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non - linearity and resolutions degradation in energy reconstruction of hadrons by calorimeters result from non - compensation effects compounded by unmeasured energy deposited in non - instrumented ( dead ) material .
calibration techniques are used to recover linearity and improve resolution .    in the year 2004
the atlas collaboration carried out a test - beam where a full central  ) . ] slice of the atlas detector was exposed to beams of electrons and pions a large energy range .
one of the main purposes of this combined test - beam was to test the atlas strategy to use a calibration based on simulation to reconstruct the correct energy of pions .
the general long - term atlas strategy to use simulation to calibrate the detector response to hadrons is shown in  @xcite , while the quality of the simulation for the combined test beam data is discussed in  @xcite .
the result of these two inputs is shown in the present report .
the experimental setup and the real and simulated data samples are briefly illustrated in sections  [ sec : expset ] and  [ sec : dataandsim ] .
the pion calibration techniques are illustrated in section  [ sec : calibtech ] .
the performance on simulation and data is discussed in terms of linearity and resolution in section  [ sec : perf ] .
the 2004 atlas combined test beam is shown in the sketch of figure  [ fig : ctb04setup ] .
it was composed of a full central slice of the atlas detector extending for about three units in pseudo - rapidity  ) is defined at @xmath0 = -log(tan(@xmath1/2 ) ) where @xmath1 is the polar angle in the detector , shown in fig  [ fig : ctb04setup].[foot : pseudo ] ] and for 0.3 radians the azimuthal direction , @xmath2 , around the beam axis .
the central semiconductor pixel and strip detectors were housed in a bending magnet and followed by the straw - tube transition radiation tracker .
the atlas central sampling calorimeters followed : one barrel module of the liquid argon - lead electromagnetic calorimeter ( lar ) with accordion shape was housed in its cryostat and put in front of three hadronic iron - scintillator modules ( tile ) stacked in the azimuthal direction , orthogonally to the incoming test beam axis .     the experimental layout for the 2004 atlas combined test beam .
see text for details . ]
the setup was exposed to beams of particles ( pions , protons , electrons and muons ) in the energy range 1 to 350 gev . at @xmath0 = 0.45 the material in front of the calorimeters
is estimated to consist of 0.44 @xmath3   and the calorimetry stretches for about 9.5 @xmath3 : 1.3 @xmath3 for lar and 8.2 @xmath3 for tile .
the lar cryostat accounts for additional 0.6 @xmath3 in between the lar and the tile .
the data consists of samples of events in which positive pions impinge on the experimental setup at @xmath2 = 0 and @xmath0 = 0.45 .
they are summarized in table  [ table : data ] .
llll positive pion data samples & & & + selected events & energy ( gev ) & proton contam .
( % ) + 8000 & 20 & 0 + 15000 & 50 & 41 + 7000 & 100 & 59 + 5000 & 180 & 75 +    the pion beams are generated from proton primary beams extracted from the cern sps accelerator : the resulting proton contamination is measured by estimating the fraction of proton events that are necessary to reproduce the observed probability of generating a high energy hit in the transition radiation detector . the pion selection is documented in  @xcite . the proton contamination required simulation of samples of pions and protons in the range 15 to 230 gev with geant 4.7  @xcite using the qgsp_bert physics  @xcite list and a consistent description of the test - beam set - up .
the 4 million events simulated were split in two statistically independent sets of samples , the first one used for deriving simulation corrections and the second for testing the expected performance .
an incoming pion in the atlas detector causes a shower that is sampled by the seven calorimeter layers of the combined electromagnetic and hadronic sections .
any hadronic calibration scheme has to recover the intrinsic losses due to the invisible energy lost in nuclear interactions .
additional imperfections in the reconstruction also need to be accounted for : corrections are required for the imperfect energy collection of the clustering algorithm ( out - of cluster ) and incomplete shower containment ( leakage of neutrons , muons and neutrinos ) .
finally corrections for energy deposits in non - instrumented material have an important role .
in particular , in the atlas central region ( barrel ) a non - negligible amount of dead material is present between the electromagnetic and hadronic compartments i.e. in the midst of the longitudinal development of most hadronic showers .
two calibration techniques are considered .
