MPI in PYTHIA 8 Richard Corke Department of Astronomy and Theoretical Physics Lund University September Richard Corke (Lund University) MPI@DESY September / 5
Overview MPI in PYTHIA 8 Enhanced screening 3 Rescattering 4 Tuning prospects 5 Summary Richard Corke (Lund University) MPI@DESY September / 5
MPI in PYTHIA 8 Interleaved evolution Note: what follows covers the current MPI framework of PYTHIA 8 Transverse-momentum-ordered parton showers MPI also ordered in p Mix of possible underlying event processes, including jets, γ, J/ψ, DY,... Radiation from all interactions Interleaved evolution for ISR, FSR and MPI ( dpmpi dp = + dp ISR dp dp dp ( p max exp p ( dpmpi dp + ) dp FSR dp + dp ISR dp + ) ) dp FSR dp dp Richard Corke (Lund University) MPI@DESY September 3 / 5
MI MPI in inpythia PYTHIA8 8 p Ordering MPI overview Other half of solution: perturbative QCD not valid at small p since q, g not asymptotic states (confinement!). Model for non-diffractive events, σ nd (/3)σ tot Ordered in decreasing using Sudakov trick Ordered in decreasing Naively breakdown p using at Sudakov trick MPI = dσ p i dp exp dp = ( dσ p i p σ min nd dp dp exp h. GeV fm r p dp i σ nd ) dσ dσ p σ nd dp dp p σ nd dp dp.7 fm.3 GeV Λ QCD QCD cross-section sectionis divergent, in pbut not valid limit, at small p as but q, q/g g not asymptotic states... but better replace r p by (unknown) colour screening length d in hadron r r r r d λ /p resolved d screened Regularisecross-section, section, introducing p is now pa free asparameter a free parameter dˆσ dˆσ α S (p ) p 4 α S (p p α s(p ) α s(p (p + p ) (p p + p ) ) dp dp p 4 Richard Corke (Lund University) Multiple Interactions in PYTHIA 8 October 8 5 / 4 Richard Corke (Lund University) MPI@DESY September 4 / 5
P T (GeV/c) MPI in PYTHIA 8 p and energy scaling p depends on energy Ansatz: scales in a similar manner to the total cross section (effective power related to the Pomeron intercept) p (E CM ) = p ref ( ECM E ref CM ) E pow CM PYTHIA Tune Z Need many measurements at different energies Rick Field, MB & UE Working Group, Tune Z (PYTHIA 6) 3.5 3..5 RDF Very Preliminary MPI Cut-Off P T (W cm ) CDF.96 TeV CMS 7 TeV. Tune Z.5 CMS 9 GeV. 4 6 8 Center-of-Mass Energy W cm (GeV) p T (W)=p T (W/W) e MPI Cut-Off versus the Center-of Mass Energy W cm : PYTHIA Tune Z was determined Richard Corke (Lund University) MPI@DESY September 5 / 5
MPI in PYTHIA 8 Impact parameter Require one interaction for a physical event Introduce impact parameter, b, with matter profile Single Gaussian; no free parameters Overlap function exp ) ( b Epow exp Double Gaussian ρ(r) β a 3 exp ( r a ) + β exp a 3 ( r ) a Time-integrated overlap of hadrons during collision Average activity at b O(b) O(b) = dt d 3 xρ(x, y, z) ρ(x + b, y, z + t) Central collisions usually more active Probability distribution broader than Poissonian Richard Corke (Lund University) MPI@DESY September 6 / 5
MPI in PYTHIA 8 PDF rescaling and primordial k ISR and MPI compete for beam momentum PDF rescaling Squeeze original x range < x < < x < ( ) x i Flavour effects Sea quark initiator (qs) leaves behind an anti-sea companion (q c) qc distribution from g q s + q c perturbative ansatz Normalisation of sea + gluon distributions fluctuate for total momentum conservation Primordial k Needed for agreement with e.g. p (Z ) distributions Give all initiator partons Gaussian k, width σ(q, m) = Q σ soft + Q σ hard + Q Q m m + m Rotate/boost systems to new frame Richard Corke (Lund University) MPI@DESY September 7 / 5
