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ϒ production at large transverse momentum as a probe of axigluons
Volume 212, number 3
PHYSICS LETTERS B
29 September 1988
~" P R O D U C T I O N AT L A R G E T R A N S V E R S E M O M E N T U M AS A P R O B E O F A X I G L U O N S Lars B E R G S T R O M Department of Physics, University of Stockholm, Vanadisv~igen 9, S-I13 46 Stockholm, Sweden
Received 2 June 1988
Large-PTproduction of J/W and Y particles is suggested as a sensitive probe of axigluons of mass less than 40 GeV at the CERN collider and 80 GeV at the Tevatron. It is shown that existing CERN collider data on large-pv/' production exclude axigluon masses less than around 20 GeV. At the projected SSC, 1"and vector toponium production at large PT through axigluon exchange by far outweighs the QCD contribution over a vast range of axigluon and toponium masses.
The success of the standard SU ( 3 ) × SU ( 2 ) × U ( 1 ) model is by now overwhelming (for a recent review, see ref. [ 1 ] ). Nevertheless, there are m a n y reasons to believe that this low-energy theory m a y be different at larger mass scales, perhaps in the TeV range. One of the most attractive extensions is to require supersymmetry at that mass scale. This leads to a rich phenomenology of new particles that is by now well studied theoretically. Another logical possibility is to have a larger gauge group such as the chiral colour gauge group SU (3) c X SU (3) R that breaks down to diagonal SU (3) ~o~ourat the same mass scale as the SU (2) × U ( 1 ) electroweak gauge group. Such ideas have been suggested before [ 2,3 ] but have recently been put in a more definite form by F r a m p t o n and Glashow [ 4 ]. (See also ref. [ 5 ]. ) There are m a n y phenomenological consequences of such models [4]. First of all, extra families of quarks and leptons have to be present to cancel anomalies. Secondly, there must exist massive colour octet gluons, probably with purely axial vector couplings to quarks (axigluons). Finally, the Higgs sector of these models tends to be very rich with many coloured and uncoloured scalar and pseudoscalar bosons. Recently, there have appeared several papers dealing with the experimental signatures of axigluons in various processes, such as V ~ a g (V: vector meson, a: axigluon, g: gluon) [6,7], Z - , a g [8], Z ~ a a [9], Z-,q~la [ 10], plb ~ a + anything [ 11 ], and forward-backward asymmetries at hadronic colliders [ 12 ]. The results of these studies are that axigluon masses below 10 GeV are excluded by data on "f decays [ 6,7 ]. The mass range between 110 GeV and 310 GeV is excluded by existing UA 1 data on jet and dijet production at the C E R N pO collider [ 11 ]. Lower mass values than these are difficult to probe using present collider data on jet production since axigluons are expected to have a large width and since the Q C D background is overwhelming [ 11 ]. This leaves a phenomenologically interesting mass region between 10 and 110 GeV to be explored at present and future experimental facilities. The Z decay processes may probe axigluon masses up to around 60 GeV, although the absence of a clear signature could make the experimental analysis difficult demanding a very large Z sample. In a previous paper [7] we investigated several decay channels of the lowest lying states of a heavy quarkonium system into axiparticles, gluons and photons. (We denote axigluons, coloured scalars and coloured pseudoscalars collectively by axiparticles.) There it was shown that the existence of axigluons lighter than such quarkonium bound states would imply drastic modifications of the usual quarkonium phenomenology. One important new feature is the appearance of a large coupling of the vector quarkonium state to a gluon and an axigluon (see also ref. [ 6 ] ). In addition, there are radiative decay modes involving axiparticles in the final states that should be easily visible if, e.g., toponium is found and if axigluons or coloured Higgs particles are lighter than the toponium ground states [ 7 ]. 386
0370-2693/88/$ 03.50 © Elsevier Science Publishers B.V. (North-Holland Physics Publishing Division )
Volume 212, number 3
