tuning & modelling uncertainties input from pythia

Tuning & Modelling Uncertainties Input from PYTHIA

PHENOmenal Meeting with ALICE April 2021

Peter Skands Monash University

Tuning — what do you want it to do?

Physically sensible parameter values, with good universality.

High fidelity (agrees with data)

Reliable Uncertainties

(Depends on quality of physics model!)

The best fit for your observable.

➤ universality tests & non-universal tunes

How to approach tuning systematically? Universality Tests

2

๏Systematic Approach to Tuning: Universality Tests + characterisation of any deviations.

‣Do independent tunes for different CM energies find universal parameters?

‣Do independent tunes for different processes find universal parameters?

‣Do independent tunes for different experiments find universal parameters?

‣Do independent tunes for different obervables find universal parameters?

‣Non-universal tune to just one observable. Can the model fit it at all? With what parameters?

๏Provides a more systematic understanding of what the model can and cannot do simultaneously ➤ phrase conclusions in a more physical way ➤ show non-universalities

‣ Professor can help automate (recommend adding 5% TH uncertainty to protect against overfitting.)

๏Some Examples of explicit studies: increasing faith in robustness and universality:

‣ E.g., arXiv:1103.3649 tested MB universality across different CM energies; ๏ Found good universality except for CR strength. Further explored in arXiv:1808.07224.

‣ arXiv:1812.07424 tuned hadronisation parameters at LEP; looked at consistency between different LEP experiments, + with/without event shapes

๏ Rejected a few extreme “outliers” which were inconsistent with bulk of tunes. ๏ Used the rest to define envelope of uncertainties which bracketed the data well.

Peter Skands UniversityMonash

https://arxiv.org/abs/1103.3649



Modelling Options in Pythia: Colour Reconnections

3

๏Monash Tune

‣ Based on “old” colour reconnection model (the QCD CR model was published a year later)

‣Contained a mistake in the D*/D ratio (thanks to D. Bardhan for alerting us to it!)

๏ StringFlav:mesonCvector = 0.88; should have been 1.25 - 1.5 ๏ (Due to taking the D* and D rates from separate, inconsistent, sources)

‣ “Brute-force” modelling of CR; no explicit flavour dependence ๏ Main effect is on <pT> vs Nch and related momentum-space quantities;

๏QCD CR Model (ColourReconnection:mode = 2)

‣ First attempt (2015) to model QCD CR effects more faithfully. Good starting point.

‣ Still acts purely in colour space. No explicit flavour dependence. ๏ Can create colour-epsilon structures in colour space more baryons! ๏ No strangeness enhancement (can even go a bit the other way, due to phase-space

constraints of occasional very small strings it produces) ๏ Phase-space constraints should probably be revisited esp in context of heavy flavours

→


Christiansen & Skands JHEP 08 (2015) 003 • e-Print: 1505.01681


What I think you have discovered!

4Peter Skands UniversityMonash

ϵijkqiqjqk

(Though maybe not 5 confidence yet - theoretically!)σ

Options for Strangeness Enhancement

5

๏Rope Model ‣ First rigorous attempt (in Pythia) to faithfully describe genuine collective effects.

๏ Elaborate physical model, formulated in spacetime, with explicit differential time evolution.

‣ Typically starts from QCD CR model.

‣ Introduces higher effective tensions in multi-string “ropes” ๏ Explicit strangeness enhancement, increasing with overall activity ๏ + Further possibility for more diquarks as well (baryons)

‣Can also add “Shoving” to generate (repulsive) collective flow

๏Close Packing ‣ Simpler model of “rope-like” behaviour (developed in context of a thermal string-breaking option)

๏ Formulated in momentum space and less sophisticated than rope model.

‣ Basic idea: assume strings still fragment ~ independently as usual, but that their vortex cores get “squeezed” by the presence of other strings nearby

‣Higher effective tensions ➤ strangeness (and baryon) enhancements (similarly to ropes)

‣ So far only implemented and available for thermal string breaking model. ๏ Extend to conventional (Schwinger) model (+ possible to incorporate repulsive flow effects as well?)


