version 1.5 Systematic analysis of identied-hadron p tspectra from 13 TeV p-p collisions Thomas A. Trainor

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version 1.5
Systematic analysis of identified-hadron ptspectra from 13 TeV p-p collisions
Thomas A. Trainor
University of Washington, Seattle, WA 98195
(Dated: October 13, 2022)
Identified-hadron (PID) ptspectra from 13 TeV p-pcollisions are compared with a two-component
(soft+hard) model (TCM) that accurately distinguishes jet-related hadron production (hard compo-
nent) from nonjet projectile-nucleon dissociation (soft component). The present p-pstudy is similar
to and is guided by recent TCM studies of PID spectra from 5 TeV p-Pb collisions. The combined
analyses serve to establish a well-understood quantitative description of PID hadron production in
small collision systems as a control experiment. The control can then be contrasted with conven-
tional interpretations of collision data from more-central A-A collisions as indicating formation of
a quark-gluon plasma (QGP). PID ptspectra from 13 TeV p-pcollisions exhibit simple consistency
with spectra from 5 TeV p-Pb collisions. Hadron species abundances are consistent with statistical-
model trends predicted prior to commencement of the large hadron collider program. Differential
spectrum structure and various ratio measures are quantitatively explained by the TCM, including
its jet contribution, and admit no room for claims of hydrodynamic flows in small collision systems.
I. INTRODUCTION
This article reports a study of the systematic variation
of identified-hadron (PID) ptspectra from 13 TeV p-p
collisions reported by Ref. [1]. The analysis method fol-
lows from several recent PID spectrum studies based on
a two-component (soft+hard) model (TCM) of hadron
production in high-energy nuclear collisions [2–4]. A ba-
sic goal is to extract all available information from PID
spectra down to the level of statistical uncertainties and
to report it in formats that are suggestive of proper phys-
ical interpretation and quantitatively comparable with
previous particle-physics results (e.g. jet properties).
A more immediate goal is providing substantive re-
sponse to claims of “collectivity” (i.e. flows) based on
data features associated with small collision systems (e.g.
p-p,p-A collisions). The apparent presence of collective
motion within collisions is then interpreted to support
claims of quark-gluon plasma (QGP) formation in those
systems [5]. Such claims are counterintuitive based on
conventional understanding of QCD and thus merit care-
ful examination of arguments and evidence in their favor.
Reference [1] observes that at low pt“...collective
phenomena are observed in...[p-p,p-Pb and A-A] colli-
sions...” with several examples given. It then asserts
that “...in order to describe bulk particle production in
A-A collisions, one usually relies on hydrodynamic and
thermodynamic modeling....” Such statements typically
set the stage for argument by analogy: If certain data
features were previously interpreted to signal collectiv-
ity and QGP formation in more-central A-A collisions,
and those same features appear in small collision sys-
tems, then it is reasonable to claim collectivity (flows)
and QGP in small systems as well, no matter that parti-
cle and energy densities there are much smaller.
That framework then provides context for presentation
and interpretation of PID ptspectra in Ref. [1]. “We
observe that the measured pTspectra become harder
[i.e. slope magnitude at low ptdecreases] with increas-
ing [event multiplicity], and the effect is more pronounced
for protons.” Such variation “...is also observed in Pb-Pb
collisions...where it is usually associated with the hydro-
dynamical evolution of the system.” It is further stated
that in Pb-Pb collisions such trends, interpreted in terms
of radial expansion (flow), are “....studied in the context
of the Boltzmann-Gibbs Blast-Wave model.” Since the
p-pspectra “...are highly reminiscent to those in p-Pb and
Pb-Pb, it is interesting to check whether the Blast-Wave
model can be extended to describe p-pcollisions.”
The present analysis addresses those arguments and
claims in the following way. The PID TCM developed in
Refs. [2–4] is introduced. As a starting point, TCM pa-
rameter values from 5 TeV p-Pb collisions are presented.
