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due to its large center of mass energy the lhc provides an ideal opportunity to test bfkl - driven observables @xcite . among them both central production processes , such as heavy quark production @xcite , forward production of high @xmath0 jets @xcite and drell - yan pairs @xcite , and processes with hard events in both forward and backward direction , _ i.e. _ forward - backward ( ` mueller - navelet ' ) jets @xcite and forward @xmath1 boson production combined with a backward jet @xcite .
an observable of particular interest is given by forward / backward jets with a rapidity gap ( ` mueller - tang ' jets ) .
this process is special since it allows to probe the non - forward bfkl kernel , unlike the previously mentioned processes restricted to the forward case . from a phenomenological point of view
the description in terms of the non - forward bfkl green s function is of relevance , since the latter describes a color singlet @xmath2-channel exchange . unlike configurations which merely suppress emissions above a certain veto scale ,
the non - forward bfkl green s function therefore describes a @xmath2-channel exchange with emissions into the gap region intrinsically absent .
while the non - forward bfkl kernel is currently available at next - to - leading order ( nlo )  @xcite , only the virtual nlo corrections to the impact factors @xcite are currently known ; phenomenological studies , see _
@xcite , are therefore limited to leading order ( lo ) impact factors . as
nlo corrections to bfkl observables are often found to be size - able , this limitation to lo impact factors is currently one of the main drawbacks of bfkl phenomenology . a powerful tool to overcome this limitation is given by lipatov s effective action  @xcite .
it is given in terms of the conventional qcd action to which a new induced term is added .
the latter contains a new effective degree of freedom , the reggeized gluon , which has been introduced in order to achieve a gauge invariant factorization of qcd amplitudes in the high energy limit .
the determination of higher order corrections within this effective action is at first plagued by both technical and conceptual difficulties .
loop corrections show a new type of divergence , which is not present in usual qcd feynman diagrams . supplementing the qcd action with the additional induced term leads to an apparent over - counting problem .
these problems have been addressed and resolved recently , first in the context of lo transition kernels  @xcite and later on in the calculation of nlo corrections to the forward quark - initiated jet vertex @xcite and the quark contribution to the two - loop gluon trajectory @xcite , for a recent review see @xcite .    in this contribution
we present some details of the determination of the missing real nlo correction to the quark - initiated mueller - tang jet impact factors .
for further details and the complete result , including the gluon - initiated jet , we refer to  @xcite .
the effective action adds to the qcd action an induced term , @xmath3 , which describes the coupling of the reggeized gluon field @xmath4 to the usual gluonic field @xmath5 .
this induced term reads @xmath6 & = \int \ !
\text{d}^4 x \,{{\rm tr}}\bigg[\bigg ( w_+[v(x ) ] - a_+(x ) \bigg)\partial^2_\perp a_-(x)\bigg ] \notag \\ &   \qquad   \qquad    \qquad + \int \ !
\text{d}^4 x \ , { { \rm tr}}\bigg[\bigg(w_-[v(x ) ] - a_-(x ) \bigg)\partial^2_\perp a_+(x)\bigg].\end{aligned}\ ] ] the infinite number of couplings of the gluon field to the reggeized gluon field are encoded in two functionals @xmath7   = v_\pm \frac{1 } { d_\pm}\partial_\pm $ ] where @xmath8 .
reggeized gluon fields are invariant under local su@xmath9 gauge transformations .
strong ordering of longitudinal momenta in high energy factorized amplitudes provides the following kinematic constraint , @xmath10 which is always implied .
quantization of the gluonic field requires to add gauge fixing and ghost terms , which we have included in the qcd action .
@xmath11{ll }      \\   \\ - i{\bm q}^2 \delta^{a c } ( n^\pm)^\nu ,   \\ \\
\qquad    k^\pm = 0 .
