SUSY-particle production at Hadron Colliders

Transcription

1 NRW Phänomenoloie-Treffen, Januar 2006 SUSY-particle production at Hadron Colliders Michael Krämer (RWTH Aachen) Basics of SUSY particle production at hadron colliders The calculation of SUSY-QCD corrections Work done in collaboration with W. Beenakker, R. Höpker, M. Klasen, T. Plehn, M. Spira, P.M. Zerwas Michael Krämer Pae 1 NRW Pänomenoloie-Treffen, Januar 2006

2 Introduction: Why Supersymmetrie? There are many ood reasons to study supersymmetric field theories and TeV-scale SUSY at colliders: SUSY is the uniue extension of the Lorentz-symmetry SUSY provides a solution to the hierarchy problem SUSY allows for aue couplin unification SUSY provides a dark matter candidate SUSY can enerate EWSB dynamically... Michael Krämer Pae 2 NRW Pänomenoloie-Treffen, Januar 2006

3 The Minimal Supersymmetric Standard Model The MSSM particle spectrum Gaue Bosons S = 1 Gauinos S = 1/2 luon, W ±, Z, γ luino, W, Z, γ Fermions S = 1/2 Sfermions S = 0 ( )( ul ν e ) L )( (ũl ν e ) L d L e L d L ẽ L u R, d R, e R His ( H 0 )( 2 H + 1 H2 H1 0 ) ( H 0 2 H 2 ũ R, d R, ẽ R Hisinos )( H + 1 H 0 1 ) Michael Krämer Pae 3 NRW Pänomenoloie-Treffen, Januar 2006

4 SUSY particle production at hadron colliders Michael Krämer Pae 4 NRW Pänomenoloie-Treffen, Januar 2006

5 SUSY particle production at hadron colliders In the MSSM one imposes a symmetry to avoid proton decay SUSY particles produced pairwise R = ( 1) 3B+L+2S { = +1 SM = 1 SUSY lihtest SUSY particle stable (dark matter candidate) Michael Krämer Pae 4 NRW Pänomenoloie-Treffen, Januar 2006

6 SUSY particle production at hadron colliders In the MSSM one imposes a symmetry to avoid proton decay SUSY particles produced pairwise R = ( 1) 3B+L+2S { = +1 SM = 1 SUSY lihtest SUSY particle stable (dark matter candidate) The interactions of MSSM particles are determined by aue symmetry and SUSY example: luon µ, a p, i no new couplin!, j suark suark = i s (T a ) ij (p + ) µ Michael Krämer Pae 4 NRW Pänomenoloie-Treffen, Januar 2006

7 SUSY particle production at hadron colliders In the MSSM one imposes a symmetry to avoid proton decay SUSY particles produced pairwise R = ( 1) 3B+L+2S { = +1 SM = 1 SUSY lihtest SUSY particle stable (dark matter candidate) The interactions of MSSM particles are determined by aue symmetry and SUSY example: luon µ, a p, i no new couplin!, j suark suark = i s (T a ) ij (p + ) µ SUSY particles should be produced copiously at hadron colliders throuh QCD processes, e.. Michael Krämer Pae 4 NRW Pänomenoloie-Treffen, Januar 2006

8 Suark and luino cross section at the LHC σ tot Tevatron LHC σ (nb) σ bbar σ jet (E T jet > s/20) σ W σ Z σ jet (E T jet > 100 GeV) events/sec for L = cm -2 s σ ttbar σ jet (E T jet > s/4) σ His (M H = 150 GeV) σ His (M H = 500 GeV) s (TeV) Michael Krämer Pae 5 NRW Pänomenoloie-Treffen, Januar 2006

9 Suark and luino cross section at the LHC σ tot Tevatron LHC σ (nb) σ bbar σ jet (E T jet > s/20) σ W σ Z σ jet (E T jet > 100 GeV) σ ttbar events/sec for L = cm -2 s -1 SUSY sinal: σ( + + ) 2 nb (M, 300 GeV) 10 8 suarks & luinos/year ( L = 30 fb 1 ) 10-4 σ jet (E T jet > s/4) σ His (M H = 150 GeV) σ His (M H = 500 GeV) s (TeV) Michael Krämer Pae 5 NRW Pänomenoloie-Treffen, Januar 2006

