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INSTITUT F ¨ UR THEORETISCHE TEILCHENPHYSIK

Direct production of states with positive charge conjugation in e+e− annihilation

J.H. K¨ uhn |

KIT – The Research University in the Helmholtz Association

www.kit.edu

1

The Principle

2

Model Results

3

Experimental Perspectives

• 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

J/Ψ e− e+ γ JPC = 1−− (quantum numbers of photon) χc e− e+ γ γ JPC = ✟✟ ✟ 0++

Spin!, 1++, 2++

(quantum numbers of 2 photons) production rates: J/Ψ ∼ |e2QcR(0)|2

χc ∼ |e4Q2

cR′(0)|2

⇒ Γ(χ1,2 → e+e−) Γ(J/Ψ → e+e−) ∼ e4Q2

c

• Φ′

χ(0)

ΦΨ(0)

• 2

≈ (4πα)2 2

3

2

0.12

χJ = nonrelativistic bound state = 3PJ

expect Γ(χJ → 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

ǫα, p p1, ǫ1 p2, ǫ2 Spin J = 1, polarization ǫα, momentum p = p1 + p2 Aαβ

1 (p1, p2, ǫ)ǫ1

αǫ2 β = ic{p2

1(ǫ, ǫ1, ǫ2, p2) + p2 2(ǫ, ǫ2, ǫ1, p1)

+ ǫ1p1(ǫ, ǫ2, p1, p2) + ǫ2p2(ǫ, ǫ1, p2, p1)}

ǫα,β, p p1, ǫ1 p2, ǫ2 Spin J = 2, polarization ǫαβ, momentum p = p1 + p2 Aαβ

2 (p1, p2, ǫ)ǫ1

αǫ2 β =

√

2cMχc2{(p1p2)ǫ1

µǫ2 ν + p1µp2ν(ǫ1ǫ2)

− p1µǫ2

ν(ǫ1p2)) − p2µǫ1 ν(ǫ2p1))}ǫµν

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 = 16πα

√

m

• 1

4π 3Q2

cΦ′(0)

1

((p1 − p2)2/4 − m2 + iǫ)2

with m = mcharm Qc = 2/3

φ′(0) = derivative of wave function at origin ǫµ

1,2 = polarization vectors of photon

ǫµ = polarization vector of χ1 ǫµν = polarization tensor of χ2

The Principle Model results Experimental Perspectives Summary J.H. K¨ uhn – States with positive charge conjugation 5/14

The structure

e− e+ k χJ γ γ

A(e+e− →

3PJ) = ie

• dp1

(2π)4 v(l+) γν/

hγµ h2p2

1p2 2

u(l−)Aµν

J (p1, p2, ǫ)

with h = l− − p1

The Principle Model results Experimental Perspectives Summary J.H. K¨ uhn – States with positive charge conjugation 6/14

Model results

A(e+e− → 3P0) = 0 (helicity) A(e+e− → 3P1) = g1vγ5/

ǫu

A(e+e− → 3P2) = g2vγµuǫµν(lν

+ − lν −)/Mχ2

leading term: short distance approximation g1 = − α2√

2 M5/2

χ1

32

3

√

4πQ2 cΦ′(0) log 2b1 Mχ1

g2 =

α2

M5/2

χ2

64

3

√

4πQ2 cΦ′(0)

• log 2b2

Mχ2 + 1 3(iπ + log 2 − 1)

• with bi = 2m − Mχi = ”binding energy”

Γ( 3P1 → − > e+e−) = 1

3

|g1|2

4π Mχ1

Γ( 3P2 → − > e+e−) = 1

5

|g2|2

8π Mχ2

The Principle Model results Experimental Perspectives Summary J.H. K¨ uhn – States with positive charge conjugation 7/14

Improvement: binding energy corrections

⇒ terms of order

• M2

χi − 4m2

/M2

χi

Γ(χ1 → e+e−) Γ(χ2 → 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 χJ to J/Ψ γ, χJ to Ψ′ γ, and χ2 to γγ, as derived from the corresponding decay rates

χc χc χc Ψ′ J/Ψ e− e+ e− e− e+ e+

QED

γγ

J/Ψγ

Ψ′γ

QED + Z 0

Γ(χ1 → e+e−)[eV]

0.43 0.10 0.01 0.09 0.41

Γ(χ2 → 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

Rpeak = Γee

∆

9 4α2

√

2ΠΓhad

Γtot

NZ

∆ = machine energy resolution ≈ 4 MeV

NZ ≈ 0.7

Γhad/Γtot ≈ 0.66 Γee = 0.1 eV - 0.5 eV ⇒ Rpeak = 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− → χJ → γ J/Ψ (→ µ+µ− ) and e+e− → γ J/Ψ (→ µ+µ− )

e− l− e+ l+ p1

χci

k

J/ψ

p2 µ+ q3 µ− q4 (a) e− l− e+ l+ p1

χci

k p2 µ+ q3 µ− q4 (b) e− l− e+ l+

J/ψ

q2 µ+ q3 µ− q4 (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◦ < θγ < 160◦; 20◦ < θµ+µ− < 160◦)

ISR+QED signal+Z0 ISR+QED signal ISR background Mχc1 = 3.51066 GeV 20o < θγ < 160o 20o < θµ−,µ+ < 160o √s (GeV ) σ (nb) 3.52 3.518 3.516 3.514 3.512 3.51 3.508 3.506 3.504 3.502 0.0215 0.021 0.0205 0.02 0.0195 0.019 0.0185 0.018 0.0175 0.017 0.0165 0.016

χ1

cuts on µ-pairs and photons

ISR+QED signal+Z0 ISR+QED signal ISR background Mχc1 = 3.51066 GeV 20o < θµ−,µ+ < 160o √s (GeV ) σ (nb) 3.52 3.518 3.516 3.514 3.512 3.51 3.508 3.506 3.504 3.502 0.094 0.093 0.092 0.091 0.09 0.089 0.088 0.087 0.086

χ1

cuts on pho- tons only (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

ISR+QED signal ISR background Mχc2 = 3.55620 GeV 20o < θγ < 160o 20o < θµ−,µ+ < 160o √s (GeV ) σ (nb) 3.58 3.575 3.57 3.565 3.56 3.555 3.55 3.545 3.54 3.535 0.03 0.028 0.026 0.024 0.022 0.02 0.018 0.016 0.014 0.012 0.01

χ2

cuts on µ-pairs and photons

ISR+QED signal ISR background Mχc2 = 3.55620 GeV 20o < θµ−,µ+ < 160o √s (GeV ) σ (nb) 3.58 3.575 3.57 3.565 3.56 3.555 3.55 3.545 3.54 3.535 0.092 0.09 0.088 0.086 0.084 0.082 0.08 0.078 0.076 0.074 0.072

χ2

cuts on pho- tons only

The Principle Model results Experimental Perspectives Summary J.H. K¨ uhn – States with positive charge conjugation 13/14

Summary

resonant production of χ1 and χ2 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