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Unidentified heavy object at the SppS collider: Excited quark or excited colour boson?
Volume 151 B, number 3,4
PHYSICS LETTERS
14 February 1985
UNIDENTIFIED H E A V Y OBJECT AT THE SpaS COLLIDER: EXCITED QUARK OR EXCITED COLOUR BOSON? S.S. GERSHTEIN, G.V. JICKIA and Yu.F. PIROGOV
Institute for High Energy Physics, Serpukhov, USSR Received 16 October 1984 Exotic events with a large missing transverse momentum (up to 80-90 GeV[c) observed at the CERN pl~ collider are shown to require, by their signature and effective cross section, the existence of an object with a mass of about 180 GeV/ c2, which would be produced in a resonance way from hadron beam constituents and would be able to decay into W jet and Z jet. An excited quark q* produced in qg fusion and decaying into Wq and Zq seems to be the most natural candidate for such an object. However, one cannot exclude excited colour boson W~ produced in qC1 collisions and decaying into Wg and Zg.
1. Introduction. Exotic events with a missing transverse momentum up to ( 8 0 - 9 0 ) GeV/e observed at the SpaS collider, i.e. singlet hadron jets and single hadron jets accompanied by a charged lepton, can serve as an indication to the existence of an unMentifiedheavy object(UHO) with mass of about 180 GeV/c 2 [ 1]. At the same time, the signature of these events, i.e. the absence o f additional prompt jets at least in a part o f the events, can be considered to indicate a single production of the UHO from the constituents of hadron beams. Such a single production could not be fulfilled otherwise than in a resonance fashion. In this, naturally, the alternatives emerge: (i) The resonance is produced in a quark (antiquark)gluon system. In this case, the UHO is an excited quark q* = (u*, d*) or the corresponding antiquark. Such a possibility has been considered previously in refs. [2, 3 ]. The interpretation of the exotic events is reduced in this case to the resonance production of the excited quark with its subsequent decays in the channels qg--+ q* -~ q W ~ .~±(~), -+ q Z ~ ,
(1)
__
* +
- (W c-, Wc0), capable of decaying in the channels
qC1--+ Wc -+ gW~+ ~+ (~), -+ g Z v~,
(2)
is required to interpret the exotic events. The hadron jet is initiated in this case by the gluon ,1 Should there exist a pp collider of the proper energy, the question of the UHO nature could be solved experimentally in a rather simple way. The reason is that the excited quarks would be produced in pp collisions with the same rate as in pl5 collisions, while the excited colour boson production would be suppressed to the sea antiquark level in the p-beams. At the same time, the question raised can be clarified by accumulating a rather large statistics at the SpaS collider if one makes use of the charged lepton x-distribution asymmetry (see later). In the present paper we consider more thoroughly the excited quark hypothesis and some of its experimentally verified consequences.
2. The cross section for the p~ -~ ]et ~ ± (-v),jet u~ processes. Note that in the general case excited quarks could belong to various multiplets corresponding to
where q = (u, d), and similarly for the antiquark. The hadron jet in this is produced by the light quark. (ii) The resonance is produced in a qgl-system. In this case the existence of an excited colour boson W~
.1 The presence of additional soft hadron jets in some of the observed events should be explained in the framework of both hypotheses by the QCD corrections to the UHO resonance production. 303
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the colour, weak isospin, radial (without changing the quantum numbers) and spin (orbital) excitations. According to (1), to explain the exotic events, the quarks we are probably dealing with in this case must belong to a colour triplet ,2. As for the spin of the excited quarks, here, apart from the ordinary value J = 1/2, it seems quite possible and even attractive in analogy with N--A to admit J = 3/2. Next, it would be natural to consider that the major contribution to the total width F. of the excited quark comes from its strong decay into a light quark and a gluon. Then, P. ~ asM , may quite reasonably be taken as an estimate, where M. is the q* mass. The widths of the q* electroweak decays with emission of a vector boson V = (W, Z, 7) are expected to be of the order of P V ~-aM.. The cross section for the qg ~ q* ~ qV resonance process is of the form 2J+ 1 6V=2x2x3X8
4rr PiPv M~, ( L ~ _ M , ) 2 + p 2 / 4 .
(3)
Here J is the excited quark spin, Pi ~ P, is the initial channel width,E is the energy of the qg beams and the factors in the denominator come from averaging over quark and gluon polarizations and colours. The differential cross section for the pl5 ~ j e t V process is d o v _ ( 2 J + l ) ( 4 1 r ) 2 Pv(d~_~qg dLqg, dx 2 X 2 X 3 X 8 M, + -'-~-] '
(4)
dx
o(pl5 ~ jet e-+(p)) "" 3.4 X 10 -2 nb, o(plS--* jet all v~ -~ 7.7 X 10 -2 nb.
