Missing Energy (E/ T ) at the LHC: The Dark matter Connection

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1 Missing Energy (E/ T ) at the LHC: The Dark matter Connection Tao Han University of Wisconsin Madison at Cornell University (Sept. 25, 2009) (Collaborators: Ian-Woo Kim, J.H. Song)

2 Outline

3 Outline Missing Energy Events

4 Outline Missing Energy Events Missing Energy and New Physics at the LHC

5 Outline Missing Energy Events Missing Energy and New Physics at the LHC Determining the Dark Matter Mass

6 Outline Missing Energy Events Missing Energy and New Physics at the LHC Determining the Dark Matter Mass Antler Decay Kinematics

7 Outline Missing Energy Events Missing Energy and New Physics at the LHC Determining the Dark Matter Mass Antler Decay Kinematics Summary

8 Missing Energy Events Pauli s Neutron, Fermi s Neutrino

9 Missing Energy Events Pauli s Neutron, Fermi s Neutrino In β decay, the electron energy spectrum is continuous: KATRIN experiment: 3 H 3 He + + e + ν e (hep-ex/ ).

10 Missing Energy Events Pauli s Neutron, Fermi s Neutrino In β decay, the electron energy spectrum is continuous: For a 2-body decay, M ab, the kinetic energy of a: K a = (M m a) 2 m 2 b 2M. KATRIN experiment: 3 H 3 He + + e + ν e (hep-ex/ ).

11 Missing Energy Events Pauli s Neutron, Fermi s Neutrino In β decay, the electron energy spectrum is continuous: For a 2-body decay, M ab, the kinetic energy of a: K a = (M m a) 2 m 2 b 2M For a 3-body decay, M abc, the kinetic energy of a: 0 K a (M m a) 2 (m b + m c ) 2. 2M KATRIN experiment: 3 H 3 He + + e + ν e (hep-ex/ )..

12 Pauli in 1930: Although only p +, e detected, there is an undetected particle neutron.

13 Pauli in 1930: Although only p +, e detected, there is an undetected particle neutron. (Chadwick in 1932 discovered the neutron, then Irene and Frederic Joliot-Curie observed neutron+p + reaction.)

14 Pauli in 1930: Although only p +, e detected, there is an undetected particle neutron. (Chadwick in 1932 discovered the neutron, then Irene and Frederic Joliot-Curie observed neutron+p + reaction.) Fermi in 1934 renamed it neutrino, and formulated the weak interaction for n p + + e + ν e : L = G F ψ p ψ n ψ e ψ νe.

15 Pauli in 1930: Although only p +, e detected, there is an undetected particle neutron. (Chadwick in 1932 discovered the neutron, then Irene and Frederic Joliot-Curie observed neutron+p + reaction.) Fermi in 1934 renamed it neutrino, and formulated the weak interaction for n p + + e + ν e : L = G F ψ p ψ n ψ e ψ νe. The neutrino was the 1 st example for missing energy.

16 Pauli in 1930: Although only p +, e detected, there is an undetected particle neutron. (Chadwick in 1932 discovered the neutron, then Irene and Frederic Joliot-Curie observed neutron+p + reaction.) Fermi in 1934 renamed it neutrino, and formulated the weak interaction for n p + + e + ν e : L = G F ψ p ψ n ψ e ψ νe. The neutrino was the 1 st example for missing energy. The non-detectable nature introduced the 1 st dark matter. Though not certain to be the cosmic relic dark matter. Chadwick s neutron is NOT dark.

17 Pauli in 1930: Although only p +, e detected, there is an undetected particle neutron. (Chadwick in 1932 discovered the neutron, then Irene and Frederic Joliot-Curie observed neutron+p + reaction.) Fermi in 1934 renamed it neutrino, and formulated the weak interaction for n p + + e + ν e : L = G F ψ p ψ n ψ e ψ νe. The neutrino was the 1 st example for missing energy. The non-detectable nature introduced the 1 st dark matter. Though not certain to be the cosmic relic dark matter. Chadwick s neutron is NOT dark. Neutrinos were caught! Cowan-Reines in 1956: ν e + p e + + n. Lederman-Schwartz-Steinberger in 1962 (BNL): ν µ + Al µ + X. DODUT collaboration in 2000 (FNAL): c ν τ + target τ + X.

