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Axigluon production at ep colliders
Volume 215, number 4
PHYSICS LETTERS B
29 December 1988
A X I G L U O N P R O D U C T I O N AT ep C O L L I D E R S R.W. R O B I N E T T Department of Ph£sics, The Pennsylvania State University, University Park, PA 16803, USA
and T.G. R I Z Z O Ames Laboratory and Department of Physics, Iowa State University, Ames, IA 50011, USA
Received 30 September 1988
We study the prospects for the production of axigluons, the massive color-octet gauge bosons present in all chiral-color models, in ep collisions. We find that HERA will likely be able to exclude the currently allowed "window" of light axigluon masses, 25 GeV
There has been some recent discussion of so-called chiral-color models [1,2], schemes in which the strong interaction gauge group at higher energies, presumably near the electroweak scale and above, is actually S U ( 3 ) L X S U ( 3 ) R . This group must, of course, be spontaneously broken to the observed vector SU (3) of color at lower energies and this fact gives rise to the most easily testable, model-independent prediction of such theories, namely the existence of axigluons (A), the massive, color-octet gauge bosons corresponding to the eight broken generators of the axial SU (3). Because the axigluons couple to quarks with the same strong interaction strength ( - i g s ~ y s ) as gluons (to ensure that parity not be violated dramatically) such bosons should be produced copiously in hadronic collisions o f sufficient energy. Bagger, Schmidt, and King [3] *~ have examined the effects of such axigluons on single jet and dijet production at C E R N collider energies and have excluded axigluons with masses in the range 125 GeV
ing axigluons in e + e - machines, specifically at the Z ° pole, have also been discussed ~2 and Z ° decays may eventually be able to exclude masses up to 40-60 GeV. Two groups [8,9] have argued that light axigluons would dominate the hadronic decays o f vector quarkonia if allowed kinematically, and by considering the contributions o f virtual axigluons one can conclude that Y decays [ 10 ] already exclude A masses up to about 25 GeV while toponium decays [ 10] ~3 could probe axigluons with masses beyond 2M,. Gaining such information from the decays of toponium or a hypothetical, fourth-generation Q = - ~ quarkonium will rely, however, on such states being accessible to current or planned accelerators. Recently, Bergstr6m [ 12 ] ~4 has turned this argument around and argued that large PT Y production in hadronic collisions can also provide similar limits which can be improved with further analysis of existing and forthcoming collider data.All of these analyses, however, leave open an allowed window for axigluon masses in the range 25 G e V < M A < 125 GeV which may well be hard to ~2 See ref. [5] for Z°-*q~lA, ref.[6] for Z°-,gA, and ref. [7] for Zo--,AA. ,3 Bergstrrm [l l] derives an expression for 3SI (QQ)~Ag decays which agrees (disagrees) with that previously found in ref. [91 (in refi [8]). ,4 See also refi [9] for a similar suggestion.
0370-2693/88/$ 03.50 © Elsevier Science Publishers B.V. (North-Holland Physics Publishing Division)
777
Volume 215, number 4
PHYSICS LETTERS B
probe with any of these techniques. In this report we will consider the other natural alternative to searches at hadron or e+e - colliders, namely the prospects for A production in ep collisions, specifically at HERA energies (x/s = 314 GeV) but also at higher energies, possibly a LEPI × LHC machine with ,,/~= 1.4 TeV. We find that axigluons can be singly produced with large cross sections in ep collisions through their couplings to the quarks in the proton and that backgrounds due to the production of other strongly interacting particles (especially heavy quark pairs which we will consider) are not nearly so severe as in hadron colliders so that ep machines such as HERA may well be able to exclude axigluons with masses in the currently allowed window. The diagrams leading to A production in ep collisions are shown in fig. 1. These graphs are, except for coupling factors, identical to the ones responsible for weak boson (W, Z) production (from the hadronic vertex) for which many calculations exist [ 13-18 ] and these previous calculations can be used'as a benchmark against which to compare axigluon production. For example, it is known from such work that the Z ° exchange contributions are ignorable, at least at HERA energies, so that we will consider the photon diagrams only. Although the results obtained in these investigations disagree somewhat (in most cases due to differing cuts imposed on the predicted cross sections) they all seem to imply observable Z ° production probabilities at HERA. Because o f the much larger coupling constant for A production (gs versus g = e/sin 0w) and group theoretical factors for producing a color-octet particle we expect a much larger cross section for the same mass boson and we indeed find this to be the case. Moreover, since we are most interested in probing A masses only up to ~ 125 GeV, phase-space suppression effects will never be much worse than for weak boson production and, for lighter axigluons, will be even less important.
j e e-
~
/
)'' zO
.-A
+ crossed
diogrom
q,~ Fig. 1. Diagrams leading to axigluon production in ep collisions.
