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over the past several months , many results on event - by - event fluctuation and correlation observables have been made available by experiments at the sps and at rhic .
this article will review the most recent results on three of these observables : net charge fluctuations , balance functions in pseudorapidity , and average transverse momentum fluctuations .
each of these observables is designed to probe a specific property of the system : net charge fluctuations are sensitive to the charge distribution within the collision volume , balance functions are sensitive to the hadronization time of the system , and average @xmath0 fluctuations are sensitive to critical fluctuations of the temperature of the system which may be present during a phase transition from hadronic matter to a quark - gluon plasma ( qgp ) . however , as with any measurement , the results can be contaminated by known processes such as charge conservation , resonance decays , elliptic flow , or even hard scattering processes .
therefore , the contribution of any known processes must be thoroughly examined prior to formulating a reliable interpretation of the results .
detailed background information on the theory behind various event - by - event observables can be found in other recent reviews @xcite .
a promising signature for the presence of a qgp is the observation of event - by - event fluctuations in the net charge of produced particles .
it is hypothesized that fluctuations in the net charge would be significantly reduced in a qgp scenario .
this is due to the fact that in a qgp , the fractional electric charges of the quarks are more evenly spread throughout the qgp volume than the unit electric charges of the hadrons in a hadronic gas volume . as a result
, the fluctuations of the net charge in a given region of phase - space would be significantly reduced in a qgp @xcite .
there has been much debate on the choice of the most appropriate observable to quote for the magnitude of net charge fluctuations .
a standard is yet to be agreed upon in the literature , so phenix @xcite quotes the normalized net charge variance , @xmath1 , star @xcite quotes a measure for dynamical fluctuations , @xmath2 , and na49 @xcite quotes the variable @xmath3 .
the latter will be quoted here .
fortunately , all of the variables listed above can be related to each other with some very reasonable assumptions @xcite .
the baseline for the measurement of net charge fluctuations is that of independent particle emission ( where @xmath1 = 1.0 , @xmath2 = 0.0 , and @xmath4 = 0.0 ) .
predictions for the magnitudes of these three fluctuation variables for a variety of physical scenarios are listed in table 1 .
keep in mind that these values are valid only for small samplings of the total number of produced charged particles since charge conservation can contribute to any observed fluctuations .
net charge fluctuation measurements can be corrected for charge conservation based upon the fraction of the total number of particles in the sample as follows @xcite : @xmath5    @lllll scenario&v(q)&@xmath2 ( star)&@xmath2 ( phenix ) & @xmath4 + independent emission&1.0&0.0&0.0&0.0 + resonance gas&0.75&-0.0013&-0.006&-0.125 + quark coalescence&0.83&-0.0008&-0.004&-0.084 + quark - gluon plasma&0.25&-0.0038&-0.019&-0.375 +    figure 1 compiles the results of net charge fluctuation measurements by na49 in @xmath6 = 17 gev pb+pb collisions @xcite , and by phenix @xcite and star @xcite in @xmath6 = 130 gev au+au collisions , all quoted in terms of the @xmath4 variable .
not included are new results from the ceres experiment @xcite . superimposed on each plot
are curves representing the predictions for independent particle emission , quark coalescence @xcite , a resonance gas @xcite , and a qgp @xcite , after correcting for charge conservation within the acceptance of each detector . at sps energies
, na49 observes fluctuations that are most consistent with the independent particle emission scenario .
the phenix measurement is also consistent with independent particle emission .
however , for a large pseudorapidity window , star reports fluctuations that are most consistent with the prediction of the quark coalescence model .
differences in the phenix and star measurements may be attributed to the reduced sensitivity of the phenix measurement , which may be improved in the analysis of au+au data at @xmath6 = 200 gev .
note that all of the measurements differ dramatically from the expectations for the pure qgp scenario , although it may be premature to rule out the possibility of the existence of a qgp based upon these results until more detailed models are consulted .
= 17 gev pb+pb collisions from na49 @xcite , b ) @xmath6 = 130 gev au+au collisions from phenix @xcite , and c ) @xmath6 = 130 gev au+au collisions from star @xcite .
the curves represent expectations for independent particle emission , a resonance gas , quark coalescence , and a qgp after correction for charge conservation effects .
