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Seeking Supersymmetry

Seeking Supersymmetry. Paul Grannis Escolo Swieca, Campos do Jordao Jan. 19 – 23, 2009. Susy.

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Seeking Supersymmetry

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  1. Seeking Supersymmetry Paul Grannis Escolo Swieca, Campos do Jordao Jan. 19 – 23, 2009

  2. Susy Supersymmetry is basically a simple idea. Translating the idea into a model which can be confronted with Nature through experiment leads to a forest of nearly an infinite number of trees and tangled pathways. Our aim in this lecture is to examine some of the interesting trees but also to gain some perspective of the forest as a whole. My expertise as a forest ranger is limited!

  3. Susy outline • Supersymmetry phenomenology • Susy breaking • Present experimental constraints • How much Susy space is left unexplored? • What can we learn from the LHC? • What will ILC add to Susy understanding?

  4. Supersymmetry Supersymmetry is the maximal extension of the Lorentz group. It has fermionic generators Q, Q which anticommute with themselves and relates fermions and bosons (differing by ½ unit of spin) Q |boson> = |fermion> Q |fermion> = |boson> And thus puts boson and fermion into the same multiplet, with the same mass (in the supersymmetry limit). (Denote supersymmetry partners = sparticles ( p ) One of the largest diseases of the SM is the hierarchy problem – the tendency of Higgs and other masses to rise to the Planck scale without incredible fine tuning. Supersymmetry solves this – for every fermionic loop diagram there is now a corresponding bosonic loop with opposite sign. So there is a cancellation in the mass divergences at every order, diagram by diagram – exact if Susy is a perfect symmetry, but good enough even if the fermion – boson mass difference is O(1 TeV) ~ EW scale. ~ ~ W W W (-) W W W ~ H H

  5. ~ eR J=1/2 eR J=0 Sparticles Every standard model spin ½ fermion (quark, lepton) has a spin 0 partner; e.g. scalar electron, scalar up quark etc. Note that the SM fermions have left- and right-handed states which are degenerate due to Lorentz invariance (a boost can turn a left handed up quark into a right handed up quark). The Susy partners (e.g. selectronL and selectronR), having no spin, cannot be so related and thus their masses need not be the same. Every standard model boson (spin 1 gauge bosons – the massless ones before EWSB – and spin 0 Higgs fields) has a spin ½ partner (wino, bino, gluino, higgsino …). For each massless gauge boson there are two gauginos, one for each of the ±1 helicity states. In supersymmetry we require at least two complex Higgs doublet fields to avoid triangle anomalies. As we have seen, 3 of these 8 degrees of freedom are eaten to provide the zero helicity states of W± and Z and the other 5 survive as the physical h, H, A and H±. Each of these 8 Higgs fields has its corresponding higgsino fields, with again 5 surviving as sparticles.

  6. Susy/SM particles particle and sparticle states (only 1st generation shown)

  7. Susy breaking Recall that the SM does not yield unification of the forces (SU(3), SU(2) and U(1) couplings do not become equal at the GUT scale). TeV scale Susy modifies the renormalization group evolution so that the couplings can meet at a common point. Susy must be a broken symmetry. There is no scalar partner of the electron at M=0.511 MeV and no spin ½ W partner at 80.399 GeV. In the SM, the gauge bosons in the symmetry limit must be zero due to gauge invariance – it is the EWSB that generates the masses of W and Z. The Susy sparticles can however have intrinsic mass terms in the Lagrangian for squarks, sleptons, higgsinos, gauginos – all presumably at the TeV scale. Additionally, we introduce ad hoc trilinear couplings A governing the squark-squark-Higgs and slepton-slepton-Higgs vertices and bilinear couplings B of Higgs supermultiplets. In the general Minimal Supersymmetric Standard Model (MSSM), these mass and couplings, and the Higgsino mass term m, are put in as 105 arbitrary parameters, to be chosen by Nature, to describe the Susy breaking. The 105 arbitrary parameters (ugly??) mean that it is effectively impossible to characterize the phenomenology for the full class of MSSM Susy models. Thus simplifying assumptions are often made about relations among the parameters. and, even more complex versions of Susy than the MSSM can be invented …

