of eq. (3) has previously been given by Ellis for the case of J/~ decays [ 8 ]. He concluded at that time that this branching ratio was very small for the J/~¢ but that it might be promising for toponium. However, we wish now to point out that already at existing e+e - machines this decay may provide a useful neutrino counting mechanism in the upsilon system. Besides the availability 284
4 February 1988
now of powerful colliders in the appropriate energy region, there are many factors that make this process much more favourable in the Y case. The quartic dependence on mass increases the ratio by a factor of 87 when passing from J[~g to ~/'. Moreover, the different electromagnetic and weak couplings of the b quark compared to the c quark gives another enhancement factor of roughly 16. Inserting numerical values in eq. (3), we obtain R r ~ 1.44X 10-4Nv .
(5)
Using the experimentally measured branching ratio ofT-~ix+/x - decays of (2.8 + 0.2)% [ 9], we find B R ( Y ~ v g ) = (0.40+0.03) × 10-SNv.
(6)
However, it is important to point out that the prediction of eq. (5) is free from the uncertainty of the IX÷ IXbranching ratio. In fact, by normalizing to muon pair production it seems that most of the systematical uncertainties of the experiments are eliminated. There remains to obtain a tag for the "invisible" T o y 9 decay. A convenient such tag is given by the decay chain Y(2S) ~ Y ( 1 S ) n x - , n x +missing energy. The branching ratio for "l'(2S)-~Y(1S)nn is around 27% [ 10]. In the present detectors at DESY and Cornell, both the charged and to some extent the neutral modes may be measured. In the upgraded CLEO detector at CorneU and the ones planned for the B meson factory, there will in fact be excellent efficiency and energy resolution for both the charged and neutral decay modes. Since these detectors also have a close to 4n acceptance, the efficiency to reconstruct the missing energy in the neutrino events should be excellent. One key factor of the e+e - machines relevant to the process we propose is the energy resolution of the beam in the vicinity ofle(2S). Since the main design factor for the B factory, for example, so far has been a maximal luminosity, the possibility to optimize the energy resolution does not seem to have been explored so far [ 5 ]. As we will see, this may be of crucial importance, and we would therefore like to urge the designers of this and similar facilities to take this into account. To estimate whether our result eq. (6) is big enough to make an experiment of this type worthwhile in the near future, we take the case of the Cornell e+e - collider CESR with the present beam energy resolution
Volume 201, number 2
PHYSICS LETTERS B
(around 4 MeV) and with an integrated effective luminosity of 5 p b - t per day which has recently been anticipated in the ongoing program of upgrades [ 9 ]. (At present, the machine has been running for long periods at 2 pb -~.) The peak cross section on the "f(2S) with this energy resolution is around 10 nb [ 11 ]. Using the value 0.27 for the Y(2S) ~ ' f ( 1 S ) n n branching ratio, we find at CESR a rate of number of~'(2S) -~nn + missing energy 30N~ per year.