(7)
The experimental cuts being taken into account, the values obtained are in rather good agreement in order of magnitude with the experimental data, i.e. several events for the ~ 100 nb -1 integrated luminosity. 3. The lepton charge asymmetry. The salient feature of the pl5-+ jet £-+ (u) processes, in case they proceed through the excited quark production, should be a charge asymmetry for the events with leptons of definite charge, or, equivalently, a forward-backward asymmetry for leptons of fixed charge. This is caused by the fact that the differential luminosity of the qg beams resuiting in leptons of, say, positive charge, is shifted towards positive values o f x due to a softer gluon distribution and relation dLug/dx ~- 2 dLdg/dx. The same luminosity for leptons of negative charge is shifted, accordingly, to negative values ofx. The charge asymmetry parame ter (A ÷ = - A - )
(8)
L+(x > O) +L-(x > 0)' 1 Xlx2fq(xl)fg(X2) M2
(x 2 + 4r)1/2
(5)
is the differential luminosity of qg beams; fq(Xl) , fg(X2) are the structure functions of quark and gluon distributions;x = x 1 - x 2 , z - X l X 2 ;Xl, 2 =½ [(x 2 + 4r)l/2 -+x], r =M2./s, and analogously for (lg. The total luminosity of the qg and (lg beams for /14. = 180 GeV/c 2 and X/s"= 540 GeV being of the orderLqg + cTg"" 2.2 X 10-5 GeV -2, we have for the total cross section of pl5 -+ jet V: ov = ( 2 J + 1 ) ( r v / M , )
1.4 X 10-32 cm 2.
(6)
. 2 The excited quarks belonging to higher colour multiplets could manifest themselves in two-jet events. The excitation of higher isospin states in qg collisions is absent in the general case, b u t it can surely take place in 7 q collisions at the e p collider.
304
+ +(-) Taking into account the branching ratios B(W- -* e- v ) "" 8 X 10-2,B(Z-* all t,~ ~ 1.8 X 10 -1 and assuming Pw ~- Pz ~- aM., one may finally expect the cross sections of the exotic processes to be
a+_ = U ( x > o) - L~(x > 0)
where dLqg_
14 February 1985
where L±(x > 0 ) = f [ dLug(ag) +
dLg(dgq dx
(9)
x>0
[L±(x > 0) =L*(x < 0)] has a noticeable value,A -+''+ 0.3. The existence of such an asymmetry could in principle be used to discriminate hypotheses (i) and (ii). Unfortunately, a charge asymmetry of the same sign exists also in the differential luminosity of the ud and dfi beams due to the difference of the u- and dquark structure functions of the proton [ fu(x) ~- 2fd(x)]. Though the asymmetry in the q~ processes A +- "" + 0.18 is considerably smaller than in qg, clg beams, the realization of the indicated possibility would require a rather large statistics. 4. Spectra o f lepton energies and missing transverse momentum. The particular form of the q* ~ qV inter-
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action was inessential for the previous consideration. The consideration was based only on the resonance fashion o f the q* p r o d u c t i o n in the qg beams and on the pecularities o f the x - d i s t r i b u t i o n o f the latter. But to study the energy spectra and angular correlations o f the q* decay products one needs a particular choice for the effective lagrangian Z ? ~ . The detailed analysis o f different possibilities is given in refs. [3,4]. Here we restrict ourselves only by the following remarks• Assuming the exact colour and electromagnetic local gauge invariance, one necessarily arrives at the lagrangians o f the gluon and p h o t o n emission q* ~ qg, q7 in the form o f the i n t e r a c t i o n with a transition magnetic m o m e n t p . . As to the W e interaction, here b o t h the m i n i m a l coupling with the field itself and the anomalous coupling with the field strength is admissible, dep e n d i n g on the a s s u m p t i o n o n the W nature, i.e. whether the W b o s o n is composite or elementary. The corresponding effective lagrangians in the most general case have the following form: for spin J = 1/2 f2e(~ft) = f , ~*(a + b 7 5 ) 7~ qW~ + h.c.,
(10)
~?eWf~)
14 February 1985 =
/.t,~q
-,
(a
i+
t
b75)ouvqWuv+h.c.,
(10')
and for spin J = 3/2 Zef~f~ --f~ Cl*(a + b 7 5 ) q W ~ + h.c., * #
(11)
Z?ef~ft)=p,f',qa(a
(ll')
b 75) 7uqWuu + h.c..