  8. Susy Lagrangian For the record, the Susy breaking Lagrangian: And the Higgs potential:

  9. R-parity and Mixing • Susy could violate baryon and lepton number conservation. To prevent this, an invariance under R parity inversion is often postulated. • R= ( -1)3B-3L+2S(B=baryon #, L=lepton #, S= spin) • All particles have R = 1 (e.g. quark with B=1/3, L=0, S=1/2 ), whereas all sparticles have R = -1 (e.g. squark with B=1/3, L=0, S=0). • R-parity invariance then implies that in any reaction initiated by SM particles, there are an even number of sparticles participating. • Thus the lightest of the sparticles = LSP (lightest Susy particle) is forbidden to decay (to all SM particles), and is a good candidate for the Dark Matter particle, as it would have very small interaction cross sections and would be cosmically stable. • Sparticles with the same quantum numbers can mix, so the observed mass eigenstates are mixtures of the Susy states shown in the table above. • 2x2 mixing matrix for (charged winos and higgsinos)  2 charginos: c1± , c2± • 2x2 matrix for squarks (L and R) and sleptons (L and R)  2 q, l states: e.g. t1, t2 • Off diagonal mass matrix elements ~quark/lepton mass, so large mixing for t, t • 4x4 matrix for neutral wino, bino, 2 higgsinos  4 neutralinos: c10, c20, c30, c40 ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~

  10. Susy breaking models Exploring a parameter space with 105 arbitrary parameters and trying to confront predictions with experiment is difficult!! Simplified models are considered, classified by the mechanism used to break the Susy symmetry. There seems not to be a way to break the symmetry through choices of the MSSM parameters. SUGRA (supergravity): Postulate some high energy scale, F, for the symmetry with spontaneous breaking transmitted to the TeV scale by gravity. The sparticle masses are scaled by the Planck scale MP as M ~ F2/MP. Implying that F~1011 GeV. In SUGRA, assume that all squarks, selectrons and Higgs have a common mass m0 at the GUT scale (F) and all gauginos have a common mass m1/2. These masses evolve and diverge as they are run down to the TeV scale. Typically squarks and gluinos are more massive than sleptons and gauginos, and decay through chains leading ultimately to the LSP. The c10 is typically the LSP and is the DM candidate. Also assume the trilinear Higgs-sfermion-sfermion couplings have a common value A0. This leaves the bilinear Susy breaking term B and the higgsino mass m, but B and m2 can be eliminated by their relation to MZ, leaving the 5 parameters {m0 m1/2A0tanb sgn(m) = ±1 } In SUGRA, the lighter chargino and neutralinos tend to be mainly gaugino (not higgsino)-like with M(c20) ≈ M(c1±) ≈ 2M(c10).

  11. Susy breaking models GMSB (Gauge Mediated Susy Breaking): Again postulate a symmetry breaking at F ~ 1010 GeV, but transmission by SU(3)xSU(2)xU(1) gauge interactions to the TeV scale. In this mechanism, the Susy partner of the graviton, the gravitino, gets its mass only through gravity and is much lighter than all other sparticles. Now the next to lightest Susy particle (NLSP) is either the lightest neutralino or the stau and decays weakly to the gravitino c10 G g or t1  G t. Unless the NSLP is the neutralino and lives long enough to escape the detectors, GMSB phenomenology is quite different from SUGRA. The photon in the NLSP decay is often a good experimental signature. There are again 5 parameters in the simplified GMSB framework. ~ ~ ~ ~ Anomaly mediated and Gaugino mediated Susy breaking schemes have also been postulated. Each has rather different characteristic sparticle mass spectra, though even within a specific model class wide variations can be found. Also, models in which R-parity is violated, at least for some of the sparticle fields, are possible (so long as B and L conservation is retained).

