arXiv:hep-ph/0602067v3 20 Oct 2006 n htamc adrfamnainfnto peaked function fragmentation harder much at a that ing ihalgtu rdw ur,peual fsoft of presumably quark, quark down charm or up a light combining a recom- for with by proposed or observation formation been [12][13] meson this also Coalesence charmed have of models [10][11]. discussion [14][15][16] in bination detailed found more be can A tion. olaigodr(L)pC acltosarewell charm agree open measured calculations the with pQCD (NLO) to-leading-order olsos[] oee,i hr arpouto,it hadroproduction, charm the in that observed However, was [8]. collisions nPTI 7)i nraoal gemn ihthe in with production agreement charm reasonable to in fits from is results [7]) PYTHIA in ula oicto atr fhayqak ntenu- [6] the function in Peterson quarks The for heavy medium. and of clear formation factors meson modification heavy nuclear for reference a provides nucleus- in produced collisions. matter QCD nucleus of state into new the insights of heavy unique properties Therefore, provide energy matter measurements dense collisions. and quark the nucleus-nucleus [3] of in properties flow heavy QCD created as probe the can such of [4][5] medium loss dynamics nuclear transport in nuclear The quarks of the conditions [1][2]. to initial the sensitive collisions for is flux production parton quark incoming for scale Charm natural a pQCD. sets the mass reli- quark heavy more the considered because able are Chromo- framework Quantum (pQCD) perturbative Dynamics the within quark Collider heavy production of Ion calculations Heavy Theoretical Relativistic energies. (RHIC) the at in collisions scatterings nuclear gluon-gluon, mostly parton-parton, initial a fe enue odsrb h hr fragmenta- charm parameter the the describe where to function, used tion been often has o-htncElectron Non-Photonic h ev ur rdcini + rpAcollisions p+A or p+p in production quark heavy The through produced be to believed are quarks Heavy z ≈ D nE.1i eddi hr hadroproduc- charm in needed is 1 Eq. in 1 ( eateto hsc n srnm,Uiest fClfri,Lo California, of University Astronomy, and Physics of Department z ≡ YHAMneCroeetgnrtri + olsosat collisions p+p in generator event Carlo Monte PYTHIA eo omto,i eddt ac h xeietldt.A data. experimental the match high to at needed consisten electrons is function, Peterson formation, the meson than harder much function ASnmes 41.x 44.b 13.20.Fc 14.40.Lb, 24.10.Lx, numbers: PACS oiatfrelectron for dominant arn r tde.W rps neprmna ehdt qu to method experimental an propose of We contributions studied. are hadrons p nttt fPril hsc,CnrlCiaNra nvriy Wu University, Normal China Central Physics, Particle of Institute ecmaetennpooi lcrnand electron non-photonic the compare We D /p c ) ∝ z c [1 -quark − D 1 p /z T and p p − hwlreucranisadthe and uncertainties large show T T eo easwt hre Hadrons Charged with Decays Meson p 1 p B ε/ T pcrm[] indicat- [9], spectrum itiuin fnext- of distributions T (1 eo eilpoi east h o-htncelectrons. non-photonic the to decays semi-leptonic meson itiuin n orltoso lcrn from Electrons of Correlations and Distributions pt e/.Creain fnnpooi lcrn ihc with electrons non-photonic of Correlations GeV/c. 8 to up ǫ − ≈ z e )] 0 + 2 . 5(default 05 e Dtd oebr6 2018) 6, November (Dated: − p and T ioa Lin Xiaoyan [17]. 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10-1 NLO c-quark with GRV98 HO NLO c-quark with GRV98 HO NLO c-quark with MRST HO FONLL uncertainty band FONLL uncertainty band -2 NLO c-quark with MRST HO 0 10 PYTHIA D with parp(67)=4 Default (ε = 0.05)

-2 PYTHIA B->e PYTHIA B->e

0 -5 -2 PYTHIA c-quark with parp(67)=4 PYTHIA D with parp(67)=4 Modified (ε = 10 ) -4 -3 PYTHIA D0 with parp(67)=1 Default (ε = 0.05) 10 PYTHIA D->e PYTHIA D->e 10 PYTHIA c-quark with parp(67)=1 PYTHIA D0 with parp(67)=1 Modified (ε = 10-5) PYTHIA Sum of D/B->e PYTHIA Sum of D/B->e 10-4 STAR EMC p+p STAR EMC p+p 10-6 -5 dy (GeV/c) 10 dy (GeV/c) parp(67)=4 parp(67)=1 T T

-6 -8 dp dp T 10 T 10

-7 N/p 10 N/p 2 2 d d -10 π π 10 10-8 1/2 1/2 0 π 0 π 10-9 STAR d+Au D (from K ) STAR d+Au D (from K ) 10-12 10-10 2 4 6 8 10 2 4 6 8 10 0 2 4 6 8 10 2 4 6 8 10 PT (GeV/c) PT (GeV/c)

