Inclusion of the P0 model in PYTHIA 8€¦ · Inclusion of the 3P 0model in PYTHIA 8 Tuesday9th April 2019, DIS 2019, Torino 2 Stringfragmentationandthe 3P 0model of polarized fragmentation

Inclusion of the 3P0 model in PYTHIA 8

Albi Kerbizi(*) and Leif Lönnblad(**)

(*)University of Trieste and INFN(**)Lund University

Tuesday 9th April 2019,DIS 2019, Torino

1

Inclusion of the 3P0 model in PYTHIA 8

Tuesday 9th April 2019,DIS 2019, Torino

2

String fragmentation and the 3P0 model of polarizedfragmentation

Interface with PYTHIA 8

Comparison with the results from the stand alone 3P0 MC

SIDIS: Implementation of transversity

Collins asymmetry for p and d

Outlook

- In the Symmetric Lund Model (SLM) the hadronization process is the left-right symmetric decay of a relativistic string by tunnelling of !"! pairs

- The string decay is simulated repeating recursively the splitting ! → ℎ + !′- The hadronization process in PYTHIA is based on this model- The quark spin is presently neglected in hadronization in PYTHIA and in the other

event generators while it is well known that it is at the origin of important effects- It can be introduced using a model for the fragmentation of a polarized quark

A. Kerbizi - DIS2019 3

Symmetric Lund Model

- For an initial quark with transverse polarization, this is a model for the Collins effect

h1

k3T

-k3T k2T

-k2T

h2h3

q1 = qAq3

q2

L2L3

q3

q2q4

L4

b)

kT

qL

z

x

y

-kT

a) qd

h1

k3T

-k3T k2T

-k2T

h2h3

q1 = qAq3

q2

L2L3

q3

q2q4

L4

b)

kT

qL

z

x

y

-kT

a) qd


The 3P0 model

-The !"! pair at string breaking is produced in the 3P0 state, i.e. L=1, S=1 and J=0

#$Pi-

#% &


The 3P0 model

The quantum mechanical formalism has been explicitly written down and implemented in a stand alone Monte Carlo one year ago

AK, X. Artru, Z. Belghobsi, F. Bradamante and A. Martin, PRD97 (2018) no.7, 074010AK, X. Artru, Z. Belghobsi and A. Martin, arXiv:1903.01736


The polarized splitting in the 3P0 model

the fragmenting quark polarization is encoded in the !×! spin density matrixρ q = (1 + ) ⋅ +,)/2

the leftover quark q’ polarization is encoded in 0 1′

we restrict to pseudo-scalar mesons

- Each polarized splitting is described by a polarized splitting function 34564(7, 9:; <4) whichgives the probability that h is emitted with longitudinal momentum fraction 7 = =>/?>and transverse momentum 9: (referred to the string axis)

- The polarized splitting function is derived by a left-right symmetric 3P0 splitting matrix@4564 as

F,5B,(Z, DE; +,) = tr T,5B,ρ q T,5B,I

DJ = KJ − KEM

- The spin density matrix of 1M is

ρ qM =T,5B,ρ q T,5B,

I

tr T,5B,ρ q T,5B,I


The polarized splitting function in the 3P0 model

The free parameters of the model are:- !" = 0.5 '()*+: linked to the probability of having a string cutting point- !, = 5.17 '()*+: suppression of 010 transverse momentum- 2 = 0.9: suppression of large 4→ fixed comparing the stand alone simulation results with p7+ distributions fromCOMPASSandwithunpolarized FFs extracted fromglobalfits

- T = 0.42 + i0.76 GeV: complex mass responsible for the Collins effect→ [\(T)/|T| fixed from comparison with aba* Collins asymmetries→ T +determined from the slope of the unpolarized c,+ distributions for c,+ → 0

The polarized splitting function is

def,h,e = iefhe+ 1 − 4

kh+

l(*mnop

q/r

sl(kh+)

!,+

t(*muvw

f q

1 + !, T + [ T+ + vy7

+ − 2[\ T z ⋅ (|}×v7y )]

as in the Lund Model implemented in PYTHIA

term arising from the 3P0mechanism→ the spin effects are parametrizedby one complex parameter → Ä(plays the role of a complex mass)