Fischer & Sjostrand JHEP 01 (2017) 140 • e-Print: 1610.09818

E.g., Bierlich et al JHEP 03 (2015) 148 • e-Print: 1412.6259 + several more recent



D Spectra

6

๏Depend on D*/D ratio + feed-down from B ‣ Possible to measure D* and B feed-down

components separately?

‣ (and hard vs )

๏Direct part (not from B) depends on rc ‣ Expresses difference between light cone of a

massless endpoint quark and smaller world sheet of a massive one (with v < c)

๏

‣ So far constrained by one LEP D* spectrum ๏ But remember the Monash tune had the wrong D* rate

(which affects the mixture)

‣Definitely interest for in-situ constraints ! ๏ Charm fragmentation in (>LEP-style) high-pT jets ๏ ~ clean reference without collective effects?

c g → cc̄

±D 0D ±*D ±sD X+cΛ cc→g ψJ/ c1

χ3685ψ

X)→

<n>

or B

R(Z

-410

-310

-210

-110

1

10Charm Rates

Pythia 8.185Data from HEPDATA/PDG

LEPPY8 Monash 13PY8 DefaultPY8 Fischer

bins/N25%χ

0.0±1.5 0.0±1.8 0.0±1.7

V I N

C I

A R

O O

T

hadrons→ee 91.2 GeV

±D 0D ±*D ±sD X+

cΛ cc→g ψJ/ c1χ

3685ψ

Theo

ry/D

ata

0

0.5

1

1.5

X+B 0±B uds

*B X0sB XbqqB

bb→g 4b 10)×(Υ

X)→

<n>

or B

R(Z

-510

-410

-310

-210

-110

1

10Beauty Rates

Pythia 8.185Data from HEPDATA/PDG

LEP+SLDPY8 Monash 13PY8 DefaultPY8 Fischer

bins/N25%χ

0.0±1.7 0.0±2.3 0.0±2.3

V I N

C I

A R

O O

T

hadrons→ee 91.2 GeV

X+B 0±B uds*B X0sB Xbqq

Bbb→g 4b 10)×(Υ

Theo

ry/D

ata

0

0.5

1

1.5

Figure 7: Hadronic Z decays atps = 91.2GeV. Rates and inclusive Z ! X branching fractions

(normalized to Z ! hadrons) of particles containing c and b quarks

splittings in the current version of PYTHIA. A more natural choice for g ! qq̄ could be µR / mqq̄,as used e.g. in the VINCIA shower model [29].

We now turn to the dynamics of heavy-quark fragmentation, focusing mainly on the b quark.For heavy quarks, the Lund fragmentation function is modified due to the (massive) endpoints not

moving along straight lightcones: as the string pulls on them, they slow down, resulting in the stringtracing out a smaller space-time area than it would for massless quarks. This modifies the implicationsof the string area law, in a manner captured by the so-called Bowler modification of the fragmentationfunction [62]

fmassive(z,mQ) /f(z)

zbrQm2Q

, (6)

with mQ the heavy-quark mass, b the same universal parameter that appears in the massless fragmen-tation function, eq. (3), and rQ a tuning parameter which is unity in the original derivation of Bowlerbut can be assigned values different from unity to reduce (rQ ! 0) or emphasize (rQ > 1) the effect.Since rQ multiplies the heavy-quark mass (squared), it can also be viewed as an effective rescalingof the mass value. The net result is a suppression of the region z ! 1, hence a relative softening ofthe fragmentation spectrum for heavy flavours (relative since the presence of m2

? in the exponent ofeq. (3) still implies an overall harder fragmentation for higher hadron masses.)

We emphasize that this is the only fragmentation function that is self-consistent within the string-fragmentation model [33, 62]. Although a few alternative forms of the fragmentation functions formassive quarks are available in the code, we therefore here work only with the Bowler type. As forthe massless function, the proportionality sign in eq. (6) indicates that the function is normalized tounity.