In this, Z?e(ffff°)must always have the form (10'), (11') because the electromagnetic gauge s y m m e t r y should n o t be b r o k e n in the W07 ~ Z7 mixing. Since it is impossible at present to give obvious preference to any statement o n the dynamics o f the q* excitation and the W nature, it seems reasonable to consider all the forms o f Z?e(fff~) to calculate the energy distributions and angular correlations in the decays q* -+ qV. The calculational results for the normalized distributions o f the n e u t r i n o (electron) energy dN./dko, as well as for the total widths o f the q* ~ q~-+ (~) decays for two variants o f the coupling, for b o t h values o f spin J = 1/2 a n d J = 3/2 are given in tables 1 and 2, respectively. In virtue o f C P invariance these results are also ap-
Table 1 Characteristics of the decay q* -} qW, W --+~ (~) v of an excited quark q* with spin J = 1/2. The first row gives the decay effective • 1 lagrangians. The form of the charged lepton current is ~Tu 2" (1 - "rs)V. For the qL production process one has a = b = 1/x/~. The second row is the absolute value squared for the decay matrix elements in terms of invariant variables, summed over helicities. Here Q is the 4-momentum of q*, p the n-momentum, k the v-momentum; f¢ is the charge sign of the decaying q* (produced 2). Invariant variables are connected thro ugh the relation kQ + pQ = l(M2. +M~V). IQ'~I2 shows energy co rrelations (ko, p o) between energies of v and ~ in the rest frame of q*. With account for the relation ko(Po ) = (M./2) ( 1 ~ v cos Ojv)/(1 + v) it also gives angular correla2 2 2 tions for neutrino-jet, where v = (M,2 - M~V)/(M , +M~) is the velocity of q , in the W rest frarne, and Ojv is the emission angle of v with respect to the jet direction in the same frame. As is seen, neutrinos of higher energy move against the jet and are accompanied by leptons of lower energy moving along the jet. The third row gives the normalized distributions of v energy and emission angle with respect to direction of q* polarization for qL production (a = b = I/x/2"-). Here e = 2ko/M , is the fractional energy of v in theq* rest frame in parts of the maximum possible one; e o ~
Anomalous coupling
f , Cl(a+ b3's) "r~q*W~ ½1Q~I2
2
I
2
M~,1 f.ff(a + bTs) Ot~vq*Wzv
2
4.f2,M~v [- ~ ( M , + M~v) + (4/M~I)(kQ) (pQ) + K 2ab(kQ - pQ)]
dN/de d cos 0
t
+ ~ 2ab(kQ - pQ)]
C -1 (e - eo) [ (1 + e 0 - e) (1 + cos 0) - 2 (eo/e) cos 0 ], K=I
1 C-1 ~e(1 - e)(1 - cos O),
c=l(1-eo) r(q* ~ qW)
2 (l+2eo)
(3C/81r) eo1 ~2.M,
2 16 f2M~v t } (M.2 + M~V) - (4/M2.) (kQ) (pQ)
1C-le(e--eo)(1--cosa),
K= 1
1 -1 "~C (l + e ) [ e o - e ) ( l + c o s O ) - 2(eo/e)cosO],
K= -1
K=--I 1
C=-~(1-e0) 2 (l+~eo) (3 C/2rO le**M , 305
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14 February 1985
Table 2 Characteristics of the decay of the excited quark q* with spin J = 3•2. Notations are the same as in table 1. Only energy distributions dN/de are presented.
¼1C~l2
Minimal coupling
Anomalous coupling
.r.¢(o + b~,s) q;~Wu
M,1 f, ff(a + b 7 5) ~Z q*Wzv
2
1 2 2 4_M~v)/M4,] (~1 (34,2 +M~/) 2 5"f* [M~v(3M*
2
•~ f . M ~
2
2 [ ~1 ( g ,2 -Mff)
+ 2[(M,2 - M ~ 2v ) / M ,2M ~ v2 ] (kQ) (pQ) - r 2ab(kQ - pQ)
- 4[(3M2, -M~I)/(3M4, -M.~/)] ( k Q ) ( p Q ) - ~ 2ab(kQ - pQ))
dN/de
r(q* -* qW)
C-12eo(1 - e) +e(1 - eo) (1 + eo -e),
~¢=1
C-l (1 + eo - e) [3 - el - (3 - eo) el,
K=I
C -12eo(e-eo) +e(1-eo)(1 +eo -e),
K----ml
C -1 e[(3- eo) e-2e0],
K=--I
2
C = ( l - c o ) 2 (1 +~e0 +Teo)
(C/32n) eo1 f2,M,
(C/32~') f2,M,
plied to the antiquark decays CI* ~ Ct£+ (v) with the substitution K ~ - K, K being the sign of the q* (Cl*) charge. Thereof one may obtain for spin J = 1/2 the distributions of the v transverse momentum M,/2
dN r dk t - k± k± j
dN dk0 dk 0 ko( k2 _ k2)1/2.
(12)
Note, it is of importance here that f o r J = 1/2 the dependence on the cosine of the neutrino (electron) emission angle, cos 0, enters into dN/dk 0 d cos 0 only linearly and hence does not contribute to dN/dk O. Therefore, this distribution is independent of the polarization o f the produced q*. However, in the case of J = 3/2 a dependence on the alignment (terms ~ cos20 in dN/dk 0 d cos 0) remains. That is why we confine ourselves in the present paper to the distribution dN/dk± only for J = 1/2. The corresponding distributions are presented in figs. 1,2. The v (~) spectra in the decays of u* (d*) coincide with those of a charged lepton £ - (£+) in the decays of d* (u*). The same results are also true for the corresponding antiquark decays. For spinJ = 3[2, the distributions for the u* (d*) quarks are qualitatively the same as the corresponding distributions for the d* (u*) quarks with spin J = 1/2. The dissimilarity in the neutrino and charged lepton spectra of the u* and d* quark decays for both spins, J = 1/2 a n d J = 3/2, 306
1 2
C = I ( 1 - e o ) 2 (1 + 10eo+ e~)
can be qualitatively illustrated with the helicity considerations [4]. The experimental study of the distributions o f the missing transverse momentum (together with x-distributions) for the events with leptons of defmite charge would allow to distinguish between the hypotheses on the spin of q* and on the effective lagrangian of its decay. Proceeding from the fact that in a small number of exotic events there are cases with a large loss of transverse momentum [up to (86 -+ 6) GeV] and taking into account fig. 2, one may come to the conclusion that the coupling with the anomalous moment is more preferable. In order to discriminate the hypotheses on J = 1/2 and J = 3•2, one should involve the information on the charge of the leptons produced in exotic events. Another possibility to investigate the structure of the q* interactions comes from the study of relative partial widths of the decays q* ~ q£ + (v), qvP, q7 [4].
