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Two muon events and new particle production
Volume 59B, number 3
PHYSICS LETTERS
TWO MUON EVENTS AND NEW PARTICLE
10 November 1975
PRODUCTION ~
K.A. MILTON and L.L. DeRAAD, Jr.
Department of Physics, University of California, Los Angeles, Calif. 90024, USA Received 11 June 1975 Revised manuscript received 4 August 1975 Schwinger's interpretation of the narrow resonances coupling to the electric current suggests that there are charged vector particles that decay weakly, having mass of perhaps 3.4 GeV. These may have already been seen in ne.utrino scattering experiments.
In the wake of the discovery of the neutral narrow resonances at 3.1 and 3.7 GeV [1, 2] much experimental and theoretical effort has been expended on the question of whether there are other particles of the same class. The most striking and substantial evidence for new particle production reported so far has been provided by high energy neutrino and anti-neutrino experiments, resulting in "dimuon" production [3], and anomalous y-distributions [4]. Presumably, a charged current event produces a particle which decays weakly into/~t7 with a branching ratio of a few percent: the mass of this particle is estimated to lie between 2 and 4 GeV. We would like to suggest that these events could be interpreted in terms of a framework which Schwinger has earlier applied to the ~k particles [5]. That idea was based upon an extension to hadrons of a broken gauge theory of weak and electromagnetic interactions so as to avoid the appearance of hyperchargechanging neutral currents [6]. A simple version of this scheme, employing vector and axial-vector fields Oab, aab (the subscripts are U 3 indices) IS expressed by the interaction Lagrange function
£' = X'/-2g m2 { A 1 1 I ° 11 1
~ a~°aa +°11 - ~ a ° a a l 1
+A21 [7(o12 +a12 ) +7(o13 +a13 ) sin 0 1 r p 1 + a21) +7(o13 +a13 ) c o s 0 ] +A12 [g(v21
(1)
+½(o31+a31)sin 0 + ~'(v31 1 , +a31 , ) cos 0] 1
+A2217(u11 1 ,
, ,
1
all)+7(o22 +a22)
I S
g
a
Oaa
+g(Oll all) + ~'1.033 +a33~ -O'aa • Work supported in part by the National Science Foundation.
Here the Aab represent the fields of the photon, W*-, and Z particles, and 0 plays, approximately, the role of the Cabibbo angle. The unprimed fields, o, a correspond to the usual vector mesons p, co, ~, K*, and their axial partners such as A 1 and 3rr. The primed fields stand for a new class of vector- and axial-vector particles that have greatly suppressed couplings to ordinary hadrons, perhaps at about the 2% level to reproduce the usual cos 0 c factor in the weak, charged, hypercharge conserving current. In ref. [5] Schwinger identifies the primed vector particles coupling to the photon in this model, designated (by analogy with the usual octet o f 1- mesons) p', co', q)', with the ~b particles. (Here p' is not be confused with the ordinary hadron p'(1600).)-The substantial suppression of the hadronic decays of these particles, with the total decay rate being roughly of the same order of magnitude as the electromagnetic, is thus anticipated, if not explained; and the suggestion is made that the residual 2% hadronic interaction is somehow "triggered" by electromagnetism. The "triggering mechanism" is to be understood as a general framework for characterizing these phenomena, reasonably independent of speculative hypotheses. We mean by the triggering mechanism that the linear coupling of ~ particles to hadrons is an induced electromagnetic effect. This general idea is abstracted from the experimental hadronic suppression, and does not preclude its explanation through a more detailed mechanism such as symmetry breaking, or in terms of a specific model (charm, dyons?). Again taking experiment as a guide, we suggest that the triggering mechaWork supported in part by the National Science Foundation. 285
Volume 59B, number 3
PHYSICS LETTERS
nism does not apply to the bilinear couplings of the ~'s, since photoproduction seems to be of small but hadronic magnitude [2], a fact which appears to be consistent with the rate for the decay if' ~ ~brrTr [7]. We here wish to observe that this scheme requires the presence of charged primed particles, such as (K*') -+, coupled to the We bosons with the same strength as the p '°, co', 6' are coupled to the photon. Then extending the triggering idea to the broken gauge theory partners of the photon, we suggest that linear couplings of the primed particles are scaled by the couplings through the gauge particles (due to dynamical symmetry breaking?), so that the decay rate of (K*') -+ relative to p'O is reduced by the factor (m d /2m w )2 ~ 10 - 5 . Thus the weak leptonic decay rate of such particles (into say/2u-) will be a substantial fraction of the total rate. Taking this analogy with the usual 1- mesons seriously, we can estimate the mass of the K*' on the basis of the usual linear mass formula [8]. That is, if we regard the if(3100) to be a combination of nearly degenerate p' and co', and ~'(3700) to be ~', the K*' would lie half-way between: inK,, = 3400 MeV. Such a mass