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in hadron - hadron collisions , production rates of collimated sprays of hadrons , called jets , are sensitive to both the dynamics of the fundamental interaction and to the partonic structure of the initial - state hadrons .
the latter is usually parameterized in parton distribution functions ( pdfs ) of the hadrons .
thus measurements of jet production properties can be used to test the predictions of quantum chromodynamics ( qcd ) as well as to constrain the pdfs .
because jet production has the largest cross - section of any high @xmath1 process at a hadron collider , the study of jet production provides the highest energy reach for the experiment and a unique sensitivity to new physics .
several jet measurements are now well established at the tevatron , including the measurement of the inclusive jet cross section and of the angular and invariant mass dependencies of dijet events  @xcite .
these measurements provide important tests of perturbative qcd ( pqcd ) and are input to pdf calculations .
measurements of multi - jet production take advantage of the fact that these processes have the same pdf sensitivity as dijet production , but are sensitive to processes to third order in the strong coupling constant @xmath2 .
fundamental to the understanding of order @xmath3 processes is the three - jet cross - section , which we present as a function of the invariant mass of the three - jet system .
studies dedicated to the dynamics of the interaction are preferably based on observables which are insensitive to the pdfs .
such observables can be constructed as ratios of cross sections for which the pdf sensitivity cancels . in this note
we report a measurement of @xmath4 , the ratio of the inclusive three - jet to the inclusive 2-jet cross - sections .    in this note
we present several recent results for the production of multijet final states in @xmath5 collisions at a center of mass energy of 1.96  tev .
these measurements , which include the cross - section for dijet and three - jet production and the ratio of three - jet to two - jet cross sections , where taken with the d  experiment  @xcite at the fermilab tevatron collider .
the data analyzed were recorded using a single jet triggers at a variety of thresholds , corresponding to an integrated luminosity of 0.7  fb@xmath6 . the event selection , jet reconstruction , jet energy and momentum correction in this measurement follow closely those used in our recent measurements of inclusive jet and dijet distributions  @xcite .
the primary tool for jet detection is the finely segmented uranium - liquid argon calorimeter that has almost complete solid angle coverage @xmath7  @xcite .
jets are defined by the run  ii midpoint cone jet algorithm  @xcite with a cone radius ( for most jet studies ) of @xmath8 in rapidity @xmath9 and azimuthal angle @xmath10 .
rapidity is related to the polar scattering angle @xmath11 with respect to the beam axis by @xmath12 $ ] with @xmath13 .
the jets in an event are ordered in descending transverse momentum @xmath1 with respect to the beam axis .    for all jet studies , a jet energy scale ( jes ) correction
is applied to jet four momentum as the measured four momentum of a jet is not the same as that of a jet entering the calorimeter due to the response of the calorimeter ; energy showering in and out of the cone ; and additional energy from detector noise , event pile - up and multiple @xmath5 interactions .
the jes correction is determined using the @xmath1 imbalance in @xmath14 jet and dijet events . the additional energy from pile - up and multiple interaction
is determined from a minimum bias sample .
the jes corrections are of the order of 50% for a jet energy of 50 gev and 20% for a jet energy of 400 gev . however , for the 0.7 pb@xmath6 data sample used for the measurements presented in this talk , collected with the d  detector during 20042005 in run  ii of the fermilab tevatron collider , the uncertainty on the jes is very small , less than 2% over jet @xmath1 s from 60 to 300 gev .     the fractional uncertainty from the jet energy scale ( jes ) for jets of cone size @xmath15 and central pseudorapidity . ]    for the sake of brevity , the reader is directed to reference  @xcite for a discussion of the inclusive jet cross section measurement , and reference  @xcite for the details on the extraction of the strong coupling constant from the inclusive jet cross section .
