Soft QCD theory

(1)

Soft QCD theory

Torbj¨ orn Sj¨ ostrand

torbjorn.sjostrand@thep.lu.se

Theoretical Particle Physics

Department of Astronomy and Theoretical Physics Lund University

S¨olvegatan 14A, 223 62 Lund

LHCP 2022, Online / Taipei, 20 May 2022

(2)

The structure of an LHC pp collision

MPI MPI dˆσ0

·

· ·

··

Meson Baryon Antibaryon

·Heavy Flavour

(2203.11601)

Hard Interaction Resonance Decays MECs, Matching & Merging FSR

ISR*

QED Weak Showers Hard Onium

Multiparton Interactions Beam Remnants*

Strings

Ministrings / Clusters Colour Reconnections String Interactions Bose-Einstein & Fermi-Dirac Primary Hadrons

Secondary Hadrons Hadronic Reinteractions (*: incoming lines are crossed)

ISR*

Strings

ISR*

Strings

Torbj¨orn Sj¨ostrand Soft QCD theory slide 2/23

(3)

Event generators

Complexity addressed by “divide and conquer” in event generators.

(1101.2599, 2203.11110)

Generators used to

predict event properties, for detector and trigger design, correct data for acceptance and smearing, and

interpret data in terms of underlying physics mechanisms.

Current general-purpose event generators for hard + soft physics:

Herwig

(1912.06509)

Pythia

(2203.11601)

(new 300+ pages guide!) Sherpa

(1905.09127)

Special generators for hard matrix elements (as input to above):

MadGraph5 aMC@NLO

(1405.0301)

PowHeg Box

(1002.2581)

Many generators for (soft) QCD, heavy ions and cosmic rays EPOS

(1306.0121)

. . .

(4)

Multiparton interactions (MPIs) – 1

MPIs essential to explain bulk properties of events, e.g. inclusive multiplicity distributions. Theory and modelling still debated.

(Adv.Ser.Direct.High Energy Phys. 29 (2018) 1)

Double Parton Scattering (DPS):

σ

^DPS_A,B

= m 2

σ

_A

σ

_B

σ

_eff,DPS

where m = 1 if A = B and m = 2 if A 6= B.

Important confirmation but tests only a tiny fraction of high-p

_⊥

events.

OBSERVATION OF TRIPLE J/ MESON PRODUCTION IN PROTON-PROTON COLLISIONS AT p

S = 13 TEV 3

tion, is obtained via (pp ! J/ J/ J/ X) = N

_sig^3J/

/(✏ L

int

B

_{J/ !µ}³ ⁺_µ

), where N

_sig^3J/

is the number of extracted signal events, L

int

the total integrated luminosity, and ✏ = ✏

trig

✏

id

✏

reco

the total efficiency composed of trig- ger, reconstruction, and identification components. System- atic uncertainties include the signal and background mod- elling, the detector’s muon reconstruction and trigger effi- ciency and luminosity measurement uncertainty, the size of the MC sample used for the efficiency studies and the J/ ! µ

⁺

µ branching fraction uncertainty. The total systematic uncertainty is 6.2% and the fiducial triple J/ cross section

(pp ! J/ J/ J/ X) = 272

⁺¹⁴¹104

(stat) ± 17(syst) fb.

The total triple-J/ cross section is expected to corre- spond to the sum of the contributions from the SPS, DPS, and TPS processes schematically shown in Figure 1, each of which contains various combinations of prompt (p) and non- prompt (np) J/ contributions,

3J/

tot

=

^3J/_SPS

+

_DPS^3J/

+

^3J/_TPS

=

= ⇣

_{3 p}

SPS

+

_SPS^2p1np

+

_SPS^1p2np

+

_SPS^{3 np}

⌘ + + ⇣

3 p

DPS

+

_DPS^2p1np

+

_DPS^1p2np

+

_DPS^{3 np}

⌘ + + ⇣

_{3 p}

TPS

+

^2p1np_TPS

+

^1p2np_TPS

+

^{3 np}_TPS

⌘ .

(3)

The DPS and TPS contributions to triple-J/ production (last row of Eq. (3)) can be written through Eqs. (1) and (2) as a combination of products of single- and double-J/ SPS cross sections as follows,

3J/

DPS

= m

1

(

_SPS^2p _SPS^1p

+

_SPS^2p ^1np_SPS

+

_SPS^1p ^1p1np_SPS

+ +

_SPS^1p1np _SPS^1np

+

_SPS^1p _SPS^2np

+

_SPS^2np _SPS^1np

)/

e↵,DPS

3J/

TPS

= m

3

✓⇣

_1p

SPS

⌘

3

+ ⇣

_1np

SPS

⌘

3

◆ +

+m

2

✓⇣

_1p

SPS

⌘

2 1np

SPS

+

_SPS^1p

⇣

_1np

SPS

⌘

2

◆ /

²_e↵,TPS

, (4)

with combinatorial prefactors m

1

= 2/2 = 1, m

2

= 3/3! = 1/2 , and m

3

= 1/3! = 1/6 . Therefore, from the eight individual SPS cross sections for single-, double-, and triple-J/ cross sections one can determine the total 3- J/ production cross section via Eqs (3) and (4). Obtain- ing values of the SPS single, double and triple prompt-J/

and nonprompt cross sections and using the Eq (4) the value

e↵,DPS

= 2.7

^+1.4_1.0

(exp)

^+1.5_1.0

(theo) mb is derived.

In Figure 3, the

e↵,DPS

value extracted in this work is compared to the world-data of effective DPS cross sections derived from double-quarkonium and electroweak boson plus quarkonium production measurements (left), as well as also from processes with jets, photons, and W bosons (right).

