Hadronization & Underlying Event QCD and Event Generators Lecture 3 of 3 Peter Skands Monash University (Melbourne, Australia) VINCIA VINCIA
From Partons to Pions ๏ Consider a parton emerging from a hard scattering (or decay) process It ends up It starts at a high It showers at a low effective factorization scale (bremsstrahlung) factorization scale Q = Q F = Q hard Q ~ m ρ ~ 1 GeV Q Q hard 1 GeV How about I just call it a hadron? → “Local Parton-Hadron Duality” 2 QCD and Event Generators P. Skands Monash U.
Parton → Hadrons? ๏ Early models: “Independent Fragmentation” • Local Parton Hadron Duality ( LPHD ) can give useful results for inclusive quantities in collinear fragmentation • Motivates a simple model: π π q “Independent Fragmentation” π ๏ But … • The point of confinement is that partons are coloured • Hadronisation = the process of colour neutralisation → Unphysical to think about independent fragmentation of a single parton into hadrons ๏ → Too naive to see LPHD (inclusive) as a justification for Independent Fragmentation ๏ (exclusive) • → More physics needed 3 QCD and Event Generators P. Skands Monash U.
Colour Neutralisation ๏ A physical hadronization model • Should involve at least two partons, with opposite color charges* • A strong confining field emerges between the two when their separation ≳ 1fm non-perturbative Late times anti-R moving along right lightcone R moving along left lightcone pQCD Time Early times (perturbative) Space *) Really, a colour singlet state 1 ; the LC colour flow rules discussed in 3 ( R ¯ B ⟩ ) R ⟩ + G ¯ G ⟩ + B ¯ ๏ lecture 1 allow us to tell which partons to pair up (at least to LC; see arXiv:1505.01681) 4 QCD and Event Generators P. Skands Monash U. •
<latexit sha1_base64="rltpBDe/D2bkRHh8ej4qc4Io78=">ACB3icbVDLSsNAFJ34rPUVdSnIYBEqYklE0I1QdOygn1AE8rNdNIOnUzCzEQoITs3/obF4q49Rfc+TdOHwtPXDhcM693HtPkHCmtON8WwuLS8srq4W14vrG5ta2vbPbUHEqCa2TmMeyFYCinAla10xz2kokhSjgtBkMbkZ+84FKxWJxr4cJ9SPoCRYyAtpIHfugUZbH+AqfeqEkGeyRyfYG8ASQJYduySU3HGwPEnZISmqLWsb+8bkzSiApNOCjVdp1E+xlIzQinedFLFU2ADKBH24YKiKjys/EfOT4ySheHsTQlNB6rvycyiJQaRoHpjED31aw3Ev/z2qkOL/2MiSTVJDJojDlWMd4FAruMkmJ5kNDgEhmbsWkDyYQbaIrmhDc2ZfnSeOs4joV9+68VL2exlFA+gQlZGLlAV3aIaqiOCHtEzekVv1pP1Yr1bH5PWBWs6s4f+wPr8AWCpl7s=</latexit> <latexit sha1_base64="rltpBDe/D2bkRHh8ej4qc4Io78=">ACB3icbVDLSsNAFJ34rPUVdSnIYBEqYklE0I1QdOygn1AE8rNdNIOnUzCzEQoITs3/obF4q49Rfc+TdOHwtPXDhcM693HtPkHCmtON8WwuLS8srq4W14vrG5ta2vbPbUHEqCa2TmMeyFYCinAla10xz2kokhSjgtBkMbkZ+84FKxWJxr4cJ9SPoCRYyAtpIHfugUZbH+AqfeqEkGeyRyfYG8ASQJYduySU3HGwPEnZISmqLWsb+8bkzSiApNOCjVdp1E+xlIzQinedFLFU2ADKBH24YKiKjys/EfOT4ySheHsTQlNB6rvycyiJQaRoHpjED31aw3Ev/z2qkOL/2MiSTVJDJojDlWMd4FAruMkmJ5kNDgEhmbsWkDyYQbaIrmhDc2ZfnSeOs4joV9+68VL2exlFA+gQlZGLlAV3aIaqiOCHtEzekVv1pP1Yr1bH5PWBWs6s4f+wPr8AWCpl7s=</latexit> <latexit