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Determining Susy/Higgs Parameters for a Physics Rich Scenario

P. Grannis LCWS Jeju Korea August 2002. Determining Susy/Higgs Parameters for a Physics Rich Scenario. We study the precision obtainable for the SM2 (SPS1) Susy scenario and a light Higgs, based on the Snowmass SM2 Run Scenario.

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Determining Susy/Higgs Parameters for a Physics Rich Scenario

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  1. P. Grannis LCWS Jeju Korea August 2002 Determining Susy/Higgs Parameters for a Physics Rich Scenario We study the precision obtainable for the SM2 (SPS1) Susy scenario and a light Higgs, based on the Snowmass SM2 Run Scenario. update of M. Battaglia et al. hep-ph/0201177

  2. Assumptions SM Higgs mass of 120 GeV (or Susy Higgs h0 in nearly decoupling limit) Use mSUGRA benchmark: Snowmass Group E2, SM2 (≈ Allanach et al., hep-ph/0202233: 'SPS1a'), (≈ Battaglia et al. hep-ph/0106204: ‘B’ ): m0 = 100 GeV m1/2 = 250 GeV tan b = 10 A0 = 0 sgn(m) = + This has relatively low mass sparticles, but the large tanb means that there are dominant t decays that make life difficult. } We assume 1000 fb-1 = 1 ab-1 luminosity acquisition (equivalent at 500 GeV ) Year 1 2 3 4 5 6 7 (Lequivdt) 10 40 100 150 200 250 250 (fb-1) 2/22

  3. SM2 sparticle masses and BR’s particle M(GeV)Final state (BR(%)) eR(mR)143c10 e (m) [100] eL(mL) 202c10 e(m) [45] c1± ne(nm) [34] c20e(m) [20] t1135c10t [100] t2 206c10 t [49] c1± nt [32] c20 t [19] ne (nm)186c10 ne(nm) [85] c1± e (m) [11] c20 ne (nm) [4] nt185c10 nt[86] c1± t [10] c20 nt[4] c1096 stable c20175t1 t [83] eRe [8] mRm [8] c30343c1±W[59] c20 Z [21] c10 Z [12] c20h [1] c10 h [2] c40364c1±W[52] nn [17] t2t [3] c10 Z [2] c20Z [2] … c1±175t1nt [97] c10 qq [2] c10ln [1] c2±364c20W [29] c1±Z [24] l nl[18] c1±h [15] nll [8] c10W [6] ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ± ~ ~ ~ ~ ~ ~ ± ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ 3/22

  4. Run Plan for SM2 Susy sparticle masses Substantial initial 500 GeV run (for “end point” mass determinations). Scans at some thresholds to improve masses. Special e-e- run and a run above 500 GeV. Beams Energy Polz’tn Ldt (Ldt)equiv comments e+e- 500 L/R 335 335sit at top energy for end point measurements e+e- MZ L/R 10 45 calibrate with Z’se+e-270 L/R 100 185 scan thresholds c10c20 (L pol.); t1t1(R pol.) e+e-285 R 50 85scan mR+mR-threshold e+e- 350 L/R 40 60scan tt thresh; scan eReL thresh (L & R pol.) scan c1+c1-thresh. (L pol.) e+e- 410 L 60 75scan t2t2 thrsh (L pol); scan mLmLthrsh (L pol) e+e-580 L/R 90 120sit above c1+c2-thresh. for c2±end pt. mass e-e-285 RR 10 95scan with e-e-for eR mass ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ S(Ldt)equiv = 1000 fb-1 4/22

  5. Initial (“end point”) mass determinations The traditional end point method: ~ ~ For: A → B + C E± = 1/2 (1±b ) (1 - mA2/mB2) ; b= (s/4mA2 -1) dN dEC (A & B are sparticles; C is observed SM particle). Measuring 2 end points gives both A and B masses. Statistics, backgrounds, resolutions smear the edges. ½ E- E+ • Making an box distribution mass measurement requires: • A given final state (& e- polarization) should be fed by only 1 dominant reaction • Two body decay with C a stable observable SM particle. • Neither of these conditions are generally true for benchmark SM2 with large BRs into t’s and nt However, it is not necessary to have a ‘box’ distribution for determining mass – any known distribution will do. But if there are not sharp edges, the precision is lower.(Recall that the top quark mass was measured to within 4% in semileptonic decays with a broad mass distribution (using templates) with only about 40 events and S/B ~ 1/2. 5/22

