Thermodynamical String Fragmentation with Torbj¨orn Sj¨ostrand – arXiv:1610.09818 Nadine Fischer - November 24th, 2016

Thermodynamical String Fragmentation

with Torbj¨orn Sj¨ostrand – arXiv:1610.09818

Nadine Fischer - November 24th, 2016 MONASHUNIVERSITY & LUNDUNIVERSITY

Motivation

p_?distributions (ratio plots)

1 2 3 4 5 6

0.6 0.81

1.21.4 Pythia 8

Charged hadron p_?at 7 TeV, |h| < 2.4, CMS

MC/Data

0.5 1 1.5 2 2.5 3

0.6 0.81 1.2 1.4

p^±p_?at 7 TeV, |y| < 0.5, ALICE

MC/Data

1 2 3 4 5 6

0.6 0.81 1.2 1.4

p, ¯p p_?at 7 TeV, |y| < 0.5, ALICE

MC/Data

1 2 3 4 5 6

0.60.81 1.2 1.4

K^±p_?at 7 TeV, |y| < 0.5, ALICE

MC/Data

Enhanced strangeness with increasing n_ch

Motivation

p_?distributions (ratio plots)

1 2 3 4 5 6

0.6 0.81

1.21.4 Pythia 8

Charged hadron p_?at 7 TeV, |h| < 2.4, CMS

MC/Data

0.5 1 1.5 2 2.5 3

0.6 0.81 1.2 1.4

p^±p_?at 7 TeV, |y| < 0.5, ALICE

MC/Data

1 2 3 4 5 6

0.6 0.81 1.2 1.4

p, ¯p p_?at 7 TeV, |y| < 0.5, ALICE

MC/Data

1 2 3 4 5 6

0.60.81 1.2 1.4

K^±p_?at 7 TeV, |y| < 0.5, ALICE

p_?[GeV/c]

MC/Data

Enhanced strangeness with increasing n_ch

|< 0.5

|η

〉 /dη Nch

〈d

10 10² 10³

)+π+−πRatio of yields to (

3

10− 2

10− 1

10−

×16)

+ ( +Ω Ω−

×6)

+ ( +Ξ Ξ−

×2) Λ ( Λ+

S

2K0

ALICE = 7 TeV s pp,

= 5.02 TeV sNN

p-Pb,

= 2.76 TeV sNN

Pb-Pb, PYTHIA8 DIPSY EPOS LHC

1/9

Lund String Fragmentation

q q

_ 2 1 3 q q q q

q q q q _

_ _

_

1 2

2 3 1

3

t x Flavour and transverse momentum of hadrons:

• string streched between q¯q

• q¯q moves apart ! energy stored in string ( potential V (r) =  r )

• creation of q_i¯q_ipairs breaks string:

m_{? qi}= 0 on-shell production in single vertex m_{? qi}> 0 tunneling probability

exp⇣

⇡ m²_{? qi}/⌘

= exp⇣

⇡ m²_qi/⌘ exp⇣

⇡ p²_{? qi}/⌘

# #

flavour selection of qi¯qi hp²_{? qi}i = /⇡ = ²

• lots of flavour parameters: – suppression of strangeness and diquarks, ⌘ and ⌘⁰ – rates for different meson multiplets

Thermodynamical String Model

Idea: hadron-level suppression

exp ( m_{? had}/T ) with m_{? had}= q

m²_had+ p²_{? had}

• generate p_{? had} according to

f_had(p_{? had})d p_{? had}= exp ( p_{? had}/T )d p_{? had}

• fourier transformation to obtain quark-level distribution

fq(p_{? q})/ Z₁

0

b J0(b p_{? q}/T ) (1 + b²)^3/4 d b



fit: N exp( c p_{? q}/T ) (p_{? q}/T )^d

• pick hadron flavour according to P_had= exp ( m_{? had}/T ) + multiplicative factors for spin-counting, SU(6) symmetry factors, ..

• heavier hadrons obtain more p_?

