Ψ(2S) and Υ(3S) Suppression in p-Pb 8 TeV Collisions and Mixed Heavy Quark Hybrid Mesons
aa r X i v : . [ h e p - ph ] J un Ψ(2 S ) and Υ(3 S ) Suppression in p-Pb 8 TeV Collisionsand Mixed Heavy Quark Hybrid Mesons Leonard S. Kisslinger Department of Physics, Carnegie Mellon University, Pittsburgh PA 15213 USA.Debasish Das , High Energy Nuclear and Particle Physics Division,Saha Institute of Nuclear Physics, 1/AF, Bidhan Nagar, Kolkata 700064, INDIA.
1) [email protected] 2)[email protected]; 3) [email protected]
Abstract
This brief report is an extension of a previus publication on Ψ(2 S ) to J/ Ψ(1 S )suppression in p-Pb collisions at 5.02 TeV to estimate Ψ(2 S ) to J/ Ψ(1 S ) and Υ(3 S )to Υ(1 S ) suppression via p-Pb collisions at 8 TeV as proposed by the LHCb. PACS Indices:12.38.Aw,13.60.Le,14.40.Lb,14.40.Nd
Recently Ψ(2 S ) suppression S A = [ σ Ψ(2 S ) /σ J/ψ ] pP b / [ σ Ψ(2 S ) /σ J/ψ ] pp in p-Pb collisions at E=5.02 TeV, and Υ(3 S ) suppression S A = [ σ Υ(3 S ) /σ Υ(1 S ) ] P bP b / [ σ Υ(3 S ) /σ Υ(1 S ) ] pp in Pb-Pb col-lisions, were estimated[1] and compared to experimental[2, 3]. By using the mixed heavyquark hybrid theory[4] it was found that the theoretical estimates agreed with experimentswithin errors in experiments and theory. This was reviewed[5] before Ref.[1] was published.Since the article Ref.[1] was published LHCb has recently submitted a document[6] tosupport the request for p-Pb and Pb-p collisions at 8 TeV to produce Ψ and Υ mesonsto measure “cold nuclear matter effects”, which we call Ψ(2 S ) / ( J/ Ψ) and Υ(3 S ) / Υ(1 S )suppression. The objective of the present work is to estimate J/ Ψ(1 S ), Ψ(2 S ), Υ(1 S ),and Υ(3 S ) suppression using the mixed heavy quark theory for p-Pb vs p-p collisions inanticipation of the future LHCb experiment[6].Three decades ago J/ Ψ suppression by the formation of the Quark-Gluon Plasma (QGP)in Reltivistic Heavy Ion Collisions (RHIC) was estimated[7]. This is closely related to usingthe mixed hybrid theory to detect the formation of the QGP via RHIC[8], since gluons inthe QGP enhance the production of Ψ(2 S ) and Υ(3 S ) states due to the active gluon in theirhybrid component. This is reviewed in the following section.In the present work the on Ψ(2 S ), J/ Ψ(1 S ), Υ(1 S ), and Υ(3 S ) suppression produced in p-Pb collisions at 8 TeV we employ the theoretical methods of Ref.[1] using scenario 1. of Ref[9],to estimate S A = [ σ Ψ(2 S ) /σ J/ψ ] pP b / [ σ Ψ(2 S ) /σ J/ψ ] pp , S A = [ σ Υ(3 S ) /σ Υ(1 S ) ] pP b / [ σ Υ(3 S ) /σ Υ(1 S ) ] pp ,in p-Pb 8 TeV collisions. 1 Theoretical
Ψ(2 S ) to J/ Ψ(1 S ) and Υ(3 S ) to Υ(1 S ) sup-pression in p-Pb collisions and the mixed heavy quarkhybrid theory In this section we start our theortical estimate of the suppression, S A , of charmonium andbottomonium states by a brief review of the mixed hybrid theory, followed by the theoreticalestimate of S A for Ψ(2 S ), J/ Ψ(1 S ), Υ(3 S ), and Υ(1 S ) in p-Pb collisions. The nature of the J/ Ψ(1 S ), Ψ(2 S ) as standard, hybrid, or mixed standard-hybrid charmo-nium states, and Υ(1 S ), Υ(3 S ) as standard, hybrid, or mixed standard-hybrid bottominiumstates was studied in, Ref.[4] making use of QCD Sum Rules[11].The operator that produces the mixed charmonium and hybrid charmonium states, with f determined from the Sum Rule, is J C − HC = f J H + q − f J HH , (1)with J H | > = | c ¯ c (0) >, J HH | > = | [ c ¯ c (8) g ](0) > , where | c ¯ c (0) > is a standard Charmoniumstate, while a hybrid Charmonium state | [ c ¯ c (8) g ](0) > has c ¯ c (8) with color=8 and a gluonwith color=8. In Ref.