5. Discussion. The crucial test of the UHO hypothesis would be the discovery of the kinematically completely determined events o f the type q* -+ jet Z~+~-, which presently with the poor statistics available might be absent [ f o r B ( Z -->e+e-)/B(Z ~ all vb-) ~- - g1] . If the further accumulation of experimental statistics confirms the hypothesis on the UHO, this will apparently signify the beginning of a new era, the era of physics of composite quarks and, possibly, of composite intermediate bosons.
18
2
14 February 1985
PHYSICS LETTERS
Volume 151B, number 3,4 36
54
i
72
t
18
90 Ko, GeV
!
2
36 I
54 l
72 I
90 K.t,GeV I
El
dR dKo
/ /
'\ \ ",
/
\\
1
/
\\
/ ! 0
/
i
t
i
I
0.5
0
i
i
i
i
2Kx
E= 2 Ko M~t 18 d__~N d Ko
b
36
54
72
I
I
I
'\ ,
/
\ \
,\
\\
\
_
\\
'
\
/
Kj.,GeV
i
~
,
,
J
\\
I'1 /./.,
\
I 0.5
,\-~
~__ 2K, M~
Fig. 1. Normalized dN/dko distributions of neutrino ( ~ energY ko (e = 2ko/M,) in the q* rest frame for the decay q* q£ ± t-if) of an excited quark with spin J = 1/2: (a) minimal coupling qLq,taqLW#; (b) anomalous coupling (I/M,) ~Lo#uq~W#u. Dash-dotted lines: u* decay, dashed lines: d* decay.
e x p e r i m e n t a l p r o g r a m m e m u s t be carried as well as pp and ep colliders, to investigate o f the excited quarks ( o r / a n d b o s o m ) . In the excited q u a r k p r o d u c t i o n in ? q - r e a c t i o n s
\
/ I' /f
-i.'/
,,,,
.
A wide o u t at plS, the nature particular,
90
i
'/
\\j /\\
t
72
/
1 -
/,
54
l:./\\/\ "\"\ '\
/ \
i
36
b
/ \\
0
/
dN d~
/ ,\
0
18
90 Ko.GeV
F, o
0.5 E- 2~
Fig. 2. Normalized neutrino transverse momentum k.L-distributions (eL = 2k±/M,) for the decay q* --, q~ + (F)of an excited quark with spin J = 1/2. Notations are the same as in fig. 1: (a) minimal coupling; (b) anomalous coupling. Solid lines: summed k±-distributions for neutrino in the p~ ~ ~ +(F)jet processes. Kinks in the dN/dk± distributions at e = eo are connected with the presence of the kinematic bound eo in the dN/dko distributions. The distributions of the missing transverse momentum in the u* (d*) decays coincide with the charged lepton transverse momentum distributions in the d* (u*) decays. Dotted lines are summed k±-distributions for the charged lepton. 307
Volume 151B, number 3,4
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provides an opportunity to investigate q* in two- and three-jet processes, e.g. q* ~ qg, q* ~ qZqct, etc., under a considerably smaller background than at p~ collider. Provided the excited quark hypothesis be experimentally confirmed, the experimental study of the effective lagrangians for the excited quark interactions will become of the most importance for the analysis of the composite quark structure. In particular, one has to study experimentally a possibility of the P-parity violation in the q* interactions with gluons and photons. To solve these problems, the comprehensive experimental programme should necessarily involve conider experiments with polarized proton and electron beams. Finally, the authors would like to express their deep gratitude to V.A. Kuz'min, A.K. Likhoded, A.A. Logunov, S.F. Sultanov, N.E. Tyurin, A.M. Zaitsev,
308
14 February 1985
Yu.M. Zinoviev and G.G. Volkov for useful discussions. We are also indebted to S.R. Slabospitsky for his computation of the quark-gluon luminosity and to W. Kozanecki for presenting us with the results of the UA1 and UA2 experiments.
References [1] UA1 Coilab., G. Arnison et al., Phys. Lett. 139B (1984) 115; UA2 CoUab.,P. Bagnaia et al., Phys. Lett. 139B (1984) 105. [2] M. Abolins et al., in: Proc. 1982 DPF Summer Study on Elementary particle physicsand future facilities (Snowmass, CO, 1982) p. 274. [3] A. De Rujula, L. Maiani and R. Petronzio, Phys. Lett. 140B (1984) 253. [4] S.S. Gershtein, G.V. Jickia and Yu.F. Pirogov,IHEP preprint 84-152, Serpukhov (1984), Yad. Fiz., to be published.
