Theory Models of Hadron Collisions

1. Theory Models of Hadron Collisions Joint UE/MB Meeting, CERN, Aug 14 2009

2. MC Models: Perturbative Part QF FSR FSR 22 22 ISR ISR ISR Underlying Event has perturbative part! • Starting point: Matrix Elements + Parton Showers • Hard parton-parton scattering • Normally22 at LO or NLO • + bremsstrahlung associated with it •  2n in (improved) LL approximation •  2n at LO up to matched order ISR FSR … FSR • But hadrons are not elementary • + QCD diverges at low pT  multiple perturbative parton-parton collisions QF QF >> ΛQCD e.g. 44, 3 3, 32 • No factorization theorem • Herwig++, Pythia, Sherpa: MPI models Underlying Event in Herwig and Pythia - 2

3. MC Models: Non-Perturbative Part QF FSR FSR 22 22 ISR ISR ISR • Hadronization • Remnants from the incoming beams • Additional (non-perturbative / collective) phenomena? • Bose-Einstein Correlations • Non-perturbative gluon exchanges / color reconnections ? • String-string interactions / collective multi-string effects ? • “Plasma” effects? • Interactions with “background” vacuum, remnants, or active medium? QF >> ΛQCD ME+ISR/FSR + perturbative MPI + Stuff at QF ~ ΛQCD ISR FSR … FSR QF Need-to-know issues for IR sensitive quantities (e.g., Nch) Underlying Event in Herwig and Pythia - 3

4. Naming Conventions FSR FSR 22 22 ISR ISR ISR Some freedom in how much particle production is ascribed to each: “hard” vs “soft” models • Many nomenclatures being used. • Not without ambiguity. I use: Qcut … ISR FSR … FSR … Qcut Multiple Parton Interactions Beam Remnants Primary Interaction (~ trigger) Underlying Event Note: each is colored  Not possible to separate clearly at hadron level Inelastic, non-diffractive Underlying Event in Herwig and Pythia - 4

5. Measurements  Constraints  “Tuning” • Models only as good as • Their underlying physics assumptions (if a model is simple, it is wrong) • Their parameter constraints (even the most fancy is useless without constraints) • E.g., even a great Tevatron tune • May be totally off at RHIC/LHC energies if energy scaling not well modeled & constrained • Even if “retunable”, which model would you trust more? One that also described RHIC, Tevatron? Or one that didn’t? • Starting at 7 TeV will help map out energy dependence  improve models • May be off for quantities that were inclusively summed over • E.g., which model would you trust more? • One that describes total Nch, pT spectra, etc, or one that also described those distributions separately for pions, Kaons, Lambdas, B mesons etc? • One that describes those spectra in the ATLAS/CMS acceptance region, or one that also describes them in the region measured by LHCb? • E.g., validate on pT and Nchdensity at η=2.0 (or in 1.8<η<2.5? Or smaller?) Underlying Event in Herwig and Pythia - 5

6. Measurements  Constraints  “Tuning” • Some examples of tuning an imperfect model • Example 1: Proton lumpiness • MPI Model A (e.g, the ‘old’ Pythia model) no showers off the MPI. • To help generate large fluctuations, need a very lumpy proton •  large difference between peripheral and central collisions. • MPI Model B (e.g., the ‘new’ Pythia one)does have showers off the MPI. • More/less active showers  more intrinsic fluctuations •  Generally need a less lumpy proton. • Example 2: ISR model • ISR Model A: DY  αS(0.2pT2)(the ‘W’ in DW et al) • ISR Model B (dipole recoils): fine with αS(pT2) • ISR Model C: Modify behaviour close to IR cutoff  less prim. kT • Different cocktails indeed – But nonetheless hard to tell apart  Proton mass distribution used to compensate for lack of MPI showers?  Arg of αS used to compensate for ‘bad’ recoil model?  Non-perturbative ‘primordial kT’ used to compensate for ‘bad’ shower in IR? Crucial to have many mutually complementary constraints Underlying Event in Herwig and Pythia - 6

7. Measurements  Constraints  “Tuning” • Some examples of tuning a good model • Example A: Rick Field’s Tunes • Tuning only used Underlying-Event data. • (‘W’ ones include Drell-Yan as well) • Robust model  Tunes also in excellent agreement with min-bias • Example B: Tune S0 and the Perugia Tunes • The converse: Tunes only used Min-Bias data. • Robust models  Tunes also in excellent agreement with Underlying-Event • Note, however, that A and B on this and the previous slides are identical Robust models have larger ranges of validity  predictivity Underlying Event in Herwig and Pythia - 7

