Saturation in central-forward jet production in p-Pb collisions at - PowerPoint PPT Presentation

Saturation in central-forward jet production in p-Pb collisions at LHC Sebastian Sapeta IPPP, Durham in collaboration with Krzysztof Kutak, arXiv:1205.5035 pA@LHC Workshop, 4-8 June 2012 CERN Sebastian Sapeta (IPPP, Durham) Saturation in central-forward jet production in p-Pb collisions at LHC 1 / 12

Central-forward jet production P 1 forward jet p 2 k 1 , x 1 k 1 p 1 S = 2 P 1 · P 2 k 2 k 2 , x 2 central jet P 2 S ( p t 1 e y 1 + p t 2 e y 2 ) 1 = x 1 ∼ 1 √ y 1 ∼ 0 , y 2 ≫ 0 S ( p t 1 e − y 1 + p t 2 e − y 2 ) 1 = x 2 ≪ 1 √ Sebastian Sapeta (IPPP, Durham) Saturation in central-forward jet production in p-Pb collisions at LHC 2 / 12

High energy factorization d σ p t 1 p t 2 1 X 8 π 2 ( x 1 x 2 S ) 2 M ag → cd x 1 f a / A ( x 1 , µ 2 ) φ g / B ( x 2 , k 2 ) dy 1 dy 2 dp 1 t dp 2 t d ∆ φ = 1 + δ cd a , c , d k 2 = p 2 t 1 + p 2 t 2 + 2 p t 1 p t 2 cos ∆ φ x 1 f a / A ( x 1 , µ 2 ) – collinear pdf in A , suitable for x 1 ∼ 1 φ g / B ( x 2 , k 2 ) – unintegrated gluon distribution in B , suitable for x 2 ≪ 1 M ag → cd – matrix element with off-shell gluon Sebastian Sapeta (IPPP, Durham) Saturation in central-forward jet production in p-Pb collisions at LHC 3 / 12

Unified BK/DGLAP evolution equation [Kwieci´ nski, Martin, Sta´ sto; Kwieci´ nski, Kutak] kinematic constraint φ p ( x , k 2 ) = φ (0) p ( x , k 2 )  l 2 φ p ( x Z 1 z , l 2 ) θ ( k 2 Z ∞ z − l 2 ) − k 2 φ p ( x z , k 2 ) + k 2 φ p ( x z , k 2 ) + α s ( k 2 ) N c dl 2 ff dz | l 2 − k 2 | l 2 | 4 l 4 + k 4 | 1 π z k 2 x 2 0 Z 1 « Z k 2 Z 1 + α s ( k 2 ) + α s ( k 2 ) „ P gg ( z ) − 2 N c “ x “ x dl 2 φ p z , l 2 ” z , k 2 ” dz dz P gq ( z )Σ 2 π k 2 z 2 π k 2 x x 0 „ l 2 "„Z ∞ « 2 # − 2 α 2 s ( k 2 ) dl 2 Z ∞ dl 2 « l 2 φ p ( x , l 2 ) + φ p ( x , k 2 ) φ p ( x , l 2 ) l 2 ln R 2 k 2 k 2 k 2 proton radius Initial condition Z 1 α S ( k 2 ) dzP gg ( z ) x “ x 0 = 1GeV 2 ” φ (0) p ( x , k 2 ) z , k 2 = z g 2 π k 2 x N (1 − x ) β (1 − Dx ) xg ( x ) = Sebastian Sapeta (IPPP, Durham) Saturation in central-forward jet production in p-Pb collisions at LHC 4 / 12

Fits to F 2 6 HERA data 400 fit non-linear 300 fit linear 250 ◮ fit in range: x < 0 . 01, all Q 2 150 200 120 5 90 70 ◮ very good fit of non-linear gluon 60 ( χ 2 = 1 . 73) 45 35 4 ◮ fit of linear gluon has problems at 27 low Q 2 and low x ( χ 2 = 3 . 86) 22 18 15 12 3 F 2 10 8.5 6.5 2 4.5 3.5 2.7 2.0 1 1.5 0 0.0001 0.001 0.01 x Sebastian Sapeta (IPPP, Durham) Saturation in central-forward jet production in p-Pb collisions at LHC 5 / 12

