Investigating the parton shower model in PYTHIA8 with pp collision data at \surd{s}=13\, TeV
IInvestigating the parton shower model in pythia8 with pp collision data at √ s = 13 TeV ∗S. K. Kundu † , T. Sarkar ‡ , M. Maity § , Visva-Bharati University, Santiniketan, India National Central University ( NCU), Taiwan.
Abstract
Understanding the production of quarks and gluons in high energy collisions andtheir evolution is a very active area of investigation. Monte carlo event generator pythia8 uses the parton shower model to simulate such collisions and is optimizedusing experimental observations. Recent measurements of event shape variables anddifferential jet cross-sections in pp collisions at √ s = 13 TeV at the Large HadronCollider have been used to investigate further the parton shower model as used in pythia8 . Matrix element calculations with fixed order treatment is not sufficient to understand theproduction of quarks and gluons, collectively called partons, in high energy collisions ortheir evolution into jets of hadrons. Comparison with experimental results demand fullyexclusive description of the final states based on the shower evolution and hadronization.Such methods are described through phenomenological models embedded in the showerMonte Carlo (MC) codes. pythia8 uses leading order(LO) calculations followed by ‘transverse momentum’ ( p ⊥ )ordered parton shower[1] with p ⊥ as evolution variable for the generation of → n ( n ≥ )final states by taking account initial (ISR) and final (FSR) state shower. Shower evolutionfor a parton like a → bc , is based on the standard (LO) DGLAP splitting kernels and thebranching probability expressed as: d P a = dp ⊥ p ⊥ (cid:88) b,c α s ( p ⊥ )2 π P a → bc ( z ) dz (1.1)where P a → bc is the DGLAP splitting function and p ⊥ represents the scale of the branching; z represents the sharing of p ⊥ of a between the two daughters, with b taking a fraction z and c the rest, − z . Here the summation goes over all allowed branchings, e.g. q → qg and q → qγ and etc. Now, the divergence at p ⊥ → is taken care of by introducing a ∗ Presented at XXIV DAE-BRNS High Energy Physics Symposium † [email protected] ‡ [email protected] § [email protected] a r X i v : . [ h e p - ph ] F e b ythia8 Monash Sampling range OptimizedParameters set values values
SpaceShower:alphaSvalue . − . . +0 . − . TimeShower:alphaSvalue . − . . +0 . − . SpaceShower:PTmaxFudge . − . . +0 . − . Table 1: Optimized result of three parameters of pythia8 is shown along with their defaultvalues in the Monash tune and the sampling range.term P noa ( p ⊥ max , p ⊥ evol ) known as Sudakov form factor [2]. This Sudakov factor ensures thatthere will be no emission between scale p ⊥ max to a given p ⊥ evol .Considering lightcone kinematics, evolution variables p ⊥ evol for a → bc at virtuality scale Q for space-like branching (ISR) and time-like branching (FSR) are given by (1 − z ) Q and z (1 − z ) Q respectively. Finally, equations 1.2 and 1.3 describe the evolutions for ISRand FSR respectively [1].d P b = d p ⊥ evol p ⊥ evol α s ( p ⊥ evol )2 π x (cid:48) f a ( x (cid:48) , p ⊥ evol ) xf a ( x, p ⊥ evol ) P a → bc ( z ) dz P no b ( x, p ⊥ max , p ⊥ evol ) (1.2)d P a = d p ⊥ evol p ⊥ evol α s ( p ⊥ evol )2 π P a → bc ( z ) d z P no a ( p ⊥ max , p ⊥ evol ) (1.3)Currently both the running re-normalisation and factorisation shower scales, i.e. thescales at which α s and the PDFs are evaluated, are chosen to be p ⊥ evol [3]. The generalmethodology of pythia8 for ISR, FSR and MPI is to start from some maximum scale p ⊥ max and evolve downward in energy towards next branching untill the daughter partons reachsome cut-off. CMS and ATLAS have done several tunning of pythia8 around its Monash tune [4] forunderlying event (UE), the strong coupling, and MPI related parameters [5, 6] [7]. In thisstudy[8] Monash tune also used as default for pythia v8.235 with NNPDF2.3 PDF (LO) setto optimize with four event shapes [9] measurement from CMS. These are - the complementof transverse thrust ( τ ⊥ ), total jet mass ( ρ Tot ), total transverse jet mass ( ρ TTot ) and total jetbroadening ( B T ).Monash tune overestimates the multijet regions of these event shapes [9], Hence weexamined ISR and FSR utilising the provision that pythia8 allows the use of separatevalues of α s (M Z ) for the showering frameworks used for these. The maximum evolution scaleinvolved in the showering is set to match the scale of the hard process itself. In pythia8 itis set equal to the factorization scale, but allows its modification by multiplicative factors SpaceShower:PTmaxFudge for ISR and
