#### New feature of low \(p_{T}\) charm quark hadronization in pp collisions at \(\sqrt{s}=7\) TeV

Eur. Phys. J. C
New feature of low pT charm quark hadronization in p p collisions √ at s = 7 TeV
Jun Song 1
Hai-hong Li 0 1
Feng-lan Shao 0
0 School of Physics and Engineering, Qufu Normal University , Jining 273165, Shandong , China
1 Department of Physics, Jining University , Jining 273155, Shandong , China
Treating the light-flavor constituent quarks and antiquarks whose momentum information is extracted from the data of soft light-flavor hadrons in pp collisions at √s = 7 TeV as the underlying source of chromatically neutralizing the charm quarks of low transverse momenta ( pT ), we show that the experimental data of pT spectra of single-charm hadrons D0,+, D∗+ Ds+, Λc+ and Ξc0 at midrapidity in the low pT range (2 pT 7 GeV/c) in pp collisions at √s = 7 TeV can be well understood by the equal-velocity combination of perturbatively created charm quarks and those light-flavor constituent quarks and antiquarks. This suggests a possible new scenario of low pT charm quark hadronization, in contrast to the traditional fragmentation mechanism, in pp collisions at LHC energies. This is also another support for the exhibition of the soft constituent quark degrees of freedom for the small parton system created in pp collisions at LHC energies. This work is supported by the National Natural Science Foundation of China under Grant Nos. 11575100, 11675091.
1 Introduction
The experimental study of the quark-gluon plasma (QGP),
a new state of matter of QCD, is mainly through the
heavyion collisions which can create the big thermal parton
system with relatively long lifetime. Relative to heavy-ion
collisions, proton-nucleus ( p A) collisions create the
“intermediate” parton system and proton-proton ( pp) collisions create
the “small” parton system. The deconfined medium is usually
assumed to be not created in p A and pp collisions, at least
up to RHIC energies. In particular, the data of pp collisions,
in the context of heavy-ion physics, are usually served as the
baseline to study the effects and/or properties of cold and hot
nuclear matter in p A and A A collisions, respectively.
The Large Hadron Collider (LHC) pushes the center of
mass energy per colliding nucleon up to TeV level, which
brings new properties even for the small parton system
created in pp collisions. Recent measurements in pp collisions
at LHC energies from CMS and ALICE collaborations find
several remarkable similarities with heavy-ion collisions. In
high-multiplicity events of pp collisions, the phenomena
such as long-range angular correlations [
1,2
] and
collectivity [
3,4
], strangeness enhancement [
5,6
], and the increased
baryon to meson ratio at low transverse momentum ( pT ) [
7–
9
] are observed. These phenomena were already observed in
heavy-ion collisions at RHIC and LHC energies and are
usually regarded as the typical behaviors related to the formation
of QGP. Theoretical studies of these striking observations
focus on what happens on the small parton system created in
pp collisions at LHC energies through different
phenomenological/theoretical methods such as the mini-QGP creation
or phase transition [
10–15
], multiple parton interaction [
16
],
string overlap and color re-connection at hadronization [
17–
20
], etc.
In recent work [
21
], we found that the mid-rapidity data
of pT spectra of light-flavor hadrons in the low pT range
( pT 6 GeV/c) in pp collisions at √s = 7 TeV can
be well understood by a phenomenological quark
combination mechanism using the equal-velocity combination of
up/down and strange quarks and antiquarks with constituent
masses at hadronization. This suggests that the constituent
quark degrees of freedom (CQdof) play an important role
in low pT hadron production in pp collisions at LHC
energies, which indicates the possible existence of the underlying
source with soft CQdof, a kind of new property for the small
parton system created in pp collisions at LHC energies.
