Hadronic Interaction Models and Accelerator Data

Transcription

1 Forschungszentrum Karlsruhe in der Helmholtz-Gemeinschaft Hadronic Interaction Models and Accelerator Data Ralph Engel, Dieter Heck, Sergey Ostapchenko, Tanguy Pierog, and Klaus Werner

2 Outline Introduction: Color flow and strings String fragmentation - Baryon-antibaryon production - Popcorn effect String configurations of different models - Configurations and data - High-density effects Model predictions and comparison with data - Accelerator data - Air shower predictions

3 Color flow and strings (i) Generic scattering diagram di-quark quark proton gluon proton quark di-quark

4 Color flow and strings (ii) Generic scattering diagram QCD color string di-quark quark proton gluon proton quark di-quark

5 quark diquark QCD string fragmentation meson meson baryon Chain of hadrons: large long. momenta near ends small trans. momenta

6 String fragmentation: baryon pairs diquark - anti-diquark pair leading meson leading baryon baryon anti-baryon pair

7 String fragmentation: popcorn effect diquark Diquark splitting: improved description of leading meson and baryon data leading meson baryon leading meson

8 SIBYLL minimum string configuration quark proton diquark proton quark diquark Special fragmentation function for leading diquarks needed for description of data

9 QGSJET minimum string configuration proton proton Generation of sea quark anti-quark pair and leading/excited hadron

10 EPOS minimum string configuration proton proton Generation of sea quark pair for each string Micro-canonical decay of remnants to hadrons

11 Data and two-string models dn/dy Two-string models: very successful long-range correlations charge distribution delayed threshold for baryon pair production Rapidity y (Capella et al., Physics Reports 994)

12 Examples of comparisons with data dn/d! E cm = 630 GeV Simulations with P238 (Harr et al.) trigger DPMJET II.55 nexus 2 QGSJET0 SIBYLL 2. Harr et al. 0 5 p p # p X, NAL Hydrogen Bubble Chamber SIBYLL 2. QGSjet 2 E lab = 405 GeV, x dn/d! E cm = 900 GeV Simulations with UA5 trigger! DPMJET II.55 nexus 2 QGSJET0 SIBYLL 2. d!/dx F (mb) 0 3 E lab = 303 GeV, x00 E lab = 205 GeV, x0 3 UA E lab = 02 GeV ! x F = 2 E p /"s

13 EPOS: string contributions remnant contributions dn/dy dn/dy y SPS low SPS high dn/dy y RHIC y dn/dy LHC y Only model for description of multi-strange baryon production (next slides)

14 EPOS remnant model and data (i) NA49 data (Liu et al., PRD 2003)

15 EPOS remnant model and data (ii) NA49 data (Liu et al., PRD 2003)

16 Two-gluon scattering: SIBYLL proton proton Kinematics etc. given by parton densities and perturbative QCD Two strings stretched between quark pairs from gluon fragmentation

17 Two-gluon scattering: QGSJET proton Two strings with high-pt kinks proton Sea quark pairs form end of strings, generated from model distribution dp dx x

18 Two-gluon scattering: EPOS proton Two strings with high-pt kinks proton Independent sea quarks form string ends

19 SIBYLL: high parton density effects SIBYLL: simple geometric criterion nucleon πr 2 0 α s(q 2 s) Q 2 s xg(x,q 2 s) nucleus log 0 ( E lab / ev ) GRV98 EHLQ (R.E. et al., ICRC 999) No dependence on impact parameter!! (mb) (GeV) E cm Total pp cross section

20 QGSJET: high parton density effects Re-summation of enhanced pomeron graphs Without enhanced graphs With enhanced graphs (Ostapchenko, PLB 2006, PRD 2006)

21 EPOS: high parton density effects (i) projectile partons projectile partons projectile partons projectile partons target partons target partons target partons target partons Parametrization No effective coupling A pom (x x 2 ) β With effective coupling A pom x β xβ ε 2 ε S = a S β S Z, ε H = a H β H Z, ()234567(3*8(59532(:; &#! ( &"! &!! %! $! #! "!! & &! &! " &! ' &! # ()*)+,-(./)0 (Werner et al., PRC 2006)

