The production of charmed and beauty hadrons in proton-proton collisions at
high energies are analyzed within the modified quark-gluon string model (QGSM)
including the internal motion of quarks in colliding hadrons. We present some
predictions for the future experiments on the beauty baryon production in $pp$
collisions at LHC energies. This analysis allows us to find interesting
information on the Regge trajectories of the heavy (b{\bar b}) mesons and the
sea beauty quark distributions in the proton.Comment: 7 pages, 7 figures. Talk given at EDS'09: 13th International
  Conference on Elastic & Diffractive Scattering, CERN, Geneva, 29th June-3rd
  July, 200

Bednyakov, V. A.

Lykasov, G. I.

Lyubushkin, V. V.

Lyubushkina, T. V.

English

arXiv

The production of charmed and beauty hadrons in proton-proton collisions at high energies are analyzed within the modified quark-gluon string model (QGSM) including the internal motion of quarks in colliding hadrons. We present some predictions for the future experiments on the beauty baryon production in $pp$ collisions at LHC energies. This analysis allows us to find interesting information on the Regge trajectories of the heavy (b{\bar b}) mesons and the sea beauty quark distributions in the proton

Lykasov, G I

Lyubushkin, V V

Lyubushkina, T V

Bednyakov, V A

CERN Document Server

Beauty Baryon Production in pp Collisions atLHC and b Quark Distribution in the ProtonG.I. Lykasov1, V.V. Lyubushkin1, T.V. Lyubushkina1 and V.A. Bednyakov11JINR, Dubna, 141980, Moscow region, RussiaThe production of charmed and beauty hadrons in proton-proton and proton-antiprotoncollisions at high energies are analyzed within the modified quark-gluon string model(QGSM) including the internal motion of quarks in colliding hadrons. We present somepredictions for the future experiments on the beauty baryon production in pp collisionsat LHC energies. This analysis allows us to find interesting information on the Reggetrajectories of the heavy (bb¯) mesons and the sea beauty quark distributions in the proton.1 IntroductionVarious approaches of perturbative QCD including the next-to-leading order calculations (NLOQCD) have been applied to construct distributions of quarks in a proton. The theoreticalanalysis of the lepton deep inelastic scattering (DIS) off protons and nuclei provides ratherrealistic information on the distribution of light quarks like u, d, s in a proton. However, to finda reliable distribution of heavy quarks like c(c¯) and especially b(b¯) in a proton describing theexperimental data on the DIS is a non-trivial task. It is mainly due to small values of D and Bmeson yields in the DIS at existing energies. Even at the Tevatron energies the B- meson yieldis not so large. At LHC energies the multiplicity of these mesons produced in pp collisions willbe significantly larger. Therefore one can try to extract a new information on the distributionof these heavy quarks in a proton. In this paper we suggest to study the distribution of heavyquarks like c(c¯) and b(b¯) in a proton from the analysis of the future LHC experimental data.The multiple hadron production in hadron-nucleon collisions at high energies and largetransfers is usually analyzed within the hard parton scattering model (HPSM) suggested in [1, 2].This model was applied to the charmed meson production both in proton-proton and meson-proton interactions at high energies, see for example [3]. The HPSM is significantly improved byapplying the QCD parton approach [4, 5], see details in [6] and references therein. Unfortunatelythe QCD including the next-to-leading order (NLO) has some uncertainties related to therenormalization parameters especially at small transverse momenta pt [6].In [6, 7] we studied the charmed and beauty meson production in pp and pp¯ collisions athigh energies within the QGSM [8] or the dual parton model (DPM) [9] based on