dilepton low pt suppression as an evidence of the cgc filedilepton low pt suppression as an evidence...

Dilepton low pT Suppression as anEvidence of the CGC

M. B. Gay Ducati†† [email protected]

High Energy Phenomenology Group

Instituto de Fısica

Universidade Federal do Rio Grande do Sul

Porto Alegre, Brazil

GFPAE - UFRGShttp://www.if.ufrgs.br/gfpae

Talk based on work with M. A. Betemps (hep-ph/0408097 Phys. Rev. D in press)

M. B. Gay Ducati - Hard Probes 2004 – p.1

Outline

Motivation

Color Glass Condensate

Dilepton production in the Color Glass Condensate

Saturation effects in the Dilepton pT spectra

Cronin effects in dilepton production

Conclusions


Motivation

Gluon High Density⇒ Saturation below a characteristic scale Qs ⇒Color Glass Condensate (CGC).

Search for signatures of the CGC description of the saturated regime.

proton-nucleus collisions⇒ ideal experiment to investigate thesaturation effects described by the CGC in the proton fragmentationregion.

Transverse momentum distribution pT at high energies:Hadron Production measured and investigated.

dilepton production ⇒ sensitive probe of the perturbativeshadowing and saturation dynamics in proton-proton,proton-nucleus or nucleus-nucleus scattering (needsmeasurements).


What we haveInclusive hadron production

To calculate the pT and y (rapidity) distributions

dσpA→hX

dq2T dyh

=dσij→kX

dq2T dyj

⊗ fi(yi, Q2h)⊗ fj(yj , Q2

h)⊗ Dk→h(z,Q2h) .

Needs a fragmentation function⇒ strongly dependent on the finalstate interactions

dilepton production

dσpA→l+l−X

dq2T dy

=dσij→kX

dq2T dy

⊗ fi(yi, Q2h)⊗ fj(yj , Q2

h).

Final state interactions are disregarded (eletromagneticinteraction).Cleaner analysis


Perturbative Shadowing in pp collisionsInvestigated in the dipole picture

N

q(x1/α)

γ∗(α)r⊥

l+

l−

g(x2)

N

q

1

Dipole ?

THE HIGH DENSITY EFFECTS IN THE DRELL-YAN

PROCESS

M. A. BETEMPS 1, M. B. GAY DUCATI 1, A. L. AYALA FILHO 2

1 Instituto de Fısica, Universidade Federal do Rio Grande do Sul. Caixa Postal

15051, CEP 91591-970 Porto Alegre, RS - Brasil.2 Instituto de Fısica e Matematica, Universidade Federal de Pelotas. Caixa Postal

354, CEP 96010-090 Pelotas, RS - Brasil.

The high density effects in the Drell-Yan process (qq → γ∗→ l+l−) are investi-

gated for pA collisions at RHIC and LHC energies. In particular, we use a set ofnuclear parton distributions that describes the present nuclear eA and pA data inthe DGLAP approach including the high density effects introduced in the pertur-bative Glauber-Mueller approach.

• r⊥ → photon-quark transverse separation,

• αr⊥ → qq (dipole) transverse separation,

• α → quark light-cone momentum fractioncarried by the photon,

• x1/α → projectile momentum fraction carriedby the quark,

• x2 → target momentum fraction carried bythe gluon.

• pT → tranverse momentum of the lepton pair.

• M2 squared lepton pair mass.

• xF = x1 − x2.

definicao: submitted to World Scientific on April 16, 2003 1

dσT,L(qN → qγ∗N)

d lnα=

∫d2r|ΨT,L

γ∗q (α, r)|2σqqdip(x2, αr)

The differential Drell-Yan cross section can be written as

d σDY

dM2dxF d2pT= αem

6πM21

(x1+x2)

∫ 1

x1

dαα F

p2

(x1

α

) dσ(qN→qγ∗N)d lnαd2pT

M.A. Betemps, MBGD, M. V. T. Machado,J. Raufeisen, Phys. Rev. D67, n. 114008,2003 M. B. Gay Ducati - Hard Probes 2004 – p.5

Perturbative Shadowing in pp collisionsPerturbative corrections in the dipole cross section byGlauber-Mueller approach (AGL evolution equations)

