- Email: [email protected]
Z and vector meson production in hadronic collisions at large transverse momentum
Volume 238, number 1
PHYSICS LETTERS B
29 March 1990
Z AND VECTOR MESON PRODUCTION I N H A D R O N I C C O L L I S I O N S AT L A R G E T R A N S V E R S E M O M E N T U M L. B E R G S T R ( J M Department of Physics, Universityof Stockholm, Vanadisv?igen9, S-113 46 Stockholm, Sweden
and R.W. R O B I N E T T Department of Physics, The Pennsylvania State University, UniversityPark, PA 16802, USA
Received 29 December 1989
Large PT production of J/~ and/' panicles in association with a Z° boson or a photon is calculated for the SSC and LHC coUiders. We briefly discuss the possible relevance of this mode for studies of multiple parton interactions at supercoUiderenergies.
The next generation of hadron (super) colliders, the SSC and LHC, will undoubtedly open a new window on fundamental physics at the TeV energy scale. The extremely high luminosities and particle multiplicities per event, however, will make the experimental environment at such machines one of the most challenging yet encountered in high energy physics. Because of this, events containing easily distinguishable features such as jets, weak bosons, and vector mesons (hereafter V = J / ~ or Y) will certainly be utilized heavily. Of these, weak bosons and vector mesons also give rise to m u o n decays which are another clear signal in such an environment and, in addition, multiple m u o n events have long been touted as a clear indicator for new physics phenomena [ 1 ]. (In fact, one extreme suggestion for coping with the large particle fluxes at a high luminosity L H C configuration is to surround the interaction region with absorber so that only muons are detected.) In this context, single W and Z production will be a benchmark process at such energies while high-pT weak boson production is already and will remain an important Q C D test [2]. Multiple (2-, 3-, and even 4-) W / Z production [ 3] will provide tests of the electroweak sector (including the 3- and 4- weak boson vertices and scalar couplings) as well as being a possible way o f probing a strongly interacting [4] electroweak sector. The detection of the standard model Higgs boson also falls into this category especially as it applies to its "gold-plated" signature [ 5] via H°--,ZZ--.muons. Such classes o f events with extremely clean signatures, even those with low event rates, hold promise in a super-collider environment. Vector meson production will also likely be useful as well, for different reasons, as, for example, a probe of the low-x gluon content of the proton while ~¢production arising from b-quark decay has been extensively discussed [ 6 ] as a possible tagging mechanism for B-meson decay. Even the rather mundane use o f ~ and ~f production as a calibration for mass measurements (as with the present C D F experiment [7 ] ) will ensure the continued usefulness of light vector mesons. Double ~t production has even been observed in the lower energy, fixed-target hadronic (Tt-p) collisions [ 8 ] and has been analyzed in terms of the lowest order (O ( o~4 ) ) gg ~ ~ + ~ diagrams. The relevance of this process at supercollider energies has recently been discussed [ 9 ] especially in relation to its possible use as a probe of multiple parton interactions. (The lowest order (O (or 4 ) ) diagrams leading to ~¢-'f production [ 10 ] have also been calculated. ) Given the extensive analyses o f single and multiple weak boson and vector meson production at supercollider 1 12
0370-2693/90/$ 03.50 © Elsevier Science Publishers B.V. ( North-Holland )
Volume 238, number 1
PHYSICS LETTERS B
29 March 1990
energies performed in an attempt to probe the physics potential for such machines, it is then natural to investigate the prospects for combined weak boson + V production. The simplest such subprocess is given by g + g - , Z ° + V (which is of order oes2o~w and would, of course also have the dramatic four charged lepton signal) and it is that process and the prospects for Z ° = V production in pp collisions at SSC and LHC energies which we will discuss in this letter. (Contributions from q + ~ - , Z ° + V will be of order a3w and will be ignored. We also note that there are no similar low-order 2-,2 processes yielding W + V states. ) The differential cross section for g ( k~ ) + g ( k2 ) -~ Z ° (Q) + V (P) is derived using the bound state formalism of Ktihn, Kaplan, and Safiani [ 11 ]. We find de /to¢20~(1 --41e Q Isin20w) 2 [Rs(0)]2my d~ ( g g ~ V Z ) = • 20wCOS'0w , sin 12 d2 X { [ ( 13/2+ 34/t/+ 13~2)~+22([+gt)d2+6g3+ (/q-u)3]m4v - [2(2/2+ 11/ti+ 2fi2)g2+ 2 ( / 2 + 8{ti+ t/2) ({+fO~-2g4+2{3f~+3/2f~2+2[f~3]rn2 - 2 ( / + ti)g 3 - [ 18(/+z1)g+ 1692+[2+f~2]m6v + (7g-[-f~)rnSv
+ (2[+(Q([+2ti)g[gt+4([+z2)d2[f~+rn~,°+2d3[fl+[3(t2+[2~ 3} X [m2v(rn2v - g - m 2 ) 2 ( m ~ , - [)2(m2v - t / ) 2] - ~ ,
(1)
