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Home Music Instrument Reviews 20 Best Drum Set Reviews 2021 (Best Drum Set Brands)
Music Instrument Reviews
20 Best Drum Set Reviews 2021 (Best Drum Set Brands)
Best Drum Set, Best Kids and Beginner Drum Set & Best Drum Set Brands
Before you set on the task of purchasing a drum set, you first need to understand the anatomy of a drum set. Once you fully understand what each component does, and its purpose, choosing the best drum set for your requirements will be a breeze.
Looking for electronic drum set instead? Check the greatest electronic set or the portable electronic drum set pad.
Accessory: Drum Bag Set, Drum Pedal, Drum Throne, Overhead Drum Mics
Top 3 Best Drum Set for the Money
The drum sets below great for intermediate and professional player.
2) Full-Sized Drum Set by Gammon Percussion
Excellent Reputation
1) Five Piece Drum Set from Pearl
Reputable Brand
New Fusion Style
3) Five Piece Drum Set from Pearl – EXX725S/C
Great for Intermediate
Comfortable Playing
Best Beginner Drum Sets for Juniors and Kids
The Mendini drum set below is great for children while the drum sets by Sound Percussions Lab and Sawtooth are ideal for adult beginners or juniors.
2) Sound Percussions Lab Drum Set
Beginner Choice
Black and White Design
1) Three Piece Drum Set by Mendini
Great for Children
Metallic Blue
3) Full-Sized Drum Set by Sawtooth
Storm Blue Sparkle
Student Choice
Great Sounding
Let's start with the basics; the foremost part of a drum set comprises of what is called the 'Batter Head', it may also be referred to as the 'Top Head'. It is the circular membrane made of plastic or animal hide that will stretch across the shell in different levels of tension or tightness.
A 'Hoop' is manufactured of stamped or cast metal, although seasoned drummers would prefer the wooden variety. This will hold the head against the shell to provide different degrees of tension.
Next, you will encounter the 'Tension Rod' which is mounted via the hold within the hoop to maintain the desired tension by the player. A 'Lug' is typically made of metal and is mounted on to the shell for the sole purpose of creating tension. It can have a variety of forms, ranging from simple to complex and have features that enable alignment.
A 'Shell' is the second most important component of a drum set that is responsible for the drum set's tone. They are made of a range of materials such as fiber glass, wood, as well as wood. As suggested by its name, the 'Vent' is responsible for the passage of air when the player strikes the head.
However, not all sets have this feature. There is also the 'Resonant Head' and 'Bottom Hoop' which is responsible for defining the tone and accommodating snares, respectively.
These features come together to form a drum set; by understanding what each component is responsible for, the player would be able to understand how to maneuver the instrument.
20 Best Drum Set Reviews and the Best Drum Set Brands
Making a purchase for the first time also requires one to be familiar with each of these components. Let's look at twenty drum sets to understand the best possible purchase for your requirements.
We have listed 12 top drum sets for the money and also 8 best drum sets for beginners, juniors and kids.
12 Best Drum Sets for the Money, Great for Intermediate and Advanced Player
1) Five Piece Drum Set from Pearl – RS525SCC706
The style from this charcoal-metallic Drum Set is 'New Fusion'. The set is easy to assemble and can be used straight out the packaging. The Shells are 7mm, 9ply and have 1.2-millimeter hoops that are triple flanged. The Head, as well as the Double Brace, are a part of its hardware.
The Pearl RS525SCC706 has several types of Drums included; this will include a Bass Drum (22×16), Toms that are 1×8 and 12×9, and another Tom that is 16×16. The Snare Drum is 14 x 5.5. It also includes Cymbals that are 16" and 14" (Crash Ride and Hybrid Hi-Hats).
For the professional player, this also had added features like a Hi-Hat and Cymbal Stands; with your purchase, you will also receive two Tom Holders, one Throne, and a Bass Drum Pedal as well. The unit weighs 50 lbs, and measures 46" x 46" x 50". The shipping weight can include an additional 5.5lbs.
In terms of suitability, it's ideal for players who are beginning their career as drummers or as a set for amateurs. This five piece Drum Set by Pearl is 'gig-ready' and is built for durability. For powerful tones, this Drum Set has a Snare, Bass, and Toms, as well as 9-ply Shells (Poplar).
For professionals, this also has a Bass Drum and locking stands; the double-braced hardware also makes it an ideal purchase for your money. All its stands and drum thrones are double braced for extra reinforcements.
Read User Reviews & Check Price On Amazon
Gammon Percussion is widely known for its excellent reputation in producing fine quality Drum Sets. This black five-piece drum set can be ordered by a Stands for Cymbals and Sticks for a player who looks for quality and finesse.
This is known to be a hot seller in the range as it comes with a complete set of all you need for seamless playing. Your purchase will avail you of a Hi-Hat, Stands, and Cymbal Sticks Stool as well. The chain-driven pedal units will accent the high-gloss finish of the drum set.
If you are laymen shopping for all five types of drums, this has it all from a Bass Drum, Floor Tom, 2 units of Mounted Toms, Snare Drums) and Pedals, Stool, Hardware and Drum Key. It's no wonder why this is a best seller.
Gammon Percussion's Drum Set measures 30.3" x 24" x 22.1" and weighs 84.4 lbs. The Unit is made for an adult who is looking for a drum set as a hobby.
The measurement of the Lug Bass is 22 x 14 inches; Snare Drum is 12×10 inches, and the two Mounted Toms are 13×10 inches. The shipping weight remains the same.
A jet black majestic Drum Set from Pearl that is bound to make you a star in your group. This can be opted for with or without its Cymbals. The Cymbals, if requested, may come in separate boxes when ordered. The set will include a lifetime warranty from the manufacturer, it's best to confirm the warranty conditions prior to ordering.
Apart from this, it will include on Demonator Pedal (P930), and new hardware, REMO Batter side-head, and Matching Snare. The EXX725S/C incorporates superior technology for its Shell.
The Mahogany Shell (Asian/Poplar) is strong and offers a powerful volume. This Drum Set from Pearl has a superior Suspension System (Opti-Loc), which guarantees a wobble-free play time with a three-way mount system.
In terms of usability, this model is recommended for a serious student who may want to pursue drumming professionally. The power-packed upgraded system has Stands that are double-braced and drum pedal which is chain-driven. The manufacturer offers a lifetime commitment to the player with a warranty that resonates its excellence in this sphere.
The Drum Unit measures 24" x 20" x 24" and weighs just 48 lbs. Shipping weight may double to 90 lbs. It's best to check if there are any limitations in shipping the units to your address.
