SUSY@ILC Abdelhak DJOUADI (LPT Orsay/Next Southampton) 1. Probing SUSY 2. Precision SUSY measurements at the ILC 3. Determining the SUSY Lagrangian 4. Summary From the physics chapter of the ILC Reference Design Report: “Physics at the ILC”, August 2007. ILC–Florence, 12/09/2007 SUSY@ILC – A. Djouadi – p.1/23
1. Introduction: motivations for low–energy SUSY If SUSY is to solve some of the most severe problems of the SM: We need light SUSY particles: M S < ∼ 1 TeV. • The hierarchy problem: radiative corrections to the Higgs masses � � � � �� � 1 λ 2 f N f M S ∆M 2 ( m 2 f − M 2 Λ + 3m 2 � H = S )log f log + O 4 π 2 Λ 2 M S m f • The unification problem: the slopes of the α i SM gauge couplings need to be fixed early enough to meet at M GUT ∼ 2 × 10 16 GeV. • The dark matter problem: the electrically neutral, weakly interacting, ∼ O ( 1 TeV) for Ωh 2 to match WMAP. stable LSP should have a mass < In this case, sparticles are accessible at future machines. – We expect great discoveries at the LHC. – We will have a great deal of exciting physics to do at the ILC. ILC–Florence, 12/09/2007 SUSY@ILC – A. Djouadi – p.2/23
1. Introduction: SUSY models Focus mainly on the Minimal Supersymmetric Standard Model (MSSM): • minimal gauge group: SU(3) × SU(2) × U(1), • minimal particle content: 3 fermion families and 2 Φ doublets, • R= ( − 1 ) ( 2s + L + 3B ) parity is conserved, • minimal set of terms (masses, couplings) breaking “softly” SUSY. To reduce the number of the (too many in general) free parameters: – impose phenomenological constraints: O (20) free parameters, – unified models, O(5) parameters (mSUGRA: m 0 , m 1 2 , A 0 , tan β, ǫ µ ), In this talk, I will concentrate on the MSSM with gravity mediated breaking. But, one should not forget that: -- other possibilities are models with GMSB/AMSB.... -- the impact of relaxing some MSSM basic assumptions can be large -- other scenarios are possible (strings, right–handed neutrinos,...) There is a need for model independent analyses... ILC–Florence, 12/09/2007 SUSY@ILC – A. Djouadi – p.3/23
1. Introduction: example of SUSY spectrum SPS1a’: m 1 / 2 = 250GeV , m 0 = 70GeV , A 0 = − 300GeV , tan β = 10 , µ> 700 SPS1a ′ mass spectrum m [GeV] ˜ g 600 ˜ t 2 q L ˜ ˜ b 2 ˜ q R ˜ b 1 500 H ± χ 0 ˜ H 0 , A 0 χ ± ˜ 4 400 χ 0 2 ˜ 3 ˜ t 1 300 ˜ 200 l L τ 2 ˜ χ 0 χ ± ˜ ˜ ν τ ˜ ν l ˜ 2 1 ˜ l R h 0 ˜ τ 1 100 χ 0 ˜ 1 0 χ 0 χ 0 χ ± ˜ ˜ p/ mass e 1 e 2 ν e τ 1 τ 2 ν τ t 1 b 1 ˜ ˜ ˜ ˜ ˜ ˜ ˜ 1 2 1 SPS1a ′ 98 184 184 125 190 172 108 195 170 366 506 96 177 176 143 202 186 133 206 185 379 492 SPS1a ILC–Florence, 12/09/2007 SUSY@ILC – A. Djouadi – p.4/23
1. Introduction: probing SUSY All these particles will be produced at the LHC (direct/cascades)... These particles can also be produced directly at the ILC... But producing these new states is not the whole story! We need to: • 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 relic density. To achieve this goal, a combination of LHC and ILC is mandatory! ILC–Florence, 12/09/2007 SUSY@ILC – A. Djouadi – p.5/23
1. Introduction: the role of the ILC At the LHC: – copious ˜ q/ ˜ g production σ + - (e e ) [fb] 100000 – ˜ ff ℓ/χ from cascades – complicated topologies 10000 WW – very large backgrounds ZZ 1000 – difficult environment. tt HZ At the ILC: 100 – direct ˜ ℓ/χ production + - 10 χ χ + - µ µ 1 1 – large production rates 1 1 t 1 t 1 0 χ χ 0 1 – good signal to bkg ratios 1 2 s[GeV] – very clean environment 0.1 200 350 500 1000 – possibility of tuning energy – initial beam polarization – more collider options... ILC–Florence, 12/09/2007 SUSY@ILC – A. Djouadi – p.6/23