[mb]

eff,DPS

σ

0 10 20 30

Preliminary

CMS 133 fb

^-1

(13 TeV)

=8 TeV, W+J/ψ s , ATLAS

Phys.Lett.B 781 (2018) 485-491

=8 TeV, Z+J/ψ s , ATLAS

Phys.Rept. 889 (2020) 1-106

J/ψ

=8 TeV, Z+b→ s , ATLAS

Nucl.Phys.B 916 (2017) 132-142

ψ+Y

=1.96 TeV, J/

s , D0

Phys.Rev.Lett. 117 (2016) 6, 062001

ψ +J/

ψ

=13 TeV, J/

s , LHCb

JHEP 10 (2017) 068

ψ +J/

ψ

=1.96 TeV, J/

s , D0

Phys.Rev.D 90 (2014) 11, 111101

ψ +J/

ψ

=8 TeV, J/

s , ATLAS

Eur.Phys.J.C 77 (2017) 2, 76

+J/ψ

=8 TeV, J/ψ s , CMS

Phys.Rept. 889 (2020) 1-106

ψ +J/

ψ

=13 TeV, J/

s , CMS

[mb]

eff,DPS

σ

0 20 40 60

Preliminary

CMS 133 fb

^-1

(13 TeV)

=13 TeV, WW s , CMS

Eur.Phys.J.C 80 (2020) 1, 41

=7 TeV, W+2-jet s , ATLAS

New J.Phys. 15 (2013) 033038

=7 TeV, W+2-jet s , CMSJHEP 03 (2014) 032

=13 TeV, 4-jet s , CMSSMP-20-007

=640 GeV, 4-jet s , UA2

Physics Letters B 268 (1991) 145-154

=1.8 TeV, 4-jet s , CDFPhys. Rev. D47 (1993) 4857-4871

=7 TeV, 4-jet s , CMS

Eur.Phys.J.C 76 (2016) 3, 155

=7 TeV, 4-jet s , CMS

Eur.Phys.J.C 76 (2016) 3, 155

+3-jet

=1.8 TeV, γ s , CDF

Phys.Rev.D 56 (1997) 3811-3832

+3-jet γ

=1.8 TeV, s , D0Phys.Rev.D 81 (2010) 052012

ψ

=8 TeV, W+J/

s , ATLAS

Phys.Lett.B 781 (2018) 485-491

=8 TeV, Z+J/ψ s , ATLAS

Phys.Rept. 889 (2020) 1-106

J/ψ

=8 TeV, Z+b→ s , ATLAS

Nucl.Phys.B 916 (2017) 132-142

+Y ψ

=1.96 TeV, J/

s ,

D0Phys.Rev.Lett. 117 (2016) 6, 062001

+J/ψ

=13 TeV, J/ψ s , LHCbJHEP 10 (2017) 068

ψ +J/

ψ

=1.96 TeV, J/

s , D0Phys.Rev.D 90 (2014) 11, 111101

+J/ψ

=8 TeV, J/ψ s , ATLAS

Eur.Phys.J.C 77 (2017) 2, 76

+J/ψ

=8 TeV, J/ψ s , CMS

Phys.Rept. 889 (2020) 1-106

ψ +J/

ψ

=13 TeV, J/

s , CMS

Figure 3. Comparison of the effective DPS cross sections

e↵,DPS

extracted in this work (top data point in both pan- els) to the same parameter derived in measurements of double- quarkonium and electroweak boson plus quarkonium produc- tion alone (left), as well as also in final states with jets, + jets, W+jets, and same-sign W bosons (right).

The first observation of the concurrent production of three J/ mesons in pp collisions is reported.

The fiducial triple J/ cross section is measured to be (pp ! J/ J/ J/ X) = 272

⁺¹⁴¹₁₀₄

(stat) ± 17(syst) fb and the DPS effective cross section

e↵,DPS

= 2.7

^+1.4_1.0

(exp)

^+1.5_1.0

(theo) mb is derived.

1. CMS Collaboration, Observation of a new excited beauty strange baryon decaying to ⌅

_b

⇡

⁺

⇡ , arXiv:2102.04524, Phys. Rev. Lett., 126 (2021) 25

2. CMS Collaboration”, Measurement of properties of B

⁰s

!

µ

⁺

µ decays and search for B

⁰

! µ

⁺

µ with the CMS ex- periment, arXiv:1910.12127,JHEP 04 (2020) 188

3. CMS Collaboration, Observation of the B

⁰s

!X(3872) decay, arXiv:2005.04764, Phys. Rev. Lett. 125 (2020) 152001

(CMS-CR-2021/174)

(5)

Multiparton interactions (MPIs) – 2

Background modelling nontrivial, especially when jets are involved.

Higher orders relevant for this.

32

3 + CP5 PW NLO 2→

2 + CP5

→ PW NLO 2

2 + CP5 MG5 NLO 2→

2,3,4 + CP5

→ MG5 LO 2 H7 + CH3 P8 + CP5

4jets (13 TeV) CMS

4jets (7 TeV) CMS

Eur.Phys.J.,C76(3):155,2016.

4jets (7 TeV) ATLAS

JHEP,11:110,2016 4jets (1.96 TeV) CDF

Phys.Rev.D,47:4857-4871,1993 4jets (0.63 TeV) UA2

Phys.Lett.B,268(1):145-154,1991

[mb]

σeff

0 5 10 15 20 25 30

measurements σeff

Figure 15: Comparison of the values for s_effextracted from data using different SPS models where events that have generated one or more hard MPI partons with p^parton_T 20 GeV, have been removed. The results from four-jet measurements performed at lower center-of-mass energies [7, 21, 25, 51] are shown alongside the newly extracted values. The error bars in each of the values of s_effrepresent the total (statistical+systematic) uncertainties.

Models based on leading order (LO) 2 ! 2 matrix elements significantly overestimate the absolute four-jet cross section in the phase space domains studied in this paper. This excess is related to an abundance of low-pTand forward jets. The predictions of the absolute cross section generally improve when next-to-leading order (NLO) and/or higher-multiplicity matrix elements are used.

The azimuthal angle between the jets with the largest separation in h, fij, has a strong discrim- inating power for different parton-shower approaches and the data favor the angular-ordered and dipole-antenna parton-shower models over those with a pT-ordered parton shower. The yield of jet pairs with large rapidity separation DY is, however, overestimated by all models, although models based on NLO and/or higher-multiplicity matrix elements are closer to the data.

The distribution of the minimal combined azimuthal angular range of three jets, Df^min_3j , also ex- hibits sensitivity to the parton-shower implementation, with data favoring p_T-ordered parton showers with the LO 2 ! 2 models for this observable. In the case of models based on NLO and/or higher-multiplicity matrix elements the comparisons are less conclusive.