T MPI I in PYTHIA in PYTHIA 8 8 olour Colour Reconnection reconnection.7 Rearrangement Rearrangement of of final-state final-state colour colour connections, connections such that overall string 6 such that overall string Total uncertainty length length is reduced is reduced 4 Systematic uncertainty Uncertainty %.9.8 η and p.4 GeV/c T Data Run II Data Run I 5 5 5 3 35 4 45 5 charged particle multiplicity Large amount of reconnection needed Probability to match for adata system to Start reconnect with N C with a harder limit, but system real-world has N C = 3 p R Changing the P = colour structure of an (p event can lead to R (dis)agreement + p ), with data p R = R p MI FIG. 7: The dependence of the average track pt on the event multiplicity. A comparison with the Run I shown. The error bars in the upper plot describe the uncertainty on the data points. This uncertainty includ uncertainty on the data and the statistical uncertainty on the total correction. In the lower plot the system (solid yellow band) and the total uncertainty are shown. The total uncertainty is the quadratic sum of the unc.5 on the data points and the systematic uncertainty. Pythia hadron level : CDF RunII Preliminary Large amount of reconnection required for agreement with data > [GeV/c] T < p > [GeV/c].4 < p.3...9.8.7.4.3...9.8.7 TuneA no MPI TuneA p =.5 T TuneA p = T Data Atlas Run Tune II η and p.4 GeV/c T η Data Run II and p T.4 GeV/c 5 5 5 3 35 4 45 5 Pythia hadron level multiplicity : TuneA no MPI TuneA p =.5 TuneA p = T ATLAS tune T Mean p as a function of multiplicity, CDF, Run II Measurement of Inelastic P P Inclusive Cross Sections at 5 5 5 3 35 4 45 5 s=.96 TeV, The CDF Collaboration, charged particle Preliminary multiplicity Richard Corke (Lund University) MPI@DESY September 8 / 5 FERMILAB-PUB-9-98-E
nhanced Enhanced Screening screening troduction Idea Idea of Gösta of Gösta Gustafson Gustafson from from work work on on modelling modeling initial initial states states with with an an extended extended Mueller Mueller dipole dipole formalism formalism Elastic and quasi-elastic pp and γ Elastic and quasi-elastic pp and γ p scattering p scattering the in the Dipole Dipole Model, Model, C. Flensburg, C. Flensburg, G. Gustafson G. Gustafson and and L. Lonnblad, L. Lönnblad, arxiv:87.35 Eur. Phys. J. C[hep-ph]. 6 (9) 33 rapidity.8.4. -. -.4 - -.4 -...4 Even at a fixed impact parameter, initial state will contain Even at fixed impact parameter, initial state will contain more/less fluctuations on an event-by-event basis more/less fluctuations on an event-by-event basis More activity more screening More activity more screening Richard Corke (Lund University) Multiple Interactions in PYTHIA 8 October 8 / 4 Richard Corke (Lund University) MPI@DESY September 9 / 5
nhanced Enhanced Screening screening troduction Idea Idea of Gösta of Gösta Gustafson Gustafson from from work work on on modelling modeling initial initial states states with with an an extended extended Mueller Mueller dipole dipole formalism formalism Elastic and quasi-elastic pp and γ Elastic and quasi-elastic pp and γ p scattering p scattering the in the Dipole Dipole Model, Model, C. Flensburg, C. Flensburg, G. Gustafson G. Gustafson and and L. Lonnblad, L. Lönnblad, arxiv:87.35 Eur. Phys. J. C[hep-ph]. 6 (9) 33 rapidity 6.8.4. -. -.4 - -.4 -...4 Even at a fixed impact parameter, initial state will contain Even at fixed impact parameter, initial state will contain more/less fluctuations on an event-by-event basis more/less fluctuations on an event-by-event basis More activity more screening More activity more screening Richard Corke (Lund University) Multiple Interactions in PYTHIA 8 October 8 / 4 Richard Corke (Lund University) MPI@DESY September 9 / 5
