#### 1. Introduction

Nowadays numerous experimental and theoretical investigations of high energy nucleus-nucleus collisions show that the quark-gluon plasma could exist in nature. Moreover, the results of CERN LHC [1] and BNL RHIC [2] experiments and the observation of the transition between hadronic matter and quark-gluon plasma at CERN SPS energies [3], [4], [5] revealed that the key question in nuclear and particle physics now is to determine the structure of the phase transition between the hadron gas and the deconfined matter. It is expected that in the phase diagram of strongly interacting matter the hadron gas and quark-gluon plasma regions are separated by a first order phase transition line at high baryo-chemical potentials and moderate temperatures. A crossover between both phases is assumed for high temperatures and low baryo-chemical potentials. The first order phase transition line then ends in a critical point. But the exact location of the critical end-point in the phase diagram is unknown. Moreover, some lattice QCD calculations suggest that there might be no critical point at all and only a crossover separates the two phases.

The strong interactions programme of NA61/SHINE, a fixed-target experiment at the CERN SPS [6], includes the study of the properties of deconfinement and the search for the critical behaviour of strongly interacting matter. The main strategy of the NA61/SHINE collaboration in the search for the critical point is to perform a comprehensive two-dimensional scan of the phase diagram of strongly interacting matter by changing the collision energy and the system size [7]. If the critical point exists it is expected that at some values of these parameters a region of increased fluctuations should be observed. At the top of this “shark fin” hill the value of the critical fluctuations is expected to be a maximum. However, the critical signal could be shadowed since results on fluctuations are sensitive to conservation laws, resonance decays, volume fluctuations in the system of the colliding nuclei, quantum statistical effects and the limited acceptance of the experiment. Hence one should try to reduce the contribution from trivial fluctuations. This led to the idea to use intensive and strongly intensive quantities as probes of the critical behaviour [8], [9].

#### 2. Quantities of interest

In order to make proper comparison of the results from different colliding systems, one should choose so-called intensive variables which are independent of the system size. Since in the vicinity of a critical point central second moments of distributions of extensive event quantity

Due to the imperfect centrality determination in A+A collisions, one should expect event-by-event volume fluctuations. Consequently, to eliminate the influence of usually poorly known distributions of the system volume, it was suggested to use strongly intensive quantities which are independent both of the volume and fluctuations of the volume within the statistical model of the ideal Boltzmann gas in the grand canonical ensemble formulation [9], [11]. Two families of strongly intensive variables

The normalization of these variables can be chosen such that [11]:

#### 3. Analysis details

The main goal of this work is to extend the investigation of the phase diagram by measuring the pseudorapidity dependence of fluctuations. Analysis of proton-proton collisions is the baseline for future investigations of nucleus-nucleus collisions.

This paper presents results referring to all charged hadrons with

The analysis has two parts. In the one window analysis the intensive quantity

#### The one window analysis

Here

and strongly intensive quantities [8]:

with normalization [11]:

#### The two windows analysis

Taking the extensive event quantities

(6)

#### Definitions of pseudorapidity intervals

All results are presented as functions of

#### 4. Results

The presented preliminary results refer to all charged hadrons with

The studied fluctuation measures significantly depend on the width and the location of the pseudorapidity intervals. Results for