18 Pauli in 1930: Although only p +, e detected, there is an undetected particle neutron. (Chadwick in 1932 discovered the neutron, then Irene and Frederic Joliot-Curie observed neutron+p + reaction.) Fermi in 1934 renamed it neutrino, and formulated the weak interaction for n p + + e + ν e : L = G F ψ p ψ n ψ e ψ νe. The neutrino was the 1 st example for missing energy. The non-detectable nature introduced the 1 st dark matter. Though not certain to be the cosmic relic dark matter. Chadwick s neutron is NOT dark. Neutrinos were caught! Cowan-Reines in 1956: ν e + p e + + n. Lederman-Schwartz-Steinberger in 1962 (BNL): ν µ + Al µ + X. DODUT collaboration in 2000 (FNAL): c ν τ + target τ + X. Dark matter direct detection.

19 W ± and Missing Energy The discovery of W ± lν l (UA1/UA2 in 1983):

20 At the Tevatron Run II: Events Missing E T - W Candidate Data PMCS+QCD QCD bkg D0 Run II Preliminary MET(GeV)

21 At the Tevatron Run II: Events Missing E T - W Candidate Data PMCS+QCD QCD bkg D0 Run II Preliminary MET(GeV) The transverse momentum of ν or e has a Jacobian peak: p T = E sin θ, dˆσ Γ dm 2 W M W eν dp2 et (m 2 eν M2 W )2 + Γ 2 W M2 W m 2 eν 1 1 4p 2. et /m2 eν

22 Transverse mass variable W eν : m 2 eν T = (E et + E νt ) 2 ( p et + p νt ) 2 = 2E et ET miss (1 cos φ) m 2 eν. Events Transverse Mass - W Candidate Data PMCS+QCD QCD bkg D0 Run II Preliminary Events Missing E T - W Candidate Data PMCS+QCD QCD bkg D0 Run II Preliminary Transverse mass(gev) MET(GeV)

23 Transverse mass variable W eν : m 2 eν T = (E et + E νt ) 2 ( p et + p νt ) 2 = 2E et ET miss (1 cos φ) m 2 eν. Events Transverse Mass - W Candidate Data PMCS+QCD QCD bkg D0 Run II Preliminary Events Missing E T - W Candidate Data PMCS+QCD QCD bkg D0 Run II Preliminary Transverse mass(gev) MET(GeV) If p T (W) = 0, then: m eν T = 2E et = 2E miss T.

24 Transverse mass variable W eν : m 2 eν T = (E et + E νt ) 2 ( p et + p νt ) 2 = 2E et ET miss (1 cos φ) m 2 eν. Events Transverse Mass - W Candidate Data PMCS+QCD QCD bkg D0 Run II Preliminary Events Missing E T - W Candidate Data PMCS+QCD QCD bkg D0 Run II Preliminary Transverse mass(gev) If p T (W) = 0, then: m eν T = 2E et = 2E miss MET(GeV) T. If p T (W) 0 (some transverse motion δp V ), then: p et p et [1 + δp V /M V ], m 2 eν T m2 eν T [1 (δp V /M V ) 2 ], m 2 eν = m 2 eν.

25 SM prediction: Large(r) missing energy events at the Tevatron: Missing E T for Low Kinematic Region 3 10 Events / 10 GeV ) Data (2.0 fb Z νν + jets W τν + jets W µν + jets W eν + jets top quark production γ + jets QCD jet production ZZ, WW, WZ Z ττ + jets Z µµ + jets -1 CDF II Preliminary (2.0 fb ) Missing E T (GeV)

26 SM prediction: Large(r) missing energy events at the Tevatron: Missing E T for Low Kinematic Region 3 10 Events / 10 GeV ) Data (2.0 fb Z νν + jets W τν + jets W µν + jets W eν + jets top quark production γ + jets QCD jet production ZZ, WW, WZ Z ττ + jets Z µµ + jets -1 CDF II Preliminary (2.0 fb ) Missing E T (GeV) First SUSY bound: CDF with 25.3 nb 1 (!) (1989) No events found with E/ T > 40 GeV σ MSSM < 0.1 nb m g, m q > 80 GeV.

