Quarkonium Resources

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Quarkonium Production Experiments

Charmonium Experiments

Differential cross sections of J/ψ and ψ' in 800 GeV/c p-Si interactions. T. Alexopoulos et al. (E771 Collaboration), Phys. Rev. D 55 (1997) 3927.

Reaction:	800 GeV (fixed target) p + Si → J/ψ, ψ'
Acceptance:	-0.05<xF<0.25, pT<3.5 GeV, -0.8<Cos(θ)<0.8
Sample size:	11660±139 J/ψ, 218±24 ψ'
Nuclear effects:	Correction using α=0.920±0.008
Results:	σ= 375±4±30 nb (J/ψ), σ= 46±3±10 nb (ψ')
Detailed xF and pT distributions are given. A fit to the Cos(θ) distribution is also presented.

Measurement of J/ψ and ψ' production in 800 GeV/c p-Au collisions. M. H. Schub et al. (E789 Collaboration), Phys. Rev. D 52 (1995) 1307.

Reaction:	800 GeV (fixed target) p + Au → J/ψ, ψ'
Acceptance:	-
Sample size:	112649±486 J/ψ, 1824±114 ψ'
Nuclear effects:	Correction using α=0.90±0.02
Results:	σ= 442±2±88 nb (J/ψ), σ= 75±5±22 nb (ψ')
The systematic error for ψ' is stated to be a lower bound. Detailed xF and pT distributions are given.

Measurement of J/ψ, ψ' and Υ total cross sections in 800 GeV/c p-Si interactions. T. Alexopoulos et al. (E771 Collaboration), Phys. Lett. B 374 (1996) 271.

Reaction:	800 GeV (fixed target) p + Si → J/ψ, ψ', Υ
Acceptance:	-0.1<xF<0.3, pT<3.5 GeV
Sample size:	11660±139 J/ψ, 218±24 ψ'
Results:	BR . σ = 21.8±0.3±1.4 nb (J/ψ), σ= 0.360±0.040±0.024 nb (ψ')

Production of Charmonium states in π^- Be collisions at 515 GeV/c. V. Koreshev et al. (E672-E706 Collaborations), Phys. Rev. Lett. 77 (1996) 4294.

Reaction:

515 GeV (fixed target) π + Be → J/ψ, ψ'

Production of J/ψ and ψ(2S) mesons in π^- Be collisions at 515 GeV/c. A. Gribushin et al. (E672-E706 Collaborations), Phys. Rev. D 53 (1996) 4723.

Reaction:	515 GeV (fixed target) π- + Be → J/ψ, ψ'
Acceptance:	0.1<xF<0.8, pT<3.5 GeV, -0.8<Cos(θ)<0.8
Sample size:	11660±139 J/ψ, 218±24 ψ'
Nuclear effects:	Correction using α=0.920±0.008
Results:	BR . σ = 9.3±0.1±1.1 nb (J/ψ, xF>0.1), BR . σ = 12.9±0.2±1.6 nb (J/ψ, xF>0.0), BR . σ = 7.4±1.5±1.2 nb (ψ', xF>0.1) Fraction of J/ψ due to ψ' = 0.083±0.017±0.013
Detailed xF and pT distributions are given. A fit to the Cos(θ) distribution is also presented.

Production of χ Charmonium via 300 GeV/c pion and proton interactions on a Lithium target. L. Antoniazzi et al. (E705 Collaboration), Phys. Rev. D 49 (1994) 543.

Reaction:	300 GeV (fixed target) p + Li → χc
Reaction:	300 GeV (fixed target) π + Li → χc

A measurement of J/ψ and ψ' production in 300 GeV/c proton, anti-proton and π^± nucleon interactions. L. Antoniazzi et al. (E705 Collaboration), Phys. Rev. D 46 (1992) 4828.

Reaction:	300 GeV (fixed target) p + Li → J/ψ, ψ'
Reaction:	300 GeV (fixed target) pbar + Li → J/ψ, ψ'
Reaction:	300 GeV (fixed target) π + Li → J/ψ, ψ'

Production of J/ψ via ψ' and χ decay in 300 GeV/c proton and π^± nucleon interactions. L. Antoniazzi et al. (E705 Collaboration), Phys. Rev. Lett. 70 (1993) 383.