Previously established √strends for TCM parameters
are used to extrapolate from 5 TeV to 13 TeV. A cor-
rection for proton inefficiency developed for 5 TeV p-Pb
collisions in Ref. [3] is updated to accommodate 13 TeV
p-pspectra. Parameters that describe the fractions of
total charge densities belonging to each hadron species
are derived directly from spectrum data. The quality
of the resulting PID TCM description is then evaluated
based on Z-scores. With the exception of pions the TCM
describes spectrum data within statistical uncertainties.
Given an accurate TCM data representation, and
the now well-understood physical interpretation of TCM
components, various data presentations and interpreta-
tions from Ref. [1] are confronted. As in previous cases
spectrum data (and data-ratio) features conventionally
interpreted as representing collectivity or flows are quan-
titatively described in terms of minimum-bias jet produc-
tion. In particular, PID yield- and spectrum-ratio results
are quantitatively examined and interpreted within a jet
context. Blast-wave (BW) model fits are considered and
rejected via Z-scores based on poor fit quality over limited
ptintervals. PID spectrum data from Ref. [1] do carry
much information but do not appear to support claims
arXiv:2210.05877v1 [hep-ph] 12 Oct 2022
2
of collectivity and QGP formation in small systems.
This article is arranged as follows: Section II intro-
duces PID spectrum data from 13 TeV p-pcollisions re-
ported in Ref. [1]. Section III defines a corresponding
PID spectrum TCM. Section IV describes the process of
estimating TCM model parameters. Section V reports fi-
nal PID TCM parameter values for 13 TeV p-pcollisions.
Section VI evaluates TCM data description quality based
on Z-scores. Section VII discusses PID yield and spec-
trum ratios in a TCM context. Section VIII evaluates
the quality and interpretability of BW fits to PID p-p
spectra. Section IX discusses systematic uncertainties.
Sections X and XI present discussion and summary.
II. 13 TeV p-p PID SPECTRUM DATA
The 13 TeV p-pPID spectrum data used for this anal-
ysis were reported by Ref. [1]. Spectrum data were de-
rived from 143 million p-pcollision events satisfying an
INEL >0 minimum-bias trigger (at least one charged
particle within |η|<1). Events were sorted into ten
multiplicity classes based on charge accumulated within
a V0 detector (V0M amplitude). Mean charge densities
dNch/dη →¯ρ0as integrated within |η|<0.5 or angular
acceptance ∆η= 1 are 26.0, 20.0 16.2, 13.8, 12.0 10.0
7.95, 6.3, 4.5 and 2.55 for n∈[1,10] respectively.
A. p-p PID spectrum data
Figure 1 shows PID spectrum data from 13 TeV p-p
collisions reported in Ref. [1] (points) as densities on pt
vs transverse rapidity ytwith pion mass assumed. Pub-
lished spectra have been divided by ptrelative to the
presentation in Fig. 1 of Ref. [1]. The spectra have
been scaled by powers of 10 according to 10n−1where
n∈[1,10] is the centrality class index and n= 10 is here
most central, following the practice in Ref. [1]. Else-
where in this paper event class n= 1 is most central
(see ¯ρ0values listed above). Solid curves are full TCM
parametrizations finalized in Sec. V D. Dashed curves are
TCM soft components zsi ¯ρsˆ
S0(yt). The differences rep-
resent minimum-bias jet contributions zhi ¯ρhˆ
H0(yt).
The baryon data in panels (c) and (d) (the Lambda
data from 5 TeV p-Pb collisions [4] are included as a ref-
erence) are expected to correspond closely. However, the
proton data in panel (c) fall well below the TCM pro-
ton prediction (solid curves). A similar apparent proton
inefficiency for 5 TeV p-Pb collisions was analyzed and
corrected in Sec. III B of Ref. [3]. The same procedure
is applied to 13 TeV p-pproton data in Sec. IV A below.
Pion spectra in panel (a) fall well above the TCM pre-
diction. Those deviations and a possible relation to the
proton inefficiency are discussed in Sec. V C.
