J/ψ, Y and B meson production in proton–proton collisions at the LHC
Mechanisms of J/ψ, Υ and B meson production in proton-proton scattering at total energy 7 TeV are studied with the help of event generator Pythia 8. Uncertainties in the total and differential cross sections due to choice of the renormalization and factorization scales are analyzed for prompt J/ψ an...
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irk-123456789-1070822016-10-14T03:02:07Z J/ψ, Y and B meson production in proton–proton collisions at the LHC Kotlyar, V.V. Krupina, N.V. Section C. Theory of Elementary Particles. Cosmology Mechanisms of J/ψ, Υ and B meson production in proton-proton scattering at total energy 7 TeV are studied with the help of event generator Pythia 8. Uncertainties in the total and differential cross sections due to choice of the renormalization and factorization scales are analyzed for prompt J/ψ and Υ production. Sensitivity of the inclusive cross sections on contributions of J/ψ from decay of b–hadrons is also discussed. Results of the calculations are compared with the ALICE, ATLAS, CMS, and LHCb data in order to assess potentialities and validity of the approaches, in particular color singlet and octet models, used in the simulations. Механизмы рождения J/ψ-,Υ- и B-мезонов в рассеянии протонов с полной энергией 7 ТэВ изучаются с помощью генератора событий Пифия 8. Неопределённости в значениях полных и дифференциальных сечений реакций, которые обусловлены выбором шкал перенормировки и факторизации, анализируются для рождения мгновенных J/ψ и Υ-мезонов. Исследуется также чувствительность инклюзивных сечений реакции к вкладам J/ψ источником которых являются распады b–адронов. Для проверки моделей, используемых в моделировании рассмотренных процессов, результаты расчётов сравниваются с данными, полученными коллаборациями ALICE, ATLAS, CMS и LHCb. Механізми народження J/ψ-, Υ- та B-мезонів у розсіянні протонів з повною енергією 7 ТеВ вивчаються за допомогою генератора подій Піфія 8. Невизначеність повних та диференційних перерізів реакцій, що зумовлена вибором шкал перенормування та факторизації, аналізується для народження миттєвих J/ψ- та Υ-мезонів. Досліджується також чутливість інклюзивних перерізів реакцій до внесків J/ψ джерелом яких є розпад b–адронів. Для перевірки моделей, що використовуються в моделюванні розглянутих процесів, результати розрахунків порівнюються з даними, що було отримано колабораціями ALICE, ATLAS, CMS та LHCb. 2012 Article J/ψ, Y and B meson production in proton–proton collisions at the LHC / V.V. Kotlyar, N.V. Krupina // Вопросы атомной науки и техники. — 2012. — № 1. — С. 183-187. — Бібліогр.: 28 назв. — англ. 1562-6016 PACS: 12.38.-t, 12.38.Bx, 12.39.St, 14.40.Gx, 13.85.Ni http://dspace.nbuv.gov.ua/handle/123456789/107082 en Вопросы атомной науки и техники Національний науковий центр «Харківський фізико-технічний інститут» НАН України |
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Section C. Theory of Elementary Particles. Cosmology Section C. Theory of Elementary Particles. Cosmology |
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Section C. Theory of Elementary Particles. Cosmology Section C. Theory of Elementary Particles. Cosmology Kotlyar, V.V. Krupina, N.V. J/ψ, Y and B meson production in proton–proton collisions at the LHC Вопросы атомной науки и техники |
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Mechanisms of J/ψ, Υ and B meson production in proton-proton scattering at total energy 7 TeV are studied with the help of event generator Pythia 8. Uncertainties in the total and differential cross sections due to choice of the renormalization and factorization scales are analyzed for prompt J/ψ and Υ production. Sensitivity of the inclusive cross sections on contributions of J/ψ from decay of b–hadrons is also discussed. Results of the calculations are compared with the ALICE, ATLAS, CMS, and LHCb data in order to assess potentialities and validity of the approaches, in particular color singlet and octet models, used in the simulations. |
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Kotlyar, V.V. Krupina, N.V. |
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Kotlyar, V.V. Krupina, N.V. |
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Kotlyar, V.V. |
| title |
J/ψ, Y and B meson production in proton–proton collisions at the LHC |
| title_short |
J/ψ, Y and B meson production in proton–proton collisions at the LHC |
| title_full |
J/ψ, Y and B meson production in proton–proton collisions at the LHC |
| title_fullStr |
J/ψ, Y and B meson production in proton–proton collisions at the LHC |
