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the cdf trigger  @xcite for run ii is a three level system : each stage rejects a sufficient fraction of the events to allow processing at the next stage with acceptable dead time .
the goal of the calorimeter trigger ( both at level 1 and level 2 ) is to trigger on electrons , photons , jets , total transverse energy ( sumet ) as well as missing transverse energy ( met ) . in the following we use a coordinate system defined by the polar angle @xmath0 , measured from the proton direction , the azimuthal angle @xmath1 , measured from the tevatron plane .
the pseudo - rapidity is defined as @xmath2 . for cdf run
ii , all calorimeter tower energy information , including both electromagnetic ( em ) energy and hadronic ( had ) energy , is digitized every @xmath3 ns and the physical towers are summed into trigger towers , weighted by @xmath4 to yield transverse energy .
a trigger tower covers 15 degree in azimuth @xmath1 and approximately 0.2 in pseudo - rapidity @xmath5 .
this results in a representation of the entire detector as a @xmath6 map in the @xmath7 plane .
the trigger tower energy information is then sent to both l1 and l2 calorimeter trigger systems with 10-bit energy resolution , using a least significant count of 125 mev and resulting in a full scale of 128 gev .
the level 1 calorimeter ( l1cal ) subsystem only uses 8 of the 10 available bits for each trigger tower , with the two least significant bits dropped , giving a least count of @xmath8 mev and a full scale of @xmath9 gev . as an example
, electron and photon primitives are formed at l1cal by simply applying energy thresholds to the em energy of a single trigger tower while jet primitives are formed using the total em+had of a single trigger tower . for electrons , tracks from the level-1 track trigger ( xft )
can be matched to the trigger towers while had energy can be used for rejection .
l1cal also calculates global sumet and met , using the lower resolution 8-bit em+had energy information .
the main task of the existing l2cal was to find clusters using the transverse energy ( @xmath10 ) of trigger towers .
the cluster finding algorithm was based on a simple algorithm used for run i , and was implemented in dedicated hardware . in this simple algorithm , the l2cal hardware forms clusters by simply combining contiguous regions of trigger towers with non - trivial energy .
each cluster starts with a tower above a `` seed '' threshold ( typically a few gev ) and all towers above a second lower `` shoulder '' threshold that form a contiguous region with the seed tower are added to the cluster .
the size of each cluster expands until no more shoulder towers adjacent to the cluster are found . because of this , large `` fake clusters '' are likely to be formed as the occupancy of the detector increases because towers which are unrelated to any jet activity have their @xmath10 boosted above clustering thresholds .
one example of such kind of `` fake cluster '' is when towers above shoulder threshold between true jets link multiple jets together into a single large cluster ( cluster merging ) .
this would reduce the efficiency , and increase the rate , for triggers requiring multiple jets at level 2 at higher luminosity , such as some important triggers for higgs and top physics .
one more limitation of the existing hardware - based l2cal system is that it does not re - calculate sumet and met using the full 10-bit resolution energy information available , instead it uses the sumet and met information directly from l1cal , which is based on 8-bit resolution .
this design feature limits its trigger selection capability , or rejection power , for triggers with global transverse energy requirements .
the existing l2cal trigger system has worked reasonably well at lower luminosity for run ii , however , as the occupancy in the calorimeter increases with luminosity , the simple hardware - based l2cal system starts to lose its rejection power .
the main goal of the upgrade is to significantly reduce the growth terms of the existing jet and met related triggers .
the basic idea of the l2 upgrade is to provide the full @xmath11 bit resolution trigger tower energy information directly to the global level 2 decision cpu where a cluster finding algorithm can reconstruct jets and recalculate met and sumet .
the upgrade approch is based on the pulsar board @xcite , a general purpose vme board developed at cdf and used for upgrading both the level-2 global decision crate @xcite and the level-2 silicon vertex tracking ( svt ) subsystem @xcite . the full resolution ( 10-bit )
calorimeter trigger tower data are received , preprocessed and merged by a set of pulsar boards before being sent to the level 2 decision cpu where more sophisticated algorithms can be implemented . since the actual cluster - finding is done inside the cpu
, it is more flexible and more robust against increasing luminosity or higher occupancy in the calorimeter . with this approach ,
jet reconstruction using a cone algorithm which is currently being done at level 3 can be moved to level 2 , albeit clustering trigger towers ( instead of physical towers ) and using only a single iteration in order to save processing time .
the new system is composed by a new hardware path connecting the l1cal directly to the l2 decision cpu ( see figure  [ hardware ] ) .
the same hardware has been used to transfer the trigger tower information , full 10-bits resolution , to an additional new pulsar boards which calculates , within the l1 timing constraints , the met for the l1 system .
bits resolution trigger towers to the l2 decision cpu .
