If quarks are composite particles then excited states are expected. We
estimate the discovery mass reach as a function of integrated luminosity for
excited quarks decaying to dijets at the Tevatron, LHC, and a Very Large Hadron
Collider (VLHC). At the Tevatron the mass reach is 0.94 TeV for Run II (2
fb^-1) and 1.1 TeV for TeV33 (30 fb^-1). At the LHC the mass reach is 6.3 TeV
for 100 fb^-1. At a VLHC with a center of mass energy, sqrt(s), of 50 TeV (200
TeV) the mass reach is 25 TeV (78 TeV) for an integrated luminosity of 10^4
fb^-1. However, an excited quark with a mass of 25 TeV would be discovered at a
hadron collider with sqrt(s)=100 TeV and an integrated luminosity of 13 fb^-1,
illustrating a physics example where a factor of 2 in machine energy is worth a
factor of 1000 in luminosity.Comment: 5 pages, 3 Figures, LaTex, macros epsf.sty, snowtimes.sty, and
  snow2e.cls. To appear in the proceedings of DPF/DPB Summer Study on New
  Directions for High Energy Physics, Snowmass, Colorado, June 25-July 12,
  1996. Postscript file of full paper also available at
  http://www-cdf.fnal.gov/physics/conf96/cdf3874_snow_excited_quarks.p

Harris, Robert M.

English

arXiv

If quarks are composite particles then excited states are expected. We estimate the discovery mass reach as a function of integrated luminosity for excited quarks decaying to dijets at the Tevatron the mass reach is 0.94 TeV for Run 11 (2 fb{sup -1}) and 1. 1 TeV for TeV33 (30 fb{sup -1}). At the LHC the mass reach is 6.3 TeV for 100 fb{sup -1}. At a VLHC with a center of mass energy {radical}s, of 50 TeV (200 TeV) the mass reach is 25 TeV (78 TeV) for an integrated luminosity of 10{sup 4} fb{sup -1}. However, an excited quark with a mass of 25 TeV would be discovered at a hadron collider with {radical}s = 100 TeV and an integrated luminosity of 13 fb{sup -1}, illustrating a physics example where a factor of 2 in machine energy is worth a factor of 1000 in luminosity

Harris, R.M.