FIG. 1: (color online) Charm quark (left) and D0 (right) FIG. 2: (color online) Electron spectra from PYTHIA calcu- spectra from PYTHIA calculations compared with next-to- lations with the modified Peterson function for charm quarks leading-order pQCD predictions for charm quark spectra and and beauty quarks compared with background subtracted sin- the STAR measured D0 spectrum from d+Au collisions scaled gle electron spectrum measured by STAR from p+p collisions by Nbin = 7.5. and the prediction for theoretical uncertainty electron band. Left panel: The spectra are from parameter set II. Right panel: The spectra are from parameter set I. from d+Au collisions at √sNN = 200 GeV have been scaled by Nbin = 7.5 – the number of binary collisions. known at RHIC. The STAR D meson spectrum covers The PYTHIA spectra have been scaled to the measured a limit pT range and is not well constrained at high pT . dN/dy of 0.028 0.004(stat.) 0.008(syst.) [23] for D0 at ± ± 0 Without further tuning other PYTHIA parameters, we mid-rapidity, where the scaling factors are 1.75 for D find that the generated bare charm quark spectra from meson spectra and 1.25 for charm quark spectra, respec- PYTHIA calculations using parameter set I and param- tively. The theoretical curve with the MRST HO PDF eter set II approximately match the STAR D meson pT has been normalized to the measured total cc cross sec- distribution. As demonstrated in the left panel of Fig. 1, tion (1.3 0.2 0.4mb) [23] by a factor of 3.4. ± ± the PYTHIA calculation with parameter set II also yields The stars in the left panel of Fig. 1 depict the a charm quark pT distribution similar to the NLO pQCD charm quark pT distribution from a PYTHIA calcula- calculations [25][28], which coincides with the STAR D tion with the following parameters (set I) from refer- meson pT spectrum as well. It is not the purpose of 2 ence [26]: PARP(67) = 1 (factor multiplied to Q ), this paper to show that the PYTHIA calculations with 2 < kt >= 1.5GeV/c, mc = 1.25GeV/c , Kfactor = 3.5, these two parameter sets and NLO pQCD calculations MSTP(33) = 1 (inclusion of K factors), MSTP(32) = are equivalent in physics contents. 2 0 4 (Q scale) and CTEQ5L PDF. We further tuned the In the right panel of Fig. 1 the D pT distribution value of PARP(67) to 4, which enhances c-quark produc- from PYTHIA calculations using the default Peterson tion probability through gluon splitting and is introduced fragmentation function is shown as open circles for pa- to take into account higher order effects in the pQCD cal- rameter set II and crosses for parameter set I. The default culation [27]. The results are shown as triangles in the Peterson function refers to the value of the parameter ε in left panel of Fig. 1. We found that this change mainly Peterson function being 0.05 for charm quarks and 0.005 affects c-quark production at high pT and can effectively for beauty quarks. The default Peterson fragmentation reproduce the NLO pQCD calculation. We will refer to for charm quarks is too soft to reproduce the measured this set of parameters as parameter set II in the rest of D0 spectrum [23] together with D∗ spectrum [24]. We the paper. modified the value of the parameter ε to 10−5 for both We compared the charm quark spectra from PYTHIA charm and beauty quarks. In this case the fragmentation calculations to the STAR published D0 spectrum [23] function is nearly δ(1 z). The results are shown as stars together with the STAR preliminary D∗ spectrum [24]. for parameter set I and− triangles for parameter set II in The combination of STAR measured D∗ and D0 me- the right panel of Fig. 1. The PYTHIA calculations using son spectra into a single D meson spectrum is ham- the modified Peterson fragmentation function (ε = 10−5) pered by the large uncertainties in the ratio D∗/D0 = with parameter set I and set II can reasonably reproduce 0.4 0.09 0.13 [24] which is experimentally not well the measured D meson pT distribution. ± ± 3

0.4 2.5 < P (trig) < 3.5 GeV/c 4.5 < P (trig) < 5.5 GeV/c T 3.5 < PT(trig) < 4.5 GeV/c T 1 0.35

0.3 2.5 - 3.5 GeV/c 3.5 - 4.5 GeV/c 4.5 - 5.5 GeV/c trig

N 0.25 ⁄ ch N 0.2 10-1 0.15 trig N

0.1 ⁄ ch

0.5 8.5 < P (trig) < 10.5 GeV/c N 5.5 < PT(trig) < 6.5 GeV/c 6.5 < PT(trig) < 8.5 GeV/c T 0.45 10-2 0.4

trig 0.35 N

⁄ 0.3

ch 0.25 N 0.2 -3 0.15 10 0.1 2 4 6 8 2 4 6 8 2 4 6 8 -3 -2 -1 0 1 2 3 -3 -2 -1 0 1 2 3 -3 -2 -1 0 1 2 3 ϕ∆ ϕ∆ ϕ∆ ∑P (GeV/c) T