Details and results in arXiv:1903.01736


Interface of the 3P0 model with PYTHIA 8

- The 3P0 model has been interfaced for the first time with PYTHIA

- The interface consists of a C++ header file and of a Fortran module

- It is implemented for DIS processes

- Presently- parton showers and multiple interactions are switched off- primordial !" is switched off- only pseudoscalar mesons are produced (the only spiecies

currently treated according to the 3P0 mechanism)

9

!

target

!" #

How the interface works

g*

$$′

- PYTHIA generates a DIS event

A. Kerbizi - DIS2019

10

!

target

!!


g*

""′

- PYTHIA sets up a string between the struck quark q and the remnant qq- We boost the system in the string rest frame


11

target

("")


g*

$$′

- PYTHIA sets up a string between the struck quark q and the remnant qq- We boost the system in the string rest frame- We choose the polarization of the active quark &'


q(&(, *+)

12

target

("")


g*

$$′

We force hadronization to evolve from the quark side to the remnant side


q(&', )*)

13

q("#, %&)

target

((()

ℎ*(+*)


- PYTHIA emits a first hadron h1 by generating a (, -(, pair → from p1 wecalculate the momentum of q2

- We accept the hadron according to the 3P0 weight

/ "#, 0,1 =12 1 −

2 Im 8 "# ⋅ ;̂×0,18 , + 0,1,

- w ≃ Prob(DPE spin effects. )/Prob no spin effects.

?

g*

88′

(,("R, 0S&)


14

!(#$, &')

target

()))

ℎ+(,+)


- If accepted, h1 is stored in the event record otherwise a new h1 is tried- The spin density matrix of q2 is calculated according to the 3P0 rules

✓

g*

--′

)/(#$0, 12')


15

target

("")

ℎ%(&%)


- The hadronization chain continues with the emission of further hadronsuntil the energy of the remaining string piece is sufficient to produce onlythe last two hadrons that join the quark jet with the remant jet

q('(, *+)

ℎ,(&,)",

ℎ-.,(&-.,)?

g*

00′

✓✓✓ …


16

target

("")

ℎ%(&%)


- The hadronization chain continues with the emission of further hadronsuntil the energy of the remaining string piece is sufficient to produce onlythe last two hadrons that join the quark jet with the remant jet

- The exit condition is handled by PYTHIA without calling the 3P0 mechanism→ the last two hadrons are generated «unpolarized»

q((), +,)

ℎ-(&-)"-

ℎ./-(&./-)ℎ./%ℎ.

X

g*

11′

…


17

Results from simulations

- We generate DIS events with

!"# $%&/( muons off a p or n target at rest → COMPASS kinematics

3P0 settings:

StringZ: aLund = 0.9, StringZ: bLund = 0.5 GeV@A,StringPT: sigma = 0.38 GeV@H, I = 0.42 + i0.76 GeV

Cuts on events:

O > 5.0 GeV, 0.2 < y < 0.9, QA > 1.0 GeVA


hz0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

coun

ts

1

10

210

310

0P3stand alone 0P3Pythia+ (std settings)0P3Pythia+

positive hadronshz

)2 (GeV2TP

0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2

coun

ts

1

10

210

310


positive hadrons2T

p

hz0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

coun

ts

1

10

210

310


negative hadronshz

)2 (GeV2TP

0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2

coun

ts

1

10

210

310 0P3stand alone 0P3Pythia+ (std settings)0P3Pythia+

negative hadrons2T

p

18

Comparison between Pythia + 3P0 and stand alone 3P0:!" and #$% distributions

- Same distributions in stand alone 3P0 MC and Pythia + 3P0 apart from some differences atsmall zh due to the different exit conditions

- p'( is slightly smaller for PYTHIA with default setting

)* > 0.1 /01/3

!" > 0.2


stand alone MC: u jetsPYTHIA + 3P0 with 3P0settingPYTHIA + 3P0 with default setting

For comparison withthe stand alone MConly (ud)0---u stringsIn PYTHIA

19

Comparison between Pythia + 3P0 and stand alone 3P0:Collins and di-hadron analysing powers

- Only transversely polarized u quarks- Same spin effects!!