PHYSICS LETTERSB
29 September 1988
In QCD, large-PT production of heavy vector mesons such as J/W and "t"in hadron-hadron collisions is quite suppressed compared to production of the C-even quarkonium states [ 13 ]. The reason for this is the fact that vector quarkonium only couples to three gluons in lowest order due to the requirement of colour and C-parity conservation, whereas the pseudoscalar and triplet P states may couple to two gluons. Gluon-gluon fusion with emission of an extra gluon through the three-gluon vertex, which is an efficient mechanism for producing largePT mesons, is therefore available only for the C-even states. However, if axigluons exist, there is a coupling of the vector state to a gluon and an axigluon, which opens up a new mechanism for large-PT production of vector mesons to order ce3 . In this paper, we will use the results for the off-shell gluon and axigluon coupling to a heavy vector meson derived in ref. [7 ] to present predictions for large-PT j/W and "f production at hadronic colliders such as the CERN collider ( x / s = 6 3 0 GeV), the Fermilab Tevatron ( x / s = 2 0 0 0 GeV) or the planned SSC (x/~ = 40 TeV). As we shall see, significant lower limits on axigluon mass may already be derived from existing CERN collider data, and more stringent ones can be expected from CERN and Fermilab in the near future. The planned SSC, if built, may probe all of the allowed low-mass window for the axigluon (as well as masses significantly larger than 1 TeV through an analysis of jet production according to the results ofref. [ 11 ] ). Besides the ordinary QCD process for producing a large-PT vector meson, the following new processes appear in order a 3 when axigluons are present in the theory (a: axigluon, g: gluon, q: quark, V: vector meson): q g ~ V q (through an exchange); qCl~a*~Vg; qCl~g*~Va; gg~g*--.Va, and g g ~ V a with axigluon exchange in the t- or u-channel ,1. We have evaluated all of these subprocesses employing physical gauges for both the gluons and the axigluons. (The Feynman rules for the gluon-axigluon interactions can be found in ref. [ 11 ]. ) The first of these subprocesses, depicted in fig. 1a, dominates for small to moderate PT values. The second is important at PT values close to (m2a--m 2 )/2m, where is causes a (not very prominent) j acobian peak. The last one, gg--,Va, is important for small axigluon masses and for large x/~ and PT; the others are much smaller. The calculations are quite involved and had to be performed using computer algebra. Summing and averaging over colours we find the differential cross section at constituent level for the dominant process q g ~ V q (where q denotes a quark or an antiquark) dad__{( q g ~ V q ) = 8zc2o~3 2 9 1m~v( 20g ) I ( 2(/'+ 2 ~-) ( f~+ g)m ~ ~2v _ ](f+4g)m4v-i'3-2df(g+D ~ F a ~ ) 2
),
(1)
where 5u(0) is the value of the wavefunction at the origin, ma and mv are the axigluon and vector meson mass, respectively, and Fa is the total decay width of the axigluon (around 0.1 ma). The cross section for the crossed process g q ~ Vq is obtained from this expression by the substitution/'--, ~. The resonant s-channel process qCl--,Vg is given by g,--,/'in the expression in the large parentheses in eq. ( 1 ). The cross section for g g ~ V a is ~ There is also a direct gg~Va contribution analogous to the QCD diagram for gg-,Vg which comes from the F term coupling of the three colour octets. This is very small, however.
9f.. (a)
........
o
(b)
Fig. 1. Diagrams that dominate large-pr production of heavy vector mesons in hadron-hadron collisions if axigluons are present. (The axigluon is symbolizedby a dotted line. ) 387
Volume 212, number 3
PHYSICS LETTERS B
d a ( g g - , V a ) , ~= 2rr2a3 [ ~ ( 0 ) 12
d--~
'
mvm2ag 2
29 September 1988
fva (s, 7, rn2v, ma2)
(2)
(~+[--m2v)2(~+f--m2)2(f--m2a)2([--m2)2'
where fv. is complicated eighth order polynomial too long to be reproduced here ~2. In the limit when mv-+O it is given by fva (x, Y, O, w) = [ ( x S + 4 x 4 y + 13x3y2+21xZy3+ 15xy4+3yS)w + (2X3+ 12x2y+ 1 3 x y Z + y 3 ) W 3 - - 2 ( X + 2 y ) W 4 X +
(2X4+12x3y+26X252+21xy3+3y4)w
WSX--X3y3--3X2y4--3xyS--y6]y(w--x--y)
2 (3)
.