  12. All flavors of sleptons are produced via s-channel Z/g*. Selectrons also have a t-channel c0 exchange diagram. Experiments sought the decay l lc10. Production of slepton pairs is possible up to the close to the kinematic limit, so the mass limits (m=-200 GeV, tanb=1.5) give M(slepton) ~ √s/2. ~ ~ What has experiment ruled out? The mapping between experiment and Susy theory is not good. Experiments must choose a particular signature (specific collection of jets, leptons, MET etc.) and see whether the rates observed violate the prediction of a particular model. Thus experimental results tend to be valid for a specific Susy breaking scheme, but not generally for the full MSSM. There are MANY specific searches at LEP, Tevatron, HERA, and other experiments – often difficult to relate to each other. Examples of searches: Charged slepton search at LEP: LEP operated at energies up to 208 GeV e+e- collisions and produces slepton pairs as shown: The LEP experiments have also ruled out charginos below 103 GeV for all but a few pathological parameter choices.

  13. Squark and gluino searches at the Tevatron: The reactions qq or gg qq or gg, qq gg, qq  qq and qg qg are sought in the SUGRA framework. Squarks/gluinos are produced by QCD with SM couplings. If the squarks are heavier than the gluino (low m0 ), q  qg with g  qq c10, qq’ c1± … If the gluino is heavier (high m0 ), g  q q, with q  q c10, q’ c1± … . - ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ What has experiment ruled out? The final state then consists of several jets (2-4 depending on the mass hierarchy) and MET from the LSP. Several optimized searches with different number of jets and MET were performed and compared to a series of predictions in the (m0 – m1/2 ) plane. The plot shows the MET distribution compared to SM backgrounds dominated by ttbar, W+jets, Z+jets. It shows possible gluino signal (heavier gluino case). The data is well modeled by the backgrounds, so limits can be set. And in the m0 – m1/2 plane, extending LEP somewhat Limits in the squark-gluino mass plane

  14. Chargino – neutralino production at the Tevatron: Collisions of quark-antiquark through an s-channel W or t-channel squark exchange can produce the reaction qq  c1± c20. With decays c1± l±c10 and c20  l+l-c10, (l = e,m,t) the final state is three charged leptons and MET. (The lower mass, higher cross section qq  c1± c10 is not accessible since c10 is invisible and backgrounds for a single charged lepton are large. ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ In SUGRA, expect M(c1±)≈M(c20) ≈2M(c10) The final states sought were eeT, mmT, emT, mtT and mtt, where e,m,t are well-identified and T is an isolated track not explicitly identified as a lepton. t hadronic decays are included. MET > 20 GeV was required, Z and W boson candidates are removed, and tracks are required to be well separated from MET. A grid of (m0-m1/2) SUGRA models with tanb=3, A0=0 and m<0 was scanned and the number of predicted and observed events compared. What has experiment ruled out? Chargino masses below about 140 GeV are ruled out. The data are not consistent with tanb <10 for M(c1±)=130 GeV. Limits in the m0 – m1/2 plane extend LEP and previous Tevatron considerably

  15. Is Susy still an attractive BSM idea? There is no experimental evidence to date for Supersymmetry – no sparticles, no convincing demonstration of new physics hiding in loops in rare processes. So is it sensible to retain Susy as a viable model? • Nevertheless Susy has many very attractive features: • It cures the hierarchy problem • Allows an explanation for EWSB that is not ad hoc • Is thought to be an essential feature of consistent string theories (though is not predicted to be at low mass scale) • Provides a dark matter candidate • Completes the Lorentz group • Retains the agreement of existing precision measurements with SM prediction. (many other models tend to produce discrepancies with experiment), and Susy reduces in many limits to the SM at present energies. So we are reluctant to give up on Supersymmetry

