Multiple production up to √s = 13 TeV with the generator GHOST adapted to Cosmic Ray simulation J.N. CAPDEVIELLE APC-CNRS and Univ.Paris Diderot, Paris Z. PLEBANIAK, B.SZABELSKA, J. SZABELSKI NCBJ, AstroPh- Lodz, Poland

Outlook Individual collisions and Violation of KNO scaling - Consequences of Feynman scaling on rapidity and pseudorapidity density distributions - limit for KNO scaling concerning total charged multiplicity - KNO scaling in central region ? In fragmentation region? - Empirical scaling and semi-inclusive data Basic features of VHE Interactions - Average charged multiplicity and central pseudorapidity density - Average pseudorapidity distribution and mean multiplicity Cosmic Ray data in the LHC energy domain

A hopeless complexity ! ( pioneers of cosmic ray muon component) Feynman’s scaling suggested one distribution of rapidity of charged secondaries in the shape of a plateau with gaussian wings and a simple relation with the distribution of pseudorapidity measured Initiation of phenomenological EAS simulation based on the results of synchrotrons, colliders, supercolliders up to LHC energies, now near of √s = 14 TeV (i.e eV for primary protons) Fluctuations of very high energy interactions, convolution with C.R. primary spectrum, random EAS development…

KNO scaling violation Fluctuations of NSD total charged multiplicity Violation between ISR (√s = 53 GeV) and UA5(√s = 540 GeV) established in 1983 UA5, Alner et al., Phys. Lett. B 180 (1986), 415

Scaling in central region Valid for I  I  Apparent scaling from 53 GeV up to collider energies of UA5 in the central region. Agreement was also observed between UA1 and UA5 for I  I< 1.5 UA5 –Collaboration, Phys. Lett. B 138 (1984), 304

Violation of KNO scaling at √ s = 7 TeV? Measurements in LHC of ATLAS for I  I< 2.5 (squares) and UA5 ( TeV) for I  I< 1.5 (triangle up) and I  I< 2.5 (triangle down) KNO scaling in central region of pseudorapidity is no more conserved for √ s = 7 TeV

Violation of KNO scaling in central region? Comparison of GHOST results (histograms) with Alice (circles) at I  I< 1.0 and Atlas I  I< 2.5 at Vs = 7 teV with UA5(.546 TeV) (I  I<1.5 and I  I<2.5

Test of scaling in fragmentation region UA5 Inelastic pseudorapidty distribution in the beam rest frame for √s=53 (triangle), 200(circle), 546(cross), 900(dark circle) GeV far from fragmentation area (-2.5 units ) No evidence for scaling UA5, ZPC 33, 1986, 1

Test of scaling in fragmentation region UA5 NSD Charged particle pseudorapidity distribution at √s= 900 GeV(open circ.), 546 GeV(dark circ.), 200 GeV(triangles ) Normalized by n ch (last point at I  I< 4.8)! Not conclusive UA5, ZPC 33, 1986, 1

Fluctuations of Multiplicity (KNO variables) KNO distribution valid from Serpukkov up to ISR Negative Binomial Distribution at larger energies Asymptotic distribution at √s = 40 TeV ?

An important guideline (NSD, ~6.6 at 13 TeV)

= − s = − s       s Another guideline ( = 95+/-2 at 13 TeV)

Gaussian hadronic generation Multiplicity N via negative binomial function  (z) with KNO scaling violation (z=N/ ) Central regularity vs z, parameters for semi-inclusive data couples (y i, p t i ) via gaussian generation of rapidity and p t Validity of the set of secondaries for a single collision, conservation laws, rejections… Treatment of SD and DD Respective cross sections for SD, DD, NSD and inelastic data

Approach with Gaussian deviates 4 gaussian functions A i {exp(-0.5u i ) + exp(-0.5v i )} u i = {(y-y i )/  i } 2 v i = {(y+y i )/  i } 2 A i = 5.21, 5.6 Y i = 4.7, 1.53  I = 1.5, 1.3 GHOST Generator Hadronic Oversteering Secondary Treatment

INTEST Option of CORSIKA with Z.Plebaniak and J. Zsabelski (no cuts on Pt)

Inelastic pseudorapidity CMS data. Calculation with the generator GHOST

NSD and INELASTIC distributions Simulation with Ghost Data from CMS (only inelastic)

Conclusion

Dictionnaire Philosophique de Voltaire, dictionnaire portatif Londres, imprimé clandestinement par Grasset à Genève, Juillet 1764, confié à Mme du Deffand (1759) définition du mot matière 300 feets under the manor of Voltaire in Ferney Voltaire, the LHCb is working …LHCb is an experiment set up to explore what happened after the Big Bang that allowed matter to survive and build the Universe we inhabit today

Matière :..des professeurs et surtout des écoliers savent parfaitement tout cela ; et quand ils ont répété que la matière est étendue et divisible, ils croient avoir tout dit ; mais quand ils sont priés de dire ce que c’est que cette chose étendue, ils sont embarrassés. Cela est composé de parties disent-ils, et ces parties de quoi sont elles composées ? Les éléments de ces parties sont ils divisibles? Alors ou ils sont muets ou ils parlent beaucoup ce qui est également suspect. Cet être inconnu qu’on nomme matière, est il éternel? Toute l’Antiquité l’a cru….