Fits to F 2 6 HERA data 400 fit non-linear 300 fit linear 250 ◮ fit in range: x < 0 . 01, all Q 2 150 200 120 5 90 70 ◮ very good fit of non-linear gluon 60 ( χ 2 = 1 . 73) 45 35 4 ◮ fit of linear gluon has problems at 27 low Q 2 and low x ( χ 2 = 3 . 86) 22 18 15 12 3 F 2 10 ◮ some mechanism damping the 8.5 6.5 gluon density at low x and low Q 2 seems to be needed 2 4.5 3.5 ◮ strong preference of non-linear 2.7 2.0 evolution! 1 1.5 0 0.0001 0.001 0.01 x Sebastian Sapeta (IPPP, Durham) Saturation in central-forward jet production in p-Pb collisions at LHC 5 / 12

Unintegrated gluon distribution in proton non-linear gluon non-linear vs linear 3.0 12.0 x = 1e-02 non-linear x = 1e-03 linear x = 1e-04 2.5 10.0 x = 1e-05 x=10 -2 ...10 -5 8.0 2.0 p p 2 ) 2 ) φ p (x,k t φ p (x,k t 6.0 1.5 4.0 1.0 2.0 0.5 0.0 0.0 0.001 0.01 0.1 1 10 100 1000 0.001 0.01 0.1 1 10 100 1000 2 [GeV 2 ] k t 2 [GeV 2 ] k t k t > 1 GeV: gluon from the unified BK/DGLAP equation φ p ( x , k 2 ) = k 2 φ p ( x , 1 GeV 2 ) [non-linear] k t < 1 GeV: φ p ( x , k 2 ) = φ p ( x , 1 GeV 2 ) [linear] ◮ significant differences between linear and non-linear gluon at low k t and low x ◮ dynamically generated maximum of non-linear gluon at low x Sebastian Sapeta (IPPP, Durham) Saturation in central-forward jet production in p-Pb collisions at LHC 6 / 12

Central-forward dijets in p-p collisions at LHC ◮ Now we take all the ingredients (off-shell matrix element, collinear gluon, unintegrated gluon) and plug them to the high energy factorization formula 10 5 10 5 linear linear non-linear non-linear data CMS data CMS 10 4 10 4 d 2 σ /dp t d η c [pb/GeV] d 2 σ /dp t d η f [pb/GeV] CENTRAL FORWARD 10 3 10 3 10 2 10 2  s = 7 TeV  s = 7 TeV √ √ p t > 35 GeV p t > 35 GeV 10 10 central: | η | < 2.8 central: | η | < 2.8 forward: 3.2 < | η | < 4.7 forward: 3.2 < | η | < 4.7 1 1 40 60 80 100 120 140 40 60 80 100 120 140 central p t [GeV] forward p t [GeV] ◮ the result reproduces the pattern of CMS data ◮ excess at low p t is due to our simple modeling with a jet being just a parton; it is a know effect which can be improved by adding parton shower Sebastian Sapeta (IPPP, Durham) Saturation in central-forward jet production in p-Pb collisions at LHC 7 / 12

Modeling the nucleus ◮ Radius of nucleus R Pb = R A 1 / 3 ◮ Unintegrated gluon distribution φ Pb ( x , k 2 ) ≡ A φ Pb / A ( x , k 2 ) where φ Pb / A ( x , k 2 ) is the distribution of gluons per nucleon The evolution equation L 1 − A 1 / 3 » – φ Pb / A ( x , k 2 ) = ˆ R 2 ˆ • φ Pb / A ( x , k 2 ) L 2 ◮ ˆ L 1 , 2 – linear and non-linear operators as in the equation for proton ◮ for the nucleus the non-linear term is enhanced by A 1 / 3 Sebastian Sapeta (IPPP, Durham) Saturation in central-forward jet production in p-Pb collisions at LHC 8 / 12

Unintegrated gluon distribution in the Pb nucleus non-linear gluon in the proton non-linear gluon in Pb nucleus 3.0 3.0 x = 1e-02 x = 1e-02 x = 1e-03 x = 1e-03 x = 1e-04 x = 1e-04 2.5 2.5 x = 1e-05 x = 1e-05 2.0 2.0 2 ) p Pb 2 ) φ Pb/A (x,k t φ p (x,k t 1.5 1.5 1.0 1.0 0.5 0.5 0.0 0.0 0.001 0.01 0.1 1 10 100 1000 0.001 0.01 0.1 1 10 100 1000 2 [GeV 2 ] 2 [GeV 2 ] k t k t ◮ significant suppression of gluon density in the Pb nucleus wrt the proton at low and moderate k t ◮ gluon’s transverse momentum: k 2 t = p 2 t 1 + p 2 t 2 + 2 p t 1 p t 2 cos ∆ φ ◮ low and moderate k t probed by configurations with ∆ φ ∼ π Sebastian Sapeta (IPPP, Durham) Saturation in central-forward jet production in p-Pb collisions at LHC 9 / 12