sha1_base64="rltpBDe/D2bkRHh8ej4qc4Io78=">ACB3icbVDLSsNAFJ34rPUVdSnIYBEqYklE0I1QdOygn1AE8rNdNIOnUzCzEQoITs3/obF4q49Rfc+TdOHwtPXDhcM693HtPkHCmtON8WwuLS8srq4W14vrG5ta2vbPbUHEqCa2TmMeyFYCinAla10xz2kokhSjgtBkMbkZ+84FKxWJxr4cJ9SPoCRYyAtpIHfugUZbH+AqfeqEkGeyRyfYG8ASQJYduySU3HGwPEnZISmqLWsb+8bkzSiApNOCjVdp1E+xlIzQinedFLFU2ADKBH24YKiKjys/EfOT4ySheHsTQlNB6rvycyiJQaRoHpjED31aw3Ev/z2qkOL/2MiSTVJDJojDlWMd4FAruMkmJ5kNDgEhmbsWkDyYQbaIrmhDc2ZfnSeOs4joV9+68VL2exlFA+gQlZGLlAV3aIaqiOCHtEzekVv1pP1Yr1bH5PWBWs6s4f+wPr8AWCpl7s=</latexit> <latexit sha1_base64="rltpBDe/D2bkRHh8ej4qc4Io78=">ACB3icbVDLSsNAFJ34rPUVdSnIYBEqYklE0I1QdOygn1AE8rNdNIOnUzCzEQoITs3/obF4q49Rfc+TdOHwtPXDhcM693HtPkHCmtON8WwuLS8srq4W14vrG5ta2vbPbUHEqCa2TmMeyFYCinAla10xz2kokhSjgtBkMbkZ+84FKxWJxr4cJ9SPoCRYyAtpIHfugUZbH+AqfeqEkGeyRyfYG8ASQJYduySU3HGwPEnZISmqLWsb+8bkzSiApNOCjVdp1E+xlIzQinedFLFU2ADKBH24YKiKjys/EfOT4ySheHsTQlNB6rvycyiJQaRoHpjED31aw3Ev/z2qkOL/2MiSTVJDJojDlWMd4FAruMkmJ5kNDgEhmbsWkDyYQbaIrmhDc2ZfnSeOs4joV9+68VL2exlFA+gQlZGLlAV3aIaqiOCHtEzekVv1pP1Yr1bH5PWBWs6s4f+wPr8AWCpl7s=</latexit> Linear Confinement ๏ Using explicit computer simulations of QCD on a 4D “lattice” (lattice QCD), one can compute the potential energy of a colour-singlet state, q ¯ q as a function of the distance, r, between the and SCALING. . . POTENTIAL: 2641 STATIC QUARK-ANTIQUARK 46 q q ¯ linear potential? Scaling plot LATTICE QCD SIMULATION. 2GeV- ๏ Bali and Schilling Phys Rev D46 (1992) 2636 Long Distances ~ Linear Potential (in “quenched” approximation) 1 GeV— 2 “Confined” Partons Short Distances ~ “Coulomb” (a.k.a. Hadrons) What physical system has a B = 6. 0, L=16 'V ~ B = 6. 0, L=32 ~ ~ I ~ B = 6. 2, L=24 linear potential? B = 6. 4, L-24 “Free” Partons I B = 6. 4, L=32 -2 A k, I 4 2' t 1. 3. 0. 5 2. 5 5 1 fm 5 l~ RK FIG. 4. All potential data of the five lattices have been scaled to a universal curve by subtracting Vo and measuring energies and V ( r ) = − a to V(R) = R — units of &E. The dashed curve correspond with κ ∼ 1 GeV/fm ( → could lift a 16-ton truck) ~/12R. Physical units are calculated “Cornell Potential” fit: distances in appropriate by exploit- r + κ r ing the relation &cr =420 MeV. 5 QCD and Event Generators P. Skands Monash U. AM~a=46. 1A~ &235(2)(13) MeV . turbative results. we are aware that our lattice Although is not yet really suScient, dare to resolution we might apply to to say, this value does not necessarily Needless of the previe~ the continuum behavior Coulomb-like full QCD. In Fig. 6(a) [6(b)] we visualize term from our results. the behavior of the confining to the long-range In addition in the K-e plane from fits to various confidence regions it is of considerable interest to investigate lattices at P=6. 0 its ul- potential on- and off-axis potentials on the 32 into the weak cou- structure. As we proceed traviolet [6. 