the default atlas local hadronic calibration ( lh in the following ) is described in detail in  @xcite . a novel technique ( described in section  [ sec : calibtech ] ) is also considered : it is based on the use of correlations between the signals at the layer level , summing the clustered energy in each calorimeter longitudinal segment .
it is called layer correlation calibration ( lc in the following ) .
the ansatz is that hadronic and electromagnetic energy deposits have different fluctuations properties and , consequently , variables that are sensitive to fluctuations in the total energy can be used both to derive all the corrections and improve the resolution of the total energy measurement .
the two techniques result in different outputs : lh produces calibrated clusters that will be used to form calibrated jets . on the other hand lc
provides calibrated layer energies : such scheme is technically extendible to jets , but it will be aimed at calibrating the given jet energy depositions in a layer .
performance is assessed in terms of linearity and relative resolution .
the total energy is fitted with a gaussian in the [ @xmath4- 2@xmath5 , @xmath4 + 2@xmath5 ] interval where @xmath4 is the mean of the initial energy distribution and @xmath5 is its standard deviation .
linearity is defined as the ratio of the expected fitted average to the beam energy as a function of the beam energy .
relative resolution is defined as the ratio of the fitted standard deviation to the fitted average as a function of the beam energy .
linearity obtained with lh from simulated positive pion events is shown in the upper plot of figure  [ fig : linhadcal ] . at the electromagnetic scale the typical linearity shape for non - compensating calorimeters is observed : about 75% of the beam energy is measured and the linearity ratio increases with beam energy due to the increasing electromagnetic fraction of the shower .
the compensation weights recover about 10% of the total beam energy . the small out - of - cluster corrections account for about 1% of the beam energy .
the remaining 10% is recovered by adding the dead material corrections .
linearity is finally recovered within 2% for beam energy larger than 20 gev .
lh scheme : linearity ( upper plot ) and relative resolution ( lower plot ) for simulated positive pion events impinging on the test - beam setup at @xmath0 = 0.45 .
the various stages of correction are shown ( see text for details).,title="fig : " ] lh scheme : linearity ( upper plot ) and relative resolution ( lower plot ) for simulated positive pion events impinging on the test - beam setup at @xmath0 = 0.45 .
the various stages of correction are shown ( see text for details).,title="fig : " ]    the relative resolution is shown in the lower plot of figure  [ fig : linhadcal ] .
dead material effects are expected to play a dominant role .
the improvement in relative resolution deriving from suppressing the various fluctuations is expected to reach 11% to 40% .
the lc technique defines the total pion energy as the sum of clustered energy for each calorimeter layer .
the event - by - event layer energy corrections are defined as a function of a specific pair of linear combinations of layer energies .
such combinations are the components of the seven - dimensional vector of layer energies along the vector space basis derived by a principal component analysis ( pca )  @xcite : the two components are used along the basis vectors whose associated pca variance gives the largest contributions to the fluctuations of the total energy .
intuitively , the corrections depend on the `` directions of largest independent fluctuations '' , @xmath7 , where @xmath8 is an integer from one to seven .
both the weights aimed at compensating the invisible energy and the corrections aimed at recovering dead material losses are derived as two dimensional look - up tables ( seven for the layer energies , one for the dead material correction ) . for both types of tables , @xmath9 ,
the linear combination of layer energies with the largest contributions to the total energy fluctuation is one of the two dimension .
@xmath10 , the linear combination with the second largest contributions to the total energy fluctuation , is the second variable for the calculation of the compensation weights .
the weight for a given layer energy in a given bin of the two dimensional table is defined as the average @xmath11 over all the events in the bin  .
an example of the weight table for the first tile layer is shown in figure  [ fig : tileweight ] .
the separation between the high weight region , dominated by invisible energy , and the low - weight region , dominated by visible energy , is evident .
lc scheme : two dimensional look - up table of compensation weights for the first layer of the tile hadronic calorimeter ( see details in the text ) .
pions and protons samples are mixed to achieve a 41% proton contamination . ]    for the dead material correction , the second dimension is represented by , @xmath12,the layer energy combination with the third largest contribution to the total energy fluctuations  .