(7)
This is already enough to distinguish between the cases Nv= 3 or 4 at the 1.5a level (90 and 120 events, respectively). However, it is clear that one order of magnitude more events would be desirable to settle the matter definitely. At Cornell, it seems that the best hope of improving the statistics further would be if the beam energy resolution could be optimized since the number of ~'(2S) 's produced is inversely proportional to the energy spread of the beam. (In most of the recent runs at both DESY and Cornell interest has been focused on B meson production which is performed at the relatively broad )e (4S) peak, where beam energy resolution is not a limitation. Therefore, a systematic effort to reduce the energy spread has, to our knowledge, not been undertaken so far.) The energy spread of DORIS at DESY is at present two or three times larger than that at Cornell. Also, the luminosity is somewhat lower which brings DORIS below the feasibility limit for this reaction at present. In the proposed B meson factory [ 5 ] the luminosity will be between one and two orders of magnitude higher and therefore an accurate measurement of N~ using this method seems relatively straightforward provided that the energy resolution is incorporated as an important factor in the optimization procedure. Just to get an indication of the importance of this factor, we may mention that the maximum cross section possible at the Y(2S) resonance is 2600 nb to be compared with the 10 nb presently visible at Cornell. We may also use the general formula (3) to compute the rate of neutrino decay of other vector mesons. The to (783) meson is quite narrow and would have been a good candidate for this process at the new hadronic machines like LEAR at CERN or CELSIUS
4 February 1988
in Uppsala that will produce a vast amount of these mesons (around 1013 to'S per year at LEAR with the ACOL installed, for instance). However, since the to is an isoscalar, there is an unfortunate cancellation in the average over the wave function in eq. (3). We get
F(to~vg)/F(to---,all) ~ 0 . 9 4 X 10-t3Nv ,
(8)
which is too small to be useful at present. The isovector p has an even smaller branching ratio due to its large hadronic width. For the 0(1020) meson, the ratio is 18.4 times the result in eq. (8), but since its production in hadronic processes is Zweig rule suppressed, it seems difficult to get a useful rate at present-day machines. The branching ratio for the JA¢ is 1.3× 10-SNv [8], which is too small even for the projected super-LEAR facility. A toponium 1S state of mass 80 GeV may have a branching ratio of the order of 3 × 10- 2Nv. However, the nrc decay of the 2S state into the 1S is expected to be very small [ 12 ], which means that a one year run at LEP will probably not be enough to give an unambiguous value for Nv. Consequently, we see that our proposed process in the upsilon system seems to be the unique window where neutrino counting may be performed in this new way in the not too distant future. For completeness, we also mention one other possible channel for neutrino counting in the upsilon system although, as we will see, it is roughly a factor of 20 less favourable in rate and has a non-negligible theoretical uncertainty. This is the decay chain Y(3S)--,gl(2P)7--,v97. Here the g~ (which is the triplet J = 1 P wave state of mass 10.255 GeV) couples through the axial part of the weak neutral current. Introducing in this case the axial decay constant
A: (015~'~75b1~) =iJAmZe~(2),
(9)
we get the rate (neglecting now the Z propagator effects) F(X, vg) =Nvf2AG~m~/(48zt),
(10)
and with a ratio to the weak neutral current production of ~t+~t- of F(X~ ~ v g ) / F ( z i --, ~t+ ~t- )
= 2Nv/[ 1 + ( 1 - 4 sin: 0w) 2] ,~ 2N~ .
(11 )
Due to C parity conservation, there is no one-photon 285
Volume 201, number 2
PHYSICS LETTERS B
contribution to the decay into lx+~t-. The two-photon rate is model dependent and has been estimated [ 13] to be between 7 and 20% o f the weak rate. This uncertainty puts a severe limitation on the accuracy of Nv that can be obtained by this method. There will also be a serious rate problem as we will now see. The branching ratio o f Y ( 3 S ) --,~ 17 is around 0.15, which is quite substantial. However, the hadronic width o f the ~ t state is expected to be quite large. Although the on-shell two-gluon decay is forbidden due to Yang's theorem, the Dalitz-like decay into gqdl contains a logarithmic divergence in the binding energy [ 14]. Using the result of this reference, we find a branching ratio
Rz =F(x~ ~ v g )/F(Zl ~hadrons ) 2 4 3 = 27NvGvmx/[2048nas log(mz/A) ] ,
(12)
where A is the binding energy of the b13 pair in the ~ 1 state. Putting a s = 0 . 2 , m x - 10.255 GeV and A = 0 . 4 GeV we find R z ~ 0 . 2 5 × 10-6Nv ,
(13)
which is more than an order of magnitude smaller than the result o f eq. (6). However, the uncertainty in the estimate of this branching ratio based on lowest-order Q C D is considerable, and if the true width turns out to be smaller then also this process may be o f interest to study experimentally. To summarize the results o f this paper, we have shown that neutrino counting in the upsilon system, especially on the T(2S), holds the promise of giving a very clean and accurate measurement o f the number o f light neutrino species in the standard model. Even with existing technology the process seems
286
4 February 1988
worthwhile studying experimentally, and in future electron-positron colliders optimized for the upsilon energy region the prospects seem very bright to measure Nv in an independent and in m a n y respects superior way to that of measuring directly the Z width. We wish to thank L. J/Snsson and M. Karliner for useful information. L.B. was sponsored by the Swedish Natural Science Research Council. H.R. wishes to thank the University o f Stockholm for hospitality.