The plotting format in Fig. 1 is desirable for two rea-
sons: (a) Soft component ˆ
S0(yt) that (for example) de-
scribes low-ptdata within their statistical uncertainties
10 -7
10 -5
10 -3
10 -1
10
10 3
10 5
10 7
10 9
10 11
10 12
0246
yt
d2nch / ptdptdyz (GeV/c)−2
pions
13 TeV p-p
S0
uncorrected
10 -8
10 -6
10 -4
10 -2
1
10 2
10 4
10 6
10 8
10 10
10 11
1 2 3 4 5 6
yt
d2nch / ptdptdyz (GeV/c)−2
kaons
13 TeV p-p S0
(a) (b)
10 -8
10 -6
10 -4
10 -2
1
10 2
10 4
10 6
10 8
10 10
1 2 3 4 5 6
yt
d2nch / ptdptdyz (GeV/c)−2
protons
13 TeV p-p
uncorrected S0
10 -7
10 -6
10 -5
10 -4
10 -3
10 -2
10 -1
1
10
10 2
10 3
10 4
10 5
10 6
10 7
10 8
1 2 3 4 5 6
yt
d2nch / ptdptdyz (GeV/c)−2
Lambdas
5 TeV p-Pb S0
(c) (d)
FIG. 1: ptspectra for identified hadrons: (a) pions, (b)
charged kaons and (c) protons from 13 TeV p-pcollisions [1]
and (d) Lambdas from 5 TeV p-Pb collisions [6]. Solid curves
represent the PID spectrum TCM from Sec. V. Data-model
discrepancies in (a) and (c) are discussed in Sec. V C.
for 5 TeV p-Pb collisions [3, 4] closely approximates a
Boltzmann exponential on mtat lower mtand thus fol-
lows an A−micosh(yt)/T trend on this semilog format
on yt(where miis the mass for hadron species iand
A is some constant). Pions are an exception because
of a resonance contribution but that is easily accommo-
dated [3]. (b) Hard component ˆ
H0(yt) that describes
high-ptdata within their statistical uncertainties for 5
TeV p-Pb collisions follows an exponential exp(−q yt) at
higher ytequivalent to a power law on mtor ptthat
manifests in this format as a straight line for yt>4.
In contrast, the plotting format chosen for Fig. 1 of
Ref. [1] shows spectra in the form d2Nch/dptdyzthat is
missing a factor 1/ptappropriate for momentum in the
transverse plane and thus does not approximate a Boltz-
mann exponential for low mt. The data are presented
on linear ptrather than logarithmic yt, and data bin-
ning is also defined on ptrequiring dramatic variation
of bin widths to control statistical uncertainties. Equal
bin widths on ytwould accomplish the same goal. On
linear ptthere is no hint of the simple data trends evi-
dent on yt. Ratios to minimum-bias INEL >0 confuse
several issues but are dominated by the strongly varying
hard/soft ↔jet/nonjet ratio in spectra that is of funda-
mental importance for the understanding of p-pcollision
dynamics.
3
B. p-p PID spectrum data interpretation
Reference [1] interprets spectrum data as follows: “We
observe that the measured pTspectra become harder
with increasing [¯ρ0], and the effect is more pronounced for
protons,” where “harder” corresponds to reduced spec-
trum slope (“flattening”) at lower ptand is said to be
similar to observations in A-A collisions: “...the mass de-
pendence of spectral shape modification is also observed
in Pb-Pb collisions...where it is usually associated with
the hydrodynamical evolution of the system.”
In Ref. [6] it is suggested that commonalities between
p-pdata and those from Pb-Pb collisions imply the pres-
ence of collective flow also in p-Pb collisions: “In heavy-
ion [A-A] collisions, the flattening of transverse momen-
tum distribution and its mass ordering find their natural
explanation in the collective radial expansion of the sys-
tem [emphasis added].” Reference [1] presents a similar
argument concerning p-pcollisions: “In large collision
systems such as Pb-Pb multiplicity-dependent modifica-
tions of hadron pTspectra can be interpreted as the hy-
drodynamical radial expansion of the system and stud-
ied in the context of the Boltzmann-Gibbs Blast-Wave
model. ... As the trends...measured in pp collisions are
highly reminiscent to those in p-Pb and Pb-Pb, it is in-
teresting to check whether the Blast-Wave model can be
extended to describe pp collisions.” Section VIII below
provides a response to that proposal.