The hadronization of the charm quarks in pp collisions
is usually described by the traditional fragmentation
mechanism or fragmentation function. In this paper, we study
the possibility of a new phenomenological feature for the
hadronization of low pT charm quarks in pp collisions at
LHC energies. As the aforementioned discussion, the
production of light-flavor hadrons in pp collisions at LHC
energies can be well described by the combination of
lightflavor constituent quarks and antiquarks of low pT . These
constituent quarks and antiquarks also serve as an
underlying source for the color neutralization of charm quarks at
hadronization to form the single-charm hadrons. Specifically,
the charm quark can pick up a co-moving light antiquark
or two co-moving quarks to form a single-charm meson or
baryon, where the momentum characteristic is the
combination pH = pc + pq¯,qq . This (re-)combination
characteristic of charm quark hadronization will reflect in the
momentum spectra of charm hadrons and, in particular, the ratio of
charm baryon to charm meson. Therefore, in this paper, we
apply a phenomenological quark (re-)combination
mechanism (QCM) to study the mid-rapidity pT spectra of
singlecharm mesons D0,+, D∗+, Ds+ and baryons Λc+, Ξc0 and
the ratios among them, and compare our results with
available experimental data and several theoretical predictions by
fragmentation mechanism.
This paper is organized as follows: Sect. 2 will introduce
a working model in quark (re-)combination mechanism for
charm quark hadronization. Section 3 presents our results and
relevant discussions. A summary is given finally in Sect. 4.
2 Charm quark hadronization in QCM
The (re-)combination mechanism of charm quark
hadronization was proposed in the early 1980s [
22–24
] and has many
applications in both hadron–hadron collisions [
25–27
] and
relativistic heavy-ion collisions [
28–31
]. Because of the
lack of the sufficient knowledge for the spatial
information of the small parton system created in pp collisions at
LHC energies, in this section, we present a working model
for the (re-)combination hadronization of charm quarks in
the low pT range in momentum space, which only
incorporates the most basic feature of QCM, i.e., the
equalvelocity combination approximation. In the unclear
nonperturbative dynamics issues such as the selection of
different spin states and the formation competition between baryon
and meson in the combination are treated as model
parameters.
2.1 Formulas in momentum space
The momentum distributions of the single-charm meson Mcl¯
and baryon Bcll in QCM, as formulated in e.g. [
32,33
] in
general, can be obtained by
RMcl¯( p1, p2; p) = κMcl¯
δ( pi − xi p),
RBcll ( p1, p2, p3; p) = κBcll
δ( pi − xi p),
where κMcl¯ and κBcll are constants which are independent of
the momentum but dependent on other ingredients such as
the quark number so that all charm quarks can be correctly
exhausted (after further including multi-charm hadrons).
Following our earlier work [
21,34
] for light-flavor hadrons
in pp and p–Pb collisions at LHC energies, we adopt the
co-moving approximation in combination, i.e., the charm
quark combines with light quark(s) of the same velocity
to form the charm hadron. Since the equal velocity implies
pi = γ vmi ∝ mi , the momentum fraction is
xi = mi /
m j ,
j
where the quark masses are taken to be the constituent
masses. For light-flavor quarks, we take mu = md = 0.33
GeV and ms = 0.5 GeV, so that the data of momentum
spectra of light-flavor hadrons are well explained [
21,34
].
The constituent mass of the charm quark is taken to have
the usual value mc = 1.5 GeV. We also consider mc to have
a larger value, 1.7 GeV, which can more suitably construct
the masses of vector single-charm mesons and single-charm
baryons in the ground state in the equal-velocity
combination of the charm quark with light-flavor quarks. The
resulting momentum spectra of single-charm hadrons only slightly
f Mcl¯( p) =
d p1d p2 fcl¯( p1, p2) RMcl¯( p1, p2; p),
f Bcll ( p) =
d p1d p2d p3 fcll ( p1, p2, p3) RBcll ( p1, p2, p3; p).
Here, fcl¯( p1, p2) is the joint momentum distribution for
charm quark (c) and light antiquark (l¯). RMcl¯( p1, p2; p) is
the combination function, that is, the probability density for
the given cl¯ with momenta p1, p2 combining into a meson
Mcl¯ with momentum p. It is similar for the baryon.