Collins analysing power defined as

!"↑→%&' = 2⟨sinϕ/⟩ϕ/ = ϕ1 − ϕ34

di-hadron analysing power definedas!"↑→%5%6&' = 2 sin ϕ78 − ϕ34

79 = (z<p>9 − ?>p<9)/z

hz0.2 0.4 0.6 0.8

h+

X®u a

0.5-

0

0.5

0P3 Pythia + +p0P3 Pythia + -p

0P3 stand alone +p0P3 stand alone -p

(GeV/c)T

p0.5 1

h+

X®u a

0.5-

0

0.5

z0.2 0.4 0.6 0.8

+X

2h 1 h

®u a

0.8-0.6-0.4-0.2-

00.20.40.60.8 0P3 Pythia + -p +p

0P3 stand alone -p +p

)2 (GeV/cppM0.5 1 1.5

+X

2h 1 h

®u a

0.8-0.6-0.4-0.2-

00.20.40.60.8

?% > 0.2EF > 0.1 HIJ/K ?%L > 0.1, NF > 0.07 (HIJK )

? = ?%> + ?%<



The interface has been validated → the 3P0 model iscorrectly implemented in PYTHIA for DIS


The interface has been validated → the 3P0 model iscorrectly implemented in PYTHIA for DIS

as first exercise → implementation of transversity

!"#!′"#

% − %′ plane

'(

22

Implementation of transversity

Bx3-10 2-10 1-10

q 1xh

0.4-

0.3-

0.2-

0.1-

0

0.1

0.2

0.3

0.4

vu

vd

!ℎ#$ ! = 3.2 !#.) 1 − ! ,

!ℎ#- ! = −4.6 !#.,, 1 − ! ,

To implement the effects of the transversity PDF h#1

a. calculate the polarization of the active quark q = u,dbefore hard scattering

213 =h#1f#1 235

235 is the polarization vector of the nucleon in the GNS

b. assign to the fragmenting quark the polarizationvector

2′13 = D88 [213 − 2 (213 ⋅ <=)<=]D88 = (1 − y)/(1 − y + yC/2)

- For this exercise parametrization DEF → from A. Martin et al, PRD91 (2015) no.1, 014034

- Parametrization of f#1 → CTEQ5L LO (default in PYTHIA)


<=

23

Collins asymmetry for proton from Pythia + 3P0

Bx3-10 2-10 1-10

p Col

lA

0.1-

0.05-

0

0.05

0.1 +p-p

hz0.2 0.4 0.6 0.8

h+

X®u a

0.1-

0.05-

0

0.05

0.1

(GeV/c)T

p0.5 1

h+

X®u a

0.1-

0.05-

0

0.05

0.1

COMPASS PLB744 (2015) 250-259

PYTHIA + 3P0Collins asymmetry in SIDIS for a protontarget:

!"#$$% =∑()*,, -(. /ℎ1( 21(3∑( -(. /41( 51(3

- PYTHIA +3P0 reproduces the trends of the Collins asymmetry seen in data asfunction of 67 and 89

- As function of :3 the trends are different at mid :3 → remainder: onlypseudoscalar mesons!!

<= > 0.1 B-C/E :3 > 0.2


24

di-hadron asymmetry for proton from Pythia + 3P0

COMPASS PLB 736 (2014) 124-131

Bx3-10 2-10 1-10

>qsi

nU

T,pRSf

sin

<A

0.1-

0.05-

0

0.05

0.1

z0.2 0.4 0.6 0.8

+X

2h 1 h

®u a

0.1-

0.05-

0

0.05

0.1

)2 (GeV/cppM0.5 1 1.5

+X

2h 1 h

®u a

0.1-

0.05-

0

0.05

0.1

di-hadron asymmetry in SIDIS for a protontarget:

!"#$ =∑'(),+ ,'" ℎ.' /.'#0#1∑' ,'" 2.' 3.'

#0#1

Similar trends as the measuredasymmetry

→ again: only pseudoscalar mesons here!!

