Saturation Physics on the Energy Frontier arxiv:1505.05183 (to appear - PowerPoint PPT Presentation

Saturation Physics on the Energy Frontier arxiv:1505.05183 (to appear in Phys. Rev. D) David Zaslavsky with Kazuhiro Watanabe, Bo-Wen Xiao, Feng Yuan Central China Normal University APS DPF Meeting — August 6, 2015

Saturation and pA Collisions 1 Saturation of 16 saturation small x ln 1 x x = 1 small Q ln Q 2 large Q Q 2 0 Saturation Physics on the Energy Frontier David Zaslavsky — CCNU

Saturation and pA Collisions 2 Advantages of p A of 16 hadron p A X saturation small x � λ � x 0 Q 2 � Q 2 s = cA 1 / 3 Q 2 0 x ln 1 x Heavy target: large A Light projectile: no x = 1 medium small Q ln Q 2 large Q Q 2 0 Saturation Physics on the Energy Frontier David Zaslavsky — CCNU

Saturation and pA Collisions 2 Advantages of p A of 16 hadron p A X saturation small x � λ � x 0 Q 2 � Q 2 s = cA 1 / 3 Q 2 0 x ln 1 x Heavy target: large A Light projectile: no x = 1 medium small Q ln Q 2 large Q Q 2 0 Saturation Physics on the Energy Frontier David Zaslavsky — CCNU

Saturation and pA Collisions 3 Hybrid Model of 16 Cross section in the hybrid formalism: � d z d 3 σ d x � x, p ⊥ � � = x xf i ( x, µ ) D h/i ( z, µ ) F P ( ξ )( . . . ) d Y d 2 � z 2 p ⊥ z i Parton distribution p (initial state projectile) x p p p h p h Dipole gluon distribution z z (initial state target) k x g p A Fragmentation function X A (final state) Perturbative factors figure adapted from Dominguez 2011. Saturation Physics on the Energy Frontier David Zaslavsky — CCNU

Inclusive Cross Section 4 History of the pA Calculation of 16 GBW Dumitru and Jalilian-Marian (2002) MV/AAMQS Gluon dist Dumitru, Hayashigaki, et al. (2006) LO BK Fujii et al. (2011) rcBK Albacete et al. (2013) b-CGC Rezaeian (2013) NLO BK Sta´ sto, Xiao, and Zaslavsky (2014) LO Cross section Kang et al. (2014) inel NLO Sta´ sto, Xiao, Yuan, et al. (2014) other NLO Altinoluk et al. (2014) rapidity NLO Watanabe et al. (2015) splitting NLO Saturation Physics on the Energy Frontier David Zaslavsky — CCNU

Inclusive Cross Section 5 First Calculation of 16 GBW MV/AAMQS Gluon dist Dumitru and Jalilian-Marian (2002) LO BK rcBK p b-CGC NLO BK A LO Cross section inel NLO No numerical results other NLO rapidity NLO splitting NLO Saturation Physics on the Energy Frontier David Zaslavsky — CCNU

Inclusive Cross Section 6 First Numerical Results of 16 Dumitru, Hayashigaki, et al. (2006) GBW MV/AAMQS Gluon dist 10 dAu BRAHMS min. bias data (h - ) at y=3.2 LO BK x- and DGLAP-evolution 1 MV model No DGLAP-evolution 0.1 rcBK dN/dy d 2 p t [GeV -2 ] 0.01 b-CGC 0.001 1e-04 NLO BK 1e-05 1e-06 LO Cross section 1e-07 Minimum bias, K = 1.6 inel NLO 1e-08 0 0.5 1 1.5 2 2.5 3 3.5 4 p t [GeV] other NLO rapidity NLO Prefactor K = 1 . 6 splitting NLO Saturation Physics on the Energy Frontier David Zaslavsky — CCNU

Inclusive Cross Section 7 Inelastic Diagrams of 16 Leading: p A Next-to-leading: p p p p A A A A Saturation Physics on the Energy Frontier David Zaslavsky — CCNU