We take independent distributions for quarks of different
flavors by neglecting correlations,
fcl¯( p1, p2) = fc( p1) fl¯( p2),
fcll ( p1, p2, p3) = fc( p1) fl ( p2) fl ( p3).
We suppose the combination takes place mainly for a quark
and/or an antiquark taking a given fraction of momentum of
the hadron so that the combination function is the product of
Dirac delta functions,
2
broaden for the same charm quark spectrum fc( p).
Therefore, we neglect the effect of the constituent mass uncertainty
of the charm quark in this paper.
Substituting Eqs. (3)–(4) and (5)–(6) into Eqs. (1)–(2), we
obtain the distributions of single-charm hadrons,
f Mcl¯( p) = κMcl¯ fc(x1 p) fl¯(x2 p),
f Bcll ( p) = κBcll fc(x1 p) fl (x2 p) fl (x3 p).
We rewrite the distribution functions of the charm hadrons,
f Mcl¯ ( p) = NMcl¯ f M(nc)l¯ ( p) ,
f Bcll ( p) = NBcll f B(ncl)l ( p) ,
(8)
(9)
(10)
(11)
(12)
(13)
(14)
(15)
where f (n) ( p) is the normalized distribution function with
Mcl¯
d p f (n) ( p) = 1. NMcl¯ is the momentum-integrated yield,
Mcl¯
κMcl¯ = Nc Nl¯ Rcl¯→Mcl¯,
NMcl¯ = Nc Nl¯ AMcl¯
= Nc Nl Nl Rcll →Bcll ,
where the coefficient A−M1cl¯ = d p fc(n) (x1 p) fl¯(n) (x2 p)
d p i3=1 fq(in) (xi p) with the normalized
and A−Bc1ll =
charm and light quark distribution d p fc(,nl)( p) = 1. We see
that Rcl¯→Mcl¯ ≡ κMcl¯/ AMcl¯ is nothing but the
momentumintegrated combination probability of cl¯ → Mcl¯. It is similar
for Rcll →Bcll ≡ κBcll / ABcll .
Rcl¯→Mcl¯ and Rcll →Bcll are parameterized. We use NMc to
denote the total number of all single-charm mesons. Ncq¯ =
Nc Nu¯ + Nd¯ + Ns¯ is the possible number of all
charmlight pairs. NMc /Ncq¯ gives the flavor-averaged probability
of a cl¯ forming a charm meson. The average number of Mcl¯
is Nc Nl¯ × NMc /Ncq¯ = Pl¯NMc where Pl¯ ≡ Nl¯/Nq¯ denotes
the probability of an antiquark with the flavor l¯. For a given
cl¯ combination, it can form different J P states, and we use
CMi,cl¯ to denote the probability of forming the particular spin
state i and finally obtain the yield of the charm meson Mi,cl¯,
NMi,cl¯ = CMi,cl¯ Pl¯NMc .
In this paper we consider only the pseudo-scalar mesons
J P = 0−(D+, D0 and Ds+ ) and vector mesons J P = 1−
(D∗+, D∗0 and D∗+ ) in the ground state. We introduce a
s
parameter RV/P to denote the relative ratio of vector meson
to pseudo-scalar meson of the same quark flavors, and we
have
CMi,cl¯ =
1
1+RV/P
RV/P
1+RV/P
for J P = 0− mesons,
for J P = 1− mesons.
We take RV/P = 1.5, the thermal weight value used in [
33,
35,36
].
