arXiv:1306.6616v4 [hep-ph] 6 Sep 2013
Ψ and Υ Production In pp Collisions at 7.0 TeV Leonard S. Kisslinger Department of Physics, Carnegie Mellon University, Pittsburgh PA 15213 USA
[email protected] Debasish Das Saha Institute of Nuclear Physics,1/AF, Bidhan Nagar, Kolkata 700064, INDIA
[email protected];
[email protected] PACS Indices:12.38.Aw,13.60.Le,14.40.Lb,14.40Nd Abstract This is an extension of recent studies for Υ(nS) and Ψ(1S, 2S) production at the √ LHC in pp collisions, s=7.0 TeV, with the ALICE detector.
Keywords:Heavy Quark Hybrid; LHC ALICE detector; rapidity cross-sections PACS Indices:12.38.Aw,13.60.Le,14.40.Lb,14.40Nd
1
Differential rapidity cross sections for heavy quark state production at ALICE
This brief report is a continuation of our work on Υ(nS) production which was published recently[1]. It is in anticipation of the publication of new ALICE experimental results[2] on J/Ψ(1S), Ψ(2S), and Υ(nS) production in the rapidity range 2.5 ≤ y ≤ 4.0. The differential rapidity cross section for λ = 0 (dominant for Υ(nS), Ψ(nS) production) is given by [3] dσpp→Φ(λ=0) 1 dx = AΦ fg (x(y), 2m)fg (a/x(y), 2m) , dy x(y) dy
(1)
with a = 4m2 /s, s = E 2 , E = 7.0 TeV, m = 5.0 GeV for Upsilon and 1.5 GeV for given in Refs[3],[1]. Charmonium states, fg the gluonic distribution function, and x(y), dx dy −6 −7 For Upsilon, Charmonium a = 2.04 × 10 , 1.8 × 10 . Φ in Eq(1) is either Ψ or Υ, with AΥ = 1.74 × 10−8 and AΨ = 6.46 × 10−7 . The gluonic distribution fg (x(y), 2m) for the range of x needed for E = 7.0 TeV is[3] fg (x(y)) = 275.14 − 6167.6 ∗ x + 36871.3 ∗ x2 .
(2)
The calculation of the production of Υ(3S) and Ψ(2S) states is done with the usual quark-antiquark model, and with the mixed heavy hybrid theory[4].
With these parameters we find for the differential rapidity cross sections for Υ(1S) and Υ(2S) production as shown in the figures below.
1.0
Υ(1S)
d σ/dy (pb)
0.8 0.6 0.4 0.2
2.5
3.0
3.5
4.0
y
Figure 1: dσ/dy for pp collisions at
√
s = 7.0 TeV producing Υ(1S).
0.040 Υ(2S)
d σ/dy (pb)
0.035 0.030 0.025 0.020
Υ
0.015 2.5
3.0
3.5
4.0
y
Figure 2: dσ/dy for pp collisions at
√
s = 7.0 TeV producing Υ(2S).
d σ/dy (pb)
The differential rapidity cross sections for Υ(3S) production with the hybrid and standard theories are shown in the figure below.
0.016 0.014
Υ(3S) hybrid
0.012 0.010 0.008 0.006 0.004 0.002
Υ(3S)
3.0
2.5
3.5
4.0
y
Figure 3: dσ/dy for pp collisions at theories.
√
s = 7.0 TeV producing Υ(3S) for usual and hybrid
The differential rapidity cross section for J/Ψ(1S) is shown in the figures below.
0.045
d σ/dy (nb)
0.043 0.041
J/psi (1S)
0.039 0.037 0.035 2.5
3.0
3.5
4.0
y
Figure 4: dσ/dy for pp collisions at
√
s = 7.0 TeV producing J/Ψ(1S).
The differential rapidity cross sections for Ψ(2S) production with the hybrid and standard theories are shown in the figure below.
0.0045 0.0040
Psi(2S)hybrid
d σ/dy (nb)
0.0035 0.0030 0.0025
Psi(2S)
0.0020 0.0015
3.0
2.5
3.5
4.0
y
Figure 5: dσ/dy for pp collisions at theories.
√
s = 7.0 TeV producing Ψ(2S) for usual and hybrid
For Υ(3S) and Ψ(2S) the standard q q¯ prediction is shown by dashed curves, while the prediction using the mixed hybrid theory[4] is shown with solid curves, with the difference explained in Ref[3].
2
Conclusions
We expect that our results for the rapidity dependence of dσ/dy shown in the figures can be useful for experimentalists studing heavy quark production in p-p collisions at the LHC. It is also a test of the validity of the mixed heavy quark hybrid theory, which we are using to test the creation of the Quark Gluon Plasma via relativistic heavy ion collisions.
Acknowledgements Author DD acknowledges the facilities of Saha Institute of Nuclear Physics, Kolkata, India. We thank Dr. Hugo Pereira Da Costa and his ALICE collaborators for sending information about their forthcoming publication.
References [1] Leonard S. Kisslinger and Debasish Das, Mod. Phys. Lett A, Vol.28, No.16 1350067 (2013) [2] Hugo Pereira Da Costa, Xavier Lopez, and Livio Bianchi, ALICE Collaboration, to be submitted 2013 [3] L.S. Kisslinger, M.X. Liu, and P. McGaughey, arXiv:1106.4049, Phys. Rev D 84, 114020 (2011). [4] L.S. Kisslinger, Phys. Rev. D 79, 114026 (2009)