• 3free parameters in total

3/9

Close-Packing of Strings

Idea: more MPIs ) closer packing of strings

• transverse region shrinks ) larger string tension

• guess momentum of next hadron, based on average quantities

• nstring = number of strings that cross hadron rapidity

• effective number of strings n^eff_string= 1 + n_string 1 1 + p²_{? had}/ p²_{? 0}

• modify Gaussian width ! ⇣ n^eff_string⌘r

(similar for temperature)

Close-Packing of Strings

Idea: more MPIs ) closer packing of strings

• transverse region shrinks ) larger string tension

• guess momentum of next hadron, based on average quantities

• nstring = number of strings that cross hadron rapidity

• effective number of strings n^eff_string= 1 + n_string 1 1 + p²_{? had}/ p²_{? 0}

• modify Gaussian width ! ⇣ n^eff_string⌘r

(similar for temperature)

default (n^eff_string)^0.25s

5 10 15 20 25 30 35 40 45 50

0 0.1 0.2 0.3 0.4 0.5 0.6

hp?i vs. nchin toy model (2–8 strings, Â E = 1 TeV)

nch hp?i[GeV/c]

4/9

Hadron Rescattering

Idea: dense hadronic gas ) hadrons might rescatter on the way out Find hadron pairs that can scatter:

• cut on the invariant mass of the hadron pair minv<q

m²₁+|~pmax|²+q

m²₂+|~pmax|²

• rescattering probability: overall probability · probability for same-string

m a x P^{m a x}

P

d s d s

max P^max

P

ij ij ij min P_ss^min

ss ss

• in CoM frame rotate around angles chosen flat in d ⌦

Hadron Rescattering

Idea: dense hadronic gas ) hadrons might rescatter on the way out Find hadron pairs that can scatter:

• cut on the invariant mass of the hadron pair minv<q

m²₁+|~pmax|²+q

m²₂+|~pmax|²

• rescattering probability: overall probability · probability for same-string

m a x P^{m a x}

P

d s d s

max P^max

P

ij ij ij min P_ss^min

ss ss

• in CoM frame rotate around angles chosen flat in d ⌦

Gaussian p_?wo hadron scattering Gaussian p_?w hadron scattering 0.2

0.25 0.3 0.35 0.4 0.45 0.5 0.55 0.6 0.65

hp?i for different hadrons in toy model (5 strings with E = mZ)

p K h, h⁰ r, w K^⇤ f p,n L, S X D S^⇤ X^⇤ W hp?i[GeV/c]

5/9

Results

Transverse momentum distributions: inclusive and pions

CMS data default Gaussian p? Thermal p?

10⁴ 10³ 10² 10¹ 1 10¹

Charged hadron p?at 7 TeV,|h| <2.4

(1/2pp?)d2nchdhdp?

1 2 3 4 5 6

0.6 0.8 1 1.2 1.4

p?[GeV/c]

MC/Data

ALICE data default Gaussian p? Thermal p?

10¹ 1 10¹

p^±transverse momentum at 7 TeV,|y| <0.5

1/Nineld2Ndydp?

0.5 1 1.5 2 2.5 3

0.6 0.8 1 1.2 1.4

p?[GeV/c]

MC/Data

Results

Transverse momentum distributions: protons and kaons

ALICE data default Gaussian p? Thermal p?

10⁴ 10³ 10² 10¹

p, ¯p transverse momentum at 7 TeV,|y| <0.5

1/Nineld2Ndydp?

1 2 3 4 5 6

0.6 0.8 1 1.2 1.4

p?[GeV/c]

MC/Data

ALICE data default Gaussian p? Thermal p?

10³ 10² 10¹ 1

K^±transverse momentum at 7 TeV,|y| <0.5

1/Nineld2Ndydp?

1 2 3 4 5 6

0.6 0.8 1 1.2 1.4

p?[GeV/c]

MC/Data

7/9

Results

Enhanced strangeness with increasing nch

2K⁰_S

2 · (L + L)

6 · (X + X⁺)

16 · (W + W⁺) default

Gaussian p_? Thermal p_? 10 ³

10 ² 10 ¹

Ratio of yields to (p⁺+ p )at 7 TeV, |h| < 0.5

Ratioofyields

|< 0.5

|η

η〉

ch/d N

〈d

10 10² 10³

)+π+−πRatio of yields to (

−3 10 2 10−

−1 10

×16) + ( +Ω Ω−

6)

× + ( Ξ

−+ Ξ

2)

× ( Λ + Λ

S 2K0

ALICE = 7 TeV s pp,

= 5.02 TeV sNN p-Pb,

= 2.76 TeV sNN Pb-Pb, PYTHIA8 DIPSY EPOS LHC

Summary and Outlook

What is new?

• option for generating p_{? had} according to exp( p_{? had}/T ) with flavour selection according to exp( m_{? had}/T )

• effect of close-packing of strings

• simple model for hadron rescattering What does it do?