References [1] P. Darriulat, rapporteur's talk at the 1987 High energy physics Conf. (Uppsala, Sweden). [2] J. Yang et al., Astrophys. J. 281 (1984) 493. [3] J. Ellis and R. Peccei, eds., Physics at LEP, CERN 86-02 (1986). [4] J. Ellis, J.S. Hagelin and S. Rudaz, Phys. Lett. B 192 (1987) 201. [ 5 ] R. Eichler et al., Motivation and design study for a B-meson factory with high luminosity, SIN PR-86-13 (1986). [ 6 ] G. Altarelli, summary talk at the 1987 High energy physics Conf. ( Uppsala, Sweden). [7] F.A. Berends, R. Kleiss and S. Jadach, Nucl. Phys. B 202 (1982) 63. [8] J. Ellis, Phys. Scr. 23 (1981) 328. [9] D.L. Rubin, CESR Luminosity Upgrade, CLNS 87/98 (1987). [ 10] Particle Data Group, M. Aguilar-Benitez et al., Review of particle properties, Phys. Lett. B 170 (1986) 1. [ 11 ] B. Gittelman and S. Stone, B meson decay, CLNS 87/81 (1987). [12] Y.P. Kuang and T.M. Yan, Proc. Cornell Z° Workshop, CLNS 81/485 (1981). [ 13] J.H. Kiihn, Acta Phys. Pol. B 12 (1981) 347. [14] R. Barbieri, R. Gatto and E. Remiddi, Phys. Lett. B 61 (1976) 465.
PHYSICS LETTERSB
4 February 1988
N E U T R I N O C O U N T I N G IN THE U P S I L O N SYSTEM Lars BERGSTROM Department of TheoreticalPhysics, Universityof Stockholm, Vanadisvdgen 9, S-113 46 Stockholm, Sweden
and Hector RUBINSTEIN Physikalisches Institut, Universityof Bonn, Nussallee 12, D-5300Bonn I, Fed. Rep. Germany
Received 29 October 1987
The rare decay Y(2S)~rc~v9 is suggestedas an unambiguousprobe of the number of light neutrino species. It is argued that the upgraded Cornell facilities and in particular the recently proposed B meson factory may provide the adequate number of )?(2S) particles to enable a definite distinction between the possibilities of Nv = 3, 4, or 5. The systematicerrors are arguedto be smaller than in methods based on measuring the width of the Z°. The radiative transition "f(3S)--.~v9is also considered.
The number of neutrino species is of greatest importance in particle physics. Besides its fundamental role in the evolution of the early universe, the number of neutrino species may also give a hint as to whether there exist more than three generations of quarks and leptons. Indeed, counting of neutrino species based on the width of the Z ° boson or the photon peak in e÷e - --'7 +missing energy is considered as a matter of highest priority at LEP and SLC. Already, there are indications from the CERN p~ collider data that the number of neutrino flavours is 5 or less [ I ]. There is also indirect astrophysical evidence that the number is in fact 4 or less [ 2]. Settling this question will be a difficult task at the new e+e coUiders [ 3 ]. In particular, there are many sources of systematic errors the size of which will be difficult to estimate. In view of this, it would certainly be important to establish this important number through an independent method. Up to now, the only realistic rare decay method has been thought to be the rare kaon decay K +-,re ÷ vg. However, this has the serious drawback that the hadronic matrix elements and weak mixing angles involved are largely unknown and On leave of absence from the WeizmannInstitute, 76100 Rehovot, Israel. 0370-2693/88/$ 03.50 © Elsevier Science Publishers B.V. (North-Holland Physics Publishing Division)
