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1 Production of Supersymmetric Particles at High-Energy Colliders Tilman Plehn { Search for the MSSM { Production of Neutralinos/Charginos { Stop Mixing { Production of Stops { R Parity violating Squarks { Conclusions and Outlook

2 Introduction to the MSSM Supersymmetric extension of Standard Model:? fermion{boson mapping! stable scalar masses m m g ~ M M EW + g log EW P? unication of gauge couplings! prediction of weak mixing angle? possible extension to supergravity and string models Particle Content: spin charge d.o.f. light quark q L ; q R / /3, /3 + squark ~q L ; ~q R /3, /3 + 5 avors top quark t L ; t R / /3 + top squark ~t L ; ~t R /3 + mixing gluon G n! d.o.f. gluino ~g / Majorana gauge bosons ; Z +3 Higgs bosons h o ; H o ; A o 3 neutralinos ~ o i / 4 Majorana gauge bosons W 3 Higgs bosons H charginos ~ i / 4 Dirac

3 Supersymmetry Breaking Mass dierence between supersymmetric partners! soft SUSY breaking leaves masses stable: L soft = (m ) ijc i C j At a given scale: (m =) j j j + h:c: 6 A ijkc i C j C k + BH H + h:c: { scalar masses m for squarks and sleptons; chosen real { gaugino masses m = { trilinear couplings A ijk ; conserving R charge { complex Higgs mass parameter B Universality at unication scale and ew. symmetry breaking:! 4 / free parameters m ; m = ; A ; tan ; sign() t sin(θ ) q m o m/ g 3 m o m/ m o m/ o χ 3 m o m/ m o m/ + χ 3 m o m/

4 Mass Spectrum m[gev] /5/3/4/+ h o χ o χ o χ o 3 χ o 4 χ + + χ g t t q A t µ B ~ W ~ Typical features:? light gauginos [m ~ B ; m ~ W jj; m Z inducing mixing] m ~B m Z s w c m Z s w s m ~W m Z c w c m z c w s m Z s w c m Z c w c m Z s w s m Z c w s C A? heavy gluino [gauge coupling unication] m ~B :4 m =? light mixing stop [m t in o-diagonal m Q + m t + 3 s w m Z c m t (A t + cot ) m t (A t + cot ) m U + m t + 3 s wm Zc m ~W :8 m = m ~g :6 m = A? heavy squark [approximate solution] m ~q & :85m ~g

5 Tevatron Searches squarks/gluinos ~q! q ~ j; q ~ + j! jets + =E T [+] + ~g! qq ~ j; q q ~ +! jets + =E j T [+] + gluinos ~g! q q ~ +! jets + =E j T + ` CDF Preliminary! like-sign leptons neutralinos/charginos ~ + ~! ` ~ ``~! ``` + =E T + ± χ σ Br(χ 3l + X) (pb) CDF Preliminary L dt = 7 pb - Baer et al., PRD 47, 739 (993) tan β =, µ = - GeV/c Isajet 7. + CTEQ 3l 95% C.L. Upper Limit stops! trileptons - M(q ) = M(g ) M(q ) =. M(g ) M(q ) =.5 M(g ) M(χ ± ) (GeV/c ) 95% Exclusion Limit on t ~ cχ~ o ~t! c~ M t ~ <M χ ~ +m c ~ Θ t = 8! mixing angle in BR χ ~ o (GeV) 5 4 ~ Θ t = 56 3 D? all limits strongly dependent on cascade decays complete set of possible decays necessary M t ~ >M χ ~ +m b +M W ~ t supergravity or gauge mediation scenarios only for rst guess

6 Neutralino/Chargino Production Leading order cross section: q γ,z χ i χ j q d^ dt " qq! ~ i ~ j = 4N c 4 C ss t i t j + u i u j sm i m j (s m Z ) 8 C st t i t j sm i m j u i u j sm i m j (s m Z )(t m ~q ) 8 C st (s m Z )(u m ~q ) + 4 C tu ti t j (t m ~q ) + u i u j (u m ~q ) sm i m j (t m ~q )(u m ~q ) # Neutralino production mechanism { s channel [Drell{Yan like] Z ~ ~ coupling to higgsinos { t; u channel q~q ~ coupling to gauginos Next-to-leading order cross section:? Real/virtual SUSY-QCD corrections! factorization scale dependence bad measure for theoretical error! improvement of error bars : :! K N =! improvement of central value

7 Regularization and Supersymmetry Dimensional regularization breaks supersymmetry e.g. non-abelian gauge theory [Jack & Jones]: S L[W a ; a ; D] n!4!! preserved Ward Z identity contains S L = h d n x [J S W + j S + j D S D + S L]i! Dimensional Regularization can be rendered consistent with SUSY Yukawa coupling in supersymmetric limit: Y (qqh) = Y (~q~qh) + g 6 C(r) = Y (q~q h) ~ + 3g 3 C(r) dierent behavior of scalar and fermion masses Y mg m q = + g 6 C(r) m ~q! g MS g(qqh) = g(~q~qh) = g(q~q ~ h) + g 3 C(r) q q? dierence removed by nite 'renormalization' [Martin & Vaughn]? check by comparison of Green's functions with dimensional reduction