In PYTHIA, separate rQ parameters are provided for c and b quarks. We consider the one for bquarks first. Its default value is rb = 0.67, but this appears to give too hard b fragmentation spectrawhen compared to LEP and SLD data, see below. For the Monash tune, we instead use

14


Heavy-Flavour Endpoint Quarks

Peter Skands 5Monash U.

๏Same starting point as for massless endpoints •Tension κ ~ 1 GeV/fm ~ 0.2 GeV2 •String breaks by Schwinger mechanism

•Same parameters govern Ds/D, Bs/B, Λc/D, Λb/B ➜ Interesting to check if Ds/D, Bs/B affected in same way in same environments where we see strangeness enhancements in light-quark sector: multiplicity dependence

๏Massive endpoints have v < c ➜ smaller string space-time area: •➜ Modified (“Lund-Bowler”) FF:

•

Schwinger Tunneling

t

x

mqmq

•➜ Suppression of strange quarks (and diquarks)

➜ StringFlav:probStoUD = 0.217

exp

�m2

q + p2?

!

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!(1� z)a

z1+ rQ bm2Q

exp

�bm2

?,h

z

!

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Massiv

e end

point

mQmQ

Massive endpoint

• (Note: Peterson etc strictly speaking incompatible with causality in string picture)

๏ with rb~rc~1

•

StringZ:rFactB = 0.855

0 0.2 0.4 0.6 0.8 1

/dx

D>

dnD

1/<n

0

0.5

1

1.5

2

2.5>0.1)

E) (x±*x(D

Pythia 8.183Data from Eur.Phys.J. C16 (2000) 597

ALEPHPY8 (Monash)PY8 (Default)PY8 (Fischer)

bins/N25%χ

0.1±1.4 0.2±2.8 0.2±3.2

V I N

C I

A R

O O

T

Ex0 0.2 0.4 0.6 0.8 1

Theo

ry/D

ata

0.60.8

11.21.4

EX0.2 0.4 0.6 0.8 1

E)/d

X*

dN

(DZh

ad1/

N

0

0.002

0.004

0.006

0.008

0.01

0.012

0.014

0.016

ALEPHHerwig++Sherpa

91 GeV ee Z (hadronic)

mcp

lots

.cer

n.ch

4.1

M e

vent

s≥

Riv

et 1

.8.2

,

Herwig++ 2.6.1a, Sherpa 1.4.1

ALEPH_1999_S4193598

spectrum (particle-level)*+-D

0.2 0.4 0.6 0.8 10.5

1

1.5Ratio to ALEPH

Figure 11: The inclusive D⇤ spectrum in hadronic Z decays [55]. Left: Monash 2013 tune com-pared with default PYTHIA 8 and the Fischer tune. Right: comparison with HERWIG (dashed) andSHERPA (dotted), from MCPLOTS [25]. Note that the plot in the left-hand pane is normalized tounity, while the one in the right-hand pane is normalized to the number of hadronic Z decays.

Monash tune gives a significant improvement in the soft region of the jet-broadening parameters inb-tagged events, while no significant changes are observed for the other event shapes. These smallimprovements are presumably a direct consequence of the softening of the b fragmentation function;it is now less likely to find an isolated ultra-hard B hadron.

We round off the discussion of heavy-quark fragmentation by noting that a similarly comprehen-sive study of charm-quark fragmentation would be desirable. However, charm-quark tagged multi-plicity and event-shape data is not available to our knowledge, and most of the D meson spectra onHEPDATA concern only specific decay chains (hence depend on the decay modeling), and/or are lim-ited to restricted fiducial regions (limiting their generality). Experimentally, the cleanest measurementis obtained from D⇤ decays, and an inclusive momentum spectrum for D⇤ mesons has been measuredby ALEPH [55]. From this distribution, shown in fig. 11, we determine a value for rc of:

