Light Stop Bound State Production at the LHC. Yeo Woong Yoon (KIAS) In collaboration with P. Ko, Chul Kim at Yonsei U.

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1 Light Stop Bound State Production at the LHC Yeo Woong Yoon (KIAS) In collaboration with P. Ko, Chul Kim at Yonsei U.

2 Outline About stop Motivation for light stop Phenomenology Formalism Summary

3 About Stop Stop is Special SUSY e s μ c τ b b W Z W ± W 0 t t Large Yukawa coupling to Higgs 3

4 light Higgs mass in MSSM : Thanks to large Yukawa coupling, stop loop correction plays crucial role for Higgs mass to avoid LEP bound. 4

5 We are interested in light stop. m < m < m + m χ χ 0 t t 0 χ 0 LSP t NLSP t 5

6 Motivation RG evolution of stop Large Yukawa coupling 6 CMSSM m0>>m/

7 Motivation Stop mixing m ma ma LL t t * t t mrr Mixing term is large due to large Yukawa coupling ( LL RR ( LL RR ) 4 t f ) m = m + m m m + ma, t Mass difference becomes bigger than before. 7

8 Motivation 3 DM relic density Neutralino LSP is one of the favorite DM candidate DM relic density : Ω = ± nbmh DM is decoupled out of equilibrium at T < T f, the abundance remains. 8 DM relic density can be obtained by solving Boltzmann eq.: dn dt ( ) = Hn n n n 3 σ eq DM in Abell 689, Image credit:hst

9 Coannihilation processes Griest, Seckel (9 ) If LSP-NLSP mass splitting is small The NLSP density is as abundant as LSP density Thus, coannihlation with NLSP play significant role for DM relic density. The Boltzmann equation is 9

10 When light stop is NLSP with small mass difference from LSP Coannihilation processes: 0. <Ω h < DM 0. GeV < δ m < 33GeV 0 Boehm, Djouadi, Drees (00 )

11 Motivation 4 EW Baryogenesis Baryon Asymmetry of Universe : Sakharov s 3 condition (967) n b n s b = (8.9 ± 0.4) 0 Senaha s talk, at KIAS Baryon Number Violation C and CP violation Out of Equilibrium Sphaleron process CPV in SM st order EW phase transition 3 λt 4 Veff D( T T0 ) v ETv + v 4 SM EWBG fails mh 48GeV 3 3 m In MSSM Veff y Tv + yv for large y and small m 3/ Light stop

12 LEP search m < m < m + m χ t 0 0 t χ M t > 9GeV ALEPH, PLB 537 (00) 5

13 CDF search m < m < m + m χ t 0 0 t χ LHC will cover this region CDF

14 Phenomenology Stop pair production 4

15 Near threshold region N N p p t soft soft t z M = = ε sˆ ε 0 threshold region soft soft p β = = sˆˆ sˆ ( m t ) ε Large logarithm ln β Nonrelativistic regime Form stop bound state Stoponium s 5

16 Stop decays We consider following kinematics: t is NLSP 0 χ Is LSP mt 0 < mt + m χ m < m + m + m t 0 W χ Possible decays are - body 4 - body b t t b 0 χ W 0 t χ 6

17 Hikasa, Kobayashi, (87 ) Γ( t c ) = e m m ~ () ev 0 0 χ χ α c t mt loop function ~ 0^(-4) tt bound state can be described by Shroedinger eq. from pnrqcd p = ψ + m C (0) Fαs V () r = r (0) () r i 0 V () r corrections ψ() r Binding Energy : ~ () GeV B.E. = mc t Fαs( mv t ) Γ( t ) Γ m bl νχ t = (0.0 ~ 0.) 0 4 ( t c χ) m χ ml : negligible L Γ( t ) B.E. It will form stop bound state before decay. 7

