Discovery Mass Reach for Excited Quarks at Hadron Colliders

Transcription

1 Dicovery Ma Reach for Excited Quark at Hadron Collider Robert M. Harri Fermilab, Batavia, IL ABSTRACT If quark are comoite article then excited tate are exected. We etimate the dicovery ma reach a a function of integrated luminoity for excited quark decaying to dijet at the Tevatron, LHC, and a Very Large Hadron Collider (VLHC). At the Tevatron the ma reach i 0:94 TeVforRunII(2fb 1 )and 1:1 TeV for TeV33 (30 fb 1 ). At the LHC the ma reach i 6:3 TeV for 100 fb 1. At a VLHC with a center of ma energy,, of TeV (200 TeV) the ma reach i 25 TeV (78 TeV) for an integrated luminoity of 10 4 fb 1. However, an excited quark with a ma of 25 TeV would be dicovered at a hadron collider with = 100 TeV and an integrated luminoity of 13 fb 1, illutratinga hyic examle where a factor of 2 in machine energy i worth a factor of 1000 in luminoity. I. EXCITED QUARKS We conider a model of comoite quark with excited tate that have in 1/2 and weak ioin 1/2. The effective Lagrangian for chromomagnetic tranition between excited quark (q )ofma M and common quark (q) i contrained by gauge invariance to be [1]: L = g f q R 4M a G a q L + h:c: (1) where G a are gluon field, a are SU(3) tructure contant, and g i the trong couling. Here we have choe the comoitene cale to be = M, by writing M in the denominator in Eq. 1, becaue the excited quark ma houldbe cloe to the energy cale of quark comoitene. The contant f deend on the unknown dynamic of the quark conituent, and i generally aumed to be equal to 1, thereby giving tandard model couling. Excited quark decay to common quark via the emiion of a gluon in aroximately 83% of all decay. Excited quark can alo decay to common quark by emitting a W, Z, or hoton, through an effective Lagrangian imilar to Eq. 1. We conider the roce qg! q! qg for dicovering an excited quark at a hadron collider. The ignal i two high energy jet, reulting from hadronization of the final tate quark and gluon, which form a eak in the dijet invarian ma ditribution. The ubroce differential cro ection i a Breit-Wigner: d^ d^t = 22 9M 4 ^ (^ M 2 ) M 2 (2) where i the trong couling, ^ and ^t are ubroce Mandeltam variable, and i thewidthoftheexcited quark. Theum of the artial width in the gluon, W, Z, and hoton channel, give a half width at half maximum of =2 0:02M. In Eq. 2 we have already averaged over the angular ditribution in the center of ma frame, dn=d co 1 + co, where i the angle between the initial tate and final tate quark in the ubroce center of ma frame. In hadron colliion thi ubroce angular ditribution reult in an iotroic dijet angular ditribtion dn=d co 1. Thi i becaue for every quark in hadron 1 that become an excited quark and emerge in the final tate at a fixed co, with rate roortonal to 1 + co, there i a quark in hadron 2 which i headed in the ooite direction, and emerge at the ame value of co with rate roortional to 1 co. The um of the two angular ditribution i iotroic. II. BACKGROUND AND CUTS Normal arton-arton cattering via QCD roduce a large background to the dijet decay of excited quark. However, QCD i dominated by t-channel gluon exchange which give a dijet angular ditribution dn=d co 1=(1 co ) 2,where i the angle between the incoming arton and the jet in ubroce center of ma. In contrat excited quark roduction and decay reult in an iotroic dijet angular ditributiona dicued above. Therefore to ure QCD background we require j co j < 2=3 and we alo require the eudoraidity of each jet atify jj < 2. We notethat any dijet analyiwillgenerally make a j co j cut to have uniform trigger accetance a a function of dijet ma, and an jj cut i to tay within a defined region of the detector. We include all lowet order QCD ubrocee in our background calculation: qq! qq, q q! gg, qg! qg, gg! gg and gg! qq. III. CROSS SECTION For both the excited quark ignal and the lowet order QCD background, we convolute the ubroce differential cro ection with CTEQ2L arton ditribution [2] of the colliding hadron, within the above range of co and. Thi give the differential cro ection a a function of dijet ma, d=dm,for both the excited quark ignal and the lowet order QCD background. For the excited quark ignal we conider only the firt generation, u and d, and we aume they are degenerate in ma. The half width of the excited quark reonance remain =2 0:02M. Thi i ignificantly more narrow than the dijet ma reolution at the Tevatron, which i roughly Gauian with RMS deviation 0:1M. If we aume a Gauian dijet reolution of width 0:1M at all hadron collider, then 90% of the dijet event from an excited quark will be inide a 16% ma window 0:84M < m < 1:16M, wherem i the dijet invariant ma. We integrate the differential cro ection, d=dm, for both the excited quark ignal and the QCD background within 1010

