Supersymmetry at the ILC

Transcription

1 Supersymmetry at the ILC Abdelhak DJOUADI (LPT Paris Sud). Introduction 2. High precision measurements 3. Determination of the SUSY lagrangian 4. Connection to cosmology 5. Conclusion For more details, see ILC Reference Design Report: Physics at the ILC, arxiv: [hep-ph]. A. Djouadi p./25

2 . Introduction If SUSY is to solve some of the most severe problems of the SM: We need light SUSY particles: M S < TeV. The hierarchy problem: radiative corrections to the Higgs masses [ ( M 2 H = λ2 f N f (m 2 4π 2 f M2 S )log ) Λ M S ( )] + 3m 2 f log M S m f + O ( Λ 2 ) The unification problem: the slopes of the α i SM gauge couplings need to be fixed early enough to meet at M GUT GeV. The dark matter problem: the electrically neutral, weakly interacting, stable LSP should have a mass < O( TeV) for Ωh 2 to match WMAP. In this case, sparticles are accessible at future machines. For instance, some of them should be soon observed at the LHC. SUSY@ILC A. Djouadi p.2/25

3 . Introduction But producing these new states will not be the whole story. We also need to determine the theory: measure the masses and mixings of the newly produced particles, their decay widths, branching ratios, production cross sections, etc...; verify that there are indeed superpartners and, thus, determine their spin and parity, gauge quantum numbers and their couplings; reconstruct the low energy soft SUSY breaking parameters with the smallest number of assumptions (model independent way); ultimately, unravel the fundamental SUSY breaking mechanism and shed light on the physics at the very high energy scale; make the connection to cosmology and predict the cosmological relic density of the dark matter superparticle. To achieve this goal, a combination of LHC and ILC is mandatory. SUSY@ILC A. Djouadi p.3/25

4 At the LHC: copious production of g, q (strong interaction processes) weakly interacting l, χ states from cascade decays of g, q. However: rather complicated topologies very large SM backgrounds difficult hadronic environment. Thus:. Introduction detection possible for m < 2 3 TeV determinantion of properties difficult precision tests not guaranteed. model independent analyses unlikely σ (fb) σ jet (E T jet > s /20) pp/pp _ cross sections σ tot σ bb _ σ W σ Z jet σ jet (E > 00GeV) T σ jet (E T jet > s /4) σ tt _ σ Higgs (M H =50GeV) σ Higgs (M H =500GeV) Tevatron pp _ pp LHC s (GeV) SUSY@ILC A. Djouadi p.4/25

5 At the ILC: direct l, χ production large production rates good signal to bkg ratios very clean environment possibility of tuning energy initial beam polarisation more collider options... Compared to LHC: additional spectrum complementary studies high precision measurements model independent analyses. Introduction HZ + µ µ - WW ff σ (e + e - ) [fb] ZZ tt + χ χ - t t 0 0 χ χ 2 s[gev] SUSY@ILC A. Djouadi p.5/25

6 . Introduction For an illustration of ILC potential: one point in msugra parameter space: SPSa : m /2 =250GeV, m 0 =70GeV, A 0 = 300GeV, tan β =0, µ>0 700 m [GeV] SPSa mass spectrum q L g q R t 2 b2 b 400 H 0, A 0 H± χ 0 χ χ ± 2 t l L νl τ 2 ν τ χ 0 2 χ ± 00 h 0 lr τ χ 0 0 p/mass χ 0 χ 0 2 χ ± ẽ ẽ 2 ν e τ τ 2 ν τ t b SPSa SPSa SUSY@ILC A. Djouadi p.6/25

7 2. Precision SUSY measurements: the χ sector Charginos: mixtures of the charged higgsinos and gauginos W ±, h ± 2/ χ±, χ ± 2 The general chargino mass matrix, in terms of M 2, µ and tan β, is M M C = 2 2MW s β, s β sin β etc 2MW c β µ Neutralinos: mixtures of the neutral higgsinos and gauginos B, W 3, H 0, H 0 2 χ 0,2,3,4 The 4x4 mass matrix depends on µ, M 2, tan β, M ; given by: M N = [ M 0 M Z s W c β M Z s W s β 0 M 2 M Z c W c β M Z c W s β M Z s W c β M Z c W c β 0 µ ] M Z s W s β M Z c W s β µ 0 SUSY@ILC A. Djouadi p.7/25