  16. How much Susy space is left? C. Berger, J. Hewett, J. Gainer, T. Rizzo, hep-ph 0812-0980 • Most experimental searches to date have been in some restricted Susy model, not the MSSM. Recently, a more general search in a model space called pMSSM (phenomenological MSSM) in which some simplifications are made: • No CP violation in Susy parameters • Minimal flavor violation • Degenerate 1st and 2nd generation squarks and sleptons This leaves 19 (not 105) Susy breaking parameters: • Masses for SU(3), SU(2) and U(1) gauginos(50 GeV < Mi < 1 TeV) • Higgsino mass m(50 GeV < m < 1 TeV) • tanb(1 < tanb < 50) • Higgs CP odd mass, MA(43.5 GeV< MA < 1 TeV) • 10 masses for squarks and sleptons(100 GeV < Mf < 1 TeV) • Trilinear couplings only for 3rd generation (b, t, t)(|Aj| < 1 TeV) Pick parameters randomly with equal probability in indicated ranges 107 times. Compute the Susy spectrum and derived quantities. Require that predictions agree with theoretical constraints or experimental results, and keep only those models that are consistent.

  17. How much Susy space is left? Flavor physics/cosmological constraints: Agree (loosely) with limits on bsg, Bs mm; Btn, gm-2, quark mixing Relic density of LSP no greater than WDMh2 = 0.121 (could be non-LSP dark matter) Constraints employed: Theoretical constraints: No tachyons No false minima in scalar potential LSP is lightest neutralino (Grand unification not required) LEP/Tevatron limits on squark, chargino masses, Higgs couplings, heavy stable particles are obeyed. For the 107 parameter sets chosen, ~7x104 survive all these constraints. For these, plot the distributions of sparticle masses, Susy parameters that are thus still compatible with data: t1 , t2 Sleptons: R sleptons tend to be lighter than L. Stau1< selectron/smu e/m L and R

  18. Top Squarks mass states after mixing light squarks: charginos neutralinos How much Susy space is left? Squarks; some solutions are below the Tevtron limit ~300 GeV where the searches made cuts that eliminated them from sample. Gauginos: lowest c1±and c10 , c20 states are quite light, often accessible to 500 GeV ILC.

  19. How much Susy space is left? Light Higgs h is almost always below 125 GeV (recall in decoupling limit, h ≈ HSM). Cases with Mh < 110 GeV have odd couplings that evaded the HSM search. H and A nearly degenerate, even away from decoupling limit. light Higgs h (log scale) heavy Higgs H/Ah Gluino masses rather uniformly distributed up to upper limit. gluino

  20. How much Susy space is left? c10 is the LSP by construction; what is the NLSP? Some preference for c1± and c20, but other possibilities are also possible. character of NLSP What are the components in the c10 = LSP after the neutralino mass mixing? Somewhat surprisingly it tends not be like SUGRA where c10 is mainly bino. There is a rather large fraction of cases which are higgsino or wino dominated. Few cases with all three significant in mixture. LSP higgsino vs. bino fraction LSP bino vs. wino fraction

  21. How much Susy space is left? tanb distribution One can ask the probability distributions for Susy parameters or observables in the selected models. Most likely value of tanb is ~ 12 Most likely value of Wh2 from the LSP is significantly lower than observed Wh2, so it implies there are other DM particles besides neutralinos (axions?) Wh2 distribution In general, the existing constraints on supersymmetry leave a large amount of parameter space still unexplored. However the observables tend to be in a range that is easily explored by the LHC, and many states have high probability for being seen at the ILC.

  22. Finding Susy at LHC The LHC produces mainly squark/gluino pairs via known strong QCD interactions. Other sparticles then occur in the decay chains that are quite model dependent, and ultimately end with a collection of SM particles and the LSP. The LHC experiments can quickly see Susy and determine the Susy scale. Define a variable Meff = MET+pT(1)+pT(2)+pT(3)+pT(4) from the missing ET and pT of the four leading jets in the event (veto on leptons) Left plot is Meff distribution: shaded histogram is SM bknd and open circles add in Susy (760 GeV gluino). Note log scale. Right plot is MSUSY (Minimum of squark or gluino mass) vs. Meff. The scale of Susy is remarkably well determined. Most studies of Susy at LHC have been done in the SUGRA framework, and even here there are very different signatures over the range of possible parameters. ATLAS and CMS have sampled this space to get an idea of what can be done, but these studies can only be representative.