778
29 December 1988
While "exact" calculations of weak boson production are possible (as in ref. [ 17] ), analyses based on the use of the Weizs~icker-Williams (WW) or effective photon approximation are simpler to implement and give consistent results [16] and that is the approach we will use here. Thus, we will consider the photoproduction of axigluons from quarks ?+q--. A + q, and then weight the resulting cross section by the probability of finding a photon in the electron and quark in the proton with a result similar to many 7/ parton induced processes in ep collisions, namely 1
1
~q q(x,M 2)
acp,Ax(S)= f d r / P v ( r / ) f tlmin
~-'min
X ayq~Aq(g=XqS),
(1)
where q(x, Q2) are the quark (antiquark) distributions inside the proton and Pv is related to the probability of finding a photon in the electron [ 19] ~5 c~ l + ( 1 - y ) 2 1 n ( ~ ) ,
Pv(Y) = 2~
(2)
y
where /max and /min are appropriate cutoff momentum transfers which we discuss below. The cross section for the parton subprocess (k) + q (p) --, A ( k' ) + q ( p ' ) is easily found to be
da dt
--
s
~(u
~wcase?~
s
+ - + u
2tM2~ ~-s , / '
(3)
where eq is the quark charge and s = ( k + p ) 2 and t= (k-k')2. (This result can be checked against the kinematic structure and color factors of well-known results for ~ , + q ~ g + q [20] and, using crossing, q + Cl--'W + g [ 21 ]. ) The resulting total cross section, obtained by integrating over the t interval ( M 2 - g , 0), is formally infinite if one ignores the quark masses because the u-channel pole lies in the region of integration and some prescription must be adopted to regulate this behaviour in the total cross section. Gabrielli [18] uses the identification tmax/tmin= (.¢-M2)/m~ and it is known [ 16] that any reasonably similar prescription will give similar results. Moreover, except for one case below, we will quote ~s As with most calculations involving processes involving energies much larger than the electron mass, we only keep the logarithmic term in the full expression for Pr"
Volume 215, number 4
PHYSICS LETTERS B
cross sections cut on the axigluon transverse m o m e n t u m for which the u-channel pole p r o b l e m does not even arise. Using these prescriptions, we find the predictions for the A production cross sections in ep collisions for x/J = 314 GeV and 1.4 TeV shown in figs. 2 and 3, respectively. (We use the quark distribution functions of Duke and Owens [22 ], set 1.) We have shown results which include the effects o f imposing m i n i m u m PT cuts on the transverse m o m e n t u m o f the axigluon, assuming that we can also use the quarkinitiated jet as part o f the signal, somewhat reducing the Q C D backgrounds. As anticipated, the cross sections for all masses in the 25-125 GeV range are quite large even after realistic cuts are i m p o s e d so that production rates should not be a problem. [Recall that at H E R A with a luminosity o f 1.0× 1031 c m - 2 s - i and 2 years o f effective running (say 2 × 107 s) one can expect 200 pb-~ o f integrated luminosity (or perhaps even up to 200-1 pb per year) so that a 1 pb cross section corresponds to 200 events.] At the higher energy, axigluons with masses up to ~ 300 GeV
29 December 1988
iO 4
I
I
'\ 10 2 _--
'°
i.Oo
I Ioo
I 200
300
MA(GeV )
10 3
Fig. 3. Cross sections (in pb) for axigluon production in ep collisions at x/s= 1.4 TeV. Curves are shown corresponding to minimum axigluon transverse momentum cuts of 5 GeV (solid curve ) and 15 GeV (dashed curve). can be p r o d u c e d but this range will be much more effectively p r o b e d at the T E V A T R O N . Drees [23] has recently argued that there is another significant contribution to weak boson production in ep collisions due to the so-called "resolved p h o t o n " mechanism• This process relies on the existence of a quark content in the photon for which there is some experimental input (as o p p o s e d to the photon's gluon content) and good theoretical understanding ~6. This m e c h a n i s m would also give contributions to A production
I0 a
o'(pb) I0
"\" \ , \\" \.
1.0
\. \. a(ep--,AX) =
• quarks M~
cU gs
P~(s/s)~g2~s /g
\• \. 50
I00 MA (GeV)
× [q~(x, M2A)OP(M~/xg, M~) 150
Fig. 2. Cross sections (in pb) for axigluon production in ep collisions at x/~=314 GeV. Curves are shown corresponding to minimum axigluon transverse momentum cuts of 5 GeV (solid curve), 10 GeV (dashed curve), and 15 GeV (dot-dashed curve).