In the baryon sector, we have
NBi,cll = CBi,cll Niter,ll Pl Pl NBc ,
(16)
where NBc is the total number of all single-charm baryons,
Niter,ll Pl Pl selects the particular flavor state ll , and CBi,cll
selects the particular spin state. Here Pl = Nl /Nq =
Nl /(Nu + Nd + Ns ) denotes the probability of a quark
with the flavor l. Niter,ll is the permutation number of ll
pair and is taken to be 1 for l = l and 2 for l = l . We
consider the production of the triplet (Λc+, Ξc+, Ξc0) with
J P = (1/2)+, the sextet (Σc0, Σc+, Σc++, Ξc0, Ξc+, Ωc0)
with J P = (1/2)+, and the sextet (Σc∗0, Σc∗+, Σc∗++, Ξc∗0,
Ξc∗+, Ωc∗0) with J P = (3/2)+, respectively, in the ground
state. We introduce a parameter RS1/T to denote the
relative ratio of J P = (1/2)+ sextet baryons to J P = (1/2)+
triplet baryons of the same quark flavors, and a parameter
RS3/S1 to denote that of J P = (3/2)+ sextet baryons to
J P = (1/2)+ sextet baryons of the same quark flavors. We
also take the effective thermal weight as a guideline [
33
]
and take RS1/T = 0.5 and RS3/S1 = 1.5, respectively. For
ll = uu, dd, ss,
1
1+RS3/S1
RS3/S1
1+RS3/S1
for Σc++, Σc0, Ωc0,
for Σc∗++, Σc∗0, Ωc∗0.
CBi,cll =
CBi,cll =
For ll = ud, us, ds,
1
⎨⎪⎧⎪ 1+RS1/RT(S11/+T RS3/S1)
1+RRS1S/1T/T(1R+S3R/SS13/S1)
⎪
⎪⎩ 1+RS1/T (1+RS3/S1)
for Λc+, Ξc0, Ξc+
for Σc+, Ξc0, Ξc+
for Σc∗+, Ξc∗0, Ξc∗+.
We note that yields and momentum spectra of the final state
Λc+, Ξc0 and Ωc0 after taking the decay contribution into
account are not sensitive to the parameters RS1/T and RS3/S1.
Considering that the single-charm mesons and baryons
consume most of the charm quarks produced in collisions,
we have the following approximated normalization to
singlecharm hadrons:
NMc + NBc ≈ Nc.
Here we treat the ratio R(Bc/)M ≡ NBc /NMc as a
parameter of the model, which characterizes the relative production
of single-charm baryons to single-charm mesons. We take
R(Bc/)M = 0.425, the same as that at mid-rapidity in p–Pb
collisions [
33
].
(17)
(18)
(19)
-1 /)V 1
c
e
G
(
)
y
d
T
p
d
/(
n
d
10−1
f (un)(pT)
f (sn)(pT)
f (cn)(pT) FONLL
used in QCM
1
10−1
10−2
(a)
(b)
2 2.5
p T (GeV/c)
3
We apply the above formulas in QCM to the one
dimensional pT space and calculate the pT spectra of single-charm
hadrons at mid-rapidity in pp collisions at √s = 7 TeV.
The pT distributions of quarks at hadronization are inputs of
the model. We have obtained the pT spectra of light-flavor
constituent quarks in the previous work [
21
]. The averaged
quark numbers in the rapidity interval |y| < 0.5 are 2.5 for
the u quark and 0.8 for the s quark, respectively. The
normalized distributions fu(n) ( pT ) and fs(n) ( pT ) are shown in
Fig.1a. The charge conjugation symmetry between quark and
antiquark and the iso-spin symmetry between up and down
quarks are applied in calculations.
In Fig. 1b, we show the normalized distribution of charm
quarks, which is obtained from the online calculation of
Fixed-Order Next-to-Leading-Logarithmic (FONLL). 1 The
points are center values and the shadow area shows the scale
uncertainties; see Refs. [
37,38
] for details. The uncertainty
due to parton distribution functions (PDFs) is not included.