Comparison with the GRV predictions

pT distribution in pp collision (forward rapidities) at RHIC and LHCenergies the DY

0 1 2 3 4pT (GeV)

10−1

100

101

M2 d4 σ/

dxFd

M2 d2 p T

(pb

GeV

−2)

GM distributionGRV94GRV 98

s1/2=500 GeVM=6.5 GeVxF=0.625

RHIC

0 1 2 3 4pT (GeV)

100

101

M2 d4 σ/

dxFd

M2 d2 p T

(pb

GeV

−2)

GM distributionGRV94GRV98

s1/2=14 TeV

xF=0.625M=6.5 GeV

LHC

Small corrections at RHIC energies

Large unitarity effects at high pT at LHC energies.

Perturbative corrections appear at large pT .M. B. Gay Ducati - Hard Probes 2004 – p.6

(Minimal) Color Glass CondensateColor⇒ Gluonic field L. McLerran, R. Venugopalan (1994)

Glass⇒ Internal dynamics evolves slowly

Condensate⇒ Dense and saturated gluon field

Use of semi-classical techniques

Nucleus

⇒ p+

p+1

p+2

p+n

= k+

Classical

fields Aµ

a

1

p+ > p+1 > p+

2 > ... > p+n

p+ >> p+n

Aµa obeys Classical Yang-Millsequations,[Dµν , F

µνa ] = δµ+ρa(x−, x⊥).

color charge sources density.

x− light-cone time.

ρa(x, x⊥) stochastic variable with zero expectation value.

average over all ρa configurations, with the gauge-invariant weightfunctional WΛ+ [ρa]

p+ > Λ+ fast gluons, p+ < Λ+ soft gluons.M. B. Gay Ducati - Hard Probes 2004 – p.7

Color Glass CondensateAny observable is calculated by averaging over the sourcesconfigurations by means of

〈Aia(x+, ~x)Ajb(x+, ~y)...〉Λ+ =

∫Dρ WΛ+ [ρ] Aia(~x)Ajb(~y).

Fundamental quantity in the CGC.

Driven by the evolution equation JIMWLK.

Phenomenology

Local Gaussian (can accommodate BFKL evolution and the gluonsaturation)

W [x, ρ] = exp

{−∫dz⊥

ρa(z⊥)ρa(z⊥)

2µ2(x)

}

Non local Gaussian (Predicted by the mean field asymptoticsolution of the JIMWLK evolution equations)

W [x, ρ] = exp

{−∫dy⊥dx⊥

ρa(x⊥)ρa(y⊥)

2µ2(x)

}

µ2(x) is related to the average of the color charge squared.M. B. Gay Ducati - Hard Probes 2004 – p.8

Dilepton Production in CGC

originally derived by Jalilian-Marian, Kovner, Leonidov and Weigert [4, 5].

This a functional equation for the statistical weight function associated with

the random variable ρa(x).

In this work one considers an approximation to the weight function which

is reasonable when we have large nuclei. This approximation consist in to

take a Gaussian form to the weight function [14, 16].

3 Dilepton production cross section

We are interested in the following subprocesses

q(p) + A → q(q)γ(k)X

q(p) + A → q(q)γ(k)A

We need to consider diagrams where the photon emission occur after and be-

fore the interaction with the nucleus, as presented in the figure (1), However

γ∗(k)

q(p) q(q)

l+

l−

l+

l−

Classical Field

Nucleus

Figure 1: Photon production in the CGC.

we need to know how the high density of gluons should be considered in the

nucleus and how the interaction with the quark is treated through the CGC.

The cross section for the dilepton production, considering the diagrams

above is written of the form [15],

dσqA→ql+l−Xincl

dzd2k⊥d log M2= πR2e2

q

2α2em

3π

d2l⊥(2π)4

C(l⊥)

{[

1 + (1 − z)2

z

]

× z2l2⊥[k2

⊥ + M2(1 − z)][(k⊥ − zl⊥)2 + M2(1 − z)]− z(1 − z)M 2

×[

1

[k2⊥ + M2(1 − z)]

− 1

[(k⊥ − zl⊥)2 + M2(1 − z)]

]2

, (2)

4

The cross section is written as

dσpA→ql+l−X

dp2T dM dxF

=4π2

MR2A

α2em

3π

1

x1 + x2

×∫

dlT(2π)3

lT W (pT , lT , x1)C(lT , x2, A),

W (pT , lT , x1) analyticalcalculations⇒ select thevalues of lT larger than pT .

