Determining Susy/Higgs Parameters for a Physics Rich Scenario P. Grannis LCWS Jeju Korea August 2002 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/

SM Higgs mass of 120 GeV (or Susy Higgs h 0 in nearly decoupling limit) Use mSUGRA benchmark: Snowmass Group E2, SM2 (≈ Allanach et al., hep-ph/ : 'SPS1a'), (≈ Battaglia et al. hep-ph/ : ‘B’ ): m 0 = 100 GeV m 1/2 = 250 GeV tan  = 10 A 0 = 0 sgn(  ) = + This has relatively low mass sparticles, but the large tan  means that there are dominant  decays that make life difficult. Assumptions Year ( L equiv dt) (fb -1 ) We assume 1000 fb -1 = 1 ab -1 luminosity acquisition (equivalent at 500 GeV ) } 2/22

SM2 sparticle masses and BR’s particle M(GeV) Final state (BR(%)) e R (  R )143    e (  ) [100] e L (  L )202    e(  ) [45]    e (  ) [34]    e(  ) [20]   1 0  [100]   206      [49]   ±  [32]     [19] e (   186    e (  ) [85]   ± e (  ) [11]     e (  ) [4]  185     [86]     [10]     [4]    96stable    175    [83] e R e [8]  R  [8]    343    W   [59]    Z [21]    Z [12]    h [1]    h [2]    364   ± W  [52] [17]    [3]    Z [2]    Z [2] …    175    [97]    qq [2]    l [1]    364    W [29]    Z [24] l [18]    h [15] l l [8]    W [6] ~ ~ ~~ ~ ~ ~~ ~ ~ ~ ~ ~ ~~ ~~ ~~ ~ ~ ~ ~~~ ~~~ ~~~~~~ ~~~~~~ ~~~~ ~~~ ~ ~~~   3/22

Beams Energy Polz’tn L dt ( L dt) equiv comments e  e  500L/R sit at top energy for end point measurements e+e- M Z L/R calibrate with Z’s e  e  270L/R scan thresholds       (L pol.);     (R pol.) e  e  285 R scan  R   R  threshold e  e  350 L/R scan tt thresh; scan e R e L thresh (L & R pol.) scan       thresh. (L pol.) e  e  410 L scan     thrsh (L pol); scan  L  L thrsh (L pol) e  e  580 L/R sit above       thresh. for    end pt. mass e  e  285 RR scan with e  e   for e R mass ~~ ~~~~ ~~ ~~ ~~ ~~~ ~ Run Plan for SM2 Susy sparticle masses  ( L dt) equiv = 1000 fb -1 ~~ 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. 4/22

Initial (“end point”) mass determinations dN dE C E  E  E  = 1/2 (1±  ) (1 - m A 2 /m B 2 ) ;  = (s/4m A 2 -1) ½ (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. For: A → B + C The traditional end point method: ~~ Making an box distribution mass measurement requires: 1.A given final state (& e  polarization) should be fed by only 1 dominant reaction 2.Two body decay with C a stable observable SM particle. Neither of these conditions are generally true for benchmark SM2 with large BRs into  ’s and  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

e  e   (left) →     152K evnts e  e   (right) →     52K evnts   ±   ±             ~~ ~~ Among all-leptonic (& missing energy) decays of sparticle pairs,  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   ,   ) are washed out. The reaction overlap problem 6/22

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. →    e has different end points from →    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. ee  ); * reaction = specific 2 body process (e.g. e  e  →       ) eLeL ~ eLeL ~ 7/22

So, how to get initial sparticle masses ? – start with the easier cases smuonR e  e  (right pol) → →     missing energy Both →     so use either  as observable. Determine both and     masses from end points. Susy b ackground is 5% In 335 fb -1, find  M( ) = GeV ;  M(    ) = 0.11 GeV smuR chi10 chi20 smuL e  e R - →     E 30.7K evnts RR ~ RR ~ RR ~ RR ~ RR ~ smuonL e  e  (left pol) → → (      ) (     ) → (      ) (        ) →     missing energy (+ cc) →     (45%), with  as observable. Susy bknd is 5% In 335 fb -1, find  M( ) = 0.70 GeV (  M(    ) = 1.9 GeV ) LL ~ LL ~ LL ~ smuL e  e L - →  ±  ± E 3.9K evnts LL ~ Mass precisions scaled from Colorado group Snowmass’01 analyses. 8/22

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

neutralino1 = LSP Several reactions have dominant decays to     from combination of just the ee and  final states (dominated by selectron pair and smuon pair), we estimate  M(    ) = 0.08 GeV Adding the channels e , , ee , eeee, all of which have a dominant reaction with a primary decay to    I guess that the precision would be  M(    ) ≈ 0.06 GeV 10/22

The harder  channels e  e   (left) →     152K evnts   ±   ±             ~~ e  e  (left pol) →       → (  ) (  ) → (       ) (       ) →     missing energy [64%] > These  ’s tend to be back to back and e  e  (left pol) →        →    (    →    (        ) →     missing energy [19%] > These  ’s tend to be collinear e + e - (left pol) → stau1 stau1 → (      ) (      ) →     missing energy [8%] >  ’s back to back 11 ~ 11 ~ 11 ~ Can assume   , e,  masses are well measured, but      , masses are all to be determined in this e  e L   →  channel, as well as with e  e R  → , e  e L  → , e  e L - → , e  e L  →  e.g.  in  channel (left pol. e   is 92% from  L →    (1400 evnts) giving m(    ) 11 ~ 11/22 ~~ ~

 channel comments Opening angle distribution of the 1 prongs from  can partially distinguish between the       and       reactions. Making a cut (  open <  /2) increases the fraction of       by a factor of 2 while retaining 73% of        open              M(stau1) One can fit the observed 1-prong energy distribution to a template to get a particular mass. All reactions feeding  are included. 335 fb -1, with BR’s accounted for. 1 prong energy Allowing just M(stau1) to vary, get M= ± 0.22 GeV. (M= input) all reactions in  final state 12/22