Inclusive Cross Section 8 Inelastic NLO Terms of 16 Albacete et al. (2013) GBW 1000 BRAHMS η=2.2 h± (x200). K-factor=1 dAu @ 200 GeV BRAHMS η=3.2 h± (x50). K-factor=1 100 MV/AAMQS g=1.119 i.c STAR η=4 π'0. K-factor=0.4 Gluon dist dN/dη/d 2 p t (GeV -2 ) only elastic 10 elas+inelas α=0.1 elas+inelas α(Q=pt) LO BK 1 rcBK 0.1 0.01 b-CGC 0.001 NLO BK 0.0001 LO 0.00001 Cross section inel NLO 1 2 3 4 5 p t (GeV) other NLO Prefactor rapidity NLO K = 1 for charged hadrons splitting NLO K = 0 . 4 for neutral hadrons Saturation Physics on the Energy Frontier David Zaslavsky — CCNU

Inclusive Cross Section 9 NLO Diagrams of 16 Leading: p A Next-to-leading: p p p p A A A A p p p p A A A A Chirilli et al. 2012, 1203.6139 . Saturation Physics on the Energy Frontier David Zaslavsky — CCNU

Inclusive Cross Section 10 NLO Numerical Result of 16 Sta´ sto, Xiao, and Zaslavsky (2014) GBW BRAHMS η = 3 . 2 10 1 LO MV/AAMQS Gluon dist NLO data LO BK 10 − 1 rcBK GeV − 2 � b-CGC � 10 − 3 d η d 2 p ⊥ d 3 N NLO BK 10 − 5 LO Cross section inel NLO 10 − 7 0 1 2 3 other NLO p ⊥ [ GeV ] rapidity NLO Includes virtual corrections splitting NLO K = 1 Saturation Physics on the Energy Frontier David Zaslavsky — CCNU

Inclusive Cross Section 11 Kinematical Constraint of 16 GBW Watanabe et al. (2015) MV/AAMQS Gluon dist LO BK 1 − ξ rcBK p b-CGC NLO BK LO Cross section A inel NLO other NLO First LHC numerical results rapidity NLO splitting NLO Alternate derivation: Altinoluk et al. 2014, 1411.2869 . Saturation Physics on the Energy Frontier David Zaslavsky — CCNU

Inclusive Cross Section 12 Challenges for Numerical Calculation of 16 Singularities � F s ( z, ξ ) � 1 � 1 � d z d ξ + F n ( z, ξ ) + F d ( z, ξ ) δ (1 − ξ ) (1 − ξ ) + τ τ z Watanabe et al. 2015, 1505.05183 . Saturation Physics on the Energy Frontier David Zaslavsky — CCNU

Inclusive Cross Section 12 Challenges for Numerical Calculation of 16 Singularities � F s ( z, ξ ) � 1 � 1 � d z d ξ + F n ( z, ξ ) + F d ( z, ξ ) δ (1 − ξ ) (1 − ξ ) + τ τ z Fourier integrals � t ⊥ e i� s ⊥ e i� ⊥ · � l ′ d 2 � s ⊥ d 2 � l ⊥ · � t ⊥ ( . . . ) Watanabe et al. 2015, 1505.05183 . Saturation Physics on the Energy Frontier David Zaslavsky — CCNU

Inclusive Cross Section 12 Challenges for Numerical Calculation of 16 Singularities � F s ( z, ξ ) � 1 � 1 � d z d ξ + F n ( z, ξ ) + F d ( z, ξ ) δ (1 − ξ ) (1 − ξ ) + τ τ z Fourier integrals � t ⊥ e i� s ⊥ e i� ⊥ · � l ′ d 2 � s ⊥ d 2 � l ⊥ · � t ⊥ ( . . . ) Leading Order Cancellations k − 2 k − 2 k − 4 � � � � � � O − O → O ⊥ ⊥ ⊥ ...plus Monte Carlo statistical error Watanabe et al. 2015, 1505.05183 . Saturation Physics on the Energy Frontier David Zaslavsky — CCNU

Results 13 RHIC Results of 16 rcBK Λ 2 QCD = 0 . 01 GBW 10 1 LO LO + NLO + NLO + L q + L g + L q + L g GeV − 2 � 10 − 1 BRAHMS BRAHMS � 10 − 3 d η d 2 p ⊥ d 3 N 10 − 5 y = 2 . 2 y = 2 . 2 10 − 7 0 . 5 1 1 . 5 2 2 . 5 3 0 . 5 1 1 . 5 2 2 . 5 3 p ⊥ [ GeV ] p ⊥ [ GeV ] New terms improve matching at low p ⊥ data: Arsene et al. 2004, nucl-ex/0403005 . plots: Watanabe et al. 2015, 1505.05183 . Saturation Physics on the Energy Frontier David Zaslavsky — CCNU