8 On-Shell Singularities N ~~ production includes G F s: gq! ~q i! q j i gq! ~q i BR(~q! q j ) pair production associated production via g q (M ) q χ jo () Possible inclusion of nite widths: { double counting of pair and associated production { breaking of gauge invariance of without { dependence on unknown physical widths () Splitting into on-shell and o-shell squark: d dm = (gq! ~q i) m ~q ~q = (M m ~q ) + m ~q ~q BR (~q! q j ) + O! (gq! ~q i ) BR (~q! q j ) (M m ~q ) + O { cross section in narrow widths approximation M m ~q M m ~q? divergences removed from? treatment compatible with experimental Monte-Carlos

9 Production Cross Sections Only ~ ~ and ~ ~+ visible at the Tevatron Whole set of processes at the LHC [ higgsino cross sections suppressed ] m(χ + ) σ tot [pb]: pp χ iχ j S = TeV N - χ o χ o χ o χ ± χ + χ - -3 χ o χ o m [GeV] m(χ o ) m(χ o ) m(χ + ) σ tot [pb]: pp χ iχ j S = 4 TeV - χ o χ o N χ o χ + χ o χ - χ o χ o. χ + χ m [GeV] m(χ o ) m(χ o ) N scale dependence good measure for theoretical uncertainty σ[pb]: pp χ o χ + +X s=4 TeV N N σ[pb]: pp χ o χ + +X s= TeV µ/m(χ ) General [mass independent] K factor for all LHC processes, but huge eects due to destructive interference 3 3 ~ ~ ~ ~ ~ 3 ~ ~ ~ ~ ~ ~ 4 ~ ~ 4 ~ ~ 3 ~ 3 ~ 4 ~ + ~ 3 ~ 3 ~ ~ + ~ 4 ~ 4 ~ + ~ K LHC ~ ~+ ~ ~ 3 ~+ ~ ~+ ~ ~+ ~ 4 ~+ ~ 3 ~+ ~ ~ ~+ ~ ~ ~ 4 ~+ ~ ~ 3 ~ ~ ~ ~ ~ ~ 4 ~ ~ 3 ~ ~ 4 K LHC

10 Stop Production Leading order cross section: qq=gg! ~t ~t ~t ~t [~t ~t ~t ~t ] t j q ^ [qq! ~t j ~ t j ] = s s ^ [gg! ~t j ~ t j ] = s s 7 3 (! 5 3m 48 + ~tj + 4s m ~ tj 3s + m4 ~tj 6s! log ) + { diagonal cross section function of nal state mass { factor =(n f ) compared to light-avor squarks { t; u channel gluino exchange missing compared to light-avor squarks { non-diagonal production via one loop amplitude; calculated for decoupled gluinos! suppressed ^ = 4 s sin (4 ~ ) 56s m ~ t C (s; m ~t ) (~t! ~t ) t t Next-to-leading order cross section? cross section strongly dependent on renormalization/factorization scale! large theoretical uncertainty? N dependence on additional mixing and mass parameters?

11 MSSM Stop Mixing stop mass matrix diagonalized by ~ N contribution ij = ji : t j t i t g g Mixing absorbed into wave function renormalization: ~t ; = Z = ~t ; = Z = D R( ~ ) = Z = D h R( ~ ) ~t R;Li R( ~ ~ ) ~t R;L with = T [CP ] written as propagator diagonalization: D ren (Q ) Z = D R( ~ ~ ) Q M LR Re (Q ) R( ~ ~ ) Z =! ~ (Q ) = Re (Q )=(m ~ t m ~ t )! ~ (Q ) ~ (Q ) / cos(~ ) m ~ t m ~ t Re h i B(Q ; m ~g ; m t ) B(Q ; m ~g ; m t ) D T Virtual stop state! complex continuation Running mixing angle: t t j t? symmetry ~t $ ~t restored? possible measurements in decays -.5? numerical dierence between schemes small Bartl et al., Djouadi et al. -. θ ~ (Q)/θ ~ (m ) t 6 8 Q [GeV]

12 Production Cross Section N cross section almost independent of additional parameters! ~t and ~t the same! no dependence on SUSY scenario [however: cascade decays] m(t ) [GeV] pp t t + X t t - σ tot [pb] S = TeV - -3 t t N : µ=m(t ) µ=[m(t )/, m(t )] : µ=m(t ) m(t ) [GeV] m(t ) [GeV] 3 pp t t + X σ tot [pb] S = 4 TeV t t t t N : µ=m(t ) µ=[m(t )/, m(t )] : µ=m(t ) m(t ) [GeV] Tevatron K factor strongly mass dependent due to fraction of incoming quarks/gluons Scale dependence strongly reduced in N! improvement of mass bounds not only for K > LHC σ ij /σ: pp/pp t t +X gg qq Tevatron gg.. qq m(t ) [GeV] 9 σ[pb]: pp t t +X s=4 TeV N N σ[pb]: pp t t +X s= TeV..4 4 µ/m(t ) σ tot [pb]: pp t t + X s= TeV - N: µ=[m(t )/, m(t )] : µ=[m(t )/, m(t )] m(t ) [GeV]