Enhancedscreening Screening Enhanced Screening in PYTHIA dˆσ dp α S (p + p ) (p + p ) α S (p + p ) (n p + p ) ES: n = no. of MI ES: n = no. of MI + ISR.3. CDF Run II Pythia 8.4 No reconnection Pythia 8.4 No reconnection + ES Pythia 8.4 No reconnection + ES <p T > [GeV/c]..9.8.7 5 5 5 3 35 Charged particle multiplicity Richard Corke (Lund University) Multiple Interactions in PYTHIA 8 October 8 / 4 Richard Corke (Lund University) MPI@DESY September / 5
Enhancedscreening Screening Enhanced Screening in PYTHIA dˆσ dp α S (p + p ) (p + p ) α S (p + p ) (n p + p ) ES: n = no. of MI ES: n = no. of MI + ISR <p T > [GeV/c].3...9 CDF Run II Pythia 8.4 No reconnection Pythia 8.4 No reconnection + ES Pythia 8.4 No reconnection + ES Pythia 8.4, RR * p = 5.56 Pythia 8.4 ES, RR * p = 4.35 Pythia 8.4 ES, RR * p = 3.8.8.7 5 5 5 3 35 Charged particle multiplicity Richard Corke (Lund University) Multiple Interactions in PYTHIA 8 October 8 / 4 Richard Corke (Lund University) MPI@DESY September / 5
Rescattering lt. int. R Rescattering dp = + dp p i ISR exp MPI Introduction dp traditionally disjoint interactions Rescattering: with Consider ISR sum aallow over 4 all 4an previous andalready a 3 MI 3 scattered process parton to interact again mult. int. p max ISR p 3 (4) Evolution interleaved with ISR (4) Transverse-momentum-ordered showers ( ) ( dpmi p dp is 3 3 instead of 4 4: hard int. interaction ISR p number dp p ( dpmi dp + ) ) dp ISR dp dp (5) Rescattering (in progress) p mult. int. Interaction cross-section is 3 3 instead of 4 4: ISR dσ int dp = dx dx f (x, Q ) f (x, Q ) dˆσ p mult. int. 3 dσ int dp Paver ISR dp = dx dx f (x, Q ) f (x, Q ) dˆσ and Treleani (984) dp p min dσ int interaction 3 dp N N ˆσ σ 4 4 (N N ˆσ)(N N number ˆσ) σ 4 4 (N N ˆσ)(N σn 3 3 ˆσ) σ 3 3 (N N ˆσ)(N ˆσ) σ 3 3 4 4 N small small σ 4 4 N Investigated by Paver and Treleani (984), size of effect But should be there! Plays a role in the collective effects of MPI Possible colour connection effects σ 3 3 (N N ˆσ)(N ˆσ) N N ˆσ Richard Corke (Lund University) Multiple Interactions in PYTHIA 8 October 8 3 / 4 Richard Corke (Lund University) MPI@DESY September / 5
Rescattering Typical case of small angle scatterings between partons from incoming hadrons, such that they are still associated with their original hadrons f (x, Q ) f rescaled (x, Q ) + n δ(x x n ) In this limit, momentum sum rule holds x f rescaled (x, Q ) dx + n x n = Original MPI interactions supplemented by: Single rescatterings: one parton from the rescaled PDF, one delta function Double rescatterings: both partons are delta functions One simplification: rescatterings always occur at later times Z preceeded by rescattering not possible Richard Corke (Lund University) MPI@DESY September / 5
Rescattering In general not possible to uniquely identify a scattered parton with an incoming hadron, so use approximate rapidity based prescription dn / dp p.5.4.3.. Step: Step function at y = Simultaneous: Partons belong to both beams simultaneously Tanh/linear: In between (a) Step Linear Tanh Simultaneous dn / dp p.5.4.3.. (b) Step Linear Tanh Simultaneous. p (GeV ). p (GeV ) Little sensitivity to choice Figure 5: Natural p distributions suppression of (a) rescatterings and (b) double rescatterings in LHC minimum bias events (pp, for single No suppression for s double = 4 TeV, rescattering, old tune). but Parameters still small for effect the different options are the same as the previous figure. Note the difference in vertical scale between (a) and (b), and that the step, linear and tanh curves are so close that they may be difficult to distinguish Richard Corke (Lund University) MPI@DESY September 3 / 5