4) Five Piece Drum Set for Adults by Novah
As a solution for adults who are looking for a comprehensive drumming kit, Novah's unit will be the perfect fix. This is a recommended model for an adult who may find a professional one too daunting and beginner's drum set too small.
As the stools are adjustable you would be able to change it as your teenager grows. It has everything from cymbal, stands, pedals, drums, sticks, and a throne to get you started.
In terms of hardware, the unit has a separate pedal and bass drum. The glossy finish just adds to the allure of the instrument. The stands are mainly for the Snare and Hi-Hat, and the Cymbals can be adjusted according to the desired height. As a beginner who has just begun touring the unit is 80lbs and measures 25" x 19" x 20".
You wouldn't have to worry about assistance to set up as this unit comes with a guide for assembly. The specifications of the unit include a Bass Drum measuring 22×16 inches, Hanging Tom Drum at 13×10 inches, and Floor Tom of 14×5.5 inches. The larger Tom measures 16×16 inches with the Snare at 16×14 inches. The unit comes in a beautiful blue and is made of Poplar and Metal.
5) Four Piece Drum Set from Pearl Masters – MCT924XEDP/C348
Available in a myriad of colors such as Absinthe Sparkle, this unit from Pearl Masters is truly a master piece that is on everyone's wish list. For the touring pro, who looks for quality and sparkle on stage, the MCT924XEDP/C348 offers power, warmth, and purity of tones unlike any other drum set on the market,
The style of the drum set is new fusion, the six-layers of premium Maple type shells do wonders to add to great sounding beats that deliver effective punches. No wonder this is called a Master's Legacy.
In terms of hardware, this unit includes a Bass Drum that measures 22×18 inches, Floor Tom that is 16×16 inches, and suspended Toms that measures 10×7 inches and 12×8 inches. The glossy finish of the drums just adds the superior finish of the product.
This is ideal for drummers who have now graduated from amateur to professional and are looking for something serious. This drum set will highlight you as a player not just because of its great looking exterior, the fact that the manufacturing of this unit is made of premium solid wood, you are guaranteed value for money in terms of your investment.
For a professional drum set, the unit only weighs 32 lbs, making it relatively lightweight. It measures 26.8" x 27" x 24.2" and can fit into a cab or tour bus without any hassle. It can be carried with ease as well.
6) Four-Piece Drum Set by Ludwig
With a sparkly black feel, you will be able to enjoy your drum time with Ludwig' set. The drum set has a forty-five-degree edge (bearing); this compact set is easy to take on tours with its mobile design.
To carry your drum set and store, Ludwig has a velvet bag for storage. The design is ideal for compact spaces like an apartment or street player, this drum set is an ideal choice. However, that's not to say that the instrument compromises on quality.
The raw and gritty drum set, it excellent for hard use and fits in any vehicle because of 'Breakbeats'. For optimum reach, it is positioned atop of risers. The unit has a Bass Drum that is 14×16 inches, Tom of 7×10 inches and one Floor Tom of 13×13 inches; a Wood Snare Drum of 5×14 inches is also included.
If you want your voice to be heard during gigs, at rehearsals, or even on the streets, this Drum Set by dialing it with the Remo heads. The shells are perfect for the added punch, with the Snare and Tom. The unit weighs 75 lbs. and 46" x 46" x 50"; shipping for this will weigh in another 52 lbs.
7) Five Piece Drum Set by Best Choice Products – 1263
With the Best Choice Products' 1263, you are assured of a complete five-piece Drum Set in jet black. You don't have to worry about purchasing any additional accessories with this model – everything you would need is already included. For easy home assembly, the kit also includes a guide, so setting up and playing is almost immediate.
Drum set model 1263 includes all five major hardware components you need; you avail yourself of a Snare Drum (14×6 inches), two Rack Toms, Bass Drum (23×16.5 inches), and one Floor Tom. A Hi-Hat, Ride Cymbal (12×14 inches), Bass Drum Pedal, a pair of 16 inch Drum Sticks, and throne are also included. The three units of Toms measures 10.5×10 inches, 12.5×10.5 inches, and 16.5×16.5 inches.
In terms of exterior, this chrome detailing on this high-gloss finish is reminiscent of a bygone era and will channel a classic look and feel. Another benefit of this five piece Drum Set by Best Choice Products is that it can be changed as you outgrow it. The solid wood frame will guarantee its durability.
The unit measures 27.5" x 23.8" x 21.6" and weighs 74 lbs. can easily fit in your home or compact apartment without any additional hassle. With the unit's Guide, you don't have to worry about having professional help for installation.
8) Five-Piece Drum Set from Gretsch Drums – CM1-E605-DCB
Choose this drum set that has maple shells of 7-ply, Remo drum heads, and a round Catalina. It also contains 2.3-millimeter hoops (triple flanged) and has a bearing edge of thirty degrees. Catalina Maple has renown for being one the most hailed brands for drum sets. Its sleek finish and modern technology are one reason why it is the professional's choice.
The hardware includes a gas cap in its technology and profile that is ultra low. It includes a Bass Drum of 16×20 inches, two racked drums of 7×10 inches and 8×12 inches, and one Floor Tom of 14×14 inches. The Snare Drum measures 5.5×14 inches.
The beautiful color it comes is rare; the deep cherry burst makes it the highlight of your band's equipment. The shells of the Gretsch are 7-ply. The unit measures only 22" x 22" x 18" and weighs 18 lbs. It also includes wingnuts (T-wing) and Bass Drum with gasket. The compact design makes it possible to store in smaller spaces and storage is made easier.
9) Five Piece Drum Set from MAPEX – RB5294FTCDR
Weighing just 60 lbs, the Mapex RB5294FTCDRincorporates a brand new design for its Lug. The unit comes with a pair of drum sticks, throne, and Cymbals.
You will be able to play the equipment right after unpacking it. The shells measure nine plies and are made of Poplar that gives the added punch and smooth tone.
All hardware is double braced with Rebel's assurance of excellence. The hardware includes a Bass Drum measuring 22×16 inches, Mounted Tom of 16×14 inches, Floor Tom of 10×7 inches, and Snare of 14×5 inches.
10) Four Piece Drum Set by ddrum SE FLYER BP
This four piece drum set by ddrum measures 46" x 46" x 50″ and weighs 50 lbs, because of this benefit it can easily fit in your storage for music room without any additional hassle. It's a piece that you would want to acquire because of vintage feel that would go well with your jazz outfit.
The shells are made of premium basswood to provide an extra punch when you play; the Rack Tom measures 8×12 inches, there is also the additional Floor Tom measuring 12×14 inches, the Bass Drum measures 14×16 and the Snare 5.5×14 inches. The flanged hoops (triple) are 1.6 millimeters.