This approximation [ still keeping mv non-zero in the denominator of eq. (2) ] may be used for a rough estimate of the differential distribution, but it gives a slight underestimate (by about a factor of two) of the exact results for this subprocess for "F production at the C E R N collider. The results apply as well [and the approximation eq. (3) even better] for J / ~ production, but here the comparison with experimental results is more complicated since there is a large standard model contribution to large-p-r J / ~ production from B meson decays (for a recent analysis, see ref. [ 14] ). In fig. 2 we give the results for the pa- distributions derived from eqs. ( 1 ) and (2) for the C E R N collider (x/~ = 630 G e V ) for the case of'l" production. To obtain numerical results when going from the constituent subprocesses in fig. 1 to the actual pp reaction we have used the quark and gluon structure functions of Duke and Owens [ 15 ] (we have checked that the results are not very sensitive to this particular choice) with Q z= ma2 + m v2 + p 2 . The value of I ~ ( 0 ) 12 w a s derived from the measured width into m u o n pairs of 1". For comparison, also the standard Q C D contribution [ 13,16] to large-pT Y production is shown in fig. 2. As can be seen, for light axigluon masses (around 20 G e V ) the contributions from axigluons are much larger than the Q C D result, especially at large PT values where the Q C D contribution drops rapidly. For PT larger than 12 GeV the contribution from a 40 GeV axigluon is larger than the Q C D piece. (For PT greater than 15 GeV even a 60 GeV axigluon dominates the Q C D contribution, .2 However, on request it may be obtained from the author in Fortran format.
da/dpT [pb/GeV
a~,/ dpr
Large-pT T
Large-pT T v~= 2 TeV
[pb/Ge\')
v~s = 630 GeV
103
~..
102
~
"~ ,~.
...,o=,0oov 102
~-~
~
\ QCD
~" ,,. "-,
10
mo2; S
"/ i
S
112
lJ6
20 PT [GeV]
Fig. 2. Differential PT d i s t r i b u t i o n da/dpT (in cm 2 GeV ' ) o f t particles produced in p15 collisons at x / ~ = 6 3 0 GeV. Curves are shown for Q C D c o n t r i b u t i o n (solid line), axigluon c o n t r i b u t i o n
for ma=20 GeV (dashed line) and ma=40 GeV (dash-dotted line). 388
N~
QCD
m~ = 40 GeV
"
~
.~.
-.
,0
1 4
N
1
i0-1
i12
i16
210
214
2iS Pr [GeVI
Fig. 3. Differential PT distribution da/@T (in cm2 GeV- J) of Y particles produced in pO collisions at x/~= 2000 GeV. Curves are shown for QCD contribution (solid line), axigluon contribution for m~=40 GeV (dashed line) and ma=80 GeV (dash-dotted line).
Volume 212, number 3
PHYSICS LETTERSB
29 September 1988
but here absolute rates are close to the limit of observability. ) The jacobian peak originating from the qdl--,Vg subprocess is barely visible in fig. 2, indicating that this is not a good way to measure the axigluon mass directly. Rather, it is the absolute magnitude of the large-px cross section that may be use to bound or determine the axigluon mass. The results are shown only for production of the ground state, Y(IS). The curves look very similar for the excited states, but they are lower in magnitude by about a factor of 2.5 for • (2S) and a factor of 4 forY(3S). There are some interesting features of the axigluon-induced cross sections that may help determine their origin experimentally, First, the cross sections deduced from eqs. (1) and (2) have a flatter rapidity distribution at large Pr than the QCD piece (this is typical of the t-exchange nature of the dominant axigluon mechanism). Secondly, the axigluon processes increase considerably with energy (almost a factor o f t e n when going from the CERN collider to the Fermilab Tevatron). The results relevant for the Tevatron (x/s = 2 TeV) are shown in fig. 3. As can be seen, at large enough Px the axigluon contributions dominate the differential cross sections. Assuming an integrated luminosity of 10 pb-1, axigluons with masses up to 80 GeV should be detectable through this process. (Making a