\end{array }   $ ] @xmath12{ll }      \delta^{ab } \frac { i/2}{{\bm q}^2 } \end{array}$ ] @xmath13{ll }   \\ \\ g f^{c_1 c_2 a } \frac{{\bm q}^2}{k_1^\pm }    ( n^\pm)^{\nu_1 } ( n^\pm)^{\nu_2 } ,   \\ \\
\quad   k_1^\pm   + k_2^\pm   = 0   \end{array}$ ]    feynman rules are given in fig .
[ fig : feynrules0p2 ] .
curly lines describe the conventional qcd gluon field and wavy lines the reggeized gluon field .
there exist an infinite number of higher order induced vertices .
for the present analysis only the order @xmath14 induced vertex in fig .
[ fig : feynrules0p2 ] is needed .
loop corrections furthermore require a regularization of the light - cone singularity @xmath15 .
as discussed in  @xcite this pole should be treated as a cauchy principal value .
the starting point for the determination of the quark induced mueller - tang jet impact factors is given by the quark - quark scattering amplitude with color singlet exchange . in the high energy limit such a scattering amplitude factorizes ( in terms of a transverse convolution integral ) into the two reggeized gluon exchange in the color singlet ( which can be understood as the lowest order contribution to the perturbative pomeron ) and two impact factors ( which describe the coupling of the two reggeized gluon state to the external quarks ) , see fig .
[ fig : mt ] .        due to high energy factorization , the longitudinal part of the loop integral _
i.e. _ the @xmath17 ( @xmath18 ) integration , can be entirely associated with the upper ( lower ) impact factor . at cross - section level , using dimensional regularization in @xmath19 dimensions , the leading order result reads , @xmath20\left [ \int \frac{d^{2 + 2\epsilon } { \bm l}_2}{\pi^{1 + \epsilon } } \frac{1}{{\bm l}_2 ^ 2 ( { \bm k } - { \bm l}_2 ) } \right ] d^{2 + 2\epsilon } { \bm k}\end{aligned}\ ] ] with the impact factor @xmath21 in agreement with @xcite . while the leading order impact factor is merely a constant , the real next - to - leading order corrections depend both on the momenta of the final state particles and the loop momentum of the reggeized gluon loop , @xmath22 and @xmath23 .
their integrated version reads @xmath24 \left [   c_f      \left ( \frac{{\bm \delta}}{{\bm \delta}^2 } - \frac{{\bm q}}{{\bm q}^2 } \right ) - { c_a}{}\left ( \frac{{\bm p}}{{\bm p}^2 } + \frac{1}{2 } \frac{{\bm \sigma}_2}{{\bm \sigma}_2 ^ 2 } + \frac{1}{2 } \frac{{\bm \upsilon}_2}{{\bm \upsilon}^2_2 } \right )    \right]\end{aligned}\ ] ] where @xmath25 , @xmath26 , and @xmath27 .
@xmath28 is the momentum transfer in the @xmath2-channel , @xmath29 the transverse momentum of the final state gluon .
@xmath30 is the real part of the @xmath31 splitting function . for the limit @xmath32
, the above expression can be shown to agree with the real part of the triple - pomeron vertex @xcite .
we would like to thank g.  chachamis , j.  madrigal  martnez and a.  sabio  vera for fruitful collaboration . m.h .
acknowledges support from the u.s .
department of energy under contract number de - ac02 - 98ch10886 and a bnl `` laboratory directed research and development '' grant ( ldrd 12 - 034 ) .
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we report on recent progress in the evaluation of next - to - leading order observables using lipatov s qcd high energy effective action . in this contribution 
 we focus on the determination of the real part of the next - to - leading order corrections to the mueller - tang impact factor which is the only missing element for a complete nlo bfkl description of quark induced dijet events with a rapidity gap .     
 address = instituto de ciencias nucleares , universidad nacional autnoma de mxico , apartado postal 70 - 543 , mxico distrito federal 04510 , mxico     address 
 = dipartimento di fisica , universit della calabria , and istituto nazionale di fisica nucleare , gruppo collegato di cosenza , i-87036 arcavacata di rende , cosenza , italy