value prohibits the decays ~0(3700) -+ K*' + K and K*' -+ ~(3100) + K which, otherwise, might take place at too fast a rate. The only known experimental number relevant to this conjectured particle is that in deep inelastic neutrino experiments, for every one thousand singte-muon events, about one 2-muon event is seen [3]. [If a cut is made for neutrino energies greater than 40 GeV, the quoted dimuon to single muon event ratio is (9 + 3) X 10 - 3 (with perhaps an additional factor of two uncertainty)]. We will now argue that this is not an unreasonable number with the above identification. We will do this by considering four related processes. (1) Our model for the 2/2 events is the following: The v(in),/2(out) act as a source for a charged W which couples to the K*'. This K*', which has large, spacelike m o m e n t u m (t), diffractively scatters off the nucleus becoming real and then decays into a/a and (fig. la). (2) A related matrix element occurs for the photoproduction Of the if(3100). For this process, the incident photon couples to the ~(3100) (t = 0) which diffractively scatters off the nucleus and then decays into a muon pair. The cross section for this process, a(TN -+ ~ + / 2 - ) + X), seems to be about 1 nb per nu286
10 November 1975
W
K~'
(a)
(b)
(c)
9
(d)
Fig. 1.(a) The 2# process. (b) Photoproduction and decay of the ~. (c) The 1# process. (d) Compton scattering. (Final hadronic states are not indicated.) cleon [2] (fig. lb). (3) For the single-muon events, the charged W typically couples to a charged t9 (t large and space-like) which is "absorbed" by the nucleus (fig. lc). (4) A matrix dement related to process (3) occurs for inelastic nuclear Compton scattering. F o r this process, the incident photon couples typically to a 19o (t = 0) which is "absorbed" by the nucleus. For large photon energies, the total cross section of a single nucleon, o(TN ~ X), is about 100/2b (fig. ld). We learn about the ratio of the 2/2 events to the 1/2 events by comparing with the related photo-processes, viz.,
(1) _ (2) (1) (4) (4) (2) (3)"
(2)
R -- (3)
As suggested above, the triggering mechanism is inoperative for the quadratic couplings of the primed particles to ordinary hadronic matter. In particular, for
PHYSICS LETTERS
Volume 59B, number 3
scattering processes in which a given primed particle retains its identity, the cross section is roughly the same for all members of the same SU 3 multiplet. Hence we make the important assumption: o(K*' + N ~ K*' + X) ~ o(~ + N - ~ ~ + X).
(3)
(Indeed, if the first cross section were much smaller, we would never see the 2t~ events). But we do assume that the triggering mechanism operates for the primed particles, that is, that the linear hadronic couplings of the ff and K*' are o f the same magnitudes as those that go through the intermediary of the photon and W bosons, respectively, as given in eq. (1). F o r the/~ events, if we assume t is large (t N m 2 . , , m.2), the mass dependence o f the propagation functions of the virtual K*' or p can be ignored; while for the comparison photo-processes, the propagation functions of the virtual ~ and O reduce to the corresponding inverse squared masses. All of this leads to the estimate
R~
o(3,N ~ ~ + / a - ) + X) ( ~ 2
~ N~)
tm2"~2 ~
"'~ ~ pJ
3 × 10 - 3
(4)
which is certainly of the same order of magnitude as seen experimentally. Essentially this same conclusion can be reached b y directly comparing processes (1) and (3) (figs. la and lc), which gives
R ~ ~,(K*'N) r(K*' -, Uv)/r(K*')
(5)
o(pN) and then assuming that the K*'-nucleon diffractive cross section, o(K*'N), is about the same as the ~-nucleon total cross section, about 1 mb [2], while the pnucleon total cross section is about 20 mb [9]. A branching ratio o f a few percent then corresponds to the value o f R found above. So, just as the total width o f the ~(3100) seems to be roughly of electromagnetic magnitude, the total width o f the K*' is weak. It could well be that, as conjectured by Schwinger,
10 November 1975
the hadronic decays o f these particles are induced b y the gauge bosons. Finally, we note that there have been reports o f other processes suggesting new particle production: In particular, SPEAR reports [10] seeing the reaction e+e - ~ eeg ~ + no visible particles at ECM = 4.8 GeV. A possible interpretation is the production of a pair o f new particles with mass < 2.4 GeV. If it is a new boson, it seems clear that it has spin 1 because of the presence o f the electron decay mode. It is possible that this particle is the K*', although the mass seems much too low. A more likely possibility is that the new particle is an axial vector primed particle. Not knowing the dynamics of the primed particles, the a'ab particles might well have masses below those o f the Oab particles. r
We thank Professor Julian Schwinger for many helpful conversations on these matters, and for reading and criticizing the manuscript. We are grateful to Dr. Wu-yang Tsai for useful suggestions, and to Professor J.J. Sakurai for comments on t h e experimental situation.