22 can already happen in pp collisions. EPOS: high parton density effects (ii) projectile partons target partons normal hadronization collective hadronization Coefficient Corresponding variable Value IV. REALIZATION OF LADDER SPLITTING EFFECT The basic quantity for a numerical treatment of the lad splitting effects is the number Z of partons available additional legs; more precisely, we have Z T for counting on the target side and Z P for counting legs on the proje side. Let us treat Z T (corresponding discussion for Z Consider a parton in the projectile nucleon i which inter with a parton in target nucleon j. The number Z T (i, j additional legs has two contributions, one counting the attached to the same nucleon j, and one counting the attached to the other nucleons j j. We assume the form s M Minimum squared screening energy (25 GeV) 2 w M Defines minimum for z w Z Global Z coefficient w B Z Impact parameter width coefficient.60 T (i, j) = z 0 exp ( bij 2 /2b 2) 0 a S Soft screening exponent a H Hard screening exponent z 0 exp( b 2 2 ij /2b ) 0, a T projectile the energy, as Transverse momentum transport a B partons Break parameter target nucleons PARTON LADDER SPLITTING AND THE RAPIDITY... z 0 = w Z j a D Diquark break probability 0.0 log j s/s M PHYSICAL, REVIEW C 74, (5) a S Strange normal break hadronization probability 0.40 a P Averageprojectile break transverse momentum 0.50 thez energy, 0 = w Zas (log s/sm ) 2 + w 2 M, (6) partons ARTON LADDER SPLITTING AND THE RAPIDITY... PHYSICAL REVIEW C 74, (2006) where [log(x) b ij is:= the max(0, distance ln(x)] and z 0 in= the w Z impact log s/s M parameter, width betwee is b and j. The 0 = w coefficients B σinelpp /π, with z 0 and z parameters z 0 0 = w w Z depend B, w (log s/sm logarithmically Z, w ) 2 M, + w 2 and s M. M, collective hadronization target normal hadronization partons We then define (Werner et al., PRC 2006) [log(x) := max(0, ln(x)] and the impact parameter wi collective hadronization Z T (j) = Z T (i, j). (7)

23 Comparison with RHIC data RHIC data: very good agreement, (some measurements inconsistent) proton-proton Ecm = 200 GeV deuteron-gold Ecm = 200 GeV (Werner et al., PRC 2006),6736!6 + -.,/ ,6736!6 + -.,/ !" +!"!!" #!!" #+!" #*!" #)!" #(!" #'!" #&!" #%!" #$!" +!"!!" #!!" #+!" #*!" #)!" #(!" #'!" #&!" #%!" #$,8,,,,,,9:,,,,,/;.<=5!,>,#"?&(!,>,#"?+(!,>,@"?+(!,>,@"?&( "! + * ) ( ' & %,-.,/02345,8,,,,,+"#)"A,,,,,/;.<=5!,>,#"?&(!,>,#"?+(!,>,@"?+(!,>,@"?&( "! + * ) ( ' & %,-.,/02345,6736!6 + -.,/ ,6736!6 + -.,/ !" +!"!!" #!!" #+!" #*!" #)!" #(!" #'!" #&!" #%!" #$!" +!"!!" #!!" #+!" #*!" #)!" #(!" #'!" #&!" #%!" #$,8,,,,,"#+"A,,,,,,,,,/;.<=5!,>,#"?&(!,>,#"?+(!,>,@"?+(!,>,@"?&( "! + * ) ( ' & %,-.,/02345,8,,,,,)"#!""A,,,,,/;.<=5!,>,#"?&(!,>,#"?+(!,>,@"?+(!,>,@"?&( "! + * ) ( ' & %,-.,/02345