+ElY(X, M~)qP(M2 /xg, M~,) ] ,
(4)
recent discussion of the hadron structure of the photon see ref. [24].
~6 F o r a
779
Volume 215, number 4
PHYSICS LETTERS B
where the sum is over all quark-antiquark pairs and qV are the quark distribution functions inside the photon (for which we use the parametrizations of Duke and Owens [ 20 ] ). We follow ref. [ 23 ] and use ln[ ( 1 --X)MA/Xm~] as the logarithmic factor in the photon distribution in the electron. (Other reasonable choices are known to give similar results.) This contribution to the total (uncut in PT) A production cross section does indeed contribute a significant ( ~ 50%) increase in the A production rate at HERA energies and we will discuss this more quantitatively below. A final possible production mechanism which may become important at very high energies would be "gluon-axigluon fusion". This process relies on the (as yet untested) gluon content of the photon and an "effective A content" of the parton. While formally of higher order in couplings, the situation here is similar to the weak boson (WW, ZZ) fusion production of Higgs bosons in hadronic collision where gauge boson fusion comes to dominate the production cross section. Proposed tests [25] of the gluon content of the photon at high energy ep machines will provide more detailed experimental information on which to base calculations for this process. For now, using the gluon content given in ref. [ 20 ] we find that this process gives a negligible contribution, at least at HERA energies. We now turn to the prospects of observing the produced axigluons which require a knowledge of their decays. The A decays in a flavor independent way into all kinematically allowed quark-antiquark pairs so if we ignore, for simplicity, any new exotic colored fermions (which are required in many chiral-color models to cancel anomalies) and the top quark, there will be five open decay channels (u, d, s, c, b) and an overall width F ( A ) = 5 o ~ s M A. Thus, detection of A decays will rely on the ability to reconstruct jets, especially jet pairs, in an ep collider environment. The question of jet resolution and reconstruction [26], the ability to accurately predict QCD backgrounds (especially to the decays of new heavy objects decaying with a two-jet signature ~7), and the relative merits a n d / o r validity of matrix element versus parton ,7 See especially ref. [ 27 ], where this question is raised explicitly but not answered. See also ref. [28 ]. K6rner, Mirkes and Schuler have recently calculated O (o~s) corrections to three-jet and two-jet rates and discussed their significance.
780
29 December 1988
shower approaches are topics of much discussion and a detailed investigation of A detection via its jet-jet decays is beyond the scope of this letter. We will argue, however, that it may well be easier to detect A decays by reconstruction of its bb decay modes. The branching ratio B R ( A ~ b B ) = 2 0 % (see above) is substantial while the production of heavy quark pairs (especially bb) is a well-studied phenomenon in ep collisions [30,3_1 ] and is thought to be calculable reliably but, of course, is highly suppressed relative to standard two-jet processes. The basic bb production process is via photon-gluon fusion and it is known that the WW approximation is also reliable for this process. We can then estimate the likelihood of seeing a bb signal from A decay over the background in the following way. The differential cross section for heavy quark pair production in WW approximation will be given by ~s I
da a ( M 2) d M 2 -s
f
---~Pv(x)G(M2/xs,M 2)
(5)
M2/s
where G(x, Q2) is the gluon distribution in the proton. (When integrated over all allowed M 2 (i.e. from 4M 2 to s) we reproduce the total bb cross section given in ref. [30].) In this expression, o'(M 2) is the ~/g--,QQ cross section for which we use the lowestorder formula ~9 a(s) = nc~a~e~{ ( 3 _ f14) ln[(1 + / ? ) / ( 1 - f l ) ] S
-2fl(2-f12)},
(6)
where fl= (1 -y)~/2, y=4M~/s, and e O is the quark charge. We can then integrate eq. (6) over a putative peak at axigluon mass M (i.e. over the range (M2-MF, M2+MF) for full width at half maxim u m ) to obtain an estimate of the continuum bb production under the A signal. This can then be compared to the uncut (in PT) total A production cross sections multiplied by 0.1 (0.2 for the bb branching ~8 We have suitably modified the result for d a / d M 2 for gg fusion production of heavy quark pairs in h a d r o n - h a d r o n collisions given in ref. [ 32 ] to the case of'/g fusion in ep collisions where the photon is described via the W W approximation. ~9 We do not include recently calculated Q C D corrections to heavy quark photoproduction. See ref. [33].
