Thermodynamical String Fragmentation with Torbjörn Sjöstrand arxiv:60.0988 Nadine Fischer - November 24th, 206 MONASH UNIVERSITY & LUND UNIVERSITY
Motivation p? distributions (ratio plots).4.2.4.2.4.2.4.2 Charged hadron p? at 7 TeV, h < 2.4, CMS Pythia 8 2 3 4 5 6 p ± p? at 7 TeV, y < 0.5, ALICE 0.5.5 2 2.5 3 p, p p? at 7 TeV, y < 0.5, ALICE 2 3 4 5 6 K ± p? at 7 TeV, y < 0.5, ALICE 2 3 4 5 6 p? [GeV/c] /9
Motivation p? distributions (ratio plots) Enhanced strangeness with increasing n ch.4.2.4.2 Charged hadron p? at 7 TeV, h < 2.4, CMS Pythia 8 2 3 4 5 6 p ± p? at 7 TeV, y < 0.5, ALICE 0.5.5 2 2.5 3 Ratio of yields to (π +π + ) 0 0 2KS Λ+Λ ( 2) + Ξ +Ξ ( 6).4.2.4.2 p, p p? at 7 TeV, y < 0.5, ALICE 2 3 4 5 6 K ± p? at 7 TeV, y < 0.5, ALICE 2 3 4 5 6 p? [GeV/c] 2 0 3 0 0 2 + Ω +Ω ( 6) ALICE pp, s = 7 TeV p-pb, s NN = 5.02 TeV Pb-Pb, s NN = 2.76 TeV PYTHIA8 DIPSY EPOS LHC 0 0 dn /dη ch 3 η < 0.5 /9
Lund String Fragmentation Flavour and transverse momentum of hadrons: string streched between q q _ q q 3 _ q q _ q q 2 3 2 _ qq q q moves apart! energy stored in string ( potential V (r) =appler ) 3 2 creation of q i q i pairs breaks string: m? qi =0 m? qi > 0 on-shell production in single vertex tunneling probability exp m 2? q i /apple =exp m 2 q i /apple exp # # q _ q p 2? q i /apple flavour selection of q i q i hp 2? q i i = apple/ = 2 t x lots of flavour parameters: suppression of strangeness and diquarks, and 0 O(20) free parameters in total rates for different meson multiplets 2/9
Thermodynamical String Model Idea: hadron-level suppression exp ( m? had /T ) with m? had = q m 2 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 Z bj 0 (bp? q /T ) f q(p? q ) / 0 ( + b 2 ) 3/4 d b apple fit: N exp( cp? 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? 3 free 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 n string = number of strings that cross hadron rapidity effective number of strings n eff string =+ n string +p 2? had /p2? 0 r modify Gaussian width! nstring eff (similar for temperature) 4/9
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 n string = number of strings that cross hadron rapidity effective number of strings n eff string =+ n string +p 2? had /p2? 0 r modify Gaussian width! nstring eff (similar for temperature) hp? i vs. n ch in toy model (2 8 strings, Â E = TeV) hp? i [GeV/c] 0.5 0.4 0.3 0.2 0. default (n eff string )0.25 s 0 5 0 5 20 25 30 35 40 45 50 n ch 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 m inv < q q m 2 + ~p max 2 + m 2 2 + ~p max 2 rescattering probability: overall probability probability for same-string P max ds P ds P max ss P ss P min ss max min ij max ij ij in CoM frame rotate around angles chosen flat in d 5/9
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 m inv < q q m 2 + ~p max 2 + m 2 2 + ~p max 2 rescattering probability: overall probability probability for same-string P max ds P ds P max ss P ss P min ss max min ij max ij ij in CoM frame rotate around angles chosen flat in d hp?i [GeV/c] 5 0.55 0.5 0.45 0.4 0.35 0.3 0.25 0.2 hp?i for different hadrons in toy model (5 strings with E = mz) Gaussian p? wo hadron scattering Gaussian p? whadronscattering p K h, h 0 r, w K f p,n L, S X D S X W 5/9