| title_full_unstemmed |
J/ψ, Y and B meson production in proton–proton collisions at the LHC |
| title_sort |
j/ψ, y and b meson production in proton–proton collisions at the lhc |
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Національний науковий центр «Харківський фізико-технічний інститут» НАН України |
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2012 |
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Section C. Theory of Elementary Particles. Cosmology |
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http://dspace.nbuv.gov.ua/handle/123456789/107082 |
| citation_txt |
J/ψ, Y and B meson production in proton–proton collisions at the LHC / V.V. Kotlyar, N.V. Krupina // Вопросы атомной науки и техники. — 2012. — № 1. — С. 183-187. — Бібліогр.: 28 назв. — англ. |
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Вопросы атомной науки и техники |
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| fulltext |
J/ψ, Υ, AND B MESON PRODUCTION IN
PROTON–PROTON COLLISIONS AT THE LHC
V.V. Kotlyar ∗and N.V. Krupina
National Science Center ”Kharkov Institute of Physics and Technology”, 61108, Kharkov, Ukraine
(Received October 31, 2011)
Mechanisms of J/ψ, Υ, and B meson production in proton-proton scattering at total energy 7 TeV are studied
with the help of event generator Pythia 8. Uncertainties in the total and differential cross sections due to choice
of the renormalization and factorization scales are analyzed for prompt J/ψ and Υ production. Sensitivity of the
inclusive cross sections on contributions of J/ψ from decay of b–hadrons is also discussed. Results of the calculations
are compared with the ALICE, ATLAS, CMS, and LHCb data in order to assess potentialities and validity of the
approaches, in particular color singlet and octet models, used in the simulations.
PACS: 12.38.-t, 12.38.Bx, 12.39.St, 14.40.Gx, 13.85.Ni
1. INTRODUCTION
Production of charmonium and bottomonium is
known as an important tool for testing perturba-
tive quantum chromodynamics (pQCD) and gaining
a better understanding of effects beyond the lead-
ing order in strong–coupling constant. Detailed dis-
cussion of models for charmonium and bottonium
production in hadron scattering can be found, e.g.
in [1–5].
Widely–used approaches for analysis of the
quarkonium hadroproduction are based on an ap-
proximation when the hard scattering of partons
is separated from soft processes related to forma-
tion of the mesons that are thought as heavy–quark
bound states. Amplitudes of short–distance par-
tonic processes are computed within pQCD, while
treatment of long–distance ones yields to consider-
ation of nonperturbative dynamics. The cross sec-
tion for quarkonium hadroproduction can be writ-
ten in a factorized form as superposition of cross sec-
tions for hard scattering of initial–state partons, e.g.
g + g → QQ̄ + g, convoluted with parton distribu-
tion functions (PDFs) for colliding hadrons that are
then weighted with matrix elements describing how
created heavy–quark pair QQ̄ evolves into a quarko-
nium state.
The cross sections of hard partonic scattering
(PDFs) depend on renormalization (factorization)
scale. In rigorous calculations, that should include
contributions beyond leading order both in the ampli-
tudes of short–distance processes and evolution equa-
tions for PDFs, the cross sections of the reactions
are expected to be independent from a particular
choice of the scales. High–order processes prove to
affect visibly the cross sections and polarization in
the quarkonium hadroproduction [6–10]. Neverthe-
less, the uncertainties, inherent to extensions of the
leading–order approaches, still remain essential.
A growing interest in the last decade at studying
the heavy–quarkonium production stems also from
the hope to use these processes for the diagnostics of
the quark–gluon medium produced in ultrarelativis-
tic heavy–ion collisions [2, 5, 11, 12].
Purpose of this report is to study mechanisms of
prompt J/ψ and Υ production, role of J/ψ, originat-
ing from b–hadron decays, and to determine quan-
titatively how variations of parameters, that define
renormalization and factorization scales, influence
the cross sections of the reactions. The present stud-
ies aim to test the color singlet and octet models for
heavy–quarkonium production [4, 13–15], employing
with this end results of recent experiments [16–22] at
the Large Hadron Collider (LHC).
2. MODELS FOR QUARKONIA
HADROPRODUCTION
In this paper the meson production is simulated mak-
ing use of event generator Pythia 8 [23]. Produc-
tion of prompt J/ψ(1S) and Υ(1S) along with non–
prompt J/ψ(1S) is considered.