10 SUSY searches at hadron colliders Distinctive sinature due to cascade decays: multiple jets (and/or leptons) with lare amount of missin enery ~ ~ t ~ ~ t 1 ~ χ2 0 ~ l + ~ χ 1 ~ χ 1 0 l - l + t W W + ν l + b b Michael Krämer Pae 6 NRW Pänomenoloie-Treffen, Januar 2006

11 SUSY searches at hadron colliders Distinctive sinature due to cascade decays: multiple jets (and/or leptons) with lare amount of missin enery ~ ~ t ~ ~ t 1 ~ χ2 0 ~ l + ~ χ 1 ~ χ 1 0 l - l + t W W + ν l + b b LHC discovery reach for suarks and luinos: M, < 2.5 TeV Michael Krämer Pae 6 NRW Pänomenoloie-Treffen, Januar 2006

12 Current limits on sparticle masses ) DØ Run II Preliminary L=310 pb Suark Mass (GeV/c UA1 UA2 DØ IA CDF IB DØ IB DØ II χ +/- LEP2 ~ LEP2 l no msugra solution 100 LEP m( ~ )<m( χ1 ) Gluino Mass (GeV/c ) Michael Krämer Pae 7 NRW Pänomenoloie-Treffen, Januar 2006

13 Current limits on sparticle masses ) 2 Suark Mass (GeV/c DØ Run II Preliminary L=310 pb UA1 UA2 DØ IA LEP 1+2 CDF IB DØ IB DØ II 0 m( ~ )<m( χ1 ) χ +/- LEP2 ~ LEP2 l no msugra solution Gluino Mass (GeV/c ) mass limits (rouhly) M M M luino M t 1 M χ 0 1 > 200 GeV > 300 GeV > 100 GeV > 50 GeV ± M χ 1 > 100 GeV M sleptons > 100 GeV Michael Krämer Pae 7 NRW Pänomenoloie-Treffen, Januar 2006

14 MSSM particle production at hadron colliders production dynamics P f P i i Q ˆσ Q j f P i P σ(pp/p p ) = dx 1 fi P (x 1, µ) dx 2 f P j (x 2, µ) σ(ij ) +O(Λ/M ) effective enery for (s)particle production ŝ = x1 x 2 s < s Michael Krämer Pae 8 NRW Pänomenoloie-Treffen, Januar 2006

15 MSSM particle production at hadron colliders Scale dependence σ = dx 1 fi P (x 1, µ F ) dx 2 f P j (x 2, µ F ) n α n s (µ R ) C n (µ R, µ F ) finite order in perturbation theory artificial µ-dependence: dσ d ln µ 2 R N = αs n (µ R ) C n (µ R, µ F ) n=0 = O(α s (µ R ) N+1 ) scale dependence theoretical uncertainty due to HO corrections Michael Krämer Pae 9 NRW Pänomenoloie-Treffen, Januar 2006

16 MSSM particle production at hadron colliders σ = Scale dependence dx 1 fi P (x 1, µ F ) n α n s (µ R ) C n (µ R, µ F ) finite order in perturbation theory artificial µ-dependence: dσ d ln µ 2 R = N n=0 dx 2 f P j (x 2, µ F ) α n s (µ R ) C n (µ R, µ F ) = O(α s (µ R ) N+1 ) scale dependence theoretical uncertainty due to HO corrections Example: Stop-pair production at leadin order LO theoretical uncertainty > ± 100% at LO σ(pp t 1t 1 +X) [pb] s=14 TeV; m(t 1) = 200 GeV 1 µ/m(t 1) must include NLO corrections Michael Krämer Pae 9 NRW Pänomenoloie-Treffen, Januar 2006

17 MSSM particle production at hadron colliders MSSM sparticle pair production suarks & luinos pp/p p,, stops pp/p p t t auinos pp/p p χ 0 χ 0, χ ± χ 0, χ + χ sleptons pp/p p l l associated production pp/p p χ, χ Michael Krämer Pae 10 NRW Pänomenoloie-Treffen, Januar 2006

18 Top-suark production t L, t R mix to form mass states t 1, t 2 potentially small t 1 mass Michael Krämer Pae 11 NRW Pänomenoloie-Treffen, Januar 2006

19 Top-suark production t L, t R mix to form mass states t 1, t 2 potentially small t 1 mass LO parton reations + t i + t i (i = 1, 2) t 1 t t 1 t 1 t t 1 Michael Krämer Pae 11 NRW Pänomenoloie-Treffen, Januar 2006

