Modelling of the interplay between hard and soft processes in pp P - PowerPoint PPT Presentation

Modelling of the interplay between hard and soft processes in pp P e t e r S k a n d s ( C E R N ) ” e g d i R “ S M Main tools for high-p T calculations C s e i t i c i l p i t l u m Factorization and IR safety k c a r T p T spectra Corrections suppressed by powers of Λ QCD /Q Hard s e l c t i r a P Soft QCD / Min-Bias / Pileup d e fi i t n e d I HADRONIZATION Baryon Transport NO HARD SCALE C o r r e l a t Typical Q scales ~ Λ QCD i o n s Extremely sensitive to IR effects C e n t r a l v s F o r w a r d → Excellent LAB for studying IR effects Collective Effects? ~ ∞ statistics for min-bias C o l o r C → Access tails, limits o r r e l a t i o n s Rapidity Gaps Universality: Recycling PU ⬌ MB ⬌ UE W o r k s h o p o n C e n t r a l i t y i n p A c o l l i s i o n s C E R N , F e b r u a r y 2 0 1 4

Is there no hard scale? Compare total (inelastic) hadron-hadron cross section to calculated parton-parton (LO QCD 2 → 2) cross section 200 GeV pp 0.2 TeV 4 Integrated Cross Section (mb) 10 Integrated cross section [mb] (p p ) vs p σ ≥ 2 → 2 T Tmin Tmin (fit) TOTEM 3 σ 10 INEL =0.130 NNPDF2.3LO α s =0.135 CTEQ6L1 α s Leading-Order pQCD 2 10 total inelastic cross section Z d σ Dijet dp 2 ⊥ dp 2 10 p 2 ⊥ Hard jets ⊥ , min 1 are a LO QCD 2 → 2 (Rutherford) small tail V I N C I A R O O T -1 10 d σ 2 → 2 / dp 2 Pythia 8.183 ⊗ PDFs ⊥ -2 10 p 4 ⊥ 1.5 RATIO Expect average pp event Ratio to reveal “partonic” 1 structure at 1-2 GeV scale 0.5 0 0 5 10 15 20 p Tmin 2 P. S k a n d s

→ 8 TeV → 100 Tev → Trivial calculation indicates hard scales in min-bias 100 TeV 8 TeV pp 100 TeV pp 8 TeV 5 10 Integrated cross section [mb] 4 Integrated Cross Section (mb) 10 Integrated cross section [mb] (p p ) vs p σ ≥ (p p ) vs p σ ≥ 2 2 → T Tmin Tmin 2 → 2 T Tmin Tmin TOTEM σ (data) TOTEM σ INEL 4 10 INEL 3 α =0.130 NNPDF2.3LO 10 =0.130 NNPDF2.3LO s α s =0.135 CTEQ6L1 α =0.135 CTEQ6L1 s α s 3 10 2 total inelastic cross section 10 2 10 10 LO QCD 2 → 2 (Rutherford) V I N C I A R O O T 10 V I N C I A R O O T 1 Pythia 8.183 Pythia 8.183 1 -1 10 → 10 GeV scale! 1.5 1.5 Expect average pp event RATIO Ratio Ratio to reveal “partonic” 1 1 structure at 4-5 GeV scale! 0.5 0.5 0 0 0 5 10 15 20 0 5 10 15 20 p p Tmin Tmin 3 P. S k a n d s

MPI Multiple perturbative parton -parton interactions Simple consequence of having lots of partons (in each hadron) and large interaction cross section h n 2 → 2 ( p ⊥ min ) i = σ 2 → 2 ( p ⊥ min ) Naively σ tot Interactions independent (naive factorization) → Poisson a solution to : m ∞ P n = � n � n � = σ n σ tot e −� n � n =0 ∞ n ! � � = n σ n σ int n =0 rgy–momentum conser σ tot ⇐ ⇒ � ⇒ � n � > 1 > σ tot ⇐ > P n σ int σ int Real Life (example) � n � = 2 Color screening: σ 2 → 2 → 0 for p ⊥ → 0 Momentum conservation suppresses high-n tail Impact-parameter dependence + physical correlations n → not simple product 0 1 2 3 4 5 6 7 4 P. S k a n d s

Impact Parameter 1. Simple Geometry (in impact-parameter plane) Simplest idea: smear PDFs across a uniform disk of size π r p2 → simple geometric overlap factor ≤ 1 in dijet cross section Some collisions have the full overlap, others only partial → Poisson distribution with different mean <n> at each b 2. More realistic Proton b-shape Smear PDFs across a non-uniform disk MC models use Gaussians or more /less peaked Overlap factor = convolution of two such distributions → Poisson distribution with different mean <n> at each b “Lumpy Peaks” → large matter overlap enhancements, higher <n> Note: this is an effective description. Not the actual proton mass density. E.g., peak in overlap function ( ≫ 1) can represent unlikely configurations with huge overlap enhancement. Typically use total σ inel as normalization. → see next talk by M. Strikman 5 P. S k a n d s