of the variables that fully specify the kinematics of dijet production in hadron collisions , the dijet invariant mass @xmath16 and rapidity difference @xmath17 ( or equivalently @xmath18 ) probe the features of lo @xmath19 processes , while measurements of the azimuthal opening angle @xmath20 and ratio of transverse momenta @xmath21 can be used to determine the effect of higher - order processes .
the dijet invariant mass cross section is particularly sensitive to the gluon contribution to pdfs at high @xmath22 .
in addition , the dijet mass spectrum can be used to search for evidence of quark compositeness or new strongly produced resonances .
d  has measured the dijet cross section as a function of the dijet invariant mass @xmath16@xcite .
this cross section is measured in six regions of @xmath23 , the rapidity of the leading jet in the event .
figure  [ fig : dijetmassspectra ] shows the resulting measurements , while figure  [ fig : dijetmassspectra ] shows the measured cross section divided by the nlo prediction from the nlojet++  @xcite program and using the mstw2008nlo pdfs  @xcite .
this measurement in an important extension of pqcd to the forward region , and includes measurements of dijet invariant masses up to 1.2  tev .
dijet mass cross sections , shown for six regions of @xmath24 .
( note that these regions scaled for plotting , wtih the exception of @xmath25 . )
full lines correspond to the nlo calculations with nlojet++ and mstw2008 pdfs . ]
dijet mass cross section divided by nlo prediction , with total systematic uncertainties indicated by the shaded bands.the dataset corresponds to an integrated luminosity of 0.7 fb@xmath26 . ]
d  has measured  @xcite the differential inclusive three - jet cross section as a function of the invariant three - jet mass for three hard , well separated jets in three regions of jet rapidities ( @xmath27 , @xmath28 , @xmath29  for all three jets ) and in three regions of the third jet transverse momentum ( @xmath30  gev , @xmath31  gev and @xmath32  gev ) with leading jet @xmath33  gev .
the three - jet mass spectra are shown in fig .
[ fig : m3jvsy ] .
this represents the first fully corrected 3-jet mass distribution to be published , and the first comparison of such a cross - section to nlo pqcd calcuations .
a ) three - jet mass cross section in regions of jet rapidities .
the @xmath29 region is scaled by a factor of 4 for readability .
systematic uncertainty is shown by shaded band .
full lines correspond to the nlo calculations with nlojet++ and mstw2008 pdfs .
no events are found in the highest @xmath34 bin in @xmath27 region .
b ) three - jet mass cross section in regions of the third jet transverse momenta .
the @xmath30  gev region is scaled by a factor of 2 for readability .
systematic uncertainty in all three - jet mass bins is shown by shaded band .
full lines correspond to the nlo calculations with nlojet++ and mstw2008 pdfs . in both figures
, the dataset corresponds to an integrated luminosity of 0.7 fb@xmath26 . ]
the data are compared to the perturbative qcd nlo predictions calculated in nlojet++@xcite program with mstw2008nlo@xcite pdfs .
the nlo prediction is corrected for hadronization and underlying event effects , with correction varied in the range from -3% to 6% , obtained from pythia@xcite simulations using tune qw@xcite .
the comparison of data to theory is shown in fig .
[ fig : m3jdthvsy ] and  [ fig : m3jdthvspt3 ] .
data to theory ratio of the three - jet mass cross section in three regions of jet rapidities.the total systematic uncertainty is shown by a shaded band .
the pdf uncertainty comes from the 20 mstw2008nlo eigenvectors .
the scale uncertainty is determined by varying the scale up and down by a factor of 2 . ]
data to theory ratio of the three - jet cross section in three regions of the third jet transverse momentum .
the total systematic uncertainty is shown by a shaded band .
the pdf uncertainty comes from the 20 mstw2008nlo eigenvectors .
the scale uncertainty is determined by varying the scale up and down by a factor of 2 . ]
the ratio of inclusive jet cross sections , @xmath35 , is less sensitive to experimental and theoretical uncertainties than the individual cross sections , due to cancelations of correlated uncertainties . here
@xmath4 is measured as a function of the leading jet @xmath1 in an event , @xmath36 , in the interval @xmath37 , for @xmath38 requirements of 50 , 70 , and 90 gev .
the results are displayed in fig .