8 2. Precision SUSY measurements: the χ sector χ production: e + Z(γ) χ i e + l χ i e χ j e χ j e + e χ ± i χ± j : s channel γ, Z and t channel ν e; large σ for i=j e + e χ 0 i χ 0 j : s channel Z and t channel ẽ; σ = O(0 fb). e ± beam polarisation selects various production channels cross section for χ ± rises steeply near threhosld, σ β cross sections for χ 0 rise less steeply in general, σ β 3 χ decays: - in general χ i Vχ j, Φχ j, f f - possibility of cascade decays signature: /E T from escaping χ 0 SUSY@ILC A. Djouadi p.8/25

9 2. Precision SUSY measurements: the χ sector Measurement of χ ± /χ 0 masses: from a threshold scan, m χ ± for m χ ± 50 MeV 200 GeV as steep rize σ β. m χ ± mass in e + e χ + χ l ± νq q χ 0 χ 0 0.% in contiuum from dijet from dijet mass, m χ 0 determination with precision (m χ ± m χ 0 )=O(50) MeV. for small m χ ± m χ 0, use e+ e χ + χ γ to measure both m χ ± /m χ 0 from spectra. e + e χ 0 2χ 0 l + l χ 0 χ 0 allows an accuracy (m χ 0 2 m χ 0 )=O(0.%) Determination of spin: idea from excitation curve and angular distribution from production sure with angular distributions of polarized χ decays with polarized e ± SUSY@ILC A. Djouadi p.9/25

10 2. Precision SUSY measurements: the χ sector σ(e + e χ + i χ j ) is binomial in the χ± mixing angles cos 2φ L,R determined in a model independent way using polarized e ± beams SPSa: c 2φL =[0.62, 0.72], c 2φR =[0.87, 0.9] at 95% CL at s= 2 TeV cos 2Φ R σ ± L σ (500) ± L (400) σ ± R (500) cos 2Φ L CPC: e + e χ + i χ j alone allows to determine basic parameters; sneutrinos can be probed up to masses of 0 TeV with polarisation; CPV: e + e χ 0 i χ0 j would be needed (direct probe of CPV). SUSY@ILC A. Djouadi p.0/25

11 2. Precision SUSY measurements: the f sector Sfermion system described by tan β, µ and 3 param.for each species: m f L, m f R and A f. For 3d generation, mixing m f to be included. M 2 f = m2 f +m2 fl +(If 3L e fs 2 W )M Z 2c 2β m f A f µ(tan β) 2I3L f m f A f µ(tan β) 2I3L f m 2 f +m2 fr +e f s 2 W M Z 2c 2β They are diagonalized by 2 2 rotation matrices of angle θ f, which turn the current eigenstates [ f L, f R into the mass eigenstates f, f 2. m 2 f,2 = m 2 f + m 2 2 LL + m2 RR (m 2 LL m2 RR )2 + 4m 2 f X2 f ] Note: mixing very strong in stop sector, X t = A t µ cot β and generates mass splitting between t, t 2, leading to light t ; mixing in sbottom/stau sectors also for large X b,τ = A b,τ µ tan β. SUSY@ILC A. Djouadi p./25

12 2. Precision SUSY measurements: the l sector l production: e + γ, Z ẽ e + χ i ẽ e ẽ e ẽ e + e µ + µ / τ + τ / ν µ,τ ν µ,τ : s channel γ,z exchange; e + e ẽ + ẽ : s channel γ, Z and t channel χ 0 exchange; e + e ν e ν e : s channel Z and t channel χ ± exchange; Again, in this case: e ± beam polarisation selects various channels/chiralities for ẽ, ν e ; ẽ L/R production in e L/R e L/R collisions; cross section for ẽ, ν e rises steeply near threhosld, σ β cross sections for 2d/3d generation rise less steeply, σ β 3 Slepton decays: in general l lχ 0 with possible cascades. SUSY@ILC A. Djouadi p.2/25

13 2. Precision SUSY measurements: the l sector Slepton mass measurement from threhold scan and in continuum: Polarized e + e : mẽr = 0.2 GeV and ΓẽR = 0.25 GeV; improvement by 4 using e e but 2 times worse for µ in e + e from E l spectra in l lχ 0 decays, O.% precision for m l and m χ 0 ν e more involved, m ν at % from e + e ν e ν e ν e χ 0 e ± χ 8 [fb] s[gev] SUSY@ILC A. Djouadi p.3/25