Because of the large theoretical uncertainty, in particular, at
low pT , we only take the FONLL calculation as a
guideline. The practically used pT spectrum of charm quarks is
reversely extracted from the data of D∗+ meson [
39,40
] in
QCM with charm quark constituent mass mc = 1.5 GeV and
is shown as the thick solid line in Fig. 1b. The cross-section of
charm quarks in |y| < 0.5 interval is 1.2 mb. The extracted
spectrum is found to be very close to the center values of
FONLL calculation for pT 1.5 GeV/c. We emphasize that
just this good agreement prompts us to consider the QCM
being the probable physical picture of low pT charm quark
hadronization. Whether this agreement is coincidental or not
can be tested in the future by the data of higher collision
energies, such as those in pp collisions at √s = 13 TeV.
1 FONLL Heavy Quark Production, http://www.lpthe.jussieu.fr/
~cacciari/fonll/fonllform.html.
1
- )c (a)
1/eV02 D0
G
(
b
μ10
)
y
d
dpT1 data
σ/( QCM
d0−1
0 2 4 6 8 10 12 14
1
- )c (c)
1/eV02 D*+
G
(
b
μ10
)
y
d
T
/(dp 1
σ
d
0−10 2 4 6 8 10 12 14
pT(GeV/c)
102
10
1
102
10
1
D+
+
Ds
In Fig. 2, we show results of differential cross-sections
of D mesons at mid-rapidity as the function of pT in pp
collisions at √s = 7 TeV, and we compare them with
experimental data [
40
]. We see that QCM well describes the data of
D mesons for pT 7 GeV/c but under-predicts the data for
larger pT . This is reasonable. In the equal-velocity
combination of charm quarks and light quarks, a charm quark with
pT,c 6 GeV/c will combine a light antiquark of pT,l¯ 1.5
GeV/c. Because most of the light quarks, see Fig. 1a, are of
such low pT , they provide the sufficient partners (or chance)
for the hadronization of charm quarks. For a charm quark
of pT,c 6 GeV/c, the combining light antiquark should
have pT,l¯ 1.5 GeV/c where the number density of light
antiquark is very small and drops exponentially. In this case,
those light antiquarks may be not enough to provide the
sufficient chance for the combination hadronization of charm
quarks of pT,c 6 GeV/c, and therefore the combination
may be not the dominated channel and the fragmentation
will take over.
In Fig. 3, we show results for the ratios of different D
mesons as a function of pT in pp collisions at √s = 7 TeV,
and we compare them with experimental data [
40
]. We see
that, within experimental uncertainties, the model results are
in agreement with the data. For the magnitudes of these four
ratios, we can give a simple explanation from the yield
(corresponding to differential cross-section) ratios of D mesons.
Using Eq. (14) and taking strong and electromagnetic decay
contribution into account where the data of decay branch
ratios are taken from PDG[
41
], we have
D+ 1 + 0.323RV/P
D0 = 1 + 1.677RV/P
≈ 0.42,
(20)
1
o
it
ra0.8
Fig. 3 Ratios of different D mesons as the function of pT in pp
collisions at √s = 7 TeV. Symbols are experimental data [
40
] and lines are
results of QCM
(21)
(22)
(23)
D∗+
RV/P
D0 = 1 + 1.677RV/P
Ds+ 1 + RV/P
D0 = 1 + 1.677RV/P
Ds+ 1 + RV/P
D+ = 1 + 0.323RV/P
≈ 0.43,
λs ≈ 0.23,
λs ≈ 0.54,
with λs = Ns /Nu = 0.32 and RV/P = 1.5. Here, we
emphasize that the value of RV/P is not specifically tuned to
reproduce the data of these four ratios but is taken from the analysis
of the effective thermal weight [
42
], which was often used in
charm meson production [
35,36
].
Theoretical pQCD calculations with fragmentation
functions were compared with experimental data of D mesons in
Refs. [
39,40
]. It is shown that pQCD calculations in large
pT range have small theoretical uncertainties and often well
explain the data. However, pQCD calculations in the small
pT range have quite large theoretical uncertainties and the
comparison with data is not conclusive. In contrast with
those pQCD calculations with fragmentation functions, our
results suggest a different mechanism for the charm quark
hadronization at low pT .