[4] it was found that for J/ Ψ(1 S ) f ≃ . S ) f ≃ . | J/ Ψ > ≃ | c ¯ c (0)(1 S ) > | Ψ(2 S ) > ≃ . | c ¯ c (0)(2 S ) > +0 . | [ c ¯ c (8) g ](0)(2 S ) > , (2)therefore the Ψ(2 S ) meson is 50% normal charmonium and 50% hybrid charmonium, whilethe J/ Ψ is a normal charmonium meson.Using a similar QCD Sum Rule calculation for bottominium states[4] it was found thatthe Υ(1 S ) is a standard bottominium meson, while the Υ(3 S ) is 50% normal and 50% hybridbottominium meson: | Υ(1 S ) > ≃ | b ¯ b (0)(1 S ) > | Υ(3 S ) > ≃ . | b ¯ b (0)(3 S ) > +0 . | [ b ¯ b (8) g ](0)(3 S ) > . (3)We shall use this to estimate the ratios of suppression of Ψ(2 S ) to J/ Ψ and Υ(3 S ) toΥ(1 S ) is in p-Pb collisions. Ψ(2 S ) to J/ Ψ(1 S ) suppression in p-Pb collisions The suppression, S A , of a charmonium state is given by the interaction with nucleons as ittraverses the nucleus. In this subsection we give a brief review of S A for standard and hybridcharmonium mesons derived in Ref.[1]. S A = e − n o σ Φ N L , (4)2here Φ is a c ¯ c or c ¯ cg meson, L is the length of the path of Φ in nuclear matter ≃ n o = . f m − , and σ Φ N is the cross sectionfor Φ- nucleon collisions.From Refs.[10] the cross section for standard charmonium c ¯ c meson via strong QCDinteractions with nucleons is given by σ c ¯ cN = 2 . α s πr c ¯ c , (5)where α s ≃ r c ¯ c ≃6 h/ (2 M c c ), with M c the charmquark mass. Using 2 M c ≃ M J/ Ψ ≃ r c ¯ c ≃ × − m = 0 . f m . Therefore, σ c ¯ cN ≃ . × − f m = 3 . × − mb.Taking L ≃ n o = . f m − n o σ c ¯ cN L ≃ . S c ¯ cA = e − n o σ c ¯ cN L ≃ . . (6)On the other hand, the cross section for hybrid charmonium c ¯ cg meson via strong QCDinteractions with nucleons has been estimated in Ref[10] as σ c ¯ cgN ≃ σ c ¯ cgN ≃ . mb , (7)with the result n o σ c ¯ cgN L ≃ .
88 to 1 . S c ¯ cgA ≃ . . . (8)Using the mixed hybrid model one finds for the ratio of Ψ(2 S ) to J/ Ψ(1 S ) suppressionin p-Pb collisions R Ψ(2 S ) / ( J/ Ψ) | theory ≃ . . ≃ .
66 to 0 . . (9)As pointed out in Ref.[12], the Color Glass Condensate model[13] overestimates thesuppression, while other theoretical models successfully estimate J/ Ψ suppression, but do nottreat the Ψ(2 S ) suppression. Since they would use a standard c ¯ c rather than the mixed hybridtheory with a c ¯ cg component as in the present work, they would probably underestimate theΨ(2 S ) suppression. Υ(3 S ) to Υ(1 S ) suppression in p-Pb collisions For a standard bottomonium meson state or a hybrid bottomonium state the equation forsuppression is given by Eq(4) where Φ is a b ¯ b or b ¯ bg meson. As for charmonium L is thelength of ≃ n o = . f m − .3rom Eq(5) the cross section for standard bottomonium b ¯ b meson via strong QCD in-teractions with nucleons, σ b ¯ bN = 2 . α s πr b ¯ b differs from σ c ¯ cN by a factor of M c /M b ≃ . σ b ¯ bN ≃ . × . × − mb ≃ × − mbn o σ b ¯ bN L ≃ . S c ¯ cA = e − n o σ c ¯ cN L ≃ . . (10)Similarly, the cross section for hybrid bottomonium b ¯ bg meson via strong QCD interac-tions with nucleons σ b ¯ bgN = σ c ¯ cgN ( M c /M b ) ≃ . σ c ¯ cgN ≃ n o σ b ¯ bgN L ≃ .
08 to 0 . S b ¯ bgA ≃ .
92 to 0 . . (11)Using the mixed hybrid model one finds for the ratio of Υ(3 S ) to Υ(1 S ) suppression inp-Pb collisions R Υ(3 S ) / Υ(1 S )) | theory ≃ .
90 to 0 . ≃ .
95 to 0 . . (12) Using the mixed heavy quark hybrid theory for Ψ(2 S ) and Υ(3 S ) states we have estimatedΨ(2 S ) to J/ Ψ and Υ(3 S ) to Υ(1 S ) suppression ratios, R Ψ(2 S ) / ( J/ Ψ) | theory and R Υ(3 S ) / Υ(1 S )) | theory ,for p-Pb vs p-p collisions at 8 TeV in anticipation of future LHCb experiments[6]. Note thatprevious experiments[2] measuring R Ψ(2 S ) / ( J/ Ψ) used p-Pb collisions at 5.02 TeV.If future experiments measure the R Ψ(2 S ) / ( J/ Ψ) and R Υ(3 S ) / Υ(1 S )) ratios for p-Pb vs p-pcollisions, with the Ψ(2 S ) meson predicted to be 50% normal charmonium and 50% hybridcharmonium and the Υ(3 S ) meson predicted to be 50% normal bottomonium and 50% hybridbottomonium[4], one would have another test of the mixed heavy quark hybrid theory. Acknowledgements
Author D.D. acknowledges the facilities of Saha Institute of Nuclear Physics, Kolkata,India. Author L.S.K. acknowledges support from the P25 group at Los Alamos NationalLaboratory.
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