Saturation at hadron colliders

Cyrille MarquetSPhT, Saclay

hep-ph/0312261to appear in PLB in collaboration with Robi Peschanski

Contents

• Introductiongluon-initiated processes and saturation

• Framework the color dipoles, the GBW model and its extension

• Forward-jet production in terms of dipoles• Mueller-Navelet cross-sections

with saturation effects

• Conclusion and outlook

• Mueller-Navelet jets (1987): considered to test the BFKL evolution at the Tevatron

Q1, Q2 » QCD exp()» 1prediction:

( >()2)• Production of heavy-flavored

and vector mesons• Can we reach saturation in these

processes?at the Tevatron or LHC ?

• How does one formulate saturation in such processes?

Gluon-initiated processes

)exp( BFKL

Saturation and the GBW model

• DIS: the Golec-Biernat and Wüsthoff (GBW) model (1998) for the dipole-proton cross-section

))(4exp(1)( 20

20 Bjdp xRrr

• photon-photon with an extension of the GBW model: a model for the dipole-dipole cross-section

)(4exp1),,( 20

2021 Rrrr effdd

Tîmneanu, Kwiecinski and Motyka (2002)

Dipole factorization for hard cross-sections

• equivalent to BFKL+kT-factorization

• in the present work, we assume this factorization property to hold in the presence of saturation

),,()Q,()Q,( 21222

(2)211

(1)2

21

2 rrrrrdrd dd

222 )Q,(ψ)Q,( rr

1. 2.

3.

Extension of the GBW model

22

21

22

212

rrrr

reff 22rreff

)ln(122 rrrreff

),max(),min( 2121 rrrrrr

)(4exp1),,( 20

2021 Rrrr effdd

• the three models exhibit color transparency

• the model 3 corresponds to the two-gluon exchange between the dipoles

2~ rdd0r

• the saturation radius is

we use the same parameters as those of dipole-proton = 0.288, 0 = 8.1 for Q0 1 GeV (universal saturation scale)

• the three scenarios we consider are

)(2

expQ1)( 0

00 R

TKM (2002)

)k(r,frrd)rkf( 202

0

20

22 )Q,(,Q,

Forward-jet in terms of dipoles

))(1(2),( 0220 krJ

kkrf

)k(r,frJπr

rdrx

α)rf(k 201

0

200

22 )Q(2QQln1ln2,Q,

Munier (2001), C.M. and R. P. (2003)

collinear factorization

dipole factorization

• the onium allows a perturbative calculation and the interpretation in the dipole formalism; in the collinear limit r0Q »1, f factorizes:

The dipole distribution in a forward jet

• large-size dipoles have a contribution to ; this is not the case for in a photon-initiated process

cannot be seen as a probability distribution

• the BFKL cross-sections calculated with are positive

)Q(2Q)Q,( 1

2 rJr

r

Peschanski (2000), C.M. and R. P. (2003)

Formulae for the hard total cross-sections

1si)ln1(

1siln1)(

2

3

uuu

uuuf

2

2

1 1)(

uu

uf

1si

1si1)(

2

2

uu

uuf

)( )(QQ2)()QQ(exp)(

QQ21 20211

20

222

21

0

2021

0ufuRIufRu

ufduR iii

i

for the different models :

C.M. and R. Peschanski (2003)

• the cross-sections are positive i > 0

• however 2’s high-Q limit (no saturation) does not behave as 1/Q2

Saturated cross-sections• model 3 with

Q1= Q2 Q

• the plot shows the expected trend: a suppression of 3 in the domain Q<Qs 1/R0()

The rapidity intervals for the different curves are: = 4, 6, 8, 10

Q0 = 1 GeV

A suitable measurement

• a ratio studied to test the BFKL evolution at the Tevatron (DØ collaboration, 1999)

• shows the influence of saturation in a more quantitative way

• experimentally, R was obtained working at fixed and using the factorization of the structure functions in the total cross-sections:

• R at LHC?

),Q,Q(),Q,Q(

21

21/

j

iji

R

),Q,Q()Q,()Q,( 21222

211

21

xFxFdxdx

d Xjjpptot

1x 2x

An potentially interesting signal

• the value of R goes down from the transparency limit towards the saturation regime where R1

• one can observe a sharper transition in the case of the gluon-initiated process

• the values of Q at the transition are weak for jet cuts at the Tevatron

• along with BFKL studies, the signal deserves to be studied at the LHC

• alternatives to bypass the small-Q problem? R 4.6/2.4 : ratio studied at theTevatron

R 8/4 : ratio realistic for the LHC

Q0 = 1 GeV

Other configurations

• asymmetric configurations ? the transition towards saturation becomes really steep more interesting: the transition is shifted towards higher Q

Q0 = 1 GeV

• alternatives to jets: heavy vector mesons J/ or D mesons with c quarks or B mesons with b quarks in asymmetric configurations?

• Introduction of the dipole formalism in the description of hadron-induced hard processes, such as Mueller-Navelet jets

• Studies of saturation effects in these processes using an extension of the Golec-Biernat and Wüsthoff model

• Proposal and predictions for an observable at hadron colliders

To do• Studies of feasability for the Tevatron and LHC: can we access the ratio R

experimentally? for which values of Q? using jets or alternatively heavy vector mesons, heavy flavors?

Theoretical extensions• Improve our description of gluon-initiated processes in terms of dipoles:

taking into account saturation effects in the emission vertex and kT-factorization breaking

• Studying pQCD saturation beyond GBW models

Conclusion and outlook