8. MC ModelsPerturbative Part

9. Why Perturbative MPI? = color-screening cutoff (Ecm-dependent, but large uncert) Saturation? Current models need MPI IR cutoff >PS IR cutoff • Analogue: Resummation of multiple bremsstrahlung emissions • Divergent σ for one emission (X + jet, fixed-order) • Finite σ for divergent number of jets (X + jets, infinite-order) • N(jets) rendered finite by finite perturbative resolution = parton shower cutoff Bahr, Butterworth, Seymour: arXiv:0806.2949 [hep-ph] • (Resummation of) Multiple Perturbative Interactions • Divergent σ for one interaction (fixed-order) • Finite σ for divergent number of interactions (infinite-order) • N(jets) rendered finite by finite perturbative resolution Underlying Event in Herwig and Pythia - 9

10. How many? • The interaction cross section • … is an inclusive number. • … so an event with n interactions … • … counts n times in σ2jbut only once in σtot With constant αs, neglecting x integrals • Poisson only exact if the individual interactions are completely independent, so will be modified in real life • Herwig++/Jimmy starts directly from Poisson  n, but includes vetos if (E,p) violated. • Pythia uses a transverse-momentum ordered Sudakov formalism, interleaved with the shower evolution ~ resummation. (E,p) explicitly conserved at each step. Underlying Event in Herwig and Pythia - 10

11. How many? • Different Cocktails  Probability distribution of NMPI Not necessary to believe in these particular numbers. But good to know this is what is obtained with out-of-the-box MC models Note: This is min-bias; <Nint> larger for UE. <Nint>new ~ 3.5 <Nint>old ~ 6.0 Important Difference: Old model had no showers off MPI PS, Perugia Proceedings, in preparation Buttar et al., Les Houches SMH Proceedings (2007) arXiv:0803.0678 [hep-ph] More plots collected at http://home.fnal.gov/~skands/leshouches-plots/ Underlying Event in Herwig and Pythia - 11

12. Different Cocktails? • Observed charged particle multiplicity Moral: vastly different cocktails can give similar answers (stable particle definition: cτ ≥ 10mm) Buttar et al., Les Houches SMH Proceedings (2007) arXiv:0803.0678 [hep-ph] More plots collected at http://home.fnal.gov/~skands/leshouches-plots/ Underlying Event in Herwig and Pythia - 12

13. Impact Parameter • Impact parameter: central vs. peripheral collisions All models currently assume f(x,b) = f(x) g(b) • Obviously not the final word. Is this connected to E-scaling? • Large fluctuations g(b) needs to be “lumpy” Large difference between peripheral and central “No” UE in peripheral collisions (low multiplicity) “Saturated” UE in central collisions (high multiplicity) “Jet pedestal” effect Pythia: default: tune A double gaussian: “hard core” (valence lumps?) Core size a2/a1 = 0.5 Contains fraction β = 0.4 Herwig++/Jimmy: EM form factor, but width rescaled to smaller radius μep = 0.7 GeV2 μ = 1.5 GeV2 Underlying Event in Herwig and Pythia - 13

14. Multi-parton pdfs Snapshot of proton: re-use 1-parton inclusive f(x) Subsequently impose (E,p) cons by vetoing events that violate it. 1-parton inclusive f(x) = pdf for “trigger” scattering Multi-parton pdfs explicitly constructed, respecting flavour and momentum sum rules Herwig Pythia quarks gluons Underlying Event in Herwig and Pythia - 14

15. Interleaved Evolution Pythia “New” Pythia model Fixed order Matrix elements parton shower (matched to further matrix elements) • Underlying Event (interactions correllated in colour: hadronization not independent) multiparton PDFs derived from sum rules perturbative “intertwining”? Beam remnants Fermi motion / primordial kT Sjöstrand, PS; JHEP03(2004)053, EPJC39(2005)129 Underlying Event in Herwig and Pythia - 15

16. MC ModelsNon-Perturbative Part

17. Now Hadronize This hadronization bbar from tbar decay pbar beam remnant p beam remnant qbar from W q from W q from W b from t decay ? Triplet Anti-Triplet Simulation from D. B. Leinweber, hep-lat/0004025 gluon action density: 2.4 x 2.4 x 3.6 fm Underlying Event in Herwig and Pythia - 17

18. Standard Assumptions • Jet universality • Jets fragment in the same way in pp as they did at LEP • Not unreasonable, but must be tested in situ • Cannot be expected to hold to infinite precision • Look for when breakdown occurs • Need tracers …(e.g., pT spectra for identified particles) • Assumed by all models / tunes • Remnant Fragmentation • Gives “Soft Component” vs “Hard” MPI component • What is the balance between the two? • Need tracers … (e.g., remnant clearly identified by having a net baryon number  Lambdabar / Lambda < 1 traces remnant breakup) Underlying Event in Herwig and Pythia - 18

