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transport coefficients such as shear viscosity represent fundamental properties of a system and contain direct information about the underlying physics . for
qcd matter in the temperature range probed by an ultra - relativistic heavy - ion collision , such quantities are exceptionally difficult to calculate from first principles . on the other hand , observables in these experiments
can be quite sensitive to transport coefficients , potentially allowing for a measurement to be extracted from data  @xcite .
thus , such a precision extraction is a topic of significant interest . in the past
, a precision extraction has been hampered by significant theoretical uncertainty , especially that arising from poor knowledge of particle production and thermalization in the earliest stages .
a number of viscous hydrodynamic calculations have been performed , which have been quite successful at reproducing flow measurements  @xcite .
typically , a small value of viscosity is required in order to fit data  not too much more than a few times the conjectured lower bound @xmath2 .
however , the precise best - fit value depends on various aspects of the calculations that are not fully constrained , and this introduces uncertainty in any extraction from data .
although these uncertainties have been the target of significant investigation , it has so far been done in a piecemeal fashion  @xcite .
no one has yet attempted to compile this information in a systematic study of all sources of uncertainty in order to place a robust and reliable upper bound on @xmath0 .
in addition , the conjectured bound is now known not to be universal , so it is of great interest to determine if one can place a lower bound on the quantity .
currently , there is no convincing evidence that measured data can not be reproduced with ideal hydrodynamics , and in fact most flow data can be reproduced quite well in such calculations  @xcite . in these proceedings
we present a proposal for how to extract @xmath0 with the smallest uncertainty currently possible , as well as preliminary results on such an extraction including a quantitative error bar obtained by systematic study of all known sources of uncertainty .
, mc - kln  @xcite v3.43 and its glauber implementation [ glauber ( discs ) ] , mckt - v1.25 with negative binomial fluctuations  @xcite ( mcrcbk ( nb ) ) , dipsy  @xcite , and urqmd  @xcite . ]    in a standard picture of a heavy - ion collision , the asymmetric region of overlap in a collision between two nuclei results in a anisotropy in the transverse density of the system at early times . over time
, this spatial anisotropy is transformed into a momentum anisotropy by a collective response that is well described by ( viscous ) hydrodynamics .
in fact , the elliptic flow coefficient @xmath3 is ( to a good approximation ) directly proportional to this initial eccentricity in a given collision event : @xmath4 .
the proportionality constant depends sensitively on the viscosity of the medium , however , poor knowledge of the earliest stages of the collision result in significant uncertainty in @xmath5 see , for example , the top left panel of fig .
[ ecc ] , which shows root - mean - square values of @xmath5 from a number of commonly - used models for initial conditions measurements are sensitive to the rms value of the event - by - event distribution of @xmath6 .
the resulting uncertainty in @xmath3 has been the largest source of uncertainty when determining @xmath0 from data  @xcite .
though there has been much recent study concerning the physics of the early stages of a collision  @xcite , it is not yet possible to make a reliable statement about what range of values of initial eccentricity are within the realm of possibility .
it is now known that quantum fluctuations are also a significant source of anisotropy in the initial state , and therefore anisotropic flow .
this is especially apparent from the presence of large odd harmonics , such as triangular flow @xmath7 , which is generated from a spatial `` triangularity '' , defined similarly to the eccentricity @xmath8 this would be zero at midrapidity in the absence of event - by - event fluctuations .
the triangularity that one sees in a calculation is largely determined by the strength of these fluctuations .
in contrast , the differences in particle production mechanisms that lead to very different @xmath5 in non - central collisions has very little effect on @xmath9 .
compare , for example , the triangularities of the mc - kln model versus glauber ( discs ) in fig .
[ ecc ] , which contain only fluctuations from random position of nucleons in the colliding nuclei , implemented in exactly the same way in the mc - kln code .
the triangularity @xmath9 is very similar , despite the fact that the two pictures of particle production result in a very different eccentricity @xmath5 .    by comparing the results from other models ,
it is clear that there still remains some uncertainty due to different way fluctuations are implemented . despite the seemingly modest reduction in uncertainty ( as compared to the uncertainty in @xmath5 ) , one can reasonably argue that the results in the second panel of fig .
