QCD at Cosmic Energies - VII May 6-20, 206 Chalkida, Greece Multiparton interactions in Herwig Frashër Loshaj
Table of Contents Introduction 2 MPI and the Underlying event 3 Soft interactions 4 Diffraction 5 Summary and outlook Frashër Loshaj Multiparton interactions in Herwig 6/5/205
Herwig Monte Carlo Event Generator Herwig is a general-purpose event generator for high energy lepton-lepton, lepton-hadron and hadron-hadron collisions. Special emphasis is put on the accurate simulation of QCD radiation. The event in Herwig is simulated including these steps: Elementary hard process, Initial and final state parton showers, Decay of heavy objects, Multiple interactions (hard and soft), Hadronization and Hadron decays. [Eur.Phys.J. C58 (2008) 639-707] Frashër Loshaj Multiparton interactions in Herwig 6/5/205
pp pp Event eventgenerator generator in Herwig Taken from Stefan Gieseke Stefan Frashër Gieseke Loshaj UA Madrid PhD course lectures Multiparton 4 7/03/206 interactions in Herwig 6/5/205 9/83
pp pp Event eventgenerator generator in Herwig Taken from Stefan Gieseke Stefan Frashër Gieseke Loshaj UA Madrid PhD course lectures Multiparton 4 7/03/206 interactions in Herwig 6/5/205 9/83
pp pp Event eventgenerator generator in Herwig Taken from Stefan Gieseke Stefan Frashër Gieseke Loshaj UA Madrid PhD course lectures Multiparton 4 7/03/206 interactions in Herwig 6/5/205 9/83
Herwig 7 Recently released: Herwig++ 3.0 Herwig 7.0 No distinction anymore between HERWIG and Herwig++; we refer to it as Herwig from now on. Most new features have to do with NLO calculations of hard processes with matching to angular-ordered and dipole shower modules. The focus of this talk: review of semi-hard and soft multiple parton interactions, recent development in diffraction and colour structure of soft scatters. Frashër Loshaj Multiparton interactions in Herwig 6/5/205
Multiple Parton Interactions (MPI) - motivation Inclusive jet cross section above transverse momentum p T σh inc (s, pt min ) = dx dx 2 dˆt Θ ( p T pt min ) + δ kl i,j,k,l ( f i h (x, µ 2 )f i h2 (x 2, µ 2 ) dσ ij kl ˆ ) (x x 2 s, t) dˆt Cross section increases with s. At moderate values of s, exceeds total cross section. A way to resolve this contradiction is MPI. [M. Bähr s talk at MPI@LHC 08.] Frashër Loshaj Multiparton interactions in Herwig 6/5/205
MPI - definitions and applications Several scatterings between partons in the same hadron collision. Important for understanding min-bias processes and the underlying event. Underlying event - all activity in a hadronic collision not related to the hard process, e.g. initial-state radiation, additional scatters in the collision, etc. Jet measurements - sensitive to the underlying event; jet algorithms gather all particles in the vicinity of the leading initial hard parton. Min-bias - events selected with least trigger bias possible; constitute the majority of the events in hadronic collisions. Frashër Loshaj Multiparton interactions in Herwig 6/5/205
MPI in Herwig Multiple scattering in a pp collision: Mean pairs of interactions at a given impact parameter b: n(b, s) = L partons ˆσ H, b L partons - parton luminosity; ˆσ H - partonic hard scattering cross section for p T > p min T. [J.M. Butterworth et al., Z.Phys. C72 (996) 637-646]. Frashër Loshaj Multiparton interactions in Herwig 6/5/205
MPI in Herwig (cont d) Assumption: dl partons = A(b)n h (x )n h2 (x 2 )dx dx 2 Profile function A(b) was factored out. We have: d 2 ba(b) =. n hi (x i ) - parton densities of hadrons (parton flavor is omitted); After performing the convolution: σh inc n(s, b) = A(b)σ inc H (s), (s) - inclusive scattering cross section. Assumption: scatters are uncorrelated; probability of having m scatters: P m (A(b)σ inc ) = ( n(b, s) )m m! exp ( n(s, b) ) Frashër Loshaj Multiparton interactions in Herwig 6/5/205