the 1/Nexpansion in QCD [10, 11]. It was shown that this approach can be applied rather successfullyat not very large values of pt. In this paper we investigate the open charm and beauty baryonproduction in pp collisions at LHC energies and very small pt within the QGSM to find newinformation on the Regge trajectories of the heavy (cc¯) and (bb¯) mesons and the sea beautyquark distributions in the proton.4222 General Formalism for Hadron Production in ppCollision within QGSMLet us present briefly the scheme of the analysis of the hadron production in the pp colli-sions within the QGSM including the transverse motion of quarks and diquarks in collidingprotons [12]. As is known, the cylinder type graphs for the pp collision presented in Fig. 1make the main contribution to this process [8]. The left diagram of Fig. 1, the so-calledone-cylinder graph, corresponds to the case where two colourless strings are formed betweenthe quark/diquark (q/qq) and the diquark/quark (qq/q) in colliding protons; then, after theirbreakup, qq¯ pairs are created and fragmented to a hadron, for example, D meson. The right dia-gram of Fig. 1, the so-called multicylinder graph, corresponds to creation of the same two colour-less strings and many strings between sea quarks/antiquarks q/q¯ and sea antiquarks/quarks q¯/qin the colliding protons. The general form for the invariant inclusive hadron spectrum withinFigure 1: The one-cylinder graph (left diagram) and the multicylinder graph (right diagram)for the inclusive pp→ hX process.the QGSM is [13, 12]Edσd3p≡ 2E∗pi√sdσdxdp2t=∞∑n=1σn(s)φn(x, pt) , (1)where E,p are the energy and the three-momentum of the produced hadron h in the laboratorysystem (l.s.) of colliding protons; E∗, s are the energy of h and the square of the initial energy inthe c.m.s of pp; x, pt are the Feynman variable and the transverse momentum of h; σn is the crosssection for production of the n-Pomeron chain (or 2n quark-antiquark strings) decaying intohadrons, calculated within the “eikonal approximation” [14]. Actually, the function φn(x, pt)is the convolution of the quark (diquark) distributions in the proton and their fragmentationfunctions (FF), see details in [8, 9, 6, 12]. To calculate the interaction function φn(x, pt) wehave to know all the quark (diquark) distribution functions in the nth Pomeron chain andthe FF. They are constructed within the QGSM using the knowledge of the secondary Reggetrajectories, see details in [8, 13].3 Heavy Baryon Production within QGSM3.1 Sea Charm and Beauty Quark Distribution in the ProtonNow let us analyze the charmed and beauty baryon production in the pp collision at LHCenergies and very small pt within the soft QCD, e.g., the QGSM. This study can be interestingBEAUTY BARYON PRODUCTION IN pp COLLISIONS AT LHC AND b-QUARK DISTRIBUTION IN . . .423for it may allow predictions for future LHC experiments like TOTEM and ATLAS and anopportunity to find new information on the distribution of sea charmed (c) and beauty (b)quarks at very low Q2. According to the QGSM, the distribution of c(c¯) quarks in the nthPomeron chain (Fig. 1, right) is, see for example [12] and references therein,f(n)c(c¯)(x) = C(n)c(c¯)δc(c¯)xacn(1− x)gcn (2)where acn = −αψ(0), gcn = αρ(0) − 2αB(0) + (αρ(0) − αψ(0)) + n − 1; δc(c¯) is the weight ofcharmed pairs in the quark sea, C(n)c(c¯) is the normalization coefficient [13], αψ(0) is the interceptof the ψ- Regge trajectory. Its value can be −2.18 assuming that this trajectory αψ(t) is linearand the intercept and the slope α′ψ(0) can be determined by drawing the trajectory through theJ/Ψ-meson mass mJ/Ψ ' 3.1 GeV and the χ-meson mass mχ = 3.554GeV [15]. Assuming thatthe ψ-Regge trajectory is nonlinear one can get αψ(0) ' 0, which follows from perturbativeQCD, as it was shown in [16]. The distribution of b(b¯) quarks in the nth Pomeron chain (Fig. 1,right) has the similar