We consider the contribution of radially excited 2^3P_{1,2} states to
psi^prime production at the Tevatron energy. Production of these states via the
conventional gluon fusion mechanism and via gluon and charm quark fragmentation
processes is considered. We find that it is possible to account for the data on
psi^prime production from the CDF experiment, by taking into account the decays
of these 2^3P_{1,2} states into psi^prime.Comment: 8 pages + 1 figure (available upon request), CERN-TH.7434/9

Ashman

Baier

Berger

Braaten

Cacciari

Chen

D.P. Roy

Gastmans

Glover

Godrey

K. Sridhar

Kokoski

Le Yaouana

Mangano

Martin

Papadimitrou

Plothow-Besch

Physics Letters B

English

arXiv

We consider the contribution of radially excited 2^3P_{1,2} states to psi^prime production at the Tevatron energy. Production of these states via the conventional gluon fusion mechanism and via gluon and charm quark fragmentation processes is considered. We find that it is possible to account for the data on psi^prime production from the CDF experiment, by taking into account the decays of these 2^3P_{1,2} states into psi^prime.We consider the contribution of radially excited 2~3P_{1,2} states to psi~prime production at the Tevatron energy. Production of these states via the conventional gluon fusion mechanism and via gluon and charm quark fragmentation processes is considered. We find that it is possible to account for the data on psi~prime production from the CDF experiment, by taking into account the decays of these 2~3P_{1,2} states into psi~prime.We consider the contribution of radially excited 2 3 P 1,2 states to Ψ′ production at the Tevatron energy. Production of these states via the conventional gluon fusion mechanism and via gluon and charm quark fragmentation processes is considered. With optimistic estimates of the decay branching fractions of these 2 3 P 1,2 states into Ψ′, it is possible to account for the large Ψ′ production cross-section observed by the CDF experiment

Roy, D.P.

Sridhar, K.

CERN Document Server

A possible resolution of the CDF $\psi$' anomaly

Crossref

A possible resolution of the CDF Ψ′ anomaly

We consider the contribution of radially excited 23P1,2 states to Ψ' production at the Tevatron energy. Production of these states via the conventional gluon fusion mechanism and via gluon and charm quark fragmentation processes is considered. We find that it is possible to account for the data on Ψ' production from the CDF experiment, by taking into account the decays of these 23P1,2 states into Ψ'

Roy, D. P.

