Heavy flavour in Pythia 8 Heavy flavour in showers only

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1 Heavy flavour in Pythia 8 Heavy flavour in showers only Stefan Prestel Heavy Flavour Production at the LHC IPPP Durham, April 2, 206 / 8

2 Outline This will be a review of some heavy flavour aspects of Pythia 8:. Parton shower initial state / final state 2. Matching & merging 3. Hadronization and particle decay.

3 Sources of mass effects in parton showers (a) Radiator masses, emission mass (e.g. tabulated in Nucl.Phys. B603 (200) ) (b) Recoiler mass, virtuality, dipole mass (c) Kinematics General belief: Parton shower should always reduce to DGLAP in the (pseudo)-collinear limit.. But keep in mind: We need to set up kinematics. Not all gluons can split into quarks! DGLAP kernels capture the phase space constraints only in particular phase space limits. Comments: DGLAP kernels contain divergences in the anti-collinear direction, which has to be removed by hand Angular ordering, dipole showers Expected differences: Different z-definitions, evolution-p, phase space factorization all give different mass effects. 3 / 8

4 Heavy flavour in ISR (I) For heavy initial quarks, ISR is split into two regions:. Above km 2 Q. Between m 2 Q < p 2 < km2 Q Above km 2 Q - Massless kernels (possibly with massless ME correction) - Massive kinematics 4 / 8

5 Heavy flavour in ISR (II) For heavy initial quarks, ISR is split into two regions:. Above km 2 Q. Between m 2 Q < p 2 < km2 Q Between m 2 Q < p 2 < km2 Q (k = 4) - Forced evolution of b-quark with only g b b conversion. No gluon radiation off b-quark. - Massive kernel - Conversion forced around threshold. Pythia will always produce a final state b-quark!. Does this have an effect? 5 / 8

6 Heavy flavour in ISR: Theory results Figure (p of b-quark in b b Z, boosted Z) taken from arxiv:4364 [hep-ph] by Nagy, Soper 6 / 8

7 Heavy flavour in ISR: Realistic results dσ(zbb)/dm(b, b) [pb/gev] 0 3 Z+ 2 b-jets Data small conversion window dσ(zbb)/d R(b, b) [pb] Z+ 2 b-jets Data small conversion window MC/Data m(b, b) [GeV] MC/Data R(b, b) Variation of b-conversion window: Default uses k = 4, small window uses k =.0 7 / 8

8 Heavy flavour in ISR: Realistic results p of b hadron in leading b jet 0 2 small conversion window Ratio p b [GeV] Variation of b-conversion window: Default uses k = (2) 2, small window uses k = (.) 2 8 / 8

9 Heavy flavour in FSR (I) Mass effects in FSR come from three sources: (a) Matrix element corrections (mostly V-emission, BSM showers) Removing ME corrections can mean no mass effects! (b) g b b splitting (c) Massive recoilers in g gg splittings The construction of g b b allows choices: Evolution variable can be different from g-emission case Energy sharing variable can be different from g-emission case Effect of finite dipole mass (phase space boundaries)? Argument of running coupling? Recent suggestion by Thaler, Maltoni and Selvaggi. Less realistic dead cone without this. Thanks! 9 / 8

10 Heavy flavour in FSR: g b b (I) Options by Sjöstrand, see online manual Choices for g b b Pythia allows to assess effect by offering various kernels. Basic observations: Quark masses for e + e γ Q Q mean dσ(e + e γ ( ) Q Q) β + cos 2 θ + 4m2 Q d cos θ m 2 sin 2 θ γ ( β z 2 + ( z) 2 + 8m2 Q m 2 γ z( z) Last part is ony true if z θ = +cos θ 2, not for z = (E+p z) Q (E+p z ) γ. Using angle directly very complicated: Depends on virtuality ( only known after z is chosen) and dipole mass m 2 γ. 0 / 8 )

11 Heavy flavour in FSR: g b b (II) Options by Sjöstrand, see online manual e + e γ Q Q does not address going from 2 to 3 on-shell particles. Rederive kernel from h gg b bg, use (z, Q 2, m 2 D) to calculate z θ New kernel option: W 4 (z θ ) = β [ z 2 θ + ( z θ ) 2 + 8rz θ ( z θ ) ] ( + δ) ( δ) ( δ)3 full ME with r = m 2 Q/Q 2, β = 4r and δ = Q 2 /m 2 D. Integrated rate agrees with DGLAP if the factor ( δ) 3 is removed: New kernel option: W 3 (z θ ) = β [ z 2 θ + ( z θ ) 2 + 8rz θ ( z θ ) ] ( + δ) ( δ) simple m D correction These options differ by their virtuality and dipole mass dependence. / 8

12 Heavy flavour in FSR: Theory results Invariant mass of b pairs at LEP, from LU TP 4-5 master thesis. 2 / 8

13 Heavy flavour in FSR: Theory results We can also investigate the effect of α s (p 2 ) α s(m 2 qq) Invariant mass of bottom quark pair dσ/dm bb [pb/gev] α s(g b b) = α s(p ) α s(g b b) = α s(m bb ) 0 6 Ratio m bb Invariant mass of b s at ee@200 GeV. Moderate overall shift. (Rivet analysis by Frank Krauss) 3 / 8

14 Heavy flavour in FSR: Realistic results Z+ 2 b-jets dσ(zbb)/dm(b, b) [pb/gev] 0 3 Data DGLAP (option ) alphas(mqq) (option 8) MC/Data m(b, b) [GeV] Invariant mass of b-jet pairs, from JHEP 40 (204) 4 4 / 8

15 Heavy flavour in FSR: Realistic results Ratio Energy fraction of c hadron in leading c jet DGLAP (option ) alphas(mqq) (option 8) E c /E c jet Ratio Energy fraction of b hadron in leading b jet DGLAP (option ) alphas(mqq) (option 8) E b /E bjet Rivet analyis by Andy Buckley. 5 / 8

16 Heavy flavour in FSR: Realistic results p of c hadron in leading c jet p of b hadron in leading b jet DGLAP (option ) alphas(mqq) (option 8) 0 2 DGLAP (option ) alphas(mqq) (option 8) Ratio p c [GeV] Ratio p b [GeV] Rivet analyis by Andy Buckley. 6 / 8

17 Heavy flavour in FSR: Realistic results dσ(zb)/d R(Z, b)/nb-jets [pb] MC/Data Z+ b-jet, pt(z) > 20 GeV Data DGLAP (option ) alphas(mqq) (option 8) R(Z, b) dσ(zbb)/d R(b, b) [pb] MC/Data Z+ 2 b-jets Data DGLAP (option ) alphas(mqq) (option 8) R(b, b) R distributions from JHEP 40 (204) 4 7 / 8

18 Hadronization of massive partons Notes: No heavy flavour produced though hadronization. Heavy hadrons can have larger momenta than parent quarks. In string model, heavy (and light) hadrons feel colour drag: Hadrons from string end connected to jet core will be dragged towards jet core. Hadrons from string end connected to beam will be dragged to beam. Drag can lead to asymmetries because of proton pp, more high-p B + than B Mostly permille-level effect. 8 / 8