Pa- cut of 24 GeV/c, an 80 GeV axigluon gives rise to around 200 r events which is more than ten times the QCD background. ) At x / s = 40 TeV, which is the projected CMS energy of the SSC, there would be copious large-pT production of J/qJ and Y through axigluon exchange for axigluon masses well in the hundred GeV range. As an example, making a P x cut of 100 G e V / c for the produced Y particles an axigluon of 100 GeV would still give rise to 2500 Y events in a three-month run with a QCD background of only a few events ~3. This would thus probe all of the allowed low-mass window for axigluon masses. (The existence of substantial initial state gluon radiation at such energies will not change these results qualitatively. ) A toponium vector state of mass 150 GeV would be produced with a PT larger than 100 G e V / c with about half the cross section of 2e production if ma-- 100 GeV. As pointed out in ref. [ 11 ], masses in the range 6 to 18 TeV for the axigluon may also be probed at the SSC through a study of the inclusive jet cross sections. At present, there exists only one experimental number for Y production at the CERN collider, namely from the UA 1 collaboration [ 17 ]. Unfortunately, in ref. [ 17 ] no analysis of the pT distribution of the Y events is presented. Only the total result for cross section times branching ratio into muon pairs of 0.98 _+0.21 _+0.19 nb is given for the sum of the 1S, 2S and 3S "f states (assuming the QCD gluon fusion mechanism). This information is sufficient only to exclude axigluon masses less than around 20 GeV, which is still the best lower limit on axigluon mass obtained so far. It is conceivable that a more detailed analysis of existing and forthcoming CERN collider data using information on the Pa- and rapidity distributions may improve on this limit to, say, 40 GeV. At the Tevatron, one should be able to cover the range up to 80 GeV, with the remaining window up to 1 l0 GeV only being probed through this process at future hadron colliders. In fact, if axigluons exist in the mass range we have discussed, the process suggested here, large-px Y production, may serve as a useful enrichment trigger for axigluons since at very large Px an important mechanism is gg-,Va which means that the meson is balanced on the opposite side by an axigluon. This could enable a study of the decay properties of axigluons in this mass range; something that is very difficult using inclusive jet studies only. The author wishes to thank M. Jacob and the CERN Theory Division for hospitality while most of this work was done. Useful discussions with T. Sj6strand are also acknowledged. This research was supported by the Swedish Natural Science Research Council (NFR). ~3The dominant diagram in this case is the one in fig. lb.
389
Volume 212, number 3
PHYSICS LETTERS B
References [ 1 ] G. Altarelli, Proc. 1987 HEP Conf. (Uppsala, Sweden), ed. O. Botner (Uppsala U.P., Uppsala). [ 2] J.C. Pati and A. Salam, Phys. Lett. B 58 (1975 ) 333. [ 3 ] L.J. Hall and A.E. Nelson, Phys. Lett. B 153 ( 1985 ) 430. [4] P.H. Frampton and S.L. Glashow, Phys. Lett. B 190 (1987) 157; Phys. Rev. lett. 58 (1987) 2168. [5] S. Rajpoot, Phys. Rev. Lett. 60 (1988) 2003. [6] F. Cuypers and P.H. Frampton, Phys. Rev. Lett. 60 (1988) 1237. [7] L. BergstrSm, USITP-88-07 (1988), unpublished. [8] E.D. Carlson, S.L. Glashow and E.E. Jenkins, Phys. Lett. B 202 (1988) 281. [ 9 ] F. Cuypers, IFP-313-UNC ( 1988 ), unpublished. [ 10] T. Rizzo, Phys. Lett. B 197 (1987) 273. [ 11 ] J. Bagger, C. Schmidt and S. King, Phys. Rev. D 37 (1988) 1188. [ 12] L.M. Sehgal and M. Wanninger, Phys. Lett. B 200 (1988) 211. [13] R. Baier and R. Rtickl, Z. Phys. C 19 (1983) 251. [ 14] B. van Eijk, CERN-EP/88-38 (1988), unpublished. [15] D. Duke and J. Owens, Phys. Rev. D 30 (1984) 49. [ 16] V. Barger, W.-Y. Keung and R.J.N. Phillips, Phys. Lett. B 91 (1980) 253. [ 17 ] UA 1 Collab., C. Albajar et al., Phys. Lett. B 186 ( 1987 ) 237.