Concerning the high-ptregion: “At higher pT(≥8
GeV/c), we find that slopes of particle spectra become
independent of the multiplicity class considered, as ex-
pected from pQCD calculations [Ref. [7] is cited].” That
characteristic of ptspectra is abundantly clear from the
straight-line trends in the format of Fig. 1 above, and the
power-law trend clearly begins near 4 GeV/c (yt≈4) in
all p-pand p-A collision systems. The same trend has
been reported in Refs. [2–4, 8–10] for example. Refer-
ence [7] does not speak to that aspect of single-particle
spectrum properties since it deals only with fragmen-
tation functions (FFs) characterizing individual recon-
structed jets. Jet contributions to high-energy p-p pt
spectra and angular correlations have been studied in
detail (e.g. Ref. [11]). The approximate power-law trend
at higher ptfor single-particle A-B spectra results from
the underlying jet energy spectrum that is a separate is-
sue [12]. The spectrum hard component (what domi-
nates spectra at higher pt) is quantitatively predicted by
a convolution of measure FFs with a measured jet en-
ergy spectrum [10]. Biases resulting from event-selection
methods may cause variation of power-law trends [13].
Whatever the current popular interpretation of spec-
trum trends in A-A collisions may be, the interpretation
of p-pcollisions as a fundamental reference system should
be undertaken sui generis employing the full understand-
ing of elementary nuclear collisions established over forty
years by the high-energy (particle-physics) community.
III. p-p PID SPECTRUM TCM
The TCM for p-pcollisions utilized in this study is the
product of phenomenological analysis of data from a va-
riety of collision systems and data formats [14–17]. As
such it does not represent imposition of a priori phys-
ical models. Physical interpretation of TCM soft and
hard components has been derived a posteriori by com-
paring inferred TCM characteristics with other relevant
measurements [9, 10], in particular measured jet char-
acteristics [12, 18]. Development of the TCM contrasts
with data models based on a priori physical assumptions
such as the BW model [19]. The TCM does not result
from fits to individual spectra (or other data formats),
which would require many parameter values. The few
TCM parameters have simple log(√s) trends on colli-
sion energy and extrapolations from minimum-bias p-p
trends and are required to be quantitatively consistent
across multiple A-B collision systems.
In what follows, a PID p-pspectrum TCM is defined,
TCM parameters derived for 5 TeV p-Pb collisions from
Ref. [3] are described, the energy dependence of TCM
parameters for nonPID p-pspectra is introduced from
Refs. [13] and [17], and those results are combined to
produce predicted PID TCM spectrum parameters for 13
TeV p-pcollisions. Those parameter values are then re-
fined based on comparison of TCM and data in Sec. V.
A. p-p spectrum TCM for unidentified hadrons
The ptor ytspectrum TCM is by definition the sum
of soft and hard model components, their details being
inferred from data (e.g. Ref. [15]). For p-pcollisions
¯ρ0(yt, ns)≈¯ρs(ns)ˆ
S0(yt) + ¯ρh(ns)ˆ
H0(yt),(1)
where nsserves as an event-class index, and factorization
of the dependences on ytand nch is a central feature of
the spectrum TCM inferred from 200 GeV p-pspectrum
data in Ref. [15]. The motivation for transverse rapid-
ity yti ≡ln[(pt+mti)/mi] (applied to hadron species
i) is described in Sec. III C. The ytintegral of Eq. (1) is
¯ρ0= ¯ρs+ ¯ρh, a sum of soft and hard charge densities with
¯ρx=nx/∆η.ˆ
S0(yt) and ˆ
H0(yt) are unit-normal model
functions approximately independent of nch, and the
centrally-important relation ¯ρh≈α¯ρ2
swith α≈O(0.01)
is inferred from p-pspectrum data [14, 15, 17]. Equation
¯ρ0≈¯ρs+α¯ρ2
sis solved to obtain ¯ρsfrom measured ¯ρ0.
To define model functions and other aspects of the p-p
spectrum TCM, measured hadron spectra are rescaled by
charge-density soft component ¯ρsto have the form
X(yt, ns)≡¯ρ0(yt;nch)
¯ρs
=ˆ
S0(yt) + x(ns)ˆ
H0(yt),(2)
where x(ns)≡¯ρh/¯ρs≈α¯ρs. The form of model ˆ
S0(yt) is
defined by data expressed as X(yt) in the limit nch →0.