The hardware is positioned in such as way that it allows minimal contact with the shells, the Bass will lift your tones with its eighteen-inch kick, the unit requires less footprint at the bass drum is mounted.
If you have a small jazz band or if you play solo, this piece of equipment is made of basswood that offers stability and security for the unit. If you are looking to start touring and want a drum set that stores easily, and doesn't weigh as much, you have found the best solution for you. The warranty conditions will depend on the shipper. The unit can be shipped to any part of the United States.
11) Four Piece Drum Set by Sonor
If you are shopping for a piece of equipment that you can transport and store easily, this drum set from Sonor makes an ideal pick. The units come with hardware including a Bass Drum measuring 12×20 inches, and Snare Drum of 5x14inches that delivers great kicks. Toms of 8×10 inches and 12×14 inches deliver a full sound.
If you are worried about the unit's resonance, the nine ply poplars will ensure it warm sounds for rich music. This Black set delivers the sounds with the punch that you are looking for.
The depth of this unit is shallow, and this allows the tone to be more open, warm and produce the boom effect. As the Cymbal is mounted as well, this will reduce the number of stands you will have to take with you at a given time.
Sonor's drum set assures the player versatility where you are into Rhythm and Blues, Hip Hop music, Fusion, Jazz, Pop or even Rock genres. The drum set is supported by the company's own patented lugs for extra protection and stability.
This will also add to the duration of keeping the drums in tune. The unit measures 7.5" x 11.4" x 7.5" and weighs only 75 lbs (the shipping weight will remain the same).
12) Five Piece Drum Set from Pacific Drums – PDCM2215TC
A brand new complete drum set in stunning Transparent Cherry weighs just 23.4 lbs and measures 25" x 25" x 37″. The hardware includes a tug (dual-turret), tension rods, STM systems, counter hoops, and DW MAG type Throw Off. There may be limitations of shipping beyond the US.
8 Best Drum Set for Beginners, Kids and Juniors
If you are a beginner or looking to buy a drum set for your kids, here are some good choices. Please take note the "Children" Drum Set might not suit adult as it is designed for kids. We included both beginner drum set and drum set for kids in the list below.
1) Children's Three Piece Drum Set for Mendini – MJDS-1-BL
This is an ideal for children or beginner who want to pursue their hobby as a Drummer – with its electrifying Metallic Blue, this is sure to set your child's passion for drumming on the path for professionalism. The recommended age for this drum set is three to eight years.
The Mendini Drum Set includes one Bass Drum of 13×8 inches, one Mounted Tom Drum of 8×6 inches, and a Mounted Snare of 10×4 inches; the Cymbal measures 8 inches. Apart from this, the MJDS-1-BL a height-adjustable drum throne, drum pedal (Bass), and one pair of wooden sticks.
For easy assembly, the MJDS-1-BL includes a manual for installation as well. For manufacturer defects, the unit includes a one-year long warranty. The aspiring drummer will appreciate the smaller-sized wooden triple-flanged hoops to start them off. For children, they will love the light-weight drum set 22 lbs. and measures 16" x 15.5" x 15.2".
2) Three Piece Drum Set by Sound Percussions Lab
This Three-Piece Drum Set comes with Bass Drum measuring 16×12 inches, a Floor Tom of 8×6 inches, and a Snare of 10×4 inches. There is a total of three Cymbals that is one Hi-Hat and Boom Stand.
Each sells as multiple ply thickness for added volume and punch. This drum set is designed for beginners who wish to pursue a career in drumming in a professional level who appreciate what remarkable hardware can do.
Don't be fooled by its powerfulness; it's built according to specifications of an adult drum set with a sleek exterior. It has shells of real wood, and replaceable at the top as well as the bottom. Other hardware includes one white throne as well. The unit measures 24.4" x 17.3" x 14.5" and weighs 36.3 lbs.
Be the talk of the town or your musical entourage with this Storm Blue Sparkle hued full-sized drum set by Sawtooth. This set is shipped and sold by GoDpsMusic. This model is recommended for students who want to pursue drum playing beyond a hobby.
The unit contains a Bass Drum (22×16 inches), two units of Toms measuring 12×8 inches and 13×9 inches, and another Floor Tom of 16×16 inches, as well as a 14×5 inch Snare Drum, are a part of the unit. The bearing edge measuring 45 degrees and shells of 6 ply is also an advantage.
Other hardware includes a two-tier stand for Cymbals, Pedal for Bass Drum, one Throne, two Tom Arms, one stand Hi-Hat, and Drum Key, and one pair of drumsticks. There are two types for the beginner to explore, one 14 inch Hi Hat and another 16-inch Crash Ride.
Sawtooth's full-sized drum is a distinct color of Storm Blue Sparkle. It's important to note that although this is a beginner's drum set, it is not a toy that should be taken lightly. It is built for durability with its 6 ply poplar set that also delivers great sounding music. Poplar produces even and smooth tones for warm music as you begin your career your music. The unit measures 30" x 24" x 24" and weighs 90 lbs.
4) Five-Piece Junior Drum Set by TKO
Measuring 23.7 x 21.3 x 13.1, this beginner's drum set comes in a vivid pink hue ideal for children who want to embrace vibrancy. The unit weighs 45.9 lbs, so storage in your home of the garage can take place without any hassle.
Don't be fooled by its soft exterior, the five-piece drum set is built for hard playing with shells that are made out hardwood and hardware that is plated with metal hardware. As your child grows, you will be able to adjust the height of the stands and the stool. It carries a year's warranty on hardware that covers all product defects.
The young student drummer will appreciate its pro-like look and feel with shells that are made of real wood, and chrome finishing. The set includes a Snare Drum that measures 10 inches, two adjusted Small Toms with four supporting Lugs of 8 and 10 inches; Floor Tom measures 13 inches, and the Bass Drum is 16 inches; they each have twelve lugs for support.
For the professional drummer look, the TKO's unit consists of an adjustable drum stool, 10 inch Brass Cymbal. The drum unit can also be purchased in other metallic hues such as green, blue, red, silver and solid colors such as wine red and black.
5) Three Piece Drum Set from Union – Union UJ3
Designed for children aged three to eight years can be treated to this three piece drum set from Union. The UJ3 measures 33" x 33" x 35" and weighs 25 lbs, can be stored and moved around with ease. The unit is available in the color black, metallic blue, red, and pink.
The hardware includes one Bass Drum measuring 10×16 inches, Tom Drum of 6×10 inches, and Snare Drum of 5×10 inches. The Cymbals that are included are the Crash and Hi-Hat; the Bass Drum Pedal and throne are also included with the unit. You will also have a tuning key with your purchase.
