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

P2 P1 k2 k1 forward jet central jet p1 p2 k1, x1 k2, x2

x1 =

1 √ S (pt1ey1 + pt2ey2)

x2 =

1 √ S (pt1e−y1 + pt2e−y2)

∼ 1 ≪ 1

y1 ∼ 0, y2 ≫ 0 S = 2P1 · P2

Sebastian Sapeta (IPPP, Durham) Saturation in central-forward jet production in p-Pb collisions at LHC 2 / 12

High energy factorization

dσ dy1dy2dp1tdp2td∆φ = X

a,c,d

pt1pt2 8π2(x1x2S)2 Mag→cdx1fa/A(x1, µ2) φg/B(x2, k2) 1 1 + δcd k2 = p2

t1 + p2 t2 + 2pt1pt2 cos ∆φ

x1fa/A(x1, µ2) – collinear pdf in A, suitable for x1 ∼ 1 φg/B(x2, k2) – unintegrated gluon distribution in B, suitable for x2 ≪ 1 Mag→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]

φp(x, k2) = φ(0)

p (x, k2)

+ αs(k2)Nc π Z 1

x

dz z Z ∞

k2

dl2 l2  l2φp( x

z , l2) θ( k2 z − l2) − k2φp( x z , k2)

|l2 − k2| + k2φp( x

z , k2)

|4l4 + k4|

1 2

ff + αs(k2) 2πk2 Z 1

x

dz „ Pgg(z) − 2Nc z « Z k2

k2

dl2 φp “x z , l2” + αs(k2) 2π Z 1

x

dz Pgq(z)Σ “x z , k2” − 2α2

s (k2)

R2 "„Z ∞

k2

dl2 l2 φp(x, l2) «2 + φp(x, k2) Z ∞

k2

dl2 l2 ln „ l2 k2 « φp(x, l2) # kinematic constraint

Initial condition

φ(0)

p (x, k2)

= αS(k2) 2πk2 Z 1

x

dzPgg(z)x z g “x z , k2

0 = 1GeV2”

xg(x) = N(1 − x)β(1 − Dx) proton radius

Sebastian Sapeta (IPPP, Durham) Saturation in central-forward jet production in p-Pb collisions at LHC 4 / 12

Fits to F2

1 2 3 4 5 6 0.0001 0.001 0.01

F2 x

1.5 2.0 2.7 3.5 4.5 6.5 8.5 10 12 15 18 22 27 35 45 60 70 90 120 150 200 250 300 400 HERA data fit non-linear fit linear

◮ fit in range: x < 0.01, all Q2 ◮ very good fit of non-linear gluon

(χ2 = 1.73)

◮ fit of linear gluon has problems at

low Q2 and low x (χ2 = 3.86)

Sebastian Sapeta (IPPP, Durham) Saturation in central-forward jet production in p-Pb collisions at LHC 5 / 12

Fits to F2

1 2 3 4 5 6 0.0001 0.001 0.01

F2 x

1.5 2.0 2.7 3.5 4.5 6.5 8.5 10 12 15 18 22 27 35 45 60 70 90 120 150 200 250 300 400 HERA data fit non-linear fit linear

◮ fit in range: x < 0.01, all Q2 ◮ very good fit of non-linear gluon

(χ2 = 1.73)

◮ fit of linear gluon has problems at

low Q2 and low x (χ2 = 3.86)

◮ some mechanism damping the

gluon density at low x and low Q2 seems to be needed

◮ strong preference of non-linear

evolution!

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

0.0 0.5 1.0 1.5 2.0 2.5 3.0 0.001 0.01 0.1 1 10 100 1000 φp(x,kt

2)

kt

2 [GeV2]

p x = 1e-02 x = 1e-03 x = 1e-04 x = 1e-05

non-linear vs linear

0.0 2.0 4.0 6.0 8.0 10.0 12.0 0.001 0.01 0.1 1 10 100 1000 φp(x,kt

2)

kt

2 [GeV2]

p x=10-2...10-5 non-linear linear

kt > 1 GeV: gluon from the unified BK/DGLAP equation kt < 1 GeV: φp(x, k2) = k2φp(x, 1 GeV2) [non-linear] φp(x, k2) = φp(x, 1 GeV2) [linear]

◮ significant differences between linear and non-linear gluon at low kt 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