Publications of the IAS Fellows

ar
X
iv
:h
ep
-p
h/
94
09
23
2v
1 
 6
 S
ep
 1
99
4
CERN-TH.7434/94
TIFR/TH/94-33
September 1994
A possible resolution of the CDF ψ′ anomaly
D.P. Roy∗
Theory Group, Tata Institute of Fundamental Research,
Homi Bhabha Road, Bombay 400 005, India.
and
K. Sridhar∗∗
Theory Division, CERN,
CH-1211, Geneva 23, Switzerland.
ABSTRACT
We consider the contribution of radially excited 23P1,2 states to ψ
′ production at the
Tevatron energy. Production of these states via the conventional gluon fusion mecha-
nism and via gluon and charm quark fragmentation processes is considered. We find
that it is possible to account for the data on ψ′ production from the CDF experiment,
by taking into account the decays of these 23P1,2 states into ψ
′.
CERN-TH.7434/94
September 1994
∗) dproy@theory.tifr.res.in
∗∗) sridhar@vxcern.cern.ch
The CDF measurement [1] of J/ψ and ψ′ production at large transverse momentum
(pT )in 1.8 TeV p¯p collisions at the Tevatron is one of the most challenging experimental
results of recent times. There is a huge discrepancy between the experimental data
and theoretical predictions of conventional models, much larger than the uncertainties
that are typical of such theoretical predictions.
The production of quarkonia at large pT is usually described by the parton-fusion
mechanism in the framework of the colour-singlet model [2, 3, 4]. In this model, the
wave-function at the origin for a S-wave (or its derivative for a P -wave) quarkonium
is convoluted with the cross-section for producing a heavy quark pair with the proper
spin, parity and charge-conjugation assignments. There is an uncertainty in the de-
termination of the wave-function parameters, and taken in quadrature with that due
to choice of scale, an overall uncertainty of a factor ∼ 3 is expected in the predicted
normalisation of the quarkonium cross-section. Within this normalisation uncertainty,
the colour- singlet model prediction agrees with the J/ψ hadroproduction data from
fixed-target and ISR experiments over a reasonable range of pT [3, 5, 6].
At higher energies where b-quark production becomes important, the decay of b
quarks is a mechanism that contributes to J/ψ and ψ′ production, in addition to
the parton-fusion mechanism of the colour-singlet model [6]. In the CDF experiment,
however, the secondary vertex information has been used to separate out the b-quark
decay contribution. The remainder are presumably produced directly by the fusion
mechanism: therefore, the discrepancy between the large J/ψ and ψ′ cross-sections
measured by CDF and the theoretical predictions shows that the fusion mechanism
grossly under-estimates the direct J/ψ and ψ′ production cross-sections.
The above discrepancy calls for a new mechanism of quarkonium production at
large pT . At high-energy colliders, where gluons and charm quarks are copiously pro-
duced, the fragmentation of these particles into quarkonium states has been suggested
as an important mechanism for large-pT quarkonium production [7]. Even though the
fragmentation process is of higher order in the strong coupling constant, αs, it can
dominate over the direct quarkonium production via fusion at large pT , where terms
of the order of p2T/m
2
Q can easily compensate for the suppression due to the extra
power of αs. The validity of this suggestion is borne out by the explicit computation
of the fusion and fragmentation contributions for the Tevatron energy, presented in
Refs. [8, 9, 10]. In these papers, it was shown that the fragmentation contribution
is the dominant contribution at the Tevatron energy; the largest contribution comes
from gluons fragmenting into χ’s, which subsequently decay into J/ψ’s. Together with
the fusion contribution it can explain the large cross-section measured by the CDF
experiment to within a factor of 2-3, which is also the typical uncertainty in the pre-
dicted normalisation. In Ref. [8], the energy dependence of the fragmentation and
fusion contributions was studied as well. It was shown that at ISR energies the fusion
1
contribution dominates over the pT range of interest, although the inclusion of the
fragmentation contribution helps to improve the quantitative agreement with the ISR
data.
In Refs. [8, 9], the production of ψ′ by fragmentation was also studied. Unlike J/ψ
production, ψ′ production does not involve the P -state contribution. Consequently,
the fragmentation contribution is comparatively smaller. The total predicted ψ′ cross-
section is more than an order of magnitude smaller than the cross-section measured
by CDF.
In this letter, we explore the possibility that radially excited P -state charmonia
contribute via their electromagnetic decays to ψ′ production. Some authors [11, 12]
have recently suggested the possibility of a large contribution of the 23P1,2 states to
ψ′ production at the Tevatron energy. These 2P states have been predicted [13] to