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PHYSICS LETTERS B
ratio and 0.5 for F W H M . ) The corresponding signals (background) in pb for x / s = 314 GeV and various axigluon masses are given in table 1, where the range of values for the background indicates the effects of varying Mb from 4.5 to 5.0 GeV and using different distribution functions (Duke and Owens, sets 1 and 2 ) and the range for the signal shows the effect of including or neglecting the "resolved-photon" contrib u t i o n discussed above, Even taking into account a reasonable bb identification probability, it still appears that a signal for axigluons in much of the mass window we consider will be detectable above background with sufficiently high statistics. Other processes can also contribute to bb production [25 ] and b identification may be i m p o r t a n t for identification of other new exotic particles [ 34 ] as well, so careful studies of b production will likely be considered important at ep machines and so can also be used to test A production. One could imagine using tt decays, if kinematically allowed, as an A signature since the standard tt production is very small [35 ] but current collider limits on the top quark mass [36] (Mr> 56 GeV) and suggestions from B-13 mixing [ 37 ] make it unlikely that axigluons in the mass " w i n d o w " we consider will have this decay mode accessible. Another possible signal might be high Pr "f' production (as in ref. [12] ) where the standard model contrib u t i o n arises from y + g ~ ' t ' + g and has recently been calculated [ 38 ] for HERA and LHC energies. In conclusion, we have argued that axigluon production cross sections for A masses in the 25-125 GeV mass range are large at HERA energies and that the identification of A decays in the bb channel ( a n d perhaps in the two-jet invariant mass distributions as well) may well allow experimentalists to exclude all of this region of mass, a region which might otherwise be difficult to probe in any other accelerator environment.
Table 1 MA (GeV) 25 50 75
Signal (background) (pb) 215 -300 (290 -200) 20 - 29 (32 - 29) 3.8 - 5.9 (6.8 - 6.0)
100
1.0 -
125
0.27- 0.44 (0.56- 0.35)
1.5
(1.9
-
1.4)
29 December 1988
This work was supported in part by grants from the National Science F o u n d a t i o n u n d e r grant PHY8606279 (R.R.) and the D e p a r t m e n t of Energy under grant W-7405-Eng-82 (T.R.). References
[ 1] P.H. Frampton and S.L. Glashow, Phys. Lett. B 190 ( 1987 ) 157; Phys. Rev. Lett. 58 (1987) 2168. [2]S. Rajpoot, Phys. Rev. Lett. 60 (1988); Phys. Rev. D 38 (1988) 417; Phys Lett. B 208 (1988) 483. [3] J. Bagger, C. Schmidt and S. King, Phys. Rev. D 37 (1988) 1188. [4] UAI Collab., C. Albajar et al., Phys. Lett. B 209 (1988) 127. [5] T.G. Rizzo, Phys. Len. B 197 (1987) 273. [6] E.D. Carlson, S.L. Glashow and E. Jenkins, Phys. Lett. B 202 (1988) 281. [7] F. Cuypers, Phys. Lett. B 206 (1988) 361. [ 8 ] F. Cuypers and P.H. Frampton, Phys. Rev. Lett. 60 ( 1987 ) 1237. [9] M.A. Doncheski, H. Grotch and R.W. Robinett, Phys. Len. B206 (1988) 137. [ 10] M.A. Doncheski, H. Grotch and R.W. Robinett, Phys. Rev. D 38 (1988) 412. [ 11 ] L. Bergstr6m, University of Stockholm preprint USITP-8807. [ 12] L. Bergstr6m, Phys. Lett. B 212 (1988) 386. [ 13] P. Salati and J.C. Wallet, Z. Phys. C 16 (1982) 155. [ 14] H. Neufeld, Z. Phys. C 17 (1983) 145. [ 15 ] A.N. Kamal,J.N. Ng and H.C. Lee, Phys. Rev. D 24 (1984) 2842. [ 16] G. Altarelli,G. Martinelli,B. Meleand R. Riickl,Nucl. Phys. B262 (1985) 204. [ 17] M. B~Shmand A. Rosado, Z. Phys. C 34 (1987) 117; C 39 (1988) 275. [ 18] E. Gabrielli, Mod. Phys. Lett. A 1 (1988) 465. [ 19] S.J. Brodsky, T. Kinoshita and H. Terazawa, Phys. Rev. D '4(1971) 1532. [20 ] See e.g.D.W. Duke and J.F. Owens, Phys. Rev. D 26 ( 1982) 1600. [21 ] See e.g.V.D. Barger and R.J.N. Phillips, Collider physics (Addison Wesley,New York, 1987). [22 ] D.W. Duke and J.F. Owens, Phys. Rev. D 30 ( 1984) 49. [23] M. Drees, Mod. Phys. Len. A 2 (1987) 573. [24] M. Drees and F. Halzen, Phys. Rev. Lett. 61 (1988) 275. [25] M. Drees and R.M. Godbole, Phys. Rev. Lett. 61 (1988) 682; University of Wisconsinpreprint MAD/PH/419. [26 ] P.N. Burrows,G. lngelmanand E. Ros, Z. Phys. C 39 ( 1988) 257. [27] G. Ingelman and T. Sj6strand, Nucl. Phys. B 301 (1988) 554. [28 ] M. Bengtsson,G. Ingelmanand B. Naroska, DESY preprint 88-095. [29] J. K6rner, E. Mirkes and G. Schuler, DESY preprint 88095. 781
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PHYSICS LETTERS B
[30] G.A. Schuler, Nucl. Phys. B 299 (1988) 21; G. Ingelman and G.A. Schuler, DESY preprint DESY 88020; G. Ingelman, DESY preprint 88-098. [ 31 ] M. Glfick, R.M. Godbole and E. Reya, Z. Phys. C 38 ( 1988 ) 441; C 39 (1988) 590 (E). [32] L.M. Jones and H.W. Wyld, Phys. Rev. D 17 (1978) 759. [33] R.K. Ellis and P. Nason, Fermilab Pub-88/54-T; R.K. Ellis and Z. Kunszt, Nucl. Phys. B 303 (1988) 653.