The production of baryons is more sensitive to the
hadronization mechanism. In Fig. 4, we show results of the
pT spectrum of baryon Λc+ and the ratio to the D0 meson,
and we compare them with the experimental data [
9
]. We
emphasize that, after taking the decay contribution of Σc and
Σc∗ into account, results of Λc+ are not sensitive to model
parameters RS1/T and RS3/S1. We see that, similar to D
mesons, our results of Λc+ spectrum and ratio Λc+/D0 are
1
- )
c
/
eV10 2
G
(
b
μ
y
dT10
p
d
/
σ
d
1
10 −10
1
0
D
+ /c
Λ0.8
+
(a) Λc
4
6
8
in good agreement with the data for pT 7 GeV/c. The
predictions of other models or event generators [
20,43–45
]
which adopt string or cluster fragmentation mechanism for
hadronization are also shown in Fig. 4b. PYTHIA8 Monash
tune [46], DIPSY with rope parameter [
43
], and HERWIG7
[
44
] predict a small Λc+/D0 ratio of 0.1 and almost constant
behavior at different pT . Considering the effect of string
formation beyond leading color approximation [
20
], PYTHIA8
(CR Mode0) increases the ratio to a certain extent and gives
the decreasing tendency with pT .
In Fig. 5, we show results of the differential cross-section
of Ξc0 at mid-rapidity multiplied by the branch ratio into
e+Ξ −νe (a) and the relative ratio to D0 (b) as the function of
pT in pp collisions at √s = 7 TeV. The decay contribution
of Ξc and Ξc∗ is included, and results of Ξc0 are not sensitive
to model parameters RS1/T and RS3/S1. Because of the lack
of the absolute branch ratio into e+Ξ −νe, our result of the
spectrum of Ξc0 is multiplied by a branch ratio 3.8%, which
is within the current range of theoretical calculations (0.83–
4.2%) [
47–49
]. We see that the model result, the thick solid
line in Fig. 5a, can well describe the data of Ξc0 for 2
pT 7 GeV/c but significantly underestimates the first data
data
QCM BR=3.8%
exp(-pT/ α) fit
for visual guide
DIPSY (rope) BR=4.2%
PYTHIA8 Monash BR=4.2%
PYTHIA8 (CR mode0) BR=4.2%
HERWIG7 BR=4.2%
(b)
0
1
2
3
4
5
6
7
8 9 10
pT(GeV/c)
Fig. 5 Differential cross-section of Ξc0 at mid-rapidity multiplied by
the branch ratio into e+Ξ −νe (a) and the ratio to D0 (b) as the function
of pT in pp collisions at √s = 7 TeV. Symbols are experimental data
[
51
] and the thick solid lines are results of QCM. Results of other models
or event generators in panel (b) are taken from [
51
]
point at pT = 1.5 GeV/c. However, the first data point, to our
knowledge, is somewhat puzzlingly high if we note that the
studied differential cross-section is dσ/d pT dy. The data of
Λc+ in Fig. 4a and D0 in Fig. 2a suggest that the differential
cross-section tends to increase slowly with the decreasing pT
for small pT 2 GeV/c and will saturate and decrease as
pT → 0. The data of light-flavor hadrons for d N /d pT dy,
e.g. K (892)∗, show this behavior more clearly [
50
]. As a
naive illustration, we see the first data point of Ξc0 at pT = 1.5
GeV/c is more than twice the exponential extrapolation from
data points of larger pT , the thin dashed line, which is not
the case for the data of D mesons and Λc+. The QCM result
of the ratio Ξc0/D0 is shown in Fig. 5b. We see that the two
data points within 2 pT 7 GeV/c can be well described
by QCM and the first data point at pT = 1.5 GeV/c is much
higher than the QCM result.