where the standard Mandelstam variables are defined via g = (k~ + k2 ) 2 = ( p + 0 ) 2,/'= (k~ - P) 2and ~/= (kl - Q) 2. The techniques leading to our result can be easily checked against known results for g + g - , V + g by simple changes in kinematics and coupling factors. In fact, also the cross section for gg--, V`/ can be obtained from wellknown results [ 12 ] for gg-,gV by the simple conversion factor i2 (0~Q2/0¢). We also give the corresponding result for pseudoscalar meson production such as qc, Tlb etc. This is given by the somewhat less awkward expression
dr~ ~¢z2ol IRs(O)12me d~ ( g g ~ P Z ) = sin2OwcoS20w 12~2 X {[ (2[+2(l--3m2)g+ (ft--m~,)[-t-2d2--flrrl 2 -f-m~,] [((~-m~,)f-dm 2 - ( t m 2 +m~,] (m 2 --m2) 2} X [ m e m z2( s, + m z 22 _rng)2([_rn2)2(~_rn2p)2] -1
(2)
When trying to exploit this channel one runs however into the trouble of finding a signature for the qc.b decays. The only reasonable change is given by the y`/mode, but this has a branching ratio at the 10 -4 level only. nevertheless, one has to keep in mind that electromagnetic calorimeters with excellent energy resolution will certainly be an integral part of LHC/SSC detectors, since those are essential for the intermediate mass Higgs search through H-~77. Numerically, we find that the rate for P + Z production is, within roughly a factor of two, the same as for V + Z production. We do not consider pseudoscalar production further here, however. Single, high-px "direct" t~ production is well studied in both hadronic collisions [ 13-15 ] and in electroproduction experiments [I 6] and we will use the results of previous successful fits to data in our analysis here. Specifically, we use values of the quarkonium wave functions derived from realistic potential models (e.g. Rs (0) 2 = 0.70 GeV 3 for n = 1 ~ and Rs (0) 2 7.3 GeV 3 for n -= 1 1"), a value of the strong coupling corresponding to c~s(Q2=M2v), as well as a K-factor, K = 2 , inferred from analyses of both single [14] and double [18] tg production. Such parameters, especially the relatively large (and fixed) values of c~s are consistent with both fixed target and collider [ 19 ] data on high-px u/production. (~ production arising from b-quark decay is also an important source at collider energies but the UA 1 collaboration [ 19 ] has demonstrated the ability to distinguish between "direct" production and that arising form B meson decay by using various isolation cuts.) For predictions at supercollider energies, we use the gluon distribution functions of Eichten, Hinchliffe, Lane, and =
113
Volume 238, number 1
PHYSICS LETTERS B
29 March 1990
Quigg (set I) [20] (EHLQ1) and present in fig. 1 (fig. 2) the differential cross section d o ' / d p T v e r s u s PT for Z ° + V production in pp collisions at SSC ( L H C ) energies for both ~t and ~' states. We have assumed v/s = 40 TeV for the S SC and ~ = 16 TeV for the LHC. (For ~ (T) states we also include a factor of 1.05 ( 1.5 ) to take into account the effects of higher radial excitations, suitably weighted by their ~t+ / g - branching ratios.) The results using EHLQ2 distributions are almost identical, whereas the Duke-Owens I distributions [ 21 ] typically give a lower result by (30-40)%. For illustrative purposes, we also plot the cross section for V +7 production arising from gluon fusion, once again with EHLQ1 distributions. (This process will suffer from backgrounds from g g ~ V / x + g subprocesses where the final state gluon leads to a jet containing ~°'s and q's which decay into photon states as in direct photon experiments. ) This process is of interest in its own right and its potential observability is presently under study. We note that there is still a large difference between V + Z ° and V +T production at these energies except at PT> 60 GeV. This is to be compared to the increasing similarity between "direct Z °'' and standard direct photon production at TEVATRON energies [22]. (We find, somewhat surprisingly, that the cross sections calculated using EHLQ2 distributions are almost identical in this case as well. ) In single V production, the gg~Vg contribution is completely dominated by g g ~ x + g (where the observed V is produced via the radiative decay z ~ V + y ) for both ~s [ 13,14 ] and "f production [ 15]. While there is no g g ~ x + 7 contribution to V + T production because of color and charge conjugation invariance (as well as no 7 + g ~ X+ g contribution to photon- or electroproduction), because of the axial vector coupling of the Z ° there will be a g g ~ Z ° + X contribution to Z ° + V production. We expect such a contribution to be small, however, as it is suppressed by having to couple via the derivative of the quarkonium wave function (R ~(0)2) instead of the wave function (Rs(0)2) while at the same time not benefitting from the presence of the three-gluon coupling (with its enhanced color factors) as well as the mediation of a higher spin ( j = 1 ) gluon and the resulting enhancements suggested by Regge ideas as occurs in the g g ~ x + g case. In other processes not involving such gluonic enhancements, such as Z°~V7, ZY [23] or double X production [10], the P-state contributions are
i
i0 z*
103 ~ , \
103
SSC EHLOI
LHC
lO2 ' ~
~02 \ k k k k
OJ
\ , \
~Y',\ X~y
Io~
~', \y~
¢'~ =7 1 -i=1 10-1 ~
~
\ "x
k
,:I
JJ
lO
,,I
"
"
"
, , , ,'~
20
. . . .