PHYSICS LETTERS
14 February 1985
UNIDENTIFIED H E A V Y OBJECT AT THE SpaS COLLIDER: EXCITED QUARK OR EXCITED COLOUR BOSON? S.S. GERSHTEIN, G.V. JICKIA and Yu.F. PIROGOV
Institute for High Energy Physics, Serpukhov, USSR Received 16 October 1984 Exotic events with a large missing transverse momentum (up to 80-90 GeV[c) observed at the CERN pl~ collider are shown to require, by their signature and effective cross section, the existence of an object with a mass of about 180 GeV/ c2, which would be produced in a resonance way from hadron beam constituents and would be able to decay into W jet and Z jet. An excited quark q* produced in qg fusion and decaying into Wq and Zq seems to be the most natural candidate for such an object. However, one cannot exclude excited colour boson W~ produced in qC1 collisions and decaying into Wg and Zg.
1. Introduction. Exotic events with a missing transverse momentum up to ( 8 0 - 9 0 ) GeV/e observed at the SpaS collider, i.e. singlet hadron jets and single hadron jets accompanied by a charged lepton, can serve as an indication to the existence of an unMentifiedheavy object(UHO) with mass of about 180 GeV/c 2 [ 1]. At the same time, the signature of these events, i.e. the absence o f additional prompt jets at least in a part o f the events, can be considered to indicate a single production of the UHO from the constituents of hadron beams. Such a single production could not be fulfilled otherwise than in a resonance fashion. In this, naturally, the alternatives emerge: (i) The resonance is produced in a quark (antiquark)gluon system. In this case, the UHO is an excited quark q* = (u*, d*) or the corresponding antiquark. Such a possibility has been considered previously in refs. [2, 3 ]. The interpretation of the exotic events is reduced in this case to the resonance production of the excited quark with its subsequent decays in the channels qg--+ q* -~ q W ~ .~±(~), -+ q Z ~ ,
(1)
__
* +
- (W c-, Wc0), capable of decaying in the channels
qC1--+ Wc -+ gW~+ ~+ (~), -+ g Z v~,
(2)
is required to interpret the exotic events. The hadron jet is initiated in this case by the gluon ,1 Should there exist a pp collider of the proper energy, the question of the UHO nature could be solved experimentally in a rather simple way. The reason is that the excited quarks would be produced in pp collisions with the same rate as in pl5 collisions, while the excited colour boson production would be suppressed to the sea antiquark level in the p-beams. At the same time, the question raised can be clarified by accumulating a rather large statistics at the SpaS collider if one makes use of the charged lepton x-distribution asymmetry (see later). In the present paper we consider more thoroughly the excited quark hypothesis and some of its experimentally verified consequences.
2. The cross section for the p~ -~ ]et ~ ± (-v),jet u~ processes. Note that in the general case excited quarks could belong to various multiplets corresponding to
where q = (u, d), and similarly for the antiquark. The hadron jet in this is produced by the light quark. (ii) The resonance is produced in a qgl-system. In this case the existence of an excited colour boson W~
.1 The presence of additional soft hadron jets in some of the observed events should be explained in the framework of both hypotheses by the QCD corrections to the UHO resonance production. 303
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the colour, weak isospin, radial (without changing the quantum numbers) and spin (orbital) excitations. According to (1), to explain the exotic events, the quarks we are probably dealing with in this case must belong to a colour triplet ,2. As for the spin of the excited quarks, here, apart from the ordinary value J = 1/2, it seems quite possible and even attractive in analogy with N--A to admit J = 3/2. Next, it would be natural to consider that the major contribution to the total width F. of the excited quark comes from its strong decay into a light quark and a gluon. Then, P. ~ asM , may quite reasonably be taken as an estimate, where M. is the q* mass. The widths of the q* electroweak decays with emission of a vector boson V = (W, Z, 7) are expected to be of the order of P V ~-aM.. The cross section for the qg ~ q* ~ qV resonance process is of the form 2J+ 1 6V=2x2x3X8
4rr PiPv M~, ( L ~ _ M , ) 2 + p 2 / 4 .
(3)
Here J is the excited quark spin, Pi ~ P, is the initial channel width,E is the energy of the qg beams and the factors in the denominator come from averaging over quark and gluon polarizations and colours. The differential cross section for the pl5 ~ j e t V process is d o v _ ( 2 J + l ) ( 4 1 r ) 2 Pv(d~_~qg dLqg, dx 2 X 2 X 3 X 8 M, + -'-~-] '
(4)
dx
o(pl5 ~ jet e-+(p)) "" 3.4 X 10 -2 nb, o(plS--* jet all v~ -~ 7.7 X 10 -2 nb.