References [1] J.J. Aubert et al., Phys. Rev. Lett. 33 (1974) 1404; J.E. Augustin et al., Phys. Rev. Lett. 33 (1974) 1406; G.S. Abrams et al., Phys. Rev. Lett. 33 (1974) 1453. [2] B. Knapp et al., Phys. Rev. Lett. 34 (1975) 1040. [3] A. Benvenuti et al., Phys. Rev. Lett. 34 (1975) 419. [4] B. Aubert et al., Phys. Rev. Lett. 33 (1974) 984; A. Benvenuti et al., Phys. Rev. Lett. 34 (1975) 597. [5] J. Sehwinger, Phys. Rev. Lett. 34 (1975) 37. [6] J. Schwinger, Phys. Rev. D8 (1973) 960. E7] J. Schwinger, K.A. Milton, W.-y. Tsai and L.L. DeRaad, Jr. UCLA preprint UCLA/75]TEP[8. [8] J. Sehwinger, Phys. Rev. t65 (1968) 1714. [9] J. Ballam et al., Phys. Rev. D7 (1973) 3150. [10] M.L. Perl, SLAC preprint, SLAC-PUB-1592, June 1975.
287
PHYSICS LETTERS
TWO MUON EVENTS AND NEW PARTICLE
10 November 1975
PRODUCTION ~
K.A. MILTON and L.L. DeRAAD, Jr.
Department of Physics, University of California, Los Angeles, Calif. 90024, USA Received 11 June 1975 Revised manuscript received 4 August 1975 Schwinger's interpretation of the narrow resonances coupling to the electric current suggests that there are charged vector particles that decay weakly, having mass of perhaps 3.4 GeV. These may have already been seen in ne.utrino scattering experiments.
In the wake of the discovery of the neutral narrow resonances at 3.1 and 3.7 GeV [1, 2] much experimental and theoretical effort has been expended on the question of whether there are other particles of the same class. The most striking and substantial evidence for new particle production reported so far has been provided by high energy neutrino and anti-neutrino experiments, resulting in "dimuon" production [3], and anomalous y-distributions [4]. Presumably, a charged current event produces a particle which decays weakly into/~t7 with a branching ratio of a few percent: the mass of this particle is estimated to lie between 2 and 4 GeV. We would like to suggest that these events could be interpreted in terms of a framework which Schwinger has earlier applied to the ~k particles [5]. That idea was based upon an extension to hadrons of a broken gauge theory of weak and electromagnetic interactions so as to avoid the appearance of hyperchargechanging neutral currents [6]. A simple version of this scheme, employing vector and axial-vector fields Oab, aab (the subscripts are U 3 indices) IS expressed by the interaction Lagrange function
£' = X'/-2g m2 { A 1 1 I ° 11 1
~ a~°aa +°11 - ~ a ° a a l 1
+A21 [7(o12 +a12 ) +7(o13 +a13 ) sin 0 1 r p 1 + a21) +7(o13 +a13 ) c o s 0 ] +A12 [g(v21
(1)
+½(o31+a31)sin 0 + ~'(v31 1 , +a31 , ) cos 0] 1
+A2217(u11 1 ,
, ,
1
all)+7(o22 +a22)
I S
g
a
Oaa
+g(Oll all) + ~'1.033 +a33~ -O'aa • Work supported in part by the National Science Foundation.