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[34] T.G. Rizzo, Ames Lab preprint IS-J-3138 (1988). [35] U. Baur and J.J. Van Der Bij, Nucl. Phys. B 304 (1988) 451. [ 36 ] UA 1 Collab., C. Albajar et al., Z. Phys. C 37 ( 1988 ) 505. [37] See e.g.J. Ellis, J.S. Hagelin, S. Rudaz and D.-D. Wu, Nucl. Plays B 304 (1988) 205. [38] Z. Kunszt, Phys. Lett. B 207 (1988) 103.
PHYSICS LETTERS B
29 December 1988
A X I G L U O N P R O D U C T I O N AT ep C O L L I D E R S R.W. R O B I N E T T Department of Ph£sics, The Pennsylvania State University, University Park, PA 16803, USA
and T.G. R I Z Z O Ames Laboratory and Department of Physics, Iowa State University, Ames, IA 50011, USA
Received 30 September 1988
We study the prospects for the production of axigluons, the massive color-octet gauge bosons present in all chiral-color models, in ep collisions. We find that HERA will likely be able to exclude the currently allowed "window" of light axigluon masses, 25 GeV
There has been some recent discussion of so-called chiral-color models [1,2], schemes in which the strong interaction gauge group at higher energies, presumably near the electroweak scale and above, is actually S U ( 3 ) L X S U ( 3 ) R . This group must, of course, be spontaneously broken to the observed vector SU (3) of color at lower energies and this fact gives rise to the most easily testable, model-independent prediction of such theories, namely the existence of axigluons (A), the massive, color-octet gauge bosons corresponding to the eight broken generators of the axial SU (3). Because the axigluons couple to quarks with the same strong interaction strength ( - i g s ~ y s ) as gluons (to ensure that parity not be violated dramatically) such bosons should be produced copiously in hadronic collisions o f sufficient energy. Bagger, Schmidt, and King [3] *~ have examined the effects of such axigluons on single jet and dijet production at C E R N collider energies and have excluded axigluons with masses in the range 125 GeV
ing axigluons in e + e - machines, specifically at the Z ° pole, have also been discussed ~2 and Z ° decays may eventually be able to exclude masses up to 40-60 GeV. Two groups [8,9] have argued that light axigluons would dominate the hadronic decays o f vector quarkonia if allowed kinematically, and by considering the contributions o f virtual axigluons one can conclude that Y decays [ 10 ] already exclude A masses up to about 25 GeV while toponium decays [ 10] ~3 could probe axigluons with masses beyond 2M,. Gaining such information from the decays of toponium or a hypothetical, fourth-generation Q = - ~ quarkonium will rely, however, on such states being accessible to current or planned accelerators. Recently, Bergstr6m [ 12 ] ~4 has turned this argument around and argued that large PT Y production in hadronic collisions can also provide similar limits which can be improved with further analysis of existing and forthcoming collider data.All of these analyses, however, leave open an allowed window for axigluon masses in the range 25 G e V < M A < 125 GeV which may well be hard to ~2 See ref. [5] for Z°-*q~lA, ref.[6] for Z°-,gA, and ref. [7] for Zo--,AA. ,3 Bergstrrm [l l] derives an expression for 3SI (QQ)~Ag decays which agrees (disagrees) with that previously found in ref. [91 (in refi [8]). ,4 See also refi [9] for a similar suggestion.