UNT Digital Library

Fermi National Accelerator Laboratory FERMILAB-Conf-96/285-E Discovery Mass Reach for Excited Quarks at Hadron Colliders Robert M. Harris Fermi National Accelerator Laboratory P.O. Box 500, Batavia, Illinois 60510 Presented at Snowmass 96: New Directions for High Energy Physics, Snowmass, Colorado, June 2!Xuly 12,1996. e- rated by Utiersili4s Fiem Assockh Inc. under Cot&act No. DE-AC02-76fXX000 tiththelJnitedStatesDepartnentdEnergj Disclaimer This report \cas prepared us un account of work sponsored by an agency of the United Stares Go\~ernment. ,Yeither the United States Go\,ernmenr nor atly agency thereoi nor an! of their employees. makes an) rt,arranrx, express or implied. or assumes atlx legal liabilin or responsibilir\ for rhe accuracy. completeness or usefulness of any inform&on. appararus. producr or process disclosed. or represenrs that its use Maould nof infringe privately obcwed rights. Reference herein to arty specific commercial product. process or service by trade name, trademark, manufacturer or orhemise, does not necessarily constirure or imp& its endorsemenr. recommendation orfa\,oring b! the United States GoL,ernment or any agenq thereof, The r,iervs and opinions of uuthors expressed herein do not necessaril! state or reflect those of rhe United States Government or any agetic! thereof Distribution Approved for public release: further dissemination unlimited. Fermilab-Conf-961285-E CDFiPUBiEXOTICiPUBLIC’3874 September 10, 1996 Discovery Mass Reach for Excited Quarks at Hadron Colliders Robert M. Harris Fermilab, Batavia, IL 60510 ABSTRACT If quarks are composite particles then excited states are ex- pected. We estimate the discovery mass reach as a function of integrated luminosity for excited quarks decaying to dijets at the Tevatron, LHC, and a Very Large Hadron Collider (VLHC). At the Tevatron the mass reach is 0.94 TeV for Run II (2 fb-‘) and 1.1 TeV for TeV33 (30 fh-‘). At the LHC the mass reach is 6.3 TeV for 100 fb- l. At a VLHC with a center of mass energy ,fi, of 50 TeV (200 TeV) the mass reach is 25 TeV (78 TeV) for an integrated luminosity of lo4 fb-‘. However, an excited quark with a mass of 25 TeV would be discovered at a hadron collider with fi = 100 TeV and an integrated luminosity of 13 fb -l, illustrating a physics example where a factor of 2 in machine en- ergy is worth a factor of 1000 in luminosity. I. EXCITED QUARKS We consider a model of composite quarks with excited states that have spin 112 and weak isospin 112. The effec- tive Lagrangian for chromomagnetic transitions between ex- cited quarks (q’) of mass M and common quarks (q) is con- strained by gauge invariance to be [ 11: pvW$,q~ + h.c. where G” are gluon fields, X, are SU(3) structure constants, and gd is the strong coupling. Here we have chose the composite- ness scale to be iz = M, by writing M in the denominator in Eq. 1, because the excited quark mass should be close to the en- ergy scale of quark compositeness. The constant fd depends on the unknown dynamics of the quark consituents, and is generally assumed to be equal to 1, thereby giving standard model cou- plings. Excited quarks decay to common quarks via the emis- sion of a gluon in approximately 83% of all decays. Excited quarks can also decay to common quarks by emitting a W, Z, or photon, through an effective Lagrangian similar to Eq. 1. We consider the process qg -+ q* -+ qg for discovering an excited quark at a hadron collider. The signal is two high en- ergy jets, resulting from hadronization of the final state quark and gluon, which form a peak in the dijet invarian mass distribu- tion. The subprocess differential cross section is a Breit-Wigner: s 9M4 (j _ M2)2 + r2M2 (2) where CY# is the strong coupling, S and i are subprocess Mandel- stam variables, and lY is the width of the excited quark. The sum of the partial widths in the gluon, W, Z, and photon channels, gives a half width at half maximum of I’/2 z 0.02M. In ~q. 2 we have already averaged over the angular distribu- tion in the center of mass frame, dN/d cos 8’ - 1 + cos e*, where 0’ is the angle between the initial state and final state quark in the subprocess center of mass frame. In hadron colli- sions this subprocess angular distribution results in an isotropic dijet angular distribtion dN/d cos 0’ - 1. This is because for every quark in hadron 1 that becomes an