(7)
The experimental cuts being taken into account, the values obtained are in rather good agreement in order of magnitude with the experimental data, i.e. several events for the ~ 100 nb -1 integrated luminosity. 3. The lepton charge asymmetry. The salient feature of the pl5-+ jet £-+ (u) processes, in case they proceed through the excited quark production, should be a charge asymmetry for the events with leptons of definite charge, or, equivalently, a forward-backward asymmetry for leptons of fixed charge. This is caused by the fact that the differential luminosity of the qg beams resuiting in leptons of, say, positive charge, is shifted towards positive values o f x due to a softer gluon distribution and relation dLug/dx ~- 2 dLdg/dx. The same luminosity for leptons of negative charge is shifted, accordingly, to negative values ofx. The charge asymmetry parame ter (A ÷ = - A - )
(8)
L+(x > O) +L-(x > 0)' 1 Xlx2fq(xl)fg(X2) M2
(x 2 + 4r)1/2
(5)
is the differential luminosity of qg beams; fq(Xl) , fg(X2) are the structure functions of quark and gluon distributions;x = x 1 - x 2 , z - X l X 2 ;Xl, 2 =½ [(x 2 + 4r)l/2 -+x], r =M2./s, and analogously for (lg. The total luminosity of the qg and (lg beams for /14. = 180 GeV/c 2 and X/s"= 540 GeV being of the orderLqg + cTg"" 2.2 X 10-5 GeV -2, we have for the total cross section of pl5 -+ jet V: ov = ( 2 J + 1 ) ( r v / M , )
1.4 X 10-32 cm 2.
(6)
. 2 The excited quarks belonging to higher colour multiplets could manifest themselves in two-jet events. The excitation of higher isospin states in qg collisions is absent in the general case, b u t it can surely take place in 7 q collisions at the e p collider.
304
+ +(-) Taking into account the branching ratios B(W- -* e- v ) "" 8 X 10-2,B(Z-* all t,~ ~ 1.8 X 10 -1 and assuming Pw ~- Pz ~- aM., one may finally expect the cross sections of the exotic processes to be
a+_ = U ( x > o) - L~(x > 0)
where dLqg_
14 February 1985
where L±(x > 0 ) = f [ dLug(ag) +
dLg(dgq dx
(9)
x>0
[L±(x > 0) =L*(x < 0)] has a noticeable value,A -+''+ 0.3. The existence of such an asymmetry could in principle be used to discriminate hypotheses (i) and (ii). Unfortunately, a charge asymmetry of the same sign exists also in the differential luminosity of the ud and dfi beams due to the difference of the u- and dquark structure functions of the proton [ fu(x) ~- 2fd(x)]. Though the asymmetry in the q~ processes A +- "" + 0.18 is considerably smaller than in qg, clg beams, the realization of the indicated possibility would require a rather large statistics. 4. Spectra o f lepton energies and missing transverse momentum. The particular form of the q* ~ qV inter-
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action was inessential for the previous consideration. The consideration was based only on the resonance fashion o f the q* p r o d u c t i o n in the qg beams and on the pecularities o f the x - d i s t r i b u t i o n o f the latter. But to study the energy spectra and angular correlations o f the q* decay products one needs a particular choice for the effective lagrangian Z ? ~ . The detailed analysis o f different possibilities is given in refs. [3,4]. Here we restrict ourselves only by the following remarks• Assuming the exact colour and electromagnetic local gauge invariance, one necessarily arrives at the lagrangians o f the gluon and p h o t o n emission q* ~ qg, q7 in the form o f the i n t e r a c t i o n with a transition magnetic m o m e n t p . . As to the W e interaction, here b o t h the m i n i m a l coupling with the field itself and the anomalous coupling with the field strength is admissible, dep e n d i n g on the a s s u m p t i o n o n the W nature, i.e. whether the W b o s o n is composite or elementary. The corresponding effective lagrangians in the most general case have the following form: for spin J = 1/2 f2e(~ft) = f , ~*(a + b 7 5 ) 7~ qW~ + h.c.,
(10)
~?eWf~)
14 February 1985 =
/.t,~q
-,
(a
i+
t
b75)ouvqWuv+h.c.,
(10')
and for spin J = 3/2 Zef~f~ --f~ Cl*(a + b 7 5 ) q W ~ + h.c., * #
(11)
Z?ef~ft)=p,f',qa(a
(ll')
b 75) 7uqWuu + h.c..
