Measurement of Prompt Charm Meson Production Cross Sections in <em>pp</em> Collisions at s√=1.96 TeV

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Measurement of Prompt Charm Meson Production Cross Sections in pp Collisions at s√=1.96 TeV

CDF II Collaboration

CAMPANELLI, Mario (Collab.), et al.

Abstract

We report on measurements of differential cross sections dσ/dpT for prompt charm meson production in pp¯ collisions at s√=1.96 TeV using 5.8±0.3 pb−1 of data from the CDF II detector at the Fermilab Tevatron. The data are collected with a new trigger that is sensitive to the long lifetime of hadrons containing heavy flavor. The charm meson cross sections are measured in the central rapidity region |y|≤1 in four fully reconstructed decay modes:

D0→K−π+, D*+→D0π+, D+→K−π+π+, D+s→φπ+, and their charge conjugates. The measured cross sections are compared to theoretical calculations.

CDF II Collaboration, CAMPANELLI, Mario (Collab.), et al . Measurement of Prompt Charm Meson Production Cross Sections in pp Collisions at s√=1.96 TeV. Physical Review Letters , 2003, vol. 91, no. 24, p. 241804

DOI : 10.1103/PhysRevLett.91.241804

Available at:

http://archive-ouverte.unige.ch/unige:38051

Disclaimer: layout of this document may differ from the published version.

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Measurement of Prompt Charm Meson Production Cross Sections in p p p Collisions at

p s

1:96 TeV

D. Acosta,¹⁴T. Affolder,⁷M. H. Ahn,²⁵T. Akimoto,⁵²M. G. Albrow,¹³D. Ambrose,⁴⁰D. Amidei,³⁰A. Anastassov,⁴⁷ K. Anikeev,²⁹A. Annovi,⁴¹J. Antos,¹M. Aoki,⁵²G. Apollinari,¹³J-F. Arguin,⁵⁰T. Arisawa,⁵⁴A. Artikov,¹¹

T. Asakawa,⁵²W. Ashmanskas,²A. Attal,⁶F. Azfar,³⁸P. Azzi-Bacchetta,³⁹N. Bacchetta,³⁹H. Bachacou,²⁶ W. Badgett,¹³S. Bailey,¹⁸A. Barbaro-Galtieri,²⁶G. Barker,²³V. E. Barnes,⁴³B. A. Barnett,²²S. Baroiant,⁵M. Barone,¹⁵

G. Bauer,²⁹F. Bedeschi,⁴¹S. Behari,²²S. Belforte,⁵¹W. H. Bell,¹⁷G. Bellettini,⁴¹J. Bellinger,⁵⁵D. Benjamin,¹² A. Beretvas,¹³A. Bhatti,⁴⁵M. Binkley,¹³D. Bisello,³⁹M. Bishai,¹³R. E. Blair,²C. Blocker,⁴K. Bloom,³⁰ B. Blumenfeld,²²A. Bocci,⁴⁵A. Bodek,⁴⁴G. Bolla,⁴³A. Bolshov,²⁹P. S. L. Booth,²⁷D. Bortoletto,⁴³J. Boudreau,⁴²

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Z. Yu,⁵⁶J. C. Yun,¹³L. Zanello,⁴⁶A. Zanetti,⁵¹I. Zaw,¹⁸F. Zetti,⁴¹J. Zhou,⁴⁷A. Zsenei,¹⁶and S. Zucchelli³ (CDF II Collaboration)

1Institute of Physics, Academia Sinica, Taipei, Taiwan 11529, Republic of China

2Argonne National Laboratory, Argonne, Illinois 60439, USA

3Istituto Nazionale di Fisica Nucleare, University of Bologna, I-40127 Bologna, Italy

4Brandeis University, Waltham, Massachusetts 02254, USA

5University of California at Davis, Davis, California 95616, USA

6University of California at Los Angeles, Los Angeles, California 90024, USA

7University of California at Santa Barbara, Santa Barbara, California 93106, USA

8Instituto de Fisica de Cantabria, CSIC –University of Cantabria, 39005 Santander, Spain

9Carnegie Mellon University, Pittsburgh, Pennsylvania 15213, USA

10Enrico Fermi Institute, University of Chicago, Chicago, Illinois 60637, USA

11Joint Institute for Nuclear Research, RU-141980 Dubna, Russia

12Duke University, Durham, North Carolina 27708, USA

13Fermi National Accelerator Laboratory, Batavia, Illinois 60510, USA

14University of Florida, Gainesville, Florida 32611, USA

15Laboratori Nazionali di Frascati, Istituto Nazionale di Fisica Nucleare, I-00044 Frascati, Italy