[ fig : result ] , where the inner error bars represent the statistical uncertainties while the total error bars represent the quadratic sums of statistical and systematic uncertainties .
the data are compared to the predictions from different monte carlo event generators .
the sherpa v1.1.3 predictions  @xcite , which include the tree - level matrix elements for 2- , 3- , and 4-jet production , are shown as solid lines in figs .
[ fig : result ] .
these were obtained using default settings and mstw2008lo pdfs and by matching the leading order matrix elements for 2- , 3- , and 4-jet production with a parton shower .
in addition , the data are compared to predictions from the pythia event generator ( version 6.422 ) .
the matrix elements implemented in pythia are only those for 2-jet production .
all additional jet emissions are produced by a parton shower .
there are two different implementations , a virtuality - ordered parton shower and a @xmath1-ordered one .
both are highly tunable and more than 50 tunes are provided in pythia v6.422 .
all tunes studies here use the cteq5l pdfs  @xcite .    in fig .
[ fig : result ] the data are compared to pythia tunes which use the @xmath1-ordered parton shower  @xcite .
these are tune `` professor pt0 ''  @xcite and two extreme tunes from the `` perugia '' series of tunes  @xcite , the tunes `` perugia hard '' and `` perugia soft '' .
all of these tunes give very different results for @xmath4 but all predict significantly higher ratios @xmath4 than what is seen in the data , even for the softest tune from the perugia series .    the ratio @xmath4 of trijet and dijet cross sections , measured as a function of the leading jet @xmath1 ( @xmath36 ) for different @xmath38 requirements for the other jets .
the predictions of sherpa and pythia ( for tunes a , bw , and dw ( top ) ; and for three tunes using the @xmath1-ordered parton shower ( bottom ) ) are compared to the data.,title="fig : " ] the ratio @xmath4 of trijet and dijet cross sections , measured as a function of the leading jet @xmath1 ( @xmath36 ) for different @xmath38 requirements for the other jets .
the predictions of sherpa and pythia ( for tunes a , bw , and dw ( top ) ; and for three tunes using the @xmath1-ordered parton shower ( bottom ) ) are compared to the data.,title="fig : " ]    the data are compared to the perturbative qcd nlo predictions calculated in nlojet++@xcite program with mstw2008nlo@xcite pdfs . the nlo prediction is corrected for hadronization and underlying event effects , with correction varied in the range from -3% to 6% , obtained from pythia@xcite simulations using tune qw@xcite .
the comparison of data to theory is shown in fig .
[ fig : result2 ] .     the ratio @xmath4 of trijet and dijet cross sections , measured as a function of the leading jet @xmath1 ( @xmath36 ) for different @xmath38 requirements for the other jets .
the predictions of next - to - leading order pqcd , calculated with nlojet++ , are compared to the data . ]
the d  experiment at the fermilab tevatron collider has been enormously successful , and continues to produce important physics measurements , including tests of the standard model and searches for new phenomena .
only a small portion of the qcd - related analyzes we have pursued could be shown in this talk .
the reader is urged to check http://www-d0.fnal.gov/results/index.html for the latest results .
my thanks to my collaborators on the d  experiment , particularly the current and past qcd physics group coordinators mike strauss , sabine lammers , dmitry bandurin and markus wobisch .
all credit for these results goes to this remarkable collaboration , while any errors in the reporting of these results are the author s own .
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in this note we present several recent results for the production of multijet final states in @xmath0 collisions at a center of mass energy of 1.96  tev . 
 these measurements , which include the cross - section for dijet and three - jet production and the ratio of three - jet to two - jet cross sections , were taken with the d  experiment at the fermilab tevatron collider .