PYTHIA + 3P0

5#6 > 0.1, ;< > 0.07 (?,@A )A. Kerbizi - DIS2019

25

Collins asymmetry for deuteron from Pythia + 3P0

COMPASS PLB673 (2009) 127-135

Bx3-10 2-10 1-10

d Col

lA

0.1-

0.05-

0

0.05

0.1 +p-p

hz0.2 0.4 0.6 0.8

h+

X®u a

0.1-

0.05-

0

0.05

0.1

(GeV/c)T

p0.5 1

h+

X®u a

0.1-

0.05-

0

0.05

0.1

PYTHIA + 3P0Collins asymmetry in SIDIS for d=p+ntarget:

!"#$$% ≃ ℎ() + ℎ(%+(, + +(%

4.()/0 + .(%/041(,0 + 1(,0

- PYTHIA+3P0 predicts a very small Collins asymmetry for deuteron as in the data (some effects at large xB)

- It is due to cancellations between ℎ()and ℎ(% in the asymmetry

23 > 0.1 89:/< => > 0.2


26

di-hadron asymmetry for deuteron from Pythia + 3P0ñ

q s

in

UT,dRS

fsi

n Aá

x z ]2c [GeV/hhM-210 -110 1

-0.15

-0.1

-0.05

0

0.05

0.2 0.4 0.6 0.8

-0.15

-0.1

-0.05

0

0.05

0.5 1 1.5 2

-0.15

-0.1

-0.05

0

0.05

ñq

sin

UT,pRS

fsi

n Aá

x z ]2c [GeV/hhM-210 -110 1

-0.15

-0.1

-0.05

0

0.05

0.2 0.4 0.6 0.8

-0.15

-0.1

-0.05

0

0.05

0.5 1 1.5 2

-0.15

-0.1

-0.05

0

0.05

COMPASS PLB 713 (2012) 10-16

Bx3-10 2-10 1-10

>qsi

nU

T,dRSf

sin

<A

0.1-

0.05-

0

0.05

0.1

z0.2 0.4 0.6 0.8

+X

2h 1 h

®u a

0.1-

0.05-

0

0.05

0.1

)2 (GeV/cppM0.5 1 1.5

+X

2h 1 h

®u a0.1-

0.05-

0

0.05

0.1PYTHIA + 3P0

The di-hadron asymmetry in SIDIS for a d target is

!"#$ = ℎ'( + ℎ'$*'+ + *'$

4-'(#.#/ + -'$#.#/40'+

#.#/ + 0'+#.#/

- Very small asymmetry as in data (some effect at large 12)

3#4 > 0.1, :; > 0.07 (>?@A )A. Kerbizi - DIS2019

!"

27

A different option for the final state in PYTHIA + 3P0


An other possible option is to allow PYTHIA generate all hadron types (vectormesons, baryons,..) but disabling spin effects when the first non pseudo-scalar hadron produced

target

#$ %

&%

#((), +,)

&.… 0%

X !2

Has still some Collins effect due to 3,4

g*

55′

&.&7

28

A different option for the final state in PYTHIA + 3P0


An other possible option is to allow PYTHIA generate all hadron types (vectormesons, baryons,..) but disabling spin effects when the first non pseudo-scalar hadron produced

Bx3-10 2-10 1-10

p Col

lA

0.1-

0.05-

0

0.05

0.1

hz0.2 0.4 0.6 0.8

h+

X®u a

0.1-

0.05-

0

0.05

0.1 (only pseudo-scalar mesons)+p (only pseudo-scalar mesons)-p (full final state and decay)+p (full final state and decay)-p

(GeV/c)T

p0.5 1

h+

X®u a

0.1-

0.05-

0

0.05

0.1 - Strong effect on the Collins asymmetry

- A retuning of the complex mass ! seemsto be needed

- For the first time the quark spin has been implemented in the hadronization in PYTHIA by interfacing the 3P0 model with PYTHIA 8

- The results are very promising!

- Already now it is possible to perform multi dimensional studies, compare with data and make predictions for future measurements, …

A write-up is in preparation and PYTHIA + 3P0 model will be available soon

... and of course this is not the end of the story!!


Conclusions

This work was supported by the LDRD project «Phenomenological study of hadronization innuclear and high-energy physics experiments».

Documents

Inclusion of the P0 model in PYTHIA 8€¦ · Inclusion of the 3P 0model in PYTHIA 8 Tuesday9th April 2019, DIS 2019, Torino 2 Stringfragmentationandthe 3P 0model of polarized fragmentation