~o
"
\
i
~ , , i l
~o
~,i - "Li L so 60
PT (GeV) Fig. 1. The differential cross section da/dpx (in p b / G e V ) is shown as a function of the transverse momentum PT (in GeV) for gluon-gluon production of various final states at the SSC (,,/s=40 TeV). The gluon structure functions according to the first set of Eichten, Hinchliffe, Lane and Quigg (EHLQ I) [20] have been used. The processes shown are gg--, Y7 (upper solid line), gg--'~g7 (upper dashed line), gg~YZ ° (lower solid line) and gg--+~gZ°) (lower dashed line).
114
\\\\ i0_1
YZ \ \ \
x\\
\
10-2
10-21
104
EHLO.I
10-3
1o
20
30
4O
5O
6O
PT(GeV) Fig. 2. The differential cross section da/dp-r (in p b / G e V ) is shown as a function of the transverse momentum PT (in GeV) for gluon-gluon production of various final states at the LHC ( x f s = 16 TeV). The gluon structure functions according to the first set of Eichten, Hinchliffe, Lane and Quigg (EHLQ I) [20] have been used. The processes shown are gg~TT (upper solid line), g g ~ y (upper dashed line), gg-~fZ ° (lower solid line) and g g ~ q Z ° (lower dashed line ).
Volume 238, number 1
PHYSICS LETTERS B
29 March 1990
considerably smaller. (We also note that our result for the matrix element squared for g g ~ Z ° + V can be used to derive the rate for Z ° ~ V g g for which calculations already exist [24] and we agree with previous results. Similarly, the results for g g ~ Z ° + q c , b can be crossed to give the k n o w n results for Z0~qc,bgg [25] and q t ~ Z ° g g [26 ].) We finally note that the process g g ~ P ' f is forbidden by C invariance. One possible use of our results would be the e x a m i n a t i o n of the production o f V + Z ° states via multiple parton interactions [27]. The observation of a large transverse m o m e n t u m ~¢/Y (balanced in Px by an away-side jet) accompanied by a Z ° produced at zero PT (bY q + q ~ Z °) due to two i n d e p e n d e n t parton interactions in a single hadronic collision would only be simulated by a higher-order single parton interaction process, such as g g - ~ Z ° + V + g and so can become competitive. Even more promising is the possibility of V + W events due to multiple parton processes as there is no substantial single parton contribution to this channel. In this case the signal would be a high-pT V (balanced by an opposing jet) accompanied by a zero-px W (decaying into a single high-pv lepton a n d missing energy). (We note that double W / Z production due to such multiple parton interactions or pileup effects (which becomes a comparable effect at SSC energies and luminosities [28] ) are not substantial. Single t~ cross sections are, however, large enough so that a ( ~ W ) = a ( ~ ) a ( W ) / a ( t o t a l ) can give rise to an observable n u m b e r o f ~ - W events [ 9 ]. ) Finally, as for all "rare" processes at SSC and LHC energies, we have to worry about possible backgrounds. One obvious source of background for g g ~ V Z with V detected through its leptonic decays is q(:l, gg--,ZT*~Z~+~ -. This has, as far as we know, not been calculated. However, qct, gg-~Zy has been calculated [29 ]. Using those results and assuming that there is no form factor suppression (this overestimates the background) we find, for a detector with i n v a r i a n t mass resolution A, cr(pp~Z~+~ - ) ~ a ( p p - ~ Z T ) " (2o~/3n) log( 1 + A / m y ) . Using the results of ref. [29 ] for pp ~ Z7 at the SSC, we find that this background is not a problem for Px < 50 GeV provided that the i n v a r i a n t mass resolution A/mv is better than a r o u n d 5%. As can be seen in fig. 1, g g ~ V Z drops quite rapidly with Px for PT > 20 GeV, whereas the background process has a flatter distribution. We are grateful to T. Dombeck, S. H e p p e l m a n n a n d G. Ingelman for help and useful conversations. This work was supported in part by the National Science F o u n d a t i o n (R.R.) u n d e r G r a n t No. PHY-8620118, and by the Swedish Natural Science Research Council (L.B.).