Rescattering In general not possible to uniquely identify a scattered parton with an incoming hadron, so use approximate rapidity based prescription Step: Step function at y = Simultaneous: Partons belong to both beams simultaneously Tanh/linear: In between dn / dp p Ratio.6.4..8.4. (a) Old Tune - Single / Normal (Step).5 New Tune - Single / Normal (Step).4.3 Old Tune - Double / Normal (Sim)... p (GeV ) Old Tune - Normal New Tune - Normal Old Tune - Single New Tune - Single Probability..5..5 Old Tune New Tune (b). Little sensitivity to choice Figure 6: Rescattering in LHC minimum bias events (pp, s = 4TeV, old Natural suppression (a) shows for the single p distribution rescattering of scatterings and single rescatterings per eve No suppression the ratio for double plot is double rescattering, rescattering but still with small the simultaneous effect beam prescriptio tune, where its effect is maximal. (b) shows the probability for a parton hard process of an event, to rescatter as a function of its initial p Richard Corke (Lund University) MPI@DESY September 3 / 5 p (GeV )
.4. Rescattering Ratio.5.4.3.. Use step prescription Old Tune - Single / Normal (Step) New Tune - Single / Normal (Step) Old Tune - Double / Normal (Sim). p (GeV ). Amount of rescattering sensitive to amount of underlying activity Figure 6: Default Rescattering tune in change LHC minimum starting bias with events (pp, PYTHIA 8.7 s = 4TeV, old and new tunes). (a) shows the p MPI: p ref distribution of scatterings =.5.5, E pow and single rescatterings per event. Included in CM =.4 the ratio plot is double rescattering with the simultaneous beam prescription using the old tune, where Matter its effect profile is from maximal. double (b) to shows single the Gaussian probability for a parton, created in the hard process ISR of activity an event, increased to rescatter as a function of its initial p Old New Probabili..5 p (GeV ) Tevatron LHC Min Bias QCD Jets Min Bias QCD Jets Scatterings.8 5.9 5.9.9 Single rescatterings.4.3.3 4. Double rescatterings..4.3.5 Scatterings.5 3.79 3.4 5.68 Single rescatterings.4.5 6 Double rescatterings.... Tevatron: p p, s =.96 TeV, QCD jet ˆp min = GeV LHC: pp, s = 4 TeV, QCD jet ˆp min = 5 GeV Table Double : Average rescattering number ofalways scatterings, small, single sorescatterings ignored and double rescatterings in minimum bias and QCD jet events at Tevatron (pp, what follows s =.96 TeV, QCD jet ˆp min = GeV) and LHC (pp, s = 4. TeV, QCD jet ˆp min = 5 GeV) energies for both the old and new tunes Richard Corke (Lund University) MPI@DESY September 4 / 5
Rescattering Rescattering Status So far nice and simple, but want fully hadronic events Preliminary framework in place to get hadronic final states Integration with showers needed Keep Non-trivial system kinematics mass/rapidity with rescattering, unchanged FSR where and primordial possible k A radiating parton will shuffle momentum with a recoiler parton Colour effects FSR: usually nearest colour neighbour Parton Primordial showers k given use dipole by boosting picture scattering for recoil sub-systems With rescattering, colour can flow between systems Rescattering: colour dipoles can span between scattering sub-systems Momentum shuffled between systems is given a different primordial k boost Temporary solution of deferring FSR until after primordial k is added Full event generation, including showers, primordial k and colour reconnections Richard Corke (Lund University) Multiple Interactions in PYTHIA 8 October 8 7 / 4 Richard Corke (Lund University) MPI@DESY September 5 / 5