  23. Finding Susy at LHC Within SUGRA models, one can scan the space to get an idea of the discovery reach. For 10 fb-1, requiring at least 2 jets that are not back-to-back (for SM rejection) and significant MET, or high pT leptons with transverse mass of leptons and MET above the W mass, one obtains discovery (>10 events, good S/√B): Lines are for different final state lepton content. Visually these plots look like the LEP/Tevatron exclusion plots shown before. Don’t be fooled – the axes are much expanded! (The Tevatron range is circled) The LHC should see the effects of Susy if it has anything to do with EWSB. LHC should see squarks/ gluinos out to > 2 TeV

  24. Determining Susy parameters at LHC It is easy to see dramatic effects at LHC if Susy exists. The harder questions are whether one can determine that it really is Susy, what the masses of the sparticles are, what are the decay branching ratios, what are the quantum numbers of the sparticles, and what is the nature of Susy symmetry breaking. The answers to these questions are again very dependent on the exact Susy model Nature has chosen. Even small changes in parameters make large qualitative differences in decay patterns and masses. Decay chain example: At ‘LHCC Point 3’, M(gluino)=300 GeV, M(squarks)≈310 GeV and gluino pair production is dominant. A representative decay chain: g  b1 b (+ h.c.) (89%) b1  c20b (86%) c20  c10l+l- (34%) (Gluino decays to bottom squark (and SM b) since light squark mass exceeds gluino mass here.) ~ ~ ~ ~ ~ ~

  25. E = 1/2 (1 b ) (1 - mA2/mX2) ; b= (s/4mA2 - 1) dN dEC ½ E- E+ Sparticle masses from end points End points: For 2 body decay of monoenergetic particle A (e.g. ee  AA )whose decay: A → X + C (X unseen, C some known SM particle) is isotropic in its decay frame, the lab frame energy distribution for C is flat between end points E- and E+. Knowing s, and measuring E+ and E-, allows solving for MX and MA. At the LHC (e.g. example in previous page), we typically do not know s due to parton momentum distribution, and usually are not dealing with a monoenergetic particle decaying into two final particles, but the upper end point continues to carry information about mass differences.

  26. ~ ~ Getting the b1 and g masses is harder. If we select the dileptons at the upper end of the distribution (around 50 GeV), both the dilepton and c10 are at low momentum, and we can solve the kinematics for momentum of c20 : ~ b1 Assumingm(c10) = ½ m(c20) (generally true in SUGRA), and combining the c20 with a b jet, compute the mass of the b1. Then adding the momentum of the second b-jet to that of the b1, we can reconstruct the g. ~ M(c20, b) ~ ~ ~ DM(g-b1) ~ ~ cut on M(b1) ~ ~ Susy Masses in gluino decay example For our example c20  c10l+l- , the dilepton mass upper end point determines the c20 - c10 mass difference (here input to be 50 GeV) to about 0.1%. (A favorable case with small backgrounds and the large BRs.) dilepton mass Get M(b1) to ~1% + 1.5DM(c10) M(g) – M(b1) ~ 10% This is a favorable scenario for LHC. Typically get only mass differences, at the level of 10-20%. And mass of c10 is known, so the absolute scale is not fixed.

  27. IF SUSY exists LHC sees it IF LHC sees something It is Susy Susy at LHC Typically LHC experiments will see evidence of Susy in many channels, so fitting them all together can give some information about the underlying model parameters, assuming a particular Susy breaking scheme. ATLAS estimates that the precision on m0, m1/2 and tanb range between a few % and 20%, after making the assumption that it is SUGRA. It is unlikely that the LHC experiments will measure the spins and parities of new particles. This is critical to establishing that what you see is Susy – if you say you see a selectron, you had better be able to demonstrate that it has spin 0! For example, 4 different models give same final state particles: (a) and (b) are Susy with different DM particle. (c) and (d) are extra dimension models with different KK state character. The LHC is a wonderful discovery machine, but the reverse engineering to let us understand clearly what is seen is difficult. This is the crux of the argument for the lepton colliders, where the simplicity of the reactions pays off. (But don’t sell the ingenuity of the LHC physicists short, once they have data in hand.)