References [ 1] H. Baer, V. Barger and H. Goldberg, Phys. Rev. Lett. 59 (1987) 860; H. Baer, V. Barger, H. Goldberg and J. Ohnemus, Phys. Rev. D 38 ( 1988 ) 3467. [2 ] For recent discussions of high Pv weak boson production, see P.B. Arnold and M.H. Reno, Nucl. Phys. B 319 ( 1989) 37; P.B. Arnold, R.K. Ellis and M.H. Reno, Phys. Rev. D 40 (1989) 912. [ 3 ] See V. Barger and T. Han, Phys. Lett. B 212 ( 1988) 117; V. Barger, T. Han and R.J.N. Phillips, Phys. Rev. D 39 (1989) 146; V. Barger, T. Han and H. Pi, Wisconsin preprint MAD/TH/478, and references contained in these papers. [4] M.S. Chanowitz and M.K. Gaillard, Phys. Lett. B 142 (1984) 85; Nucl. Phys. B 261 (1985) 379; M. Golden and S. Sharpe, Nucl. Phys. B 261 (1985) 217; M.S. Chanowitz, M. Golden and H. Georgi, Phys. Rev. Lett. 57 (1986) 2374; Phys. Rev. D 35 (1987) 1490. [ 5 ] See, for example, H.-U. Bengtssonand A. Savoy-Navarro,Phys. Rev. D 37 ( 1988 ) 1787, for a recent discussion. [6] B. Cox and D.E. Wagoner,in: Proc. 1986 Summer Study on The physics of the SuperconductingSupercollider, eds. R. Donaldson and J. Marx (Division of Particles and Fields of the American Physical Society, New York, 1987) p. 83; see also K.J. Foley et al., in: Proc. Workshop on Experiments, detectors, and experimental areas for the Supercollider, eds. R. Donalson and M.G.D. Gilchriese (Division of Particles and Fields of the American Physical Society, New York, 1987) p. 759. [ 7 ] CDF Collab., F. Abe et al., Phys. Rev. Lett. 63 (1989) 720. [ 8 ] NA3 Collab., J. Badier et al., Phys. Lett. B 124 ( 1983 ) 535. [9] R.W. Robinett, Phys. Lett. B 230 (1989) 153. 115
Volume 238, number 1
PHYSICS LETTERS B
29 March 1990
[ 10] S. Heppelmann, R.W. Robinett and P. Moxhay, Phys. Lett. B 233 (1989) 245. [ 11 ] J.H. Kiihn, J. Kaplan and E.G.O. Safiani, Nucl. Phys. B 157 (1979) 125. [ 12] R. Gastmans, W. Troost and T.T. Wu, Phys. Lett. B 184 (1987) 257; Nucl. Phys. B 291 (1987) 731; B. Humpert, Phys. Lett. B 184 (1987) 105; see also C.-H. Chang, Nucl. Phys. B 172 (1980) 425; R. Baler and R. Riickl, Z. Phys. C 19 (1983) 251. [ 13] F. Halzen, F. Herzog, E.W.N. Glover and A.D. Martin, Phys. Rev. D 30 (1984) 700; E.W.N. Glover, F. Halzen and A.D. Martin, Phys. Lett. B 185 (1987) 441. [ 14 ] E.W.N. Glover, A.D. Martin and W.J. Stirling, Z. Phys. C 38 ( 1988 ) 472. [ 15] B. van Eijk and R. Kinnunen, Z. Phys. C 41 (1989) 489; B. van Eijk, in: New aspects of high-energy proton-proton collisions, ed. A. All (Plenum, New York, 1989) p. 223. [ 16 ] See A.D. Martin, C.-K. Ng and W.J. Stirling, Phys. Lett. B 191 ( 1987 ) 200; Z. Kunszt, Phys. Lett. B 207 ( 1988 ) 103, and references therein. [ 17 ] K. Hagiwara, A.D. Martin and A.W. Peacock, Z. Phys. C 33 (1986) 135; P. Moxhay and J.L. Rosner, Phys. Rev. D 28 ( 1983 ) 1132; for a recent review of heavy quarkonia and potential models, see W. Kwong, J.L. Rosner and C. Quigg, Annu. Rev. Nucl. Sci. 37 (1988) 325. [ 18 ] R.E. Ecclestone and D.M. Scott, Phys. Lett. B 120 (1983) 237; Z. Phys. C 19 ( 1983 ) 29; B. Humpert and P. Mery, Phys. Lett. B 124 ( 1983 ) 265; Z. Phys. C 20 ( 1983 ) 83. [ 19] UAI Collab., C. Albajar et al., Phys. Lett. B 200 (1988) 380. [20] E. Eichten, I. Hinchliffe, K. Lane and C. Quigg, Rev. Mod. Phys. 56 (1984) 574; 58 (1986) 1065 (E). [21 ] D.W. Duke and J.F. Owens, Phys. Rev. D 30 (1984) 49. [ 22 ] J.L. Rosner and L. Stodolsky, Phys. Rev. D 40 (1989) 1667. [ 23 ] B. Guberina, J.H. Kiihn, R.D. Peccei and R. Riickl, Nucl. Phys. B 174 (1980) 317. [24] W.-Y. Keung, Phys. Rev. D 23 ( 1981 ) 2072; K.J. Abraham, Z. Phys. C 44 (1989) 467. [25 ] V. Barger, K. Cheung and W.-Y. Keung, preprint M A D / P H / 5 2 3 (1989). [26] L. Bergstr6m, Phys. Rev. D 38 (1988) 3502. [ 27 ] For a recent review of the role of multiple parton processes at colliders (focusing on multi-jet events), see N. Paver, in: New aspects of high-energy proton-proton collisions, ed. A. All (Plenum, New York, 1989 ) p. 309. [ 28 ] F. Paige and E.M. Wang, Brookhaven preprint BNL-43151 ( 1989 ). [29] J.J. Van der Bij and E.W.N. Glover, Phys. Lett. B 206 (1988) 701; see also L1. Ametller et al., Phys. Rev. D 32 (1980) 1699.