Other observables, such as the azimuthal angle between the two softest jets, DfSoft, and their transverse momentum balance, DpT,Soft, indicate the need for a DPS contribution in the models to various degrees, as confirmed by the extracted values of seff.

(2109.13822)

Full model range even larger spread!

For Gaussian matter distribution expect

σ

_eff

≈ 20 fm . Lower σ

eff

⇒ “hot spots”?

Enhanced DPS rate should dampen at small p

_⊥

scales.

Not seen in 3 J/ψ.

(CMS-CR-2021/174)

Probe with cccc events?

(6)

Colour reconnection (CR)

MPIs + parton showers ⇒ many partons in an event

⇒ colour fields (“strings”) run criss-cross.

CR: fields rearrange, to (mainly) reduce string length:

Colour correlations

!p

_⊥

#(n

ch

) is very sensitive to colour flow

p p

long strings to remnants ⇒ much n

_ch

/interaction ⇒ !p

_⊥

#(n

ch

) ∼ flat

p p

short strings (more central) ⇒ less n

_ch

/interaction ⇒ !p

_⊥

#(n

ch

) rising

Colour correlations

!p_⊥#(nch) is very sensitive to colour flow

p p

long strings to remnants ⇒ much nch/interaction⇒ !p_⊥#(nch) ∼ flat

p p

short strings (more central) ⇒ less nch/interaction⇒ !p_⊥#(nch) rising

Two main confirmations:

hp

⊥

i(n

ch

) is steadily rising in pp/pp data

(UA1, Tevatron, LHC)

, but would be (almost) flat if no CR.

Combined LEP data on e

⁺

e

⁻

→ W

⁺

W

⁻

→ q

1

q

₂

q

₃

q

₄

is best described with 49% CR, 2.2σ away from no-CR.

(hep-ex/0612034)

(7)

Colour reconnection models

“Recent” Pythia option: QCD-inspired CR (QCDCR)

(1505.01681)

:

Possible reconnections

Ordinary string reconnection

(qq: 1/9, gg: 1/8, model: 1/9)

Triple junction reconnection

(qq: 1/27, gg: 5/256, model: 2/81)

Double junction reconnection

(qq: 1/3, gg: 10/64, model: 2/9)

Zipping reconnection

(Depends on number of gluons)

Jesper Roy Christiansen (Lund) Non pertubative colours November 3, MPI@LHC 10 / 15

Stefan Gieseke, Patrick Kirchgaeßer, Simon Pl¨atzer: Baryon production from cluster hadronization 3

referred to as a mesonic cluster

3 ⌦ ¯3 = 8 1. (5)

In strict SU (3)

C

the probability of two quarks having the correct colours to form a singlet would be 1/9. Next we consider possible extensions to the colour reconnec- tion that allows us to form clusters made out of 3 quarks.

A baryonic cluster consists of three quarks or three anti- quarks where the possible representations are,

3 ⌦ 3 ⌦ 3 = 10 8 8 1, (6)

¯ 3 ⌦ ¯3 ⌦ ¯3 = 10 8 8 1. (7) In full SU (3)

C

the probability to form a singlet made out of three quarks would be 1/27. In the following we will introduce the algorithm we used for the alternative colour reconnection model. In order to extend the current colour reconnection model, which only deals with mesonic clus- ters, we allow the reconnection algorithm to find configu- rations that would result in a baryonic cluster.

2.3 Algorithm

As explained before the colour reconnection algorithms in Herwig are implemented in such a way that they lower the sum of invariant cluster masses. For baryonic recon- nection such a condition is no longer reasonable because of the larger invariant cluster mass a baryonic cluster carries.

As an alternative we consider a simple geometric picture of nearest neighbours were we try to find quarks that ap- proximately populate the same phase space region based on their rapidity y. The rapidity y is defined as

y = 1 2 ln

✓ E + p

z

E p

z

◆ , (8)

and is usually calculated with respect to the z-axis. Here we consider baryonic reconnection if the quarks and the antiquarks are flying in the same direction. This reconnec- tion forms two baryonic clusters out of three mesonic ones.

The starting point for the new rapidity based algorithm is the predefined colour configuration that emerges once all the perturbative evolution by the parton shower has fin- ished and the remaining gluons are split non-perturbative- ly into quark-antiquark pairs. Then a list of clusters is created from all colour connected quarks and anti-quarks.

The final algorithm consists of the following steps:

1. Shu✏e the list of clusters in order to prevent the bias that comes from the order in which we consider the clusters for reconnection

2. Pick a cluster (A) from that list and boost into the rest-frame of that cluster. The two constituents of the cluster (q

A

, ¯ q

A

) are now flying back to back and we define the direction of the antiquark as the positive z-direction of the quark axis.

3. Perform a loop over all remaining clusters and cal- culate the rapidity of the cluster constituents with re- spect to the quark axis in the rest frame of the original cluster for each other cluster in that list (B).

Fig. 2. Representation of rapidity based colour reconnection where the quark axis of one cluster is defined as the z-axis in respect to which the rapidities of the constituents from the possible reconnection candidate are calculated. (A) and (B) are the the original clusters. (C) and (D) would be the new clusters after the reconnection.

Fig. 3. Configuration of clusters that might lead to baryonic reconnection. The small black arrows indicate the direction of the quarks. A reconnection is considered if all quarks move in the same direction and all antiquarks move in the same direction.

4. Depending on the rapidities the constituents of the cluster (q

B

, ¯ q

B

) fall into one of three categories:

Mesonic: y(q

B

) > 0 > y(¯ q

B

) . Baryonic: y(¯ q

B

) > 0 > y(q

B

) . Neither.

If the cluster neither falls into the mesonic, nor in the baryonic category listed above the cluster is not con- sidered for reconnection.

5. The category and the absolute value |y(q

B

) | + |y(¯q

B

) | for the clusters with the two largest sums is saved (these are clusters B and C in the following).