13 Addendum: R Parity violating Squarks Soft SUSY breaking! three-scalar interaction! leptoquark-like supereld couplings LQD! R = ( ) 3B+L+S conservation Broken R parity: eq! ~q HERA production q q=gg! ~q~q Tevatron production K[eq q +X] d { soft breaking coupling parameter free [running] { SU(3) gauge couplings xed as for stop! QCD corrections to HERA process and Tevatron cross section xed -.5. u.5 s = 3 GeV. µ = m(q ) s.5 CTEQ3M m(q ) [GeV] σ[pb]: pp q +q +X s= TeV N : µ=m(q ) µ=[m(q )/, m(q )] : µ=m(q ) Combined analysis of BR(~q! eq): m(q )[GeV] m ~q = GeV e + d! ~c e + d! ~t e + s! ~t HERA: p BR :7 :5 :5 :33 :5 :5 APV:. :55. :55 LEP:. :6 BR & : :4 BR & : :4 BR & :5 : Tevatron: BR BR. :5 :7 BR. :5 :7 BR. :5 :7! heavy gauginos! heavy gauginos

14 Conclusions and Outlook Processes in next-to-leading order SUSY QCD: Stop cross sections at hadron colliders Neutralino/Chargino cross sections at hadron colliders Results:? QCD corrections to stop cross sections between % and +5%? QCD corrections to neutralino/chargino cross sections around +3% [up to interference eects]? Scale dependence small in N Conclusions & Outlook:? N stop cross sections only mildly dependent on mixing angle and internal masses? Corrections to neutralino/chargino cross section non-negligiable and dependent on scenario =) N analyses at upgraded Tevatron and LHC

15 σ tot [pb]: pp g g, q q, t t, χ o + χ - S = TeV m(χ o ) = GeV m(t ) = 3 GeV m(q ) = 38 GeV m(g ) = 45 GeV q q - χ o χ + t t g g -3 N m [GeV] 3 σ tot [pb]: pp g g, q q, t t, χ o χ +, ẽ + L ẽ L N q q g g t t S = 4 TeV χ o + χ m(χ o ) = GeV m(ẽ L ) = 55 GeV m(t ) = 3 GeV m(q ) = 38 GeV - ẽ L ẽ L m(g ) = 45 GeV m [GeV]

16 5 CDF Preliminary

17 3l + X) (pb) ± χ σ Br(χ CDF Preliminary L dt = 7 pb - Baer et al., PRD 47, 739 (993) tan β =, µ = - GeV/c Isajet 7. + CTEQ 3l 95% C.L. Upper Limit - M(q ) = M(g ) M(q ) =. M(g ) M(q ) =.5 M(g ) M(χ ± ) (GeV/c )

18 M neutralino (GeV/c ) Search for Scalar Top BR (t c + χ ) = % Θ stop = for LEP D/ 7.4 pb - ) M(t )=M(c)+M(χ LEP (ALEPH) CDF 95% CL excluded M(t )=M(b)+M(W)+M(χ M stop (GeV/c ) CDF Preliminary 88 pb - )

19 m(χ + ) σ tot [pb]: pp χ iχ j S = TeV - χ o o χ χ o ± χ χ + χ N - -3 χ o o χ -4 m [GeV] m(χ o ) m(χ o ) m(χ + ) σ tot [pb]: pp χ iχ j S = 4 TeV - χ o o χ N χ o + χ χ o χ - χ o o χ. χ + χ -3 m [GeV] m(χ o ) m(χ o )

20 N σ[pb]: pp χ o χ + +X s=4 TeV N σ[pb]: pp χ o χ + +X s= TeV µ/m(χ )

21 m(t ) [GeV] - pp t t + X σ tot [pb] S = TeV t t N : µ=m(t ) µ=[m(t )/, m(t )] : µ=m(t ) m(t ) [GeV] t t m(t ) [GeV] 3 pp t t + X σ tot [pb] S = 4 TeV t t - N : µ=m(t ) µ=[m(t )/, m(t )] : µ=m(t ) m(t ) [GeV] t t

22 LHC σ ij /σ: pp/pp t t +X Tevatron gg qq gg qq m(t ) [GeV]

23 σ[pb]: pp t t +X s= TeV σ[pb]: pp t t +X s=4 TeV N N..4 4 µ/m(t ) σ tot [pb]: pp t t + X s= TeV - - N: µ=[m(t )/, m(t )] : µ=[m(t )/, m(t )] m(t ) [GeV]

24 K[eq q +X] d u.5..5 s = 3 GeV µ = m(q ) CTEQ3M s m(q ) [GeV] - σ[pb]: pp q +q +X s= TeV N : : µ=m(q ) µ=[m(q )/, m(q )] µ=m(q ) m(q )[GeV]