  6. ~ ~ ~ ~ t1+ t1- t1+ t1- The reaction overlap problem Among all-leptonic (& missing energy) decays of sparticle pairs, tt is the dominant final state. It is fed by 9 different sparticle pair reactions ! (and moreover the taus are not stable, so the “end points” of the observed final state (1 prong p±, r± ) are washed out. c1± c1± c10 c20 c10 c20 c1± c1± e+e-(left)→t+t- 152K evnts e+e-(right)→t+t- 52K evnts 6/22

  7. ~ ~ eL eL A new look at ‘end points’ in SM2 Examine all final states involving 2, 4 or 6 leptons plus missing energy (with no hadrons in final state). These should be low background from SM sources, and relatively free of cross-talk due to misidentification of leptons Do the spreadsheet for the contributing reactions to each channel more completely than before. Keep the sub-reactions distinct e.g. → c10 e has different end points from → c20 e and must be treated separately. Assume no SM backgrounds Begin to look at mass determinations for cases without ‘box’ distributions. Coupled channel analyses – fitting several distributions with several unknown masses will be needed There are many cross-checks – get a mass from a dominant channel, but can check it in subdominant channels. *channel = specific final state (e.g. eett); * reaction = specific 2 body process (e.g. e+e- → c10 c20 ) 7/22

  8. ~ ~ ~ ~ ~ mR+ mR- mR mR mR ~ ~ ~ ~ mL+ mL- mL mL So, how to get initial sparticle masses ? – start with the easier cases smuonRe+e-(right pol)→ →m+m- missing energy Both → c10m , so use eithermas observable. Determine both andc10masses from end points. Susy background is 5% In 335 fb-1, find dM( ) = 0.077 GeV ; dM(c10) = 0.11 GeV smuL smuL chi10 chi20 smuR smuR e+eR- → m+m- E 30.7K evnts smuonL e+e-(left pol)→ → (c10 m+) (nm c1-) → (c10 m+)(nmntt- c10)→ m+t- missing energy (+ cc) → c10m(45%) , withmas observable. Susy bknd is 5% In 335 fb-1, find dM( ) = 0.70 GeV (dM(c10) = 1.9 GeV ) smuL smuL e+eL- → m±t± E 3.9K evnts Mass precisions scaled from Colorado group Snowmass’01 analyses. 8/22

  9. ~ ~ eL+ eL+ ~ ~ ~ eR eR eR ~ ~ ~ eL eL eL ~ ~ eL- eL- ~ ~ eR- eR- selectrons L & R 4 distinct coupled reactions – analyze them together e+e-(left pol) → / / / →e+e- missing energy Both and → c10 e . Colorado group has analyzed the coupled channels using double differences between e+ and e-for L and R polarization. Determine , and c10 masses from end points. Background is 5% (left Pol), 0% (right Pol) In 335 fb-1, find dM( ) = 0.19 GeV ; dM( ) = 0.27 GeV dM(c10) = 0.13 GeV ~ ~ eR+ eR+ selL+ selL- chi10 chi20 chi10 chi20 selR+ selL- selL+ selL- selL+ selR- selR+ selL- selR+ selR- selR+ selR- e+eR- → e+e- E 210K evnts e+eL-→ e+e- E 62.7K evnts selL+ selR- 9/22

  10. neutralino1 = LSP Several reactions have dominant decays to c10 ; from combination of just the ee and mm final states (dominated by selectron pair and smuon pair), we estimate dM(c10) = 0.08 GeV Adding the channels et, mt, eett, eeee, all of which have a dominant reaction with a primary decay to c10 I guess that the precision would bedM(c10) ≈ 0.06 GeV 10/22

  11. ~ ~ ~ ~ t1+ t1- t1- t1 ~ ~ t1+ t1- The harder t channels e+e-(left)→t+t- 152K evnts c10 c20 c1± c1± e+e-(left pol)→ c1+ c1- → ( nt) ( nt) → (t+ nt c10) (t- nt c10) → t+t- missing energy[64%] > These t’s tend to be back to back and e+e-(left pol)→ c10 c20→ c10( t+) → c10 (t- c10 t+) → t+t- missing energy[19%] > These t’s tend to be collinear e+e-(left pol)→stau1 stau1 → (t+ c10) (t- c10) → t+t- missing energy [8%] > t’s back to back Can assume c10, e, m masses are well measured, but c1±, c20, masses are all to be determined in this e+ eL-→ tt channel, as well as with e+eR- → tt, e+eL- → mmtt, e+eL- → mttt, e+eL- → tttt e.g. m in mttt channel (left pol. e-) is 92% from mL →m c20 (1400 evnts) giving m(c20) ~ ~ ~ 11/22