4
The form of ˆ
H0(yt) is defined by spectrum data contri-
butions complementary to soft-component model ˆ
S0(yt).
B. p-p spectrum TCM for identified hadrons
Given the p-pspectrum TCM for unidentified-hadron
spectra in Eq. (1) a corresponding TCM for identified
hadrons can be generated by assuming that each hadron
species icomprises certain fractions of soft and hard
TCM components denoted by zsi and zhi (both ≤1).
The PID spectrum TCM can then be written as
¯ρ0i(yt, ns) = Si(yt, ns) + Hi(yt, ns) (3)
≈zsi(ns)¯ρsˆ
S0i(yt) + zhi(ns)¯ρhˆ
H0i(yt)
with rescaled spectra
Xi(yt, ns)≡¯ρ0i(yt, ns)
¯ρsi(ns)
≈ˆ
S0i(yt) + ˜zi(ns)x(ns)ˆ
H0i(yt),(4)
where ˜zi(ns)≡zhi(ns)/zsi(ns) and unit-integral model
functions ˆ
S0i(yt) and ˆ
H0i(yt) may depend on hadron
species i. For identified hadrons of species ithe rescale
factor ¯ρsi =zsi(ns)¯ρscan be expressed in terms of factor
zsi(ns) defined in Eq. (8), but for p-pcollisions ν→1
in that equation. Unit-normal model functions ˆ
S0i(yt)
and ˆ
H0i(yt) must be determined for each hadron species,
but close correspondence to unidentified-hadron models
is expected. The further differential spectrum quantity
Yi(yt, ns)≡1
˜zi(ns)x(ns)[Xi(yt, ns)−ˆ
S0i(yt)] (5)
≈ˆ
H0i(yt)
may be compared with model functions ˆ
H0i(yt). Those
expressions have been used in a previous PID TCM spec-
trum analysis [2]. A more precise strategy developed in
Refs. [3, 4] is utilized in Sec. IV.
C. PID TCM model functions
For spectra structured as in Eq. (3) and the trend
x(ns)∼ns∼nch the soft-component model function
is defined as the limit of Xi(yt, ns) as nch (or ns) goes to
zero. As noted, hard components of data spectra are then
defined as complementary to model soft components.
The data soft component for a specific hadron species
i(except pions) is typically well described by a L´evy
distribution as a density on mti =pp2
t+m2
i. The unit-
integral soft-component model is
ˆ
S0i(mti) = Ai
[1 + (mti −mi)/niTi]ni,(6)
where mti is the transverse mass for hadrons iof mass
mi,niis the L´evy exponent, Tiis the slope parameter
and coefficient Aiis determined by the unit-integral con-
dition. Parameters (T, n) for 5 TeV p-Pb data in Ref. [3]
are slightly adjusted for 13 TeV p-pdata (see Table V).
As defined, the soft-component model is a density on pt
or mt(since mtdmt=ptdpt) which may be plotted vs yt.
The unit-integral hard-component model is simply de-
fined on pion ytπ ≡ln((pt+mtπ)/mπ) as a Gaussian, with
exponential (on yt) or power-law (on pt) tail at higher yt
ˆ
H0(yt)≈Bexp −(yt−¯yt)2
2σ2
ytnear mode ¯yt(7)
∝exp(−qyt) for higher yt– the tail,
where the transition from Gaussian to exponential on yt
is determined by slope matching [10]. The ˆ
H0tail density
varies on ptapproximately as power law 1/pq+2.2
t. Co-
efficient Bis determined by the unit-integral condition.
Initial PID model parameters (¯yt, σyt, q) as in Table I are
also derived from p-Pb data in Ref. [3] (see Table V).
Spectra for the present study are presented as densi-
ties on ptplotted vs pion rapidity ytπ with pion mass
assumed. ˆ
S0i(mti) for species iis defined by Eq. (6).
