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Non-Photonic Electron $ P {T} $ Distributions and Correlations Of

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Non-Photonic Electron $ P {T} $ Distributions and Correlations Of Non-Photonic Electron pT Distributions and Correlations of Electrons from B and D Meson Decays with Charged Hadrons Xiaoyan Lin Institute of Particle Physics, Central China Normal University, Wuhan 430079, China Department of Physics and Astronomy, University of California, Los Angeles, CA 90095, USA (Dated: November 6, 2018) 0 We compare the non-photonic electron and D meson pT distributions measured at RHIC with the PYTHIA Monte Carlo event generator in p+p collisions at √sNN = 200 GeV. A delta fragmentation function much harder than the Peterson function, consistent with recombination scheme for charm meson formation, is needed to match the experimental data. Attempts to fit the non-photonic electrons at high pT show large uncertainties and the B meson semi-leptonic decays may not be dominant for electron pT up to 8 GeV/c. Correlations of non-photonic electrons with charged hadrons are studied. We propose an experimental method to quantitatively determine the relative contributions of D and B meson semi-leptonic decays to the non-photonic electrons. PACS numbers: 24.10.Lx, 14.40.Lb, 13.20.Fc Heavy quarks are believed to be produced through Thus the charmed hadron pT would coincide with the initial parton-parton, mostly gluon-gluon, scatterings in bare charm quark pT distribution in this hadronization nuclear collisions at the Relativistic Heavy Ion Collider scheme. These various hadron formation schemes can (RHIC) energies. Theoretical calculations of heavy quark lead to significantly different charmed meson pT distribu- production within the perturbative Quantum Chromo- tion when interpreting non-photonic electron pT spectra Dynamics (pQCD) framework are considered more reli- from experimental measurements. able because the heavy quark mass sets a natural scale for Recently STAR and PHENIX collaborations have ob- the pQCD. Charm quark production is sensitive to the served a suppression of non-photonic electrons much incoming parton flux for the initial conditions of nuclear larger than predicted in the pT 4 8 GeV/c re- collisions [1][2]. The transport dynamics of the heavy gion [18][19]. This observation challenges∼ − theoretical pre- quarks in nuclear medium such as flow [3] and energy dictions based on energy loss via induced gluon radia- loss [4][5] can probe QCD properties of the dense matter tion for heavy quarks [20][21]. The fact that the relative created in nucleus-nucleus collisions. Therefore, heavy contributions of D and B meson semi-leptonic decays to quark measurements provide unique insights into QCD the experimental non-photonic electron spectrum is cur- properties of the new state of matter produced in nucleus- rently not measured at RHIC severely restricts the under- nucleus collisions. standing of the heavy quark energy loss. A nonzero non- The heavy quark production in p+p or p+A collisions photonic electron v2 has been measured in the pT < 2.0 provides a reference for heavy meson formation and for GeV/c region, while at higher pT the v2 is observed to de- nuclear modification factors of heavy quarks in the nu- crease with pT [22]. Quantitative understanding of this clear medium. The Peterson function [6] feature in heavy quark measurements requires relative arXiv:hep-ph/0602067v3 20 Oct 2006 charm and bottom contributions to non-photonic elec- 1 D(z pD/pc) (1) trons. ≡ ∝z[1 1/z ε/(1 z)]2 − − − In this paper we evaluate the pT distribution of has often been used to describe the charm fragmenta- D mesons from PYTHIA v6.22 [7] and compare the tion function, where the parameter ǫ 0.05 (default PYTHIA results with the STAR measurements [23][24]. in PYTHIA [7]) is in reasonable agreement≈ with the The charm quark fragmentation function will be mod- results from fits to charm production in e+e− and γp ified from the default Peterson function and the other collisions [8]. However, in charm hadroproduction, it PYTHIA parameters are tuned in order to describe the was observed that the c-quark pT distributions of next- experimental D meson data as well as the STAR non- to-leading-order (NLO) pQCD calculations agree well photonic electron spectra [18]. We study the correlations with the measured open charm pT spectrum [9], indicat- between non-photonic electrons and charged hadrons in ing that a much harder fragmentation function peaked order to guide the experimental investigations of the rela- at z 1 in Eq. 1 is needed in charm hadroproduc- tive contributions to the non-photonic electron spectrum ≈ tion. A more detailed discussion of this observation at high pT from B and D meson decays. can be found in [10][11]. Coalesence [12][13] or recom- Fig. 1 shows charm quark and D0 meson spectra bination [14][15][16] models have also been proposed for from PYTHIA calculations and NLO pQCD predictions charmed meson formation by combining a charm quark for charm quark spectra [25] together with the STAR 0 0 with a light up or down quark, presumably of soft pT [17]. D spectrum [23], where the measured D data points 2 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].
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