27 SM prediction: Large(r) missing energy events at the Tevatron: Missing E T for Low Kinematic Region 3 10 Events / 10 GeV ) Data (2.0 fb Z νν + jets W τν + jets W µν + jets W eν + jets top quark production γ + jets QCD jet production ZZ, WW, WZ Z ττ + jets Z µµ + jets -1 CDF II Preliminary (2.0 fb ) Missing E T (GeV) First SUSY bound: CDF with 25.3 nb 1 (!) (1989) No events found with E/ T > 40 GeV σ MSSM < 0.1 nb m g, m q > 80 GeV. Current SUSY bound: CDF with 2 fb 1 σ MSSM < 0.1 pb m g > 320 GeV, m q > 390 GeV.

28 At LEP I (L3): Neutrino counting: e + e γ + ν i ν i N ν 3. Missing energy events in e + e collisions

29 Missing Energy and New Physics at LHC New Physics Expectation in E/ T : M. Mangano, arxiv: [hep-ph].

30 Missing Energy and New Physics at LHC New Physics Expectation in E/ T : Setting a bound for mass scale may not be too hard. Establishing E/ T signal would be challenging, that would be a revolutionary discovery for BSM physics! M. Mangano, arxiv: [hep-ph].

31 It has been shown quite promising (msugra at ATLAS ) D. R. Tovey, Eur. Phys. J. C4, N4 (2002).

32 Steps to follow: Dark matter connection: LHC vs. Cosmology Discover missing-energy events at a collider and estimate the mass of the WIMP. Observe dark matter particles in direct detection experiments and determine whether their mass is the same as that observed in collider experiments. Baltz, Battaglia, Peskin and Wizansky, hep-ph/

33 Dark matter connection: LHC vs. Cosmology Steps to follow: Discover missing-energy events at a collider and estimate the mass of the WIMP. Observe dark matter particles in direct detection experiments and determine whether their mass is the same as that observed in collider experiments. Cosmic relic density: Ω χ h 2 1 σv m2 χ α 2. By crossing, χχ annihilation is related to scattering. Baltz, Battaglia, Peskin and Wizansky, hep-ph/

34 Dark matter connection: LHC vs. Cosmology Steps to follow: Discover missing-energy events at a collider and estimate the mass of the WIMP. Observe dark matter particles in direct detection experiments and determine whether their mass is the same as that observed in collider experiments. Cosmic relic density: Ω χ h 2 1 σv m2 χ α 2. By crossing, χχ annihilation is related to scattering. After that, Determine the qualitative physics model that leads to missing-energy events. Determine the parameters of this model that predict the relic density. Determine the parameters of this model that predict the direct and indirect detection cross sections. Measure products of cross sections and densities from astrophysical observations to reconstruct the density distribution of dark matter. Baltz, Battaglia, Peskin and Wizansky, hep-ph/

35 Optimistic conclusions were obtained for msugra and for MSSM parameter-determinations: msugra : tanβ=10, A 0 =0, µ>0, m t =171.4 GeV m 1/2 (TeV) m q = 3 TeV 4 TeV 4 TeV 1.4 m g = 3 TeV TeV 2 TeV TeV 0.5 TeV 1 TeV m 0 (TeV) 0 < Ωh 2 < < Ωh 2 < Excluded LEP2 For a review: Baer and Tata, arxiv: Baltz, Battaglia, Peskin and Wizansky, hep-ph/

36 Optimistic conclusions were obtained for msugra and for MSSM parameter-determinations: msugra : tanβ=10, A 0 =0, µ>0, m t =171.4 GeV m 1/2 (TeV) m q = 3 TeV 4 TeV 4 TeV 1.4 m g = 3 TeV TeV 2 TeV TeV 0.5 TeV 1 TeV m 0 (TeV) 0 < Ωh 2 < < Ωh 2 < Excluded LEP2 For most general cases, situations may be much more complex: The LHC inverse problem : Data many possible solutions! For a review: Baer and Tata, arxiv: Baltz, Battaglia, Peskin and Wizansky, hep-ph/ Akani-Hamed, Kane, Thaler and Wang, hep-ph/

37 Determining the Dark Matter Mass Model-independent approaches at colliders

38 The difficulties: Determining the Dark Matter Mass Model-independent approaches at colliders Two missing particles in each event; Unknown parton frame leads to less constrained kinematics.