Union's three piece drum set is designed and tested in the United States for extra durability. It's easy to use as it can be assembled right out of the packaging. The shells are wooden and have a replaceable type of drum heads.
This is not recommended to be used as a toy, it's best for a child who has serious interest in pursuing drums as an instrument. Even though it's a beginner's one, it has all the features of an adult drum set. Warranty is offered and will depend on the shipper's conditions.
6) Three-Piece Drum Kit from Music Alley
Who wouldn't love a bright red three piece drum set to start your musical journey? Music Alley's three-piece drum kit is the perfect brand for beginners. Ideal for children aged between four to seven, this three piece drum kit can harness your child's musical talent in no time.
Music Alley's children's drum set includes one Bass Pedal, Bass Drums supported by Lugs, and two units of suspended Toms. The aspiring rock star will love this drum sets that the standard for quality and tone, for you, it's an affordable gift option.
The Bass Drum is the largest of this collection; the low tones can be acquired with the unit's foot pedal. The cushioned stool (throne) completes the look for this rock-star drum set and can be raised as your child grows.
The unit weighs just 16.1 lbs; it's perfect for children to set up or their parents to carry around the house for assembly. Measuring 25.6" x 29.5" x 25.6", this unit can be stored away with perfect ease even in compact environments like your apartment or garage. Shipping will require an additional 19.9 lbs.
7) Three Piece Drum Set for Children by Best Choice Products
Does your toddler show promise of being a great musician? Does your child seem to favor the drums above everything? If you are looking for a drum set to stir their passion and commitment, you can invest in this stunning three piece drum set in a bright red tone. Your child will love this for its great versatility and great range.
Ideal for children aged three and above, this is three piece drum set is constructed entirely of wood and accented with hardware that is chrome-plated for durability and great sounding music. The design mimics a professional drum set but is replicated in a fun size to harness the talent of your young drummer.
Suited for gifting, this unit measures 19" x 17" x 12" and weighs just 18.7 lbs., making it ideal to store in compact spaces like your apartment or garage. It does require a fair amount of assembly that can be managed with adult supervision.
The unit contains one Bass Drum that measures 12.5×11.75 inches, two units of Tom Drums of 8.5x 6.75 inches and 10.5×5.5 inches. Other hardware included in your purchase are one pair of drumsticks, one throne, and one unit of Cymbals.
8) Beginner's Drum Set by RockJam – RJ105-MB
Allow your child to pursue his dreams of becoming the next Ringo Starr with this beautiful Metallic Blue hued Drum Set by Rock Jam. If you want them to pursue their passion with a beginner's set, this is the perfect start.
Unlike most children's drum sets which comprise of three-pieces, this is a full five-piece to give your child a feeling of what a professional drummer plays if they are between the ages of three and ten.
The hardware of the drum set has a Bass Drum of 16×12 inches, supported by four lugs and chain foot pedal. The Snare Drums are stand-alone units, the larger one measures 10×5 inches and has a stand; the Tom-Tom is 13×10 inches, this too has four lugs to support it.
The Crash Cymbal is 10 inches, and the Hi-Hat measures 8 inches. Your child may want to spend hours experimenting with this drum set, that's why this includes a throne and a pair of Drum Sticks.
For you as a parent, the Drum Set from RockJam is affordable. The Drummers in Training can indulge their passions, while you don't have to worry about the cost of additional accessories. It is a well-known fact that learning to play a musical instrument can develop a child's brain.
It's an excellent source to deposit your child's extra energy into something useful. The unit is relatively lightweight and can be shifted around your home with ease; it weighs 39.7 lbs and measures 49.2" x 35.4" x 31.5".
Choosing the Best Drum Set from the Best Drum Set Brands
Where you are making a purchase of a drum set or you are a seasoned player, there are a few things you would need to consider prior to making your purchase.
First, decide on the actual purchase of making this purchase – are you a hobbyist? Is your child looking for an instrument to experiment with or is this something they would want to pursue professionally.
As you do your findings, you will discover that drum sets even for beginners do not come cheap. Therefore, by first understanding your requirement you would be able to filter out many brand and models.
Next, it is important to decide on the space in your home.
Do you live in an apartment?
You would then that to consider a model that is compact. Next, you would have to decide on your budget. Once you get started, it would be great to receive professional assistance to get you started. Regular tuning and cleaning will ensure that you drum set performs at its optimum levels at all times and lasts long.
What are the Best Drum Set for the Money?
The drum sets below great for intermediate and advanced drum player.
Best Drum Set for Beginners, Kids and Juniors
Mendini drum set is great for chidren while the drum set by Sound Percussions Lab and Sawtooth are ideal for adult beginners and juniors.
As a buyer, you might also want to look at the warranty conditions offered by the seller as well. This will cover you on any production defects. If you are looking to making a purchase, the above models reviewed will be beneficial for you.
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"Graphic abstraction" was Ann Demeulemeester's catchphrase for Spring. The makeup, the hair, the music contributed to a mood that was like silent-movie expressionism: stark and dark. It inspired a strong show whose single-minded message was rammed home by repetition. Demeulemeester claimed the notion of protection defined the collection. So there were buckled breastplates, quilted obis, and funnel collars rearing up over the face, all of them cocooning the body in defensive ways. At the same time, these structured items loaned a sculptural quality that felt new for Demeulemeester. If in the past she has offered flowing, poetic volumes, this collection found power in restraint: the military precision of a fitted jacket and short skirt, the volume of a parka cooped up under a fencing jacket. The designer hiked a skirt high on one thigh and let the rest of it fall to the floor on the other leg, a perfect paradigm for control and release. Quite how that notion translates to the shop floor is a matter for Demeulemeester and her store buyers, but the feel of this collection was definitely tighter and more contemporary, more sci-fi, less neo-medieval.
Read Sarah Mower's review of Ann Demeulemeester's Spring 2011 ready-to-wear fashion show.