StringZ:rFactC = 1.32

We note that the low-x part of the D⇤ spectrum originates from g ! cc̄ shower splittings, whilethe high-x tail represents prompt D⇤ production from leading charm in Z ! cc̄ (see [55] for a nicefigure illustrating this). The intermediate range contains a large component of feed-down from b ! cdecays, hence this distribution is also indirectly sensitive to the b-quark sector. The previous defaulttune had a harder spectrum for both b- and c-fragmentation, leading to an overestimate of the high-xpart of the D⇤ distribution. The undershooting at low xD⇤ values, which remains unchanged in theMonash tune, most likely indicates an underproduction of g ! cc̄ branchings in the shower. We notethat such an underproduction may also be reflected in the LHC data on D⇤ production, see e.g. [65].We return to this issue in the discussion of identified particles at LHC, section 3.5.

17

Z → cc̄

feeddownZ → bb̄

g → cc̄

Baryon Spectra — Conventional String Breaks

7

๏Conventional string breaks: charm string endpoint picks up a light diquark

‣ Spectrum sensitive to the aExtraDiquark parameter.

‣Normally constrained from proton and spectra at LEP (see eg Monash tune paper) ๏ But again, in-situ universality tests probably a very good idea.

‣ Relative rates of spin-3/2 vs spin-1/2 states? (And vs ) ๏ ~ProbQQ1toQQ0 = 0.0275 so spin-1 diquarks very heavily suppressed! ๏ (Note: no flavour dependence here?)

๏Local baryon number conservation in string breaks ๏ Diquark-antidiquark pair must be close in phase space (modulo popcorn!) ๏ Baryon-antibaryon correlations! (LEP measurements hard to recycle today)

Λ

Σ Λ


From Single-Hadron Spectra to Hadron Correlations

13

๏Further precision non-perturbative aspects: How local is hadronisation? •Baryon-Antibaryon correlations — both OPAL measurements were statistics-limited (Kluth); would reach OPAL systematics at 108 Z decays (→ 109 with improved systematics?) •+ Strangeness correlations, pT, spin/helicity correlations (“screwiness”?)

•+ Bose-Einstein Correlations & Fermi-Dirac Correlations ๏ Identical baryons (pp, ΛΛ) highly non-local in string picture — puzzle from LEP; correlations

across multiple exps & for both pp and ΛΛ → Fermi-Dirac radius ~ 0.1 fm rp (Metzger)≪

Leading baryons in g jets? (discriminates between string/cluster models)

High-x baryons

Octet neutralisation? (zero-charge gluon jet with rapidity gaps) → neutrals

Colour reconnections, glueballs, …

q q̄qq q̄q̄ ss̄q q̄ q q̄ q q̄

How local? How local? How local?

(see also FCC-ee QCD workshops & writeups)

The point of MC generators: address more than one hadron at a time!


13





High-x baryons







c


13





High-x baryons







c


13





High-x baryons








13





High-x baryons







vs“popcorn"

Baryon Meson AntibaryonAntibaryonBaryon

Eg:

Junction Baryons

8

๏Junction baryons (e.g, from CR) are expected to be different ‣ In junction fragmentation, two junction legs get combined, one of which can

be a c quark charm diquarks + a quark from a string break.

‣ Radically new possibility. ๏ ~probQQ1toQQ0join = {0.5,0.7,0.9,1.0} really only guesses

๏ But note can be vastly different from that of string-breaks (0.0275)

‣Also junction baryons should be less correlated in momentum space ๏ Junction and antijunction not necessarily so “close" ➤ longer-distance correlations?

→


Controls charm baryons

q

q̄

q̄

q q̄

q q̄

q

(a) Type I: ordinary dipole-style reconnection

q

q̄

q̄

q q̄

q q̄

q

J J̄

(b) Type II: junction-style reconnection

q

q̄

q̄

q q̄

q q̄

qJ J̄

q̄q q̄q

(c) Type III: baryon-style junction reconnection

q

q̄q

q q̄

q

J J̄

q̄q̄

g

gg

g

g

g

g

g

(d) Type IV: zipper-style junction reconnection

Figure 7: The four different allowed reconnection types. Type I (a) is the ordinary string reconnection.Type II (b) is the formation of a connected junction antijunction pair. Type III (c) is the formation ofjunction and antijunction, which are not directly connected. Type IV (d) is similar to type II exceptthat it allows for gluons to be added between the two junctions.