0370-2693/88/$ 03.50 © Elsevier Science Publishers B.V. (North-Holland Physics Publishing Division)
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Volume 215, number 4
PHYSICS LETTERS B
probe with any of these techniques. In this report we will consider the other natural alternative to searches at hadron or e+e - colliders, namely the prospects for A production in ep collisions, specifically at HERA energies (x/s = 314 GeV) but also at higher energies, possibly a LEPI × LHC machine with ,,/~= 1.4 TeV. We find that axigluons can be singly produced with large cross sections in ep collisions through their couplings to the quarks in the proton and that backgrounds due to the production of other strongly interacting particles (especially heavy quark pairs which we will consider) are not nearly so severe as in hadron colliders so that ep machines such as HERA may well be able to exclude axigluons with masses in the currently allowed window. The diagrams leading to A production in ep collisions are shown in fig. 1. These graphs are, except for coupling factors, identical to the ones responsible for weak boson (W, Z) production (from the hadronic vertex) for which many calculations exist [ 13-18 ] and these previous calculations can be used'as a benchmark against which to compare axigluon production. For example, it is known from such work that the Z ° exchange contributions are ignorable, at least at HERA energies, so that we will consider the photon diagrams only. Although the results obtained in these investigations disagree somewhat (in most cases due to differing cuts imposed on the predicted cross sections) they all seem to imply observable Z ° production probabilities at HERA. Because o f the much larger coupling constant for A production (gs versus g = e/sin 0w) and group theoretical factors for producing a color-octet particle we expect a much larger cross section for the same mass boson and we indeed find this to be the case. Moreover, since we are most interested in probing A masses only up to ~ 125 GeV, phase-space suppression effects will never be much worse than for weak boson production and, for lighter axigluons, will be even less important.
j e e-
~
/
)'' zO
.-A
+ crossed
diogrom
q,~ Fig. 1. Diagrams leading to axigluon production in ep collisions.
778
29 December 1988
While "exact" calculations of weak boson production are possible (as in ref. [ 17] ), analyses based on the use of the Weizs~icker-Williams (WW) or effective photon approximation are simpler to implement and give consistent results [16] and that is the approach we will use here. Thus, we will consider the photoproduction of axigluons from quarks ?+q--. A + q, and then weight the resulting cross section by the probability of finding a photon in the electron and quark in the proton with a result similar to many 7/ parton induced processes in ep collisions, namely 1
1
~q q(x,M 2)
acp,Ax(S)= f d r / P v ( r / ) f tlmin
~-'min
X ayq~Aq(g=XqS),
(1)
where q(x, Q2) are the quark (antiquark) distributions inside the proton and Pv is related to the probability of finding a photon in the electron [ 19] ~5 c~ l + ( 1 - y ) 2 1 n ( ~ ) ,
Pv(Y) = 2~
(2)
y
where /max and /min are appropriate cutoff momentum transfers which we discuss below. The cross section for the parton subprocess (k) + q (p) --, A ( k' ) + q ( p ' ) is easily found to be
da dt
--
s
~(u
~wcase?~
s
+ - + u
2tM2~ ~-s , / '
(3)
where eq is the quark charge and s = ( k + p ) 2 and t= (k-k')2. (This result can be checked against the kinematic structure and color factors of well-known results for ~ , + q ~ g + q [20] and, using crossing, q + Cl--'W + g [ 21 ]. ) The resulting total cross section, obtained by integrating over the t interval ( M 2 - g , 0), is formally infinite if one ignores the quark masses because the u-channel pole lies in the region of integration and some prescription must be adopted to regulate this behaviour in the total cross section. Gabrielli [18] uses the identification tmax/tmin= (.¢-M2)/m~ and it is known [ 16] that any reasonably similar prescription will give similar results. Moreover, except for one case below, we will quote ~s As with most calculations involving processes involving energies much larger than the electron mass, we only keep the logarithmic term in the full expression for Pr"
Volume 215, number 4
PHYSICS LETTERS B
cross sections cut on the axigluon transverse m o m e n t u m for which the u-channel pole p r o b l e m does not even arise. Using these prescriptions, we find the predictions for the A production cross sections in ep collisions for x/J = 314 GeV and 1.4 TeV shown in figs. 2 and 3, respectively. (We use the quark distribution functions of Duke and Owens [22 ], set 1.) We have shown results which include the effects o f imposing m i n i m u m PT cuts on the transverse m o m e n t u m o f the axigluon, assuming that we can also use the quarkinitiated jet as part o f the signal, somewhat reducing the Q C D backgrounds. As anticipated, the cross sections for all masses in the 25-125 GeV range are quite large even after realistic cuts are i m p o s e d so that production rates should not be a problem. [Recall that at H E R A with a luminosity o f 1.0× 1031 c m - 2 s - i and 2 years o f effective running (say 2 × 107 s) one can expect 200 pb-~ o f integrated luminosity (or perhaps even up to 200-1 pb per year) so that a 1 pb cross section corresponds to 200 events.] At the higher energy, axigluons with masses up to ~ 300 GeV
29 December 1988
iO 4
I
I
'\ 10 2 _--
'°
i.Oo
I Ioo
I 200
300
MA(GeV )
10 3
Fig. 3. Cross sections (in pb) for axigluon production in ep collisions at x/s= 1.4 TeV. Curves are shown corresponding to minimum axigluon transverse momentum cuts of 5 GeV (solid curve ) and 15 GeV (dashed curve). can be p r o d u c e d but this range will be much more effectively p r o b e d at the T E V A T R O N . Drees [23] has recently argued that there is another significant contribution to weak boson production in ep collisions due to the so-called "resolved p h o t o n " mechanism• This process relies on the existence of a quark content in the photon for which there is some experimental input (as o p p o s e d to the photon's gluon content) and good theoretical understanding ~6. This m e c h a n i s m would also give contributions to A production
I0 a
o'(pb) I0
"\" \ , \\" \.