lie about 200-300 MeV above the open charm threshold, but their DD¯ decay width
is expected to be suppressed due to L = 2 phase-space as well as dynmical effects
[11, 14]. Consequently, the branching ratios due to the decays 23P1,2 → 23S1 + γ can
be substantial, and, hence, the 2P states could potentially contribute a significant
fraction of the measured ψ′ cross-section 1 [11, 12]. We present the first quantitative
estimate of this contribution.
The theoretical set-up which we need to compute the pT distributions has been
discussed in detail in Ref. [8]. We will compute the contributions from the fusion and
the fragmentation processes to the direct production of ψ′ as well as to that of the 2P
states. The large-pT production cross-section for the fusion process is given as
dσ
dpT
(AB → (2S, 2P1,2)X) =
∑ ∫
dydx1x1Ga/A(x1)x2Gb/B(x2)
4pT
2x1 − x¯T ey
dσˆ
dtˆ
(ab→ (2S, 2P1,2)c), (1)
where the sum, in the above equation, runs over all the partons contributing to the
subprocesses ab → (2S, 2P1,2)c. Ga/A and Gb/B are the distributions of the partons a
and b in the hadrons A and B with momentum fractions x1 and x2, respectively, and
x2 is given as
x2 =
x1x¯T e
−y − 2τ
2x1 − x¯T ey , (2)
where τ = M2/s, with M the mass of the resonance, s the centre-of-mass energy and
y the rapidity at which the resonance is produced.
x¯T =
√
x2T + 4τ ≡
2MT√
s
, xT =
2pT√
s
(3)
1The contribution of the 1D2 state to the ψ
′ yield is expected to be small. For a discussion, see
Ref. [11].
2
The expressions for the subprocess cross-sections, dσˆ/dtˆ, are explicitly given in Refs. [3]
and [16].
The dominant fragmentation contribution comes from the fragmentation of gluons
and charm quarks. It is computed by factorising the cross-section for the process AB →
(2S, 2P1,2)X into a part containing the hard-scattering cross-section for producing a
gluon or a charm quark and a part which specifies the fragmentation of the gluon (or
the charm quark) into the required charmonium state, i.e.
dσ(AB → (2S, 2P1,2)X) =
∑ ∫ 1
0
dz dσ(AB → cX)Dc→(2S,2P1,2)(z, µ), (4)
where c is the fragmenting parton (either a gluon or a charm quark) and the sum in
the above equation runs over the contributing partons. D(z, µ) is the fragmentation
function. The fragmentation function which is computed perturbatively at an initial
scale of the order of the charm quark mass is evolved to the scale typical of the frag-
menting parton which is of the order of pT/z, using the Altarelli-Parisi equation. For
the production cross-sections of the gluons and charm quarks we will use the lowest-
order cross-sections, dσˆ/dtˆ(ab → cd), just as in the case of the fusion contribution.
The full set of initial fragmentation functions that we need to obtain the 2S and 2P
contributions are : Dg→2S [7], Dg→2P [17], Dc→2S [18] and Dc→2P [19, 20]. The final
cross-section for the fragmentation process is given by a formula similar to Eq. 1 but
with an extra integration over z, or equivalently over x2.
As mentioned earlier, a major uncertainty in these calculations is due to the wave-
functions. In the computation of the fusion contribution these appear in the subprocess
cross-sections, whereas for the fragmentation contribution, the fragmentation functions
at the initial scale are proportional to the wave-function factors. The wave function
factor R20 for ψ
′ is reasonably well-determined [5], but we have to make assumptions
for the parameters that describe the 2P states. In Ref. [17] the fragmentation function
for g → χ is written in terms of two parameters H1 and H ′8, where H1 is related to R′1,
and H ′8 is a parameter that describes the g → χ fragmentation via a S-wave cc¯ colour-
octet state. We assume that the H1 for the 2P states is about the same magnitude
as that of the 1P states [13]. The parameter H ′8 has a large range of uncertainty even
for the 1P states. On general grounds one expects the H ′8 parameter for the 2P state
to lie in the same range [11]. Firstly the H1 and H
′
8 contributions to any P -wave
quarkonium production are expected to be comparable in size. Secondly the wave
function factor R20, which is the colour singlet analogue of H
′
8, is similar in size for the
1S and 2S states. Therefore we assume the same H ′8 parameter for the 2P state as for
1P ; whether or not they are exactly equal is immaterial in view of the large uncertainty
in this parameter. The parameter values used are R20 = 0.49 GeV
3 [5], H1 = 15.0 MeV
and H ′8 = 3.0 MeV [7, 17]. We take the masses of the 2
3P1 and the 2
3P2 states to
be 3.95 GeV and 3.98 GeV, respectively [13]. In our computations, we use [21] the
3
updated MRSD-′ parametrisations [22] for the parton densities in the nucleon, evolved
to a scale Q2 = µ2/4, where µ is chosen to be MT for the fusion process, and equal to
pg,cT = pT/z for the fragmentation process. The fragmentation functions are evolved to
the scale pT/z.
Finally, we come to the branching ratios for the radiative decay 23P1,2 → 23S1+γ.