36 A MULTIPLE-INTERACTION MODEL FOR THE EVENT. . . 2031 treme of a ftx overlap Each system diffractive is represented by a string the use of the formal- system. Oo(b) (with in Sec. IV, i. e. , requiring stretched between a diquark in the forward end and a ism at least one semihard in- in the other one. Except for some tries with a dou- quark teraction so as to minimize per event, other differences). ble string stretched from a diquark and a quark in the for- The three other matter distributions, Gauss- solid sphere, to a central gluon, ward direction which gave only modest ian and exponential, are in between, and are all compati- changes in the results, no attempts have been made with ble with the data. models for diHractive states. the total more detailed Within the model, distribution multiplicity can be separated into the contribution from (double-) V. MULTIPLICITY DISTRIBUTIONS diffractive events, events with one interaction, events and so on, Fig. 13. While 45% of with two interactions, The distribution charged-multiplicity is interesting, all events contain one interaction, the low-multiplicity its since most despite deceptive simplicity, physical tail is dominated by double-diffractive events and the mechanisms (of those a role in minimum bias playing one by events with several interactions. high-multiplicity to the multiplicity This was events) contribute buildup. The average charged increases the multiplicity with in Sec. III. From illustrated now on we will use the of interactions, Fig. 14, but not proportionally: number model, i. e. , including interactions complete multiple and each additional interaction gives a smaller contribution impact to look more closely at the varying parameters, of than the one. This preceding is partly because data. Single- and double-difFractive events are now also energy-momentum-conservation effects, be- and partly included; with the UA5 triggering conditions roughly up" —, cause the additional messing when new string of the generated double-diffractive events are retained, pieces are added has less effect when al- many strings the contribution from single diffraction is negligi- while ready are present. The same phenomenon is displayed in Charged Multiplicity ble. of the "enhancement factor" Fig. 15, here as a function f (b), i. e. , for increasingly central collisions. The multiplicity for the 200- and 900-GeV distributions A. Total multiplicities UA5 data have not been but published, the moments ' and a comparison A final comparison the UA5 data at 540 GeV is with have, with these is presented in Table I. The (n, t, ) value in Fig. 12, for the double Gaussian matter dis- presented was brought in reasonable agreement tribution. The agreement is now generally good, although with the data, at each energy of separately, by a variation the value at the peak is still a bit high. In this distribu- the pro scale. The moments thus obtained are in reason- tion, the varying do not play a major impact parameters able agreement with the data. role; for comparison, Fig. 12 also includes the other ex- B. Energy dependence i. 10 of aver- Extrapolating to higher the evolution energies, I I I I I I I age charged in Fig. 16. multiplicity with is shown energy 1982 DATA UA5 w UA5 1981 DATA ' ' I I I tl 10 variable b fixed b 1P 3— C O -3 10 no MPI with MPI 10-4 Number of Number of t 10 I I i 1 ~ & & 1 j j j I j Charged Tracks Charged Tracks 0 20 40 60 80 100 120 10 0 I I I I I I I I I I 40 60 20 ep 100 120 FIG. 13. Separation of multiplicity at 540 GeV distribution of interactions by number in event for double-Gaussian matter FIG. 12. Charged-multiplicity distribution at 540 GeV, UA5 distribution. Long dashes, double diffractive; dashed-dotted (Ref. 32) vs multiple-interaction results im- one interaction; model with variable thick solid line, two interactions; dashed line, pact parameter: solid line, double-Gaussian matter distribution; three interactions; dotted line, four or more interactions; thin [i. e. , 00(b)] solid line, sum of everything. dashed line, with fix impact parameter Sjöstrand & v. Zijl, Phys.Rev.D36(1987)2019 6 P. S k a n d s

The Pedestal Effect (now called the Underlying Event) As you trigger on progressively higher p T , the entire event increases … … until you reach a plateau (“max-bias”) Leading Track or Jet Interpreted as impact-parameter effect Qualitatively reproduced by MPI models “TOWARDS” REGION Δφ with respect to “TRANSVERSE” leading REGION track/jet “AWAY” Sum(pT) Density (TRANS) REGION ~ Recoil Jet LHC from 900 to 7000 GeV - ATLAS 7 P. S k a n d s