formf(n)b(b¯)(x) = C(n)b(b¯)δb(b¯)xabn(1− x)gbn (3)where abn = −αΥ(0), gbn = αρ(0)− 2αB(0) + (αρ(0)− αΥ(0)) + n− 1; αρ(0) = 1/2 is the wellknown intercept of the ρ-trajectory; αB(0) ' −0.5 is the intercept of the baryon trajectory,αΥ(0)) is the intercept of the Υ- Regge trajectory, its value also has an uncertainty. Assumingits linearity one can get αΥ(0)) = −8,−16, while for nonlinear (bb¯) Regge trajectory αΥ(0) ' 0,see details in [17]. Inserting these values to the form for f(n)c(c¯)(x) and f(n)b(b¯)(x) we get the largesensitivity for the c and b sea quark distributions in the nth Pomeron chain. Note that theFFs also depend on the parameters of these Regge trajectories. Therefore, the knowledge of theintercepts and slopes of the heavy-meson Regge trajectories is very important for the theoreticalanalysis of open charm and beauty production in hadron processes.Note that all the quark distributions obtained within the QGSM are different from theparton distributions obtained within the perturbative QCD which are usually compared withthe experimental data on the deep inelastic lepton scattering (DIS) off protons. To match thesetwo kinds of quark distributions one can apply the procedure suggested in [18]. The quantitiesgcn or gbn entering into Eq. (2) and Eq. (3) are replaced by the following new quantitiesdepending on Q2g˜cn = gcn(1 +Q2Q2 + c); g˜bn = gbn(1 +Q2Q2 + d)(4)The parameters c and d are chosen such that the structure function constructed from thevalence and sea quark (antiquark) distributions in the proton should be the same as the one atthe initial conditions at Q2 = Q20 for the perturbative QCD evolution. A similar procedure canbe used to get the Q2 dependence for the powers acn and abn entering into Eqs. (2) and (3) [18].Then, using the DGLAP evolution equation [19], we obtain the structure functions at large Q2.3.2 Charmed and Beauty Baryon Production in pp CollisionThe information on the charmonium (cc¯) and bottomonium (bb¯) Regge trajectories can be foundfrom the experimental data on the charmed and beauty baryon production in pp collisions atG I LYKASOV, V V LYUBUSHKIN, T V LYUBUSHKINA, AND V A BEDNYAKOV42410-410-310-210-11100 0.2 0.4 0.6 0.8 1xdσ/dx (mb)p p Õ Λc XR422R608αΨ = 0αΨ = -2.18Figure 2: The differential cross section dσ/dx for the inclusive process pp → ΛcX at √s =62 GeV.10-610-510-410-310-210-110 0.2 0.4 0.6 0.8 1xdσ/dx (mb)p p Õ Λb XαΥ = 0αΥ = -8αΥ = -1610-410-310-210-10 2 4 6 8 10Pt2 (GeV 2)dσ/dP t2  (mb  / GeV 2 )p p Õ Λb XαΥ = 0αΥ = -8αΥ = -16Figure 3: The differential cross section dσ/dx (left) and dσ/dP 2t (right) for the inclusive processpp→ ΛbX at √s = 4 TeV.high energies. For example, Fig. 2 illustrates the sensitivity of the inclusive spectrum dσ/dxof the produced charmed baryons Λc to different values for αψ(0). The solid line correspondsto αψ(0) = 0, whereas the dashed curve corresponds to αψ(0) = −2.18. Unfortunately theexperimental data presented in Fig. 2 have big uncertainties; therefore, one cannot extract theinformation on the αψ(0) values from the existing experimental data. A high sensitivity of theinclusive spectrum dσ/dx of the produced beauty baryons Λb to different values for αΥ(0) isBEAUTY BARYON PRODUCTION IN pp COLLISIONS AT LHC AND b-QUARK DISTRIBUTION IN . . .425presented in Fig. 3 (left). The pt-inclusive spectrum of Λb has much lower sensitivity to thisquantity, according to the results presented in Fig. 3 (right). Actually, our results presented inFig. 