390
29 September 1988
PHYSICS LETTERS B
29 September 1988
~" P R O D U C T I O N AT L A R G E T R A N S V E R S E M O M E N T U M AS A P R O B E O F A X I G L U O N S Lars B E R G S T R O M Department of Physics, University of Stockholm, Vanadisv~igen 9, S-I13 46 Stockholm, Sweden
Received 2 June 1988
Large-PTproduction of J/W and Y particles is suggested as a sensitive probe of axigluons of mass less than 40 GeV at the CERN collider and 80 GeV at the Tevatron. It is shown that existing CERN collider data on large-pv/' production exclude axigluon masses less than around 20 GeV. At the projected SSC, 1"and vector toponium production at large PT through axigluon exchange by far outweighs the QCD contribution over a vast range of axigluon and toponium masses.
The success of the standard SU ( 3 ) × SU ( 2 ) × U ( 1 ) model is by now overwhelming (for a recent review, see ref. [ 1 ] ). Nevertheless, there are m a n y reasons to believe that this low-energy theory m a y be different at larger mass scales, perhaps in the TeV range. One of the most attractive extensions is to require supersymmetry at that mass scale. This leads to a rich phenomenology of new particles that is by now well studied theoretically. Another logical possibility is to have a larger gauge group such as the chiral colour gauge group SU (3) c X SU (3) R that breaks down to diagonal SU (3) ~o~ourat the same mass scale as the SU (2) × U ( 1 ) electroweak gauge group. Such ideas have been suggested before [ 2,3 ] but have recently been put in a more definite form by F r a m p t o n and Glashow [ 4 ]. (See also ref. [ 5 ]. ) There are m a n y phenomenological consequences of such models [4]. First of all, extra families of quarks and leptons have to be present to cancel anomalies. Secondly, there must exist massive colour octet gluons, probably with purely axial vector couplings to quarks (axigluons). Finally, the Higgs sector of these models tends to be very rich with many coloured and uncoloured scalar and pseudoscalar bosons. Recently, there have appeared several papers dealing with the experimental signatures of axigluons in various processes, such as V ~ a g (V: vector meson, a: axigluon, g: gluon) [6,7], Z - , a g [8], Z ~ a a [9], Z-,q~la [ 10], plb ~ a + anything [ 11 ], and forward-backward asymmetries at hadronic colliders [ 12 ]. The results of these studies are that axigluon masses below 10 GeV are excluded by data on "f decays [ 6,7 ]. The mass range between 110 GeV and 310 GeV is excluded by existing UA 1 data on jet and dijet production at the C E R N pO collider [ 11 ]. Lower mass values than these are difficult to probe using present collider data on jet production since axigluons are expected to have a large width and since the Q C D background is overwhelming [ 11 ]. This leaves a phenomenologically interesting mass region between 10 and 110 GeV to be explored at present and future experimental facilities. The Z decay processes may probe axigluon masses up to around 60 GeV, although the absence of a clear signature could make the experimental analysis difficult demanding a very large Z sample. In a previous paper [7] we investigated several decay channels of the lowest lying states of a heavy quarkonium system into axiparticles, gluons and photons. (We denote axigluons, coloured scalars and coloured pseudoscalars collectively by axiparticles.) There it was shown that the existence of axigluons lighter than such quarkonium bound states would imply drastic modifications of the usual quarkonium phenomenology. One important new feature is the appearance of a large coupling of the vector quarkonium state to a gluon and an axigluon (see also ref. [ 6 ] ). In addition, there are radiative decay modes involving axiparticles in the final states that should be easily visible if, e.g., toponium is found and if axigluons or coloured Higgs particles are lighter than the toponium ground states [ 7 ]. 386
0370-2693/88/$ 03.50 © Elsevier Science Publishers B.V. (North-Holland Physics Publishing Division )
Volume 212, number 3
PHYSICS LETTERSB
29 September 1988