  28. Susy at the ILC For supersymmetry studies, the ILC is very complementary to the LHC. Whereas the LHC seems assured to produce most of the Susy particles, the ILC is limited in energy (500 GeV to 1 TeV) so if the sparticles are heavy they may be inaccessible. (recall that sparticles are produced in pairs) But for those sparticles that can be produced, much more incisive measurements are possible at ILC than at the LHC. The colliding partons (e+ e-) have a fixed energy; the beam particles can be polarized to enhance cross sections and reduce backgrounds, the events are cleaner, and the initial state is known. The ILC can measure the masses of the accessible particles accurately, and can usually determine their quantum numbers (recall that knowing the spins is crucial for saying that what we see is Susy). The mixing matrices can be measured, and CP violations in these mixings can be sought. Working together, the two machines amplify the results of each other. For example, the ILC can measure the mass of the LSP c10; this allows the mass differences of the heavier sparticles measured at the LHC to be converted to mass measurements. And with results from both machines, the nature of the Susy symmetry breaking mechanism can be illuminated.

  29. ~ Consider the illustrustative case of the mR (scalar partner of the right-handed muon). Production is e+e- mR+mR- (s-channel g,Z) ~ ~ The final state is two isotropic monoenergetic particles, so the kinematic end point analysis given above is valid for the decays: mR c10 m . The energy spectrum of the muons is flat between lower and upper end points whose values can be measured and translated into the mass of thec10 and the mR. ~ ~ ~ ~ ILC smuons Can measure both the smuon and LSP mass to <% accuracy from runs at the maximum energy. Once one knows the mass from the end point spectrum, one can set the energy of the collider to near the smuon pair threshold. In this case, the threshold behavior is b3 (p-wave). From the location of the threshold, one can measure the mass more precisely (~0.1% in this case). End point mass measurements for all observable Susy particles can be done simultaneously at full energy. But separate threshold scans are typically needed for each reaction.

  30. ILC smuon Q#s & couplings The thresholdbehavior (for smuons, b vs b3) and the angular distribution of the final m’s determine the quantum numbers of the mR. To verify it is Susy, the smuons should be spin 0 and there should be (non-degenerate) partners for both left- and right-handed m. The dominant particles produced (mR or mLpairs) can be selected by altering the polarization of the incident electron. Supersymmetry requires that analogous couplings between Susy particles and SM particles are identical. e.g. g(mnW)= g(mnW) The sparticle couplings can be directly measured from the cross sections to verify if it is Supersymmetry or some other model. Similar techniques work for the selectrons (harder because one can produce eL+ eR- and eR+ eL- also) and staus (harder because final state t’s are harder). ~ ~ ~ ~ ~ ~ ~ ~ ~ ~

  31. e+ ~ g,Z e+ ~ e- e- ILC selectron studies Production of selectron pairs -- have two diagrams; typically the t-channel c0 exchange dominates and allows measurement of neutralino couplings (gaugino vs. higgsino) to lepton/slepton. Bkgnd WW production is suppressed for beam eR- . ~ e+ e+ c0 ~ e ±distributions for both e- polarizations e- e- End point measurements for selectrons are more complex as can reach eR+eR-, eR+eL-, eL+eR-, and eL+eL- final states from same initial state. But can disentangle to get masses. ~ ~ ~ ~ ~ ~ ~ ~ Scan at threshold for very accurate masses Here use e-e- since this is s-wave (b1), not p-wave (b3) as for e+e-. Can achieve 20 MeV (0.01%). ~ Angular distributions of decay electrons e  e c10with polarized beams give quantum numbers, coupling of exchanged c10 and give information on nature of neutralino mixing (gaugino/higgsino), hence the underlying Susy mass parameters.