Multi-reggeon interactions - AGK rules Eikonal model n pomeron amplitude A (n) (s, b) = ( χ(s, b)) n, with χ(s, b) = 2iA () (s, b) 2i n! Using AGK rules, the k cut pomeron cross section is σ k (s) = d 2 b (2χ)k k! exp ( 2χ) Frashër Loshaj Multiparton interactions in Herwig 6/5/205
MPI - eikonal model Jet production cross section due to exactly k uncorrelated hard interactions σ k (s) = d 2 b P k (A(b)σ inc ) = d 2 b ( ) Aσ inc k H k! exp ( AσH inc ) Similar to the eikonal model if χ H (s, b) = 2A(b, µ)σinc H (s, pmin T ). We have introduced the parameter µ explicitly which is tuned in Herwig. Prob. of having n scatters, given there is one: d P n (σ inc 2 bp n (A(b)σ inc ) ) = d 2 b k= P k(a(b)σ inc ) = σn(σinc ) σ inel(σ inc ) This expression is the basis of underlying event calculations. Describes well the data ([M. Bähr, S. Gieseke, and M. H. Seymour JHEP 07 (2008), 076)]). Frashër Loshaj Multiparton interactions in Herwig 6/5/205
Underlying event - Tevatron The direction of the leading jet is used to partition the event into three parts: towards, away and transverse. Towards, away, transverse π φ η [Phys. Rev. D65 (2002) 092002] Stefan Gieseke UA Madrid PhD course lectures 4 7/03/206 47/83 Frashër Loshaj Multiparton interactions in Herwig 6/5/205
Detailed Underlying lookevent at observables: - Tevatron Transverse Region <N chg > transv 5 4 3 data, uncorrected pt min =3.5, 2 =.50,χ2 tot /N =3. pt min =3.5, 2 =.25,χ2 tot /N =2.9 pt min =4.0, 2 =.50,χ2 tot /N =2.8 Tevatron Run 2 MC/Data 0.4.2.0 0 0 20 30 40 50 p ljet t (GeV) [JHEP 0807 (2008) 076] Stefan Frashër Gieseke Loshaj UA Madrid PhD course lectures Multiparton 4 7/03/206 interactions in Herwig 6/5/205 5/83
Detailed Underlying lookevent at observables: - Tevatron Transverse Region <p t sum > transv (GeV) 6 5 4 3 2 data, uncorrected pt m =3.5, 2 =.50, 2 tot /N =3. pt m =3.5, 2 =.25, 2 tot /N =2.9 pt m =4.0, 2 =.50, 2 tot /N =2.8 Tevatron Run MC/Data 0.4.2.0 0 0 20 30 40 50 p ljet t (GeV) [JHEP 0807 (2008) 076] Stefan Frashër Gieseke Loshaj UA Madrid PhD course lectures Multiparton 4 7/03/206 interactions in Herwig 6/5/205 5/83
Underlying Event event -(ATLAS (900 900 GeV) Also include Std deviation! Transverse region N chg density vs. p (leading track) Std. dev. Transverse region N chg density vs. p (leading track) d 2 N chg/dηdφ ATLASread tune H++ ATLASread Std. dev. d 2 N chg/dηdφ ATLASread tune H++ ATLASread 0 0 MC/data.4.2 2 3 4 5 6 7 8 9 0 p (leading track) [GeV] MC/data.4.2 2 3 4 5 6 7 8 9 0 p (leading track) taken from Stefan Gieseke Stefan Frashër Gieseke Loshaj UA Madrid PhD course lectures Multiparton 4 7/03/206 interactions in Herwig 6/5/205 53/83
Underlying Event event -(ATLAS (900 900 GeV) Also include Std deviation! Transverse region p density vs. p (leading track) Std. dev. Transverse region p density vs. p (leading track) d 2 p /dηdφ [GeV] 0 ATLASread tune H++ ATLASread Std. dev. d 2 p /dηdφ[gev] 0 ATLASread tune H++ ATLASread MC/data.4.2 2 3 4 5 6 7 8 9 0 p (leading track) [GeV] MC/data.4.2 2 3 4 5 6 7 8 9 0 p (leading track) taken from Stefan Gieseke Stefan Frashër Gieseke Loshaj UA Madrid PhD course lectures Multiparton 4 7/03/206 interactions in Herwig 6/5/205 53/83
Underlying Event event -(ATLAS (77 TeV) N ch /StdDev transverse vs p lead t /GeV. Read off from ATLAS MC (tune000-0) MC (run) Read off from ATLAS MC (tune000-0) MC (run) 0 MC/data 0.4.2 MC/data.4.2 2 4 6 8 0 2 4 6 8 20 2 4 6 8 0 2 4 6 8 20 taken from Stefan Gieseke Stefan Frashër Gieseke Loshaj UA Madrid PhD course lectures Multiparton 4 7/03/206 interactions in Herwig 6/5/205 54/83
