Direct production of states with positive charge conjugation in e + e - PowerPoint PPT Presentation

Direct production of states with positive charge conjugation in e + e − annihilation J.H. K¨ uhn | INSTITUT F ¨ UR THEORETISCHE TEILCHENPHYSIK www.kit.edu KIT – The Research University in the Helmholtz Association

The Principle 1 Model Results 2 Experimental Perspectives 3 H. Czy˙ z, J.H. K¨ uhn, S. Tracz, Phys. Rev. D94, 034033 (2016) J. K¨ uhn, J. Kaplan, E.G.O. Safiani, NPB 157 (1979) 125 D. Yang, S. Zhao, Eur. Phys. J.C. (2012) 72 N. Kivel, M. Vanderhaegen, JHEP 1602 (2016) 032 A. Denig et al. Phys. Lett. B736 (2014) 221 The Principle Model results Experimental Perspectives Summary J.H. K¨ uhn – States with positive charge conjugation 2/14

The Principle e − J PC = 1 −− γ (quantum numbers of photon) J/ Ψ e + e − γ J PC = ✟✟ 0 ++ Spin ! , 1 ++ , 2 ++ ✟ χ c (quantum numbers of 2 photons) e + γ production rates: 2 Φ ′ J / Ψ ∼ | e 2 Q c R ( 0 ) | 2 ⇒ Γ( χ 1 , 2 → e + e − ) � χ ( 0 ) � Γ( J / Ψ → e + e − ) ∼ e 4 Q 2 � � c � � Φ Ψ ( 0 ) χ c ∼ | e 4 Q 2 c R ′ ( 0 ) | 2 � � � 2 � 2 ≈ ( 4 πα ) 2 0 . 1 2 3 χ J = nonrelativistic bound state = 3 P J expect Γ( χ J → e + e − ) ∼ ( 0 . 05 − 0 . 5 ) eV The Principle Model results Experimental Perspectives Summary J.H. K¨ uhn – States with positive charge conjugation 3/14

The Structure p 1 , ǫ 1 Spin J = 1, polarization ǫ α , ǫ α , p momentum p = p 1 + p 2 p 2 , ǫ 2 A αβ 1 ( p 1 , p 2 , ǫ ) ǫ 1 α ǫ 2 β = ic { p 2 1 ( ǫ, ǫ 1 , ǫ 2 , p 2 ) + p 2 2 ( ǫ, ǫ 2 , ǫ 1 , p 1 ) + ǫ 1 p 1 ( ǫ, ǫ 2 , p 1 , p 2 ) + ǫ 2 p 2 ( ǫ, ǫ 1 , p 2 , p 1 ) } p 1 , ǫ 1 Spin J = 2, polarization ǫ αβ , ǫ α,β , p momentum p = p 1 + p 2 p 2 , ǫ 2 √ A αβ 2 ( p 1 , p 2 , ǫ ) ǫ 1 α ǫ 2 2 cM χ c 2 { ( p 1 p 2 ) ǫ 1 µ ǫ 2 ν + p 1 µ p 2 ν ( ǫ 1 ǫ 2 ) β = − p 1 µ ǫ 2 ν ( ǫ 1 p 2 )) − p 2 µ ǫ 1 ν ( ǫ 2 p 1 )) } ǫ µν The Principle Model results Experimental Perspectives Summary J.H. K¨ uhn – States with positive charge conjugation 4/14

The Structure where, in quarkonium model � c = 16 πα 1 1 c Φ ′ ( 0 ) 4 π 3 Q 2 √ (( p 1 − p 2 ) 2 / 4 − m 2 + i ǫ ) 2 m with m = m charm Q c = 2 / 3 φ ′ ( 0 ) = derivative of wave function at origin ǫ µ 1 , 2 = polarization vectors of photon ǫ µ = polarization vector of χ 1 ǫ µν = polarization tensor of χ 2 The Principle Model results Experimental Perspectives Summary J.H. K¨ uhn – States with positive charge conjugation 5/14

The structure e − γ χ J k γ e + ( 2 π ) 4 v ( l + ) γ ν / � d p 1 h γ µ A ( e + e − → u ( l − ) A µν 3 P J ) = ie J ( p 1 , p 2 , ǫ ) h 2 p 2 1 p 2 2 with h = l − − p 1 The Principle Model results Experimental Perspectives Summary J.H. K¨ uhn – States with positive charge conjugation 6/14

Model results A ( e + e − → 3 P 0 ) = 0 (helicity) A ( e + e − → 3 P 1 ) = g 1 v γ 5 / ǫ u A ( e + e − → 3 P 2 ) = g 2 v γ µ u ǫ µν ( l ν + − l ν − ) / M χ 2 leading term: short distance approximation g 1 = − α 2 √ 2 3 c Φ ′ ( 0 ) log 2 b 1 4 π Q 2 32 √ M 5 / 2 M χ 1 χ 1 � � α 2 c Φ ′ ( 0 ) log 2 b 2 3 4 π Q 2 M χ 2 + 1 g 2 = 3 ( i π + log 2 − 1 ) 64 √ M 5 / 2 χ 2 with b i = 2 m − M χ i = ”binding energy” | g 1 | 2 Γ( 3 P 1 → − > e + e − ) = 1 4 π M χ 1 3 | g 2 | 2 Γ( 3 P 2 → − > e + e − ) = 1 8 π M χ 2 5 The Principle Model results Experimental Perspectives Summary J.H. K¨ uhn – States with positive charge conjugation 7/14