In QCD, large-PT production of heavy vector mesons such as J/W and "t"in hadron-hadron collisions is quite suppressed compared to production of the C-even quarkonium states [ 13 ]. The reason for this is the fact that vector quarkonium only couples to three gluons in lowest order due to the requirement of colour and C-parity conservation, whereas the pseudoscalar and triplet P states may couple to two gluons. Gluon-gluon fusion with emission of an extra gluon through the three-gluon vertex, which is an efficient mechanism for producing largePT mesons, is therefore available only for the C-even states. However, if axigluons exist, there is a coupling of the vector state to a gluon and an axigluon, which opens up a new mechanism for large-PT production of vector mesons to order ce3 . In this paper, we will use the results for the off-shell gluon and axigluon coupling to a heavy vector meson derived in ref. [7 ] to present predictions for large-PT j/W and "f production at hadronic colliders such as the CERN collider ( x / s = 6 3 0 GeV), the Fermilab Tevatron ( x / s = 2 0 0 0 GeV) or the planned SSC (x/~ = 40 TeV). As we shall see, significant lower limits on axigluon mass may already be derived from existing CERN collider data, and more stringent ones can be expected from CERN and Fermilab in the near future. The planned SSC, if built, may probe all of the allowed low-mass window for the axigluon (as well as masses significantly larger than 1 TeV through an analysis of jet production according to the results ofref. [ 11 ] ). Besides the ordinary QCD process for producing a large-PT vector meson, the following new processes appear in order a 3 when axigluons are present in the theory (a: axigluon, g: gluon, q: quark, V: vector meson): q g ~ V q (through an exchange); qCl~a*~Vg; qCl~g*~Va; gg~g*--.Va, and g g ~ V a with axigluon exchange in the t- or u-channel ,1. We have evaluated all of these subprocesses employing physical gauges for both the gluons and the axigluons. (The Feynman rules for the gluon-axigluon interactions can be found in ref. [ 11 ]. ) The first of these subprocesses, depicted in fig. 1a, dominates for small to moderate PT values. The second is important at PT values close to (m2a--m 2 )/2m, where is causes a (not very prominent) j acobian peak. The last one, gg--,Va, is important for small axigluon masses and for large x/~ and PT; the others are much smaller. The calculations are quite involved and had to be performed using computer algebra. Summing and averaging over colours we find the differential cross section at constituent level for the dominant process q g ~ V q (where q denotes a quark or an antiquark) dad__{( q g ~ V q ) = 8zc2o~3 2 9 1m~v( 20g ) I ( 2(/'+ 2 ~-) ( f~+ g)m ~ ~2v _ ](f+4g)m4v-i'3-2df(g+D ~ F a ~ ) 2
),
(1)
where 5u(0) is the value of the wavefunction at the origin, ma and mv are the axigluon and vector meson mass, respectively, and Fa is the total decay width of the axigluon (around 0.1 ma). The cross section for the crossed process g q ~ Vq is obtained from this expression by the substitution/'--, ~. The resonant s-channel process qCl--,Vg is given by g,--,/'in the expression in the large parentheses in eq. ( 1 ). The cross section for g g ~ V a is ~ There is also a direct gg~Va contribution analogous to the QCD diagram for gg-,Vg which comes from the F term coupling of the three colour octets. This is very small, however.
9f.. (a)
........
o
(b)
Fig. 1. Diagrams that dominate large-pr production of heavy vector mesons in hadron-hadron collisions if axigluons are present. (The axigluon is symbolizedby a dotted line. ) 387
Volume 212, number 3
PHYSICS LETTERS B
d a ( g g - , V a ) , ~= 2rr2a3 [ ~ ( 0 ) 12
d--~
'
mvm2ag 2
29 September 1988
fva (s, 7, rn2v, ma2)
(2)
(~+[--m2v)2(~+f--m2)2(f--m2a)2([--m2)2'
where fv. is complicated eighth order polynomial too long to be reproduced here ~2. In the limit when mv-+O it is given by fva (x, Y, O, w) = [ ( x S + 4 x 4 y + 13x3y2+21xZy3+ 15xy4+3yS)w + (2X3+ 12x2y+ 1 3 x y Z + y 3 ) W 3 - - 2 ( X + 2 y ) W 4 X +
(2X4+12x3y+26X252+21xy3+3y4)w
WSX--X3y3--3X2y4--3xyS--y6]y(w--x--y)
2 (3)
.