24 Model comparison: fixed target p-p data p + p " # + P lab =00 GeV p t = 0.3 GeV/c p + p " K + P lab =00 GeV p + p " # - P lab =00 GeV p t = 0.3 GeV/c p + p " K - P lab =00 GeV p t = 0.3 GeV/c p t = 0.3 GeV/c ev 2 ) p + p " p P lab =00 GeV p t = 0.3 GeV/c p + p " ap P lab =00 GeV QGSJET II-3 EPOS.60 QGSJET0 SIBYLL 2. long. Momentum (GeV

25 Model comparison: fixed target π-p data " + + p # " + P lab =00 GeV QGSJET II-3 EPOS.60 QGSJET0 SIBYLL 2. 0 " + + p # " - P lab =00 GeV p t = 0.3 GeV/c 0 - p t = 0.3 GeV/c " + + p # K + P lab =00 GeV " + + p # K - P lab =00 GeV 0-2 p t = 0.3 GeV/c 0-3 p t = 0.3 GeV/c

26 Model comparison: fixed target p-c data p + C " # + P lab =00 GeV p + C " # - P lab =00 GeV (see also talk by E.-J. Ahn this meeting) 0 - p t = 0.3 GeV/c 0 - p t = 0.3 GeV/c p + C " K + P lab =00 GeV p + C " K - P lab =00 GeV QGSJET II-3 EPOS.60 QGSJET0 SIBYLL p t = 0.3 GeV/c 0-2 p t = 0.3 GeV/c Note: SIBYLL plotting error, has to be scaled down by ~20%

27 Model comparison: fixed target π-c data " + + C # " + P lab =00 GeV " + + C # " - P lab =00 GeV p t = 0.3 GeV/c p t = 0.3 GeV/c " + + C # K + P lab =00 GeV " + + C # K - P lab =00 GeV QGSJET II-3 EPOS.60 QGSJET0 SIBYLL p t = 0.3 GeV/c 0-2 p t = 0.3 GeV/c Note: SIBYLL plotting error, has to be scaled down by ~30%

28 Model comparison: Tevatron data p + ap " chrg at.8 TeV 0 p + ap 0 - p " + ap chrg " at chrg.8 TeV at.8 TeV Model comparison !!! " Fermilab!!! " p + ap " chrg at.8 TeV QGSJET II p + ap " chrg at.8 Model comparison EPOS.60 Fermilab 2 NSD QGSJET !!! " QGSJET II 0.25 SIBYLL 2. EPOS QGSJET SIBYLL peusdorapidity! NSD 0-5 p t (GeV/c) multiplicity n p + ap " K 0 p + ap " chrg s at.80tev at.8 TeV 0-2 p + ap " # at.8 TeV p + ap " chrg 0 at.8-7 TeV !!! " peusdorapidity 0-3!!! " -!!! " !!!! " p t p + ap " # at TeV p + ap " K s at.8 TeV!!! 0-5 " p + ap " chrg at.8!!! " !!! " ev/c) p t (GeV/c) multiplicity 5 n ity! 0p -7 t (GeV/c) 0-6 p t (GeV/c) p + ap at.8 GeV dn/d! dn/dyd dn/dyd 2 p 2 t p (c 2 /GeV 2 ) t (c 2 /GeV 2 ) /$ dn/d! dn/dyd 2 p t (c 2 /GeV 2 ) dn/dyd 2 p t (c 2 /GeV 2 ) P(n) P(n) dn/dyd 2 p t (c 2 /GeV 2 ) dn/dyd 2 p t (c 2 /GeV 2 ) P(n) t dn/d! dn/dyd 2 p t (c 2 /GeV 2 )

29 Mean depth of shower maximum HiRes-MIA HiRes p ) 2 <X max > (g/cm Yakutsk 200 Fly s Eye Yakutsk 993 QGSJET 0 Fe QGSJET II-3 SIBYLL 2. EPOS Energy 0 (ev)

30 Mean number of muons at ground -2 0 Fe ) -???? N µ /E (GeV QGSJET 0 SIBYLL 2. EPOS.60 p QGSJET II Iron (QGSJET) = proton (EPOS) Energy 0 8 (ev) (at 0 8 ev)