C(lT , x2, A) color field correla-tion ⇒ interaction of the quarkwith the condensated gluonicfield (Classical field).

F. Gelis, J.Jalilian-Marian, Phys. Rev. D 66,094014 (2002)

0 5 10 15 20 25 30lT (GeV)

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

W(p

T,l T,

x 1) (G

eV −2

)

pT = 0 GeVpT = 2 GeVpT = 4 GeV


Color Field CorrelationC(lT ) ≡

∫d2x⊥e

ilT ·x⊥〈U(0)U †(x⊥)〉ρ,

related to the Fourier transform of non-integrated gluon distribution

C(lT )=1

σ0

∫d2reilT ·r[σdip(r →∞)− σdip(r)],

We have analyzed somemodels for the correlationfunction

McLerran-VenugopalanGBWIancu, Itakura and Munier(CGCfit)

We use McLerran-Venugopalan

0 1 2 3 4 5 6 7 8 9 10lT (GeV)

−0.5

0.5

1.5

2.5

3.5

4.5

5.5

6.5

7.5

C(l T,

x,A

) (G

eV−2

)

C(lT,x,A) (F,T, fit CGC dip)C(lT,x,A) (F.T. GBW)C(lT,x,A) (MVmod Qs GBW)C(lT,x,A) (MVmod asymptotic)

0 2 4 6 8 1010−610−510−410−310−210−1

100101

A=197x=10−3


Local × Non-localWe use McLerran-Venugopalan model with an energy dependenceinto the saturation scale

Q2s(x,A) = A1/3

(x0

x

)λparameters

{x0

λ

Local Gaussian

C MVmod(lT , x, A) =

∫d2x⊥

× eilT ·x⊥e−Q2s(x,A)

π

R dp

p3 (1−J0(px⊥)).

Non-local Gaussian

C (lT , x, A)≡∫d2x⊥e

ilT ·x⊥

× e− 2γc

R dpp (1−J0(x⊥p)) ln

„1+

„Q2

2(x,A)

p2

«γ«

, 0 1 2 3 4 5 6lT (GeV)

0

1

2

3

4

5

6

C(l T,

x,A

) (G

eV−2

)

C(lT,x,A) (MVmod local)C(lT,x,A) (MVmod non−local)

A=197x=10−3


Dilepton pT spectra

RHIC

0 1 2 3 4 5 6 7pT (GeV)

10−2

10−1

100

101

102

dσ/d

Mdx

Fdp T2 (µ

b/G

eV−3

)

MVmod (Qs CGCfit mq=10 MeV)MVmod (Q GBW)MVmod asymp. (Qs CGCfit mq=10 MeV)MV (Qs

2= 3.2 GeV2)

s1/2=350 GeV

A=197

maximum RHIC energyM = 3 GeV and y = 2.2

fits Q2s (x = 10−3)A = 197)

GBW 4.114 GeV2

CGCfit 3.069 GeV2

mq = 10 MeV

Large suppression effects atsmall pT ;

Suppression below thesaturation scale (Qs);

Dependence on the Qs valueat large pT ;

Large value of Qs increasesthe spectra at large pT ;

Qs x evolution yields a reduc-tion at large pT in compari-son with the no evolution case(Magenta line).


Dilepton pT spectra

LHC

0 1 2 3 4 5 6 7pT (GeV)

101

102

103

104

105

dσ/d

Mdx

Fdp T2 (µ

b G

eV−3

)

MVmod (Qs CGCfit mq=10 MeV)MVmod (Qs GBW)MVmod asymp. (Qs CGCfit mq=10 MeV)MV (Qs

2 = 8 GeV2)

s1/2=8.8 TeV A=197

maximum LHC energyM = 3 GeV and y = 2.2

fits Q2s (x = 10−3)A = 197)

GBW 4.114 GeV2

CGCfit 3.069 GeV2

mq = 10 MeV

Large suppression effects atsmall pT ;

Suppression below thesaturation scale (larger thanat RHIC energies);

Large value of Qs increasesthe spectra at large pT ;

Qs x evolution yields a reduc-tion at large pT in compari-son with the no evolution case(Magenta Line).