Improvement: binding energy corrections � M 2 χ i − 4 m 2 � / M 2 ⇒ terms of order χ i Γ( χ 1 → e + e − ) Γ( χ 2 → e + e − ) b = + 0 . 5 GeV leading term 0.0226 eV 0.0243 eV full result 0.0317 eV 0.0159 eV b = − 0 . 5 GeV leading term 0.164 eV 0.0512 eV full result 0.141 eV 0.0731 eV significant impact! The Principle Model results Experimental Perspectives Summary J.H. K¨ uhn – States with positive charge conjugation 8/14

Improvement: Short and Long distance corrections include correct coupling of χ J to J / Ψ γ , χ J to Ψ ′ γ , and χ 2 to γγ , as derived from the corresponding decay rates e − e − e − J/ Ψ Ψ ′ χ c χ c χ c e + e + e + Ψ ′ γ QED + Z 0 γγ J / Ψ γ QED Γ( χ 1 → e + e − ) [eV] 0.43 0.10 0.01 0.09 0.41 Γ( χ 2 → e + e − ) [eV] 4.25 0.04 1.41 0.45 - The Principle Model results Experimental Perspectives Summary J.H. K¨ uhn – States with positive charge conjugation 9/14

Experimental Perspectives 1.) Hadronic final state √ R peak = Γ ee 9 2 ΠΓ had N Z 4 α 2 ∆ Γ tot ∆ = machine energy resolution ≈ 4 MeV N Z ≈ 0 . 7 Γ had / Γ tot ≈ 0 . 66 Γ ee = 0.1 eV - 0.5 eV ⇒ R peak = 2 · 10 − 3 − 1 · 10 − 2 The Principle Model results Experimental Perspectives Summary J.H. K¨ uhn – States with positive charge conjugation 10/14

2.) Leptonic final state e + e − → χ J → γ J / Ψ ( → µ + µ − ) and e + e − → γ J / Ψ ( → µ + µ − ) µ + µ + µ + e − q 3 e − q 3 e − q 3 l − l − l − J/ψ χ ci χ ci J/ψ p 2 q 4 p 2 q 4 q 2 k k µ − µ − l + l + l + q 4 p 1 p 1 e + e + e + µ − (a) (b) (c) nontrivial phase relation between signal and background The Principle Model results Experimental Perspectives Summary J.H. K¨ uhn – States with positive charge conjugation 11/14

Experiment angular cuts on photon and leptons (20 ◦ < θ γ < 160 ◦ ; 20 ◦ < θ µ + µ − < 160 ◦ ) 0 . 0215 ISR background 0 . 021 ISR+QED signal ISR+QED signal+ Z 0 χ 1 0 . 0205 0 . 02 0 . 0195 σ ( nb ) 0 . 019 0 . 0185 20 o < θ γ < 160 o cuts on µ -pairs 0 . 018 20 o < θ µ − ,µ + < 160 o 0 . 0175 M χ c 1 = 3 . 51066 GeV 0 . 017 and photons 0 . 0165 0 . 016 3 . 502 3 . 504 3 . 506 3 . 508 3 . 51 3 . 512 3 . 514 3 . 516 3 . 518 3 . 52 √ s ( GeV ) 0 . 094 ISR background ISR+QED signal 0 . 093 ISR+QED signal+ Z 0 χ 1 0 . 092 0 . 091 σ ( nb ) 0 . 09 0 . 089 cuts on pho- 20 o < θ µ − ,µ + < 160 o 0 . 088 M χ c 1 = 3 . 51066 GeV tons only 0 . 087 0 . 086 3 . 502 3 . 504 3 . 506 3 . 508 3 . 51 3 . 512 3 . 514 3 . 516 3 . 518 3 . 52 √ s ( GeV ) (most optimistic choice for couplings; important effect of phase) The Principle Model results Experimental Perspectives Summary J.H. K¨ uhn – States with positive charge conjugation 12/14

Experiment 0 . 03 ISR background ISR+QED signal 0 . 028 χ 2 0 . 026 20 o < θ γ < 160 o 0 . 024 20 o < θ µ − ,µ + < 160 o 0 . 022 M χ c 2 = 3 . 55620 GeV σ ( nb ) 0 . 02 0 . 018 cuts on µ -pairs 0 . 016 0 . 014 and photons 0 . 012 0 . 01 3 . 535 3 . 54 3 . 545 3 . 55 3 . 555 3 . 56 3 . 565 3 . 57 3 . 575 3 . 58 √ s ( GeV ) 0 . 092 ISR background ISR+QED signal 0 . 09 χ 2 0 . 088 0 . 086 0 . 084 σ ( nb ) 0 . 082 0 . 08 cuts on pho- 20 o < θ µ − ,µ + < 160 o 0 . 078 0 . 076 M χ c 2 = 3 . 55620 GeV tons only 0 . 074 0 . 072 3 . 535 3 . 54 3 . 545 3 . 55 3 . 555 3 . 56 3 . 565 3 . 57 3 . 575 3 . 58 √ s ( GeV ) The Principle Model results Experimental Perspectives Summary J.H. K¨ uhn – States with positive charge conjugation 13/14

Summary resonant production of χ 1 and χ 2 in e + e − annihilation is possible hadronic final states and leptonic final states are accesible in principle precise numerical predictions are strongly model dependent The Principle Model results Experimental Perspectives Summary J.H. K¨ uhn – States with positive charge conjugation 14/14