6. Consider the clusters for reconnection depending on their category. If the two clusters with the largest sum (B and C) are in the category baryonic consider them for baryonic reconnection (to cluster A) with probabil- ity p

B

. If the category of the cluster with the largest sum is mesonic then consider it for normal reconnec- tion with probability p

R

. If a baryonic reconnection oc- curs, remove these clusters (A, B, C) from the list and do not consider them for further reconnection. A pic- ture of the rapidity based reconnection for a mesonic configuration is shown in Fig. 2 and a simplified sketch for baryonic reconnection is shown in Fig. 3.

7. Repeat these steps with the next cluster in the list.

We note that with this description we potentially exclude clusters from reconnection where both constituents have a configuration like y(q

B

) > y(¯ q

B

) > 0 w.r.t. the quark axis but assume that these clusters already contain con- stituents who are close in rapidity and fly in the same direction. The exclusion of baryonically reconnected clus- ters from further re-reconnection biases the algorithm to- wards the creation of baryonic clusters whose constituents are not the overall nearest neighbours in rapidity. The ex- tension to the colour reconnection model gives Herwig an

Triple-junction also in Herwig cluster model.

(1710.10906)

(8)

The beauty baryon enhancement

average reconstructed to true pT(Hb) as a function of m(Hcµ ) and is determined using simulation. It varies from 0.75 for m(Hcµ ) equals 3 GeV to unity at m(Hcµ ) = m(Hb).

The distribution of fs/(fu+ fd) as a function of pT(Hb) is shown in Fig. 3. We perform a linear ²fit incorporating a full covariance matrix which takes into account the bin-by- bin correlations introduced from the kaon kinematics, and PID and tracking systematic uncertainties. The factor A in Eq. 1 incorporates the global systematic uncertainties described later, which are independent of pT(Hb). The resulting function is

fs

fu+ fd

(pT) = A [p1+ p2⇥ (pT hpTi)] , (1) where pThere refers to pT(Hb), A = 1± 0.043, p1= 0.119± 0.001, p2= ( 0.91± 0.25) · 10³GeV ¹, andhpTi = 10.1 GeV. The correlation coefficient between the fit parameters is 0.20. After integrating over pT(Hb), no ⌘ dependence is observed (see the Supplemental material).

We determine an average value for fs/(fu+fd) by dividing the yields of B⁰_ssemileptonic decays by the sum of B⁰and B semileptonic yields, which are all efficiency-corrected, between the limits of pT(Hb) of 4 and 25 GeV and ⌘ of 2 and 5, resulting in

fs

fu+ fd= 0.122± 0.006,

where the uncertainty contains both statistical and systematic components, with the latter being dominant, and discussed subsequently. The total relative uncertainty is 4.8%.

) [GeV]

H

b T

(

5 10 15

p

20 25

Fractions

0 b

Λ and

s

B

0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4

LHCb = 13 TeV s

fu d + f

fs

fu d + f

Λb

f

Figure 3: The ratios f_s/(f_u+ f_d) and f_⇤0

b/(f_u+ f_d) in bins of p_T(H_b). The B⁰_sdata are indicated by solid circles, while the ⇤⁰_bby triangles. The smaller (black) error bars show the combined bin-by-bin statistical and systematic uncertainties, and the larger (blue) ones show the global systematics added in quadrature. The fits to the data are shown as the solid (green) bands, whose widths represents the±1 uncertainty limits on the fit shapes, and the dashed (black) lines give the total uncertainty on the fit results including the global scale uncertainty. In the highest two p_Tbins the points have been displaced from the center of the bin.

6

In 2019 LHCb found enhancement of Λ

⁰_b

production at small p

_⊥

, but flat in η.

(1902.06794)

No model comparisons.

1.2 Table of b-fractions versus p

T

(H

b

)

Table 4: Values of fs/(fu+ fd) and f_⇤0

b/(fu+ fd) in each pT(Hb) bin. The first uncertainty is statistical and incorporates both the uncertainties due to the data sample size and the finite amount of simulated events, while the second is the overall systematic uncertainty, including global and bin-dependent systematic uncertainties.

p

T

(H

b

)[GeV] f

s

/(f

u

+ f

d

) f

_⇤⁰

b

/(f

u

+ f

d

) 4–5 0.125 ± 0.001 ± 0.007 0.324 ± 0.001 ± 0.025 5–6 0.125 ± 0.001 ± 0.007 0.281 ± 0.001 ± 0.018 6–7 0.122 ± 0.001 ± 0.006 0.257 ± 0.001 ± 0.017 7–8 0.125 ± 0.001 ± 0.006 0.245 ± 0.001 ± 0.017 8–9 0.116 ± 0.001 ± 0.006 0.227 ± 0.001 ± 0.015 9–10 0.120 ± 0.001 ± 0.006 0.210 ± 0.001 ± 0.015 10–11 0.121 ± 0.001 ± 0.006 0.194 ± 0.001 ± 0.013 11–12 0.116 ± 0.001 ± 0.006 0.191 ± 0.001 ± 0.014 12–13 0.116 ± 0.001 ± 0.006 0.172 ± 0.001 ± 0.013 13–14 0.122 ± 0.001 ± 0.007 0.159 ± 0.001 ± 0.012 14–16 0.112 ± 0.001 ± 0.006 0.165 ± 0.001 ± 0.012 16–18 0.107 ± 0.001 ± 0.006 0.136 ± 0.001 ± 0.010 18–20 0.115 ± 0.001 ± 0.008 0.126 ± 0.001 ± 0.010 20–25 0.111 ± 0.001 ± 0.007 0.109 ± 0.001 ± 0.009

1.3 Fraction ratios as functions of ⌘

Figure 4 shows measurements of the fraction ratios f

s

/(f

u

+ f

d

) and f

_⇤0

b

/(f

u

+ f

d

) as functions of ⌘, integrated over p

T

. No ⌘ dependence is visible with the current data sample.

η

2 3 4 5

uf + df

sf

0 0.05 0.1 0.15 0.2 0.25

LHCb = 13 TeV s

η

2 3 4 5

uf + df

bΛf

0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4

LHCb = 13 TeV s

Figure 4: Measurement of the fraction ratios (a) fs/(fu+ fd) and (b) f_⇤0

b/(fu+ fd) as functions of ⌘ integrated over pT.