4]. We observe that the impact of lattice discretization on e decreases by a factor 2, as we step up from P = 6. 0 to pling regime lattice simulations are expected to meet per- 150 Barkai '84 o '90 MTC Our results:--- 140 130- 120- 110- 100- 80— 5. 6 5. 8 6. 2 6. 4 c = &E /(a AL ) ] as a function of P. Our results are combined FIG. 5. The on-axis string tension [in units of the quantity with pre- and Rebbi [11]. vious values obtained by the MTc collaboration [10] and Barkai, Moriarty,
Motivates a Model ๏ A high-energy quark-gluon-antiquark system is created and starts to fly apart ( ) g B ¯ • Quarks → String Endpoints R • Gluons → Transverse Excitations (kinks) Hadrons • Physics then in terms of 1+1- ( ) q R dim string “worldsheet” 𝒬 ∝ exp ( evolving in spacetime − m 2 − p 2 ) ⊥ String breaking • Probability of string break (by ( κ / π ) quantum tunneling) constant ( ) q ¯ Heavier quarks suppressed. Prob(d:u:s:c) ≈ 1 : 1 : 0.2 : 10 -11 ¯ B per unit space-time area and Gaussian pT spectrum (transverse to local string axis) → “STRING EFFECT” Computer algorithms to model this process began to be developed in late 70’ies and early 80’ies ➜ Monte Carlo Event Generators Modern MC hadronization models : PYTHIA (string), HERWIG (cluster), SHERPA (cluster) 6 QCD and Event Generators P. Skands Monash U.
The (Lund) String Hadronization Model PYTHIA (org JETSET) ↔ ๏ Simple space-time picture ( ) g B ¯ • Highly predictive, few free R parameters • Causality and Lorentz invariance “Lund Hadrons ⟹ ( ) q R Symmetric Fragmentation Function” with two free parameters a and b : “Famous" Prediction: "The String Effect” Fewer hadrons produced inbetween the two f ( z ) ∝ (1 − z ) a exp( − bm 2 ⊥ / z ) quark jets. (Non-perturbative coherence.) ( ) q ¯ ¯ B • z Confirmed by JADE in 1980. • with z ∼ E hadron / E quark → “STRING EFFECT” ๏ Details of string breaks more complicated • Many free parameters for flavour & spin of produced hadrons ➜ fit to e + e − → hadrons 7 QCD and Event Generators P. Skands Monash U.
Iterative String Breaks ๏ String breaks are separated by spacelike intervals ➜ causally disconnected • ➜ We do not have to consider the string breaks in any specific time order ➜ choose the most convenient order for us: starting from the endpoints (“outside-in”) Note: using light-cone coordinates: p + = E + p z u ( � p ⊥ 0 , p + ) shower Q UV � + ( � p ⊥ 1 , z 1 p + ) Q IR p ⊥ 0 − � · · · d ¯ d Perturbative Domain K 0 ( � p ⊥ 2 , z 2 (1 − z 1 ) p + ) p ⊥ 1 − � Main parameter: α s Different “tunes” use different α seff (m Z ) values Non-Perturbative Domain s ¯ s E.g., Monash: 0.1365, A14: 0.129 Fragmentation function f(z,Q IR ) ... + p T / flavour /… parameters, hadron decay tables ๏ Hadron Spectra = combination of α s choice & non-perturbative parameters 8 QCD and Event Generators P. Skands Monash U.
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