FIG. 3: (color online) ∆ϕ distributions between non-photonic FIG. 4: (color online) Summed pT distributions of charged electrons and charged hadrons with different electron trigger hadrons around triggered non-photonic electrons with differ- pT cuts and associated hadron pT > 0.1 GeV/c. Solid lines ent trigger pT cuts. Solid lines show electrons from B meson show electrons from B meson decays. Dashed lines show elec- decays. Dashed lines show electrons from D meson decays. trons from D meson decays.

and bottom in p+p collisions [28]. The FONLL predic- While the kT broadening can make the charm pT dis- tion of electron spectrum gives a fair description of the tribution harder at low beam energies [11], the intrinsic shape of the measured spectra. But there is a discrepancy kT has little effect on the pT distribution at RHIC ener- in the overall scale and the FNOLL calculation is signifi- gies [25]. A harder fragmentation function is needed for cant below the STAR data at high pT . More discussions the hadronization of charm quarks if the pQCD calcula- can be found in [18]. The PYTHIA calculations with pa- tion is to describe the measured STAR data. rameter set II and modified heavy quark fragmentation The STAR independent measurements of the recon- function can simultaneously describe the STAR direct structed D0 meson and single electrons from heavy quark D meson pT distribution [23][24] and the STAR EMC semi-leptonic decays measured with TOF and TPC are non-photonic electron data [18]. This modified scheme consistent [23]. The electron measurement there only indicates that the contribution of electrons from B me- covers up to pT < 4 GeV/c and has no sensitivity to the son decays is not dominant for the measured pT region up to 8 GeV/c assuming σ ¯/σcc¯ 0.45% 0.60% based B meson contribution. We also checked the consistency bb ∼ − between D meson data and non-photonic single electron on NLO pQCD calculation. The measurement of elec- data in p+p collisions within our PYTHIA calculations. tron pT distribution alone has a reduced sensitivity to the Fig. 2 shows the electron spectra from PYTHIA calcula- pT distribution of D mesons as shown in reference [30]. tions using the modified Peterson fragmentation function Within the statistical and systematic errors of the elec- for charm quarks and beauty quarks with parameter set tron data, the PYTHIA calculation with parameter set II in the left panel and parameter set I in the right panel. I and the modified Peterson function for both c and b The parameters for beauty quarks in set II and set I are quarks can yield an electron pT distribution similar to 2 all the same as for charm quarks except mb =4.8GeV/c . the measurement [18]. In this case, as shown in the bot- The PYTHIA spectra of electrons from charm meson tom panel of Fig. 2, electrons from b quark decays are not decays are scaled by the same factor used to scale the the dominant source for the pT region up to 6 GeV/c. It PYTHIA D0 spectra to the measured dN/dy(D0) at mid- is critical that the B and D meson decay contributions to rapidity. The electron spectra from beauty meson decays non-photonic electrons to be separated experimentally. are normalized by the ratio of σb¯b/σcc¯ based on the NLO We have studied the azimuthal correlations between pQCD calculation [29]. The band corresponds to the heavy quark semi-leptonic decay electrons and inclusive theoretical uncertainty of this ratio (0.45% - 0.60%) [29], charged hadrons. Fig. 3 shows the ∆ϕ distributions where the theoretical error may be an underestimate ac- between non-photonic electrons and inclusive charged cording to recent calculations [28]. We used the value hadrons, with different electron trigger pT cuts and the at the center of this range to calculate the sum of the associated hadron pT > 0.1 GeV/c. The distributions are electrons. Fig. 2 also shows the comparison to the STAR scaled by the number of electron triggers. These plots are measured non-photonic single electron data in p+p colli- from PYTHIA calculation with parameter set II and the sions [18] and the FONLL calculation for the theoretical modified heavy quark fragmentation function. The solid uncertainty band of the electron spectrum from charm lines in Fig. 3 are for electrons from B meson decays and 4

TABLE I: Fractions of B meson decay contributions from TABLE II: Fractions of B meson decay contributions from electron spectra and ∆ϕ distribution fitting in PYTHIA cal- electron spectra and summed pT histogram fitting in PYTHIA culations with parameter set II and modified Peterson frag- calculations with parameter set II and modified Peterson frag- mentation function for charm and beauty quarks. mentation function for charm and beauty quarks.