This approximation [ still keeping mv non-zero in the denominator of eq. (2) ] may be used for a rough estimate of the differential distribution, but it gives a slight underestimate (by about a factor of two) of the exact results for this subprocess for "F production at the C E R N collider. The results apply as well [and the approximation eq. (3) even better] for J / ~ production, but here the comparison with experimental results is more complicated since there is a large standard model contribution to large-p-r J / ~ production from B meson decays (for a recent analysis, see ref. [ 14] ). In fig. 2 we give the results for the pa- distributions derived from eqs. ( 1 ) and (2) for the C E R N collider (x/~ = 630 G e V ) for the case of'l" production. To obtain numerical results when going from the constituent subprocesses in fig. 1 to the actual pp reaction we have used the quark and gluon structure functions of Duke and Owens [ 15 ] (we have checked that the results are not very sensitive to this particular choice) with Q z= ma2 + m v2 + p 2 . The value of I ~ ( 0 ) 12 w a s derived from the measured width into m u o n pairs of 1". For comparison, also the standard Q C D contribution [ 13,16] to large-pT Y production is shown in fig. 2. As can be seen, for light axigluon masses (around 20 G e V ) the contributions from axigluons are much larger than the Q C D result, especially at large PT values where the Q C D contribution drops rapidly. For PT larger than 12 GeV the contribution from a 40 GeV axigluon is larger than the Q C D piece. (For PT greater than 15 GeV even a 60 GeV axigluon dominates the Q C D contribution, .2 However, on request it may be obtained from the author in Fortran format.
da/dpT [pb/GeV
a~,/ dpr
Large-pT T
Large-pT T v~= 2 TeV
[pb/Ge\')
v~s = 630 GeV
103
~..
102
~
"~ ,~.
...,o=,0oov 102
~-~
~
\ QCD
~" ,,. "-,
10
mo2; S
"/ i
S
112
lJ6
20 PT [GeV]
Fig. 2. Differential PT d i s t r i b u t i o n da/dpT (in cm 2 GeV ' ) o f t particles produced in p15 collisons at x / ~ = 6 3 0 GeV. Curves are shown for Q C D c o n t r i b u t i o n (solid line), axigluon c o n t r i b u t i o n
for ma=20 GeV (dashed line) and ma=40 GeV (dash-dotted line). 388
N~
QCD
m~ = 40 GeV
"
~
.~.
-.
,0
1 4
N
1
i0-1
i12
i16
210
214
2iS Pr [GeVI
Fig. 3. Differential PT distribution da/@T (in cm2 GeV- J) of Y particles produced in pO collisions at x/~= 2000 GeV. Curves are shown for QCD contribution (solid line), axigluon contribution for m~=40 GeV (dashed line) and ma=80 GeV (dash-dotted line).
Volume 212, number 3
PHYSICS LETTERSB
29 September 1988
but here absolute rates are close to the limit of observability. ) The jacobian peak originating from the qdl--,Vg subprocess is barely visible in fig. 2, indicating that this is not a good way to measure the axigluon mass directly. Rather, it is the absolute magnitude of the large-px cross section that may be use to bound or determine the axigluon mass. The results are shown only for production of the ground state, Y(IS). The curves look very similar for the excited states, but they are lower in magnitude by about a factor of 2.5 for • (2S) and a factor of 4 forY(3S). There are some interesting features of the axigluon-induced cross sections that may help determine their origin experimentally, First, the cross sections deduced from eqs. (1) and (2) have a flatter rapidity distribution at large Pr than the QCD piece (this is typical of the t-exchange nature of the dominant axigluon mechanism). Secondly, the axigluon processes increase considerably with energy (almost a factor o f t e n when going from the CERN collider to the Fermilab Tevatron). The results relevant for the Tevatron (x/s = 2 TeV) are shown in fig. 3. As can be seen, at large enough Px the axigluon contributions dominate the differential cross sections. Assuming an integrated luminosity of 10 pb-1, axigluons with masses up to 80 GeV should be detectable through this process. (Making a Pa- cut of 24 GeV/c, an 80 GeV axigluon