the same full resolution information are sent to an additional dedicated hardware , which re - calculates the met for the level 1.,width=336 ]
.,width=336 ]     gev as a function of the instantaneous luminosity : upgraded l2cal vs existing l2cal , width=336 ]     met for the new level 2 met trigger with @xmath12 gev threshold ( after l2cal upgrade ) and for the level 1 met trigger with @xmath13 gev threshold ( before the l1met upgrade).,width=336 ]     met for the new level 1 met trigger with @xmath13 gev threshold : before and after the l1met upgrade.,width=336 ]    the pulsar - based l2cal upgrade has improved both jet and met measurements at level 2 . during the design stage of the new system
, extensive studies have already shown that level 2 jets found using the new algorithm are nearly equivalent to offline jets in terms of @xmath10 , cluster centroid and efficiency , a vast improvement over the current situation .
in addition , the calculation of met at level 2 with resolution closer to that at level 3 will significantly reduce level 2 rates for triggers requiring met .
the upgraded l2cal system has performed as expected in real data taking . as an example , figure  [ efficiency ] shows the difference between the level 2 and level 3 in met and jet transverse energy , for the existing system as well as for the upgraded system .
these improvements allow a significant rate reduction as well as efficiency improvement in jet and met based triggers . as examples ,
figure  [ jet40 ] shows the level 2 jet40 trigger cross section growth with luminosity before and after the upgrade .
several higgs - dedicated triggers have been developed exploiting the potentialities of the l2cal upgrade .
in particular the request of a even lower met at level 2 increases the acceptance on the signal . before the l1met upgrade the different resolution at level 1 and level 2 set a bottleneck to the lowest met threshold at level 2 .
figure  [ prel1met ] shows the met trigger efficiencies for the new l2cal system with a cut of @xmath12 gev ( full resolution ) and the l1met system ( before the l1met upgrade ) with a cut of @xmath13 gev .
since the turn on of the level 1 is very slow the trigger has low efficiency when instaed the level 2 is fully efficient , causing a loosing of trigger capability . before the l1met upgrade
the only solution was keeping a higher threshold at level 2 .
the l1met upgrade makes available at level 1 the same met trigger capability of the level 2 increasing the flexibility of the met - based triggers ( see figure  [ afterl1met ] ) .
we have presented the design , the hardware and software implementation and the performance of the new calorimeter system for cdf experiment .
the new l2cal system makes the full resolution calorimeter trigger tower information directly available to the level 2 decision cpu .
the upgrade system allows more sophisticated algorithms to be implemented in software and both level 2 jets and met are made nearly equivalent to offline quality , thus significantly improving the performance and flexibility of the jet and met related triggers . as a natural expansion of the upgraded level 2 trigger system we pushed the improved met resolution downto the level 1 , and these are big steps forward to have enough flexibility to deal with potential new challenges at the highest luminosities , and to improve cdf new physics reach sensitivities beyond baseline .
we foresee many opportunities for additional improvements in trigger purity and efficiency , most notably for physics triggers searching for higgs and new physics .
1 r. blair et al ( cdf ii collaboration ) , _ the cdf runii detector technical design report _ , fermilab - pub-96/390 e , 1996 .
pulsar project web page : http://hep.uchicago.edu/~thliu/projects/pulsar .
k.anikeev et al .
, _ cdf level 2 trigger upgrade _ , ieee trans .
vol.53 , no 2 , 2006 pp.653 - 658 .
j. adelman et al . ,
_ fist step in the silicon vertex trigger upgrade at cdf _ , nuclear science symposium conference record , 2005 ieee vol . 1 ,
october 23 - 29 , 2005 , pp.603 - 607 .
as the tevatron luminosity increases sophisticated selections are required to be efficient in selecting rare events among a very huge background . to cope with this problem 
 , cdf has pushed the offline calorimeter algorithm reconstruction resolution up to level 2 and , when possible , even up to level 1 , increasing efficiency and , at the same time , keeping under control the rates .    
 the cdf run ii level 2 calorimeter trigger is implemented in hardware and is based on a simple algorithm that was used in run i. this system has worked well for run ii at low luminosity . as the tevatron instantaneous luminosity increases , the limitation due to this simple algorithm starts to become clear : some of the most important jet and met ( missing et ) related triggers have large growth terms in cross section at higher luminosity . in this paper , we present an upgrade of the level 2 calorimeter system which makes the calorimeter trigger tower information available directly to a cpu allowing more sophisticated algorithms to be implemented in software . both level 2 jets and met can be made nearly equivalent to offline quality , thus significantly improving the performance and flexibility of the jet and met related triggers . however in order to fully take advantage of the new l2 triggering capabilities having at level 1 the same l2 met resolution is necessary . 
 the new level-1 met resolution is calculated by dedicated hardware . 
 this paper describes the design , the hardware and software implementation and the performance of the upgraded calorimeter trigger system both at level 2 and level 1 .