Transverse momentum distributions of baryons at LHC energies

0.45 MB·English

by  A. A. Bylinkin

Transverse momentum distributions of baryons at LHC energies
A. A. Bylinkin∗
Moscow Institute of Physics and Technology, MIPT, Moscow, Russia
National Research Nuclear University MEPhI, Moscow, Russia
O. I. Piskounova†
P.N.Lebedev Physical Institute, LPI, Moscow, Russia
√
Transverse momentum spectra of protons and anti-protons from RHIC ( s = 62 and 200 GeV)
√
and LHC experiments ( s= 0.9 and 7 TeV) have been considered. The data are fitted in the low
p regionwiththeuniversalformulathatincludesthevalueofexponentslopeasamainparameter.
T
It is seen that the slope of low-p distributions is changing with energy. This effect impacts on the
T
energy dependence of average transverse momenta, which behaves approximately as s0.06 that is
similar to the previously observed behavior for Λ0-baryon spectra. In addition, the available data
√
5
on Λ production from LHCb at s=7 TeV were also studied. The estimated average <p > is
c T
1
biggerthanthisvalueforprotonsproportionallytomasses. Thepreliminarydependenceofhadron
0
average transverse momenta on their masses at LHC energy is presented.
2

n
(cid:112)
a I. INTRODUCTION where,m = p2 +m2,m isthemassoftheproduced
T T 0 0
J hadron and B is the slope parameter for the considered
0
0 The transverse momentum distributions are the pri- energy. Intheearlypaper[2], itwasalsoshownthatthe
3 mary data that can be obtained in the study of hadron value of the slope parameter B0 becomes dependent on