therefore the theoretical prediction is uncertain by a factor of around eight [4]. This is clearly not good enough to establish the number of neutrino species unambiguously. In this letter, we will show that a much better method is provided by studying the decay chain "f(2S)~Y(1S)nn --, vvnn, and also (although an order of magnitude less favourable) Y(3S) ~X~(2P)7 ~ v ~ . We shall see that the rate for the former process is large enough for a dedicated measurement of this decay at the upgraded Cornell facility CESR to give an unambiguous result for Nv, the number of neutrino species. At the proposed B meson factory [ 5 ], the measurement should be quite simple. In this method, there is the experimentally very appealing possibility to normalize the measured result to the corresponding decay with the neutrino pair replaced by an e+e - or ~t+~t- pair, which has identical kinematics and angular distributions, and which can be calculated unambiguously. This will cancel many systematic errors and provide a useful check of the apparatus, making this a very clean method of determining Nv. The decay Y( 1S)--. v9 proceeds through the vector part of the weak neutral current. Defining the vector coupling constantfv by 283
Volume 201, number 2
(015?~blY) =ifvm?ceu(2),
PHYSICS LETTERS B
(1)
where mr is the mass of'I'(1S) and eU(2) its polarization vector, we find the decay width for T(1S) / ' v =N~G~(48n) -) (sign (eQ) -- 4eQ sin 20w ) 2 m~.f2v × [(1 --mZ/m~) 2 + ( F z / m z ) 2] -'
(2)
Here ( ) denotes an average over the quarks in the wave function; in our case T consists of pure bb, so this factor is - 1 + ~ sin20w (we will use the value sinZ0w = 0.227 [6] in our numerical calculations). The correction from the Z propagator is only a two percent effect and is very insensitive to the Z width F z which we take to be 2.8 GeV; Mz is put at 93 GeV. The vector decay constant fv is related to the value of the wave function at the origin; however, we will take advantage of the fact that it is actually measured in Y--.e+e - or IX+Ix- decays so that we can make the model independent prediction for the ratio R between the two decay modes:
R =I"(~-,vg)/F(~;-.IX+IX -) = NvG~m~c/(64n2a 2) (sign(eQ)--4eQ sinZ0w) 2 X (eQ) - 2 C ( m r / m z ) ,
(3)
where the correction factor C includes the Z - 7 interference and Z propagator effects and is given by
C ( m r / m z ) -l = (1 _ff2)2 +p2 +if4 (UQ)2(/)2 +aZ)/(eQ )2
+ 2pZ(1--pZ)(VQ)Vo/(eQ).
(4)
Here p=rnr/mz, ~ =Fz/mz, vf= [ sign(er) 4efsin20w]/(4 sin 0w cos 0~) and af= - s i g n ( e r ) / ( 4 × sin 0w cos 0w). In our case, we find C ~ 1.02. Electromagnetic radiative corrections should be incorporated in the standard way for the final IX+IX- pair [7]. An approximative version of eq. (3) has previously been given by Ellis for the case of J/~ decays [ 8 ]. He concluded at that time that this branching ratio was very small for the J/~¢ but that it might be promising for toponium. However, we wish now to point out that already at existing e+e - machines this decay may provide a useful neutrino counting mechanism in the upsilon system. Besides the availability 284
4 February 1988
now of powerful colliders in the appropriate energy region, there are many factors that make this process much more favourable in the Y case. The quartic dependence on mass increases the ratio by a factor of 87 when passing from J[~g to ~/'. Moreover, the different electromagnetic and weak couplings of the b quark compared to the c quark gives another enhancement factor of roughly 16. Inserting numerical values in eq. (3), we obtain R r ~ 1.44X 10-4Nv .
(5)
Using the experimentally measured branching ratio ofT-~ix+/x - decays of (2.8 + 0.2)% [ 9], we find B R ( Y ~ v g ) = (0.40+0.03) × 10-SNv.