  12. tt channel comments Opening angle distribution of the 1 prongs from t can partially distinguish between the c1+ c1- and c10 c20 reactions. Making a cut (Qopen < p/2) increases the fraction of c10 c20 by a factor of 2 while retaining 73% of c10 c20 c1+ c1- c10 c20 Qopen Qopen One can fit the observed 1-prong energy distribution to a template to get a particular mass. All reactions feeding tt are included. 335 fb-1 , with BR’s accounted for. c2 all reactions in tt final state Allowing just M(stau1) to vary, get M=134.88 ± 0.22 GeV. (M=134.89 input) M(stau1) 1 prong energy 12/22

  13. ~ t1 tt channel comments Can do better than use 1-prong energy – e.g. larger of the two 1-prong energies Or with the good calorimeter, see the p0 and can use the r± (p0 p± ) energy for the dominant case of t → r nt These more sharply peaked distributions offer better mass determination. NEEDS a proper study, but I am guessing that the c1± , c20 and masses can be found to ~ 1 GeV, good enough to fix the energy for scans. 13/22

  14. ~ t2 stau2 does not dominate any channel besides the 6t final state – for which there are only 262 evnts (L pol) or 93 evnts (R pol) (before t BRs). 6% of tt E (L pol) 152K events total 6% of tt E (R pol) 52K events 2% of eett E (L pol) 25K events 3% of mmtt E (L pol) 8.6K events 6% of mmtt E (R pol) 1.5K events 8% of ttttE (L pol) 35K events 20% of tttt E (R pol) 4.8K events Thus we would use the selectronL/R and smuonL/R masses and the measured stau1 mass to estimate the stau2 mass (model dependent) for a subsequent energy scan. Nevertheless, since stau2 contributes to many reactions, there is a least a good cross-check of the mass estimate! 14/22

  15. Higher mass gauginos The c30 is special as it has decays c30 → c10 Z (12%) and c30 → c20Z (21%) with Z → ee/mm The cross section at 500 GeV for e+eR- → c10 c30 is 16 fb. Taking into account the Z BRs , we estimate that using the Z as an end point particle (we scale from a Colorado group measurement of c2+ → c1+ Z ) dM(c30) = 8.5 GeV (statistics are limited but bknd negligible) c40 :The c10 c40threshold is 460 GeV, but the event rates are too small to allow a measurement. c2± : Threshold for e+e- → c1+ c2- is 539 GeV. Do special run at 580 GeV, trading luminosity for energy. Decays c2+ → c1+ Z (Z → ee/mm) give 55 events, allowing dM(c2+) ≈ 4 GeV 15/22

  16. ~ ~ ~ ~ ~ ~ ~ ~ ne* ne* ne* ne nm ne ne nt sneutrinos e+eL-→ → (c1+ e- ) (c1- e+) → e+e-t+t- E is 15% of eett final state (25K total events; major contributors are selectron pairs and c20 c20 pairs. e+eL- → → (c1+ e- ) (c20ne) → emmt E is 39% of emmtfinal state (628 total events). The rest are from selectron L. e+eL- → → (c1+ e- ) (c20ne) → ettt E is 39% of etttfinal state (6.5K total events). The rest are from selectron L. Can these be dug out? If one knows the selectron and c10 masses precisely, one should be able to estimate the snue mass to a few GeV? and : These never come close to dominating any final state – seems very tough to get end point masses for these ! NEEDS A STUDY! 16/22

  17. Threshold scans for sparticle masses Martyn & Blair (hep-ph/9910416) studied the mass precision available from scans near two-body thresholds (Tesla point RR1). For s-wave threshold (gaugino pairs), s ~ b1, while for p-wave (sfermion pairs), s ~ b3. Martyn-Blair used 10 points – perhaps not optimal. Strategy should depend on # events, d(sBR)/sBR, backgrounds and b-dependence. Mizukoshi et al. (hep-ph/0107216) studied ne,nm,nt thresholds (low sBR and large t decays) and found that 2 points on the rise and one well above threshold was better. Blair at Snowmass found that 2-point scans could be optimal for dm and G (Benchmark SPS1a): can get dG/G ~ 30% for typical sparticles). Cahn (Snowmass) did analytic study of mass precision from scans vs N = # pts, spaced at DE and found: With L = total scan luminosity and su = XS at upper end of scan. Good agreement with MC results. Little improvement for N>3, particularly for p-wave. ~ ~ ~ 0.36 √N DE √18Lsu (1 + ) 0.38 √N (1 + ) DE N-1/4 √2.6Lsu dm ≈ dm ≈ (p-wave) (s-wave) 17/22