[ fig:1 ] ]
the balance function analysis method is designed to determine whether hadronization from a system occurs early ( @xmath7 fm / c ) or at a later time @xcite .
the method is based upon the fact that charge is conserved locally due to produced pairs that are initially correlated in coordinate space .
concentrating on balance functions in pseudorapidity , the balance function is defined as : @xmath8\ ] ] here , @xmath9 refers to a histogram of @xmath10 for all possible pairs of the subscripted charge signs within a single event , summed over all events . @xmath11 and @xmath12 are the total number of positive and negative charged particles in the event , respectively .
when examining the pseudorapidity of produced pairs if hadronization occurs at an early time , the pairs have more time to separate in @xmath13 due to a combination of the expansion of the system and rescattering . therefore , if there is a delayed hadronization scenario ( as might be expected in central collisions ) , the analysis would yield a narrower balance function than the early hadronization scenario ( as might be expected in more peripheral collisions ) .
balance functions in pseudorapidity have been measured by star @xcite and na49 @xcite .
the behavior of the balance functions are studied as a function of centrality by plotting the widths of the balance functions in pseudorapidity ( @xmath14 ) obtained from a gaussian fit or from a weighted mean in @xmath15 .
a reduction of the magnitude of @xmath16 for small @xmath15 is observed due to the hbt effect , but it has little effect on the extracted widths .
figure 2 compares the balance function widths as a function of centrality at both sps and rhic energies . in both cases
, there is a significant narrowing of the balance function observed for more central collisions .
star has shown that the widths in the most central collisions can be reproduced by a thermal model , but only if an unrealistically high value of the transverse flow velocity , @xmath17 is used with a low temperature of 105 mev @xcite . taking the interpretation at face value ,
this behavior is indicative of a late hadronization scenario .
however , contributions from other known sources must first be considered when interpreting the results .
an obvious contributor to the width of balance functions are neutral resonance decays , which will register in the balance function as produced particle pairs that occur at a late time , serving to broaden the function .
the magnitude of resonance decay contributions using a thermal model baseline with @xmath18 0.5c has been investigated by p. bozek et al . @xcite .
the results of the calculation can reproduce widths as a function of centrality that are consistent with the star data .
the behavior of balance functions as a function of centrality has also been investigated in the context of the quark coalescence model @xcite .
this model can also reproduce the centrality - dependence and magnitude of the widths of the star data with @xmath18 0.5c , but without the inclusion of resonance decay contributions .    ) as a function of centrality for a ) @xmath6 = 17 gev pb+pb collisions from na49 @xcite , and b ) @xmath6 = 200 gev au+au collisions from star @xcite . in both cases ,
the balance functions are narrower for more central collisions .
[ fig:2 ] ]
event - by - event fluctuations in the average transverse momentum may be sensitive to temperature fluctuations near the qcd tri - critical point @xcite .
there have been many recent results from the sps ( na49 @xcite and ceres @xcite ) and rhic ( phenix @xcite and star @xcite ) experiments .
all experiments report a positive signal of non - random fluctuations , each with an apparent maximum in mid - peripheral collisions , as shown in figure 3 . as with the charge fluctuation measurements ,
a standard observable has not been agreed upon in the literature , and each experiment quotes a different variable to describe the magnitude of the fluctuations : @xmath19 , @xmath20 , @xmath21 , and @xmath22 .
fortunately , the variables can all be related with very reasonable assumptions @xcite .
all of the variables measure the difference in the width of the event - by - event average @xmath23 distribution , @xmath24 , from a random expectation , which can be expressed as a gamma distribution that is directly calculable using the inclusive @xmath23 and number of particles per event , n , distributions @xcite .
since a positive signal is observed and confirmed , contributions to the signal from known sources should first be studied .
the various analyses have addressed this with respect to contributions from hbt , resonance decays , and elliptic flow .
the contributions from all of these sources have been found to be very small or negligible , each confirmed by independent analyses .
another possible source to the signal is that from hard scattering processes , which would be expected to produce correlations in @xmath23 with a stronger contribution at higher @xmath23 . in this context ,
both phenix and ceres observe that the majority of the contribution to the non - random fluctuations occur at high @xmath23 .