(6)
However, it is important to point out that the prediction of eq. (5) is free from the uncertainty of the IX÷ IXbranching ratio. In fact, by normalizing to muon pair production it seems that most of the systematical uncertainties of the experiments are eliminated. There remains to obtain a tag for the "invisible" T o y 9 decay. A convenient such tag is given by the decay chain Y(2S) ~ Y ( 1 S ) n x - , n x +missing energy. The branching ratio for "l'(2S)-~Y(1S)nn is around 27% [ 10]. In the present detectors at DESY and Cornell, both the charged and to some extent the neutral modes may be measured. In the upgraded CLEO detector at CorneU and the ones planned for the B meson factory, there will in fact be excellent efficiency and energy resolution for both the charged and neutral decay modes. Since these detectors also have a close to 4n acceptance, the efficiency to reconstruct the missing energy in the neutrino events should be excellent. One key factor of the e+e - machines relevant to the process we propose is the energy resolution of the beam in the vicinity ofle(2S). Since the main design factor for the B factory, for example, so far has been a maximal luminosity, the possibility to optimize the energy resolution does not seem to have been explored so far [ 5 ]. As we will see, this may be of crucial importance, and we would therefore like to urge the designers of this and similar facilities to take this into account. To estimate whether our result eq. (6) is big enough to make an experiment of this type worthwhile in the near future, we take the case of the Cornell e+e - collider CESR with the present beam energy resolution
Volume 201, number 2
PHYSICS LETTERS B
(around 4 MeV) and with an integrated effective luminosity of 5 p b - t per day which has recently been anticipated in the ongoing program of upgrades [ 9 ]. (At present, the machine has been running for long periods at 2 pb -~.) The peak cross section on the "f(2S) with this energy resolution is around 10 nb [ 11 ]. Using the value 0.27 for the Y(2S) ~ ' f ( 1 S ) n n branching ratio, we find at CESR a rate of number of~'(2S) -~nn + missing energy 30N~ per year.
(7)
This is already enough to distinguish between the cases Nv= 3 or 4 at the 1.5a level (90 and 120 events, respectively). However, it is clear that one order of magnitude more events would be desirable to settle the matter definitely. At Cornell, it seems that the best hope of improving the statistics further would be if the beam energy resolution could be optimized since the number of ~'(2S) 's produced is inversely proportional to the energy spread of the beam. (In most of the recent runs at both DESY and Cornell interest has been focused on B meson production which is performed at the relatively broad )e (4S) peak, where beam energy resolution is not a limitation. Therefore, a systematic effort to reduce the energy spread has, to our knowledge, not been undertaken so far.) The energy spread of DORIS at DESY is at present two or three times larger than that at Cornell. Also, the luminosity is somewhat lower which brings DORIS below the feasibility limit for this reaction at present. In the proposed B meson factory [ 5 ] the luminosity will be between one and two orders of magnitude higher and therefore an accurate measurement of N~ using this method seems relatively straightforward provided that the energy resolution is incorporated as an important factor in the optimization procedure. Just to get an indication of the importance of this factor, we may mention that the maximum cross section possible at the Y(2S) resonance is 2600 nb to be compared with the 10 nb presently visible at Cornell. We may also use the general formula (3) to compute the rate of neutrino decay of other vector mesons. The to (783) meson is quite narrow and would have been a good candidate for this process at the new hadronic machines like LEAR at CERN or CELSIUS
4 February 1988
in Uppsala that will produce a vast amount of these mesons (around 1013 to'S per year at LEAR with the ACOL installed, for instance). However, since the to is an isoscalar, there is an unfortunate cancellation in the average over the wave function in eq. (3). We get
F(to~vg)/F(to---,all) ~ 0 . 9 4 X 10-t3Nv ,
(8)
which is too small to be useful at present. The isovector p has an even smaller branching ratio due to its large hadronic width. For the 0(1020) meson, the ratio is 18.4 times the result in eq. (8), but since its production in hadronic processes is Zweig rule suppressed, it seems difficult to get a useful rate at present-day machines. The branching ratio for the JA¢ is 1.3× 10-SNv [8], which is too small even for the projected super-LEAR facility. A toponium 1S state of mass 80 GeV may have a branching ratio of the order of 3 × 10- 2Nv. However, the nrc decay of the 2S state into the 1S is expected to be very small [ 12 ], which means that a one year run at LEP will probably not be enough to give an unambiguous value for Nv. Consequently, we see that our proposed process in the upsilon system seems to be the unique window where neutrino counting may be performed in this new way in the not too distant future. For completeness, we also mention one other possible channel for neutrino counting in the upsilon system although, as we will see, it is roughly a factor of 20 less favourable in rate and has a non-negligible theoretical uncertainty. This is the decay chain Y(3S)--,gl(2P)7--,v97. Here the g~ (which is the triplet J = 1 P wave state of mass 10.255 GeV) couples through the axial part of the weak neutral current. Introducing in this case the axial decay constant
A: (015~'~75b1~) =iJAmZe~(2),
(9)
we get the rate (neglecting now the Z propagator effects) F(X, vg) =Nvf2AG~m~/(48zt),
(10)
and with a ratio to the weak neutral current production of ~t+~t- of F(X~ ~ v g ) / F ( z i --, ~t+ ~t- )
= 2Nv/[ 1 + ( 1 - 4 sin: 0w) 2] ,~ 2N~ .