ˆ
H0(ytπ) in Eq. (7) is defined as a density on ytπ where it
has a simple form and is then converted to ˆ
H0(pt) via the
Jacobian factor ytπ/mtπ pt. In general, plotting spectra
as densities on ptagainst logarithmic variable ytper-
mits superior visual access to important low-ptstructure
where the majority of jet fragments appears. A further
motivation is comparison of spectrum hard components
interpreted to arise from a common underlying jet spec-
trum on pt[9, 10], in which case ytπ serves simply as a
logarithmic measure of hadron ptwith well-defined zero.
D. 5 TeV p-Pb TCM PID spectrum parameters
In this subsection TCM model parameters for PID
spectra from 5 TeV p-Pb collisions reported in Ref. [3] are
presented. If p-Pb collisions are linear superpositions of
p-N collisions, as seems apparent from centrality depen-
dence of p-Pb spectrum data, then this parametrization
is a starting point for a PID TCM for p-pcollisions.
Table I shows TCM model parameters for hard compo-
nent ˆ
H0(yt) (first three) and soft component ˆ
S0(yt) (last
two). Hard-component parameters vary slowly but sig-
nificantly with hadron species. Modes ¯ytshift to higher yt
with increasing mass. Widths σytare greater for mesons
than for baryons. Only K0
sand Λ p-Pb data extend to
sufficiently high ptto determine exponent qwhich is sub-
stantially greater for baryons than for mesons.
Parameter values in Table I for 5 TeV p-Pb collisions
define a fixed TCM reference independent of centrality
that describes the most central event class (wherein ¯yt≈
3.0 for baryons) [3]. In Ref. [4] variation of some hard-
component model parameters is determined so as to de-
scribe all event classes within statistical uncertainties (see
Fig. 4 of Ref. [4]). The required variations are linear on
hard/soft ratio x(ns)ν(ns): hard-component modes shift
5
to higher ytfor baryons while hard-component widths
above the mode decrease for mesons.
TABLE I: TCM model parameters for identified hadrons
from 5 TeV p-Pb collisions from Table VI of Ref [3]: hard-
component parameters (¯yt, σyt, q) and soft-component param-
eters (T, n). Numbers without uncertainties are adopted from
a comparable hadron species with greater accuracy.
¯ytσytq T (MeV) n
π±2.46 ±0.01 0.57 ±0.01 4.1±1 145 ±3 8.5±0.5
K±2.65 0.57 4.1 200 14
K0
s2.65 ±0.01 0.57 ±0.01 4.1±0.1 200 ±5 14 ±2
p2.99 ±0.01 0.47 5.0 210 ±10 14 ±4
Λ 2.99 ±0.01 0.47 ±0.01 5.0±0.05 210 14
Soft-component model parameter T≈145 MeV for pi-
ons is consistent with that for unidentified hadrons found
to be universal over all A-B collision systems and colli-
sion energies [17]. The values for higher-mass hadrons are
substantially greater. L´evy exponent n≈8.5 for pions
is also consistent with that for unidentified hadrons at 5
TeV and has a log(√s/10 GeV) energy dependence [17].
Exponent nvalues for more-massive hadrons are not well-
defined because the hard-component fraction is much
greater than for pions. Varying nthen has little impact
on the overall spectra.
Table II shows PID parameters z0iand ˜zi=zhi/zsi for
five hadron species determined from PID spectrum data
in Ref. [3]. While z0was found to be independent of
p-Pb centrality within uncertainties the p-Pb ˜zi(ns) ex-
hibit significant centrality dependence as shown in Fig. 8
of Ref. [3]. It is notable that the ˜zi(ns) depend only
on hadron mass, not on strangeness or baryon identity.
Measurements of individual centrality trends for zsi(ns)
and zhi(ns) are presented in Sec. IV of Ref. [3]. Individ-
ual fractions zs(ns) and zh(ns) may also be derived from
model parameters ˜zi(ns) and z0ivia the relation
zsi(ns) = 1 + x(ns)ν(ns)
1 + ˜zi(ns)x(ns)ν(ns)z0i,(8)
with zhi(ns) = ˜zi(ns)zsi(ns). 5 TeV p-Pb geometry (cen-
trality) parameters x(ns) and ν(ns) are determined in
Refs. [16, 20, 21] based on ensemble-mean ¯ptdata. For
p-pcollisions ν≡2Nbin/Npart →1. The ˜zi=zhi/zsi
values included in Table II represent averages over p-Pb
centrality. Given the TCM expression in Eq. (3) the cor-
rect rescaling via ¯ρsi =zsi(ns)¯ρsresults in data spectra
coinciding with ˆ
S0(yt) as yt→0 for all centralities.