Dijet azimuthal distance and rapidity distributions at 7 TeV 350 70 25 p-p linear p-p linear p-p linear p-p non-linear p-p non-linear p-p non-linear 300 60 p-Pb p-Pb p-Pb 20 250 50  s = 7 TeV  s = 7 TeV  s = 7 TeV √ √ √ d σ /d ∆φ [ µ b] p t > 15 GeV p t > 25 GeV 15 p t > 35 GeV d σ /d ∆φ [ µ b] d σ /d ∆φ [ µ b] 200 40 central: 0 < y < 2.8 central: 0 < y < 2.8 central: 0 < y < 2.8 forward: 3.2 < y < 4.7 forward: 3.2 < y < 4.7 forward: 3.2 < y < 4.7 150 30 10 100 20 5 50 10 0 0 2.5 2.6 2.7 2.8 2.9 3 3.1 2.5 2.6 2.7 2.8 2.9 3 3.1 2.5 2.6 2.7 2.8 2.9 3 3.1 ∆φ ∆φ ∆φ 2.5 p-p linear p-p linear 8 p-p linear 50 p-p non-linear p-p non-linear p-p non-linear p-Pb p-Pb 7 p-Pb 2.0 40 6 √  s = 7 TeV  s = 7 TeV √  s = 7 TeV √ p t > 15 GeV p t > 25 GeV 5 1.5 p t > 35 GeV d σ /dy [ µ b] d σ /dy [ µ b] d σ /dy [ µ b] 30 central: 0 < y < 2.8 central: 0 < y < 2.8 central: 0 < y < 2.8 4 forward: 3.2 < y < 4.7 forward: 3.2 < y < 4.7 forward: 3.2 < y < 4.7 1.0 20 3 2 0.5 10 1 0.0 0 0 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 y y y Sebastian Sapeta (IPPP, Durham) Saturation in central-forward jet production in p-Pb collisions at LHC 10 / 12

Dijet azimuthal distance at 5 and 8.8 TeV 300 70 25 p-p p-p p-p p-Pb p-Pb p-Pb 60 250 20  s = 5 TeV and 8.8 TeV  s = 5 TeV and 8.8 TeV  s = 5 TeV and 8.8 TeV √ √ √ 50 200 d σ /d ∆φ [ µ b] 15 d σ /d ∆φ [ µ b] d σ /d ∆φ [ µ b] 40 p t > 15 GeV p t > 25 GeV p t > 35 GeV 150 central: 0 < y < 2.8 central: 0 < y < 2.8 central: 0 < y < 2.8 30 10 forward: 3.2 < y < 4.7 forward: 3.2 < y < 4.7 forward: 3.2 < y < 4.7 100 20 5 50 10 0 0 2.5 2.6 2.7 2.8 2.9 3 3.1 2.5 2.6 2.7 2.8 2.9 3 3.1 2.5 2.6 2.7 2.8 2.9 3 3.1 ∆φ ∆φ ∆φ ◮ significant suppression due to saturation for both energies ◮ dip near ∆ φ ≃ π comes from ∼ k 2 behaviour of the unintegrated gluon at low k 2 ; hence ∆ φ distribution useful to test shape of gluon in this region Sebastian Sapeta (IPPP, Durham) Saturation in central-forward jet production in p-Pb collisions at LHC 11 / 12

Summary We presented analysis of e-p, p-p and p-Pb collisions in the framework of high energy factorisation – single approach which allows one to study saturation using hard final states ◮ We found that the above formalism with the unintegrated gluon density determined from from nonlinear QCD evolution equation can successfully account for features of e-p and p-p data Then we used the non-linear framework to estimate effects of gluon saturation in the nucleus ◮ We found that saturation in the Pb nucleus can manifest itself as a factor two suppression of central-forward jet decorrelation in the region ∆ φ ∼ π ◮ It also leads to ∼ 30% suppression of rapidity spectra Sebastian Sapeta (IPPP, Durham) Saturation in central-forward jet production in p-Pb collisions at LHC 12 / 12