Reaction:	300 GeV (fixed target) p + Li → χc, ψ' → J/ψ
Reaction:	300 GeV (fixed target) π + Li → χc, ψ' → J/ψ

Bottomonium Experiments

Measurement of J/ψ, ψ' and Υ total cross sections in 800 GeV/c p-Si interactions. T. Alexopoulos et al. (E771 Collaboration), Phys. Lett. B 374 (1996) 271.

Reaction:	800 GeV (fixed target) p + Si → J/ψ, ψ', Υ
Acceptance:	-0.1<xF<0.3, pT<3.5 GeV
Sample size:	10±4 Upsilon
Results:	BR . σ = 8.0±3.3±0.6 nb (Υ+Υ')

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NRQCD Production Matrix Elements

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Notation: H_c(^SL_J) for long distance matrix elements [eg: J/ψ₈(³S₁) for the J/ψ colour octet, spin triplet, S wave, J=1 matrix element]. The production matrix elements are distinct from the decay matrix elements (see BBL).

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J/psi Matrix Elements

J/ψ₁(³S₁)

• Baek et al use a value 0.73 GeV³ without attribution.
• Cho and Leibovich quote a value 1.2 GeV³ using a potential model computation. The value is not cross checked against any experimental data.
• Beneke, Maltoni and Rothstein quote a value 1.16 GeV³ using the same potential model as above.

J/ψ₈(³S₁)

• Baek et al use a value 0.015 GeV³ without attribution.
• Cho and Leibovich quote a value 0.012 GeV³ from the J/psi rate and the observed Chi_c to direct J/psi ratio at the TEVATRON.
• Beneke and Kraemer find the three values
  • (1.06±0.14)10^-2GeV³ for use with CTEQ4L densities
  • (1.12±0.14)10^-2GeV3 for the GRV (94) LO set
  • (1.40±0.22)10^-2GeV³ using the MRS-R2 set
• Gupta and Sridhar have used (6.6±2.1) 10^-3 GeV³.

J/ψ₈(¹S₀) +7 J/ψ₈(³P₀)/(2 m²)

or similar combinations appear in the computation of the P_T spectrum of J/psi produced at the Tevatron.

• Beneke and Kraemer find the three values
  • (4.38±1.15)10^-2GeV³ for use with CTEQ4L densities
  • (3.90±1.14)10^-2GeV³ for the GRV (94) LO set
  • (10.9±2.07)10^-2GeV³ using the MRS-R2 set

J/ψ₈(¹S₀) +3.1 J/ψ₈(³P₀)/m²

• Beneke, Maltoni and Rothstein quote the range (0.4-2.3) 10^-2 GeV³ using CLEO measurements of the branching ratio B→J/ψ+X. The other matrix elements input to this computation use the CTEQ4L compatible values.

J/ψ₈(¹S₀) +3 J/ψ₈(³P₀)/m² +4 J/ψ₈(³P₂)/(5 m²)

appears in low energy hadro- and photo-production of J/psi.

• Fleming and Maksymyk extracted a value 0.200±0.001 GeV³ from almost elastic photo-production data. The diffractive component was not removed before fitting.

χ_c Matrix Elements

χ¹₁(³P₁)

are related to the derivative of the wavefunction of Chi_c(J) states at the origin. Using heavy quark spin symmetry it can be shown that the values for different J are in the ratio 2J+1 upto relative order v².

• Cho and Leibovich quote a value 0.32 GeV⁵ using a potential model computation. The value is not cross checked against any experimental data.
• Beneke, Maltoni and Rothstein quote the range 0.144 m_c² GeV⁵ using the same potential model.
• Mangano and Petrelli quote a value for the derivative of the Chi_c wavefunction at the origin based on a fit to data on decay widths. The derivative value gives for the decay matrix element 0.06±0.01 GeV⁵.

χ¹₈(³S₁)

is usually the only matrix element in this family which is quoted. All corresponding χ_c(J) matrix elements may be obtained from this to order v² accuracy using the heavy quark spin symmetry relation that they are in the ratio of (2J+1).

• Cho and Leibovich quote a value 0.016 GeV⁵ from the J/ψ rate and the observed χ_c to direct J/ψ ratio at the TEVATRON.
• Gupta and Sridhar have used (9.8±1.3) 10^-3 GeV³.
• Beneke, Maltoni and Rothstein quote the range (3)(4.5-6.5) 10^-3 GeV³ from fits to CLEO data on the decay B → χ₂+anything. (The first factor of 3 is the 2J+1 factor.) However, this gives too small a branching fraction for χ₁.