String/cluster fragmentation usually under-predicts the
production of Ξc0. Here, we show predictions of several
models or event generators which adopt string/cluster
fragmentation at hadronization. They are taken from Ref. [
51
] and are
1
- )
c
/
V
e
G
b 1
(
μ
y
dpT
d
σ/d10−1
- ν)e
+ Ξe
0 →c10−2
Ξ
(
R
B
0
D
/)
- νe10−2
+ Ξe
0 →c
Ξ
(
10−3
shown as different kinds of thin lines in Fig. 5b. The decay
branch Ξc0 → e+Ξ −νe is taken to be 4.2%, and therefore
these predictions correspond to the up limits. HERWIG7 [
44
]
which adopts the cluster fragmentation predicts the
decreasing ratio for pT 1 GeV/c but is lower than the data about
an order of the magnitude. PYTHIA8 (Monash tune) [
46
]
and DIPSY with rope parameter [
43
] which adopt sting
fragmentation predict the increasing ratio as the function of pT
but the magnitude of the ratio is significantly lower than the
data. PYTHIA8 (CR mode0) [
20
], which takes the color
reconnection into account by considering the string formation
beyond the leading color approximation, increases the
prediction of ratio to a large extent but the prediction is still only
one third of the data.
4 Summary and discussion
We have shown the experimental data of pT spectra of
singlecharm hadrons D0,+, D∗+ Ds+, Λc+ and Ξc0 at mid-rapidity
in the low pT range (2 pT 7 GeV/c) in pp collisions at
√s = 7 TeV can be well understood by the equal-velocity
combination of perturbatively created charm quarks and the
light-flavor constituent quarks and antiquarks. We emphasize
the following aspects to address the physical importance of
our results: (1) The property, i.e., the pT distributions, of
light-flavor constituent quarks and antiquarks at
hadronization is obtained from the data of pT spectra of light-flavor
hadrons in work [
21
] where it is found that equal-velocity
combination of light-flavor quarks can reasonably describe
the data of light-flavor hadrons in the low pT range. The
existence of the underlying source of light-flavor quarks is a
new property of small parton system, maybe related to the
creation of the deconfined parton system in pp collisions at
LHC energies. (2) The good performance for the combination
of charm quarks and those light-flavor quarks and antiquarks
in comparison with the data suggests a new scenario of the
low pT charm quark hadronization in the presence of the
underlying light quark source in pp collisions at LHC
energies, in contrast to the usually adopted fragmentation
mechanism. (3) Most of the light quarks combine into light-flavor
hadrons that reproduces the data of light-flavor hadrons. A
small fraction of light quarks combine with charm quarks,
which also well explains the data of single-charm hadrons in
low pT range. This suggests a possible universal picture for
the production of low pT hadrons in pp collisions at LHC
energies. Finally, such a new picture is also expected in the
production of other heavy-flavor hadrons, and can be further
tested in the future by the data of high spin charm hadrons
as well as those of bottom hadrons.
Several discussions on the limitation of our model and
results are necessary. The present work only focuses on the
characteristic of hadron production in (transverse)
momentum space. It is still unclear that what kind of the spatial
property for the (light-flavor dominated) small parton
system leads to the effective combination of charm quarks and
those light-flavor quarks. In particular, in the light-flavor
sector we adopt the concept of the constituent quarks. What
kind of the spatial property for the small parton system is
responsible for the exhibition of the soft light-flavor
constituent quarks degrees of freedom? Is it related to the
possible de-confinement in the small system of pp collisions at
LHC energies? These interesting and important questions are
deserving of study in the future.
Acknowledgements We thank Gang Li, Zuo-tang Liang, Wei Wang,
and Rui-qin Wang for helpful discussions.
Open Access This article is distributed under the terms of the Creative
Commons Attribution 4.0 International License (http://creativecomm
ons.org/licenses/by/4.0/), which permits unrestricted use, distribution,
and reproduction in any medium, provided you give appropriate credit
to the original author(s) and the source, provide a link to the Creative
Commons license, and indicate if changes were made.
Funded by SCOAP3.
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