Prompt mesons originate from a heavy quark–
antiquark pairs QQ̄ that hadronize into colorless
states. It is assumed that the QQ̄ pairs, where Q = c
or b, are created in short–range processes:
g + g → QQ̄
[
2S+1LJ(a)
]
+ g, (1)
q + g → QQ̄
[
2S+1LJ(a)
]
+ q, (2)
q + q̄ → QQ̄
[
2S+1LJ(a)
]
+ g, (3)
with definite values of orbital angular momentum L,
spin S, and total angular momentum J in color sin-
glet (CS) or octet (CO) states, that are indicated by
a = 1 or 8, respectively.
∗Corresponding author E-mail address: kotlyarv@kipt.kharkov.ua
PROBLEMS OF ATOMIC SCIENCE AND TECHNOLOGY, 2012, N 1.
Series: Nuclear Physics Investigations (57), p. 183-187.
183
CS QQ̄ pairs with 2S+1LJ = 3S1 spring from hard
gluon scattering (1). CO QQ̄ states 1S0 and 3S1 are
produced in all processes (1)–(3). CS and CO QQ̄
pairs in P–wave states 3PJ with J = 0, 1, 2 and J = 0,
respectively, are generated in (1)–(3). Subsequent
transition between CO QQ̄ and colorless quarkonium
states is accompanied by soft gluon emission.
The prompt mesons originate also from decays of
higher quarkonium states, e.g.
χ2c(1P ) → γ+J/ψ(1S) or χ0b(1P ) → γ+Υ(1S).
Decays of b–hadrons, such as B–mesons, Λb, Σb,
Ξb, Ωb, etc., serve as a source of non–prompt J/ψ(1S),
for example,
B+∗ → γ +B+, B+ → J/ψ(1S) +K+.
Cross sections for non–prompt J/ψ(1S) production
receive substantial contributions from the reaction
p + p → B + X. Description of the latter relies on
the Lund string model [24] being a framework for im-
plementation of fragmentation processes in Pythia.
3. CROSS SECTIONS OF QUARKONIA
AND B MESON PRODUCTION
The simulation of the quarkonia production is per-
formed with Pythia 8.145 using the default tune and
PDFs CTEQ6.6M [25]. The renormalization and fac-
torization scales are expressed through the transverse
masses of outgoing particles in (1)–(3)
Q2
R = cR
(
(M2
QQ̄ + p2
T )(M2 + p2
T )
)1/2
, (4)
Q2
F = cF
(
M2 + p2
T
)
, (5)
where pT (M) denotes the transverse momentum (the
mass) of u, d, s, c, b quark or gluon, MQQ̄ is the mass
of QQ̄ pair.
Fig. 1. Dependence of the total cross section for
bb̄–pairs production on choice of the renormalization
scale
The total cross sections σQQ̄ for production of cc̄
or bb̄ pairs, obtained with (1)–(3), appear to be not
independent from values of the renormalization and
factorization scales. As seen in Figs. 1 and 2, func-
tions σbb̄(cR, cF = const) and σbb̄(cR = const, cF )
vary rapidly for cR < cF . At the same time, decrease
of σbb̄(cR, cF = const) is relatively slow for cR � 1
and cR � cF . The cross section σcc̄ reveals qualita-
tively the same behaviour as in Figs. 1 and 2.
Fig. 2. Dependence of the total cross section for
bb̄–pairs production on choice of the factorization
scale
Calculations of the differential cross sections un-
der conditions of experiments [16–22] have been car-
ried out for various sets of parameters cR and cF .
Results for some sets both at the diagonal in (cR, cF )–
plane and outside it are displayed in Figs. 3 – 6. Val-
ues cR = cF = 0.49 correspond to the minimum in
σcc̄ for p+ p→ cc̄+X.
Fig. 3. Differential cross section for J/ψ produc-
tion in the central rapidity region. Points are taken
from Ref. [17]
Fig. 4. The same as in Fig. 3. The data are from
Ref. [16]. The branching fraction of the J/ψ decay
into two muons is B(J/ψ → μ+μ−)
184
Fig. 5. The same as in Fig. 3. The data are
from Ref. [18]
Fig. 6. Differential cross section for J/ψ pro-
duction in the forward rapidity region. The data
are from Ref. [19]
The analysis of the pT distributions in Figs. 3−6
covers wide area of emission angles of the mesons
from central to forward regions. Calculations show
that the transverse–momentum spectra of J/ψ(1S),
measured by the ALICE, ATLAS, CMS, and LHCb
collaborations in the central–rapidity region, lie
within the band of theoretical uncertainties. Re-
sults of the LHCb in the forward region are near the
low edge of this band. Note, that predictions [28]
within the kT –factorization approach in CS model
agree with the LHC experimental data in both cen-
tral and forward regions.