1.0
\. \. a(ep--,AX) =
• quarks M~
cU gs
P~(s/s)~g2~s /g
\• \. 50
I00 MA (GeV)
× [q~(x, M2A)OP(M~/xg, M~) 150
Fig. 2. Cross sections (in pb) for axigluon production in ep collisions at x/~=314 GeV. Curves are shown corresponding to minimum axigluon transverse momentum cuts of 5 GeV (solid curve), 10 GeV (dashed curve), and 15 GeV (dot-dashed curve).
+ElY(X, M~)qP(M2 /xg, M~,) ] ,
(4)
recent discussion of the hadron structure of the photon see ref. [24].
~6 F o r a
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where the sum is over all quark-antiquark pairs and qV are the quark distribution functions inside the photon (for which we use the parametrizations of Duke and Owens [ 20 ] ). We follow ref. [ 23 ] and use ln[ ( 1 --X)MA/Xm~] as the logarithmic factor in the photon distribution in the electron. (Other reasonable choices are known to give similar results.) This contribution to the total (uncut in PT) A production cross section does indeed contribute a significant ( ~ 50%) increase in the A production rate at HERA energies and we will discuss this more quantitatively below. A final possible production mechanism which may become important at very high energies would be "gluon-axigluon fusion". This process relies on the (as yet untested) gluon content of the photon and an "effective A content" of the parton. While formally of higher order in couplings, the situation here is similar to the weak boson (WW, ZZ) fusion production of Higgs bosons in hadronic collision where gauge boson fusion comes to dominate the production cross section. Proposed tests [25] of the gluon content of the photon at high energy ep machines will provide more detailed experimental information on which to base calculations for this process. For now, using the gluon content given in ref. [ 20 ] we find that this process gives a negligible contribution, at least at HERA energies. We now turn to the prospects of observing the produced axigluons which require a knowledge of their decays. The A decays in a flavor independent way into all kinematically allowed quark-antiquark pairs so if we ignore, for simplicity, any new exotic colored fermions (which are required in many chiral-color models to cancel anomalies) and the top quark, there will be five open decay channels (u, d, s, c, b) and an overall width F ( A ) = 5 o ~ s M A. Thus, detection of A decays will rely on the ability to reconstruct jets, especially jet pairs, in an ep collider environment. The question of jet resolution and reconstruction [26], the ability to accurately predict QCD backgrounds (especially to the decays of new heavy objects decaying with a two-jet signature ~7), and the relative merits a n d / o r validity of matrix element versus parton ,7 See especially ref. [ 27 ], where this question is raised explicitly but not answered. See also ref. [28 ]. K6rner, Mirkes and Schuler have recently calculated O (o~s) corrections to three-jet and two-jet rates and discussed their significance.