ψ' Matrix Elements

ψ'₁(³S₁)

• Cho and Leibovich quote a value 0.76 GeV³ using a potential model computation. The value is not cross checked against any experimental data.
• Beneke, Maltoni and Rothstein also use the same value.

ψ'₈(³S₁)

appears in the production cross section for ψ' at the Tevatron.

• Cho and Leibovich quote a value 0.0073 GeV³.
• Beneke and Kraemer find the three values

  (0.44±0.08) 10-2 GeV3	for use with CTEQ4L densities,
  (0.46±0.08) 10-2 GeV3	for the GRV (94) LO set and
  (0.56±0.11) 10-2 GeV3	using the MRS-R2 set.

ψ'₈(¹S₀) +7 ψ'₈(³P₀)/(2 m²)

or similar combinations appear in the computation of the P_T spectrum of ψ' produced at the Tevatron.

• Beneke and Kraemer find the three values

  (1.80±0.56) 10-2 GeV3	for use with CTEQ4L densities,
  (1.60±0.51) 10-2 GeV3	for the GRV (94) LO set and
  (4.36±0.96) 10-2 GeV3	using the MRS-R2 set.

ψ'₈(¹S₀) +3.1 ψ'₈(³P₀)/m²

• Beneke, Maltoni and Rothstein quote the range (0.0-1.0) 10^-2 GeV³ using CLEO measurements of the branching ratio B→Psi'+X. The other matrix elements input to this computation use the CTEQ4L compatible values.

Υ Matrix Elements

Υ₁(³S₁)

• Cho and Leibovich quote a value 9.3 GeV³ using a potential model computation. The value is not cross checked against any experimental data.

Υ₈(³S₁)

• Cho and Leibovich use a scaling relation to relate this to the corresponding J/psi matrix element and get 0.0095GeV³.

Υ'₁(³S₁)

• Cho and Leibovich quote a value 4.6 GeV³ using a potential model computation. The value is not cross checked against any experimental data.

Υ'₈(³S₁)

• Cho and Leibovich use a scaling relation to relate this to the corresponding Psi' matrix element and get 0.0057GeV³.

Υ''₁(³S₁)

• Cho and Leibovich quote a value 3.5 GeV³ using a potential model computation. The value is not cross checked against any experimental data.

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References

1. S. Baek, P. Ko, J. Lee and H. S. Song, Phys Rev D 55 (1997) 6839.
   Quote values for two J/ψ production matrix elements without attribution.
2. M. Beneke and M. Kramer, Phys Rev D 55 (1997) 5269.
   Performs a fit to the Tevatron data to extract two combinations of J/ψ and ψ' octet matrix elements. The results are reported for m_c=1.5 GeV and a choice of factorisations scale of (P_T²+4m_c²)^1/2. Uncertainties from choice of scale, structure function set etc are systematically explored.
3. Peter Cho and Adam K. Leibovich, Phys Rev D 53 (1996) 150.
   Uses a quark potential model to compute several colour singlet matrix elements. Some colour octet matrix elements are obtained by a fit to Tevatron data on total J/ψ and ψ' cross sections as well as the χ_c contribution to the total J/ψ rate.
4. Peter Cho and Adam K. Leibovich, Phys Rev D 53 (1996) 6203.
   
5. Sean Fleming and Igor Maksymyk, hep-ph/9603266.
   Fits a particular combination of J/ψ octet matrix elements to data on almost elastic photo-production. The diffractive component of the data is not removed before fitting.
6. M. L. Mangano and Andrea Petrelli, Phys Lett B 352 (1995) 445.
   Uses data on decays of the χ_c states into two photons and light hadrons to fix the decay matrix elements. Comparison with Braaten, Brodsky and Lepage is necessary to convert their parameters into the standard form. Subsequently, the singlet decay matrix elements may be converted to production matrix elements using the vacuum saturation approximation.
7. M. Beneke, F. Maltoni and I. Z. Rothstein, hep-ph/9808360.
   Obtains the long-distance matrix elements from the decays $B→H(cc)+X$.

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Compiled by: Sourendu Gupta, June 12, 1997.