11

(9)

The charm baryon enhancement

In 2017/21 ALICE found/confirmed strong enhancement of charm baryon production, relative to LEP, HERA and default Pythia.

(1712.09581, 2105.06335)

Fragmentation fractions and charm production cross section ALICE Collaboration

D0 D⁺ D_s⁺ Λ_c⁺ Ξ_c⁰ D*⁺ 0.2

0.4 0.6 0.8 1.0 )c H→(c f

= 5.02 TeV s ALICE, pp,

= 10.5 GeV s

−,

+e B factories, e

mZ

= s

−,

+e LEP, e HERA, ep, DIS HERA, ep, PHP

−2

×10

4 10⁻¹2×10⁻¹ 1 2 3 4 10 (TeV) s 10

102 103

b)µ (|<0.5y||y/dccσd

ALICE PHENIX STAR

FONLL NNLO

Figure 2: Left: Charm-quark fragmentation fractions into charm hadrons measured in pp collisions atps = 5.02 TeV in comparison with experimental measurements performed in e⁺e collisions at LEP and at B factories, and in ep collisions at HERA [63]. The D^⇤+meson is depicted separately since its contribution is also included in the ground-state charm mesons. Right: Charm production cross section at midrapidity per unit of rapidity as a function of the collision energy. STAR [11] and PHENIX [66] results, slightly displaced in the horizontal direction for better visibility, are reported. Comparisons with FONLL [13–15] (red band) and NNLO [67–69] (violet band) pQCD calculations are also shown.

An increase of about a factor 3.3 for the fragmentation fractions for theL⁺_c baryons with respect to e⁺e and ep collisions, and a concomitant decrease of about a factor 1.4–1.2 for the D mesons, are observed. The significance of the difference considering the uncertainties of both measurements, is about 5s for L⁺c baryons. This in turn decreases the fragmentation into D⁰mesons at midrapidity by 6s with respect to the measurements in e⁺e and ep collisions. In previous measurements in e⁺e and ep collisions no value for theX⁰_cwas obtained and the yield was estimated according to the assumption f (c ! X⁺c)/f (c ! L⁺c)= f (s ! X )/ f (s ! L⁰)⇠ 0.004 [63]. The fraction f (c ! X⁰c)was measured for the first time and f (c ! X⁰c)/f (c ! L⁺c)= 0.39 ± 0.07(stat)^+0.080.07(syst) was found [28]. A first attempt to compute the fragmentation fractions in pp collisions at the LHC was performed in [63] assuming universal fragmentation, since at that time the measurements of charm baryons at midrapidity were not yet available. The measurements reported here challenge that assumption.

The updated fragmentation fractions obtained for the first time taking into account the measurements of D⁰, D⁺, D⁺_s,L⁺_c, andX⁰_cat midrapidity in pp collisions at ps = 5.02 TeV, allowed the recomputation of the charm production cross sections per unit of rapidity at midrapidity in pp collisions at ps = 2.76 and 7 TeV. TheL⁺c/D⁰ratios measured in pp at different collision energies, as well as theX⁰c/D⁰ratio, are compatible [25, 28, 56]. The charm cross sections were obtained by scaling the pT-integrated D⁰-meson cross section [1, 3] for the relative fragmentation fraction of a charm quark into a D⁰meson measured in pp collisions at ps = 5.02 TeV and applying the two correction factors for the different shapes of the rapidity distributions of charm hadrons and c¯c pairs. The p_T-integrated D⁰-meson cross section was used because at the other energies not all charm hadrons were measured and the D⁰measurements are the most precise. The uncertainties of the fragmentation fraction (FF) were taken into account in calculating the cc production cross section as was the uncertainty introduced by the rapidity correction factors. The BR of the D⁰! K p⁺decay channel was also updated, considering the latest value reported in the PDG [47].

6

Fragmentation fractions and charm production cross section ALICE Collaboration

D+ D*⁺ Ds+ c+

Λ Ξ_c⁰ Ωc0 J/ψ

0 / DcH

0 0.2 0.4 0.6 0.8 1

1.2 ALICE, pp, s = 5.02 TeV PYTHIA 8: JHEP 08 (2015) 003

Monash 2013 CR Mode 0 CR Mode 2 CR Mode 3

30

× 30

×

D+ D* ⁺ Ds+ c+

Λ Ξ_c⁰ Ωc0 J/ψ

0 / DcH

0 0.2 0.4 0.6 0.8 1

1.2 ALICE, pp, s = 5.02 TeV SHM: Phys. Lett. B 795 (2019) 117-121

= 160 MeV Th PDG,

= 160 MeV Th RQM,

= 170 MeV Th PDG,

= 170 MeV Th RQM,

30

× × 30

Figure 1: Transverse-momentum integrated production cross sections of the various charm meson [4, 5, 48] and baryon [24, 25, 28] species per unit of rapidity at midrapidity normalised to that of the D⁰meson measured in pp collisions at ps = 5.02 TeV. The measurements are compared with PYTHIA 8 calculations [36, 49] (left panel) and with results from a SHM [35] (right panel) (see text for details). For J/y the inclusive cross section was used.

The J/y/D⁰ratio, as well as the model calculations for theW⁰_c/D⁰ratio, are multiplied by a factor 30 for visibility.

gates are measured as well and the results are averaged. The cross sections of D⁰and D⁺mesons were measured down to pT=0 [5]. The cross sections for D^⇤+and D⁺_s mesons were measured down to pT= 1 GeV/c, corresponding to about 80% of the integrated cross section [4]. TheL⁺_c baryon cross section was measured down to pT=1 GeV/c, corresponding to about 70% of the integrated cross sections [24, 25].

TheX⁰_cbaryon was measured down to pT=2 GeV/c, corresponding to about 40% of the integrated cross section [28]. The systematic uncertainties of the meson and baryon measurements include the following sources: (i) extraction of the raw yield; (ii) prompt fraction estimation; (iii) tracking and selection efficiency; (iv) particle identification efficiency; (v) sensitivity of the efficiencies to the hadron pTshape generated in the simulation; (vi) pT-extrapolation for the hadrons not measured down to pT=0. In addition, an overall normalisation systematic uncertainty induced by the branching ratios (BR) [47] and the integrated luminosity [46] were considered.