spectra at the modern collider experiments. Interpreta- the collision energy.
]
h tion of these distributions as in strongly theoretical per- Asthenextapproach,thewidelyknownTsallisparam-
p turbative QCD approaches as in various phenomenologi- eterization[3,4]thatisgivingrathergooddescriptionof
p- calmodelscanshedalightuponthephysicsofhadropro- hadroproduction spectra might be used. Transverse mo-
e duction processes at high energies. We apply the phe- mentum distribution can be expressed in this model by
h nomenological approach based on the previous attempts the following formula:
[
of the description of p spectrum in the framework of
T
1 Quark-Gluon String Model [1].
v The model has described the data of previous collid- dσ A
√ = (2)
06 pers’sutphattogeivneesrgmieasin cson=trib2u0t0ioGnetVo tahtetahveeraagreeavaolfueloowf pTdpT (1+ ETTNkin)N
T
7 transverse momenta. Recently Λ0-hyperon production with a temperature-like parameter T and the power-like
7
has been studied [2] in terms of the QGSM. We suggest N. In this forumula (2) E - is the transverse energy
0 Tkin
heretocomparethelatestdatameasuredatLHConpro- that can be calculated in the following way:
.
1 ton production and to show the resulting average trans-
0
verse momenta, < p >, as a function of c.m.s. energy,
5 √ T
s, of colliding protons. It seems interesting as well to (cid:113)
1 E = p2 +M2−M, (3)
: compile the available data on <pT > at LHC energy for Tkin T
v
all sorts of hadrons and to present them as the function
i with M equal to the hadron mass.
X of produced hadron mass.
Recently a two component model for hadroproduction
r
has also been developed [5]. It was suggested to param-
a
eterize the large variety of charged particle spectra by a
II. MODELS FOR THE PROTON SPECTRA
sumofanexponential(Boltzmann-like)andapower-law
p distributions:
Let us first describe the QGSM approach, which has T
been applied for recent studies of Λ0. According to this dσ A
=A exp(−E /T )+ , (4)
approach the spectra of baryon production can be pa- pTdpT e Tkin 1 (1+ p2T )n
rameterized in the following way: T2·n
2
dσ In[6,7]ithavebeenconcluded, bytheway, thatspectra
=A exp[−B ·(m −m )], (1)
p dp 0 0 T 0 of baryon production can be described at high energies
T T
with only power-law term of the equation (4).
Theresultsofthesethreeapproachesareshowninthe
figure 1 in the comparison with the available experimen-
∗ [email protected] taldataonprotonproductioninppcollisionsatdifferent
† [email protected] energies.
2
FIG. 1. FIG. 2.
Proton production spectra [8, 9] shown with arbitrary Mean transverse momenta of charged baryons [8–11] as a
√
normalization together with various phenomenological function of c.m.s energy s. Lines show the power-law
approaches. Black solid line shows the QGSM (1), green dependece s0.055).
pointed line - Tsallis-fit (2) and red dashed line - the
power-law (4).
behaves as s0.35. This dependence would refer to the in-
tercept of supercritical Pomeron, δ (0), that causes the
P
It should be noticed after all, that these three ap- hadroproduction cross section dependence like sδP(0) ≈
proacheshavetheexponential-likebehaviorinthelow-pT s0.12. Unfortunately, the growing of <pT >s have noth-
region and give a reasonable description of the exper- ingtodowiththegrowthofcrosssections, because, first
imental data. Therefore, for the analysis suggested in of all, mean transverse momenta are not of the same di-
the present paper considering the mean transverse mo- mension as cross sections, see the formula 5. There is
mentum < pT > of produced baryons one can use any no room for pomeron-intercept dependence in the mean
of these models, since high transverse momenta particles transverse momenta definition.
(not measured by PHENIX and CMS) do not add a big
contribution to the mean value.
If we take the experimental data, it is clearly seen in <p >= (cid:82) pT · ddpσT (5)
the shapes of transverse momentum dependences that T (cid:82) dσ
thespectraofproducedbaryonsbecomeharderwiththe dpT
higher energies. Thus, it is interesting to study the vari- The similar misleading appears if we postulate the ex-
ation of the mean transverse momentum < pT > with ponential behavior of spectra at low pT as hadron evap-
the collision energy in order to estimate the power of its oration, see [13]. Analyzing the transverse momentum
growing. distributions in [14], it was concluded that spectra in
proton-proton and antiproton-proton collisions have dif-
ferent forms in this very region of low-p . Why antipro-
T
III. MEAN TRANSVERSE MOMENTA tons should evaporate so differently than protons? The
reasonsthatdiscussedabovemakethisresearchmorein-
Let us now discuss the mean transverse momenta of teresting from the point of view of further higher energy
produced baryons and look at its dependence on the hadron experiments.
√
collision energy, s. It seems reasonable also to com- Another interesting implication can be revealed from
pare the values calculated for the proton spectra with the comparison of the mean transverse momenta of vari-
otheravailabledataonbaryonproduction: Λ,Ξ[10]and ousproducedbaryonsatthecertaincollisionenergyasa
Λ [11] spectra. Figure 2 shows such dependence for the function of their masses, shown in figure 3. Let us note
c
various experimental data. The steep rise of the mean that a linear dependence between the mean transverse
transverse momenta < p > is seen as a function of en- momenta < p > and the baryon mass M is observed.
√ T T √
ergy s. Remarkably, this rise can be parameterized Remarkably, at s = 7000 TeV the transverse momen-
by the same power-like s0.055 behavior in case of all the tum reaches the value of baryon mass, t.e. <p >∼M.
T
species of produced baryons. These observations mean Further measurements at LHC Run-II can shed light on
that the transverse distributions of baryons might have whetherornottheaveragetransversemomentumexpan-
the same nature and their variations are not dependent sioninthebaryonproductionhasalimit<p >=M. It
T
on the quark-composition of the produced baryon. also might be interesting to compare <p >s as a func-
T
Remarkably, in [12] it was shown that the < p >, tion of produced baryon mass M with the mass depen-
T
which were estimated with the power-law spectra alone, dence of the mean transverse momenta that have been
3
√
experiments ( s= 0.9 and 7 TeV) have been described
in the QGSM approach. This model seems working for
the up-to-date collider energies, because spectra at low
p are giving the main part of integral cross section.
T
The enhancement of power-low contribution into the
spectra at high−p (cid:48)s causes the change of low p expo-
T T
nential slopes, so that < p > are growing with energy.
T
If we are analyzing the spectra of different baryons their
average transverse momenta grow linearly with masses.
The LHC experiment has obtained more data on heavy
b
quarkbaryonsandmesonswhicharegoingtosupplyour
analysis.
Nevertheless,theobservedchangesinhadroproduction
spectra seem not to be so dramatic to cause the ”knee”
FIG. 3. in proton spectra measured in cosmic rays due to just
Mean transverse momenta of charged baryons [9–11, 15] as a the interactions into the detector at the laboratory sys-
√
function of their mass at the energy s=7000 TeV. Red temenergiesthatcorrespondtotheenergyrangeofLHC
dashed line shows linear dependence. experiments.
calculated from the description of charged meson pro-
duction.
V. AKNOWLEDGEMENTS
IV. CONCLUSION
AuthorsexpresstheirgratitudetoProf. K.G.Boreskov
Transverse momentum spectra of protons and anti- and to Prof. M.G. Ryskin for numerous discussions and
√
protons from RHIC ( s = 62 and 200 GeV) and LHC useful advises.
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