In Fig. 7 and 8 the differential cross sections for
the reactions pp → B0,+X, obtained in the present
report with Tune 4C in Pythia 8.153 and PDFs
CTEQ6.6M, are compared with the results of mea-
surements and simulations, performed by CMS col-
laboration [26, 27]. In CMS papers Pythia 6 with
Tune D6T and PDFs CTEQ6L1 is used. Figs. 7
and 8 show that the different codes lead to the cross
sections, that do not differ visibly at considered pT –
region and are close to the experimental data.
Cross sections for prompt Υ(1S) production, com-
puted in the framework of the CS and CO models,
turn out be strong scale sensitive, as can be inferred
from Fig. 9.
Fig. 7. Differential cross section for B0 produc-
tion. The points are from Ref. [26]
Fig. 8. Differential cross section for B+ production.
The points are from Ref. [27]
Transverse–momentum and rapidity dependen-
cies of the cross sections are displayed in Figs. 9 and
10 under conditions of CMS experiment [21]. Com-
parison with ATLAS [20] and LHCb [22] data will be
presented elsewhere.
Detailed analysis shows that process (1) with
2S+1LJ(a) = 3P1(1),3P2(1), and 3P0(8) gives main
contributions to the cross section of J/ψ(1S) produc-
tion for cR = cF = 0.49. Thus, reaction mechanisms
that involve creation of χ1c(1P ) and χ2c(1P ) mesons
in the CS intermediate states are enhanced in the
calculations. At pT � 10 GeV/c CS channel 3P1(1)
turns out to be the most important.
Transitions via (1) with 2S+1LJ(a) = 3P2(1) and
3P0(8) (3S1(8)) dominate in Υ(1S) production when
scale parameters cR = cF = 0.3 (cR = cF = 1.0) are
used in the calculations. For cR = cF = 1.0 ratio of
CS and CO cross section for (1) is
σbb̄(
3S1(1))/σbb̄(
3S1(8)) = 0.45.
For pT � 40 GeV/c both the CS and CO chan-
nels appear to be comparable. Strengthened contri-
butions of the CO intermediate states may be respon-
sible for the overestimation of the data by the theory
as observed in Figs. 9 and 10.
185
Fig. 9. Transverse–momentum dependence of the
differential cross section for Υ(1S) production. The
points are from Ref. [21]
Fig. 10. Rapidity dependence of the differential
cross section for Υ(1S) production. The points are
from Ref. [21]. The branching fraction of the Υ(1S)
decay into two muons is B(Υ(1S) → μ+μ−)
4. CONCLUSIONS
Production of J/ψ,Υ, and B mesons in proton-proton
collisions at total energy 7 TeV is simulated with the
help of event generator Pythia 8. Studies of the reac-
tions pp→ J/ψ(1S)X and pp→ Υ(1S)X, performed
within the color singlet and color octet models, have
demonstrated the strong dependence of the cross sec-
tions to parameters, that define renormalization and
factorization scales. Results of the calculations are
compared with the experimental data, obtained by
the ALICE, ATLAS, CMS, and LHCb collaborations
at the LHC. Transverse–momentum distributions of
the emitted mesons, computed in the central–rapidity
region, agree reasonably with the data. Nevertheless,
some discrepancies appear in the forward region.
Acknowledgements
The authors would like to thank A.Yu. Korchin for
useful discussions. N.V. Krupina acknowledges the
partial support from National Academy of Science of
Ukraine under contract 50/53− 2011.
References
1. M. Kramer. Quarkonium production at high-
energy colliders // Prog. Part. Nucl. Phys. 2001,
v. 47, p. 141-201.
2. N. Brambilla et al. Heavy quarkonium physics //
arXiv : 0412158 [hep-ph], 2004, 487 p.
3. J.P. Lansberg. J/ψ, ψ′ and Υ production at
hadron colliders: A Review // Int. J. Mod. Phys.
2006, v. A21, p. 3857-3915.
4. N. Brambilla et al. Heavy quarkonium: progress,
puzzles, and opportunities // Eur. Phys. J. 2011,
v. C71, p. 1534, 181 p.
5. Z. Conesa del Valle et al. Quarkonium produc-
tion in high energy proton-proton and proton-
nucleus collisions // Nucl. Phys. Proc. Suppl.
2011, v. 214, p. 3-36.
6. J.M. Campbell, F. Maltoni, F. Tramontano.
QCD corrections to J/psi and Upsilon produc-
tion at hadron colliders // Phys. Rev. Lett. 2007,
v. 98, 252002, 4 p.