Seeking Cronin effect in DileptonNuclear modification factor

RpA =

1R2A

dσpA→l+l+X

dp2T dMdy

A1/3 1R2p

dσpp→l+l+Xdp2T dMdy

Using the expressions to the cross section,

RpA(y, pT ) =

∫d2lTW (pT , lT , x1)CA(lT , x2, A)

A1/3∫d2lTW (pT , lT , x1)Cp(lT , x2)

,

ratio between color field correlation weighted by the functionW (pT , lT , x1);

Similar ratio used to investigate the Cronin effect in the hadronproduction;


Cronin effect in the CGC approachcharged hadrons

pT (GeV)

Rd+Au

0

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

1.8

2

0 1 2 3 4 5 6

pT (GeV)

Rd+Au

0

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

1.8

2

0 1 2 3 4 5 6

pT (GeV)

Rd+Au

0

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

1.8

2

0 1 2 3 4 5 6

pT (GeV)

Rd+Au

0

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

1.8

2

0 1 2 3 4 5 6

Nuclear modification factorRdA.

RdA =

dσdA→hX

dp2T dy

Ncoll dσpp→hXdp2T dy

data from dA collisions at√s = 200 GeV.

BRAHMS data.KKP fragmentation function

Consider valence quarks

Introduce a functon to takeinto account large x gluon be-havior

D. Kharzeev, Y. V. Kovchegov, K. Tuchin,hep-ph/0405045.


RpA Local Gaussian (dileptons)

0 1 2 3 4 5 6 7pT (GeV)

0

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

1.8

RpA

=Rp2 d

σpA/A

1/3 R

A2 d

σpp

RHIC (y=2.2)RHIC (y=3.2)LHC (y=2.2)LHC (y=3.2)

Suppression at small pT ;

Cronin peak appears atintermediated pT ;

The peak increases and isshifted to large pT with theincrement in the rapidity;

Disagreement with the sup-pression presented in theRHIC data on inclusivehadron sector


Local× Non-local Gaussian

0 1 2 3 4 5 6pT (GeV)

0

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

1.8

RpA

=Rp2 d

σpA/A

1/3 R

A2 d

σpp

Local (y=2.2)Local (y=3.2)Non−local (y=2.2)Non−local (y=3.2)

RHIC energies

The suppression of the Cronin peak is reached;

The suppression is enlarged for large values of rapidity;

RHIC data present the suppression of the Cronin peak at largerapidities;

Effect of the evolution [Albacete, Armesto, Kovner, Salgado, Wiedemann, Phys.

Rev. D 92, 082001 (2004)]. M. B. Gay Ducati - Hard Probes 2004 – p.17

Local× Non-local Gaussian

0 1 2 3 4 5 6pT (GeV)

0

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

1.8

RpA

=Rp2 d

σpA/A

1/3 R

A2 d

σpp

Local (y=2.2)Local (y=3.2)Non−local (y=2.2)Non−local (y=3.2)

LHC energies

The suppression of the Cronin peak is reached;

The suppression is intensified for large values of rapidity;

Simulation of the quantum evolution.


Non-local Gaussian

0 1 2 3 4 5 6pT (GeV)

0

0.2

0.4

0.6

0.8

1

1.2

1.4

RpA

=Rp2 dσ

pA/A

1/3 R

A2 d

σpp

RHIC (y=2.2)RHIC (y=3.2)LHC (y=2.2)LHC (y=3.2)

Non−local Gaussian

The suppression is intensified for large energies;

Measurements on dilepton sector are needed.


Conclusions

The suppression at small and moderated pT is an evidence of thesaturation effects (CGC).

The ratio RpA shows a Cronin type peak with local Gaussian andpresents a suppression with a non-local Gaussian, considering thedilepton pT spectra.

The dilepton pT distribution indicates the Cronin effect as an initialstate effect.

Measurements on the dilepton pT distribution at high energies arerequired.


dilepton low pt suppression as an evidence of the cgc filedilepton low pt suppression as an evidence...

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