2 Figure 1: Lowet order arton level cro ection within a 16% wide earch window for QCD dijet (dahed curve) and excited quark decaying to dijet (olid curve) are hown a a function of excited quark ma at a) the future energy of the Tevatron, b) the LHC, c) a VLHC with center of ma energy TeV, and d) 200 TeV. All cro ection are for dijet with jj < 2, j co j < 2=

3 Figure 2: The redicted cro ection for dijet decay of excited quark (olid curve) i comared to the 5 dicovery reach (dotted curve) at variou luminoitie for a) the future energy of the Tevatron, b) the LHC, c) a VLHC with center of ma energy TeV, and d) 200 TeV. All cro ection are for dijet with jj < 2, j co j < 2=3, and invariant ma within 16% of the excited quark eak auming a 10% dijet ma reolution. 1012

4 the 16% ma window to obtain an etimate of the ignal and background cro ection for a earch. Figure 1 how the reulting total ignal and background cro ection in the earch window at the Tevatron, LHC and VLHC a a function of excited quark ma. IV. DISCOVERY MASS REACH The QCD background rate i ued to find the 5 dicovery cro ection. Thi i conervatively defined a the cro ection which i above the background by 5, where i the tatitical error on the meaured cro ection (not the background). For examle, if the background were zero event the 5 dicovery rate would be 25 event. In Fig. 2 we comare the excited quark cro ection to the 5 dicovery cro ection at variou luminoitie for the future Tevatron, the LHC, and the VLHC. The excited quark dicovery ma reach, defined a the ma at which an excited quark would be dicovered with a 5 ignal, i tabulated a a function of ma for the LHC and VLHC rotonroton collider in Table I. We have alo erformed the calculation for VLHC roton-antiroton collider, where the QCD background i lightly higher but the excited quark ignal i exactly the ame, which yield a 3% maller ma reach. Becaue of ace limitation, Fig. 1 and 2 do not dilay curve for a 100 TeV VLHC, but the ma reach of a 100 TeV VLHC tabulated in Table I wa determined from curve imilar to thoe in Fig. 2. The ma reach at the future Tevatron i 0:94 TeV for colliderrunii(2fb 1 )and1:1 TeV for TeV33 (30 fb 1 ). Thi can be comared to the ublihed 95% CL limit of 570 GeV from CDF [3] and the the reliminary limit of 7 GeV from CDF and 720 GeV from D0 [4]. The ma reach at the LHC i 6.3 TeV for 100 fb 1, which could be obtained by running for one year ( 10 7 econd) at the deign luminoity of cm 2 1. Since the deign luminoity may not be quickly achieved, we note that with only 10 fb 1 at the beginning of the LHC the ma reach i till5.3 TeV. Ultimately, thelhc may beable to integrate 1000 fb 1, which will rovide a ma reach of 7.3 TeV. The ma reach at the VLHC varie widely deending on the energy of the machine and it luminoity. A TeV machine with only 1 fb 1 of integrated luminoity ha a ma reach of 10:5 TeV, ignificantly better than LHC with any conceivable luminoity. At the other extreme, a 200 TeV machine with 10 4 fb 1 would have a ma reach of 78 TeV. The ma reach in table I aear to be a mooth function of the roton-roton center of ma energy,, and integrated luminoity, L. The following analytic function exactly reroduce the VLHC ma reach in Table I for the energy range < < 200 TeV and the luminoity range 1 <L<10 4 fb 1 : M =7+3log 2 + k(1 + log 10 L) (3) where k deend on the energy of the machine according to k = (4) Although Eq. 3 and 4 reroduce the VLHC ma reach, at LHC thee equation give a ma reach that i 40% lower than the Table I: The 5 dicovery ma reach for excited quark of a roton-roton collider a a function of integrated luminoity i tabulated for the LHC with a center of ma energy of 14 TeV and the VLHC with a center of ma energy of, 100 and 200 TeV. Excited Quark Ma Reach Integrated LHC VLHC VLHC VLHC Luminoity (fb 1 ) (TeV) (TeV) (TeV) (TeV) number in Table I. We rovide Eq. 3 and 4 for interolation among the VLHC entrie in Table I only. We do not recommend thee equation be ued for extraolation outide the energy range < < 200 TeV and the luminoity range 1 <L<10 4 fb 1. V. ENERGY VS. LUMINOSITY To clarify the uerior gain obtained by increaing the energy of a machine, a ooed to increaing the luminoity, we how in Fig. 3 the ma reach for the VLHC which i alo tabulated in Table I. Note that the ma reach i roortional to the logarithm of the luminoity, but i almot directly roortional to the energy of the machine. To clarify the energy v. luminoity tradeoff conider the following hyothetical cae. A. Dicovery of New Scale at LHC Suoe the LHC ee a claic ignal of new hyic: an exce of high tranvere energy jet which alo have an angular ditributionthat i ignificantly more iotroic than redicted by QCD, an effect that cannot be due to arton ditribution within the roton. Suoe further that thi meaurement correond to a cale of new hyic 15 TeV, which i roughly the larget contact interaction that the LHC could ee in the jet channel. We would have trong evidence of new hyic, and the angular ditribution might begin to earate between comoitene and other ource of new hyic. But, we would robably not know for certain which ource of new hyic the cale 15 TeV correonded too, and we would need an indeendent exerimental confirmation that quark were comoite. If the ource of new hyic were quark comoitene, we would exect to ee excited quark with ma cloe to the comoitene cale. To be afe, we uoe the excited quark ma could be a high a 25 TeV, and we want to decide which machine to build to find the excited quark and confirm that the new hyic i quark comoitene. 1013