• improves some observables, such as p_?spectra, hp_?i(mhad)

• does not improve everything, e.g. kaon p_?remains difficult

• hadron decays are a limiting factor

Further work required!

• microscopic tracing of the full space-time evolution (partons and hadrons, production and decay vertices)

• more detailed understanding and modelling

9/9

Summary and Outlook

What is new?

• option for generating p_{? had} according to exp( p_{? had}/T ) with flavour selection according to exp( m_{? had}/T )

• effect of close-packing of strings

• simple model for hadron rescattering What does it do?

• improves some observables, such as p_?spectra, hp_?i(mhad)

• does not improve everything, e.g. kaon p_?remains difficult

• hadron decays are a limiting factor Further work required!

• microscopic tracing of the full space-time evolution (partons and hadrons, production and decay vertices)

• more detailed understanding and modelling

Backup

10/9

Flavour Asymmetry in Thermodynamical Model

Toy model with d and s quarks only

• (d ! s) competes with (d ! d) ! d¯s obtains larger p?

• (s ! d) competes with (s ! s) ! s¯d obtains smaller p?

(d ! s) with hp?i = 0.46 (s ! d) with hp?i = 0.41

0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8

Same T for (d ! s) and (s ! d) transitions

1/NdN/dp?

0 0.5 1 1.5 2

0.60.81 1.2 1.4

p_?[GeV/c]

(s!d)/(d!s)

(d ! s) with hp?i = 0.46 (s ! d) with hp?i = 0.46

0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8

Different T for (d ! s) and (s ! d) transitions

1/NdN/dp?

0 0.5 1 1.5 2

0.60.81 1.2 1.4

p_?[GeV/c]

(s!d)/(d!s)

Rapidity Distributions

-10 -5 0 5 10

0 2 4 6 8

10Rapidity distribution of the strings in an event

y nstring

-10 -5 0 5 10

0 2 4 6 8

10Rapidity distribution of the strings in an event

y nstring

12/9

Limiting factor: Decays

pion transverse momentum @ LHC, with and without decays, similar for protons

Gaussian p?wo decays Gaussian p_?w decays Termal p_?wo decays Termal p_?w decays

0 0.5 1 1.5 2

0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8

2p^±transverse momentum at LHC

p?[GeV/c]

1/NdN/dp?

0.60.81

1.21.4 w/wo (Gaussian)

ratio

0.60.81

1.21.4 w/wo (Thermal)

ratio

0.60.81

1.21.4 Thermal/Gaussian (wo)

ratio

0 0.5 1 1.5 2

0.60.81

1.21.4 Thermal/Gaussian (w)

p?[GeV/c]

ratio

) decays wash out effects present after fragmentation

Hadron Rescattering

hp?i in toy model ( 5 strings with E = mZon the z axis)

Gaussian p?wo hadron scattering Gaussian p?w hadron scattering 0.2

0.25 0.3 0.35 0.4 0.45 0.5 0.55 0.6 0.65

hp?ifor different hadron species

hp?i[GeV/c]

0.70.8 0.91.0 1.11.2 1.31.4

p K h, h⁰ r, w K^⇤ f p,n L, S X D S^⇤ X^⇤ W

w/wo

Termal p?wo hadron scattering Termal p?w hadron scattering 0.2

0.25 0.3 0.35 0.4 0.45 0.5 0.55 0.6 0.65

hp?ifor different hadron species

hp?i[GeV/c]

0.70.8 0.91.0 1.11.2 1.31.4

p K h, h⁰ r, w K^⇤ f p,n L, S X D S^⇤ X^⇤ W

w/wo

14/9

Results

Average transverse momentum: as a function of nchand mhad

ATLAS data default Gaussian p? Thermal p? 0.1

0.2 0.3 0.4 0.5 0.6 0.7

0.8Ch.hp?ivs. nchat 7 TeV, p? track>100 MeV, nch 2,|h| <2.5

hp?i[GeV/c]

20 40 60 80 100 120 140 160 180 200

0.9 0.95 1.0 1.05

nch

MC/Data

p⁺ K⁺

K^{⇤ 0} p

f X

S^{⇤ ±} X^{⇤ 0} W ALICE data

default Gaussian p? Thermal p?

1

Mean transverse momentum vs. mass at 7 TeV,|y| <0.5

hp?i[GeV/c]

0.2 0.4 0.6 0.8 1 1.2 1.4 1.6

0.7 0.8 0.9 1.0 1.1 1.2 1.3

m [GeV/c²]

MC/Data