7. G.T. Bodwin. NRQCD factorization and quarko-
nium production at hadron–hadron and ep col-
liders // arXiv :1012.4215, 2010, 6 p.
8. Y.-Q. Ma, K. Wang, K.-T. Cha. J/ψ(ψ′) Pro-
duction at the Tevatron and LHC at O(α4
Sv
4)
in Nonrelativistic QCD // Phys. Rev. Lett. 2011,
v. 106, 042002, 4 p.
9. M. Butenschoen, B.A. Kniehl. World data of J/ψ
production consolidate NRQCD factorization at
NLO // Phys. Rev. 2011, v. D84, 051501, 5 p.
10. Z.-B. Kang, J.-W. Qiu, G. Sterman. Heavy
quarkonium production and polarization //
arXiv :1109.1520, 2011, 11 p.
11. F. Carminati et al. (The ALICE Collaboration).
ALICE: Physics Performance Report, Vol. I
// J. Phys. G: Nucl. Part. Phys. 2004, v. 30,
p. 1517–1763.
12. R. Rapp, D. Blaschke, P. Crochet. Charmo-
nium and bottomonium in heavy–ion collisions //
Prog. Part. Nucl. Phys. 2010, v. 65, p. 209–266.
13. C.-H. Chang. Hadronic production of J/ψ associ-
ated with a gluon // Nucl. Phys. 1980, v. B172,
p. 425-434.
14. P. Cho, A. Leibovich. Color octet quarkonia pro-
duction // Phys. Rev. 1996, v. D53, p. 150-162.
15. E. Braaten, S. Fleming, A. Leibovich. NRQCD
analysis of bottomonium production at the Teva-
tron // Phys. Rev. 2001, v. D63, 094006, 12 p.
186
16. G. Aad et al. (The ATLAS Collaboration). Mea-
surement of the differential cross-sections of in-
clusive, prompt and non-prompt J/ψ production
in proton-proton collisions at
√
s = 7 TeV //
Nucl. Phys. 2011, v. B850, p. 387-444.
17. K. Aamodt et al. (The ALICE Collaboration).
Rapidity and transverse momentum dependence
of inclusive J/ψ production in pp collisions at
√
s
= 7 TeV // Phys. Lett. 2011, v. B704, p. 442-455.
18. V. Khachatryan et al. (The CMS Collaboration).
Prompt and non-prompt J/ψ production in pp
collisions at
√
s = 7 TeV // Eur. Phys. J. 2011,
v. C71, 1575, 26 p.
19. R. Aaij et al. (The LHCb Collaboration). Mea-
surement of J/ψ production in pp collisions at√
s=7 TeV // Eur. Phys. J. 2011, v. C71, 1645,
17 p.
20. G. Aad et al. (The ATLAS Collaboration). Mea-
surement of the Υ(1S) Production Cross-Section
in pp Collisions at
√
s = 7 TeV in ATLAS //
Phys. Lett. 2011, v. B705, p. 9–27.
21. V. Khachatryan et al. (The CMS Collaboration).
Υ production cross section in pp collisions at
√
s
= 7 TeV // Phys. Rev. 2011, v. D83, 112004,
27 p.
22. L. Li Gioi. (The LHCb Collaboration). Studies
with Onia at LHCb // arXiv : 1109.3398, 2011,
8 p.
23. T. Sjostrand, S. Mrenna, P.Z. Skands. A Brief
Introduction to PYTHIA 8.1 // Comput. Phys.
Commun. 2008, v. 178, p. 852-867.
24. B. Andersson. The Lund model // Camb.
Monogr. Part. Phys. Nucl. Phys. Cosmol. 1997,
v. 7, p. 1-471.
25. P.M. Nadolsky et al. Implications of CTEQ
global analysis for collider observables // Phys.
Rev. 2008, v. D78, 013004, 21 p.
26. S. Chatrchyan et al. (The CMS Collaboration).
Measurement of the B0 production cross section
in pp Collisions at
√
s = 7 TeV // Phys. Rev.
Lett. 2011, v. 106, 252001, 15 p.
27. V. Khachatryan et al. (The CMS Collaboration).
Measurement of the B+ Production Cross Sec-
tion in pp Collisions at
√
s = 7 TeV // Phys.
Rev. Lett. 2011, v. 106, 112001, 15 p.
28. S.P. Baranov, A.V. Lipatov, N.P. Zotov. Prompt
J/ψ production at LHC: new evidence for the
kT –factorization // arXiv : 1108.2856, 2011, 14 p.
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