In this, Z?e(ffff°)must always have the form (10'), (11') because the electromagnetic gauge s y m m e t r y should n o t be b r o k e n in the W07 ~ Z7 mixing. Since it is impossible at present to give obvious preference to any statement o n the dynamics o f the q* excitation and the W nature, it seems reasonable to consider all the forms o f Z?e(fff~) to calculate the energy distributions and angular correlations in the decays q* -+ qV. The calculational results for the normalized distributions o f the n e u t r i n o (electron) energy dN./dko, as well as for the total widths o f the q* ~ q~-+ (~) decays for two variants o f the coupling, for b o t h values o f spin J = 1/2 a n d J = 3/2 are given in tables 1 and 2, respectively. In virtue o f C P invariance these results are also ap-
Table 1 Characteristics of the decay q* -} qW, W --+~ (~) v of an excited quark q* with spin J = 1/2. The first row gives the decay effective • 1 lagrangians. The form of the charged lepton current is ~Tu 2" (1 - "rs)V. For the qL production process one has a = b = 1/x/~. The second row is the absolute value squared for the decay matrix elements in terms of invariant variables, summed over helicities. Here Q is the 4-momentum of q*, p the n-momentum, k the v-momentum; f¢ is the charge sign of the decaying q* (produced 2). Invariant variables are connected thro ugh the relation kQ + pQ = l(M2. +M~V). IQ'~I2 shows energy co rrelations (ko, p o) between energies of v and ~ in the rest frame of q*. With account for the relation ko(Po ) = (M./2) ( 1 ~ v cos Ojv)/(1 + v) it also gives angular correla2 2 2 tions for neutrino-jet, where v = (M,2 - M~V)/(M , +M~) is the velocity of q , in the W rest frarne, and Ojv is the emission angle of v with respect to the jet direction in the same frame. As is seen, neutrinos of higher energy move against the jet and are accompanied by leptons of lower energy moving along the jet. The third row gives the normalized distributions of v energy and emission angle with respect to direction of q* polarization for qL production (a = b = I/x/2"-). Here e = 2ko/M , is the fractional energy of v in theq* rest frame in parts of the maximum possible one; e o ~
Anomalous coupling
f , Cl(a+ b3's) "r~q*W~ ½1Q~I2
2
I
2
M~,1 f.ff(a + bTs) Ot~vq*Wzv
2
4.f2,M~v [- ~ ( M , + M~v) + (4/M~I)(kQ) (pQ) + K 2ab(kQ - pQ)]
dN/de d cos 0
t
+ ~ 2ab(kQ - pQ)]
C -1 (e - eo) [ (1 + e 0 - e) (1 + cos 0) - 2 (eo/e) cos 0 ], K=I
1 C-1 ~e(1 - e)(1 - cos O),
c=l(1-eo) r(q* ~ qW)
2 (l+2eo)
(3C/81r) eo1 ~2.M,
2 16 f2M~v t } (M.2 + M~V) - (4/M2.) (kQ) (pQ)
1C-le(e--eo)(1--cosa),
K= 1
1 -1 "~C (l + e ) [ e o - e ) ( l + c o s O ) - 2(eo/e)cosO],
K= -1
K=--I 1
C=-~(1-e0) 2 (l+~eo) (3 C/2rO le**M , 305
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Table 2 Characteristics of the decay of the excited quark q* with spin J = 3•2. Notations are the same as in table 1. Only energy distributions dN/de are presented.
¼1C~l2
Minimal coupling
Anomalous coupling
.r.¢(o + b~,s) q;~Wu
M,1 f, ff(a + b 7 5) ~Z q*Wzv
2
1 2 2 4_M~v)/M4,] (~1 (34,2 +M~/) 2 5"f* [M~v(3M*
2
•~ f . M ~
2
2 [ ~1 ( g ,2 -Mff)
+ 2[(M,2 - M ~ 2v ) / M ,2M ~ v2 ] (kQ) (pQ) - r 2ab(kQ - pQ)
- 4[(3M2, -M~I)/(3M4, -M.~/)] ( k Q ) ( p Q ) - ~ 2ab(kQ - pQ))
dN/de
r(q* -* qW)
C-12eo(1 - e) +e(1 - eo) (1 + eo -e),
~¢=1
C-l (1 + eo - e) [3 - el - (3 - eo) el,
K=I
C -12eo(e-eo) +e(1-eo)(1 +eo -e),
K----ml
C -1 e[(3- eo) e-2e0],
K=--I
2
C = ( l - c o ) 2 (1 +~e0 +Teo)
(C/32n) eo1 f2,M,
(C/32~') f2,M,
plied to the antiquark decays CI* ~ Ct£+ (v) with the substitution K ~ - K, K being the sign of the q* (Cl*) charge. Thereof one may obtain for spin J = 1/2 the distributions of the v transverse momentum M,/2
dN r dk t - k± k± j
dN dk0 dk 0 ko( k2 _ k2)1/2.
(12)
Note, it is of importance here that f o r J = 1/2 the dependence on the cosine of the neutrino (electron) emission angle, cos 0, enters into dN/dk 0 d cos 0 only linearly and hence does not contribute to dN/dk O. Therefore, this distribution is independent of the polarization o f the produced q*. However, in the case of J = 3/2 a dependence on the alignment (terms ~ cos20 in dN/dk 0 d cos 0) remains. That is why we confine ourselves in the present paper to the distribution dN/dk± only for J = 1/2. The corresponding distributions are presented in figs. 1,2. The v (~) spectra in the decays of u* (d*) coincide with those of a charged lepton £ - (£+) in the decays of d* (u*). The same results are also true for the corresponding antiquark decays. For spinJ = 3[2, the distributions for the u* (d*) quarks are qualitatively the same as the corresponding distributions for the d* (u*) quarks with spin J = 1/2. The dissimilarity in the neutrino and charged lepton spectra of the u* and d* quark decays for both spins, J = 1/2 a n d J = 3/2, 306
1 2
C = I ( 1 - e o ) 2 (1 + 10eo+ e~)
can be qualitatively illustrated with the helicity considerations [4]. The experimental study of the distributions o f the missing transverse momentum (together with x-distributions) for the events with leptons of defmite charge would allow to distinguish between the hypotheses on the spin of q* and on the effective lagrangian of its decay. Proceeding from the fact that in a small number of exotic events there are cases with a large loss of transverse momentum [up to (86 -+ 6) GeV] and taking into account fig. 2, one may come to the conclusion that the coupling with the anomalous moment is more preferable. In order to discriminate the hypotheses on J = 1/2 and J = 3•2, one should involve the information on the charge of the leptons produced in exotic events. Another possibility to investigate the structure of the q* interactions comes from the study of relative partial widths of the decays q* ~ q£ + (v), qvP, q7 [4].