39 Edges, End-points etc. Simple decay chain: l n l f Z Y X In general, m max ll = M Z M X (gives mass difference). If Y is also on-shell, m max ll = (MZ 2 M2 Y )(M2 Y M2 X )/M Y / 197 P P P Events/0.5 GeV/100 fb M ll (GeV) Bachacou, Hinchliffe and Paige, arxiv:hep-ph/

40 Longer decay chain: q l l q χ 0 2 l χ 0 1 Similarly, m max qll = (M 2 q M2 χ 2 )(M 2 χ 2 M 2 χ 1 )/M χ / 6 A A Events/20 GeV/100 fb M llq (GeV) Bachacou, Hinchliffe and Paige, arxiv:hep-ph/

41 Longer decay chain: q l l q χ 0 2 l χ 0 1 Similarly, m max qll = (M 2 q M2 χ 2 )(M 2 χ 2 M 2 χ 1 )/M χ / 6 A A Events/20 GeV/100 fb M llq (GeV) Only probe mass differences. May encounter combinatoric ambiguities. Bachacou, Hinchliffe and Paige, arxiv:hep-ph/

42 Kinematical on-shell conditions Fully Constructable Kinematics Cheng, Gunion, Z. Han and McElrath, arxiv:

43 Kinematical on-shell conditions Fully Constructable Kinematics Assume: n signal events: particles 3,5,7; 4,6,8 observed; 1, 2 missing. Unknowns: masses N, X, Y, Z (4); 4-momenta of 1, 2 (8n) 4 + 8n. Cheng, Gunion, Z. Han and McElrath, arxiv:

44 Kinematical on-shell conditions Fully Constructable Kinematics Assume: n signal events: particles 3,5,7; 4,6,8 observed; 1, 2 missing. Unknowns: masses N, X, Y, Z (4); 4-momenta of 1, 2 (8n) 4 + 8n. Constraints: missing transverse momenta (x,y): 2n. on-shell conditions (both chains) 8n. Total 10n. Cheng, Gunion, Z. Han and McElrath, arxiv:

45 Kinematical on-shell conditions Fully Constructable Kinematics Assume: n signal events: particles 3,5,7; 4,6,8 observed; 1, 2 missing. Unknowns: masses N, X, Y, Z (4); 4-momenta of 1, 2 (8n) 4 + 8n. Constraints: missing transverse momenta (x,y): 2n. on-shell conditions (both chains) 8n. Total 10n. Let constraints unknowns n 2. Cheng, Gunion, Z. Han and McElrath, arxiv:

46 Kinematical on-shell conditions Fully Constructable Kinematics Assume: n signal events: particles 3,5,7; 4,6,8 observed; 1, 2 missing. Unknowns: masses N, X, Y, Z (4); 4-momenta of 1, 2 (8n) 4 + 8n. Constraints: missing transverse momenta (x,y): 2n. on-shell conditions (both chains) 8n. Total 10n. Let constraints unknowns n 2. With many events (n), it s an over-constrained system. If only 3 on-shell particles in each chain, there will be fewer constraints than unknowns. Cheng, Gunion, Z. Han and McElrath, arxiv:

47 4 10 Simulated results: Entries solutions/gev mass (GeV) Cheng, Gunion, Z. Han and McElrath, arxiv:

48 4 10 Simulated results: Entries solutions/gev mass (GeV) Entries solutions/gev mass (GeV) Cheng, Gunion, Z. Han and McElrath, arxiv:

49 4 10 Simulated results: Entries solutions/gev mass (GeV) Entries solutions/gev mass (GeV) Remarks: Very selective channels. Very restrictive kinematics. Realistic experimental conditions will further dilute the solutions. Cheng, Gunion, Z. Han and McElrath, arxiv:

50 Transverse Mass Variables M T2 In the attempt to determine the absolute masses (parent and missing one), without fully reconstructing the events, M T2 was introduced. C. Lester and D. Summers, hep-ph/

51 Transverse Mass Variables M T2 In the attempt to determine the absolute masses (parent and missing one), without fully reconstructing the events, M T2 was introduced. Recall the invariant mass/transverse mass of ab (or eν): m 2 ab = m2 a + m 2 b + 2(Ea T Eb T cosh η pa T pb T ) m2 T. C. Lester and D. Summers, hep-ph/

52 Transverse Mass Variables M T2 In the attempt to determine the absolute masses (parent and missing one), without fully reconstructing the events, M T2 was introduced. Recall the invariant mass/transverse mass of ab (or eν): m 2 ab = m2 a + m 2 b + 2(Ea T Eb T cosh η pa T pb T ) m2 T. Consider a pair production/decay D 1 a 1 b 1, D 2 a 2 b 2 : m 2 D max(m2 TD 1, m 2 TD 2 ). C. Lester and D. Summers, hep-ph/

