Inclusive hadronic distributions in jets in the vacuum and in the medium Redamy Perez Ramos Universitat de Val` encia, IFIC-CSIC, Spain Rencontres de Physique des Particules 2010, Lyon-France Redamy Perez Ramos (IFIC-CSIC) Jets in QCD RPP 2010 in Lyon, France 1 / 15
Outline Jets in perturbative Quantum Chromodynamics: production of jets Redamy Perez Ramos (IFIC-CSIC) Jets in QCD RPP 2010 in Lyon, France 2 / 15
Outline Jets in perturbative Quantum Chromodynamics: production of jets some resummation approaches in pQCD: MLLA and DGLAP evolution equations Redamy Perez Ramos (IFIC-CSIC) Jets in QCD RPP 2010 in Lyon, France 2 / 15
Outline Jets in perturbative Quantum Chromodynamics: production of jets some resummation approaches in pQCD: MLLA and DGLAP evolution equations Results Single inclusive differential one-particle distribution as a function of k ⊥ d σ d ln k ⊥ in MLLA and Next-to-MLLA; comparison with CDF p-p data Redamy Perez Ramos (IFIC-CSIC) Jets in QCD RPP 2010 in Lyon, France 2 / 15
Outline Jets in perturbative Quantum Chromodynamics: production of jets some resummation approaches in pQCD: MLLA and DGLAP evolution equations Results Single inclusive differential one-particle distribution as a function of k ⊥ d σ d ln k ⊥ in MLLA and Next-to-MLLA; comparison with CDF p-p data Extension of some perturbative techniques to the phenomenology of heavy-ion collisions at RHIC and LHC, Borghini-Wiedemann model (Charged hadronic multiplicities in jets, gluon to quark multiplicity ratio, FFs and collimation.. . ) Redamy Perez Ramos (IFIC-CSIC) Jets in QCD RPP 2010 in Lyon, France 2 / 15
Outline Jets in perturbative Quantum Chromodynamics: production of jets some resummation approaches in pQCD: MLLA and DGLAP evolution equations Results Single inclusive differential one-particle distribution as a function of k ⊥ d σ d ln k ⊥ in MLLA and Next-to-MLLA; comparison with CDF p-p data Extension of some perturbative techniques to the phenomenology of heavy-ion collisions at RHIC and LHC, Borghini-Wiedemann model (Charged hadronic multiplicities in jets, gluon to quark multiplicity ratio, FFs and collimation.. . ) Conclusions Redamy Perez Ramos (IFIC-CSIC) Jets in QCD RPP 2010 in Lyon, France 2 / 15
Production of jets Redamy Perez Ramos (IFIC-CSIC) Jets in QCD RPP 2010 in Lyon, France 3 / 15
Production of jets Partonic cascade: traited in pQCD planar gauge: tree amplitudes ⇒ parton shower picture (probabilistic interpretation) Redamy Perez Ramos (IFIC-CSIC) Jets in QCD RPP 2010 in Lyon, France 3 / 15
Production of jets Partonic cascade: traited in pQCD planar gauge: tree amplitudes ⇒ parton shower picture (probabilistic interpretation) Hadronization: advocates for Local Parton Hadron Duality Hypothesis (LPHD) partonic distributions ≃ hadronic distributions: factor K ch “limiting spectrum:” Q 0 ∼ Λ QCD Redamy Perez Ramos (IFIC-CSIC) Jets in QCD RPP 2010 in Lyon, France 3 / 15