The Flower And Bird Print Strap Bird Dial has a beautifully attractive dial with rose gold-tone case. The dial is stunning and this model is also powered by precision Quartz.
First Class Watches are Cath Kidston watch retail partners so you can be assured your sparkling new watch will arrive with a stamped manufacturer's warranty, packaging and instructions.


Last weekend weve uploaded our live visual from Second Reality on youtube.
and I hope it won't take too long.
something really strange going on.
I feel like I haven't slept in ages.
casting a shadow on my mind.
but I know I have to hang on.
we know who it is we want.
we have a collective mind.
we don't miss a single step.
we know we serve someone else.
we have swallowed our pride.
we march to this tune of loss.
we take this in our stride.
and my mind has almost turned insane.
please help me turn back the pages.
I want to go back, from where I came!
I can feel they're almost here.
so my last thought is just your name.
and it is all that will remain.


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Locating Health Statistics & Data Sets
Hamline Resources
Minnesota Center for Health Statistics
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MDH: Data & Statistics by topic
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2016 Annual Report. You can select different years on page.
Minnesota Department of Labor & Industry: Research and Statistics
American Fact Finder
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National Center for Education Statistics
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US Bureau of Labor Statistics
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US Census Bureau
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World Health Organization: Global Health Observatory (GHO) data
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Global Health Data Exchange (GHDx)
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World Bank Open Data
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International Statistical Agencies
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United Nations: Statistics Division
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Statistics including demographics, economics, environment, and energy
International Human Development Indicators
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UNICEF: Country Statistics
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URL: https://bushlibraryguides.hamline.edu/c.php?g=645395
Subjects: Public Health Sciences