53 Transverse Mass Variables M T2 In the attempt to determine the absolute masses (parent and missing one), without fully reconstructing the events, M T2 was introduced. Recall the invariant mass/transverse mass of ab (or eν): m 2 ab = m2 a + m 2 b + 2(Ea T Eb T cosh η pa T pb T ) m2 T. Consider a pair production/decay D 1 a 1 b 1, D 2 a 2 b 2 : m 2 D max(m2 TD 1, m 2 TD 2 ). Only knowing p Tb1 + p Tb2 = E/ T, one defines: M 2 T2 (m a1, m a2 ; m b ) = min ptb1 + p Tb2 =E/ T [max(m 2 T1, m2 T2 )]. C. Lester and D. Summers, hep-ph/

54 Transverse Mass Variables M T2 In the attempt to determine the absolute masses (parent and missing one), without fully reconstructing the events, M T2 was introduced. Recall the invariant mass/transverse mass of ab (or eν): m 2 ab = m2 a + m 2 b + 2(Ea T Eb T cosh η pa T pb T ) m2 T. Consider a pair production/decay D 1 a 1 b 1, D 2 a 2 b 2 : m 2 D max(m2 TD 1, m 2 TD 2 ). Only knowing p Tb1 + p Tb2 = E/ T, one defines: M 2 T2 (m a1, m a2 ; m b ) = min ptb1 + p Tb2 =E/ T [max(m 2 T1, m2 T2 )]. This is a functional : For each event (E/ T ), run through trial p Tb1 and p Tb2 = E/ T p Tb1 : It is smaller than the true max(m 2 TD 1, m 2 TD 2 ); With many events, it still doesn t go over it. C. Lester and D. Summers, hep-ph/

55 Thus, one defines: M max T2 (m b) = max (all events) M T2 (m a1, m a2 ; m b ). a function of the trial missing mass m b. W.S. Cho, K. Choi, Y.G. Kim, C.B. Park, arxiv:

56 Thus, one defines: M max T2 (m b) = max (all events) M T2 (m a1, m a2 ; m b ). a function of the trial missing mass m b. The kink structure: When varying the trial missing mass below to above the true value of m b, the curve M max T2 (m b) (for multi-body decay) changes the slope: (GeV) 950 Gluino stransverse mass (max) Heavy squark (GeV) M χ W.S. Cho, K. Choi, Y.G. Kim, C.B. Park, arxiv: W.S. Cho, K. Choi, Y.G. Kim, C.B. Park, arxiv:

57 Thus, one defines: M max T2 (m b) = max (all events) M T2 (m a1, m a2 ; m b ). a function of the trial missing mass m b. The kink structure: When varying the trial missing mass below to above the true value of m b, the curve M max T2 (m b) (for multi-body decay) changes the slope: (GeV) 950 Gluino stransverse mass (max) Heavy squark (GeV) M χ For simple 2-body decay, no clear kink; For multi-body decays, combinatorics dilute the kink. W.S. Cho, K. Choi, Y.G. Kim, C.B. Park, arxiv: W.S. Cho, K. Choi, Y.G. Kim, C.B. Park, arxiv:

58 Antler Decay Kinematics The Antler decay D, a SM-like particles; B, X carry a new quantum number. TH, I.-W. Kim and J. Song, arxiv:

59 Antler Decay Kinematics The Antler decay D, a SM-like particles; B, X carry a new quantum number. Advantages: More constrained kinematics: M D is known from other SM modes. TH, I.-W. Kim and J. Song, arxiv:

Antler Decay Kinematics The Antler decay D, a SM-like particles; B, X carry a new quantum number. Advantages: More constrained kinematics: M D is known from other SM modes.

60 Antler Decay Kinematics The Antler decay D, a SM-like particles; B, X carry a new quantum number. Advantages: More constrained kinematics: M D is known from other SM modes. Many channels: MSSM: H χ χ 0 2 Z χ0 1 + Z χ0 1 ; Z SUSY: Z l + + l l χ l + χ 0 1; UED: Z (2) L (1) + L (1) l + γ (1) + l γ (1) ; LHT: H t + t ta H + ta H. ILC: e + e B 1 + B 2 a 1 X 1 + a 2 X 2. TH, I.-W. Kim and J. Song, arxiv:

61 A new kinematical feature: cuspy structures! Massive SM particles Massless SM particles Massless SM particle Massive SM particles dγ dm [1/GeV] [1/GeV] dγ dpt m [GeV] p T [GeV]

62 A new kinematical feature: cuspy structures! Massive SM particles Massless SM particles Massless SM particle Massive SM particles dγ dm [1/GeV] [1/GeV] dγ dpt m [GeV] p T [GeV] Pronounced peaks appear, suitable for observation!

