Barklow, Timothy L

Markiewicz, T W

Raubenheimer, T O

Thompson, K A

CERN Document Server

OPTIMIZATION OF THE LUMINOSITY SPECTRUM IN THE NLCK.A. Thompsony , T.L. Barklow, T.W. Markiewicz, T.O.Raubenheimer,Stanford Linear Accelerator Center, Stanford, CA 94309AbstractThe energy spectrum of electrons at the interaction point ofa linear collider is determined largely by the beamstrahlungspectrum. The beamstrahlung spectrum in turn is sensi-tive to the design parameters at the interaction point. Inthis paper we examine the optimization of the luminosityspectrum for discovery and detailed exploration of variousphysics processes of interest in the NLC, in particular, topand stop pair production, and a class of processes occuringvia W-W scattering.1 INTRODUCTIONThe energy spectrum of electrons at the interaction point ofa linear collider is determined largely by the beamstrahlungspectrum (emission of photons due to the interaction of anelectron with the collective field of the oncoming beam),with additional effects due to initial state radiation and en-ergy spread in the beam coming from upstream. The beam-strahlung spectrum depends on the design parameters at theinteraction point. Typically there is roughly half the lumi-nosity very near the nominal center of mass energy, withthe remaining luminosity distributed in a tail extending tosignificantly lower energies. While we realize various pro-cesses must be studied individually in greater detail than ispresented here, our goal is to examine optimization trade-offs for some important classes of physics processes in fu-ture linear colliders. In this paper, we focus mostly on pro-cesses with cross sections increasing with energy over therange of interest.2 NLC BASELINE DESIGNSWe give some luminosity-related parameters for the basicNLC designs near (but not necessarily exactly at!) 500,1000, 1500 GeV c.m. energy in Tables 1, 2, and 3[1]. Thevalues shown for the pinch enhancement HD, number ofbeamstrahlung photons per incoming particlen, and aver-age beamstrahlung energy loss Bare obtained from simu-lations using the beam-beam code Guineapig[2] and agreeto within a few percent with those obtained from analyticformulas in the literature[3].Note that for a given design, the c.m. energy decreaseswith higher bunch charge N because of beam loading,which due to costs is not completely compensated. Thereis also variation in other parameters among different designversions near a given energy. For purposes of understand-ing the physics tradeoffs, it is also useful to vary only oneWork supported by Department of Energy Contract DE-AC03-76SF00515.y Email: kthom@SLAC.Stanford.eduTable 1: IP parameters for three 1/2 TeV c.m. NLC de-signsA-500 B-500 C-500Ebeam[GeV] 267.5 257.5 250.N [1010] 0.75 0.95 1.1x=y[m-r] 4.0/0.06 4.5/0.1 5.0/0.14x=y[mm] 10/0.1 12/0.12 13/0.2z[m] 90. 120. 145.x=y[nm] 276/3.4 327/4.9 365/7.6avg0.14 0.11 0.09HD1.36 1.30 1.49n1.08 1.18 1.24B4.3% 3.9% 3.7%Bunches/train 95 95 95Rep. rate 120 120 120LD[1033 cm 2sec 1] 7.42 6.66 5.94Table 2: IP parameters for three1 TeV c.m. NLC designsA-1000 B-1000 C-1000Ebeam[GeV] 523. 504. 489.N [1010] 0.75 0.95 1.1x=y[m-r] 4.0/0.06 4.5/0.1 5.0/0.14x=y[mm] 10/0.125 12/0.15 13/0.2z[m] 90. 120. 145.x=y[nm] 198/2.7 234/3.9 261/5.4avg0.39 0.30 0.25HD1.50 1.44 1.50n(sim) 1.39 1.53 1.62B(sim) 9.5% 9.2% 8.7%Bunches/train 95 95 95Rep. rate 120 120 120LD[1033 cm 2sec 1] 14.33 12.95 11.67Table 3: IP parameters for two1.5 TeV c.m. NLC designsA-1500 B-1500Ebeam[GeV] 703 739N [1010] 1.4 0.95x=y[m-r] 4.5/0.14 4.5/0.1x=y[mm] 15/0.2 13/0.2z[m] 130. 