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text:
\section{Introduction} \label{sec:introduction}

For at least the next 6 years the Fermilab Tevatron will remain the
highest energy collider in the world. The Tevatron upgrade will
provide an exciting opportunity for discovering physics beyond the
Standard Model.  The hadronic environment at the Tevatron presents a
number of challenges and extracting new physics signals can be
difficult. In this respect, signatures with low Standard Model
(especially QCD) backgrounds are extremely valuable, as they may
provide our best opportunity for finding new physics before the LHC
turns on.

Supersymmetry (SUSY) \cite{original} has been fascinating particle
physicists for more than 25 years.  It seems an intrinsic component of
theories unifying gravity and gauge interactions such as string
theory, M-theory or supergravity, and has played an important role in
the `second string revolution' of the last few years. The minimal
supersymmetric extension of the Standard Model (MSSM) is a
well-defined, renormalizable and calculable model, which offers a
technical solution to the hierarchy problem \cite{hierarchy}, if the
masses of the superpartners of the standard model particles are of
order the weak scale. Our belief that supersymmetry might be relevant
at energy scales accessible at present colliders is reinforced by the
successful gauge coupling unification \cite{gauge unification}. Also,
due to decoupling the MSSM is generally in agreement with precision
data \cite{precision fits}. In addition, a generic prediction of the
MSSM is the existence of a light Higgs boson \cite{light
Higgs, Higgs constraints}, which is preferred by fits to data
\cite{Higgs mass fit}.  In summary, the MSSM is a well-motivated
extension of the Standard Model, which has a very rich and interesting
phenomenology \cite{MSSM review}.

Because of the relatively low (compared to the LHC or NLC)
center of mass energy and integrated luminosity in Run II,
the Tevatron is able to explore only the low end of the
superpartner spectrum. Searches for colored superpartners
(squarks and gluinos) are done in jetty channels, which suffer
from relatively large backgrounds. On the other hand, $SU(2)$-gaugino
pair production leads to a unique clean trilepton signature
\cite{3L,Mrenna}, which has been considered a `gold-plated'
mode for SUSY discovery at the Tevatron. Both CDF and D0 have
already performed Run I trilepton analyses \cite{3L-exp}.
In light of the importance of this channel in Run II, it is clamant to
\begin{itemize}
\item have a reliable estimate of both signal and background rates.
We would prefer to determine background rates from data, but until Run
II we primarily rely on Monte Carlo simulations.  ISAJET and PYTHIA
have been two of the most commonly used event generators in SUSY
analyses.  While there is a reasonable agreement for the signal,
PYTHIA-based studies \cite{Mrenna,LM} have obtained larger values for
the trilepton backgrounds (mainly $WZ$ and $ZZ$) than ISAJET-based
analyses \cite{3L,BPT,BK}. This discrepancy was noticed and discussed
in the TeV 2000 Report \cite{TeV2000}, but was attributed to the
different lepton rapidity cuts used in the various analyses.
\item use an optimized set of cuts, which will maximize the Tevatron
reach. A first step in this direction was taken in Refs.~\cite{BK},
where softer lepton $p_T$ cuts have been proposed, thus enhancing
signal over background throughout a large part of parameter space.
\item include next-to-leading order (NLO) corrections to the
production cross sections. The corrections to diboson production
\cite{VV_corr}, $t\bar{t}$ production \cite{tt_corr} and Drell-Yan
\cite{DY_corr}, have been known for some time, and the corrections
will soon be available for chargino-neutralino production as well
\cite{Chi_corr}.
\item identify regions of parameter space where the reach via the
trilepton signature is diminished and try to find an alternative
search strategy in those regions. An example of this sort is the large
$\tan\beta$ region with light sleptons, where one often finds that
both the chargino and the neutralino decay predominantly to tau
leptons. Then the trilepton signal has a very small branching ratio
{\em and} the leptons are quite soft, which can make it unobservable
at Run II, even for chargino masses as low as 100 GeV. In this case it
is possible to recover sensitivity by considering alternative
signatures with tau jets \cite{LM}. Another alternative to the
trilepton signature is the inclusive like-sign dilepton channel
\cite{JN}, where the signal acceptance is increased by not requiring
the odd-sign lepton in the event.
\end{itemize}
In this paper, we shall try to address most of these issues.  We
perform detailed Monte Carlo simulations of signal and background
using both PYTHIA and ISAJET and explain the cause for the largest
background discrepancy. We also determine the maximum reach by
applying an optimal set of cuts at each point in the supersymmetric
parameter space.

