Date: Tue, 16 Feb 1999 12:58:22 -0600 (CST) From: Dave Toback To: "Horst D. Wahl" Cc: Gerald Blazey Subject: L1CFT Output format Hi Horst, I've tried to put down the basic arguements for the various L1CFT output format into a document. This issue has simmered for a while and we really should try and settle it. The three proposals are A and H, H and Pt, and a hybrid. I didn't include the option which is to cut at L1 on different values than we send to L2. My understanding is that this was an idea that was floated by Fred, but since it was never really thought of as being easily feasible it is no longer being actively considered. I should also mention that Marvin and I had talked about an A and PT proposal, but I haven't heard from him in a while. He mentioned that if the new boards split up the right way this becomes an option in a way that didn't use to be feasable. There certainly have been a number of studies about the effects of the different proposals at L1 and L2 and some attempts to try and quantify the effective road widths and efficiencies for these methods. Have you confirmed that the H and Pt does in fact give you wider roads and reduced efficiency? If the loss is intolerable does the hybrid solution meet your needs? Hopefully, putting down the arguements will enable us to try and find a way to put this question to rest. Comments? Thoughts? Thanks, Dave ************************************************************************** The old Format (what most people remember, A and H format): FE_board Number (0-79) H layer fiber number (0-43) Offset (0-15) Sign (0-1) This information is equivalent to passing the A and H layer hit information. Advantages: 1) Some studies have shown that this method defines a good road width in the SMT. 2) The STT algorithms are simplified. Also, well studied. Disadvantages: 1) To decide if a track passes a trigger threshold, it must be in a trigger bin. These are defined by offset. => Fixed turn on curves (can only group offsets) => Slow turn on curves (see plot) 2) The Pt is not a function of Offset. Said differently, a track with offset of 7 may have a higher Pt than a track with an offset of 8 and vice versa. This causes (not unsurmountable) sorting problems in L2CFT. 3) Because we only look at tracks with Pt>1.5 GeV, the largest offset used is 13. Thus, we loose two bits off the 4 bit full scale. ******************************* H and PT proposal: Sort the equations at L1 and make the trigger thresholds (bins) by Pt rather than by offset. Send Pt and H information to L2. Advantages: 1) Significantly sharpens the L1 threshold turn-on curves (See plot) 2) Allows us to dial the location of the turn on curves 3) The 4 threshold bins would be indicated by the two most significant bits of PtWord. The output from the concentrator more closely resembles the L1 decision and algorithms. 4) Sorting by PtWord in L2CFT is the same as sorting by Pt. This helps L2CFT. 5) The information sent to L2CFT is already sorted in the first two bits. Thus, only the lower bits need to be sorted. This significantly reduces the sorting time in L2. 6) The number of tracks per bin are more equitably spaced and again help the sorting. Disadvantages: 1) Makes the L2STT algorithm (potentially) more complicated 2) May make the road width larger (studies still in progress). This is very dependent on the number of different bins allowed (4 bits vs. 6 bits). Comparison to A-H method: To compare the Pt-H and A-H methods, we have tried to quantify the discussion by comparing the road widths at the A layer. In the A-H method, the A-H method the road width is, by definition, 1 fiber width. In the Pt-H method, the road width is not as well defined. For a given track, when all 8 hits are used in a full track fit, the routines return a range of Pt's which when averaged and combined with the H information uniquely specify a location in the A layer. Studies comparing this position to the true position (i.e, DeltaPhi(Pred-True)) yields a gaussian with an RMS of about a 1/4 of a fiber width. This makes sense since using more fiber information should yield a better estimate of where the track went through the A layer. However, to be fully efficient, one must integrate the full gaussian and to be 100% efficient requires going to almost a full fiber width (Marvin tells me that by removing the low probability tracks from the list we can reduce the tails of this distribution). Finally, the real problem is that we do not get the best information (i.e, the equation number or pt ranges) from the tracker, rather for every track the Pt equations are grouped. The equations in each group determine both the RMS and the tails of the road width. On average it is better than for A-H, but to be 100% efficient the road width can be worse (depending on the Pt binning). ***** Hybrid proposal: Since the road width problem appears to be mostly for low Pt bins, we could use a hybrid system. A-H for low Pt, H-PT for high Pt. Advantages: 1) Allows us to use PT for high PT where the trigger decisions are made (gives sharper and adjustable turn on curves). 2) Potentially allows A-H road width for where the most tracks are for L2STT. This may be an advantage (studies still in progress). 3) Allows a single method for when the L2STT is in the system and when it is not. Disadvantages: 1) 5 years from now it will be hard to remember what the Pt is given a value of 0010 in the "PT word". 2) It's not clear we need it. We wouldn't use this if the STT weren't there. Fred's current proposal is to make the Pt information come in 6 bits: 2 bits to denote the threshold bin and 4 bits to denote the Pt value within the bin. This would work by sorting the equations first into the four Pt threshold bins by Pt value, and them sorting the maximum and high bins by Pt value within each threshold bin. To satisfy the requirements of the STT it looks like we must sort the medium and low Pt threshold bins by offset value. Extending the Pt index from 4 to 6 bits gives us 16 possible bins within each Pt threshold bin. But we will keep the total number of bins to 16 and will use the extra bits to allow us to distribute those bins anywhere within the 4 Pt threshold bins. We can only assign indexes to the tracks once, so the scheme needed for STT and L2CFT must be the one used for L1Muon.