150.x=y[nm] 222/4.5 201/3.7avg0.60 0.41HD1.61 1.50n2.2 1.7B17% 12%Bunches/train 95 95Rep. rate 60 90LD[1033 cm 2sec 1] 14.3 12.30-7803-5573-3/99/$10.00@1999 IEEE. 3489Proceedings of the 1999 Particle Accelerator Conference, New York, 1999Table 4: Fractional luminosities for NLC designs500 1000 1500-A 1500-Bbeamst. only:L99:5%(sim) 61% 46% 31% 40%L99%(sim) 67% 52% 35% 45%L98%(sim) 75% 59% 41% 52%L95%(sim) 86% 72% 54% 65%L90%(sim) 94% 83% 66% 77%L80%(sim) 99% 94% 82% 90%L50%(sim)  100%  100% 99%  100%beamst.+ISR:L99:5%(sim) 37% 27% 18% 23%L99%(sim) 44% 33% 22% 29%L98%(sim) 54% 41% 28% 36%L95%(sim) 69% 56% 41% 50%L90%(sim) 81% 70% 55% 64%L80%(sim) 91% 84% 73% 80%L50%(sim) 98% 97% 95% 97%parameter at a time (for instance, N , z, x, y, y, orx). In doing such parameter variations, one finds[4] thatthe best “knobs” for increasing luminosity at the high en-ergy end of the spectrum are yand N . It is difficult todecrease yvery much, but one may consider increasingN if one is willing either to let the energy drop or compen-sate for the beam-loading.We show the luminosity spectra for the nominal designs,with beamstrahlung only and with both beamstrahlung andinitial state radiation (ISR) in Table 4. The fractional lu-minosities are shown, e.g., L99%denotes the percentage ofthe luminosity with c.m. energy greater than or equal to99% of the nominal c.m. energy. (These numbers are notsignificantly different for the A, B, and C variations of thedesigns at 500 and 1000 GeV.)Figure 1: Cross sections for e Le+R!~tR~tR(dot-dashedcurve). e Re+L!~tR~tR(dotted curve). e Le+R!~tL~tL(solidcurve), e Re+L!~tL~tL(dashed curve).Table 5: Number of top and stop pair production events in a107 second running year, for nominal designs near 1/2 TeVc.m.A-500 B-500 C-500e Le+R! tt 785000 674000 581000e Re+L! tt 357000 305000 262000e Le+R!~tR~tR22000 17500 14200e Re+L!~tR~tR92000 74000 60200e Le+R!~tL~tL178000 143000 116500e Re+L!~tL~tL4900 3900 3200Table 6: Number of top and stop pair production eventsin a 107 second running year, for modified B-500 design(varying N and keeping energy fixed).N [1010] 1.1 1.3 1.5e Le+R! tt 927000 1347000 1856000e Re+L! tt 420000 609000 837700e Le+R!~tR~tR23900 34000 46000e Re+L!~tR~tR101000 144000 195000e Le+R!~tL~tL195000 279000 377000e Re+L!~tL~tL5300 7600 102003 SUSY SCALAR PRODUCTIONWe compare the rates of top and stop production in a 500-GeV collider, assuming m~t= mt. The total top and stoppair production cross-sections are plotted in Figures 2 and 1respectively.The production rates (# events in a running year of 107sec) are shown in Table 5 for the three nominal designsnear 1/2 TeV c.m. energy. The rates with bunch charge Npushed up from the nominal B-500 design value are shownin Table 6. Here we assume it is reasonable to compensatethe extra beam loading to keep the energy fixed.Figure 2: Cross sections for e Le+R! tt (solid curve) ande Re+L! tt (dashed curve).3490Proceedings of the 1999 Particle Accelerator Conference, New York, 1999Table 7: e+e  ! tt; MH= 100 GeV; No polarizationNo. of % change nevents B-1000A-1000 2800 +26% 1.4B-1000 2220 0% 1.5C-1000 1780 -20% 1.6B-1000, y# 0.08m-r 2520 +13% 1.5B-1000, y# 0.06m-r 2960 +33% 1.5B-1000, y# 0.04m-r 3780 +70% 1.5B-1000, N " 1.11010 2990 +35% 1.8B-1000, N " 1.31010 4200 +89% 2.0B-1000, N " 1.51010 5620 +153% 2.3B-1000, N " 1.11010,E#978 2670 +20% 1.8B-1000, N " 1.31010,E#935 3110 +40% 