 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   and can use the   (     ) energy for the dominant case of  →   These more sharply peaked distributions offer better mass determination. NEEDS a proper study, but I am guessing that the   ,    and masses can be found to ~ 1 GeV, good enough to fix the energy for scans. 11 ~ 13/22

does not dominate any channel besides the 6  final state – for which there are only 262 evnts (L pol) or 93 evnts (R pol) (before  BRs). 6% of  E (L pol) 152K events total 6% of  E (R pol) 52K events 2% of ee  E (L pol) 25K events 3% of  E (L pol) 8.6K events 6% of  E (R pol) 1.5K events 8% of  E (L pol) 35K events 20% of  E (R pol) 4.8K events Thus we would use the selectron L/R and smuon L/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! stau2 22 ~ 14/22

Higher mass gauginos The    is special as it has decays    →    Z (12%) and    →    Z (21%) with Z → ee/  The cross section at 500 GeV for e  e R  →       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    →    Z )  M(    ) = 8.5 GeV (statistics are limited but bknd negligible)     :  The        threshold is 460 GeV, but the event rates are too small to allow a measurement.    : Threshold for e  e  →       is 539 GeV. Do special run at 580 GeV, trading luminosity for energy. Decays    →    Z (Z → ee/  ) give 55 events, allowing  M(    ) ≈ 4 GeV 15/22

e+e L  → → (    e  ) (    e  ) → e  e      E is 15% of ee  final state (25K total events; major contributors are selectron pairs and       pairs. e  e L  → → (    e  ) (    e ) → e  E is 39% of e  final state (628 total events). The rest are from selectron L. e+e L - → → (    e  ) (    e ) → e  E is 39% of e  final state (6.5K total events). The rest are from selectron L. Can these be dug out? If one knows the selectron and    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! sneutrinos e ~ e * ~ e ~ ~ e ~ ~  ~  ~ 16/22

Threshold scans for sparticle masses Martyn & Blair (hep-ph/ ) studied the mass precision available from scans near two-body thresholds (Tesla point RR1). For s-wave threshold (gaugino pairs),    while for p-wave (sfermion pairs),    ~~~ Martyn-Blair used 10 points – perhaps not optimal. Strategy should depend on # events,  BR)/  BR, backgrounds and  -dependence. Mizukoshi et al. (hep-ph/ ) studied e,    thresholds (low  BR and large  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  m and  (Benchmark SPS1a): can get  ~ 30% for typical sparticles). Cahn (Snowmass) did analytic study of mass precision from scans vs N = # pts, spaced at  E and found: With L = total scan luminosity and  u = XS at upper end of scan. Good agreement with MC results. Little improvement for N>3, particularly for p-wave.  m ≈  E √18 L  u  m ≈  E N -1/4 √2.6 L  u ( 1 + ) 0.36 √N ( 1 + ) 0.38 √N (p-wave)(s-wave) 17/22

Threshold scans Feng & Peskin (hep-ph/ ) study showed that e  e  operation (both beams R polarized) at the e R e R threshold (  1 ) could give substantially better  m(e R ) than the e  e  scan (  3 ), even after inclusion of beamsstrahlung. We adopt this idea in our run plan. ~~ In establishing the mass precisions from scans, we have scaled the  m’s from existing studies by the ratio of assumed √  (500 GeV)  L t. (Probably naïve to ignore details of backgrounds at different benchmarks, and the effect of uncertain  BR’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! 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.) With  E bm & beamstrahlung  m(e R ) = ±0.1 GeV ~ ~ 18/22

Sparticle mass precision sparticle  M EP  M TH  M COMB (end pt) (scan) (combined) e R GeV e L  R  L    ~1 –    e ~1 -- ~1   7 ?? -- 7 ??           ~1 –           ~    For run plan indicated for SM2 ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ 19/22

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  MSB, 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, (’01); S.Y. Choi et al., hep-ph/ , G. Kane, hep-ph/ Here we ask the more restricted question: Assuming we live in mSUGRA (as for benchmark SM2), what are the Susy parameter errors ? Parameter SM2 m 0 (GeV) 100±0.08 m 1/2 (GeV) 250±0.20 A 0 (GeV) 0±13 tan  10±0.47   m 0 mainly from e R,  R masses   m 1/2 mainly from       masses   A 0 mainly from     masses   tan  mainly from       masses Conservative, since additional info from t, H/A,  L/R will give added constraints on mSUGRA parameters ~~ ~~ ~~ ~~ Mass resolutions quoted for our Run Plan give: 20/22

Higgs, top quark parameter errors Relative errors on Higgs parameters (in %) parameter error M Higgs 0.03 %  Tot 7 %  (ZH) 3 ZZH 1  (WW) 3 WWH 1 BR(bb) 2 bbH 2 BR(cc) 8 ccH 4 BR(  ) 5  H 2 BR(gg) 5 ttH 30 Errors on top quark parameters M top 150 MeV (0.09%)  top ≈70 MeV (7%) Scale the errors fromTESLA TDR & Snowmass Orange Book Systematics limited 21/22

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.

eLeL ~ eReR ~ eLeL ~ eReR ~ eReR ~ LL ~ RR ~ LL ~ RR ~ LL ~ RR ~ eLeL ~ 11 ~ 22 ~ 11 ~ 22 ~ 11 ~ 22 ~ e ~ e * ~