18 Formalism SCET (Soft Collinear Effective Theory) Example: Consider Heavy to light decay n p set order parameter λ = m p = n p n + n pn + p µ µ µ µ for decaying quark: λ w.r.t. mb n-collinear field n p~, n p~, p ~ λ b b p µ = ( λ,, λ) p µ = (, λ, λ) p µ ( n p, n p, p ) = ( λλλ,, ) sγ p µ = ( λ, λ, λ ) n n µ = (,0,0,) n µ = (,0,0, ) n-collinear n-collinear Soft Ultra Soft n 8

19 Integrate out Hard interaction region +perm = S +perm = W n ( ) n ( x ) s x W ( x) = P exp ig ds n A ( sn) n S( x) = P exp ig ds n A ( sn) J µ = ψ µ sγ ψ b J = CP (, µξ ) WΓ S h µ µ eff n n v 9 SU(3) gauge transformation J µ eff Collinear gauge transformation Soft gauge transformation Usoft gauge transformation is Collinear, soft gauge invariant SCET operator usoft term is decoupled from the operator. It reproduces all the Infra-Red nature of full theory.

20 We do for given process Construct gauge invariant SCET operators. Typical coll. gauge invariant n collinear field: χ = W ξ, n n n σ = H J S B = nw G W µ µν n ν n n n Derive Factorization formula H : J : S : Hard scattering function process dependant Jet function universal Soft function universal Calculate each perturbative functions. Use RGE Large Log resummation can be automatically performed 0

21 Effective Operator: µ,a c ν,b d incoming color state: 8 8 = 8S 8A outgoing color state: 3 3= 8 Effective Opeartor: R f = C ( µ ) m= ( Ri, Rf ) { (,), (8 S,8), (8 A,8) } eff 3 m m mt m µ + ( ) ( µ ) ( ) ( ) ( m) a b * c * d m = Eabcd n n n n v v v v ( ρν ) ( x) = in g G ( x) : n-collinear gauge invariant gluon field a, µ ρ µν ba b n, n n, v ( x ) s ( x ) n ( x) = P exp ig ds v A ( sv) : soft Wilson lines ( v = nnv,, ) ab c cab ( x) = P exp ig ds n A ( sn) : collinear Wilson line in adjoint Rep. n R i

22 Factorization formula: N N dσ ( NN ttx ) = dπ ttx NN ttx eff s X = dπ NN O O NN s tt eff k k eff dσ ( NN ttx ) = H PDF J H S PDF Hard (H) PDF Coulomb Interaction (J) Soft (S)

23 Hard function : HM (, µ )= CM (, µ ) matching + many more We are working on NLO hard function 3

24 Soft function : Beneke, Falgari, Schwinn (00 ) s S(, ), ( z, µ ) = δ ( z) + α ( C C ) A( z, µ ) CB( z, µ ) π + + I I F I I F Idilbi, Chul Kim, Mehen (0 ) By running S( z, µ ) from µ S to we can resum the large logarithmic term ( α ln β) n NLO+NLL s µ F 4

25 Coulomb Interaction function : ψ R n ( x) is NR wave function 3 ( R, α ) R* d k R + a b On = Cα ab M ψ (k) (k) ( k) 3 n Sv Sv ( π ) Then + r s ( Rf, α) ( Rf, α) + * v * w v v k k v v 0 S S O O S S 0 = R * R R αrs Cαvw ψ k f f f MC (0) 5 k where R f k ψk = R δ( q M ) (0) Im G (0,0, E) f Mπ ψ ψ GR ( xx,, E) = x x = H E E E R k R R* k ( x) k ( x) α ( µ ) iµ G E C m f s R (0,0,, µ ) = R t + ln + ( κ) Beneke, f 4π κ mv t k

26 Summary Our GOAL is to predict resonance signal with high precision (NLO+NLL) for pp t t γγ, WW, ZZ ( ) dσ pp tt + ( γγ ) dσ pp S S 6 Kiyo, Kuhn, Moch, Steinhauser, Uwer (09 ) Idilbi, Chul Kim, Mehen (0 )

27 Summary Light stop is favored in both theory and phenomenology. Waiting for light stop search at the LHC. To be or not to be... SCET is powerful tool for describing the light stop bound state production near threshold region. NLO+NLL precision will be helpful for stop bound state search at the LHC. 7