63 Origin of the cusps:

64 Origin of the cusps: Limiting cases (at the corners) a 2 X 2 B 2 D B 1 a 1 X 1 Back-to-back: (cos θ 1,cos θ 2 ) = (+1, 1) + Maximum M aa configuration. Head-on: (cos θ 1,cos θ 2 ) = ( 1,+1) + Medium M aa configuration. Parallel: (cos θ 1,cos θ 2 ) = (±1, ±1) +, + Zero M aa configurations.

65 Origin of the cusps: Limiting cases (at the corners) a 2 X 2 B 2 D B 1 a 1 X 1 Back-to-back: (cos θ 1,cos θ 2 ) = (+1, 1) + Maximum M aa configuration. Head-on: (cos θ 1,cos θ 2 ) = ( 1,+1) + Medium M aa configuration. Parallel: (cos θ 1,cos θ 2 ) = (±1, ±1) +, + Zero M aa configurations. Upon variable projection (losing info), singularities may be developed. It is purely kinematical, and new (rigorous singularity theorems in math).

66 The rapidities η and ζ in the parent-rest frame: cosh η = m D c η, cosh ζ = m2 B m2 X + m2 a c ζ, 2m B 2m a m B thus : η, ζ (plus m D ) = m B, m a.

67 The rapidities η and ζ in the parent-rest frame: cosh η = m D c η, cosh ζ = m2 B m2 X + m2 a c ζ, 2m B 2m a m B thus : η, ζ (plus m D ) = m B, m a. Cusp and Edge: (M a = 0 case) The end-point, instead of being M max M max aa M cusp aa aa = m B = m B ( ( = m D 2m X, becomes 1 m2 X m 2 B 1 m2 X m 2 B ) ) e η, e η.

68 The rapidities η and ζ in the parent-rest frame: cosh η = m D c η, cosh ζ = m2 B m2 X + m2 a c ζ, 2m B 2m a m B thus : η, ζ (plus m D ) = m B, m a. Cusp and Edge: (M a = 0 case) The end-point, instead of being M max Thus, M max aa M cusp aa aa = m B = m B ( ( = m D 2m X, becomes 1 m2 X m 2 B 1 m2 X m 2 B Maa max /Maa cusp = e 2η, (D B) Maa max Maa cusp = m 2 B ( 1 m2 X m 2 B ) ) e η, e η. ) 2. (B X)

69 Algebraically/graphically, dγ dm aa { 2ηMaa, if 0 M aa M cusp aa ; M aa ln Mmax aa M aa, if Maa cusp M aa M max aa.

70 Algebraically/graphically, dγ dm aa [1/GeV] dγ { 2ηMaa, if 0 M aa M cusp aa ; dmaa M aa ln Mmax aa M aa, if Maa cusp M aa M max aa. Mass I Mass II Mass III Mass IV 1 Γ M aa [GeV] m D (GeV) m B (GeV) m a (GeV) m X (GeV) Mass I Mass II Mass III Mass IV m Z 100 Mass I: near threshold case (Z (2) decay in the UED model). Mass II: boundary case (m B 0.44m D ). Mass III: large mass gap case. Mass IV: massive case (Z, t,... in the final state)

71 Massive SM final state: (M a 0) For a massive case a = Z, t,..., dγ/dm aa may develop two cusps: 40 R 2 30 R 1 d Φ 4 d(m/m max ) 20 R m/m max

72 Cusp in Angular Distribution: (M a = 0) Θ is the angle of a visible particle (a 1 ) in the a 1 a 2 c.m. frame with respect to the c.m. moving direction. Then { dγ sin dcosθ 3 Θ, if cosθ tanh η, 0, otherwise.