14 2. Precision SUSY measurements: the l sector Slepton spin determination: conceptually very simple in e + e hint from the P wave onset of the excitation curve (not sufficient). the sin 2 θ behavior of the cross section (for ẽ near threshold). Coupling determination: check of the SUSY identity g gauge = g Yukawa from ẽ and ν e production cross sections (t channel contributions) more efficient in χ ± and χ 0 production (works also for heavy l). In the case of τ : τ mixing and final state τ slightly complicate pattern mass determination as above for µ but accuracy 3 times worse, complication (γγ bkg) when τ almost degenerate with the LSP χ 0, mixing θ τ measurable from σ(e + e τ τ ) with beam polarization, polarisation of τ -lepton measurable and helps for model discrimination, µ, A τ and tan β can be determined from σ( τ τ) and τ polarisation H, A τ τ 2 decays give extra information (A τ measurement)... SUSY@ILC A. Djouadi p.4/25

15 2. Precision SUSY measurements: the Q sector Third generation Q = t, b possibly lightest squarks due to mixing In particular, t is in general the lightest squark (RGE+mixing). Light stops needed in models with electroweak baryogenesis. Light stops are very difficult to detect at the LHC (large tt bkg) Q production at ILC: e + e t t / b b : via s channel γ,z exchange; e + e γ, Z Q Q t decays: if heavy, two body t tχ 0, bχ + otherwise multi body decays or loop induced t cχ 0 decays SUSY@ILC A. Djouadi p.5/25

16 2. Precision SUSY measurements: the Q sector Phenomenology of t and b similar to that of τ : masses and mixing obtained from production with e ± pol. ex: study of σ(e R e+ L, e L e+ R t t ) for t bχ ±, cχ 0 Top quark polarisation in t, b decays provides information ex: top polarization in e + L e R b b tχ + tχ + at 500GeV at TeV. cosθ t tanβ m t [GeV] P b tχ ± SUSY@ILC A. Djouadi p.6/25

17 2. Precision SUSY measurements: summary m [GeV] m] Comments χ ± simulation threshold scan, 00 fb χ ± estimate χ ± χ 2, spectra χ± 2 Zχ ±, W χ 0 χ combination of all methods χ simulation threshold scan χ 0 2χ 0 2, 00 fb χ spectra χ 0 3 Zχ 0,2, χ0 2,4χ 0 3, 750 GeV, > ab χ spectra χ 0 4 W χ ±, χ0 2,3χ 0 4, 750 GeV, > ab ẽ R e e threshold scan, 0 fb ẽ L e e threshold scan 20 fb ν e simulation energy spectrum, 500 GeV, 500 fb µ R simulation energy spectrum, 400 GeV, 200 fb µ L estimate threshold scan, 00 fb τ simulation energy spectra, 400 GeV, 200 fb τ estimate threshold scan, 60 fb t estimate b-jet spectrum, m min ( t ), TeV, ab SUSY@ILC A. Djouadi p.7/25

18 3. Determination of the SUSY parameters: Once m i, σ, P i are measured, determine the low energy SUSY parameters from inversion of the mass and cross section formulae: Chargino/neutralino system: M = Σ i m 2 M 2 χ 2 µ 2 2M 2 0 Z, M 2 =M W Σ [c2φr +c 2φL ] i µ =M W Σ+ [c2φr +c 2φL ], tan β = (+ )/( ) with = m 2 χ ± 2 m 2 χ ± 4M 2 W Sfermion system:, = (c 2φR c 2φL, Σ= m 2 χ ± 2 +m 2 χ ± 2M 2 W. m 2 f L,R = M 2 f L,R + M 2 Z cos 2β (I3 L,R Q f sin 2 θ W ) + m 2 f A f µ(tan β) 2If 3 = (m 2 f m 2 f 2 )/(2m f ) sin 2θ f Higgs system: Precise M h measurement: M 2 h = M2 Z cos 2β 2 + 3g2 log m2 t 2π 2 M 2 W m 2 t Φ τ τ 2, Φ χχ, ττ Φ, e + e t tφ, b bφ, χχφ,... m 4 t SUSY@ILC A. Djouadi p.8/25