31 Electron-muon number correlation EPOS.60 QGSJETII SIBYLL 2. QGSJET ev ev ) µ (N log 5 Fe 6 0 ev 4.5???? ev p log 0 (N ) ch

32 Lateral particle distribution! density (m -2 ) gamma EPOS.55 + FLUKA QGSJET0 + FLUKA QGSJET-II3 + FLUKA SIBYLL2 + FLUKA p E 0 =0 9 ev vertical preliminary???? e! density (m -2 ) e + + e - preliminary Note: Xmax similar for EPOS and SIBYLL p E 0 =0 9 ev vertical EPOS: much flatter lateral distribution for both muons and em. particles "! density (m -2 ) p E 0 =0 9 ev vertical " + + " - preliminary core distance (km)

33 Why is EPOS so much different? Possible sources of differences: baryon antibaryon pair production rate & spectra leading meson production (?) (Pierog & Werner, astro-ph/063) EPOS predicts up to 5 times more baryons in hadronic shower core at high energy Relevant effects (confirmed with modified version of SIBYLL): baryon quantum number conservation transverse momentum distribution of baryons

34 Fixed target data on baryon production (i) Initial momentum 00 GeV Initial momentum 00 GeV QGSJET II EPOS.60 QGSJET0 SIBYLL p + C " ap p + C " ap QGSJET II EPOS.60 QGSJET0 SIBYLL p + C " # + + # p + C " # + + # - 00 GeV lab # + + C " p + ap # + + C " p + ap # + + C " # + + # # + + p " p + ap 0 - # + + C " # + + # long. Momen # + + p " p + ap

35 Fixed target data on baryon production (ii) E xd!/dx # + + p " p xd!/dx # - + p " ap Data: possible misidentification of π+ and p??? Need more data (MIPP, NA49) d"/dx GeV lab xl # + + p! $ 250 GeV lab - 0 xl xl xl xl 0 # + + p! a$ d"/dx xl

36 Tevatron data on baryon production ratio ap/$ dn/dyd 2 p t (c 2 /GeV 2 ) dn/dyd 2 p t (c 2 /GeV 2 ) /$ p + p at.8 GeV Model Model comparison comparison Fermilab Fermilab 0.75 QGSJET QGSJET II II 0.5 EPOS EPOS QGSJET0 QGSJET SIBYLL 2. SIBYLL dn ch /dy(0) p -2 p + ap " # at.8 TeV + ap " # at.8 TeV !!! "!!! " t d 2 p t (c 2 /GeV 2 ) dn/d! dn/dyd 2 p t (c 2 /GeV 2 ) p t (GeV/c) p t (GeV/c) 0-4 p + p at.8 GeV dn/d! 4 dn/dyd 2 p t (c 2 /GeV 2 ) 6 p + ap p + " ap chrg " chrg at.8 at TeV.8 TeV 4 dn/dyd 2 p t (c 2 /GeV 2 ) p NSD NSD p + ap " chrg -7 Model comparison Fermilab peusdorapidity peusdorapidity 4!! QGSJET II 0EPOS p - p + ap.60 + ap " K " K s at.8 s at.8 TeV TeV 0 - p QGSJET SIBYLL 2.!!! "!!! " NSD p + ap " # at.8 TeV /$ dn/d! d 2 p t (c 2 /GeV 2 ) P(n)!!! 0 " p0-3 t (GeV/c) p t (GeV/c) p + ap at.8 GeV dn/dyd 2 p t (c 2 /GeV 2 ) P(n) peu Multiplicity: not really conclusive, EPOS better than other models Transverse momentum important p + ap " K s at!!! 0" 0

37 Model comparison: high energy x F dn/dx F x F dn/dx F EPOS predicts up to 0-5 times more baryons in hadronic 0-2 shower core x F dn/dx F p + C! " + +" - at 2 TeV F dn/dy p + p! ap at 2 TeV Feynman x F 0 - p + C! p at 2 TeV Feynman x F Feynman x F x F dn/dx F x F dn/dx F p + p " ap at 2 TeV p + C! " 0 at 2 TeV Feynman yx F p + C! ap at 2 TeV Feynman x F x F dn/dx F dn/dyd 2 p t (c 2 /GeV 2 )