20 Top-suark production t L, t R mix to form mass states t 1, t 2 potentially small t 1 mass LO parton reations + t i + t i (i = 1, 2) t 1 t t 1 t 1 t t 1 ˆσ LO [ ] = α2 sπ s 2 27 β3 (β 2 = 1 4m 2 /s) c.f. top production: ˆσ LO[ ] α2 s π s σ top /σ stop 10 at the Tevatron β Michael Krämer Pae 11 NRW Pänomenoloie-Treffen, Januar 2006

21 Top-suark production t L, t R mix to form mass states t 1, t 2 potentially small t 1 mass LO parton reations + t i + t i (i = 1, 2) t 1 t t 1 t 1 t t 1 ˆσ LO [ ] = α2 sπ s 2 27 β3 (β 2 = 1 4m 2 /s) c.f. top production: ˆσ LO[ ] α2 s π s σ top /σ stop 10 at the Tevatron β + ḡ t i + t i (i = 1, 2) ˆσ LO [] = α2 sπ s [ β ( ) ( m2 2m s 3s ) ] + m4 lo 1 β 6s β no MSSM parameter dependence Michael Krämer Pae 11 NRW Pänomenoloie-Treffen, Januar 2006

22 SUSY-QCD corrections self eneries: + vertex corrections: + box diarams: + + luon emission: + luon-uark scatterin: + Michael Krämer Pae 12 NRW Pänomenoloie-Treffen, Januar 2006

23 SUSY-QCD corrections self eneries: + NLO cross section depends on suark & luino masses stop mixin anle vertex corrections: + dependence numerically small box diarams: + + luon emission: + luon-uark scatterin: + Michael Krämer Pae 12 NRW Pänomenoloie-Treffen, Januar 2006

24 SUSY-QCD corrections self eneries: + vertex corrections: + NLO cross section depends on suark & luino masses stop mixin anle dependence numerically small NLO cross section near threshold β 1: box diarams: + + σ α2 s (µ2 ) m 2 π 54 β3 ( 1 + 4πα s (µ 2 ) { 1 48β + 2 3π 2 ln2 (8β 2 ) π 2 ln(8β2 ) 2 3π 2 ln(8β2 ) ln ( µ 2 m 2 ) }) luon emission: + luon-uark scatterin: + σ α2 s (µ2 ) m 2 7π 384 β ( 1 + 4πα s (µ 2 ) { β + 3 2π 2 ln2 (8β 2 ) π 2 ln(8β2 ) 2 3π 2 ln(8β2 ) ln ( µ 2 m 2 )}) lare NLO corrections in channel Michael Krämer Pae 12 NRW Pänomenoloie-Treffen, Januar 2006

25 SUSY-QCD corrections: results Michael Krämer Pae 13 NRW Pänomenoloie-Treffen, Januar 2006

26 SUSY-QCD corrections: results reduced scale dependence < 15% LO (Beenakker, MK, Plehn, Spira, Zerwas) σ(pp t 1t 1 +X) [pb] s=2 TeV; m(t 1) = 200 GeV 0.3 NLO µ/m(t 1) Michael Krämer Pae 13 NRW Pänomenoloie-Treffen, Januar 2006

27 SUSY-QCD corrections: results reduced scale dependence < 15% K-faktor K = σ(nlo)/σ(lo) (Beenakker, MK, Plehn, Spira, Zerwas) 1.7 (Beenakker, MK, Plehn, Spira, Zerwas) LO σ(pp t 1t 1 +X) [pb] s=2 TeV; m(t 1) = 200 GeV pp/pp t 1t 1 +X K = σ(nlo)/σ(lo) LHC NLO Tevatron ( s=2 TeV) µ/m(t 1) m(t 1) Michael Krämer Pae 13 NRW Pänomenoloie-Treffen, Januar 2006

28 Top-suark production: NLO cross sections Tevatron LHC m(t 1) [GeV] m(t 1) [GeV] pp t t + X σ tot [pb] S = 1.8 TeV t 1t 1 10 pp t t + X σ tot [pb] S = 14 TeV t 1t NLO : µ = m(t ) µ = [ m(t )/2, m(t ), 2m(t ) ] LO : µ = m(t ) m(t 2) [GeV] t 2t 2 NLO : µ = m(t ) µ = [ m(t )/2, m(t ), 2m(t ) ] LO : µ = m(t ) m(t 2) [GeV] t 2t 2 small dependence on SUSY-Parameters Michael Krämer Pae 14 NRW Pänomenoloie-Treffen, Januar 2006