The results above for 5 TeV p-Pb collisions can be
compared with final results for 13 TeV p-pcollisions pre-
sented in Table VI. With the exception of pion ˜zithe zxi
values determined for the two collision systems are con-
sistent within data uncertainties. The significant change
for pion ˜ziis explained in Sec. IV C.
TABLE II: TCM model parameters for identified hadrons
from 5 TeV p-Pb collisions in Ref. [3]. Numbers without
uncertainties are adopted from a comparable hadron species
with greater accuracy. Values for ˜zi=zhi/zsi are averages
over p-Pb centrality. Parameters ¯pts and ¯pth are determined
by model functions ˆ
S0(yt) and ˆ
H0(yt) defined by Table I.
z0˜zi¯pts (GeV/c) ¯pth (GeV/c)
π±0.82 ±0.01 0.88 ±0.05 0.40 ±0.02 1.15 ±0.03
K±0.128 ±0.002 2.7±0.2 0.60 1.34
K0
s0.064 ±0.002 2.7±0.2 0.60 ±0.02 1.34 ±0.03
p0.065 ±0.002 5.6±0.2 0.73 ±0.02 1.57 ±0.03
Λ 0.034 ±0.002 6.5±0.5 0.76 ±0.02 1.65 ±0.03
E. TCM variation with collision system and energy
Based on determination of PID TCM model functions
for 5 TeV p-Pb collisions summarized above, prediction
of PID model parameters for 13 TeV p-pcollisions pro-
ceeds as follows. As noted, previous analysis suggests
that 5 TeV p-Pb collisions are linear superpositions of
p-N collisions. Relevant parameters for 5 TeV p-Pb col-
lisions then approximate 5 TeV p-pcollisions. In Sec. VI
of Ref. [17] the energy dependence of nonPID spectra
from non-single-diffractive (NSD) p-pcollisions is sum-
marized based on TCM spectrum analysis from 17 GeV
to 13 TeV. Those trends are used to extrapolate 5 TeV
TCM parameters to 13 TeV.
Table III (upper six rows) shows p-pTCM nonPID
spectrum parameters over a range of energies [17]. The
lowest two rows show updated numbers from Ref. [13].
Those studies demonstrate that parameter variations fol-
low simple functional forms. For instance, L´evy expo-
nent nvaries as 1/n ≈0.0475pln(√s/10 GeV), and
1/q ∝ln(√s/6 GeV), the latter being a measure of jet
energy spectrum width on rapidity [17]. Parameters ¯yt
and σytincrease slowly and linearly with ln(√s). The
absolute values for σytand qmay depend on event se-
lection method and resulting bias [13]. This table and
Ref. [17] demonstrate the predictivity of the TCM.
Table IV shows PID TCM model-function parameters
extrapolated from 5 TeV p-Pb collisions and based on
measured energy dependence of nonPID spectra derived
from NSD p-pcollisions. Those predictions are the basis
for the current analysis of PID spectra for 13 TeV p-pcol-
lisions. One may compare with final results in Sec. V D.
IV. p-p PID TCM PARAMETER ESTIMATION
PID TCM spectrum parameter estimation requires two
steps: (a) refine soft- and hard-component model pa-
rameters based on predictions developed in the previous
section and (b) estimate parameters zsi(ns) and zhi(ns)
based on direct analysis of PID spectra. Task (b) requires
estimation and possible correction of PID spectrum sys-
摘要：

version1.5Systematicanalysisofidenti ed-hadronptspectrafrom13TeVp-pcollisionsThomasA.TrainorUniversityofWashington,Seattle,WA98195(Dated:October13,2022)Identi ed-hadron(PID)ptspectrafrom13TeVp-pcollisionsarecomparedwithatwo-component(soft+hard)model(TCM)thataccuratelydistinguishesjet-relatedhadronpr...

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