116
PHYSICS LETTERS B
29 March 1990
Z AND VECTOR MESON PRODUCTION I N H A D R O N I C C O L L I S I O N S AT L A R G E T R A N S V E R S E M O M E N T U M L. B E R G S T R ( J M Department of Physics, Universityof Stockholm, Vanadisv?igen9, S-113 46 Stockholm, Sweden
and R.W. R O B I N E T T Department of Physics, The Pennsylvania State University, UniversityPark, PA 16802, USA
Received 29 December 1989
Large PT production of J/~ and/' panicles in association with a Z° boson or a photon is calculated for the SSC and LHC coUiders. We briefly discuss the possible relevance of this mode for studies of multiple parton interactions at supercoUiderenergies.
The next generation of hadron (super) colliders, the SSC and LHC, will undoubtedly open a new window on fundamental physics at the TeV energy scale. The extremely high luminosities and particle multiplicities per event, however, will make the experimental environment at such machines one of the most challenging yet encountered in high energy physics. Because of this, events containing easily distinguishable features such as jets, weak bosons, and vector mesons (hereafter V = J / ~ or Y) will certainly be utilized heavily. Of these, weak bosons and vector mesons also give rise to m u o n decays which are another clear signal in such an environment and, in addition, multiple m u o n events have long been touted as a clear indicator for new physics phenomena [ 1 ]. (In fact, one extreme suggestion for coping with the large particle fluxes at a high luminosity L H C configuration is to surround the interaction region with absorber so that only muons are detected.) In this context, single W and Z production will be a benchmark process at such energies while high-pT weak boson production is already and will remain an important Q C D test [2]. Multiple (2-, 3-, and even 4-) W / Z production [ 3] will provide tests of the electroweak sector (including the 3- and 4- weak boson vertices and scalar couplings) as well as being a possible way o f probing a strongly interacting [4] electroweak sector. The detection of the standard model Higgs boson also falls into this category especially as it applies to its "gold-plated" signature [ 5] via H°--,ZZ--.muons. Such classes o f events with extremely clean signatures, even those with low event rates, hold promise in a super-collider environment. Vector meson production will also likely be useful as well, for different reasons, as, for example, a probe of the low-x gluon content of the proton while ~¢production arising from b-quark decay has been extensively discussed [ 6 ] as a possible tagging mechanism for B-meson decay. Even the rather mundane use o f ~ and ~f production as a calibration for mass measurements (as with the present C D F experiment [7 ] ) will ensure the continued usefulness of light vector mesons. Double ~t production has even been observed in the lower energy, fixed-target hadronic (Tt-p) collisions [ 8 ] and has been analyzed in terms of the lowest order (O ( o~4 ) ) gg ~ ~ + ~ diagrams. The relevance of this process at supercollider energies has recently been discussed [ 9 ] especially in relation to its possible use as a probe of multiple parton interactions. (The lowest order (O (or 4 ) ) diagrams leading to ~¢-'f production [ 10 ] have also been calculated. ) Given the extensive analyses o f single and multiple weak boson and vector meson production at supercollider 1 12
0370-2693/90/$ 03.50 © Elsevier Science Publishers B.V. ( North-Holland )
Volume 238, number 1
PHYSICS LETTERS B
29 March 1990
energies performed in an attempt to probe the physics potential for such machines, it is then natural to investigate the prospects for combined weak boson + V production. The simplest such subprocess is given by g + g - , Z ° + V (which is of order oes2o~w and would, of course also have the dramatic four charged lepton signal) and it is that process and the prospects for Z ° = V production in pp collisions at SSC and LHC energies which we will discuss in this letter. (Contributions from q + ~ - , Z ° + V will be of order a3w and will be ignored. We also note that there are no similar low-order 2-,2 processes yielding W + V states. ) The differential cross section for g ( k~ ) + g ( k2 ) -~ Z ° (Q) + V (P) is derived using the bound state formalism of Ktihn, Kaplan, and Safiani [ 11 ]. We find de /to¢20~(1 --41e Q Isin20w) 2 [Rs(0)]2my d~ ( g g ~ V Z ) = • 20wCOS'0w , sin 12 d2 X { [ ( 13/2+ 34/t/+ 13~2)~+22([+gt)d2+6g3+ (/q-u)3]m4v - [2(2/2+ 11/ti+ 2fi2)g2+ 2 ( / 2 + 8{ti+ t/2) ({+fO~-2g4+2{3f~+3/2f~2+2[f~3]rn2 - 2 ( / + ti)g 3 - [ 18(/+z1)g+ 1692+[2+f~2]m6v + (7g-[-f~)rnSv
+ (2[+(Q([+2ti)g[gt+4([+z2)d2[f~+rn~,°+2d3[fl+[3(t2+[2~ 3} X [m2v(rn2v - g - m 2 ) 2 ( m ~ , - [)2(m2v - t / ) 2] - ~ ,
(1)