Angular Ordering Θ Θ Θ 1 2 3 Θ 1 > > Θ Θ 2 3 necessary condition to the construction of QCD evolution equations ⇔ to the k ⊥ -ordering of Dokshitzer-Gribov-Lipatov-Altereli-Parisi (DGLAP) evolution equations in the DIS Redamy Perez Ramos (IFIC-CSIC) Jets in QCD RPP 2010 in Lyon, France 4 / 15
Resummation schemes DLA: α s log(1 / x )log Θ ( α s log 2 ∼ 1 ⇒ log ∼ α − 1 / 2 ): resummation of s soft and collinear gluons main ingredient to the estimation of inclusive observables in jets neglects the energy balance Redamy Perez Ramos (IFIC-CSIC) Jets in QCD RPP 2010 in Lyon, France 5 / 15
Resummation schemes DLA: α s log(1 / x )log Θ ( α s log 2 ∼ 1 ⇒ log ∼ α − 1 / 2 ): resummation of s soft and collinear gluons main ingredient to the estimation of inclusive observables in jets neglects the energy balance Single Logs (SL): α s log Θ collinear splittings (i.e. DGLAP FO approach or LLA of FFs, PDFs at large x ∼ 1 (DIS). . . ) s log n Θ” running of α s ( k ⊥ → Q 0 ) . . . “ ⇒ β × α n Redamy Perez Ramos (IFIC-CSIC) Jets in QCD RPP 2010 in Lyon, France 5 / 15
Resummation schemes DLA: α s log(1 / x )log Θ ( α s log 2 ∼ 1 ⇒ log ∼ α − 1 / 2 ): resummation of s soft and collinear gluons main ingredient to the estimation of inclusive observables in jets neglects the energy balance Single Logs (SL): α s log Θ collinear splittings (i.e. DGLAP FO approach or LLA of FFs, PDFs at large x ∼ 1 (DIS). . . ) s log n Θ” running of α s ( k ⊥ → Q 0 ) . . . “ ⇒ β × α n MLLA: α s loglog + α s log : the SL corrections to DLA � �� � � �� � O ( √ α s ) O (1) “partially restore” the energy balance take into account the running of α s ( k ⊥ ) Redamy Perez Ramos (IFIC-CSIC) Jets in QCD RPP 2010 in Lyon, France 5 / 15
Resummation schemes DLA: α s log(1 / x )log Θ ( α s log 2 ∼ 1 ⇒ log ∼ α − 1 / 2 ): resummation of s soft and collinear gluons main ingredient to the estimation of inclusive observables in jets neglects the energy balance Single Logs (SL): α s log Θ collinear splittings (i.e. DGLAP FO approach or LLA of FFs, PDFs at large x ∼ 1 (DIS). . . ) s log n Θ” running of α s ( k ⊥ → Q 0 ) . . . “ ⇒ β × α n MLLA: α s loglog + α s log : the SL corrections to DLA � �� � � �� � O ( √ α s ) O (1) “partially restore” the energy balance take into account the running of α s ( k ⊥ ) + α s loglog − 1 Next-to-MLLA: α s loglog + α s log � �� � � �� � � �� � O ( √ α s ) O (1) O ( α s ) improve the restoration of the energie balance and allow to increase the range in “ x ” ( k ⊥ ≈ xE jet Θ) Redamy Perez Ramos (IFIC-CSIC) Jets in QCD RPP 2010 in Lyon, France 5 / 15