Here the Aab represent the fields of the photon, W*-, and Z particles, and 0 plays, approximately, the role of the Cabibbo angle. The unprimed fields, o, a correspond to the usual vector mesons p, co, ~, K*, and their axial partners such as A 1 and 3rr. The primed fields stand for a new class of vector- and axial-vector particles that have greatly suppressed couplings to ordinary hadrons, perhaps at about the 2% level to reproduce the usual cos 0 c factor in the weak, charged, hypercharge conserving current. In ref. [5] Schwinger identifies the primed vector particles coupling to the photon in this model, designated (by analogy with the usual octet o f 1- mesons) p', co', q)', with the ~b particles. (Here p' is not be confused with the ordinary hadron p'(1600).)-The substantial suppression of the hadronic decays of these particles, with the total decay rate being roughly of the same order of magnitude as the electromagnetic, is thus anticipated, if not explained; and the suggestion is made that the residual 2% hadronic interaction is somehow "triggered" by electromagnetism. The "triggering mechanism" is to be understood as a general framework for characterizing these phenomena, reasonably independent of speculative hypotheses. We mean by the triggering mechanism that the linear coupling of ~ particles to hadrons is an induced electromagnetic effect. This general idea is abstracted from the experimental hadronic suppression, and does not preclude its explanation through a more detailed mechanism such as symmetry breaking, or in terms of a specific model (charm, dyons?). Again taking experiment as a guide, we suggest that the triggering mechaWork supported in part by the National Science Foundation. 285
Volume 59B, number 3
PHYSICS LETTERS
nism does not apply to the bilinear couplings of the ~'s, since photoproduction seems to be of small but hadronic magnitude [2], a fact which appears to be consistent with the rate for the decay if' ~ ~brrTr [7]. We here wish to observe that this scheme requires the presence of charged primed particles, such as (K*') -+, coupled to the We bosons with the same strength as the p '°, co', 6' are coupled to the photon. Then extending the triggering idea to the broken gauge theory partners of the photon, we suggest that linear couplings of the primed particles are scaled by the couplings through the gauge particles (due to dynamical symmetry breaking?), so that the decay rate of (K*') -+ relative to p'O is reduced by the factor (m d /2m w )2 ~ 10 - 5 . Thus the weak leptonic decay rate of such particles (into say/2u-) will be a substantial fraction of the total rate. Taking this analogy with the usual 1- mesons seriously, we can estimate the mass of the K*' on the basis of the usual linear mass formula [8]. That is, if we regard the if(3100) to be a combination of nearly degenerate p' and co', and ~'(3700) to be ~', the K*' would lie half-way between: inK,, = 3400 MeV. Such a mass value prohibits the decays ~0(3700) -+ K*' + K and K*' -+ ~(3100) + K which, otherwise, might take place at too fast a rate. The only known experimental number relevant to this conjectured particle is that in deep inelastic neutrino experiments, for every one thousand singte-muon events, about one 2-muon event is seen [3]. [If a cut is made for neutrino energies greater than 40 GeV, the quoted dimuon to single muon event ratio is (9 + 3) X 10 - 3 (with perhaps an additional factor of two uncertainty)]. We will now argue that this is not an unreasonable number with the above identification. We will do this by considering four related processes. (1) Our model for the 2/2 events is the following: The v(in),/2(out) act as a source for a charged W which couples to the K*'. This K*', which has large, spacelike m o m e n t u m (t), diffractively scatters off the nucleus becoming real and then decays into a/a and (fig. la). (2) A related matrix element occurs for the photoproduction Of the if(3100). For this process, the incident photon couples to the ~(3100) (t = 0) which diffractively scatters off the nucleus and then decays into a muon pair. The cross section for this process, a(TN -+ ~ + / 2 - ) + X), seems to be about 1 nb per nu286
10 November 1975
W
K~'
(a)
(b)
(c)
9
(d)
Fig. 1.(a) The 2# process. (b) Photoproduction and decay of the ~. (c) The 1# process. (d) Compton scattering. (Final hadronic states are not indicated.) cleon [2] (fig. lb). (3) For the single-muon events, the charged W typically couples to a charged t9 (t large and space-like) which is "absorbed" by the nucleus (fig. lc). (4) A matrix dement related to process (3) occurs for inelastic nuclear Compton scattering. F o r this process, the incident photon couples typically to a 19o (t = 0) which is "absorbed" by the nucleus. For large photon energies, the total cross section of a single nucleon, o(TN ~ X), is about 100/2b (fig. ld). We learn about the ratio of the 2/2 events to the 1/2 events by comparing with the related photo-processes, viz.,
(1) _ (2) (1) (4) (4) (2) (3)"
(2)
R -- (3)
As suggested above, the triggering mechanism is inoperative for the quadratic couplings of the primed particles to ordinary hadronic matter. In particular, for
PHYSICS LETTERS
Volume 59B, number 3
scattering processes in which a given primed particle retains its identity, the cross section is roughly the same for all members of the same SU 3 multiplet. Hence we make the important assumption: o(K*' + N ~ K*' + X) ~ o(~ + N - ~ ~ + X).