The absolute value of these widths have been estimated by rescaling the known values
for the bottomonium system [11]. One gets Γ(23P1,2 → 23S1+γ) ∼ 0.1−0.2 MeV. The
corresponding total widths have been estimated, assuming phase-space and dynamical
suppressions into open charm states, to be ∼ 2 − 5 MeV each [11]. The resulting
branching ratios for 23P1,2 → 23S1 + γ lie in the range 2 – 10%. The results presented
below are based on the optimistic value of the branching ratios = 10%.
In Fig. 1 we present our results for Bdσ/dpT for ψ
′ production in p¯p collisions at√
s = 1.8 TeV and integrated over a pseudo-rapidity interval |η| ≤ 0.5, and compare
our predictions to the data from the CDF experiment [1]. B = 7.7 × 10−3 is the ψ′
branching ratio into leptons. As in the case of J/ψ production [8], we find the g → P -
state fragmentation contribution to be dominant. The inclusion of the contribution
of the 2P states increases the ψ′ cross-section significantly, and assuming a value of
10% for the branching ratios this is capable of explaining the bulk of the observed
cross-section. It should be noted of course that this choice of the 2P → 2S branching
ratios corresponds to the upper end of the estimated range. Within the lattitude of this
range the cross-section can go down by a factor of 5. Further there is an uncertainty
of a factor of 3 on either side in the production cross-section of the 2P states, arising
largely from the H1 and H
′
8 parameters. Consequently the predicted normalisation of
the ψ′ cross-section can be anywhere between the experimentally observed range and an
order of magnitude below. Thus it is premature to rule out the necessity of more exotic
contributions, e.g. from the hybrid states suggested in [11]. It is remarkable nonetheless
that the inclusion of the 2P contributions can push up the predicted ψ′ cross-section
by the required factor of ∼ 30 within the lattitude of the model parameters.
In conclusion, we find the 23P1,2 contribution to ψ
′ production at CDF to be very
important. We have computed the fusion and fragmentation contributions to these 2P -
states and to the 2S ψ′ state, and find that with an optimistic choice of the 2P → 2S
branching, it is possible to explain the anomalously large cross-section for ψ′ production
reported by at the CDF experiment.
We are grateful to Frank Close for communicating his work of Ref. [11] to us before
its public distribution.
4
References
[1] F. Abe et al., Phys. Rev. Lett. 69 (1992) 3704; V. Papadimitrou, CDF Collab-
oration, presented at the “Rencontres de la Vallee d’Aoste”, La Thuile, March
1994; M. Mangano, CDF collaboration, presented at the “XXIX Rencontres de
Moriond on QCD and High Energy Hadronic Interactions”, Meribel, March 1994;
CDF Collaboration, presented at the 27th International Conference on High En-
ergy Physics, Glasgow, July (1994), Fermilab-Conf-94/136-E.
[2] E.L. Berger and D. Jones, Phys. Rev. D 23 (1981) 1521.
[3] R. Baier and R. Ru¨ckl, Z. Phys. C 19 (1983) 251.
[4] A.J. Ashman et al., Z. Phys. C 51 (1992) 21.
[5] G.A. Schuler, CERN preprint CERN-TH.7170/94.
[6] E.W.N. Glover, A.D. Martin and W.J. Stirling, Z. Phys. C 38 (1988) 473.
[7] E. Braaten and T.C. Yuan, Phys. Rev. Lett. 71 (1993) 1673.
[8] D.P. Roy and K. Sridhar, CERN preprint CERN-TH.7329/94.
[9] E. Braaten, M.A. Doncheski, S. Fleming and M. Mangano, Phys. Lett. B 333
(1994) 548.
[10] M. Cacciari and M. Greco, Frascati preprint LNF-94/024(P).
[11] F.E.Close, Rutherford preprint RAL-94-093.
[12] P. Cho, M.B. Wise and S.P. Trivedi, Fermilab preprint FERMILAB-PUB-
94/256-T.
[13] S. Godfrey and N. Isgur, Phys. Rev. D 32 (1985) 189.
[14] R. Kokoski and N. Isgur, Phys. Rev. D 35 (1987) 907.
[15] A. Le Yaouanc, L. Oliver, O. Pene and J.C. Raynal, Phys. Lett. B 71 (1977)
397.
[16] R. Gastmans, W. Troost and T.T. Wu, Phys. Lett. B 184 (1987) 257.
[17] E. Braaten and T.C. Yuan, Fermilab preprint FERMILAB-PUB-94/040-T.
[18] E. Braaten, K. Cheung and T.C. Yuan, Phys. Rev. D 48 (1993) 4230.
[19] Y.Q. Chen, Phys. Rev. D 48 (1993) 5181.
5
[20] T.C. Yuan, U.C. Davis preprint UDC-94/2.
[21] PDFLIB: H. Plothow-Besch, Comp. Phys. Comm. 75 (1993) 396.
[22] A.D. Martin, R.G. Roberts and W.J. Stirling, Phys. Lett. B 306 (1993) 145;
Phys. Lett. B 309 (1993) 492.
6
Figure captions
Fig. 1 The cross-section Bdσ/dpT (integrated over the pseudorapidity range−0.5 < η <
0.5) for the process p¯p→ ψ′X as a function of pT at
√
s = 1.8 TeV. The data are
taken from Ref. [1]. The different curves correspond to the direct production via
fusion (dashed line), the gluon fragmentation contribution (dashed-dotted line),
the charm quark fragmentation term (dotted line) and the sum of all contribu-
tions (solid line).
7
This figure "fig1-1.png" is available in "png"
 format from:
http://arXiv.org/ps/hep-ph/9409232v1


A possible resolution of the CDF Ψ' anomaly

http://repository.ias.ac.in/41064/1/15_aut.pdf