excited quark and emerges in the final state at a fixed cos 8*, with rate proportonal to 1 + cos 8’) there is a quark in hadron 2 which is headed in the opposite direction, and emerges at the same value of cos 8’ with rate proportional to 1 - cos 0’. The sum of the two angular distributions is isotropic. II. BACKGROUND AND CUTS Normal pax-ton-parton scattering via QCD produces a large background to the dijet decays of excited quarks. However, QCD is dominated by t-channel gluon exchange which gives a dijet angulardistributiondN/dcos8* - l/( 1 -cos e*)l, where 8’ is the angle between the incoming pat-ton and the jet in sub- process center of mass. In contrast excited quark production and decay results in an isotropic dijet angular distribution as dis- cussed above. Therefore to suppress QCD backgrounds we re- quire 1 cos 8’ 1 < 2/3 and we also require the pseudorapidity of each jet satisfy 171 < 2. We note that any dijet analysis will gen- erally make a 1 cos 8’ ] cut to have uniform trigger acceptance as a function of dijet mass, and an ]r]( cut is to stay within a defined region of the detector. We include all lowest order QCD sub- processes in our background calculation: qq -+ qq, qq + gg, 49 - 497 99 - gg and gg - qq. III. CROSS SECTION For both the excited quark signal and the lowest order QCD background, we convolute the subprocess differential cross sec- tion with CTEQ2L parton distributions [2] of the colliding hadrons, within the above range of cos 8’ and r]. This gives the differential cross section as a function of dijet mass, da/dm, for both the excited quark signal and the lowest order QCD back- ground. For the excited quark signal we consider only the first generation, r~* and d’, and we assume they are degenerate in mass. The half width of the excited quark resonance remains r/2 z 0.02M. This is significantly more narrow than the dijet mass resolution at the Tevatron, which is roughly Gaussian with RMS deviation 0 x 0.1 M. If we assume a Gaussian dijet res- olution of width Q % 0.1 M at all hadron colliders, then 90% of the dijet events from an excited quark will be inside a 16% mass window 0.84M < m < l.l6M, where m is the dijet invari- ant mass. We integrate the differential cross section, du/dm, for both the excited quark signal and the QCD background within IO !- F 2.0 TeV pp 1 m-- -1 E 10 F 1 ! 0 0.5 1 1.5 Excited Quark Mass (TeV) Excited Quark Mass (TeV) l( loLr 'y F 10 F '\\ 1,k \ '\ \ . \ . '0 ,!E \ \ '. 200 I” 0 ExcitedOQuorkl~ss CT:;“, Figure 1: Lowest order parton level cross sections within a 16% wide search window for QCD dijets (dashed curve) and excited quarks decaying to dijets (solid curve) are shown as a function of excited quark mass at a) the future energy of the Tevatron, b) the LHC. c) a VLHC with center of mass energy 50 TeV. and d) 200 TeV. All cross sections are for dijets with 171 < 2, / cos 0’ / < Z/3. 1 -1 10 , I 1 I I / ! I 1 1 / 1 0 0.5 Excited Quark iass (TLG) -4F (,,, /,1111 I,,, I,), In 1: 3 z IO687 I j , z 105; c 104L 1 0 3 k \ c) 3 = 1::: j 0 ,- ..,.,, g j()Zk.,.. 3% I” 0 2.5 5 7.5 10 Excited Quark Mass (TeV) lo46 103k 102b 10 h 1,k 10 -E- I ‘4 j 10’ fb-’ i ~....___.____.___.._._.._............... = 10’ fb-’ 1 ~‘~....___..._______..............~..... 102fb-’ 1 ~~~~~....._._,_..___._.___._..... ‘..... lo3 fb-’ 1 I I I I ! 0 Excite56)Quork’Ess (Tkz Figure 2: The predicted cross section for dijet decays of excited quarks (solid curve) is compared to the 50 discovery reach (dotted curves) at various luminosities for a) the future energy of the Tevatron, b) the LHC, c) a VLHC with center of mass energy 50 TeV, and d) 200 TeV. All cross sections are for dijets with jqi < 2. / cos 8’ ! < 2/3, and invariant mass within 16% of the excited quark peak assuming a 10% dijet mass resolution. 