(3)
(Indeed, if the first cross section were much smaller, we would never see the 2t~ events). But we do assume that the triggering mechanism operates for the primed particles, that is, that the linear hadronic couplings of the ff and K*' are o f the same magnitudes as those that go through the intermediary of the photon and W bosons, respectively, as given in eq. (1). F o r the/~ events, if we assume t is large (t N m 2 . , , m.2), the mass dependence o f the propagation functions of the virtual K*' or p can be ignored; while for the comparison photo-processes, the propagation functions of the virtual ~ and O reduce to the corresponding inverse squared masses. All of this leads to the estimate
R~
o(3,N ~ ~ + / a - ) + X) ( ~ 2
~ N~)
tm2"~2 ~
"'~ ~ pJ
3 × 10 - 3
(4)
which is certainly of the same order of magnitude as seen experimentally. Essentially this same conclusion can be reached b y directly comparing processes (1) and (3) (figs. la and lc), which gives
R ~ ~,(K*'N) r(K*' -, Uv)/r(K*')
(5)
o(pN) and then assuming that the K*'-nucleon diffractive cross section, o(K*'N), is about the same as the ~-nucleon total cross section, about 1 mb [2], while the pnucleon total cross section is about 20 mb [9]. A branching ratio o f a few percent then corresponds to the value o f R found above. So, just as the total width o f the ~(3100) seems to be roughly of electromagnetic magnitude, the total width o f the K*' is weak. It could well be that, as conjectured by Schwinger,
10 November 1975
the hadronic decays o f these particles are induced b y the gauge bosons. Finally, we note that there have been reports o f other processes suggesting new particle production: In particular, SPEAR reports [10] seeing the reaction e+e - ~ eeg ~ + no visible particles at ECM = 4.8 GeV. A possible interpretation is the production of a pair o f new particles with mass < 2.4 GeV. If it is a new boson, it seems clear that it has spin 1 because of the presence o f the electron decay mode. It is possible that this particle is the K*', although the mass seems much too low. A more likely possibility is that the new particle is an axial vector primed particle. Not knowing the dynamics of the primed particles, the a'ab particles might well have masses below those o f the Oab particles. r
We thank Professor Julian Schwinger for many helpful conversations on these matters, and for reading and criticizing the manuscript. We are grateful to Dr. Wu-yang Tsai for useful suggestions, and to Professor J.J. Sakurai for comments on t h e experimental situation.
References [1] J.J. Aubert et al., Phys. Rev. Lett. 33 (1974) 1404; J.E. Augustin et al., Phys. Rev. Lett. 33 (1974) 1406; G.S. Abrams et al., Phys. Rev. Lett. 33 (1974) 1453. [2] B. Knapp et al., Phys. Rev. Lett. 34 (1975) 1040. [3] A. Benvenuti et al., Phys. Rev. Lett. 34 (1975) 419. [4] B. Aubert et al., Phys. Rev. Lett. 33 (1974) 984; A. Benvenuti et al., Phys. Rev. Lett. 34 (1975) 597. [5] J. Sehwinger, Phys. Rev. Lett. 34 (1975) 37. [6] J. Schwinger, Phys. Rev. D8 (1973) 960. E7] J. Schwinger, K.A. Milton, W.-y. Tsai and L.L. DeRaad, Jr. UCLA preprint UCLA/75]TEP[8. [8] J. Sehwinger, Phys. Rev. t65 (1968) 1714. [9] J. Ballam et al., Phys. Rev. D7 (1973) 3150. [10] M.L. Perl, SLAC preprint, SLAC-PUB-1592, June 1975.
287