Rescattering 6 dσ / dp (nb / GeV) 5 (a) -> 3 3 -> 3 Compare sources of 3- and 4-jets at the parton level 4 Contributions to 3-jet rate 3 3 from single radiation 3 3 from single rescattering 4 3 double parton scattering with one jet lost 4 6 8 4 6 8 p Contributions to (GeV) 4-jet rate p (GeV) Figure 3: Breakdown 4 from double of contributions radiation to the (a) three-jet and (b) four-jet cross sections (see text) 3 for 4 LHC from minimum single radiation bias events + single (pp, rescattering s = 4 TeV, new tune) when no p or rapidity 4 cuts are 4 from applied DPS 4 4 from two single rescatterings 4 3 (a) -> 3 3 -> 3 4 -> 3 dσ / dp (nb / GeV) 6 5 4 3 (b) (b) -> 4 3 -> 4 4 -> 4 4 -> 4 -> 4 3 -> 4 4 -> 4 dσ / dp (nb / GeV) dσ / dp (nb / GeV) - - - - 3 4 5 6 7 8 9 3 4 5 6 7 8 9 p (GeV) p (GeV) pp, s = 4 TeV, new tune, p > GeV, η <. Figure 4: Breakdown of contributions to the (a) three-jet and (b) four-jet cross sections Richard Corke (Lund University) MPI@DESY September 6 / 5
Rescattering Hadron level Feed results into FastJet, anti-k algorithm, R =.4 -, 3- and 4-jet exclusive cross sections Some increase in jet rates, but contributions can be compensated by changes in parameters elsewhere Also studied dσ / dp (nb / GeV) Ratio 5 4 3..8.4 -jet Normal 3-jet Normal 4-jet Normal -jet 3-jet 4-jet 3 4 5 6 7 8 9 p (GeV) -jet Rescatter 3-jet Rescatter 4-jet Rescatter pp, s = 4 TeV, old tune, p >.5 GeV, η <. Figure 9: Two-, three- and four-jet exclusive cross sections for LHC minimu (pp, s = 4 TeV, p jet >.5 GeV, η <., old tune) Colour reconnections Cronin effect are very deeply entangled in the downward evolution of the final state, so it any such signatures may exist. For the three-jet sample of Fig. 9, we stud R & φ distributions R value between the different pairs of jets per event. One could hope that th of R values from three-jet events where rescattering is involved is somehow the background events (e.g. three-jet events from radiation which may be cha peaked in the small R region). For the four-jet sample, we instead stud and largest φ values between the jets per event. It is known that DPS characteristic φ peak at π, but there are also radiative contributions wh rescattering. Unfortunately, for both samples, the results with and withou are essentially indistinguishable. No smoking-gun signatures for rescattering Would any effects be visible in a full tune? Richard Corke (Lund University) MPI@DESY September 7 / 5
References PYTHIA references PYTHIA 6.4 Physics and Manual, T. Sjöstrand, S. Mrenna and P. Z. Skands, JHEP 65 (6) 6 A Brief Introduction to PYTHIA 8., T. Sjöstrand, S. Mrenna and P. Z. Skands, Comput. Phys. Commun. 78 (8) 85 Model references A Multiple Interaction Model for the Event Structure in Hadron Collisions, T. Sjöstrand and M. van Zijl, Phys. Rev. D 36 (987) 9 Multiple interactions and the structure of beam remnants, T. Sjöstrand and P. Z. Skands, JHEP 43 (4) 53 Transverse-momentum-ordered showers and interleaved multiple interactions, T. Sjöstrand and P. Z. Skands, Eur. Phys. J. C 39 (5) 9 Multiparton Interactions and Rescattering, R. Corke and T. Sjöstrand, JHEP () 35 Richard Corke (Lund University) MPI@DESY September 8 / 5
Tuning prospects FSR and hadronisation tuned to LEP data (H. Hoeth) Already default for PYTHIA 8.5 and later Problems with simultaneous tuning of MB and UE Transverse region charged particle density Transverse region charged p density N ch /dη dφ..8.4. CDF data PYTHIA 8.35 p track T /dη dφ / GeV.5.5 CDF data PYTHIA 8.35 MC/data.4..8 5 5 5 3 35 4 pt(leading jet) / GeV MB well described, but UE rises too fast! MC/data.4..8 5 5 5 3 35 4 pt(leading jet) / GeV Richard Corke (Lund University) MPI@DESY September 9 / 5