3 the 16% mass window to obtain an estimate of the signal and background cross section for a search. Figure 1 shows the re- sulting total signal and background cross section in the search window at the Tevatron, LHC and VLHC as a function of ex- cited quark mass. IV. DISCOVERY MASS REACH i I Excited Quark Mass Reach The QCD background rate is used to find the 5 d discovery cross section. This is conservatively defined as the cross sec- tion which is above the background by 5 cr, where c~ is the sta- tistical error on the measured cross section (not the background). For example, if the background were zero events the 50 discov- ery rate would be 25 events. In Fig. 2 we compare the excited quark cross section to the 5 0 discovery cross section at various luminosities for the future Tevatron, the LHC, and the VLHC. The excited quark discovery mass reach, defined as the mass at which an excited quark would be discovered with a 50 signal, is tabulated as a function of mass for the LHC and VLHC proton- proton colliders in Table I. We have also performed the calcu- lation for VLHC proton-antiproton colliders, where the QCD background is slightly higher but the excited quark signal is ex- actly the same, which yields a 3% smaller mass reach. Because of space limitations,Figs. 1 and 2 do not display curves for a 100 TeV VLHC, but the mass reach of a 100 TeV VLHC tabulated in Table I was determined from curves similar to those in Fig. 2. Integrated LHC I VLHC VLHC / VLHC Luminosity 14 , 50 100 1 200 W’) / (TeV) 1 (TeV) / (TeV) 1 (TeV) 1 - 1 10.5 / 17 1 26 10 100 103 lo4 - / 24.5 45 1 78 j numbers in Table I. We provide Eq. 3 and 4 for interpolation among the VLHC entries in Table I only. We do not recom- mend these equations be used for extrapolation outside the en- ergy range 50 < fi < 200 TeV and the luminosity range 1 < L < 104 fb-1. The mass reach at the future Tevatron is 0.94 TeV for col- lider run II (2 fb-‘) and 1.1 TeV for TeV33 (30 fb-‘). This can be compared to the published 95% CL limit of 570 GeV from CDF [3] and the the preliminary limits of 750 GeV from CDF and 720 GeV from DO [4]. The mass reach at the LHC is 6.3 TeV for 100 fb-‘, which could be obtained by running for one yea (- lo7 seconds) at the design luminosity of 1O34 cmma s-l. Since the design luminosity may not be quickly achieved, we note that with only 10 fb-’ at the beginning of the LHC the mass reach is still 5.3 TeV. Ultimately, the LHC may be able to integrate 1000 fh- ‘, which will provide a mass reach of 7.3 TeV. The mass reach at the VLHC varies widely depending on the en- ergy of the machine and it’s luminosity. A 50 TeV machine with only 1 fh-’ of integrated luminosity has a mass reach of 10.5 TeV, significantly better than LHC with any conceivable lumi- nosity. At the other extreme, a 200 TeV machine with lo4 fb-’ would have a mass reach of 78 TeV. V. ENERGY VS. LUMINOSITY To clarify the superior gains obtained by increasing the energy of a machine, as opposed to increasing the luminosity, we show in Fig. 3 the mass reach for the VLHC which is also tabulated in Table I. Note that the mass reach is proportional to the log- arithm of the luminosity, but is almost directly proportional to the energy of the machine. To clarify the energy vs. luminosity tradeoff consider the following hypothetical case. A. Discovery of New Scale at LHC Suppose the LHC sees a classic signal of new physics: an ex- The mass reach in table I appears to be a smooth function of the proton-proton center of mass energy, fi, and integrated lu- minosity, L. The following analytic function exactly reproduces the VLHC mass reach in Table I for the energy range 50 < fi < 200 TeV and the luminosity range 1 < L < lo4 fb-l: cess of high transverse energy jets which also have an angular distribution that is significantly more isotropic than predicted by QCD, an effect that cannot be due to pat-ton distributions within the proton. Suppose further that this measurement corresponds to a scale of new physics A - 15 TeV, which is roughly the largest contact interaction that the LHC could see in the jet chan- nel. We would have strong evidence of new physics, and the angular distribution might begin to separate between compos- iteness and other sources of new physics. But, we would proba- bly not know for certain which source of new physics the scale A x 15 TeV corresponded too, and we would need an indepen- dent experimental confirmation that quarks were composite. If the source of new physics were quark compositeness, we would expect to see excited quarks with mass close to the composite- ness scale. To be safe, we suppose the excited quark mass could be as high as 25 TeV, and we want to decide which machine to build to find the excited quark and confirm that the new physics is quark compositeness. A M=7+310ga jo +lc(l+log,,L) ( > (3) where k depends on the energy of the machine according to k=;+;($)-;($-1)’ (4) Although Eq. 3 and 4 reproduces the VLHC mass