Stefano Carignano 12/2010. Phenomenology of particle production in pp collisions

Transcription

1 Phenomenology of particle production in pp collisions Stefano Carignano 12/2010

2 Outline Some very basic stuff Modeling interactions in pp collisions Strings and hadronization

3 Motivation pp collisions provide one of the cleanest environments for studying properties of strong interaction at high energies Possibility to study rare processes, involving Higgs etc. Necessary for heavy ion data (R AA,... ) Need for some theoretical guidance to experiments: models for particle production

4 Kinematics for dummies Beam axis gives a preferential direction Customary distinction: longitudinal (z) direction vs. transverse (x,y) directions

5 Rapidity Outcoming particle kinematics is often described in terms of rapidity: ( ) y = tanh 1 (v z ) = tanh 1 pz = 1 ( ) p 0 2 log p0 + p z p 0 p z For a particle moving along z with speed β p 0 = γm ; p z = γmβ Non-relativistic limit y = 1 ( ) 1 + β 2 log 1 β β y v z

6 Rapidity II Some useful relations (m T = m 2 + p T 2 ) p 0 = m T cosh(y), p z = m T sinh(y) Additive property of rapidity: y = y 1 ( ) 1 + β 2 log 1 β Rapidity distribution shape doesn t change when boosting!

7 Pseudorapidity Rapidity is determined by 2 quantities (ie. energy and longitudinal momentum) Often useful to introduce pseudorapidity η = 1 ( ) ( ) p + 2 log pz θ = log tan p p z 2 θ = angle between momentum and beam axis For large energies, p = p 0 η = y

8 (Pseudo)Rapidity distributions Rapidity and pseudorapidity spectra are related by dn m = 1 2 dn dηdp T mt 2 cosh2 y dydp T Characteristic plateau for dn/dy at midrapidity results into a small dip in dn/dη distribution

9 Quantites of interest Multiplicities N p T (or m T ) spectra (Pseudo-)rapidity spectra

10 pp collisions: some general features pp cross-section: σ pp 30 s GeV 70-80% of σ pp is inelastic

11 Feynman scaling Distributions factorize in terms of p T and x F = p z / s Hypotesis: Energy is shared between produced particle species with a ratio independent of s Production probability for a particle i with given energy E and momentum (p T, p z ) is then f i (p T, x F )dp z d 2 p T /E 1 σ E d 3 σ dp z d 2 p T = f i (p T, x F ) Average particle multiplicity is then N = d 3 p E f i(p T, x F ) log( s) s

12 Modeling of pp collisions

13 Some things we are pretty confident about When building models for pp collisions, we start from Parton model: nucleons are not elementary particles Confinement: the elementary constituents cannot be observed as free particles QCD is the accepted fundamental theory describing strong interactions

14 The dynamics of the interaction Matrix element methods Parton shower mechanisms

15 Matrix element methods Fixed order predictions: Feynman diagrams σ ij k = dx 1 dx 2 fi 1 (x 1 )fj 2 (x 2 )ˆσ ij k f a i (x) = PDF, characterizing the probability of finding a given parton i in a particle a with a momentum fraction x Advantage: makes full use of the underlying theories CompHEP, MadGraph, Alpgen,...

16 Matrix element methods (II) Limitation: perturbative approach not so good for QCD! NLO corrections can be big Hard to calculate higher orders QCD processes plagued by soft and collinear divergencies Computational power required increases greatly!

17 Parton showers Soft and collinear limit To all orders, probability of not radiating a gluon above some (transverse) momentum k T P(no emission above k T ) (k T, Q) [ (k T, Q) exp 2α Q ] sc F de π/2 dθ π E θ Θ(Eθ k T ) (k T, Q) = Sudakov form factor Natural iterative application : q q MC q qg MC q qgg MC q qggg MC...

18 Parton showers (II) Gluon k T spectra dp = d (k T, Q) dk T dk T Advantage: Simplified process Shower process continues until soft scale Q 0 Limitation: soft kinematics, fails for hard+large angle radiation

19 Practical implementations Event generators: Pythia, Herwig,...

20 Modeling of NN collisions (Reprise!) The two particle beams cross

21 Modeling of NN collisions (II) Partons interact via a hard process like qg qg, gg q q, qg qγ, q q W + W,...

22 Modeling of NN collisions (III) Partons from each particle initiate a shower via processes like q qg, q qγ, g gg, g q q...

23 Modeling of NN collisions (IV) Outgoing particles create other parton showers

24 Modeling of NN collisions (V) Rinse and repeat for the other partons

25 Fragmentation After the collision + radiation shower jets of partons Below Q 0 : fragmentation from partons to hadrons Non-perturbative! How to model it?

26 String picture Useful for describing soft hadron phenomenology The idea: consider a q q pair Due to non-abelian properties of QCD, color electric field is confined in a well defined region between the two ( color string ) Linearly rising energy density in the string confinement!

27 Lattice Lattice and the string picture

28 Regge slope More hints suggesting the string picture: Hadron spectroscopy Plot hadron resonances with same quantum numbers as a function of angular momentum Similar resonances lie on the same line! J(M 2 ) = α 0 + α 1 M 2 Almost universal slope α 1 How can this property be modeled?

29 Rotating string model Rotating massless relativistic string model E = 2 J = 2 L 0 L 0 dxγκ = πκl dxxγκv = 1 2 πκl2 J = 1 2πκ M2 α 1 M 2 α 1 1 2πκ κ 1GeV fm 1

30 Schwinger particle production In presence of a strong constant (color-)electric field ε E = 1 2 ε2 AL L Introducing V (z) 0 z < 0 V (z) = κz z > 0 &z < L κl z > L Particle production quantum-mechanical tunnelling

31 Schwinger particle production II Schroedinger-like eq. description { [ ]} pz 2 m T (E V (z))2 + f (z) = 0 2m T 2 2m T Tunneling process, with probability { P exp 2 dz } { } 2m T (V (z) E) exp πm2 T κ

32 String fragmentation: Lund model The Lund model is the practical implementation of string breaking mechanism adopted in Pythia Starting from a q q pair, sequential production of q i q i pairs

33 String fragmentation: Lund model (II)

34 Cluster fragmentation An alternative hadronization mechanism Group q and q into colorless clusters Clusters turn then into hadrons

35 Some other things I forgot to mention Beam remnants Decays of unstable particles in the final state Baryons?

36 Wrapup pp collisions are a fundamental test ground for new physics and a necessary comparison for heavy ions Phenomenological models necessary to predict/describe spectra Several models and approaches on the market Much has been done already Still a lot of work to do

37 Useful references (and source for pics) T. Sjostrand, Monte Carlo generators for the LHC Pythia manual, arxiv:hep-ph/ G. Salam, arxiv: JF Grosse-Oetringhaus and K. Reygers, arxiv: C.Y. Wong, Introduction to high-energy HIC W. Florkowski, Phenomenology of ultra-relativistic HIC