Results Transverse momentum distributions: inclusive and pions (/2pp?) d 2 nch dh dp? 0 Charged hadron p? at 7 TeV, h < 2.4 0 0 2 0 3 CMS data default Gaussian p? Thermal p? /N inel d 2 N dy dp? 0 0 p ± transverse momentum at 7 TeV, y < 0.5 ALICE data default Gaussian p? Thermal p? 0 4.4.2 2 3 4 5 6 p? [GeV/c].4.2 0.5.5 2 2.5 3 p? [GeV/c] 6/9
Results Transverse momentum distributions: protons and kaons /N inel d 2 N dy dp? 0 0 2 p, p transverse momentum at 7 TeV, y < 0.5 ALICE data default Gaussian p? Thermal p? /N inel d 2 N dy dp? 0 0 2 K ± transverse momentum at 7 TeV, y < 0.5 ALICE data default Gaussian p? Thermal p? 0 3 0 3 0 4.4.2 2 3 4 5 6 p? [GeV/c].4.2 2 3 4 5 6 p? [GeV/c] 7/9
Results Enhanced strangeness with increasing n ch Ratio of yields to (p + + p ) at 7 TeV, h < 0.5 Ratio of yields 0 2K 0 S 2 (L + L) Ratio of yields to (π +π + ) 0 0 2KS Λ+Λ ( 2) + Ξ +Ξ ( 6) 6 (X + X + ) 0 2 2 0 + Ω +Ω ( 6) 0 3 default Gaussian p? Thermal p? 6 (W + W + ) 3 0 0 ALICE pp, s = 7 TeV p-pb, s NN = 5.02 TeV Pb-Pb, s NN = 2.76 TeV PYTHIA8 DIPSY EPOS LHC 2 0 0 dn /dη ch 3 η < 0.5 0 n ch 8/9
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(m had ) does not improve everything, e.g. kaon p? remains difficult hadron decays are a limiting factor 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(m had ) 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
Backup 0/9
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? /N dn/dp? (s! d) / (d! s).8.6.4.2 0.4 0.2 0.4 Same T for (d! s) and (s! d) transitions (d! s) with hp? i = 0.46 (s! d) with hp? i = 0.4.2 0 0.5.5 2 p? [GeV/c] /N dn/dp? (s! d) / (d! s).8.6.4.2 0.4 0.2 0.4 Different T for (d! s) and (s! d) transitions (d! s) with hp? i = 0.46 (s! d) with hp? i = 0.46.2 0 0.5.5 2 p? [GeV/c] /9
Rapidity Distributions nstring Rapidity distribution of the strings in an event 0 8 nstring Rapidity distribution of the strings in an event 0 8 6 6 4 4 2 2 0-0 -5 0 5 0 y 0-0 -5 0 5 0 y 2/9
Limiting factor: Decays pion transverse momentum @ LHC, with and without decays, similar for protons /N dn/dp? p ± transverse momentum at LHC 2.8.6.4.2 0.4 0.2 Gaussian p? wo decays Gaussian p? wdecays Termal p? wo decays Termal p? wdecays 0 0.5.5 2 p? [GeV/c] ratio ratio ratio ratio.4 w/wo (Gaussian).2.4 w/wo (Thermal).2.4 Thermal/Gaussian (wo).2.4 Thermal/Gaussian (w).2 0 0.5.5 2 p? [GeV/c] ) decays wash out effects present after fragmentation 3/9
Hadron Rescattering hp? i in toy model ( 5 strings with E = m Z on the z axis) hp?i [GeV/c] w/wo 5 0.55 0.5 0.45 0.4 0.35 0.3 0.25 0.2.4.3.2..0 0.9 0.7 hp?i for different hadron species Gaussian p? wo hadron scattering Gaussian p? whadronscattering p K h, h 0 r, w K f p,n L, S X D S X W hp?i [GeV/c] w/wo 5 0.55 0.5 0.45 0.4 0.35 0.3 0.25 0.2.4.3.2..0 0.9 0.7 hp?i for different hadron species Termal p? wo hadron scattering Termal p? whadronscattering p K h, h 0 r, w K f p,n L, S X D S X W 4/9
Results Average transverse momentum: as a function of n ch and m had hp?i [GeV/c] Ch. hp?i vs. n ch at 7 TeV, p? track > 00 MeV, n ch 2, h < 2.5 0.7 0.5 0.4 0.3 0.2 0. ATLAS data default Gaussian p? Thermal p? hp?i [GeV/c] Mean transverse momentum vs. mass at 7 TeV, y < 0.5 p + ALICE data default Gaussian p? Thermal p? K + K 0 p f X S ± X 0 W.3.05.0 0.95 0.9 20 40 60 80 00 20 40 60 80 200 n ch.2..0 0.9 0.7 0.2 0.4.2.4.6 m [GeV/c 2 ] 5/9