Sensitivity of the parameters measured in pp collisions on the gluon PDF. arXiv:1001.0613v1 [hep-ph] 5 Jan 2010 $^{∗}$Electronic address: ecuautle@nucleares.unam.mx $^{†}$Electronic address: antonio.ortiz@nucleares.unam.mx $^{‡}$Electronic address: guypaic@nucleares.unam.mx I. INTRODUCTION II. EVENT SHAPE VARIABLES T ≡ max ︸ ︷︷ ︸ − → n t ∑ i | − → p$_{t,i}$ · − → n$_{t}$ | i | − → p$_{t,i}$ | (1) R ≡ 1 ∑ i | − → p$_{t,i}$ | | ∑ i − → p$_{ti}$ | . (2) coil distributions; in the section III we discuss the parton distribution functions used and the way the simulations were done in the framework of minimum bias PYTHIA. The results are presented in section IV and finally, in section V the conclusion are drawn. Event shape variables allow us to measure geometrical properties of QCD final state [4]. Those variables has been used to analyze dijet production in hadron-hadron collisions and to study the sensitivity of physical param- eters [4]. The shape variables at hadron colliders are defined over particles within the acceptance of the detec- tor. The thrust ( T ) is defined in the transverse plane as follows: where the sum runs over all particles in the final state within the acceptance, − → p$_{t,i}$ represent the transverse com- ponent of the momenta of emitted particles and − → n$_{t}$ is the transverse vector that maximizes the ratio. In the literature it is more common to find the quantity 1 − T related to the transverse sphericity of the event. In the present work we do reference to this as sphericity. The range of sphericity is between 0 (for events with narrow back-to-back jets) and 1 − 2 /π (for events with a uniform momentum distribution). Another interesting observable is the recoil, defined as: It is an indirect measurement for the radiation which re- mains undetected for acceptance effects (high inbalance: R → 1, small inbalance: R → 0). The calculation of the production cross sections at hadron colliders relies upon a knowledge of the distribu- tion of the momentum fraction x of the partons (quarks and gluons) in a proton in the relevant kinematic range, and the corresponding fragmentation functions. Most probably, at LHC, we will be confronted with a copious production of jets what will severely limit the exclusive analysis of individual jets. It seems therefore interesting to separate the events in function of their multi-jetiness and to study the parameters of the collisions e.g. mean p$_{t}$ , mean multiplicity, etc., in function of different par- ton distribution functions (PDF’s) present on the mar- ket, which as quoted by the CTEQ group allows for an uncertainty of about 10-20% [1]. Obviously this uncer- tainty will reflects in the quantification of the kinematical processes. The PDF’s are of importance to analyze stan- dard model processes at LHC energies [2], and the usual leading order event generators use the PDF’s as an input to evaluate hard subprocess matrix elements. In those calculations the multiple parton interactions that make up the bulk of the underlying event, require extensive tuning which depends strongly on the details of the in- put parton distributions. The Event Shape Analysis (ESA) has been applied suc- cessfully to the restricted acceptance experiments at RHIC and ALICE to survey the possibilities of the method to analyze and isolate specific jet topology events [3]. In the present paper we are investigating the bulk properties of the event shape variables obtained in minimum bias pp events: the sensitivity obtained at dif- ferent collisions energies focussing to minimum bias col- lisions, corresponding to the minimum x-Bjorken ( x$_{B}$ ) achievable. The article is organized as follows: in the section II we give the relation for the sphericity and re- PACS numbers: 24.85.+p, 12.38.-t The sphericity distribution in minimum bias events obtained with PYTHIA event generator, in- corporating different parton distribution functions is presented. The results show that for minimum bias pp collisions the sphericity distribution for different parameters like the mean transverse mo- mentum and multiplicity exhibit strong sensitivity on the parton distribution function used. The results indicate that early data at the LHC could be used in this type of analysis to fix the gluon distribution function in the proton. E. Cuautle, ∗ A. Ortiz, † and G. Pai´ c ‡ Instituto de Ciencias Nucleares, Universidad Nacional Aut´ onoma de M´ exico Apartado Postal 70-543, M´ exico Distrito Federal 04510, M´ exico. (Dated: November 17, 2018)