16University of Geneva, CH-1211 Geneva 4, Switzerland

17Glasgow University, Glasgow G12 8QQ, United Kingdom

18Harvard University, Cambridge, Massachusetts 02138, USA

19The Helsinki Group: Helsinki Institute of Physics; and Division of High Energy Physics, Department of Physical Sciences, University of Helsinki, FIN-00014 Helsinki, Finland

20Hiroshima University, Higashi-Hiroshima 724, Japan

21University of Illinois, Urbana, Illinois 61801, USA

22The Johns Hopkins University, Baltimore, Maryland 21218, USA

23Institut fu¨r Experimentelle Kernphysik, Universita¨t Karlsruhe, 76128 Karlsruhe, Germany

24High Energy Accelerator Research Organization (KEK), Tsukuba, Ibaraki 305, Japan

25Center for High Energy Physics: Kyungpook National University, Taegu 702-701, Korea; Seoul National University, Seoul 151- 742, Korea; and SungKyunKwan University, Suwon 440-746, Korea

241804-2 241804-2

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26Ernest Orlando Lawrence Berkeley National Laboratory, Berkeley, California 94720, USA

27University of Liverpool, Liverpool L69 7ZE, United Kingdom

28University College London, London WC1E 6BT, United Kingdom

29Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA

30University of Michigan, Ann Arbor, Michigan 48109, USA

31Michigan State University, East Lansing, Michigan 48824, USA

32Institution for Theoretical and Experimental Physics, ITEP, Moscow 117259, Russia

33University of New Mexico, Albuquerque, New Mexico 87131, USA

34Northwestern University, Evanston, Illinois 60208, USA

35The Ohio State University, Columbus, Ohio 43210, USA

36Okayama University, Okayama 700-8530, Japan

37Osaka City University, Osaka 588, Japan

38University of Oxford, Oxford OX1 3RH, United Kingdom

39Universita´ di Padova, Istituto Nazionale di Fisica Nucleare, Sezione di Padova-Trento, I-35131 Padova, Italy

40University of Pennsylvania, Philadelphia, Pennsylvania 19104, USA

41Istituto Nazionale di Fisica Nucleare, University and Scuola Normale Superiore of Pisa, I-56100 Pisa, Italy

42University of Pittsburgh, Pittsburgh, Pennsylvania 15260, USA

43Purdue University, West Lafayette, Indiana 47907, USA

44University of Rochester, Rochester, New York 14627, USA

45The Rockefeller University, New York, New York 10021, USA

46Instituto Nazionale de Fisica Nucleare, Sezione di Roma, University di Roma I, ‘‘La Sapienza,’’ I-00185 Roma, Italy

47Rutgers University, Piscataway, New Jersey 08855, USA

48Texas A&M University, College Station, Texas 77843, USA

49Texas Tech University, Lubbock, Texas 79409, USA

50Institute of Particle Physics, University of Toronto, Toronto M5S 1A7, Canada

51Istituto Nazionale di Fisica Nucleare, Universities of Trieste and Udine, Italy

52University of Tsukuba, Tsukuba, Ibaraki 305, Japan

53Tufts University, Medford, Massachusetts 02155, USA

54Waseda University, Tokyo 169, Japan

55University of Wisconsin, Madison, Wisconsin 53706, USA

56Yale University, New Haven, Connecticut 06520, USA (Received 25 July 2003; published 12 December 2003)

We report on measurements of differential cross sections d=dp_T for prompt charm meson production inppp collisions atps

1:96 TeV using5:80:3 pb¹ of data from the CDF II detector at the Fermilab Tevatron. The data are collected with a new trigger that is sensitive to the long lifetime of hadrons containing heavy flavor. The charm meson cross sections are measured in the central rapidity regionjyj 1 in four fully reconstructed decay modes:D⁰!K,D !D⁰,D! K,D_s !, and their charge conjugates. The measured cross sections are compared to theoretical calculations.

DOI: 10.1103/PhysRevLett.91.241804 PACS numbers: 13.85.Ni, 12.38.Qk, 13.25.Ft, 14.40.Lb

Measurements of the production cross sections of hadrons containingbquarks or charm quarks (heavy flavor hadrons) inppp collisions provide an opportunity to test predictions based on quantum chromodynamics (QCD).