(11 )
Due to C parity conservation, there is no one-photon 285
Volume 201, number 2
PHYSICS LETTERS B
contribution to the decay into lx+~t-. The two-photon rate is model dependent and has been estimated [ 13] to be between 7 and 20% o f the weak rate. This uncertainty puts a severe limitation on the accuracy of Nv that can be obtained by this method. There will also be a serious rate problem as we will now see. The branching ratio o f Y ( 3 S ) --,~ 17 is around 0.15, which is quite substantial. However, the hadronic width o f the ~ t state is expected to be quite large. Although the on-shell two-gluon decay is forbidden due to Yang's theorem, the Dalitz-like decay into gqdl contains a logarithmic divergence in the binding energy [ 14]. Using the result of this reference, we find a branching ratio
Rz =F(x~ ~ v g )/F(Zl ~hadrons ) 2 4 3 = 27NvGvmx/[2048nas log(mz/A) ] ,
(12)
where A is the binding energy of the b13 pair in the ~ 1 state. Putting a s = 0 . 2 , m x - 10.255 GeV and A = 0 . 4 GeV we find R z ~ 0 . 2 5 × 10-6Nv ,
(13)
which is more than an order of magnitude smaller than the result o f eq. (6). However, the uncertainty in the estimate of this branching ratio based on lowest-order Q C D is considerable, and if the true width turns out to be smaller then also this process may be o f interest to study experimentally. To summarize the results o f this paper, we have shown that neutrino counting in the upsilon system, especially on the T(2S), holds the promise of giving a very clean and accurate measurement o f the number o f light neutrino species in the standard model. Even with existing technology the process seems
286
4 February 1988
worthwhile studying experimentally, and in future electron-positron colliders optimized for the upsilon energy region the prospects seem very bright to measure Nv in an independent and in m a n y respects superior way to that of measuring directly the Z width. We wish to thank L. J/Snsson and M. Karliner for useful information. L.B. was sponsored by the Swedish Natural Science Research Council. H.R. wishes to thank the University o f Stockholm for hospitality.
References [1] P. Darriulat, rapporteur's talk at the 1987 High energy physics Conf. (Uppsala, Sweden). [2] J. Yang et al., Astrophys. J. 281 (1984) 493. [3] J. Ellis and R. Peccei, eds., Physics at LEP, CERN 86-02 (1986). [4] J. Ellis, J.S. Hagelin and S. Rudaz, Phys. Lett. B 192 (1987) 201. [ 5 ] R. Eichler et al., Motivation and design study for a B-meson factory with high luminosity, SIN PR-86-13 (1986). [ 6 ] G. Altarelli, summary talk at the 1987 High energy physics Conf. ( Uppsala, Sweden). [7] F.A. Berends, R. Kleiss and S. Jadach, Nucl. Phys. B 202 (1982) 63. [8] J. Ellis, Phys. Scr. 23 (1981) 328. [9] D.L. Rubin, CESR Luminosity Upgrade, CLNS 87/98 (1987). [ 10] Particle Data Group, M. Aguilar-Benitez et al., Review of particle properties, Phys. Lett. B 170 (1986) 1. [ 11 ] B. Gittelman and S. Stone, B meson decay, CLNS 87/81 (1987). [12] Y.P. Kuang and T.M. Yan, Proc. Cornell Z° Workshop, CLNS 81/485 (1981). [ 13] J.H. Kiihn, Acta Phys. Pol. B 12 (1981) 347. [14] R. Barbieri, R. Gatto and E. Remiddi, Phys. Lett. B 61 (1976) 465.