Energy extrapolation to 00 TeV Underlying event - Energy extrapolation to 00 TeV 5 50 µ 2 4 3 2 0 5 χ 2 /N.d.f. 2 3 4 5 6 p min,0 taken from Andrzej Siodmok Despite quite different extrapolation of different tunes we get quite similar description of the data. Different tunes give similar results due to the strong correlation between The reasonp min for this is a strong correlation of µ 2 and p min t and µ2. Frashër Loshaj Multiparton interactions in Herwig 6/5/205
Underlying event - Energy extrapolation to 00 TeV Energy extrapolation to 00 TeV - UE results d 2 N chg/dηdφ MC/Data 3.5 3 2.5 2.5 0.5 0.4.2 Transverse N chg density vs. p trk, s = 00 TeV Data UE-EE-5-CTEQ6L 00 TeV UE-EE-4-CTEQ6L 00 TeV 2 4 6 8 0 2 4 6 8 20 p (leading track) [GeV] d 2 p /dηdφ [GeV] MC/Data 4.5 4 3.5 3 2.5 2.5 0.5 0.4.2 Transverse p density vs. p trk, s = 00 TeV Data UE-EE-5-CTEQ6L 00 TeV UE-EE-4-CTEQ6L 00 TeV 2 4 6 8 0 2 4 6 8 20 p (leading track) [GeV] taken from BothAndrzej tunes despite Siodmokdifferent extrapolation of p min t give similar results @ 00 TeV. It would be interesting to compare the results with other models. It would be interesting to see similar results for different PDF set. Frashër Loshaj Multiparton interactions in Herwig 6/5/205
Soft interactions Extend the model to include interactions with p T < p min T. Add to the eikonal function the soft contribution ([JHEP 09 (2002), p. 05]): χ(s, b) = χ H (s, b) + χ S (s, b) = 2 [ A(b, µ)σ inc H (s, pmin T ) + A(b, µ s)σ inc ] The cross section for j soft and k hard uncorrelated interactions σ inc s σ jk = d 2 b (2χ S) j j! (2χ H ) k exp [ 2(χ S + χ H )] k! and µ s are obtained by fitting to experimental data. s Frashër Loshaj Multiparton interactions in Herwig 6/5/205
Soft interactions Extending Generic into(nonperturbative) the soft region gluon-gluon interactions are generated at p T < pt min. We require dσinc H /dp2 T to match the soft Continuation of the differential counterpart at T = pt min cross. section into the soft region p t < p min (here: p t integral kept fixed) t / (5 GeV) d /dp t (/GeV) 5 4 3 2 pt min =3 GeV, = 0.5 GeV 2 pt min =5 GeV, =0.06 GeV 2 d soft p dp t t e (p t p 2 min,2 t ) 0 0 2 4 6 8 0 p t (GeV) Stefan Gieseke UA Madrid PhD course lectures 4 7/03/206 7/83 Frashër Loshaj Multiparton interactions in Herwig 6/5/205
Hadronization Colour preconfinement AfterLarge parton N C shower limit and planar MPI, graphs quarks dominate. and gluons must hadronize. The basis Gluon for = colour hadronization anticolourpair in Herwig is the colour preconfinement property - cluster model: Nonperturbative Parton showergluon organises splitting partons to quark-antiquark in colour space. Colour pair. Largepartners N c limit: (=colour non-planar singletgraphs pairs) end areupsubleading. close phase space. Cluster hadronization model Stefan Gieseke UA Madrid PhD course lectures 4 7/03/206 89/83 Frashër Loshaj Multiparton interactions in Herwig 6/5/205
Colour connections Event with multiple hard subprocesses Soft subprocess with disrupted color lines (exceptional case) Frashër Loshaj Multiparton interactions in Herwig 6/5/205
Colour connections in Herwig t Soft gluon Soft gluon t The current connections are and Frashër Loshaj Multiparton interactions in Herwig 6/5/205
Colour reconnection Allow reshuffling of clusters (rs) + (lm) if total mass is lower: M rl + M sm < M rs + M lm [Eur.Phys.J.C72 (202) 2225] Frashër Loshaj Multiparton interactions in Herwig 6/5/205