1 10 102 103 104 105 40 60 80 100 120 140 d2σ/dptdηc [pb/GeV] central pt [GeV] √ s = 7 TeV pt > 35 GeV central: |η| < 2.8 forward: 3.2 < |η| < 4.7 CENTRAL linear non-linear data CMS 1 10 102 103 104 105 40 60 80 100 120 140 d2σ/dptdηf [pb/GeV] forward pt [GeV] √ s = 7 TeV pt > 35 GeV central: |η| < 2.8 forward: 3.2 < |η| < 4.7 FORWARD linear non-linear data CMS

◮ the result reproduces the pattern of CMS data

◮ excess at low pt 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

RPb = R A1/3

◮ Unintegrated gluon distribution

φPb(x, k2) ≡ A φPb/A(x, k2) where φPb/A(x, k2) is the distribution of gluons per nucleon The evolution equation

φPb/A(x, k2) = » ˆ L1 − A1/3 R2 ˆ L2 –

• φPb/A(x, k2)

◮ ˆ

L1,2 – linear and non-linear operators as in the equation for proton

◮ for the nucleus the non-linear term is enhanced by A1/3

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

0.0 0.5 1.0 1.5 2.0 2.5 3.0 0.001 0.01 0.1 1 10 100 1000 φp(x,kt

2)

kt

2 [GeV2]

p x = 1e-02 x = 1e-03 x = 1e-04 x = 1e-05

non-linear gluon in Pb nucleus

0.0 0.5 1.0 1.5 2.0 2.5 3.0 0.001 0.01 0.1 1 10 100 1000 φPb/A(x,kt

2)

kt

2 [GeV2]

Pb x = 1e-02 x = 1e-03 x = 1e-04 x = 1e-05

◮ significant suppression of gluon density in the Pb nucleus wrt the proton

at low and moderate kt

◮ gluon’s transverse momentum: k2 t = p2 t1 + p2 t2 + 2pt1pt2 cos ∆φ

◮ low and moderate kt 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

50 100 150 200 250 300 350 2.5 2.6 2.7 2.8 2.9 3 3.1 dσ/d∆φ [µb] ∆φ √ s = 7 TeV pt > 15 GeV central: 0 < y < 2.8 forward: 3.2 < y < 4.7 p-p linear p-p non-linear p-Pb 10 20 30 40 50 60 70 2.5 2.6 2.7 2.8 2.9 3 3.1 dσ/d∆φ [µb] ∆φ √ s = 7 TeV pt > 25 GeV central: 0 < y < 2.8 forward: 3.2 < y < 4.7 p-p linear p-p non-linear p-Pb 5 10 15 20 25 2.5 2.6 2.7 2.8 2.9 3 3.1 dσ/d∆φ [µb] ∆φ √ s = 7 TeV pt > 35 GeV central: 0 < y < 2.8 forward: 3.2 < y < 4.7 p-p linear p-p non-linear p-Pb 10 20 30 40 50 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 dσ/dy [µb] y √ s = 7 TeV pt > 15 GeV central: 0 < y < 2.8 forward: 3.2 < y < 4.7 p-p linear p-p non-linear p-Pb 1 2 3 4 5 6 7 8 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 dσ/dy [µb] y √ s = 7 TeV pt > 25 GeV central: 0 < y < 2.8 forward: 3.2 < y < 4.7 p-p linear p-p non-linear p-Pb 0.0 0.5 1.0 1.5 2.0 2.5 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 dσ/dy [µb] y √ s = 7 TeV pt > 35 GeV central: 0 < y < 2.8 forward: 3.2 < y < 4.7 p-p linear p-p non-linear p-Pb 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

50 100 150 200 250 300 2.5 2.6 2.7 2.8 2.9 3 3.1 dσ/d∆φ [µb] ∆φ √ s = 5 TeV and 8.8 TeV pt > 15 GeV central: 0 < y < 2.8 forward: 3.2 < y < 4.7 p-p p-Pb 10 20 30 40 50 60 70 2.5 2.6 2.7 2.8 2.9 3 3.1 dσ/d∆φ [µb] ∆φ √ s = 5 TeV and 8.8 TeV pt > 25 GeV central: 0 < y < 2.8 forward: 3.2 < y < 4.7 p-p p-Pb 5 10 15 20 25 2.5 2.6 2.7 2.8 2.9 3 3.1 dσ/d∆φ [µb] ∆φ √ s = 5 TeV and 8.8 TeV pt > 35 GeV central: 0 < y < 2.8 forward: 3.2 < y < 4.7 p-p p-Pb

◮ significant suppression due to saturation for both energies ◮ dip near ∆φ ≃ π comes from ∼ k2 behaviour of the unintegrated gluon at

low k2; 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