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shower approaches are topics of much discussion and a detailed investigation of A detection via its jet-jet decays is beyond the scope of this letter. We will argue, however, that it may well be easier to detect A decays by reconstruction of its bb decay modes. The branching ratio B R ( A ~ b B ) = 2 0 % (see above) is substantial while the production of heavy quark pairs (especially bb) is a well-studied phenomenon in ep collisions [30,3_1 ] and is thought to be calculable reliably but, of course, is highly suppressed relative to standard two-jet processes. The basic bb production process is via photon-gluon fusion and it is known that the WW approximation is also reliable for this process. We can then estimate the likelihood of seeing a bb signal from A decay over the background in the following way. The differential cross section for heavy quark pair production in WW approximation will be given by ~s I
da a ( M 2) d M 2 -s
f
---~Pv(x)G(M2/xs,M 2)
(5)
M2/s
where G(x, Q2) is the gluon distribution in the proton. (When integrated over all allowed M 2 (i.e. from 4M 2 to s) we reproduce the total bb cross section given in ref. [30].) In this expression, o'(M 2) is the ~/g--,QQ cross section for which we use the lowestorder formula ~9 a(s) = nc~a~e~{ ( 3 _ f14) ln[(1 + / ? ) / ( 1 - f l ) ] S
-2fl(2-f12)},
(6)
where fl= (1 -y)~/2, y=4M~/s, and e O is the quark charge. We can then integrate eq. (6) over a putative peak at axigluon mass M (i.e. over the range (M2-MF, M2+MF) for full width at half maxim u m ) to obtain an estimate of the continuum bb production under the A signal. This can then be compared to the uncut (in PT) total A production cross sections multiplied by 0.1 (0.2 for the bb branching ~8 We have suitably modified the result for d a / d M 2 for gg fusion production of heavy quark pairs in h a d r o n - h a d r o n collisions given in ref. [ 32 ] to the case of'/g fusion in ep collisions where the photon is described via the W W approximation. ~9 We do not include recently calculated Q C D corrections to heavy quark photoproduction. See ref. [33].
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ratio and 0.5 for F W H M . ) The corresponding signals (background) in pb for x / s = 314 GeV and various axigluon masses are given in table 1, where the range of values for the background indicates the effects of varying Mb from 4.5 to 5.0 GeV and using different distribution functions (Duke and Owens, sets 1 and 2 ) and the range for the signal shows the effect of including or neglecting the "resolved-photon" contrib u t i o n discussed above, Even taking into account a reasonable bb identification probability, it still appears that a signal for axigluons in much of the mass window we consider will be detectable above background with sufficiently high statistics. Other processes can also contribute to bb production [25 ] and b identification may be i m p o r t a n t for identification of other new exotic particles [ 34 ] as well, so careful studies of b production will likely be considered important at ep machines and so can also be used to test A production. One could imagine using tt decays, if kinematically allowed, as an A signature since the standard tt production is very small [35 ] but current collider limits on the top quark mass [36] (Mr> 56 GeV) and suggestions from B-13 mixing [ 37 ] make it unlikely that axigluons in the mass " w i n d o w " we consider will have this decay mode accessible. Another possible signal might be high Pr "f' production (as in ref. [12] ) where the standard model contrib u t i o n arises from y + g ~ ' t ' + g and has recently been calculated [ 38 ] for HERA and LHC energies. In conclusion, we have argued that axigluon production cross sections for A masses in the 25-125 GeV mass range are large at HERA energies and that the identification of A decays in the bb channel ( a n d perhaps in the two-jet invariant mass distributions as well) may well allow experimentalists to exclude all of this region of mass, a region which might otherwise be difficult to probe in any other accelerator environment.
Table 1 MA (GeV) 25 50 75
Signal (background) (pb) 215 -300 (290 -200) 20 - 29 (32 - 29) 3.8 - 5.9 (6.8 - 6.0)
100
1.0 -
125
0.27- 0.44 (0.56- 0.35)
1.5
(1.9
-
1.4)
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This work was supported in part by grants from the National Science F o u n d a t i o n u n d e r grant PHY8606279 (R.R.) and the D e p a r t m e n t of Energy under grant W-7405-Eng-82 (T.R.). References
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[30] G.A. Schuler, Nucl. Phys. B 299 (1988) 21; G. Ingelman and G.A. Schuler, DESY preprint DESY 88020; G. Ingelman, DESY preprint 88-098. [ 31 ] M. Glfick, R.M. Godbole and E. Reya, Z. Phys. C 38 ( 1988 ) 441; C 39 (1988) 590 (E). [32] L.M. Jones and H.W. Wyld, Phys. Rev. D 17 (1978) 759. [33] R.K. Ellis and P. Nason, Fermilab Pub-88/54-T; R.K. Ellis and Z. Kunszt, Nucl. Phys. B 303 (1988) 653.
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[34] T.G. Rizzo, Ames Lab preprint IS-J-3138 (1988). [35] U. Baur and J.J. Van Der Bij, Nucl. Phys. B 304 (1988) 451. [ 36 ] UA 1 Collab., C. Albajar et al., Z. Phys. C 37 ( 1988 ) 505. [37] See e.g.J. Ellis, J.S. Hagelin, S. Rudaz and D.-D. Wu, Nucl. Plays B 304 (1988) 205. [38] Z. Kunszt, Phys. Lett. B 207 (1988) 103.