3 could be considered as some predictions for future experiments at LHC, see Fig. 4.Now let us analyze the production of the beauty hyperon, namely Λ0b , at small scatteringangles θΛ0b in the pp collision at LHC energies. This study would be reliable for the futureforward experiments at LHC. The produced Λ0b baryon can decay as Λ0b → J/ΨΛ0, and J/Ψdecays into µ+µ−, its branching ratio (Br = Γj/Γ) is 5.93± 0.06 percent, or into e+e− (Br =5.93± 0.06%), whereas Λ0 can decay into ppi− (Br = Γj/Γ = 63.9± 05%), or into npi0 (Br =35.8± 0.5%), see Fig. 4.Figure 4: The decay Λb → JΨ Λ0 → µ+µ−(e+e−) ppi−(npi0).dσd3p1dM34=∫dσdM12dM34(5)δ(3)(p1 + p2 − p12)dM12 ,wheredσdM12dM34=∫d2ptΛbdσpp→ΛbXdxd2ptΛbBrΛb→J/ΨBrJ/Ψ→µ+µ−BrΛ0→ppipi32M2effM12M34λ1/2(M2eff ,M212,M234)λ1/2(M212,M21 ,M22 )λ1/2(M234,M23 ,M24 ) ,BrΛb→J/Ψ = (4.7± 2.8) · 10−4; BrJ/Ψ→µ+µ− = (5.93± 0.06)%; BrΛ0→ppi = (63.9± 0.5)%.Here λ(x2, y2, z2) = ((x2 − (y + z)2)((x2 − (y − z)2)One can get the following relationd3p1 =12pξpdφ1dξpdtp , (6)where ξp = ∆p/p is the energy loss, tp = (pin − p1)2 is the four-momentum transfer, φ1 is theazimuthal angle of the final proton with the three-momentum p1.Experimentally one can measure the differential cross sectiondσdξpdtpdMJ/Ψ=12pξp∫dσd3p1dM34dφ1 (7)G I LYKASOV, V V LYUBUSHKIN, T V LYUBUSHKINA, AND V A BEDNYAKOV426This distribution could be reliable for the TOTEM experiment, where J/Ψ decays into µ+µ−and Λ0b decays into pi−p or for the ATLAS forward experiment, where Λ0b decays as Λ0b →J/Ψ Λ0 → e+e− pi0n (Fig. 4).0 5 10 15 20 25 30 35 40 45 50θ(J/ψ), mradArbitrary eventsαΥ = 0αΥ = -8αΥ = -160.99 0.992 0.994 0.996 0.998 1ξpArbitrary eventsαΥ = 0αΥ = -8αΥ = -16Figure 5: The distributions of θJ/Ψ (left) and ξp (right) for the inclusive process pp→ ΛbX →µ+µ−ppi−X at√s = 4TeVIn Fig. 5 the distributions over θJ/Ψ (left) and ξp (right) are presented at different valuesof the intercept αΥ(0) = 0 (solid line), αΥ(0) = −8 (dashed line) and αΥ(0) = −16 (dottedline), where θJ/Ψ is the scattering angle for the final J/Ψ. Fig. 5 shows a sensitivity of thesedistributions to the intercept of the αΥ Regge trajectory. Actually, the result presented inFig. 5 is a prediction for future LHC experiments on the heavy flavour baryon production atthe LHC energies.4 ConclusionIt was shown [6, 7] that the modified QGSM including the intrinsic longitudinal and transversemotion of quarks (antiquarks) and diquarks in colliding protons allowed us to describe rathersatisfactorily the existing experimental data on inclusive spectra of heavy hadrons produced inpp and pp¯ collisions It allows us to make some predictions for future LHC forward experiments onthe beauty baryon production in pp collisions which can give us new information on the beautyquark distribution in the proton and very interesting information on the Regge trajectories of(bb¯) mesons.AcknowledgementsWe thank M. Deile, K. Eggert, D. Elia, P. Grafstro¨m, A. B. Kaidalov, A. D. Martin, M. Poghosyanand N. I. Zimin for very useful discussions. This work was supported in part by the RFBRgrant N 08-02-01003.BEAUTY BARYON PRODUCTION IN pp COLLISIONS AT LHC AND b-QUARK DISTRIBUTION IN . . .427References[1] A.V. Efremov, Yad. Fiz. 19 179 (1974).[2] R.D. Field and R.P. Feyman, Phys. Rev. D15 2590 (1977); R.D. Field, R.P. Feyman and G.C. Fox, Nucl.Phys. B128 1 (1977).[3] V.A. Bednyakov V.A., Mod.Phys.Lett. A10 61 (1995).[4] P. Nasson, S. Dawson and R.K. Ellis, Nucl. Phys. B303 607 (1988); ibid. B327 49 (1989); ibid. B335 260E(1989).[5] B.A. Kniehl and G. Kramer, Phys.Rev. D60 014006 (1999).[6] G.I. Lykasov, Z.M. Karpova, M.N. Sergeenko and V.A. Bednyakov, Europhys. Lett. 86 61001 (2009);arXiv:hep-ph/0812.3220 (2009).[7] G.I. Lykasov, V.V. Lyubushkin and V.A. Bednyakov, arXiv:hep-ph/0909.5061 (2009).[8] A.B. Kaidalov, Phys. Lett. B116 459 (1982); A.B. Kaidalov and K. A. Ter-Martirosyan, Phys. Lett. B117247 (1982).[9] A. Capella, U. Sukhatme, C. I. Tan, J. Tran Than Van, Phys. Rep. 236 225 (1994).[10] G. t’Hooft, Nucl.Phys. 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Beauty baryon production in pp collisions at LHC and b quark distribution in proton

Beauty baryon production in pp collisions at LHC and b quark
  distribution in proton

Beauty baryon production in pp collisions at LHC and b quark distribution in proton

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