Min-bias ATLAS (900 GeV) Good agreement with data; example from [Eur.Phys.J.C72 (202) 2225] Charged particle η at 900GeV, track p > 500MeV, for N ch 6 Charged multiplicity 6 at 900GeV, track p > 500MeV /NevdN ch/dη 2.6 2.4 2.2 2.8.6.4.2 ATLAS data Hw++ 2.4, µ 2 =.0, p min = 3.0 Hw++ 2.5, MB900-CTEQ6L /σdσ/dn ch 0.4 0.2 0. 0.08 0.06 0.04 0.02 ATLAS data Hw++ 2.4, µ 2 =.0, p min = 3.0 Hw++ 2.5, MB900-CTEQ6L.4 0.4 MC/data.2 MC/data.2-2 - 0 2 η 0 5 20 25 30 35 40 45 N ch Charged particle p at 900GeV, track p > 500MeV, for N ch 6 Charged p vs. N ch at 900GeV, track p > 500MeV, for N ch /Nev/2πp dσ/dηdp 0 0 2 0 3 0 4 0 5 0 6 0 7 0 8 ATLAS data Hw++ 2.4, µ 2 =.0, p min = 3.0 Hw++ 2.5, MB900-CTEQ6L p [GeV] 0.4 0.2 ATLAS data Hw++ 2.4, µ 2 =.0, p min = 3.0 Hw++ 2.5, MB900-CTEQ6L 0 9.4 0.4 MC/data.2 MC/data.2 0 p [GeV] 5 0 5 20 25 30 35 40 45 N ch Fig. 2 Comparison of Herwig 2.4.2 without CR and Herwig 2.5 with PCR to ATLAS minimum-bias distributions at Frashër Loshaj s = 0.9 TeV with Nch 6, p > 500 MeV and η < 2.5. The ATLAS data was published in Ref. [5]. Multiparton interactions in Herwig 6/5/205
Min-bias ATLAS (7 TeV) MC/Data /Nev dn ch/dη 4 3.5 3 2.5 2.5 0.5 0.4.2 Charged particle η at 7 TeV, track p > 500 MeV, for N ch 6 Data LHC-MB -2-0 2 η MC/Data /Nev /2πp dσ/dηdp 0 0 2 0 3 0 4 0 5 0 6.4.2 Charged particle p at 7 TeV, track p > 500 MeV, for N ch 6 Data LHC-MB 0 p [GeV] Data taken from [New J.Phys. 3 (20) 053033]. Plotted with Rivet. Default Herwig 7.0 soft MPI model; default tune. Frashër Loshaj Multiparton interactions in Herwig 6/5/205
Min-bias - Energy extrapolation to 00 TeV We use UE-EE-4 to get MB extrapolated results. Example of results @ 00 TeV: Charged particle η at 7 TeV, track p > 00 MeV, for N ch 2 Charged p vs. N ch at 7 TeV, track p > 500 MeV, for N ch MC/Data /Nev dn ch/dη 6 4 2 0 8 6 4 Data UE-EE-4-00TeV 2 0.4.2-2 - 0 2 η MC/Data p [GeV].2 0.4 0.2 Warnings: taken from Andrzej Siodmok Only Results thebased underlying on tuneevent to UE is data tuned. only. No soft diffraction model. Data UE-EE-4-00TeV 0.4.2 20 40 60 80 00 20 N ch Frashër Loshaj Multiparton interactions in Herwig 6/5/205
Challenge: the Bump problem Forward pseudorapidity gap η F. Defined as the larger of two pseudorapidities from the last particle to the edge of the detector. [Eur.Phys.J. C72 (202) 926] Too many events with large rapidity gaps, especially if colour reconnection is switched on. Frashër Loshaj Multiparton interactions in Herwig 6/5/205
MPI - summary Miminum bias model includes the following pieces: Hard MPI Soft MPI Colour connection Hadronization Diffraction Soft diffraction is not implemented in Herwig 7.0. In the following we construct a new soft interaction model and soft diffraction model. Frashër Loshaj Multiparton interactions in Herwig 6/5/205
Soft scatter kinematics - Multi-peripheral ladder Consider one pomeron cut; N log E cm /m, p i+ = ( x ) ( x i+ )x i p A+, x i /2. p A p B... p 2 p 3 [Phys.Rept. 28 (976) -43] Ordering in rapidity. No correlations. Amplitude not large when sub-energies s i,i+ = (p i + p i+ ) 2 large. Challenges for Herwig: What are color connections. what is the multiplicity. Frashër Loshaj Multiparton interactions in Herwig 6/5/205
Colour connection of multiple ladders Many pomeron cuts; average number n(s, µ s ) = A(b, µ s )σ s (s). Colour connections: Needs to be tuned and matched with the hard MPI. Frashër Loshaj Multiparton interactions in Herwig 6/5/205