where the standard Mandelstam variables are defined via g = (k~ + k2 ) 2 = ( p + 0 ) 2,/'= (k~ - P) 2and ~/= (kl - Q) 2. The techniques leading to our result can be easily checked against known results for g + g - , V + g by simple changes in kinematics and coupling factors. In fact, also the cross section for gg--, V`/ can be obtained from wellknown results [ 12 ] for gg-,gV by the simple conversion factor i2 (0~Q2/0¢). We also give the corresponding result for pseudoscalar meson production such as qc, Tlb etc. This is given by the somewhat less awkward expression
dr~ ~¢z2ol IRs(O)12me d~ ( g g ~ P Z ) = sin2OwcoS20w 12~2 X {[ (2[+2(l--3m2)g+ (ft--m~,)[-t-2d2--flrrl 2 -f-m~,] [((~-m~,)f-dm 2 - ( t m 2 +m~,] (m 2 --m2) 2} X [ m e m z2( s, + m z 22 _rng)2([_rn2)2(~_rn2p)2] -1
(2)
When trying to exploit this channel one runs however into the trouble of finding a signature for the qc.b decays. The only reasonable change is given by the y`/mode, but this has a branching ratio at the 10 -4 level only. nevertheless, one has to keep in mind that electromagnetic calorimeters with excellent energy resolution will certainly be an integral part of LHC/SSC detectors, since those are essential for the intermediate mass Higgs search through H-~77. Numerically, we find that the rate for P + Z production is, within roughly a factor of two, the same as for V + Z production. We do not consider pseudoscalar production further here, however. Single, high-px "direct" t~ production is well studied in both hadronic collisions [ 13-15 ] and in electroproduction experiments [I 6] and we will use the results of previous successful fits to data in our analysis here. Specifically, we use values of the quarkonium wave functions derived from realistic potential models (e.g. Rs (0) 2 = 0.70 GeV 3 for n = 1 ~ and Rs (0) 2 7.3 GeV 3 for n -= 1 1"), a value of the strong coupling corresponding to c~s(Q2=M2v), as well as a K-factor, K = 2 , inferred from analyses of both single [14] and double [18] tg production. Such parameters, especially the relatively large (and fixed) values of c~s are consistent with both fixed target and collider [ 19 ] data on high-px u/production. (~ production arising from b-quark decay is also an important source at collider energies but the UA 1 collaboration [ 19 ] has demonstrated the ability to distinguish between "direct" production and that arising form B meson decay by using various isolation cuts.) For predictions at supercollider energies, we use the gluon distribution functions of Eichten, Hinchliffe, Lane, and =
113
Volume 238, number 1
PHYSICS LETTERS B
29 March 1990
Quigg (set I) [20] (EHLQ1) and present in fig. 1 (fig. 2) the differential cross section d o ' / d p T v e r s u s PT for Z ° + V production in pp collisions at SSC ( L H C ) energies for both ~t and ~' states. We have assumed v/s = 40 TeV for the S SC and ~ = 16 TeV for the LHC. (For ~ (T) states we also include a factor of 1.05 ( 1.5 ) to take into account the effects of higher radial excitations, suitably weighted by their ~t+ / g - branching ratios.) The results using EHLQ2 distributions are almost identical, whereas the Duke-Owens I distributions [ 21 ] typically give a lower result by (30-40)%. For illustrative purposes, we also plot the cross section for V +7 production arising from gluon fusion, once again with EHLQ1 distributions. (This process will suffer from backgrounds from g g ~ V / x + g subprocesses where the final state gluon leads to a jet containing ~°'s and q's which decay into photon states as in direct photon experiments. ) This process is of interest in its own right and its potential observability is presently under study. We note that there is still a large difference between V + Z ° and V +T production at these energies except at PT> 60 GeV. This is to be compared to the increasing similarity between "direct Z °'' and standard direct photon production at TEVATRON energies [22]. (We find, somewhat surprisingly, that the cross sections calculated using EHLQ2 distributions are almost identical in this case as well. ) In single V production, the gg~Vg contribution is completely dominated by g g ~ x + g (where the observed V is produced via the radiative decay z ~ V + y ) for both ~s [ 13,14 ] and "f production [ 15]. While there is no g g ~ x + 7 contribution to V + T production because of color and charge conjugation invariance (as well as no 7 + g ~ X+ g contribution to photon- or electroproduction), because of the axial vector coupling of the Z ° there will be a g g ~ Z ° + X contribution to Z ° + V production. We expect such a contribution to be small, however, as it is suppressed by having to couple via the derivative of the quarkonium wave function (R ~(0)2) instead of the wave function (Rs(0)2) while at the same time not benefitting from the presence of the three-gluon coupling (with its enhanced color factors) as well as the mediation of a higher spin ( j = 1 ) gluon and the resulting enhancements suggested by Regge ideas as occurs in the g g ~ x + g case. In other processes not involving such gluonic enhancements, such as Z°~V7, ZY [23] or double X production [10], the P-state contributions are
i
i0 z*
103 ~ , \
103
SSC EHLOI
LHC
lO2 ' ~
~02 \ k k k k
OJ
\ , \
~Y',\ X~y
Io~
~', \y~
¢'~ =7 1 -i=1 10-1 ~
~
\ "x
k
,:I
JJ
lO
,,I
"
"
"
, , , ,'~
20
. . . .