Figure 1 shows the pT-integrated production cross sections per unit of rapidity of the various open- and hidden-charm meson (D⁺, D⁺s, D^⇤+, and J/y) [4, 5, 48] and baryon (L⁺c andX⁰c) [24, 25, 28] species, obtained in pp collisions at ps = 5.02 TeV, as the average of particle and antiparticle, and normalised to the one of the D⁰meson. When computing the ratios between the different hadron species, systematic uncertainties due to tracking, the feed-down from beauty-hadron decays, the pT-extrapolation, and the luminosity were propagated as correlated. For theX⁰_cbaryons, the additional contribution to the beauty feed-down systematic uncertainty due to the assumedX^0,_b -baryon production relative to that ofL⁺_b baryons [28, 29] was considered as uncorrelated with the uncertainties related to the beauty feed-down subtraction for the other charm hadron species. In the J/y/D⁰ratio all the systematic uncertainties were propagated as uncorrelated, with the exception of the luminosity uncertainty. The treatment of the systematic uncertainties is also the same for the computation of the other quantities reported here.

In the left panel of Fig. 1 the experimental data are compared with results from the PYTHIA 8 generator, using the Monash 2013 tune [49], and tunes that implement colour reconnections (CR) beyond the leading-colour approximation [36]. In the Monash 2013 tune, the parameters governing the heavy-quark fragmentation are tuned to measurements in e⁺e collisions. The CR tunes introduce new colour reconnection topologies, including junctions, that enhance the baryon production and, to a lesser extent,

3

The QCDCR model does much better, with junctions ⇒ baryons.

(10)

Charm baryon differential distributions

Measurement of prompt D⁰,L⁺c, andS^0,++c production in pp collisions at ps = 13 TeV ALICE Collaboration

1 10

) c (GeV/

pT

0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8

Cross section ratios

/ D0 +

Λc

= 5 TeV s pp,

= 13 TeV s pp, ALICE

| < 0.5 y

|

2 4 6 8 10 12 14

) c (GeV/

pT

0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8

10

× PYTHIA 8.243, Monash 2013 PYTHIA 8.243, CR-BLC:

Mode 0 Mode 2 Mode 3

SHM+RQM Catania QCM

3/2 / D0 0,++× Σc

= 13 TeV s pp,

2 4 6 8 10 12 14

) c (GeV/

pT

0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8

+

Λc

3/2 /

×

0,++) Σc

←

+( Λc

= 13 TeV s pp,

Figure 2: Prompt-charm-hadron cross-section ratios: L⁺c/D⁰ (left), S^0,+,++c /D⁰ (middle), and L⁺_c S^0,+,++c /L⁺_c (right), in pp collisions at ps = 13 TeV, compared with model expectations [25–

27, 29] and (left) with data from pp collisions at ps = 5.02 TeV [3]. The horizontal lines reflect the width of the pTintervals. The PYTHIA Monash 2013 curve is scaled by a factor of 10 in the middle panel.

verse of the quadratic sum of the relative statistical and uncorrelated systematic uncertainties as weights.

The total systematic uncertainty of the averagedSccross section varies from 20% at low pTto 13% at high pT. The cross-section ratiosL⁺c/D⁰andS^0,+,++c /D⁰are compared with model expectations in Fig. 2 (left and middle panels). In the ratios, the systematic uncertainties of the track-reconstruction efficiency and luminosity, considered as fully correlated, cancel partly and completely, respectively. The feed-down uncertainty is propagated as partially correlated, while all other uncertainties are treated as uncorrelated.

TheL⁺c/D⁰ratio decreases with increasing pTand is significantly larger than the ⇡0.12 values observed in e⁺e and ep collisions at several collision energies [12–15, 45–47]. The values measured in pp collisions at ps = 13 TeV are compatible, within uncertainties, with those measured at ps = 5.02 TeV [3, 4].

As shown in Fig. 2 (middle), theS^0,+,++c /D⁰ratio is close to 0.2 for 2 < pT<6 GeV/c, and decreases with pTdown to about 0.1 for 8 < pT<12 GeV/c, though the uncertainties do not allow firm conclusions about the pTdependence to be made. From Belle measurements (Table IV in Ref. [24]), theS^0,+,++c /L⁺c

ratio in e⁺e collisions at ps = 10.52 GeV can be evaluated to be around 0.17 and, thus, theS^0,+,++c /D⁰ ratio can be estimated to be around 0.02. Therefore, a remarkable difference is present between the pp and e⁺e collision systems. Although rather approximate, such comparison is corroborated by the fact that a simulation performed with the default version of PYTHIA 6.2 reasonably reproduces Belle data [24], while the default version of PYTHIA 8.243 (Monash 2013 tune) severely underpredicts ALICE data, despite the very similar modelling of charm fragmentation in the two simulations. Figure 2 (right) shows the ratioL⁺c S^0,+,++c /L⁺c as a function of pT, which quantifies the fraction ofL⁺c feed-down fromS^0,+,++c . In order to better exploit the cancellation of correlated uncertainties, this is calculated as the weighted average of the ratios measured separately in theL⁺c ! pK p⁺andL⁺c! pK⁰_Sdecay chan- nels. The pT-integrated value in the measured pT>2 GeV/c interval is 0.38 ± 0.06(stat) ± 0.06(syst), significantly larger than the ratioS^0,+,++c /L⁺c ⇠ 0.17 from Belle data and the ⇠0.13 expectation from PYTHIA 8 (Monash 2013) simulations. This indicates a larger increase forS^0,+,++c /D⁰than for the direct-L⁺_c/D⁰ratio from e⁺e to pp collisions. The larger feed-down fromS^0,+,++c partially explains the difference between theL⁺c/D⁰ratios in pp and e⁺e collisions.

As shown in Figure 2, the CR-BLC (for which the three variations defined in Ref. [25] are considered), SHM+RQM, and Catania models describe, within uncertainties, both theL⁺_c/D⁰andS^0,+,++c /D⁰ratios.