pT (trig) (GeV/c) From Spectra (%) From Fitting (%) pT (trig) (GeV/c) From Spectra (%) From Fitting (%) 2.5 - 3.5 12.64 0.04 12.64 1.37 2.5 - 3.5 8.25 0.05 8.25 1.50 ± ± ± ± 3.5 - 4.5 21.65 0.12 21.65 2.55 3.5 - 4.5 14.94 0.13 14.94 2.54 ± ± ± ± 4.5 - 5.5 30.50 0.26 30.50 4.76 4.5 - 5.5 22.60 0.29 22.60 4.13 ± ± ± ± 5.5 - 6.5 36.66 0.48 36.66 7.87 ± ± 6.5 - 8.5 42.24 0.71 42.24 11.10 We further studied the particle production within a ± ± 8.5 - 10.5 49.82 1.72 49.82 25.11 cone around triggered high pT electrons from heavy quark ± ± decays. We focused on the scalar summed pT distri- butions of inclusive charged hadrons in the cone (pT refers to the transverse momentum in the laboratory the dashed lines are for electrons from D decays. As frame). Here the cone is defined by ηh ηe < 0.35 demonstrated in Fig. 3, there is a significant difference | − | and ϕh ϕe < 0.35 (η is pseudorapidity and ϕ is az- between B and D meson decays in the near-side corre- | − | imuthal angle). The summed pT distributions of inclu- lations. The width of near-side peak for electrons from sive charged hadrons in three triggered electron pT ranges D decays is much narrower than those for the B decays. are shown in Fig. 4. The distributions are scaled to unit. The wide width from B meson decays is due to the larger The dashed lines are for D decays and the solid lines are energy release (Q value) in the B meson semi-leptonic for B decays. These plots are from PYTHIA calcula- decays leading to a broad angular correlation between tion with parameter set II and the modified heavy quark daughter hadrons and electrons. An electron at high pT , fragmentation function. We also can see that there is if it is from B meson decays, the B meson does not have a significant difference between B decays and D decays. to be at high transverse momentum because the electron The summed pT distributions for D meson decays are can get large momentum from the b-quark mass. In the much wider than those for B meson decays. This dif- case of D meson decays, the D meson needs to have a ference can also be used to distinguish B and D decay large momentum in order to boost the daughter electron contributions. We use the summed pT histograms from to a high pT . In experimental effort we cannot differen- B decays and D decays to fit the summed pT histogram tiate heavy quark decay hadrons from others, we used from PYTHIA inclusive case to determine the B decay inclusive hadrons in our correlation study. We found the contribution. The results are shown in Table II. The re- difference in the near-side correlations between D decays sults are consistent with those directly from the electron and B decays is largely due to the decay kinematics, not spectra. The ratios for the same trigger pT ranges are the production dynamics. This difference can help us es- different between Table II and Table I. It is because we timate the relative B and D contributions to the yields removed those electrons which have no hadrons in the for non-photonic electrons. cone around them when we calculated the bottom con- The bottom contribution to the non-photonic electrons tribution from the electron spectra for Table II. This can be determined directly from the electron spectra in removes different fractions from B and D decays, which PYTHIA. The results are given in the second column of has to be corrected by simulations. This was done to Table I. However, this way to determine the bottom con- make the results directly from the electron spectra com- tribution is not experimentally feasible. In order to ex- parable to the results from hadron summed pT histogram perimentally determine the bottom contribution fraction, fitting. It will be more valuable for the small acceptance we use the ∆ϕ distributions for B decays and D decays experiments to investigate the B decay contribution us- to fit the ∆ϕ distribution for PYTHIA inclusive case (ei- ing summed pT histogram fitting. ther B decays or D decays), and let the B contribution In conclusion, we found that in order to match the fraction as a parameter. The fraction is determined by STAR measured pT shape of D mesons from d+Au col- 2 the minimum value of χ . And the fitting error is deter- lisions at RHIC using the PYTHIA Monte Carlo gener- 2 mined by one σ shift of χ /ndf from the minimum value. ator, a harder charm quark fragmentation function must The fitting error will reduce by increasing the statistics. be used. Since the D meson production at high pT is The results are shown in the third column of Table I. not well constrained by the STAR data and the mea- The results are consistent with those directly from the surement of electrons alone has a reduced sensitivity on electron spectra. This indicates that the method we pro- the pT shape of D mesons, PYTHIA calculations with posed is self-consistent. This approach can be used to parameter set I and set II can simultaneously describe experimentally estimate the B and D contributions to the pT distributions of D mesons and non-photonic elec- the non-photonic electrons. trons from semi-leptonic decays of heavy quarks. These 5 calculations predict that the beauty quark decay elec- B 495 (1997) 3; G.A. Alves et al., E769 Collaboration, 77 trons are not a dominant contribution over the entire pT Phys. Rev. Lett. (1996) 2392. region up to 6-8 GeV/c depending on parameters. The [10] R. Vogt et al., Nucl. Phys. 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