~o
"
\
i
~ , , i l
~o
~,i - "Li L so 60
PT (GeV) Fig. 1. The differential cross section da/dpx (in p b / G e V ) is shown as a function of the transverse momentum PT (in GeV) for gluon-gluon production of various final states at the SSC (,,/s=40 TeV). The gluon structure functions according to the first set of Eichten, Hinchliffe, Lane and Quigg (EHLQ I) [20] have been used. The processes shown are gg--, Y7 (upper solid line), gg--'~g7 (upper dashed line), gg~YZ ° (lower solid line) and gg--+~gZ°) (lower dashed line).
114
\\\\ i0_1
YZ \ \ \
x\\
\
10-2
10-21
104
EHLO.I
10-3
1o
20
30
4O
5O
6O
PT(GeV) Fig. 2. The differential cross section da/dp-r (in p b / G e V ) is shown as a function of the transverse momentum PT (in GeV) for gluon-gluon production of various final states at the LHC ( x f s = 16 TeV). The gluon structure functions according to the first set of Eichten, Hinchliffe, Lane and Quigg (EHLQ I) [20] have been used. The processes shown are gg~TT (upper solid line), g g ~ y (upper dashed line), gg-~fZ ° (lower solid line) and g g ~ q Z ° (lower dashed line ).
Volume 238, number 1
PHYSICS LETTERS B
29 March 1990
considerably smaller. (We also note that our result for the matrix element squared for g g ~ Z ° + V can be used to derive the rate for Z ° ~ V g g for which calculations already exist [24] and we agree with previous results. Similarly, the results for g g ~ Z ° + q c , b can be crossed to give the k n o w n results for Z0~qc,bgg [25] and q t ~ Z ° g g [26 ].) We finally note that the process g g ~ P ' f is forbidden by C invariance. One possible use of our results would be the e x a m i n a t i o n of the production o f V + Z ° states via multiple parton interactions [27]. The observation of a large transverse m o m e n t u m ~¢/Y (balanced in Px by an away-side jet) accompanied by a Z ° produced at zero PT (bY q + q ~ Z °) due to two i n d e p e n d e n t parton interactions in a single hadronic collision would only be simulated by a higher-order single parton interaction process, such as g g - ~ Z ° + V + g and so can become competitive. Even more promising is the possibility of V + W events due to multiple parton processes as there is no substantial single parton contribution to this channel. In this case the signal would be a high-pT V (balanced by an opposing jet) accompanied by a zero-px W (decaying into a single high-pv lepton a n d missing energy). (We note that double W / Z production due to such multiple parton interactions or pileup effects (which becomes a comparable effect at SSC energies and luminosities [28] ) are not substantial. Single t~ cross sections are, however, large enough so that a ( ~ W ) = a ( ~ ) a ( W ) / a ( t o t a l ) can give rise to an observable n u m b e r o f ~ - W events [ 9 ]. ) Finally, as for all "rare" processes at SSC and LHC energies, we have to worry about possible backgrounds. One obvious source of background for g g ~ V Z with V detected through its leptonic decays is q(:l, gg--,ZT*~Z~+~ -. This has, as far as we know, not been calculated. However, qct, gg-~Zy has been calculated [29 ]. Using those results and assuming that there is no form factor suppression (this overestimates the background) we find, for a detector with i n v a r i a n t mass resolution A, cr(pp~Z~+~ - ) ~ a ( p p - ~ Z T ) " (2o~/3n) log( 1 + A / m y ) . Using the results of ref. [29 ] for pp ~ Z7 at the SSC, we find that this background is not a problem for Px < 50 GeV provided that the i n v a r i a n t mass resolution A/mv is better than a r o u n d 5%. As can be seen in fig. 1, g g ~ V Z drops quite rapidly with Px for PT > 20 GeV, whereas the background process has a flatter distribution. We are grateful to T. Dombeck, S. H e p p e l m a n n a n d G. Ingelman for help and useful conversations. This work was supported in part by the National Science F o u n d a t i o n (R.R.) u n d e r G r a n t No. PHY-8620118, and by the Swedish Natural Science Research Council (L.B.).