The QCM model uses theL⁺c/D⁰data in pp collisions at ps = 7 TeV to set the total charm baryon- 6

X⁰cproduction in pp collisions at ps = 5.02 TeV ALICE Collaboration

PYTHIA 8 event generator previously described. All PYTHIA 8 tunes underestimate the measured pT-differentialX⁰c/D⁰ratio. The Monash tune significantly underestimates the data by a factor of about 21–24 in the low pTregion and by a factor of about 7 in the highest pTinterval, as also observed for the L⁺c/D⁰ratio [17]. All three CR modes yield a similar magnitude and shape of theX⁰c/D⁰ratio, and despite predicting a larger baryon-to-meson ratio with respect to the Monash tune, they still underestimate the measuredX⁰c/D⁰ratio by a factor of about 4–5 at low pT. The models with CR tunes describe better theL⁺c/D⁰and theS^0,+,++c /D⁰ratios than theX⁰c/D⁰one [9, 17, 19, 26], which involves a charm-strange baryon.

The measuredX⁰c/D⁰ratio is also compared with a SHM calculation [32] in which additional excited charm-baryon states not yet observed are included. The additional states are added based on the relativistic quark model (RQM) [34] and lattice QCD calculations [35]. Charm- and strange-quark fugacity factors are used in the model to account for the suppression of quarks heavier than u and d in elementary collisions. The uncertainty band in the model is obtained by varying the assumption of the branching ratios of excited charm-baryon states decaying to the ground stateX^0,+c , where an exact isospin symme- try betweenX⁺c andX⁰cis assumed. This model, which was observed to describe theL⁺c/D⁰ratio [17], underestimates the measuredX⁰c/D⁰ratio by the same amount as PYTHIA 8 with CR tunes.

The QCM model [36] underpredicts theX⁰c/D⁰ratio by the same amount as it does for theX⁰c-baryon production cross section. The Catania model [37, 46] implements charm-quark hadronisation via both coalescence and fragmentation. In the model a blast wave parametrisation [71] for light quarks at the hadronisation time with the inclusion of a contribution from mini-jets is considered, while for charm quarks the spectra from FONLL calculations are used. The coalescence process of heavy quarks with light quarks, which is modelled using the Wigner function formalism, is tuned to have all charm quarks hadronising via coalescence at pT' 0. At finite pT, charm quarks not undergoing coalescence are hadronised via an independent fragmentation. The Catania model describes theX⁰c/D⁰ratio in the full pTinterval of the measurement.

This newX⁰cmeasurement therefore provides important constraints to models of charm quark hadronisation in pp collisions, being in particular sensitive to the description of charm-strange baryon production in the colour reconnection approach, and to the possible contribution of coalescence to charm quark

0 2 4 6 8 10

) c (GeV/

pT 2

10− 1

10−

1 10 102

103 )c -1b GeVµ) (ydTp/(dσ2d

2.1% lumi. unc. not shown

± ALICE

baryon

0

Ξc

= 5.02 TeV s pp,

| < 0.5 y

|

Data BR unc.

PYTHIA 8 Monash2013 PYTHIA 8 Mode 2 PYTHIA 8 Mode 0 PYTHIA 8 Mode 3 QCM

0 2 4 6 8 10

) c (GeV/

pT

0.1 0.2 0.3 0.4

0 / D_{0 c}Ξ

Data BR unc.

PYTHIA 8 Monash2013 PYTHIA 8 Mode 2 PYTHIA 8 Mode 0 PYTHIA 8 Mode 3 QCM Catania (coal.+fragm.) SHM+RQM ALICE

= 5.02 TeV s pp,

| < 0.5 y

|

Figure 6: Left panel: pT-differential production cross section of promptX⁰_c baryons in pp collisions at ps = 5.02 TeV compared with model calculations [28, 31, 36]. Right panel: X⁰_c/D⁰ratio as a function of pT measured in pp collisions at ps = 5.02 TeV compared with model calculations [28, 31, 32, 36, 37] (see text for details).

13 Charm-hadron yield ratios versus multiplicity in pp at√s = 13 TeV ALICE Collaboration

0 10 20 30 40

0.5

<

| η

〉|

η d

ch/ N d

〈 0.1

0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 0 / D+ cΛ

| < 0.5 y ALICE, |

PYTHIA 8.243 Monash 2013 CR-BLC Mode 0 CR-BLC Mode 2 CR-BLC Mode 3

stat.

syst.

extr.

= 13 TeV s pp,

= 5.02 TeV s pp,

= 5.02 TeV sNN Pb,

− p

Figure 5: Ratios of pT-integrated yields ofΛ⁺cand D⁰hadrons as a function of "dNch/dη# in pp collisions at

√s = 13 TeV. Measurements performed in pp and p–Pb collisions at √sNN=5.02 TeV from Ref. [13] are also shown. Statistical and systematic uncertainties are shown by error bars and empty boxes, respectively. Shaded boxes represent the extrapolation uncertainties. The corresponding PYTHIA predictions [20, 22] are also shown.

lation factor. The fraction of extrapolated yield from the lowest to the highest multiplicity interval is about 39% (31%), 28% (22%), 20% (16%), and 15% (13%) forΛ⁺c(D⁰). The procedure was repeated considering also the CR-BLC Mode 0 and Mode 3 as well as two different functions fitted to the spectra (a Tsallis-Lévy [60] and a power-law function). The fits were performed considering the statistical and pT-uncorrelated sources of systematic uncertainties, and also shifting up and down the data by one sigma of the pT-correlated systematic uncertainties. The envelope of the extrapolation factors obtained with all the trials was assigned as the extrapolation uncertainty onΛ⁺cand D⁰, and it was propagated to theΛ⁺c/D⁰ratio, resulting in a value that ranges from 2% to 21% depending on multiplicity. The same procedure was used to estimate the pT-integrated D⁺syields and D⁺s/D⁰yield ratios in the different multiplicity intervals, reported in Ref. [50]. TheΛ⁺cand D⁰pT-integrated yields are also reported in Ref. [50], together with the pT-integratedΛ⁺c/D⁰yield ratios in the visible pTrange, and the tables with the numerical values of the pT-integrated ratios. The pT-integratedΛ⁺c/D⁰yield ratio as a function of