Tuning prospects New in PYTHIA 8: FSR interleaving Final-state dipoles can stretch to the initial state (FI dipole) How to subdivide FSR and ISR in an FI dipole? Large mass large rapidity range for emission m >> p m p In dipole rest frame Double counted p m/ Suppress final-state radiation in double-counted region Richard Corke (Lund University) MPI@DESY September / 5
Tuning prospects Also study how well the parton shower fills the phase space Compare against 3 real matrix elements Would changing the shower starting scale give better agreement? Qualitatively, PS doing a good job. p 3 PS p 3 ME. p 4 PS p 4 ME dσ / dp [nb / GeV]... dσ / dp [nb / GeV]... e-5 3 4 5 p [GeV] e-5 3 4 5 p [GeV]. p 5 PS p 5 ME dσ / dp [nb / GeV]... e-5 p min 3 p min 5 = 5. GeV = 5. GeV Rsep =.5 e-6 3 4 5 p [GeV] Richard Corke (Lund University) MPI@DESY September / 5
Tuning prospects Is a simultaneous MB/UE Tevatron tune now possible? Tunes C and M CTEQ6L and MRST LO** PDF tunes to Tevatron data Start with by-hand tune Compare against Pro-Q and Perugia Underlying event description improved! Transverse region charged particle density Transverse region charged p density N ch /dη dφ.8.4. CDF data PYTHIA 6.4 Pro-Q PYTHIA 6.4 Perugia PYTHIA 8.4 Tune C PYTHIA 8.4 Tune M p track T /dη dφ / GeV.5.5 CDF data PYTHIA 6.4 Pro-Q PYTHIA 6.4 Perugia PYTHIA 8.4 Tune C PYTHIA 8.4 Tune M MC/data.4..8 5 5 5 3 35 4 pt(leading jet) / GeV MC/data.4..8 5 5 5 3 35 4 pt(leading jet) / GeV Richard Corke (Lund University) MPI@DESY September / 5
Tuning prospects More plots: http://www.thep.lu.se/ richard/pythia8 pt / GeV MC/data Mean track pt vs multiplicity, η <, p >.4 GeV.4..8.6.4..8.4..8 CDF data PYTHIA 6.4 Pro-Q PYTHIA 6.4 Perugia PYTHIA 8.4 Tune C PYTHIA 8.4 Tune M 5 5 5 3 35 4 45 N ch dσ/dn ch MC/data 3 4 5.4..8 Charged multiplicity at s = 8 GeV, η <, pt >.4 GeV CDF data PYTHIA 6.4 Pro-Q PYTHIA 6.4 Perugia PYTHIA 8.4 Tune C PYTHIA 8.4 Tune M 5 5 5 3 35 4 N ch Broadly in line with previous tunes MRST LO** has more momentum Lower αs and higher p ref Use overlap function for matter profile Parameter gives handle on width of multiplicity distributions Suggests slightly wider than single Gaussian Reduced colour reconnection Richard Corke (Lund University) MPI@DESY September 3 / 5
Tuning prospects New LHC data Measurements of MB/UE at new energies! Experiments appear consistent with themselves But tension with older data? Move from NSD/INEL to INEL> Reproducible definitions! Diffractive description more important? New framework in PYTHIA 8 for high-mass diffraction Diffraction in Pythia, S. Navin, arxiv:5.3894 [hep-ph] Based on Ingelman Schlein picture Single diffraction: Pomeron emitted from one incoming hadron interacts with incoming hadron on the other side Total cross sections Early look at MB numbers suggest dampening diffractive cross sections? New possibility to dampen rise available ATLAS-CONF--48: Both PYTHIA8 and PHOJET would do slightly better in describing the data if there was an increase in the ND component Richard Corke (Lund University) MPI@DESY September 4 / 5
Summary PYTHIA 8 MPI model Well established model that has evolved over time Fully interleaved with parton showers Rich mix of possible underlying event processes Still under development Enhanced screening Perhaps part of a solution towards lowering colour reconnections More evidence to come from DIPSY? Rescattering First model to include such effects No distinctive signatures; perhaps full tune would reveal more Future project: x-dependent proton profile Tuning prospects Simultaneous MB/UE tuning within reach Initial tunes to Tevatron data Impact of LHC data still uncertain Article in preparation Richard Corke (Lund University) MPI@DESY September 5 / 5