  32. c+ e+ e+ c+ g, Z ~ n e- c- c- e- ~ c1+ M2 2MWcosb W+ c2+ 2MWsinbm H+ [ ] ( ( ) ) = ~ Right polarized e- removes the t-channel diagram. Cross section and AFB give the higgsino/wino content of c1+. Tests of Susy relations possible: e.g. measure MW to ~20 MeV from purely Susy quantities. eL-e+c1+ c1- allows test of Susy coupling relation g(c1+ne) = g(W+ne) eL-e+  c1+ c1- has strong s & t channel interference. Cross section sensitive to M(n) to ≈2 ECM. ~ ~ ILC chargino studies Both s-channel and t-channel processes contribute. Masses are measured to few % from end points in reaction e+ e- c1+c1-with decays c1+  c10W+ or c10ln or c10q’q. The mass values of c1+, c2+ constrain the parameters of the mixing matrix taking (W+H+) to the mass eigenstates (c1+, c2+) and determine M2 (mass of the SU(2) Susy boson) and m (Higgsino mass parameter). ~ ~ M2(c1+)+M2(c2+) = M22 + 2MW2 +m2 M(c1+) x M(c2+) = mM2 – MW2 sin(2b) Thresholds for gaugino pairs are b1 (thus better mass precision than for scalars).

  33. ILC neutralino studies ~ ~ ~ ~ The mass matrix for the 4 J=1/2 neutral gauginos (b, w3, H1, H2) depends on the U(1) and SU(2) gaugino masses M1, M2, the higgsino mass m and tanb. The mass matrix can be diagonalized to give the physical state ci0, i=1,4. There are 14 possible CP violating phases in the neutralino sector alone (46 overall in the MSSM). Unitarity relations yield unitarity quadrangles which in principle can be determined experimentally, through a combination of neutralino production cross sections, and fermion-sfermion-neutralino vertix determinations. These, together with the chargino measurents, make it possible to extract the underlying Susy parameters even in the case of CP violation. We need to know |M1|eiF1, M2, |m|eiFm, tanb to fix the low energy Susy model. ~

  34. ILC gaugino studies Measurement of cross sections for c1+c1- and c1+c2- with polarized beams give us M2, meiFm, tanb Measurement of c10and c20 masses and s(c10 c20)then give|M1|and its phaseFm → → → CP violating observables like pe·(p+x p-) in reaction e+e- → c10c20 → c10c10 l +l- can directly signal CP violation.

  35. ILC third generation sfermion studies ~ ~ ~ ~ The (tL , tR) or (tL , tR)states mix to non-degenerate mass eigenstates (t2 , t1) or(t1 , t2) through SM fermion Yukawa terms ; hence the mixing is most pronounced for third generation sfermions. The mass mixing matrix is sensitive to the soft Susy-breaking parameters and trilinear couplings ~ ~ ~ ~ ~ ~ t1t2 tLtR cosqtsinqt -sinqtcosqt = ~ ~ ~ Cross sections with polarized e- , and mass of t’s, allow determination of sinqt to 0.03 (100 fb-1). Polarization oft can be determined to ~ 7% from the t decay asymmetry; This yields information on the c10 and t mixing (and also yields info on tanb– there are many independent ways to measure the Susy parameters!) tR- → tR- + Gaugino tL- →tL- + Higgsino A valuable tool for independent study of gaugino mixing ~ ~ ~ Using polarized e- beams, one can measure the stop mass to ~2 GeV and cosqt to ~0.02. The mixing angle can be improved to ~ 0.001 through measurement of ALR for t t. ~ ~ Sfermion measurements allow probe of the Yukawa Susy couplings and departures from simple mSUGRA models.

  36. ILC Susy studies The Linear Collider can determine the Susy model, and make progress to understand the high energy supersymmetry breaking scale. To do this, one would like to see the full spectrum of sleptons, gaugino/higgsino states. The question is whether the full set of Susy particles will be kinematically accessible. Thresholds for selected sparticle pair productions – at LHC mSUGRA model points. Point 1 2 3 4 5 6 GeV GeV GeV GeV GeV GeV reaction RED: Accessible at 500 GeV BLUE:added at 1 TeV c10 c10336 336 90160 244 92 c10 c20494 489 142 228 355 233 c1+ c1-650 642192294 464 304 c1+ c2-1089858368462750 459 e e/ m m920 9224221620396 470 t t860 850412 1594 314 264 Z h 186 207 160 203 184 203 Z H/A 1137 828 466 950 727 248 H+ H - 2092 14827561724 1276364 q q 1882 1896 630 1828 1352 1010 ~ ~ ~ ~ ~ ~ The pMSSM study above of models that satisfy theoretical and expt constraints tend to confirm that low mass c10, c20, c1± are preferred. ~ ~ It is likely however that in the case that supersymmetry exists, one will want ILC upgrades in energy to at least 1 TeV.