73 Cusp in Angular Distribution: (M a = 0) Θ is the angle of a visible particle (a 1 ) in the a 1 a 2 c.m. frame with respect to the c.m. moving direction. Then { dγ sin dcosθ 3 Θ, if cosθ tanh η, 0, otherwise. a sharp end-point (another cusp) at the boundary: cosθ max = tanh η = 1 4m 2 B /m2 D. 1.6 Mass I 0, II Mass III 0, IV 0 dγ d cosθ 1 Γ cosθ 0.5 1

74 Cusp in Angular Distribution: (M a = 0) Θ is the angle of a visible particle (a 1 ) in the a 1 a 2 c.m. frame with respect to the c.m. moving direction. Then { dγ sin dcosθ 3 Θ, if cosθ tanh η, 0, otherwise. a sharp end-point (another cusp) at the boundary: cosθ max = tanh η = 1 4m 2 B /m2 D. 1.6 Mass I 0, II Mass III 0, IV 0 dγ d cosθ 1 Γ cosθ Complementarity: Large-mass gap worse for M aa, better for cosθ.

75 Robustness of the proposal (a). Back to the lab-frame: Lorentz boost M aa not effected, cosθ peaks diluted: 1.2 Mass III 0 :D 1 Mass 1:D dγ d cosθ 1 Γ Mass 1:pp Mass III 0 : pp cosθ (b). Dynamical effects: matrix elements, spin-correlations etc. M aa, cosθ not appreciably effected,

76 (c). Off-shell decays: finite width effects m B = 600 GeV Γ B = 0.01 GeV 5 GeV 60 GeV 300 GeV [1/GeV] dγ dmaa 1 Γ M aa [GeV] Γ B 10% not good anymore.

77 On-going studies: Reconstruct the antler kinematics: D, a SM-like particles; B (on-shell) and X (missing). TH, I.-W. Kim and J. Song, in progress.

78 On-going studies: Reconstruct the antler kinematics: D, a SM-like particles; B (on-shell) and X (missing). MSSM: H χ χ 0 2 Z χ Z χ 0 1; Z SUSY: Z l + + l l χ l + χ 0 1; UED: Z (2) L (1) + L (1) l + γ (1) + l γ (1) ; LHT: H t + t ta H + ta H. ILC: e + e B 1 + B 2 a 1 X 1 + a 2 X 2. TH, I.-W. Kim and J. Song, in progress.

79 On-going studies: Reconstruct the antler kinematics: D, a SM-like particles; B (on-shell) and X (missing). MSSM: H χ χ 0 2 Z χ Z χ 0 1; Z SUSY: Z l + + l l χ l + χ 0 1; UED: Z (2) L (1) + L (1) l + γ (1) + l γ (1) ; LHT: H t + t ta H + ta H. ILC: e + e B 1 + B 2 a 1 X 1 + a 2 X 2. Other channels with cusps: Decay chain kinematics: cusps as well. Multi-particle final states: some dilution. TH, I.-W. Kim and J. Song, in progress. A. Agashe, M. Toharia et al.; P. Osland, Miller et al.

80 Summary Determining the missing particle mass of fundamental importance. e.g.: Ever since the neutrino was proposed and observed, its mass measurement is still actively pursued.

81 Summary Determining the missing particle mass of fundamental importance. e.g.: Ever since the neutrino was proposed and observed, its mass measurement is still actively pursued. The LHC may well be the discovery machine for new physics via large(r) E/ T, difficult for the mass determination: key information for studying cosmic relic dark matter.

82 Summary Determining the missing particle mass of fundamental importance. e.g.: Ever since the neutrino was proposed and observed, its mass measurement is still actively pursued. The LHC may well be the discovery machine for new physics via large(r) E/ T, difficult for the mass determination: key information for studying cosmic relic dark matter. We proposed to search for new processes antler decays, with distinctive features: kinematical cusps, that may simultaneously determine both masses: knowing m D, measuring m B, m X.

83 Summary Determining the missing particle mass of fundamental importance. e.g.: Ever since the neutrino was proposed and observed, its mass measurement is still actively pursued. The LHC may well be the discovery machine for new physics via large(r) E/ T, difficult for the mass determination: key information for studying cosmic relic dark matter. We proposed to search for new processes antler decays, with distinctive features: kinematical cusps, that may simultaneously determine both masses: knowing m D, measuring m B, m X. We are all eagerly waiting for the excitement from the LHC!

Collider Phenomenology From basic knowledge to new physics searches

Collider Phenomenology From basic knowledge to new physics searches Tao Han University of Wisconsin Madison BUSSTEPP 2010 Univ. of Swansea, Aug. 23 Sept. 3, 2010 Outline: Lecture I: Colliders and Detectors