19 3. Determination of SUSY parameters: summary In reality, life is more complicated than the tree-level results above: complete analysis with sophisticated programs: Sfittino, Sfitter,... LHC ILC LHC+ILC SPSa LHC+ILC SPSa tan β ±9. ±0.3 ±0.2 0 ±0.3 0 µ ±7.3 ±2.3 ± ±. 396 M A fixed ±0.9 ± ± A t ±9 ±2.7 ± ± M ±5.3 ±0. ± ± M 2 ±7.3 ±0.7 ± ± M 3 ±5 fixed ± ± M τl fixed ±.2 ± ± MẽL ±5. ±0.2 ± ± MẽR ±5.0 ±0.05 ± ± M Q3L ±0 ±4.4 ± ± M Q L ±3 fixed ± ± M dr ±20 fixed ± ± SUSY@ILC A. Djouadi p.9/25

20 3. Determination of SUSY parameters Once the low energy SUSY parameters have been obtained, try to determine the SUSY parameters at the very high scale (M GUT, M P ). pin down the model/susy breaking (msugra, AMSB, GMSB,..), determine the few fundamental unified parameters of the model. Example of msugra, using all previous measurements at LHC/ILC: SPSa LHC ILC LHC+ILC SPSa LHC+ILC m 0 00 ±4.0 ±0.09 ± m /2 250 ±.8 ±0.3 ± tan β 0 ±.3 ±0.4 ± A 0 00 ±3.8 ±4.43 ± The same type of analysis in other breaking schemes/models. To be absolutely sure: only with model dependent analyses at ILC. SUSY@ILC A. Djouadi p.20/25

21 3. Determination of SUSY parameters: One can check the fundamental assumptions at high (GUT) scale. For example: gaugino and scalar mass unification in msugra... /M i [GeV ] M 2 j [03 GeV 2 ] Q [GeV] Q [GeV] Or probe non universality, intermediate scales, extra matter, etc... SUSY@ILC A. Djouadi p.2/25

22 4. Connections to cosmology WMAP: the Univers is made by 25% of cold dark matter (CDM) Needs a WIMP. In MSSM, we have an ideal candidate: neutralino χ 0 Question: does χ 0 has the right cosmological relic density? WMAP: 0.09 Ω DM h at 99% CL PLANCK Ω DM h 2 2% A very challeging/important goal: predict Ω DM and check with Planck. Measure everything: masses, production cross sections and asymmetries, decay widths and BRs in sparticle and Higgs production Determine the couplings of these particles (in practice softs terms) when including RC and all experimental and theoretical errors... Inject all in Ω χ or σ ann and check if OK with WMAP or PLANCK If yes, Bingo! A great success of HEP and/plus COSMO If not, we have a problem: other sources? other cosmo scenario?... The high precision measurements at the ILC can achieve this goal. SUSY@ILC A. Djouadi p.22/25

23 4. Connections to cosmology Good DM regions in the msugra model: generically four regions m 0 No EWSB LCC2 m h, b sγ Focus Point Region LCC4 Funnel Region g 2 Bulk Region LCC LCC3 co Annihilation Region Charged LSP m /2 There are also other possible regions: the h pole region where χχ h bb, WW (light spectrum) the t χ 0 co-annihilation region (good for EW baryogenesis) SUSY@ILC A. Djouadi p.23/25

24 4. Connections to cosmology In SPSa, ILC does a very good job: O(%) determination of Ωh 2 [O(0%) at LHC] However, in many other cases, a less good job but far better than LHC. (improvements...). Point m 0 m tan β m 2 χ 0 ILC Ω χ h 2 ILC ( LHC LCC ± ± 0.24% (7.2%) LCC ± ± 7.6% (82%) LCC ± ± 8% (67%) LCC ± ± 9% (405%) More work is needed to match PLANCK... SUSY@ILC A. Djouadi p.24/25

25 5. Summary If SUSY is the solution to the SM pbs: SUSY particles should be light. Colored and non colored sparticles observable very soon at LHC. The ILC will be needed as it will provide very crucial information: very clean environment, large production rates with low backgrounds, tunable energy to perform threshold scans and increase rates, beam polarisation which allow to select various channels, additional options (e e, γγ, eγ) for complementgary studies, high precision analyses and a true probe of SUSY phenomena. Only coherent/combined analyses of LHC+ILC data will allow for: better/model independent reconstruction of low energy SUSY parameter connect weak-scale SUSY with more fundamental physics at GUT scale, provide input to predict the LSP density and connection with cosmology Here: gave illustration of ILC performance in msugra type MSSM, Many interesting analyses/physics can also be done in other scenarios. SUSY@ILC A. Djouadi p.25/25