  37. ILC Susy run plan The measurements we have outlined at ILC require running at several different conditions (beam particles, energies, polarizations), unlike LHC where one runs the machine only at full 14 TeV energy. At ILC, one wants runs at full energy to seek new physics and measure Susy reaction end points. Then do special runs at the thresholds for some Susy reactions and tt production. Can one do this program achieve the sort of precision we have outlined in a finite time? Examine a run scenario for the first 1000 fb-1 of ILC running at 500 GeV (~7 years). Take Mh=120 GeV. Assume Susy parameters that assure many particles are accessible, thus many run conditions are needed. The SM2 SUGRA point gives masses and BRs as indicated. Remember that all Susy reactions allowed occur together, so Susy forms an important background in many studies. m0= 100 GeV m1/2 = 250 GeV tanb = 10 A0 = 0 sgn(m) = +

  38. ~ Also special run above 500 GeV for c2± threshold (trade L for √s), and e-e- run for eR eR (s-wave). ~ ~ ILC Susy run plan Cross sections are specified given the SUGRA parameters: note that L and R polarized e- XSs differ (assume Pe-= 80%). Propose run plan shown: Calibrate detectors with Z pole runs. Initial running at 500 GeV to get Susy reaction end points. e+ e-threshold scans for:

  39. ILC Susy run plan We focus on specific decay topologies (e.g. 4 leptons and MET). Take into account that other Susy reactions provide background and note that several reactions may feed a particular final state. For each channel sum the contributions from all reactions that feed it. We choose the e- polarization state to enhance particular reactions of interest. Since the decay BRs and backgrounds depend sensitively on the specific Susy model, this exercise is an existence proof but is not directly translatable to other models. Sparticle mass precision achieved in 1000 fb-1 Precision on Higgs mass/couplings and top quark parameters Sugra parameter precision Even for a very rich accessible Susy spectrum, the ILC should be able to make measurements at the desired precision.

  40. ILC and LHC are synergistic If Susy exists, the LSP provides a dark matter candidate. The ILC in particular measures its mass very accurately and the Susy cross sections allow the calculation of the DM cosmic density. If these agree with the density measurements from Cosmic Microwave Background measurements, we have provided full understanding of the character of dark matter. DM cosmic density  If the density from colliders disagrees with mwave background, we know that there are other contributing dark matter particles. DM mass 

  41. ILC and LHC synergy Measurements of the gluino, wino and bino masses can be extrapolated by renormalization group to high scales, and we can see if there is a grand unification, thus telling us about the scale of Susy breaking. m1/2 The sfermion mass terms extrapolated to high scale reveal the nature of the Susy breaking – shown here for Sugra and Gauge mediated symmetry breaking. LHC High mass Sugra and GMSB patterns are distinctive. m0 ILC

  42. ILC and LHC synergy ILC measures masses, couplings and mixings of the accessible Susy spectrum much more precisely than LHC. LHC can observe higher mass sparticles. Either LHC and ILC alone gives an incomplete view of the new physics. Acting in concert, like binocular vision, they give a depth of view that can tell us much more than either alone. “Pardon me, I thought you were much farther away”

  43. Supersymmetry summary • Low mass supersymmetry offers many desireable properties: • Cures the hierarchy problem • Provides a dark matter candidate • Allows for unification of Strong, EM, Weak gauge forces • Has possible sources of CP violation that could address the baryon-antibaryon asymmetry • And Susy is an ingredient of string theories If Susy provides these explanations, it will surely be found at the LHC. The ILC, to the extent that it can access the Susy particles, will make precision measurements of masses, quantum numbers, and couplings to tell us which Susy breaking model is at work.

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