reach, at LHC these equations give a mass reach that is 40% lower than the Table I: The 5u discovery mass reach for excited quarks of a proton-proton collider as a function of integrated luminosity is tabulated for the LHC with a center of mass energy of 14 TeV and the VLHC with a center of mass energy of 50, 100 and 200 TeV. 4 B. Discovery of 25 TeV q* at VLHC In Fig. 3 the horizontal dashed line at 25 TeV intersects the VLHC excited quark mass reach at an integrated luminosity of about 1.3 x lo4 fb-’ for a 50 TeV machine, 13 fb-’ for a 100 TeV machine, and 0.9 lb-l for a 200 TeV machine. Clearly, to find a 25 TeV excited quark, one would build either the 100 TeV or possible even the 200 TeV machine and quickly accumulate the relatively low integrated luminosities of l-10 fb-‘, rather than build a 50 TeV machine and have to integrate between 3 and 4 orders of magnitude more luminosity. Note that the common accelerator wisdom that a factor of 2 in energy is worth a fac- tor of 10 in luminosity is only roughly right for comparing the 100 TeV and 200 TeV machines; when comparing the 50 TeV and 100 TeV machines discovery potential for a 25 TeV excited quark, a factor of 2 in energy is worth a factor of 1000 in lumi- nosity! the mass reach of a real search. To get a rough idea of the ef- fect of systematics, we examine the TeV2000 report [5], which included systematics in the mass reach for excited quarks. Our discovery mass reach for the future Tevatron is about 10% better than the 95% CL mass reach quoted in the TeV2000 report, be- cause ours is for fi = 2.0 TeV instead of 1.8 TeV and because ours does not include systematic uncertainties. If we increase the mass reach in the TeV2000 report by 10% to account for the increase in center of mass energy from 1.8 to 2.0 TeV, then the two results are roughly the same. From this we see that includ- ing systematic uncertainties would roughly change our .j, re- sult to merely a 95% CL result. However, the systematics in the TeV2000 report were likely overestimates, because they were based on previous dijet searches for excited quarks [3] in which there was no signal: if a signal is present the systematic uncer- tainties will likely be smaller. VII. SUMMARY AND CONCLUSIONS We have estimated the discovery mass reach for excited quarks at future hadron colliders. The mass reach at the Teva- tron is 0.94 TeV for Run II (2 fb-‘) and 1.1 TeV for TeV33 (30 fb-l). The mass reach at the LHC is 6.3 TeV for 100 fb-l. At a VLHC with a center of mass energy of 50 TeV (200 TeV) the mass reach is 25 TeV (78 TeV) for an integrated luminosity of lo4 fb- ‘. However, an excited quark with a mass of 25 TeV would be discovered at a hadron collider with fi = 100 TeV ! and an integrated luminosity of only 13 fb-‘: here a factor of 2 increase in energy from a 50 TeV to a 100 TeV machine is worth a factor of 1000 increase in luminosity at a fixed machine energy of 50 TeV. When the goal is to discover new physics at high en- ergy scales, even a modest increase in machine energy can be more desirable than a large increase in luminosity. VIII. REFERENCES [l] 3 U. Baur, I. Hinchliffe and D. Zeppenfeld, Int. J. of Mod. Phys. A2, 0 - 1285 (1987) and U. Baur, M. Spira and P. M. Zerwas, Phys. Rev. 1 10 lo2 3 1 D42.8 15 (1990). Integrated Eminosity (;ob-‘) [2] J. Botts er al., Phys. Lett. B304, 159 (1993). [3] F. Abe et al.. Phys. Rev. Lett. 74,3538 (1995). Figure 3: The discovery mass reach for dijet decays of excited [4] I. Bertram private communication. quarks is shown as a function of integrated luminosity for a VLHC of energy 50 TeV, 100 TeV and 200 TeV (solid curves), [5] D. Amidei and R. Brock, Report of the TeV2000 Srudy Group. Fermilab-Pub-96i082. The horizontal dashed line is for a hypothetical 25 TeV excited quark discussed in the text. VI. SYSTEMATICS In this analysis, we have not included any systematic uncer- tainties on the signal. and we have assumed that the shape and magmtude of the qcd background spectrum is reasonably ap- proximated by lowest order QCD. We also assumed that the dijet mass resolution will be roughly 10% at all hadron colliders, ig- noring a long tail to low mass caused by radiation. Adding sys- tematics on the signal and the background will likely decrease 5 

Discovery Mass Reach for Excited Quarks at Hadron Colliders

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