Previous measurements ofBmeson production cross sections inppp collisions at ps

1:8 TeV [1,2] were about 3 times larger than next-to-leading-order (NLO) QCD predictions [3], although recent calculations with a more accurate description of b quark fragmentation have re- duced this discrepancy to a factor 1.7 [4,5]. Charm meson production cross sections have not been measured inppp collisions and may help with understanding this disagree- ment. The upgraded Collider Detector at Fermilab (CDF II) has a new capability to trigger on tracks dis- placed from the beam line originating from the decay of long-lived hadrons containing heavy flavor quarks. We report here measurements of prompt charm meson cross

sections using data recorded with this trigger in February and March 2002, corresponding to 5:80:3 pb¹ of integrated luminosity.

An overview of the CDF II detector can be found elsewhere [6]; only the components relevant to this analysis are described here. The CDF coordinate system has the z axis pointing along the proton momentum; ’ is the azimuth,is the polar angle, andris the distance from the proton beam axis. The CDF II central tracking region covers the pseudorapidity region jj 1, where lntan=2. A superconducting solenoid provides a nearly uniform axial field of 1.4 T. The silicon vertex detector (SVX II) [7] consists of double-sided microstrip sensors arranged in five concentric cylindrical shells with radii between 2.5 and 10.6 cm. Surrounding the SVX II is the central outer tracker (COT) [8], an open cell drift chamber covering radii from 40 to 137 cm. The COT has

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96 layers, organized in 8 superlayers, alternating between axial and2stereo readout.

CDF II has a three-level trigger system. We describe here the trigger used in this analysis. At the first trigger level, charged tracks are reconstructed in the COT axial projection by a hardware processor (XFT) [9]. The trigger for hadronic charm decays requires two oppositely charged tracks with p_T 2 GeV=c and the scalar sum of thep_T’s larger than5:5 GeV=c, wherep_T is the mag- nitude of the component of the momentum transverse to the beam axis. At the second trigger level, the silicon vertex tracker (SVT) [10] associates axial strip clusters from the four inner SVX II layers with XFT track information. The SVT measures the distance of the closest approach of a track relative to the beam axis (impact parameter or d₀) with a resolution of 50m, which includes a contribution of 30m from the beam spot transverse size. Events containing hadronic decays of heavy flavor hadrons are selected by requiring two tracks with 120md₀ 1 mm each. At the third trigger level, a farm of computers performs complete event reconstruction online; the opening angle’ between the two trigger tracks is required to be between2 and90, and the intersection point in ther-’plane projected along the net momentum vector of the two tracks must be more than200mfrom the beam line.

We reconstruct charm mesons in the following decay modes: D⁰ !K, D !D⁰ with D⁰ !K, D!K, D_s ! with !KK, and their charge conjugates. For every track pair that satisfies the trigger requirements (trigger pair), we form oneD⁰ ! K candidate and a second candidate with the mass assignments swapped. No particle identification is used in this analysis.D⁰ candidates within 3 standard deviations of theD⁰mass are combined with a third track withp_T 0:5 GeV=cto formD !D⁰candidates. The three- body decays of the D and D_s are reconstructed by combining a trigger pair with a third track having axial hits in at least three out of five SVX II layers and perform- ing a vertex fit based on axial track information only. For D_s reconstruction, we specifically require the K pair to satisfy the trigger requirements, since the typical opening angle between two kaons fromdecay is close to the’2trigger requirement. Eachcandidate is required to have a mass within 20 MeV of the world averagemass [11]. TheDmeson candidates are binned inp_Tas indicated in Table I. The signals summed over all p_T bins are shown in Fig. 1.

The D⁰ yield is obtained from a binned maximum likelihood fit to the K invariant mass distribution, with a linear function for the combinatoric background, a narrow Gaussian for theD⁰ signal, and a wide Gaussian with the same normalization describing D⁰ !K with the wrong mass assignment. We determine the shape of the mass distribution resulting from the wrong mass assignment usingD⁰ fromD decay where the charge of

the low-momentum pion determines the mass assignment of theD⁰decay products. TheD yield is extracted from the distribution ofmmK mK, the mass difference between the K and the K combination. The signal is modeled with two Gaussians with equal means, and the background is characterized

asa

mm

p expbmm, whereaandbare free parameters in the fit. TheDsignal is described with two Gaussians, and the background is described with a linear function. In themode, we model the invariant mass distribution as a linear background with two Gaussians, one corresponding to theD and one to theD_s. We find 36 804409, D⁰!K; 551585, D !D⁰; 28 361294, D!K; and 85143, D_s ! , where the uncertainties quoted are statistical only.