19. Underlying Event and Color • The colour flow determines the hadronizing string topology • Each MPI, even when soft, is a color spark • Final distributions crucially depend on color space Note: this just color connections, then there may be color re-connections too Need tracers … Underlying Event in Herwig and Pythia - 19

20. Underlying Event and Color • The colour flow determines the hadronizing string topology • Each MPI, even when soft, is a color spark • Final distributions crucially depend on color space Note: this just color connections, then there may be color re-connections too Need tracers … Underlying Event in Herwig and Pythia - 20

21. Min-bias data at Tevatron and RHIC showed a surprise Charged particle pT spectra were highly correlated with event multiplicity: not expected For his ‘Tune A’, Rick Field noted that a high correlation in color space between the interactions could account for the behavior But needed ~ 100% correlation. So far not explained Virtually all ‘tunes’ now employ these more ‘extreme’ correlations But existing models too crude to access detailed physics What is their origin? Why are they needed? Underlying Event and Color 2 Not only more (charged particles), but each one is harder Tevatron Run II Pythia 6.2 Min-bias <pT>(Nch) Tune A Diffractive? old default Non-perturbative <pT> component in string fragmentation (LEP value) Peripheral Small UE Central Large UE SO: the hadron-level pT spectra depend non-trivially on UE model. The parton-level ones do not.  frag. corr. depends on UE (but levels off  const for hard triggers?) Successful models: string interactions (area law) PS & D. Wicke : EPJC52(2007)133 ; J. Rathsman : PLB452(1999)364 Underlying Event in Herwig and Pythia - 21

22. Theory Uncertainties • Large uncertainties  need more than just ‘central’ tunes • Similar to PDFs  Need MCs with uncertainty bands • Perugia Tunes • Begin to address this issue  small set of systematically different tunes • 320 Perugia 0 : Central CTEQ5L Tune • Also includes 2009 LEP fragmentation tunes by Professor Group (Bowler, etc.) • 321 Perugia HARD : harder ISR/FSR, less non-pert. • αS(0.5pT)CMW, PARP(67)=4, PARP(71)=4, larger ΛFSR, higher MPI cutoff, prim kT = 1.0 GeV • 322 Perugia SOFT : softer ISR/FSR, more non-pert. • αS(sqrt(2)pT)MSbar, PARP(67)=0.5, PARP(71)=1, smaller ΛFSR, lower MPI cutoff • 323 Perugia 3 : different ISR/MI balance  different energy scaling • 324 Perugia NOCR : best tune without color reconnections • 325 Perugia LO* : LO* has more glue, so harder MPI • Higher MPI cutoff, αS(sqrt(2)pT)CMW • 326 Perugia 6 : CTEQ6L1 has different glue  different scaling • Obviously not the last word • Using a few main model parameters as substitutes for eigenvectors • Note: one could imagine some well-motivated further variations • E.g., a tune weighting B fragmentation higher, to be used for B physics? Underlying Event in Herwig and Pythia - 22

23. Perugia Tunes: Min-Bias • Huge model building and tuning efforts by many groups (Herwig, Professor, Pythia, Sherpa, … ) • Summarized at a recent workshop on MPI in Perugia (Oct 2008) • For Pythia (PYTUNE), 6.4.20 now out  “Perugia” and “Professor” tunes • Scaling to LHC much better constrained, HARD/SOFT, + CTEQ6, LO* • TeV-1960, TeV-1800, TeV-630, (UA5-900, UA5-546, UA5-200) (stable particle definition: cτ ≥ 10mm) Underlying Event in Herwig and Pythia - 23

24. Drell-Yan • Both the CDF and D0 analyses have been included • NB: Very tricky point: photon bremsstrahlung! • Need to make sure corrections are done (and documented) in an “MC-friendly” way Underlying Event in Herwig and Pythia - 24

25. Extrapolations to 10 TeV (yes, I know…) • Useful to get a first-order idea of uncertainties • Encourage tuning groups to do systematic MIN/MAX variations along these lines (not necessarily exactly as done here) • As with all kinds of uncertainties, can be misleading. Important to get effort started. • Compare with PDF uncertainties: still on a learning curve. Good thing they started trying to develop a systematic approach already some years ago. (stable particle definition: cτ ≥ 10mm) Underlying Event in Herwig and Pythia - 25

26. Pythia 8 – Tune 1 • First complete tune of Pythia 8 • Tune to LEP data by professor group, then by hand to Tevatron + UA5 data, roughly same procedure as for Perugia tunes • In fact, only minor readjustments were needed • For the parameters (for Pythia 8.125), just ask Torbjörn or me. Will be included with next Pythia-8 release Underlying Event in Herwig and Pythia - 26