"dNch/dη# is shown in Fig. 5, where the systematic uncertainties from the extrapolation (shaded boxes, assumed to be uncorrelated among multiplicity intervals) are drawn separately from the other sources of systematic uncertainties (empty boxes). The sources related to the raw-yield extraction, the multiplicity- interval limits, the high-multiplicity triggers, the multiplicity-independent prompt fraction assumption, and the statistical uncertainties on the efficiencies are also considered uncorrelated with multiplicity. The other systematic uncertainties are assumed to be correlated. The measurements performed in pp and p–

Pb collisions at √s = 5.02 TeV [13] are also shown. The result does not favour an increase of the yield ratios with multiplicity, as also observed for theΛ/K⁰Sratio in Ref. [39], and the trend is compatible with a constant function. This suggests that the increasing trend observed for the 1 < pT<24 GeV/c range comes from a re-distribution of pTthat acts differently for baryons and mesons, while this is not observed in the meson-to-meson ratios, as shown in Fig. 3 for D⁺s/D⁰and in Ref. [54] for K/π. The results are compared to the pT-integrated PYTHIA predictions. The measurements exclude the Monash prediction in the whole multiplicity range, and tend to be significantly below the CR-BLC Mode 2 for the three highest multiplicity intervals.

13

(2106.08278, 2105.05616, 2111.11948)

QCDCR does well for some distributions, less so for others.

Improvements needed, but good starting point.

(11)

Models of and conclusions on particle composition

Other models, in a heavy-ion physics spirit:

QCM: Quark (re)Combination Mechanism, with co-moving light quarks being picked up.

(1801.09402)

SHM+RQM: Statistical Hadronization Model + Relativistic Quark Model. Thermo-statistical production with extensive feeddown from heavier charm baryon states.

(1902.08889)

Catania: use AA models of quark–gluon plasma formation.

Coalescence of nearby quarks at small p

_⊥

, while “normal”

fragmentation at higher p

_⊥

.

(2012.12001)

Tentative conclusion:

“Vacuum” evolution at large p

_⊥

, like in e

⁺

e

⁻

and ep.

Collective effects take over at small p

_⊥

, where MPIs give close-packing of quarks/gluons/strings/clusters/hadrons.

Breakdown of jet universality, like for strangeness!

(12)

Beam drag effects

Colour flow connects hard scattering to beam remnants. Can have consequences, e.g. in π

⁻

p:

A(x

F

) = σ(D

⁻

) − σ(D

⁺

) σ(D

⁻

) + σ(D

⁺

)

0.8 0.6 0.4 0.2 0.0 0.2 0.4 0.6 0.8

xF

1.0 0.5 0.0 0.5 1.0

A(xF)

Asymmetry

A(xF) =(D⁻−D⁺)/(D⁻+D⁺)

qq→cc

@ 500 GeV

gg→cc

@ 500 GeV combined WA82 @ 340 GeV E769 @ 250 GeV E791 @ 500 GeV

(hep-ph/0005110,2203.09503)

Beam drag e↵ects (E. Norrbin & TS, 2000)

Torbj¨orn Sj¨ostrand Nonperturbative models in PYTHIA slide 8/23

If low-mass string e.g.:

cd : D

⁻

, D

^∗−

cud : Λ

⁺_c

, Σ

⁺_c

, Σ

^∗+_c

⇒ flavour asymmetries

Beam drag e↵ects (E. Norrbin & TS, 2000)

Torbj¨orn Sj¨ostrand Nonperturbative models in PYTHIA slide 8/23

Can give D “drag” to larger x

F

than c quark.

(13)

Bottom asymmetries

uncertainties on the Pythia models shown here are only due to the limited sample size of about 12.5 million events. The results of the Pythia hadronisation model describing the data best, along with the predictions of the heavy-quark recombination model are presented in Fig. 11. The uncertainties on the heavy-quark recombination model are the systematic uncertainties given in Ref. [5]. Overall, the predictions from the heavy-quark recombination model are consistently higher than the 8 TeV measurements, but remain within uncertainties. For Pythia, only the model CR1 shows a good agreement with the p s = 7 TeV measurements but it is also consistently higher at 8 TeV. The two other tested settings predict asymmetries that are too large, exhibiting the strongest deviation at low transverse momentum.

2 2.5 3 3.5 4

0y Λb 0

2 4 6 8 10 12 14

[%]Aprod 16 ^{Data 1}^fb^-1

Pythia8 (CR1) Pythia8 (CR2) Pythia8 (Monash) = 7 TeV s LHCb

0 10 20

] c [GeV/

pT 0

Λb 0

2 4 6 8 10 12 14

[%]prodA ^-1^fb^{Data 1}

2 2.5 3 3.5 4

0y Λb 0

2 4 6 8 10 12 14

[%]Aprod 16 ^{Data 2}^fb^-1

0 10 20

] c [GeV/

pT 0

Λb 0

2 4 6 8 10 12 14

[%]prodA ^-1^fb^{Data 2}

Figure 10: Comparison of the ⇤⁰_b production asymmetry predicted by the various Pythia models, where CR1 refers to the QCD-inspired model and CR2 refers to the gluon-move model, and the measured production asymmetries. Results versus ⇤⁰_b(left) rapidity y and (right) pTare shown for centre-of-mass energies of (top)p

s = 7 TeV and (bottom)p

s = 8 TeV. Uncertainties on the predictions are due to limited simulation sample sizes.

9 Conclusions

The most precise measurements of the ⇤

⁰_b

production asymmetry in p s = 7 TeV and 8 TeV proton-proton collisions have been presented. A new method to estimate asymmetries in the interaction of protons and antiprotons with the detector material has been developed.

21

(2107.09593)

A(y ), A(p

_⊥

) = σ(Λ

⁰_b

) − σ(Λ

⁰b

) σ(Λ

⁰_b

) + σ(Λ

⁰_b

) CR1 = QCDCR, with no enhancement at low p

_⊥

.

Enhanced Λ

b

production at low p

_⊥

, like for Λ

c

, dilutes asymmetry?

Asymmetries observed also for other charm and bottom hadrons.

Warning: fragmentation function formalisms unreliable at low p

_⊥