For instance: ((N)MLLA ev. eq., gluon and quark jets) � ℓ � y � � 0 ( ℓ ′ + y ′ ) − ( a 1 + a 2 ψ ℓ ( ℓ ′ , y ′ )) δ ( ℓ ′ − ℓ ) D h ˜ d ℓ ′ dy ′ γ 2 g ( ℓ, y ) = δ ( ℓ ) + 1 ���� 0 0 � �� � DLA gluon jet × ˜ g ( ℓ ′ , y ′ ) D h = δ ( ℓ ) + C F ˜ a 2 ψ ℓ ) . . . ˜ D h D h g ( ℓ ′ , y ′ ) , q ( ℓ, y ) . . . (˜ a 1 , ˜ ℓ = ln(1 / x ) , y = ln( k ⊥ / Λ) N c � �� � � �� � � �� � infrared collinear quark jet Redamy Perez Ramos (IFIC-CSIC) Jets in QCD RPP 2010 in Lyon, France 6 / 15
For instance: ((N)MLLA ev. eq., gluon and quark jets) � ℓ � y � � 0 ( ℓ ′ + y ′ ) − ( a 1 + a 2 ψ ℓ ( ℓ ′ , y ′ )) δ ( ℓ ′ − ℓ ) D h ˜ d ℓ ′ dy ′ γ 2 g ( ℓ, y ) = δ ( ℓ ) + 1 ���� 0 0 � �� � DLA gluon jet × ˜ g ( ℓ ′ , y ′ ) D h = δ ( ℓ ) + C F ˜ a 2 ψ ℓ ) . . . ˜ D h D h g ( ℓ ′ , y ′ ) , q ( ℓ, y ) . . . (˜ a 1 , ˜ ℓ = ln(1 / x ) , y = ln( k ⊥ / Λ) N c � �� � � �� � � �� � infrared collinear quark jet Logic of Low-Barnet-Kroll theorem: DLA (LO) term: ∝ O (1) hard corrections: ∝ a 1 ∼ O ( √ α s ) & ∝ a 2 ( ψ ℓ = ∂ D h ∂ℓ ) ∼ O ( α s ) Redamy Perez Ramos (IFIC-CSIC) Jets in QCD RPP 2010 in Lyon, France 6 / 15
For instance: ((N)MLLA ev. eq., gluon and quark jets) � ℓ � y � � 0 ( ℓ ′ + y ′ ) − ( a 1 + a 2 ψ ℓ ( ℓ ′ , y ′ )) δ ( ℓ ′ − ℓ ) D h ˜ d ℓ ′ dy ′ γ 2 g ( ℓ, y ) = δ ( ℓ ) + 1 ���� 0 0 � �� � DLA gluon jet × ˜ g ( ℓ ′ , y ′ ) D h = δ ( ℓ ) + C F ˜ a 2 ψ ℓ ) . . . ˜ D h D h g ( ℓ ′ , y ′ ) , q ( ℓ, y ) . . . (˜ a 1 , ˜ ℓ = ln(1 / x ) , y = ln( k ⊥ / Λ) N c � �� � � �� � � �� � infrared collinear quark jet Logic of Low-Barnet-Kroll theorem: DLA (LO) term: ∝ O (1) hard corrections: ∝ a 1 ∼ O ( √ α s ) & ∝ a 2 ( ψ ℓ = ∂ D h ∂ℓ ) ∼ O ( α s ) � � σ 0 � � σ 1 + σ 2 e − σ 3 s �� d ω d ν (2 π i ) 2 e ωℓ e ν y � ∞ ˜ ω ( ν + s ) D h d s ν g = ( ℓ + y ) 0 ν + s ( ω + s ) ν ν + s 1 σ 1 = a 1 σ 2 = − a 2 σ 3 = − a 2 σ 0 = β 0 ( ω − ν ) , β 0 , β 0 ( ω − ν ) , β 0 + λ � ˜ √ α s + r 2 α s � ˜ q ≃ C F D h D h 1 + r 1 g N c Redamy Perez Ramos (IFIC-CSIC) Jets in QCD RPP 2010 in Lyon, France 6 / 15
Reminder: Dokshitzer et al. D h ≡ K ch × 1 d σ d ln (1 / x ) at Z 0 peak, Q = 91 . 2 Hump-backed plateau: ˜ σ GeV Redamy Perez Ramos (IFIC-CSIC) Jets in QCD RPP 2010 in Lyon, France 7 / 15
Reminder: Dokshitzer et al. D h ≡ K ch × 1 d σ d ln (1 / x ) at Z 0 peak, Q = 91 . 2 Hump-backed plateau: ˜ σ GeV 7 MLLA limiting spectrum OPAL data 6 5 4 D 3 2 1 0 0 1 2 3 4 5 6 ln(1/x) Q ≫ Q 0 ∼ Λ QCD ≈ m ( π ± ) = 230 MeV, γ 0 ≈ 0 . 5, good agreement though! Redamy Perez Ramos (IFIC-CSIC) Jets in QCD RPP 2010 in Lyon, France 7 / 15
d σ Inclusive k ⊥ -one particle distribution d ln k ⊥ d σ Inclusive one particle d ln k ⊥ : obtained from the correlation between one particle and the energy flux (jet axis) Angle d’ouverture du jet Angle de production de h (Θ < Θ ) 0 h k = xE Θ > Q0 Θ0 xE A Θ h DA 0 D A A uE A0 E (Jet Axis) Collision Etat vituel (u~1) Parton initiant le jet Redamy Perez Ramos (IFIC-CSIC) Jets in QCD RPP 2010 in Lyon, France 8 / 15
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