2.0B-1000, N " 1.51010,E#891 3410 +54% 2.3B-1000, y" 0.30 mm 1910 -14% 1.5Figure 3: Cross sections for e+e  ! eett for MH=100 GeV (solid curve), MH= 1000 GeV (dashed curve),MH=1 (dotted curve).4 WW-SCATTERING PROCESSESThe class of processes e+e  ! ``X occurring via WWscattering, where one or both `’s is a neutrino and Xcould be for example tt, W ’s and/or Z’s, have cross sec-tions which are rising with energy through the TeV en-ergy scale . Taking as a representative example the processe+e  ! eett, (see Figure 3) we show the number ofevents in 107 seconds of running for designs near 1 TeVin Table 7. In addition to the nominal A, B, and C de-signs, we show the increase in luminosity attainable withydecreased from its nominal value of 0:1m-r, or withN increased from its nominal value of 0:95  1010, withand without compensation of the extra beam-loading. Thebiggest gain is to be had by increasing N and keeping theenergy fixed; note also that further study is needed to seehow high ncan be allowd to go. We have also noted[4]that substantially increasingy(which relaxes machine tol-erances) does not reduce luminosity very much; for our ex-ample we see only a 14% reduction in the number of eventsTable 8: e+e  ! tt; MH= 100 GeV; No polarizationNo. of % change nevents B-1500A-1500 8610 -9% 2.2B-1500 9420 0% 1.7B-1500, N " 1.11010 12800 +36% 2.0B-1500, N " 1.31010 18000 +90% 2.3B-1500, N " 1.51010 23900 +154% 2.6B-1500, y" 0.30 mm 8700 -8% 1.7when yis doubled from its nominal value. Similar resultsfor designs near 1.5 TeV are shown in Table 8.5 DISCUSSION AND CONCLUSIONSWe have not discussed the very important issue of detectorbackgrounds in this paper – our general philosophy is thatwhen total rate for the various processes considered here isoptimized, one will indeed end up with a larger number ofuseful events even after appropriate cuts are applied to re-duce backgrounds. However, we mention some issues thatmust be kept in mind when designing and optimizing theinteraction region and detector. For example, the process ! WW (where the ’s are bremsstrahlung photons) isa significant background to e+e ! WW , since the ethat radiate the photons are typically close to the beam axisand may escape tagging. For these electroweak symmetrybreaking studies, electron tagging capability down to about150 mrad is needed[5]. Other processes, for instance someSUSY parameter determinations[6] as well as studies of theperturbative QCD pomeron (BFKL dynamics) in  !hadrons[7, 8] have even more stringent angular coveragerequirements, down to about 40 mrad.We thank Lance Dixon and Michael Peskin for usefuldiscussions and comments.6 REFERENCES[1] See http://www-project.slac.stanford.edu/lc/nlc-tech.htmlunder Accelerator Physics parameters.[2] D.Schulte, Ph.D. thesis, 1996.[3] Yokoya,K. and Chen,P., in M.Dienes,et.al. (ed.), Frontiersof Particle Beams: Intensity Limitations (Springer-Verlag,1988).[4] K.Thompson and T.Raubenheimer, NLC collider note LCC-0014 (1999).[5] V.Barger, K.Cheung, T.Han, R.Phillips, Phys.Rev.D., 52,3815 (1995).[6] N.Danielson and E.Goodman, COLO-HEP-422, unpub-lished.[7] S.Brodsky, F.Hautmann, and D.Soper, 5th InternationalWorkshop on Deep Inelastic Scattering and QCD, Chicago,14-18 April, 1997, hep-ph/9707444.[8] J.Bartels, A.DeRoeck, and H.Lotter, hep/9710500.3491Proceedings of the 1999 Particle Accelerator Conference, New York, 1999

Optimization of the luminosity spectrum in the NLC

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