Diffraction in hadron collisions Events with rapidity gaps A Rapidity gap B Cross section behaves as dσ = dσ e B t dσ ( B t ), dt dt dt t=0 t=0 in analogy with diffraction in optics I(θ) I(0) ( Bk 2 θ 2). A definition: diffraction is a high energy process in which no quantum numbers are exchanged between colliding particles. Frashër Loshaj Multiparton interactions in Herwig 6/5/205
Generating diffractive events From Regge theory, for single diffraction, we have: ( d 2 σ SD ( s ) αp(0) dm 2 dt B 0 +2α ( ln e M 2 Similarly for double diffraction d 2 σ DD ( ) αp (0) ( ) αp (0) s dm 2dM2 2 dt s0 M 2 M2 2 e s M 2 )) t b+2α ln ss 0 M 2 t M2 2 where b is very small and s 0 /α. We also use the following values of parameters: α(0) =.058, B 0 = 0. GeV 2, α = 0.25 GeV 2. Damping factor ( M 2 /s) was used to include points in phase space not covered by Regge theory.. Frashër Loshaj Multiparton interactions in Herwig 6/5/205
Diffractive events in Herwig We implement soft diffraction in Herwig by modelling it with the following matrix element A A B B q A B q Quark (q) and diquark (qq) form a cluster with diffractive mass, stretched along the dissociated proton. Frashër Loshaj Multiparton interactions in Herwig 6/5/205
Diffraction (preliminary) results Rapidity gap size in η starting from η = ±4.9, pt > 200 MeV Rapidity gap size in η starting from η = ±4.9, pt > 400 MeV dσ/d η F [mb] 0 2 0 MC (LHC-Diffraction) dσ/d η F [mb] 0 2 0 MC (LHC-Diffraction) MC/Data 0.4.2 0 2 3 4 5 6 7 8 η F MC/Data 0.4.2 0 2 3 4 5 6 7 8 η F (Data taken from [Eur.Phys.J. C72 (202) 926]. Plotted with Rivet.) Reproduces well the plateau. Relative weight between single and double diffraction may need to be tuned simultaneously with other parameters. Frashër Loshaj Multiparton interactions in Herwig 6/5/205
Combining min-bias and diffractive runs (preliminary) Rapidity gap size in η starting from η = ±4.9, pt > 200 MeV Rapidity gap size in η starting from η = ±4.9, pt > 400 MeV dσ/d η F [mb] 0 2 0 MC (LHC-MB-Total) dσ/d η F [mb] 0 2 0 MC (LHC-MB-Total) MC/Data 0.4.2 0 2 3 4 5 6 7 8 η F MC/Data 0.4.2 0 2 3 4 5 6 7 8 η F (Data taken from [Eur.Phys.J. C72 (202) 926]. Plotted with Rivet.) The soft interaction model still produces rapidity gaps. Tuning needed to get the correct multiplicity. Frashër Loshaj Multiparton interactions in Herwig 6/5/205
Min-bias with the new soft model (preliminary) /Nev dn ch/dη MC/Data 9 8 7 6 5 4 3 2 0.4.2 Charged particle η at 7 TeV, track p > 00 MeV, for N ch 2 MC (LHC-MB-CRpt3) MC (LHC-MB-CRpt2p5) -2-0 2 η /Nev /2πp dσ/dηdp MC/Data 0 0 0 2 0 3 0 4 0 5.4.2 Charged particle p at 7 TeV, track p > 00 MeV, for N ch 2 0 0 MC (LHC-MB-CRpt3) MC (LHC-MB-CRpt2p5) p [GeV] Charged particle η at 7 TeV, track p > 500 MeV, for N ch 6 Charged particle p at 7 TeV, track p > 500 MeV, for N ch 6 /Nev dn ch/dη MC/Data 4 3.5 3 2.5 2.5 MC (LHC-MB-CRpt3) MC (LHC-MB-CRpt2p5) 0.5 0.4.2-2 - 0 2 η MC/Data /Nev /2πp dσ/dηdp 0 0 2 0 3 0 4 0 5 0 6.4.2 MC (LHC-MB-CRpt3) MC (LHC-MB-CRpt2p5) 0 p [GeV] Plots with p min Correlation between p min = 2 and 3 GeV. we have one more tunable parameter. and µ may not exist anymore, therefore Frashër Loshaj Multiparton interactions in Herwig 6/5/205
Summary and outlook We reviewed the hard and soft MPI models in Herwig. Good agreement with data. Challenge: the so-called bump problem: the soft interaction model in Herwig produces too many events with large rapidity gaps. To address the problem we: modified the soft interaction model and implemented soft diffraction. Preliminary results show qualitative improvement, but more work is needed. Proper tuning has to be done and other observables should be checked as well. Diffraction and soft interaction model have to be sampled properly. Frashër Loshaj Multiparton interactions in Herwig 6/5/205