38 Popcorn effect: leading mesons x F dn/dx F p + p! " + +" - at 2 TeV x F dn/dx F p + p! " 0 at 2 TeV x F dn/dx F p + p! K + +K - at 2 TeV Feynman x F Feynman x F Feynman x F x F dn/dx F 0 - p + p! p at 2 TeV Feynman x F Model comparison pp 2 TeV dn/d! x F dn/dx F QGSJET II EPOS.60 2 QGSJET0 SIBYLL p + p! ap at 2 TeV p + p " chrg at 2 TeV Feynman x F dn/dyd 2 p t (c 2 /GeV 2 ) p + p! " 0 at 2 TeV p t (GeV/c) Tevatron measurements would be extremely helpful dn/dy p + p " # + at 2 TeV

39 Estimated signal for Auger tanks Prediction can be tested with Auger hybrid events Cherenkov density (VEM/m 2 ) Cherenkov density gamma contribution positron contribution electron contribution muon contribution EPOS.55 + FLUKA vertical proton E 0 =0 9 ev Cherenkov density (VEM/m 2 ) EPOS.55 + FLUKA QGSJET0 + FLUKA QGSJET-II3 + FLUKA SIBYLL2 + FLUKA Cherenkov density proton E 0 =0 9 ev vertical preliminary core distance (km) /03/27 preliminary core distance (km)

40 Hybrid measurement: HiRes-MIA Mean depth of shower maximum ! = (0.5) sys. + stat. sys. Muon density at 600 m 2 X max (g/cm ) (600m) (m )! " = (0.02) sys. sys. + stat. 600 p Fe QGSJet log (E/eV) 0 0. QGSJet Iron QGSJet Proton (HiRes-MIA, PRL 2000) 0. 8 E ( 0 ev)

41 Simulation of HiRes-MIA data 900 Mean depth of shower maximum ) HiRes-MIA p 2 <X max > (g/cm HiRes Fe QGSJET 0 EPOS.60 Muon density at 600 m MIA stat+syst err Fe Energy 8 (ev) 9 0 ) -2 p Simulation done for QGSJET and EPOS!(600) (m - 0 QGSJET 0 EPOS.60 (Pierog & Werner, astro-ph/063) 7 0 Energy (ev) 8 0

42 Conclusions Different model concepts Models in reasonable agreement with pion production data Some discrepancies for K+ production Baryon antibaryon production underestimated EPOS gives very good description of data More fixed target measurements needed Tevatron and LHC measurements would help Cosmic ray data will help to discriminate between models (KASCADE: Ne-Nμ, hadrons; Auger hybrid events; inclusive muon flux measurements)

43 Hybrid measurement: A n g l e Pierre Auger Observatory S h o w e r p l a n e 29th International Cosmic Ray Conference Pune (2005) 00, 0 06 First Estimate of the Primary Cosmic Ray Energy Spectrum above 3 EeV from the Pierre Auger Observatory The Pierre Auger Collaboration Presenter: P. Sommers (sommers@physics.utah.edu) F l y ' s E y e w i t h activated phototubes Measurements of air showers are accumulating at an increasing rate while construction proceeds at the Pierre Auger Observatory. Although the southern site is only half complete, the cumulative exposure is already similar to those achieved by the largest forerunner experiments. A measurement of the cosmic ray energy spectrum in the southern sky is reported here. The methods are simple and robust, exploiting the combination of fluorescence detector (FD) and surface detector (SD). The methods do not rely on detailed numerical simulation or any assumption about the chemical composition. I m p a c t p o i n t C e r e n k o v t a n k s Simulation: particles at ground correspond to 25% higher shower energy than measured shower profile P. Sommers et al. astro-ph/ Caution: within current systematic uncertainty