[ ecc ] represent the full range of results that can be expected , in marked contrast to the results in the first panel .
the models with the lowest triangularity are known to be missing important sources of fluctuations , while the large fluctuations in the models with the largest @xmath9 can not be reconciled with constraints from @xmath10 measurements  @xcite .
one might thus propose to extract @xmath0 from measurements of @xmath7 to minimize uncertainty from the initial conditions .
however , we can make use of more experimental constraints by noting that in the most central collisions , all harmonics are generated entirely from fluctuations , and the above discussion still applies .
one further convenient factor is that , for ultra - central collisions , the approximate proportionality @xmath11 holds for all @xmath12  @xcite .
this allows for a comprehensive parameter study with reasonable computing resources .
thus , our proposal is to extract @xmath0 from a simultaneous fit to @xmath1-integrated @xmath13 measurements from ultra - central collisions at the highest - energy heavy - ion collisions .
these data are least sensitive to uncertain aspects of theory , and therefore allow for the the most precise extraction of @xmath0 with the smallest possible uncertainty .
such data are available from the atlas collaboration for @xmath3@xmath14 in the 1% of most central collisions  @xcite .     for n = 26 at 01% centrality , as a function of the ratio of shear viscosity to entropy density @xmath0 .
right : fit values corresponding to the minimum chi - squared curves in the left plot .
the green bars represent measured values from the atlas collaboration  @xcite ; the vertical thickness represents the combined statistical and systematic error .
models with large fluctuations and a correspondingly large best - fit @xmath0 tend to have a steeper slope than models with smaller eccentricities .
the range of best - fit viscosity values for the curves in the left plot gives an indication of the uncertainty in an extraction of @xmath0 due to the uncertain initial anisotropy in the initial state ( @xmath15 0.05 ) .
, title="fig : " ]   for n = 26 at 01% centrality , as a function of the ratio of shear viscosity to entropy density @xmath0 .
right : fit values corresponding to the minimum chi - squared curves in the left plot .
the green bars represent measured values from the atlas collaboration  @xcite ; the vertical thickness represents the combined statistical and systematic error .
models with large fluctuations and a correspondingly large best - fit @xmath0 tend to have a steeper slope than models with smaller eccentricities .
the range of best - fit viscosity values for the curves in the left plot gives an indication of the uncertainty in an extraction of @xmath0 due to the uncertain initial anisotropy in the initial state ( @xmath15 0.05 ) .
, title="fig : " ]
in a theoretical calculation , the viscosity of the medium can be taken to be a free parameter . with all other parameters fixed ,
one can calculate @xmath13 as a function of @xmath0 , and perform a least - squares fit to find the preferred value . if a particular parameter is uncertain , one can vary that parameter within the allowed range and redo the fit .
the shift of best - fit @xmath0 indicates the size of the resulting error bar in @xmath0 due to this particular source of uncertainty .
if one then varies all possible aspects of the theory in all possible combinations , the smallest and the largest extracted values thus represent a robust , if conservative , upper and lower error bar for the quantity .
this is the idea behind the preliminary results shown at this conference .
details will be given in a forthcoming publication , but an example fit for a calculation using a single set of hydrodynamic parameters but different initial conditions is shown in fig .
it is notable that hydrodynamics can , in fact , simultaneously give a good description of all @xmath13 .
however , it is also interesting to note the tendency for tension in the relative values of @xmath3 and @xmath7 for all initial conditions tested .
we reported a preliminary result of @xmath16 , but a few comments are in order .
first , the calculations used a constant value of @xmath0 during the hydrodynamic evolution .
therefore , the result is an average value that corresponds to the viscosity at the typical time when flow is built up .
the lower bound indicates that purely ideal hydrodynamic calculations can not describe these data .
this is a significant result .
however , it is technically possible that the viscosity could dip below our lower bound at some point during the evolution , so this result does _ not _ represent a lower bound for the viscosity of qcd over its entire temperature range .
second , since it has never before been done , we want to be confident at every stage that we have a robust and reliable error bar .
the preliminary result , therefore , is fairly conservative , and the error bar will likely be smaller in the final result after further study .
we argue that at the current time , the most precise value for the shear viscosity to entropy density ratio @xmath0 of the quark - gluon plasma can be obtained by a fit to @xmath1-integrated @xmath13 measurements in ultra - central collisions .
we further report preliminary results such an extraction , including an error bar from a systematic study of all known sources of uncertainty .
we thank the phobos collaboration , adrian dumitru , yasushi nara , and christoffer flensburg for providing their code to the public , which allowed us to calculate the eccentricities in various montre - carlo models , and hannah petersen for calculating them for us using urqmd .    00 b.  h.  alver , c.  gombeaud , m.  luzum and j.  y.  ollitrault , phys .
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we propose a method for extracting the shear viscosity over entropy density ratio ( @xmath0 ) of the quark - gluon plasma from experimental data . 
 we argue that uncertainty due to poor knowledge of the earliest stages of a heavy - ion collision is smallest for ultra - central events . 
 the most precise value of @xmath0 can thus be obtained from a global fit to @xmath1-integrated fourier harmonics of azimuthal correlations . 
 we further outline a method for quantifying the overall uncertainty in the extracted value . only after a comprehensive and systematic accounting of all sources of uncertainty can a reliable measurement be claimed . in these proceedings 
 we report preliminary results ; full and final results will be presented in a separate publication .