TimeShower:PTmaxFudge for FSR. The latter is seennot to have much effect on the ESVs, it is excluded from the optimization.For each point in the parameter space, resulting distributions have been comparedwith data in terms of χ / NDF . Then professor v2.3.0 [10] along with
RIVET v2.6 [11]has been used to optimize the complete set of ESV distributions from pythia8 [9]. Postoptimization, the new parameter set is checked[8] using other relevant results from the CMS[12] and ATLAS [13]. 2 - - - - - - - ) t / N d N / d l n (
13 TeV) (cid:214)
Data(CMS /NDF: 1.14 c Pythia8(Monash) - /NDF: 5.39 c Pythia8(Prof2-tune) - < 225 GeV
T,2
165 < H - - - - - - ) t ln( M C / D a t a - - - - - - - - - - ) T o t r / N d N / d l n (
13 TeV) (cid:214)
Data(CMS /NDF: 13.63 c Pythia8(Monash) - /NDF: 4.38 c Pythia8(Prof2-tune) - < 225 GeV
T,2
165 < H - - - - - - - ) Tot r ln( M C / D a t a - - - - - - - -
10 1 ) T / N d N / d l n ( B
13 TeV) (cid:214)
Data(CMS /NDF: 21.30 c Pythia8(Monash) - /NDF: 7.17 c Pythia8(Prof2-tune) - < 225 GeV
T,2
165 < H - - - - - - ) T ln(B M C / D a t a - - - - - - ) T o t T r / N d N / d l n (
13 TeV) (cid:214)
Data(CMS /NDF: 2.56 c Pythia8(Monash) - /NDF: 4.60 c Pythia8(Prof2-tune) - < 225 GeV
T,2
165 < H - - - - - ) TotT r ln( M C / D a t a Figure 1: Predictions of the optimized parameter set is compared with CMS data andMonash tune for H T,2 range < H
T,2 < . normalized distributions of the τ ⊥ (top left), ρ Tot (top right), B T (bottom left) and ρ TTot (bottom right) b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b bb
DataMonash-tune, χ / n = . Prof -tune, χ / n = . − − − CMS, p ( s ) = TeV, Inclusive AK jets, 0.5 < | y | < d σ / d p T d y [ p b / G e V ] b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b . . . . . . . . p T [GeV] M C / D a t a b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b bb DataMonash-tune, χ / n = . prof -tune, χ / n = . − − − − − Inclusive jet cross section as a function of jet p T (0.5 < | y | < d σ / d p T d y [ p b / G e V ] b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b . . . . . . . . . Jet p T [GeV] M C / D a t a Figure 2: Normalized distributions of differential inclusive cross-section for anti- k T jets(R=0.4) for CMS(left) and ATLAS(right) are compared with the predictions of pythia8 with the optimized parameter set and Monash tune.3 Validation of results
The optimized values of the three parameters (see, table 1) are used to calculate the ESVs.Agreement with data deteriorates slightly for τ ⊥ and ρ TTot (figure 1) compared to the goodagreement with the Monash tune. But, there is significant improvement in agreement withdata for ρ Tot and B T (figure 1)compared to the Monash tune. Since ρ Tot and B T had arather poor agreement between data and the Monash tune, overall this new set of parametersis better.Inclusive jet cross-section measurements being sensitive to PDF of protons and α s arealso compared with those optimized values. CMS [12] and ATLAS [13] studies with the 13TeV data considered for this validation. The CMS measurements of inclusive cross-sectionsfor anti- k T jets with R = 0.4, 0.7. Figures 2 show that the new parameter set improves theagreement between data and the Monash tune of Pythia8. Similar improvement is seen forthe ATLAS measurement of anti- k T jets with R = 0.4 (figure 2).Since pythia8 is widely used, its optimization is important. This study shows thatcertain aspects of the experimental observations can be better described with this optimizedset of parameters. References [1] T. Sjostrand, P.Z. Skands, Eur. Phys. J.
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