2. Precision SUSY measurements: the χ sector • Charginos: mixtures of the charged higgsinos and gauginos W ± , ˜ ˜ h ± → χ ± 1 , χ ± 2 / 1 − 2 The general chargino mass matrix, in terms of M 2 , µ and tan β , is √ M 2 2 M W s β , s β ≡ sin β etc M C = √ 2 M W c β µ • Neutralinos: mixtures of the neutral higgsinos and gauginos B , ˜ ˜ W 3 , ˜ 1 , ˜ H 0 H 0 → χ 0 2 − 1 , 2 , 3 , 4 The 4x4 mass matrix depends on µ, M 2 , tan β, M 1 ; given by: M 1 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 N = − 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 ILC–Florence, 12/09/2007 SUSY@ILC – A. Djouadi – p.7/23
2. Precision SUSY measurements: the χ sector χ i e + χ production: χ i e + Z ( γ ) ˜ ℓ χ j e − χ j e − • 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 ˜ e ; σ = O (10 fb). – e ± beam polarization selects various production channels – cross section for χ ± rises steeply near threshold, σ ∝ β – cross sections for χ 0 rise less steeply in general, σ ∝ β 3 χ decays: - in general χ i → V χ j , Φ χ j , f˜ f - possibility of cascade decays E T from escaping χ 0 – signature: / 1 ILC–Florence, 12/09/2007 SUSY@ILC – A. Djouadi – p.8/23
2. Precision SUSY measurements: the χ sector Measurement of χ ± /χ 0 masses: • from a threshold scan, ∆m χ ± 1 ∼ 50 MeV 1 ∼ 200 GeV as steep rise σ ∝ β . for m χ ± • ∆m χ ± 1 ∼ 0 . 1 % in continuum from dijet mass in e + e − → χ + 1 χ − 1 → ℓ ± ν q¯ q ′ χ 0 1 χ 0 1 • from dijet mass, m χ 0 1 determination with precision ∆( m χ ± 1 − m χ 0 1 )= O (50) MeV. 1 , use e + e − → χ + 1 χ − • for small m χ ± 1 − m χ 0 1 γ to measure both m χ ± 1 /m χ 0 1 from spectra. • e + e − → χ 0 2 χ 0 1 → ℓ + ℓ − χ 0 1 χ 0 1 allows an accuracy ∆ ( m χ 0 2 − m χ 0 1 )= O ( 0 . 1 %) ILC–Florence, 12/09/2007 SUSY@ILC – A. Djouadi – p.9/23
2. Precision SUSY measurements: the χ sector Determination of spin: – idea from excitation curve and angular distribution from production, – sure with angular distributions of polarized χ decays with e ± pol . Determination of Majorana nature of neutralinos: – guess from β 3 threshold behavior of σ ( e + e − → χ 0 i χ 0 j ) , – e − e − → ˜ e − occurs only because Majorana χ 0 exchange. e − ˜ Verification of the SUSY identity of gauge/Yukawa couplings: – production cross sections for χ 0 , χ ± ∝ ˆ eχ 0 ) , ˆ νχ ± ) , g ( e ˜ g ( e ˜ g ′ = 0 . 2% – combing with ˜ ℓ production, ∆˜ g = 0 . 7% and ∆˜ Determination of the chargino/neutralino mixing angles: σ ( e + e − → χ + j ) is binomial in the χ ± mixing angles cos2 φ L , R i χ − → determined in a model independent way using polarized e ± beams (neutralino mixing from χ 0 production/decay, see Jan Kalinowski). ILC–Florence, 12/09/2007 SUSY@ILC – A. Djouadi – p.10/23
2. Precision SUSY measurements: the χ sector SPS1a: c 2 φ L =[ 0 . 62 , 0 . 72 ] , c 2 φ R =[ 0 . 87 , 0 . 91 ] at 95% CL at √ s = 1 2 TeV cos 2Φ R σ ± L ( 500 ) σ ± 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 10 TeV with polarization. – CPV: e + e − → χ 0 i χ 0 j would be needed (with direct probe of CPV). ILC–Florence, 12/09/2007 SUSY@ILC – A. Djouadi – p.11/23
2. Precision SUSY measurements: the ˜ f sector Sfermion system described by tan β, µ and 3 param.for each species: f L , m ˜ f R and A f . For 3d generation, mixing ∝ m f to be included. m ˜ m f A f − µ (tan β ) − 2 I 3 L m 2 f + m 2 f L +( I 3 L f − e f s 2 W ) M 2 Z c 2 β f ˜ M 2 f = ˜ m f A f − µ (tan β ) − 2 I 3 L m 2 f + m 2 f R + e f s 2 W M 2 Z c 2 β f ˜ 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 1 , ˜ f 2 . � � RR ) 2 + 4m 2 � m 2 f 1 , 2 = m 2 f + 1 m 2 LL + m 2 ( m 2 LL − m 2 f X 2 RR ∓ ˜ f 2 Note: mixing very strong in stop sector, X t = A t − µ cot β and generates mass splitting between ˜ t 1 , ˜ t 2 , leading to light ˜ t 1 ; mixing in sbottom/stau sectors also for large X b ,τ = A b ,τ − µ tan β . ILC–Florence, 12/09/2007 SUSY@ILC – A. Djouadi – p.12/23
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