gives rise to around 200 r events which is more than ten times the QCD background. ) At x / s = 40 TeV, which is the projected CMS energy of the SSC, there would be copious large-pT production of J/qJ and Y through axigluon exchange for axigluon masses well in the hundred GeV range. As an example, making a P x cut of 100 G e V / c for the produced Y particles an axigluon of 100 GeV would still give rise to 2500 Y events in a three-month run with a QCD background of only a few events ~3. This would thus probe all of the allowed low-mass window for axigluon masses. (The existence of substantial initial state gluon radiation at such energies will not change these results qualitatively. ) A toponium vector state of mass 150 GeV would be produced with a PT larger than 100 G e V / c with about half the cross section of 2e production if ma-- 100 GeV. As pointed out in ref. [ 11 ], masses in the range 6 to 18 TeV for the axigluon may also be probed at the SSC through a study of the inclusive jet cross sections. At present, there exists only one experimental number for Y production at the CERN collider, namely from the UA 1 collaboration [ 17 ]. Unfortunately, in ref. [ 17 ] no analysis of the pT distribution of the Y events is presented. Only the total result for cross section times branching ratio into muon pairs of 0.98 _+0.21 _+0.19 nb is given for the sum of the 1S, 2S and 3S "f states (assuming the QCD gluon fusion mechanism). This information is sufficient only to exclude axigluon masses less than around 20 GeV, which is still the best lower limit on axigluon mass obtained so far. It is conceivable that a more detailed analysis of existing and forthcoming CERN collider data using information on the Pa- and rapidity distributions may improve on this limit to, say, 40 GeV. At the Tevatron, one should be able to cover the range up to 80 GeV, with the remaining window up to 1 l0 GeV only being probed through this process at future hadron colliders. In fact, if axigluons exist in the mass range we have discussed, the process suggested here, large-px Y production, may serve as a useful enrichment trigger for axigluons since at very large Px an important mechanism is gg-,Va which means that the meson is balanced on the opposite side by an axigluon. This could enable a study of the decay properties of axigluons in this mass range; something that is very difficult using inclusive jet studies only. The author wishes to thank M. Jacob and the CERN Theory Division for hospitality while most of this work was done. Useful discussions with T. Sj6strand are also acknowledged. This research was supported by the Swedish Natural Science Research Council (NFR). ~3The dominant diagram in this case is the one in fig. lb.
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PHYSICS LETTERS B
References [ 1 ] G. Altarelli, Proc. 1987 HEP Conf. (Uppsala, Sweden), ed. O. Botner (Uppsala U.P., Uppsala). [ 2] J.C. Pati and A. Salam, Phys. Lett. B 58 (1975 ) 333. [ 3 ] L.J. Hall and A.E. Nelson, Phys. Lett. B 153 ( 1985 ) 430. [4] P.H. Frampton and S.L. Glashow, Phys. Lett. B 190 (1987) 157; Phys. Rev. lett. 58 (1987) 2168. [5] S. Rajpoot, Phys. Rev. Lett. 60 (1988) 2003. [6] F. Cuypers and P.H. Frampton, Phys. Rev. Lett. 60 (1988) 1237. [7] L. BergstrSm, USITP-88-07 (1988), unpublished. [8] E.D. Carlson, S.L. Glashow and E.E. Jenkins, Phys. Lett. B 202 (1988) 281. [ 9 ] F. Cuypers, IFP-313-UNC ( 1988 ), unpublished. [ 10] T. Rizzo, Phys. Lett. B 197 (1987) 273. [ 11 ] J. Bagger, C. Schmidt and S. King, Phys. Rev. D 37 (1988) 1188. [ 12] L.M. Sehgal and M. Wanninger, Phys. Lett. B 200 (1988) 211. [13] R. Baier and R. Rtickl, Z. Phys. C 19 (1983) 251. [ 14] B. van Eijk, CERN-EP/88-38 (1988), unpublished. [15] D. Duke and J. Owens, Phys. Rev. D 30 (1984) 49. [ 16] V. Barger, W.-Y. Keung and R.J.N. Phillips, Phys. Lett. B 91 (1980) 253. [ 17 ] UA 1 Collab., C. Albajar et al., Phys. Lett. B 186 ( 1987 ) 237.
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