Also, we make use of the presence of a sharp edge in the dilepton
invariant mass distribution of the signal by applying a more
restrictive invariant mass cut, thus reducing the $WZ$ and $ZZ$
backgrounds.  As the NLO corrections to gaugino production are not yet
available, we conservatively use leading order cross sections for all
processes.  Preliminary results \cite{Chi_corr} show that the
$k$-factor is roughly the same for both signal and background. Hence,
we expect that the Tevatron reach will be improved once NLO
corrections are incorporated.

We show our results for the discovery potential of the upgraded
Tevatron in the so-called minimal supergravity model (mSUGRA)
\cite{SUGRA}.  This model has universal soft parameter boundary
conditions at the grand unification scale, and its spectrum displays
characteristic properties. For example, the imposition of electroweak
symmetry breaking results in\footnote{$\mu$ is the Higgsino mass
parameter and $M_2$ is the soft supersymmetry breaking SU(2) gaugino
mass.}  $|\mu|>M_2$, so that the lightest chargino and lightest two
neutralinos are gaugino-like. Also, the squark and slepton masses are
generation independent, except at large $\tan\beta$ where the third
generation masses can be lighter. This model has five input
parameters: the scalar mass $M_0$, the gaugino mass $M_{1/2}$, the
$A$-term $A_0$, the ratio of vacuum expectation values $\tan\beta$,
and the sign of the $\mu$ term. We show results for $\mu>0$ and
$A_0=0$.

We adopt a signature driven approach by comparing and contrasting
three of the cleanest channels for Run II -- the trilepton (3L)
\cite{3L, Mrenna}, like-sign dilepton (2L) \cite{JN} and dilepton plus
tau jet (2L1T) \cite{LM} channels. The 3L channel is the long studied
``gold-plated'' channel. The 2L channel has larger signal acceptance
compared to 3L, but it is not {\it a priori} clear whether this
advantage will be spoiled by the concomitant increase in the
background. The 2L1T channel is known to be important at large
$\tan\beta$, where the right-handed tau-slepton is lighter than the
first two generation sleptons. Here we will discuss this channel at
small $\tan\beta$ as well.

We describe in detail our numerical analysis in
Section~\ref{sec:analysis}, where we also describe the cuts we
consider for each signature.  We discuss all non-negligible
backgrounds and their evaluation in Section~\ref{sec:backgrounds}.
Then, in Section~\ref{sec:SUGRA}, we map our results for the Tevatron
reach onto the parameter space of the mSUGRA model.
We reserve Section~\ref{sec:conclusions} for our conclusions.

\section{Analysis} \label{sec:analysis}

In this section we describe our numerical analysis.  We use
PYTHIA v. 6.115 \cite{PYTHIA} and ISAJET v. 7.42 \cite{ISAJET} for
event generation, and the SHW v. 2.2 detector simulation package
\cite{SHW}, which mimics an average of the CDF and D0 Run II detector
performance. We use PYTHIA for the background determinations, together
with TAUOLA \cite{tauola} to account for the correct (on average) tau
polarization in tau decays.  We have made several modifications in
SHW, which are appropriate for our purposes:
\begin{enumerate}
\item We extend the tracking coverage to $|\eta|<2.0$, which increases
the electron and muon acceptance, as is expected in Run II \cite{TDR}.
For muons with $1.5<|\eta|<2.0$, we apply the same fiducial efficiency
as for $1.0<|\eta|<1.5$. However,
we still require that tau jets are reconstructed only up to $|\eta|<1.5$.
\item We retain the existing electron isolation requirement and add a
muon isolation requirement $I<2$ GeV, where $I$ is the total
transverse energy contained in a cone of size $\Delta
R=\sqrt{\Delta\phi^2+\Delta\eta^2}=0.4$ around the muon.
\item We increase the jet cluster $E_T$ cut to 15 GeV and correct the
jet energy for muons. We also add a simple electron/photon rejection cut
$E_{em}/E_{had}<10$ to the jet reconstruction algorithm, where
$E_{em}$ ($E_{had}$) is the cluster energy from the
electromagnetic (hadronic) calorimeter.
\item We correct the calorimeter $\rlap{\,/}E_T$ for muons.
\item We account for an incorrect assignment of neutralino particle
id's in the ISAJET translation of STDHEP v. 4.05 \cite{STDHEP}
\footnote{The assignment has been corrected in STDHEP v. 4.06.}.
\end{enumerate}
The addition of the muon isolation cut and the jet $E_{em}/E_{had}$
cut allows us to uniquely resolve the ambiguity arising in SHW v. 2.2,
when a lepton and a jet are very close.