29 Top-suark searches Top-suark search in e ± e ± + 2j final startes (CDF, Phys. Rev. Lett. 83 (1999)) σ(pp t 1t 1 + X) BR(t 1 t 1 ee + 2j) [pb] 1 σ : µ=[m(t )/2, 2m(t )] NLO σ LO : µ=[m(t )/2, 2m(t )] CDF 95% C.L. upper limit (prel.) m(χ o )=m(t 1)/2 1 M LO M NLO m(t 1) [GeV] M t1 > 110 ± 15 GeV LO 120 ± 5 GeV NLO Michael Krämer Pae 15 NRW Pänomenoloie-Treffen, Januar 2006

30 Current project: associated pp/p p χ, χ production Michael Krämer Pae 16 NRW Pänomenoloie-Treffen, Januar 2006

31 Current project: associated pp/p p χ, χ production semi-weak process, but χs are liht in most models Michael Krämer Pae 16 NRW Pänomenoloie-Treffen, Januar 2006

32 Current project: associated pp/p p χ, χ production semi-weak process, but χs are liht in most models χ pp/p p χ Beenakker, MK, Plehn, Spira, Zerwas; Berer, Klasen, Tait Michael Krämer Pae 16 NRW Pänomenoloie-Treffen, Januar 2006

33 Current project: associated pp/p p χ, χ production semi-weak process, but χs are liht in most models χ pp/p p χ Beenakker, MK, Plehn, Spira, Zerwas; Berer, Klasen, Tait χ pp/p p χ LO scale uncertainty O(100%) need NLO calculation Michael Krämer Pae 16 NRW Pänomenoloie-Treffen, Januar 2006

34 SUSY-QCD corrections + + χ + χ + Michael Krämer Pae 17 NRW Pänomenoloie-Treffen, Januar 2006

35 SUSY-QCD corrections + + SUSY breakin in dimensional reularization, χ: 2 d.o.f., γ, Z: (n 2) d.o.f. restauration throuh finite counter terms χ + χ + Michael Krämer Pae 17 NRW Pänomenoloie-Treffen, Januar 2006

36 SUSY-QCD corrections + SUSY breakin in dimensional reularization, χ: 2 d.o.f., γ, Z: (n 2) d.o.f. + restauration throuh finite counter terms χ + double countin: χ (if m > m χ ) dσ res dm 2 = σ( ) m Γ /π (M 2 m 2 )2 + m2 Γ2 BR( χ ) χ σ( )BR( χ )δ(m 2 m 2 ) + resonance contributions to be subtracted Michael Krämer Pae 17 NRW Pänomenoloie-Treffen, Januar 2006

37 SUSY-QCD corrections: preliminary results reduced scale dependence Tevatron LHC 0.08 Beenakker, MK, Plehn, Spira, Zerwas 0.5 Beenakker, MK, Plehn, Spira, Zerwas preliminary σ(pp _ ~ χ 2 +X)[pb] s = 1.96 TeV CTEQ5M preliminary σ(pp ~ χ 2 +X)[pb] s = 14 TeV CTEQ5M NLO 0.03 NLO LO 0.15 LO Q/m Q/m Michael Krämer Pae 18 NRW Pänomenoloie-Treffen, Januar 2006

38 Summary NLO SUSY-QCD corrections for MSSM particle production at hadron colliders public code PROSPINO (Beenakker, MK, Plehn, Spira, Zerwas) Michael Krämer Pae 19 NRW Pänomenoloie-Treffen, Januar 2006

39 Summary NLO SUSY-QCD corrections for MSSM particle production at hadron colliders public code PROSPINO (Beenakker, MK, Plehn, Spira, Zerwas) χ o + 2 χ 1 σ tot [pb]: pp,, t 1t 1, χ 2 o χ + 1, ν ν, χ o 2, χ o 2 ν ν t 1t 1 χ o 2 χ o S = 14 TeV NLO LO m [GeV] Michael Krämer Pae 19 NRW Pänomenoloie-Treffen, Januar 2006