Results 13 RHIC Results of 16 10 1 LO LO + NLO + NLO + L q + L g + L q + L g GeV − 2 � 10 − 1 BRAHMS BRAHMS � 10 − 3 d η d 2 p ⊥ d 3 N 10 − 5 y = 3 . 2 y = 3 . 2 10 − 7 0 . 5 1 1 . 5 2 2 . 5 3 0 . 5 1 1 . 5 2 2 . 5 3 p ⊥ [ GeV ] p ⊥ [ GeV ] New terms improve matching at low p ⊥ data: Arsene et al. 2004, nucl-ex/0403005 . plots: Watanabe et al. 2015, 1505.05183 . Saturation Physics on the Energy Frontier David Zaslavsky — CCNU

Results 14 LHC Results of 16 rcBK Λ 2 QCD = 0 . 01 GBW 10 1 LO LO + NLO + NLO 10 0 + L q + L g + L q + L g GeV − 2 � ATLAS ATLAS 10 − 1 10 − 2 � d η d 2 p ⊥ 10 − 3 d 3 N 10 − 4 10 − 5 y = 1 . 75 y = 1 . 75 10 − 6 1 2 3 4 5 6 1 2 3 4 5 6 p ⊥ [ GeV ] p ⊥ [ GeV ] rcBK calculation matches neatly up to p ⊥ ≈ 6 GeV data: Milov 2014, 1403.5738 . plots: Watanabe et al. 2015, 1505.05183 . Saturation Physics on the Energy Frontier David Zaslavsky — CCNU

Results 15 Importance of Higher Rapidity of 16 rcBK Λ 2 QCD = 0 . 01 GBW 10 1 LO LO + NLO + NLO 10 0 + L q + L g + L q + L g GeV − 2 � ATLAS y = 1 . 75 ATLAS y = 1 . 75 10 − 1 10 − 2 � d η d 2 p ⊥ 10 − 3 d 3 N 10 − 4 10 − 5 y = 1 . 75 y = 1 . 75 10 − 6 1 2 3 4 5 6 1 2 3 4 5 6 p ⊥ [ GeV ] p ⊥ [ GeV ] Higher rapidity alters low- p ⊥ result Saturation Physics on the Energy Frontier David Zaslavsky — CCNU

Results 15 Importance of Higher Rapidity of 16 rcBK Λ 2 QCD = 0 . 01 GBW 10 1 LO LO + NLO + NLO 10 0 + L q + L g + L q + L g GeV − 2 � ATLAS y = 1 . 75 ATLAS y = 1 . 75 10 − 1 10 − 2 � d η d 2 p ⊥ 10 − 3 d 3 N 10 − 4 10 − 5 y = 2 . 5 y = 2 . 5 10 − 6 1 2 3 4 5 6 1 2 3 4 5 6 p ⊥ [ GeV ] p ⊥ [ GeV ] Higher rapidity alters low- p ⊥ result Saturation Physics on the Energy Frontier David Zaslavsky — CCNU

Results 15 Importance of Higher Rapidity of 16 rcBK Λ 2 QCD = 0 . 01 GBW 10 1 LO LO + NLO + NLO 10 0 + L q + L g + L q + L g GeV − 2 � ATLAS y = 1 . 75 ATLAS y = 1 . 75 10 − 1 10 − 2 � d η d 2 p ⊥ 10 − 3 d 3 N 10 − 4 10 − 5 y = 3 . 5 y = 3 . 5 10 − 6 1 2 3 4 5 6 1 2 3 4 5 6 p ⊥ [ GeV ] p ⊥ [ GeV ] Higher rapidity alters low- p ⊥ result Saturation Physics on the Energy Frontier David Zaslavsky — CCNU

Conclusion 16 Summary of 16 10 1 GeV − 2 � 10 − 1 d 5 σ pA → hX = � 10 − 3 d Y d 2 p ⊥ d 2 b ⊥ d η d 2 p ⊥ � d z d x d 3 N d 5 σ tot qA z 2 q ( x, Q 2 f ) D q/h ( z, Q 2 f ) d Y q d 2 q ⊥ d 2 b ⊥ 10 − 5 y = 3 . 2 10 − 7 0 . 5 1 1 . 5 2 2 . 5 3 p ⊥ [ GeV ] Complete numerical implementation of NLO pA → h + X Critical step More forward-rapidity data from LHC experiments Saturation Physics on the Energy Frontier David Zaslavsky — CCNU