5. Discussion. The crucial test of the UHO hypothesis would be the discovery of the kinematically completely determined events o f the type q* -+ jet Z~+~-, which presently with the poor statistics available might be absent [ f o r B ( Z -->e+e-)/B(Z ~ all vb-) ~- - g1] . If the further accumulation of experimental statistics confirms the hypothesis on the UHO, this will apparently signify the beginning of a new era, the era of physics of composite quarks and, possibly, of composite intermediate bosons.
18
2
14 February 1985
PHYSICS LETTERS
Volume 151B, number 3,4 36
54
i
72
t
18
90 Ko, GeV
!
2
36 I
54 l
72 I
90 K.t,GeV I
El
dR dKo
/ /
'\ \ ",
/
\\
1
/
\\
/ ! 0
/
i
t
i
I
0.5
0
i
i
i
i
2Kx
E= 2 Ko M~t 18 d__~N d Ko
b
36
54
72
I
I
I
'\ ,
/
\ \
,\
\\
\
_
\\
'
\
/
Kj.,GeV
i
~
,
,
J
\\
I'1 /./.,
\
I 0.5
,\-~
~__ 2K, M~
Fig. 1. Normalized dN/dko distributions of neutrino ( ~ energY ko (e = 2ko/M,) in the q* rest frame for the decay q* q£ ± t-if) of an excited quark with spin J = 1/2: (a) minimal coupling qLq,taqLW#; (b) anomalous coupling (I/M,) ~Lo#uq~W#u. Dash-dotted lines: u* decay, dashed lines: d* decay.
e x p e r i m e n t a l p r o g r a m m e m u s t be carried as well as pp and ep colliders, to investigate o f the excited quarks ( o r / a n d b o s o m ) . In the excited q u a r k p r o d u c t i o n in ? q - r e a c t i o n s
\
/ I' /f
-i.'/
,,,,
.
A wide o u t at plS, the nature particular,
90
i
'/
\\j /\\
t
72
/
1 -
/,
54
l:./\\/\ "\"\ '\
/ \
i
36
b
/ \\
0
/
dN d~
/ ,\
0
18
90 Ko.GeV
F, o
0.5 E- 2~
Fig. 2. Normalized neutrino transverse momentum k.L-distributions (eL = 2k±/M,) for the decay q* --, q~ + (F)of an excited quark with spin J = 1/2. Notations are the same as in fig. 1: (a) minimal coupling; (b) anomalous coupling. Solid lines: summed k±-distributions for neutrino in the p~ ~ ~ +(F)jet processes. Kinks in the dN/dk± distributions at e = eo are connected with the presence of the kinematic bound eo in the dN/dko distributions. The distributions of the missing transverse momentum in the u* (d*) decays coincide with the charged lepton transverse momentum distributions in the d* (u*) decays. Dotted lines are summed k±-distributions for the charged lepton. 307
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provides an opportunity to investigate q* in two- and three-jet processes, e.g. q* ~ qg, q* ~ qZqct, etc., under a considerably smaller background than at p~ collider. Provided the excited quark hypothesis be experimentally confirmed, the experimental study of the effective lagrangians for the excited quark interactions will become of the most importance for the analysis of the composite quark structure. In particular, one has to study experimentally a possibility of the P-parity violation in the q* interactions with gluons and photons. To solve these problems, the comprehensive experimental programme should necessarily involve conider experiments with polarized proton and electron beams. Finally, the authors would like to express their deep gratitude to V.A. Kuz'min, A.K. Likhoded, A.A. Logunov, S.F. Sultanov, N.E. Tyurin, A.M. Zaitsev,
308
14 February 1985
Yu.M. Zinoviev and G.G. Volkov for useful discussions. We are also indebted to S.R. Slabospitsky for his computation of the quark-gluon luminosity and to W. Kozanecki for presenting us with the results of the UA1 and UA2 experiments.
References [1] UA1 Coilab., G. Arnison et al., Phys. Lett. 139B (1984) 115; UA2 CoUab.,P. Bagnaia et al., Phys. Lett. 139B (1984) 105. [2] M. Abolins et al., in: Proc. 1982 DPF Summer Study on Elementary particle physicsand future facilities (Snowmass, CO, 1982) p. 274. [3] A. De Rujula, L. Maiani and R. Petronzio, Phys. Lett. 140B (1984) 253. [4] S.S. Gershtein, G.V. Jickia and Yu.F. Pirogov,IHEP preprint 84-152, Serpukhov (1984), Yad. Fiz., to be published.