References [ 1] H. Baer, V. Barger and H. Goldberg, Phys. Rev. Lett. 59 (1987) 860; H. Baer, V. Barger, H. Goldberg and J. Ohnemus, Phys. Rev. D 38 ( 1988 ) 3467. [2 ] For recent discussions of high Pv weak boson production, see P.B. Arnold and M.H. Reno, Nucl. Phys. B 319 ( 1989) 37; P.B. Arnold, R.K. Ellis and M.H. Reno, Phys. Rev. D 40 (1989) 912. [ 3 ] See V. Barger and T. Han, Phys. Lett. B 212 ( 1988) 117; V. Barger, T. Han and R.J.N. Phillips, Phys. Rev. D 39 (1989) 146; V. Barger, T. Han and H. Pi, Wisconsin preprint MAD/TH/478, and references contained in these papers. [4] M.S. Chanowitz and M.K. Gaillard, Phys. Lett. B 142 (1984) 85; Nucl. Phys. B 261 (1985) 379; M. Golden and S. Sharpe, Nucl. Phys. B 261 (1985) 217; M.S. Chanowitz, M. Golden and H. Georgi, Phys. Rev. Lett. 57 (1986) 2374; Phys. Rev. D 35 (1987) 1490. [ 5 ] See, for example, H.-U. Bengtssonand A. Savoy-Navarro,Phys. Rev. D 37 ( 1988 ) 1787, for a recent discussion. [6] B. Cox and D.E. Wagoner,in: Proc. 1986 Summer Study on The physics of the SuperconductingSupercollider, eds. R. Donaldson and J. Marx (Division of Particles and Fields of the American Physical Society, New York, 1987) p. 83; see also K.J. Foley et al., in: Proc. Workshop on Experiments, detectors, and experimental areas for the Supercollider, eds. R. Donalson and M.G.D. Gilchriese (Division of Particles and Fields of the American Physical Society, New York, 1987) p. 759. [ 7 ] CDF Collab., F. Abe et al., Phys. Rev. Lett. 63 (1989) 720. [ 8 ] NA3 Collab., J. Badier et al., Phys. Lett. B 124 ( 1983 ) 535. [9] R.W. Robinett, Phys. Lett. B 230 (1989) 153. 115
Volume 238, number 1
PHYSICS LETTERS B
29 March 1990
[ 10] S. Heppelmann, R.W. Robinett and P. Moxhay, Phys. Lett. B 233 (1989) 245. [ 11 ] J.H. Kiihn, J. Kaplan and E.G.O. Safiani, Nucl. Phys. B 157 (1979) 125. [ 12] R. Gastmans, W. Troost and T.T. Wu, Phys. Lett. B 184 (1987) 257; Nucl. Phys. B 291 (1987) 731; B. Humpert, Phys. Lett. B 184 (1987) 105; see also C.-H. Chang, Nucl. Phys. B 172 (1980) 425; R. Baler and R. Riickl, Z. Phys. C 19 (1983) 251. [ 13] F. Halzen, F. Herzog, E.W.N. Glover and A.D. Martin, Phys. Rev. D 30 (1984) 700; E.W.N. Glover, F. Halzen and A.D. Martin, Phys. Lett. B 185 (1987) 441. [ 14 ] E.W.N. Glover, A.D. Martin and W.J. Stirling, Z. Phys. C 38 ( 1988 ) 472. [ 15] B. van Eijk and R. Kinnunen, Z. Phys. C 41 (1989) 489; B. van Eijk, in: New aspects of high-energy proton-proton collisions, ed. A. All (Plenum, New York, 1989) p. 223. [ 16 ] See A.D. Martin, C.-K. Ng and W.J. Stirling, Phys. Lett. B 191 ( 1987 ) 200; Z. Kunszt, Phys. Lett. B 207 ( 1988 ) 103, and references therein. [ 17 ] K. Hagiwara, A.D. Martin and A.W. Peacock, Z. Phys. C 33 (1986) 135; P. Moxhay and J.L. Rosner, Phys. Rev. D 28 ( 1983 ) 1132; for a recent review of heavy quarkonia and potential models, see W. Kwong, J.L. Rosner and C. Quigg, Annu. Rev. Nucl. Sci. 37 (1988) 325. [ 18 ] R.E. Ecclestone and D.M. Scott, Phys. Lett. B 120 (1983) 237; Z. Phys. C 19 ( 1983 ) 29; B. Humpert and P. Mery, Phys. Lett. B 124 ( 1983 ) 265; Z. Phys. C 20 ( 1983 ) 83. [ 19] UAI Collab., C. Albajar et al., Phys. Lett. B 200 (1988) 380. [20] E. Eichten, I. Hinchliffe, K. Lane and C. Quigg, Rev. Mod. Phys. 56 (1984) 574; 58 (1986) 1065 (E). [21 ] D.W. Duke and J.F. Owens, Phys. Rev. D 30 (1984) 49. [ 22 ] J.L. Rosner and L. Stodolsky, Phys. Rev. D 40 (1989) 1667. [ 23 ] B. Guberina, J.H. Kiihn, R.D. Peccei and R. Riickl, Nucl. Phys. B 174 (1980) 317. [24] W.-Y. Keung, Phys. Rev. D 23 ( 1981 ) 2072; K.J. Abraham, Z. Phys. C 44 (1989) 467. [25 ] V. Barger, K. Cheung and W.-Y. Keung, preprint M A D / P H / 5 2 3 (1989). [26] L. Bergstr6m, Phys. Rev. D 38 (1988) 3502. [ 27 ] For a recent review of the role of multiple parton processes at colliders (focusing on multi-jet events), see N. Paver, in: New aspects of high-energy proton-proton collisions, ed. A. All (Plenum, New York, 1989 ) p. 309. [ 28 ] F. Paige and E.M. Wang, Brookhaven preprint BNL-43151 ( 1989 ). [29] J.J. Van der Bij and E.W.N. Glover, Phys. Lett. B 206 (1988) 701; see also L1. Ametller et al., Phys. Rev. D 32 (1980) 1699.
116