We vary the signal and background models and attribute systematic uncertainties on the signal yield in the range of 1%–6%, depending on the decay mode and thep_T range of the candidates.

We separate charm directly produced in ppp interactions (prompt charm) from charm fromBdecay (secondary charm) using the impact parameter of the net momentum vector of the charm candidate to the beam line [12]. Prompt charm mesons point to the beam line.

The shape of the impact parameter distribution of secondary charm is obtained from a generator-level NLO Monte Carlo (MC) simulation ofBmeson production [2]

and decay [13], smeared with a resolution function (Gaussian exponential tails) obtained from a sample of K_S⁰! decays that satisfy the trigger requirements. The impact parameter distribution of the reconstructed charm samples, shown for theD⁰ in Fig. 2, is fit to a prompt and a secondary component. The prompt fraction is measured for each p_T bin. Averaged over all p_T bins,86:60:4%of the D⁰ mesons, 88:11:1%

of D ,89:10:4%of D, and77:33:8%of D_s are promptly produced (statistical uncertainties only).

The systematic uncertainties on the prompt fractions are estimated by removing the non-Gaussian tail in the resolution function and evaluating the variation. The relative uncertainty is found to be in the3%–4%range, depending on the decay mode.

Using a hit-level simulation of the COT, overlaid with data events from the hadronic heavy flavor trigger to reproduce a realistic occupancy, we measure a reconstruction efficiency in the COT of 99% for tracks with p_T 2 GeV=c, falling to95%atp_T 0:5 GeV=c. The efficiency for finding three SVX II axial hits on a reconstructed track is measured from data to be about85%. The efficiencies of the trigger hardware XFT and SVT to reconstruct tracks are measured from data samples with- out XFT or SVT requirements [12]. The XFT tracking efficiency is greater than95%. In the data-taking period considered, the SVX II and the SVT were not yet fully operational, and the efficiency varied as certain SVX II modules were included or excluded from the trigger.

241804-4 241804-4

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Therefore, we measured the SVT efficiency in 42 periods, each corresponding to oneppp store of the Tevatron, and characterized the efficiency as a function of the track azimuth ’, the longitudinal positionz₀, the polar angle , and the transverse momentump_T. The average single- track efficiency of the SVT for this early data-taking period was about 42%.

The measured efficiencies are applied to a generator- level NLO MC simulation of charm meson production and decay to calculate the trigger and reconstruction efficiencies, taking into account decay in flight and hadronic interactions of the charm meson decay products.

The MCp_T spectrum of the charm mesons is reweighted to match the measuredp_Tspectrum. The integrated cross-

section _i in each p_T bin i with jyj 1 [where y

1 2ln^Ep_Ep^z

z and E is the energy of the charm meson] is calculated using the following equation:

_i N_i=2f_D;i

RLdt _iB; (1) where N_iis the number of charm mesons in eachp_T bin and f_D;i is the fraction of prompt charm in that bin. The integrated luminosity R

Ldtat CDF is normalized to an inelastic cross section of_p_p_p 60:72:4 mb [14]. The rate of inelastic collisions is measured with Cherenkov luminosity counters [15] and has an uncertainty of 4.4%.

The factor ¹₂ is included because we count both D and D

D mesons, but we report cross sections for D alone.

We verified that the D and DD cross sections are equal within statistical uncertainties. The branching fractions Bare taken from Ref. [11]. For theD⁰ cross section, we sum the branching fractions of D⁰ !K and D⁰! K, since both contribute to the observed signal. The combined reconstruction and trigger efficiency _i varies

2] ) [GeV/c π+

m(K−

1.8 1.85 1.9

2Entries per 2 MeV/c

0 1000 2000 3000

π+

K−

→

D0 (a)

2] ) [GeV/c π+

)-m(K−

π+

m(K−

0.14 0.15 0.16

2Entries per 0.3 MeV/c

0 200 400 600

800 D*⁺→D⁰π⁺, π+

K−

→ D0 (b)

2] ) [GeV/c π+

π+

m(K−

1.7 1.8 1.9 2

0 1000 2000

π+

K−

→

D+ (c)

2] ) [GeV/c π+

K−

m(K+

1.8 1.9 2 2.1

0 100 200

300 +

π φ

→

s

D+

π+

φ

→ D+

(d)

FIG. 1. Charm signals summed over allpTbins: (a) invariant mass distribution ofD⁰!K candidates; (b) mass difference distribution of D !D⁰ candidates; (c) invariant mass distribution ofD!Kcandidates; (d) invariant mass distribution ofD! and D_s ! candidates.