the look - up table is shown in figure  [ fig : dmtot ] where the high dead material correction region is well separated form the rest . the correction is derived as a function of the normalized linear combinations mentioned above ( each combination is divided by the best estimate of the total energy ) and it is expressed as a fraction of the total energy itself .
lc scheme : two dimensional look - up table of corrections for energy loss in dead material ( as a fraction of total energy ) between tilecal and lar electromagnetic calorimeter ( see details in the text ) .
pions and prootn samples are mixed to achieve a 41% proton contamination . ]
a small correction for the leakage , dead material energy losses upstream of the calorimeters and in between the first ( presampler ) and second ( `` strips '' ) lar layers is calculated by a parametrization obtained from simulation as a function of the total energy estimate @xmath13  ] .
an iterative procedure is then applied : a given total energy estimate provides a new dead material correction which can in turn be used to determine the total energy .
a few iterations are required to obtain a stable result .
all look - up tables are filled by the full set of simulated samples from 15 to 230 gev so as to reduce the beam energy dependence of the correction as much as possible .      in the case of the lc scheme a mix of pions and protons
was used to derive the corrections and to simulate the data .
the contamination values are those from table  [ table : data ] .
the upper plot of figure  [ fig : lclinres ] shows the linearity obtained for both data and simulation : the agreement is within 2% at all stages of calibration .
the resulting picture is similar to that outlined in section  [ sec : hcalexpperf ] for the lh scheme .
the reconstruction at the electromagnetic scale is accounting for 75% of the beam energy .
the compensation weights recover about 12% of the beam energy while the dead material correction accounts for about 10% .
the dead material correction for losses between tile and lar represents about 80% of the total dead material corrections .
the lc method recovers linearity within 3% over the whole energy range .
the relative resolution is shown the lower plot of figure  [ fig : lclinres ] .
the simulation foresees a relative improvement of 17 to 24% : the data behave consistently showing an improvement of 17 to 21% .
even though the relative behaviour is the same , the simulation underestimates the resolution in the data by about 25% .
geant4.9  @xcite is expected to improve the data description .
figure  [ fig : lcvslhlin ] shows the comparison for the resulting linearity when applying both calibration techniques to the same data set   the result is quite consistent : the linearity is recovered within 2 to 5% by both techniques .
lc scheme : linearity ( upper plot ) and relative resolution ( lower plot ) for positive pion events impinging on the test - beam setup at @xmath0 = 0.45 at the various stages of correction ( see text for details ) .
data are shown in filled symbols , simulated events are represented by horizontal lines.,title="fig : " ] lc scheme : linearity ( upper plot ) and relative resolution ( lower plot ) for positive pion events impinging on the test - beam setup at @xmath0 = 0.45 at the various stages of correction ( see text for details ) .
data are shown in filled symbols , simulated events are represented by horizontal lines.,title="fig : " ]     comparison of linearity for the lh and lc schemes . only the electromagnetic scale and the fully corrected scale
are shown . ]
a simulation - based cell - weighting technique for hadronic signal calibration was applied to pion energy reconstruction in 2004 atlas combined test beam for beam energy in the range 20 to 180 gev . a novel technique based on the correlation amongst layer energies
was also used .
the linearity of response to charged pions is recovered within 2 to 5% by both approaches in good agreement between data and simulation ; compensation weights and dead material effects have similar impact . according to simulation
, the relative energy resolution is expected to improve ( by 20 - 30% to 40% ) .
lc actually achieves an improvement of 17 to 21% .
simulation underestimates data resolution by 10 to 25% ; dead material effects are dominant .
data - simulation discrepancies at the electromagnetic scale keep their size at all stages of calibration , thus simulation performance is the limiting factor .    the essential collaboration of tancredi carli , karl - johan grahn and peter speckmayer is gratefully acknowledged .
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pion energy reconstruction is studied using the data collected during the 2004 atlas combined test beam . the strategy to extract corrections for the non - compensating nature of the atlas calorimeters for dead material losses and for leakage effects 
 is discussed and assessed . the default atlas strategy based on a weighting technique of the energy deposits in calorimeter cells 
 is presented and compared to a novel technique exploiting correlations among energy deposited in calorimeter layers .