5 B. Dicovery of 25 TeV q at VLHC In Fig. 3 the horizontal dahed line at 25 TeV interect the VLHC excited quark ma reach at an integrated luminoity of about 1: fb 1 for a TeV machine, 13 fb 1 for a 100 TeV machine, and 0:9 fb 1 for a 200 TeV machine. Clearly, to find a 25 TeV excited quark, one would build either the 100 TeV or oible even the 200 TeV machine and quickly accumulate the relatively low integrated luminoitie of 1-10 fb 1,rather than build a TeV machine and have to integrate between 3 and 4 order of magnitude more luminoity. Note that the common accelerator widom that a factor of 2 in energy i worth a factor of 10 in luminoity i only roughly right for comaring the 100 TeV and 200 TeV machine; when comaring the TeV and 100 TeV machine dicovery otential for a 25 TeV excited quark, a factor of 2 in energy i worth a factor of 1000 in luminoity! Figure 3: The dicovery ma reach for dijet decay of excited quark i hown a a function of integrated luminoity for a VLHC of energy TeV, 100 TeV and 200 TeV (olid curve). The horizontal dahed line i for a hyothetical 25 TeV excited quark dicued in the text. the ma reach of a real earch. To get a rough idea of the effect of ytematic, we examine the TeV2000 reort [5], which included ytematic in the ma reach for excited quark. Our dicovery ma reach for the future Tevatron i about 10% better than the 95% CL ma reach quoted in the TeV2000 reort, becaue our i for =2:0TeV intead of 1.8 TeV and becaue our doe not include ytematic uncertaintie. If we increae the ma reach in the TeV2000 reort by 10% to account forthe increae in center of ma energy from 1:8 to 2:0 TeV, then the two reult are roughly the ame. From thi we ee that including ytematic uncertaintie would roughly change our 5 reult to merely a 95% CL reult. However, the ytematic in the TeV2000 reort were likely overetimate, becaue they were baed on reviou dijet earche for excited quark [3] in which there wa no ignal: if a ignal i reent the ytematic uncertaintie will likely be maller. VII. SUMMARY AND CONCLUSIONS We have etimated the dicovery ma reach for excited quark at future hadron collider. The ma reach at the Tevatron i 0:94 TeV for Run II (2 fb 1 )and1:1 TeV for TeV33 (30 fb 1 ). The ma reach at the LHC i 6:3 TeV for 100 fb 1.At a VLHC with a center of ma energy of TeV (200 TeV) the ma reach i 25 TeV (78 TeV) for an integrated luminoity of 10 4 fb 1. However, an excited quark with a ma of 25 TeV would be dicovered at a hadron collider with = 100 TeV and an integrated luminoity of only 13 fb 1 : here a factor of 2 increae in energy from a TeV to a 100 TeV machine i worth a factor of 1000 increae in luminoity at a fixed machine energy of TeV. When the goal i to dicover new hyic at high energy cale, even a modet increae in machine energy can be more deirable than a large increae in luminoity. VIII. REFERENCES [1] U. Baur, I. Hinchliffe and D. Zeenfeld, Int. J. of Mod. Phy. A2, 1285 (1987) and U. Baur, M. Sira and P. M. Zerwa, Phy. Rev. D42, 815 (1990). [2] J. Bott et al., Phy. Lett. B304, 159 (1993). [3] F. Abe et al.,phy.rev.lett.74, 3538 (1995). [4] I. Bertram rivate communication. [5] D. Amidei and R. Brock, Reort of the TeV2000 Study Grou, Fermilab-Pub-96/082. VI. SYSTEMATICS In thi analyi, we have not included any ytematic uncertaintie on the ignal, and we have aumed that the hae and magnitude of the qcd background ectrum i reaonably aroximated by lowet order QCD. We alo aumed that the dijet ma reolution will be roughly 10% at all hadron collider, ignoring a long tail to low ma caued by radiation. Adding ytematic on the ignal and the background will likely decreae 1014