The curves show the results of the fits described in the text.

µm]

[ Impact Parameter

mµEntries per 10

1 10 10² 10³

-400 -200 0 200 400

π+

K−

→ D0

FIG. 2. The impact parameter distributions of theD⁰mesons, measured from the 2 signal region of the invariant mass distribution and corrected for combinatoric background measured in the invariant mass sidebands. The solid curve is the fit result summed over all p_T bins. The dashed curve shows the contribution of secondary charm fromBdecay.

TABLE I. Summary of the measured prompt charm meson differential cross sections and their uncertainties at the center of each p_Tbin. The first error is statistical and the second systematic. The products of the branching fractions [11] used are3:810:09%, 2:570:06%,9:10:6%, and1:80:5%forD⁰,D ,D, andD_s, respectively.

djyj 1=dp_T

p_Trange Centralp_T nb=GeV=c

GeV=c GeV=c D⁰ D D D_s

5:5–6 5:75 7837220884

6–7 6:5 405693441 2421108424 196169332

7–8 7:5 205258227 114748145 98628156

8–10 9:0 89025107 4271654 375962 2362067

10–12 11:0 3271541 148818 136424 64919

12–20 16:0 39:92:35:3 23:81:33:2 19:00:63:2 9:01:22:7

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from 0:12% to1:9% depending on the decay mode and the p_T bin. Systematic uncertainties on the trigger and reconstruction efficiency arise predominantly from the uncertainty on single-track efficiencies and two-track efficiency correlations. They also have contributions from ionization energy loss, hadronic interactions in the inner tracker material, and the size of the interaction region. The combined systematic uncertainty on the trigger and reconstruction efficiency is in the range of 8%–14%, depending on the decay mode and thep_T range of theDmesons.

The total cross sections are obtained by summing over allp_T bins. However, the lastp_T bin is replaced by an inclusive bin with p_T >12 GeV=c. We find D⁰; p_T 5:5 GeV=c;jyj 1 13:30:21:5b, D ; p_T 6:0 GeV=c;jyj 1 5:20:10:8b, D; p_T 6:0 GeV=c;jyj 1 4:30:10:7b, and D_s; p_T 8:0 GeV=c;jyj 1 0:750:05 0:22b, where the first uncertainty is statistical and the second systematic. To calculate the differential cross sections, we divide_i by the width of thep_T bin. Since we reportd=dp_T at the center of each p_T bin, we apply a correction to account for the nonlinear shape of the cross section, using thep_T reweighted MC to obtain the shape of the cross section inside each p_T bin. The results are listed in Table I.

The measured differential cross sections are compared to two recent calculations [16,17], as shown in Fig. 3. The uncertainties on the calculated cross sections are eval- uated by varying independently the renormalization and factorization scales between 0.5 and 2 times the default scale. Reference [16] uses a default scale of

m²_cp²_T q

, where m_c1:5 GeV=c² is the c quark mass, while Ref. [17] uses a default scale of 2

m²_cp²_T q

.

Contributions from other sources, such as the charm quark mass, the value of the strong coupling constant, and the fragmentation functions, were reported to be smaller and are not taken into account.

In conclusion, the measured differential cross sections are higher than the theoretical predictions by about 100%

at low p_T and 50% at high p_T. However, they are com- patible within uncertainties. The same models also under- estimateBmeson production atps

1:8 TeVby similar factors [2,4,5].

We thank the Fermilab staff and the technical staffs of the participating institutions for their vital contributions.

This work was supported by the U.S. Department of Energy and National Science Foundation; the Italian Istituto Nazionale di Fisica Nucleare; the Ministry of Education, Culture, Sports, Science and Technology of Japan; the Natural Sciences and Engineering Research Council of Canada; the National Science Council of the Republic of China; the Swiss National Science Foundation; the A.P. Sloan Foundation; the Bundes- ministerium fuer Bildung und Forschung, Germany; the Korean Science and Engineering Foundation and the Korean Research Foundation; the Particle Physics and Astronomy Research Council and the Royal Society, U.K.; the Russian Foundation for Basic Research; and the Comision Interministerial de Ciencia y Tecnologia, Spain.

[1] D0 Collaboration, B. Abbottet al., Phys. Lett. B487, 264 (2000).

[2] CDF Collaboration, D. Acosta et al., Phys. Rev. D65, 052005 (2002).

[GeV/c]

pT