  18. Threshold scans One needs to allocate scans carefully – there is a trade off between luminosity at 500 GeV (all end points and searches) and use of lower energy (at reduced luminosity). Do only those scans that give the most restrictive information on Susy model parameters. (In SM2, get some scans ‘for free’ as as thresholds overlap.) Feng & Peskin (hep-ph/0105100) study showed that e- e- operation (both beams R polarized) at the eReR threshold (b1) could give substantially better dm(eR) than the e+ e- scan (b3), even after inclusion of beamsstrahlung. We adopt this idea in our run plan. ~ ~ ~ With DEbm & beamstrahlung Dm(eR) = ±0.1 GeV ~ In establishing the mass precisions from scans, we have scaled the dm’s from existing studies by the ratio of assumed √s(500 GeV)*Lt. (Probably naïve to ignore details of backgrounds at different benchmarks, and the effect of uncertain sBR’s.) (Used only dominant reaction/polarization, so is conservative) • Note that for scans, we need not identify particular exclusive decays -- the total visible cross section may be used. But beware overlapping thresholds! 18/22

  19. Sparticle mass precision sparticledMEP dMTHdMCOMB (end pt) (scan) (combined) eR0.19 0.02 0.02GeV eL0.27 0.30 0.20 mR0.08 0.13 0.07 mL0.70 0.76 0.51 t1~1 – 2 0.64 0.64 t2 -- 1.1 1.1 ne~1 -- ~1 nm7 ?? -- 7 ?? nt-- -- -- c100.07 -- 0.07 c20~1 – 2 0.12 0.12 c308.5 -- 8.5 c40 -- -- -- c1±~1 - 2 0.18 0.18 c2±4 -- 4 ~ For run plan indicated for SM2 ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ 19/22

  20. mSUGRA parameter determination The ultimate aim of the Susy program at the LC is to determine the character of the Susy breaking (GMSB, mSUGRA, AMSB cMSB, NMSSM, etc.), and illuminate the physics at the unification scale. This will require measurements of the sparticle masses, cross-sections and branching ratios, mixing angles and CP violating observables. A start on this has been made: G. Blair, et al. PRD D63, 017703 (’01); S.Y. Choi et al., hep-ph/0108117, G. Kane, hep-ph/0008190. Here we ask the more restricted question: Assuming we live in mSUGRA (as for benchmark SM2), what are the Susy parameter errors ? Mass resolutions quoted for our Run Plan give: • dm0 mainly from eR, mR masses • dm1/2 mainly from c1± , c2± masses • dA0 mainly from t1, t2 masses • dtanb mainly from c1± , c10 masses Conservative, since additional info from t, H/A, sL/R will give added constraints on mSUGRA parameters ~ ~ Parameter SM2 m0 (GeV) 100±0.08 m1/2 (GeV) 250±0.20 A0 (GeV) 0±13 tanb 10±0.47 ~ ~ ~ ~ ~ ~ 20/22

  21. Higgs, top quark parameter errors Scale the errors fromTESLA TDR & Snowmass Orange Book Relative errors on Higgs parameters (in %) parameter error parameter error MHiggs 0.03 % GTot 7 % s(ZH) 3 lZZH 1 s(WW) 3 lWWH 1 BR(bb) 2 lbbH 2 BR(cc) 8 lccH4 BR(tt) 5 lttH 2 BR(gg) 5 lttH 30 Errors on top quark parameters Mtop 150 MeV (0.09%) Gtop ≈70 MeV (7%) Systematics limited 21/22

  22. Conclusinos • Even for the physics rich scenarios of Susy benchmarks SM2 and low Higgs mass, the Linear Collider can do an good job on precision measurements in a reasonable time. • Runs at the highest energy should dominate the run plan -- to optimize searches for new phenomena, and to get sparticle masses from kinematic end points. • The details of the run plan depend critically on the exact Susy model -- there is large variation as models or model parameters vary. It will be a challenge to understand the data from LHC and LC well enough to sort out sparticle masses/cross sections and predict the appropriate threshold energies. • For Susy, it remains very likely that higher energy will be needed to complete the mass determination and fix the Susy breaking mechanism.

  23. ~ eR ~ eR+ ~ ~ ~ eL+ eL- eL ~ eR- ~ ~ ~ mR+ mR- mR ~ ~ ~ mL+ mL- mL ~ ~ ~ ~ ~ ne* t1+ ne t1- t1 ~ ~ ~ t2+ t2- t2

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