phenix observes a large 243% increase in the signal when the maximum of the @xmath23 range over which the average @xmath23 is calculated increases from 1.0 to 2.0 gev / c .
this very large increase can not be attributed to number fluctuations since the number of particles increases by less than 15% over that range .    in order to investigate possible contributions due to jet production
, phenix has applied a two - component model consisting of 1 ) a simulation of soft processes by reproducing the inclusive @xmath23 and n distributions as a function of centrality , and 2 ) a simulation of hard scattering processes by embedding pythia jet events at a given rate per produced particle in step 1 ( while strictly conserving the n distribution so as not to introduce unnecessary number fluctuations ) .
the simulation is performed as a function of centrality within the detector acceptance in two modes : a ) with the pythia event embedding rate kept constant for all centralities , and b ) with the pythia event embedding rate scaled by the nuclear modification factor , @xmath25 , for each centrality bin .
the result of the simulation superimposed with the phenix data is shown in the bottom plot of figure 3 .
the simulation with the @xmath25-scaled rate agrees with the centrality - dependent ( and also the @xmath23-dependent @xcite ) data trends remarkably well . within this simulation , the decrease of fluctuations in the most peripheral collisions
is attributed to the fact that the signal begins to compete with the magnitude of the number fluctuations , while most of the decrease of fluctuations in the most central collisions can be attributed to the onset of jet suppression . when the simulation is performed at @xmath6 = 130 gev within the star acceptance with the same pythia event embedding rate that reproduces the phenix data , agreement with the star
more central data is achieved within errors .
the simulation predicts a 15 - 20% increase in the fluctuation signal from star at @xmath6 = 200 gev .
although the jet production cross section is much reduced at sps energies , it is non - zero , and there may also be a residual jet contribution present .
the identical simulation performed at @xmath6 = 17 gev within the na49 acceptance can also reproduce the trend of the na49 data as a function of centrality
.    a promising method in which to directly compare the fluctuation measurements from all four experiments is to estimate the magnitude of any residual event - by - event temperature fluctuations present using the prescription outlined in @xcite .
the most central fluctuation values thus correspond to temperature fluctuations of 1.8% in phenix , 1.7% in star , 1.3% in ceres , and 0.6% in na49 .
the residual temperature fluctuations are small and do not significantly increase between sps and rhic energies .
alternative interpretations of the observed average @xmath23 signal have been presented .
one such interpretation is that the signal may be due to the onset of thermal equilibrium within the system @xcite .
this model is successful in reproducing both the centrality - dependence of the fluctuation signal and the inclusive @xmath26 distributions from star and phenix .
fluctuations as a function of centrality for a ) @xmath6 = 17 gev pb+pb collisions from na49 @xcite , b ) @xmath6 = 130 gev au+au collisions from star @xcite , and c ) @xmath6 = 200 gev au+au collisions from phenix @xcite . the error bars include statistical and systematic errors .
the curves are the results of a model that estimates the relative contribution due to jet production as a function of centrality @xcite for a fixed pythia event embedding rate ( dashed lines ) and for an @xmath25-scaled embedding rate ( solid lines ) .
uncertainties on the simulation are 0.3 mev / c for na49 , 2.1 mev / c for star , and 1.0 mev / c for phenix .
[ fig:3 ] ]
there has been nearly a doubling in the quantity of preliminary or published results on event - by - event fluctuation and correlation observables over the past year .
long thought of as the exclusive domain of large acceptance detectors , the scope of the results are demonstrating that event - by - event physics is accessible to smaller acceptance experiments with only a small sacrifice in sensitivity .
the development of event - by - event analysis techniques is continuing to mature at a rapid pace , including extensions to multi - dimensional correlations and methods to relate fluctuation observables directly to correlation functions .
it is becoming clear from what we have learned so far that these methods can provide additional tools with which to study the underlying dynamics of the collision system .
a great deal of recent data on event - by - event fluctuation and correlation measurements has been released by several experiments at the sps and rhic . 
 recent results on charge fluctuations , balance functions in pseudorapidity , and average transverse momentum fluctuations will be reviewed . 
 the results will be compared to various model predictions after examining contributions to each observable from known physics processes .