15

Conclusions

9

๏QCD CR probably the most realistic as far as CR goes

‣ But only works in colour space: baryons but no extra strangeness

‣ Junction baryons have different properties (S=3/2/S=1/2, ) & correlations ๏ But theoretical model was not especially formulated for heavy quarks; there is need to look

into the effect of phase-space constraints when “free string energy” gets small ๏ Inadvertent suppression of high-mass states? (Some evidence of that in meson sector. Physical or

unphysical?) And technical issues like failure to find “Junction Rest Frame”?

๏ (Also: personally I never was quite happy with the causality structure ➤ want to revisit time dilation)

๏For strangeness (and flow) expect you need something like ropes

‣Also intend to investigate simple “close packing” model (with J. Altmann, V. Zaccolo)

Σ/Λ


q

q̄

q̄

q q̄

q q̄

q

(a) Type I: ordinary dipole-style reconnection

q

q̄

q̄

q q̄

q q̄

q

J J̄

(b) Type II: junction-style reconnection

q

q̄

q̄

q q̄

q q̄

qJ J̄

q̄q q̄q

(c) Type III: baryon-style junction reconnection

q

q̄q

q q̄

q

J J̄

q̄q̄

g

gg

g

g

g

g

g

(d) Type IV: zipper-style junction reconnection

Figure 7: The four different allowed reconnection types. Type I (a) is the ordinary string reconnection.Type II (b) is the formation of a connected junction antijunction pair. Type III (c) is the formation ofjunction and antijunction, which are not directly connected. Type IV (d) is similar to type II exceptthat it allows for gluons to be added between the two junctions.

15

c c

(Exacerbated for double-

heavy baryons!)

Extra Slide

10

๏Disclaimer: many very recent measurements are of high interest to us; I apologise if this list is not up to date!

‣ Input from S. Mrenna


PYTHIA

No bounds

With surrogate models and HPCs, we can expand the number ofparameters we vary at the LHC

Can/should try to tune hadronization parameters using LHC data

ALICE flavor and hadronization measurements

https://arxiv.org/abs/1709.08522v1 (no Rivet analysis) Fig 1https://arxiv.org/abs/1802.09145v1 (no HepData) Fig 7https://arxiv.org/abs/1708.08745v1 (HepData and Rivet available)https://arxiv.org/abs/1807.11186 (no HepData)https://arxiv.org/abs/1807.11321 (no HepData)https://arxiv.org/abs/1811.01535

10 / 12

ALICE measurements mentioned in our last Pythia tuning meeting

How to approach tuning systematically? Universality Tests

11

๏Systematic Approach to Tuning: Universality Tests + characterisation of any deviations.

‣Do independent tunes for different CM energies find universal parameters?

‣Do independent tunes for different processes find universal parameters?

‣Do independent tunes for different experiments find universal parameters?

‣Do independent tunes for different obervables find universal parameters?

‣Non-universal tune to just one observable. Can the model fit it at all? With what parameters?

๏Provides a more systematic understanding of what the model can and cannot do simultaneously ➤ phrase conclusions in a more physical way ➤ show non-universalities

‣ Professor can help automate (recommend adding 5% TH uncertainty to protect against overfitting.)

๏Some Examples of explicit studies: increasing faith in robustness and universality:

‣ E.g., arXiv:1103.3649 tested MB universality across different CM energies; ๏ Found good universality except for CR strength. Further explored in arXiv:1808.07224.

‣ arXiv:1812.07424 tuned hadronisation parameters at LEP; looked at consistency between different LEP experiments, + with/without event shapes

๏ Rejected a few extreme “outliers” which were inconsistent with bulk of tunes. ๏ Used the rest to define envelope of uncertainties which bracketed the data well.





tuning & modelling uncertainties input from pythia

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