As we mentioned in the introduction, we show results for three of the
cleanest SUSY channels in Run II at the Tevatron -- trileptons,
inclusive like-sign dileptons and dileptons plus a tau jet. In our
analysis we consider both channel specific and channel independent
cuts. In most of those cases, we use several alternative values for
the cut on a particular variable. For example, we try several $\rlap{\,/}E_T$
cuts, several sets of $p_T$ cuts, etc. We employ a parameter space
dependent cut optimization: at each point in SUSY parameter space, we
consider all possible combinations of cuts, and determine the best
combination by maximizing $S/\sqrt{B}$.  In contrast to superior
neural network analyses, the additional CPU requirements when
employing this simple optimization are negligible.  We concede that it
may not be possible to perform an identical analysis with real data,
particularly due to trigger issues. Even so, it is useful and
interesting to see which cuts work best in the different parts of
parameter space, and to see how much one can gain by choosing optimal
cuts.

We first list the channel-independent cuts, which in general are designed
to suppress backgrounds common to all three channels.
\begin{enumerate}
\item Four $\rlap{\,/}E_T$ cuts: $\rlap{\,/}E_T>\{15,20,25\}$ GeV or no cut.
\item Six high-end invariant mass cuts for any pair of opposite sign,
same flavor leptons. The event is discarded if: $|M_Z -
m_{\ell^+\ell^-}|<\{10,15\}$ GeV; or $m_{\ell^+\ell^-}>\{50,60,70,80\}$ GeV.
\item Four azimuthal angle cuts on opposite sign, same flavor leptons:
two cuts on the difference of the azimuthal angle of the two highest
$p_T$ leptons, $|\Delta\varphi|<\{2.5,2.97\}$, one cut
$|\Delta\varphi|<2.5$ for {\em any pair} leptons, and no cut.
\item An optional jet veto (JV) on QCD jets in the event.
\end{enumerate}

We list the channel-specific $p_T$ cuts in Table~\ref{pt cuts}.  In
the 3L channel, the first four $p_T$ cuts in the table also require a
central lepton with $p_T>11$ GeV and $|\eta|<1.0$ or 1.5.

\begin{table}[t!]
\centering
\renewcommand{\arraystretch}{1.5}
\begin{tabular}{||c||c|c|c||}
\hline\hline
Channel   & \multicolumn{3}{c||}{$p_T$ cuts} \\
\hline\hline
3L   & $p_T(\ell_1)$ & $p_T(\ell_2)$ & $p_T(\ell_3)$ \\ \hline
1    &   11       &     5      &     5  \\ \hline
2    &   11       &     7      &     5  \\ \hline
3    &   11       &     7      &     7  \\ \hline
4    &   11       &    11      &    11  \\ \hline
5    &   20       &    15      &    10  \\ \hline
\hline
\end{tabular}
\vspace{5mm}
\begin{tabular}{||c||c|c||}
\hline\hline
2L   & $p_T(\ell_1)$ & $p_T(\ell_2)$ \\ \hline
\hline
1    &   11       &     9    \\ \hline
2    &   11       &    11    \\ \hline
3    &   13       &    13    \\ \hline
4    &   15       &    15    \\ \hline
5    &   20       &    20    \\ \hline
\hline
\end{tabular}
\vspace{5mm}
\begin{tabular}{||c||c|c|c||}
\hline
\hline
2L1T & $p_T(\ell_1)$ & $p_T(\ell_2)$ & $p_T(\tau)$\\ \hline
\hline
1    &    8       &     5      &    10   \\ \hline
2    &    8       &     5      &    15   \\ \hline
3    &   11       &     5      &    10   \\ \hline
4    &   11       &     5      &    15   \\ \hline
\hline
\end{tabular}
\parbox{5.5in}{
\caption{Channel-specific sets of $p_T$ cuts. \label{pt cuts}}}
\end{table}

For all channels we impose a low-end invariant mass cut on any pair of
opposite sign, same flavor leptons, $m_{\ell^+\ell^-}>11$ GeV. This
cut is designed to suppress a number of backgrounds, e.g. Drell-Yan,
$b\bar{b}$, $c\bar{c}$, and the contribution from $W\gamma^*$ (see
below). It is common for lepton analyses to include a cut on the
$(\Delta\eta,\Delta\varphi)$ distance between any two leptons $\Delta
R>0.4$, which suppresses background from $b\bar{b}$, $c\bar{c}$, and
anomalously reconstructed cosmics. We choose not to include this cut,
since we do not simulate those backgrounds. (Monte Carlo simulations
do not reliably estimate the backgrounds from $b\bar{b}$ and
$c\bar{c}$ production.) We have checked, however, that the effect of
the $\Delta R$ cut on signal and background is negligible.

In the next section we briefly discuss the main backgrounds for the
three channels. This will also motivate the choice of some of the cuts
above.

\section{Backgrounds}\label{sec:backgrounds}

We simulate the following background processes (with the generated
number of events in parentheses): $ZZ$ ($10^6$), $WZ$ ($10^6$), $WW$
($10^6$), $t\bar{t}$ ($10^6$), $Z+$jets ($8\cdot10^6$) and $W+$jets
($8\cdot10^6$).

\subsection{Backgrounds to the trilepton channel}

We start with the $WZ$ background, which is known to be the major
source of background for the 3L channel. The total $WZ$ cross section
at Run II will be $\sim 2.6$ pb. Folding in the branching ratios of
$W$ and $Z$ to leptons, we get a 3L WZ background cross section
production of 46 fb.  It has a reducible and an irreducible
component. The irreducible component ($\sim 3$ fb) is due to
$Z\rightarrow\tau^+\tau^-\rightarrow \ell^+\ell^-$ decays. The
invariant mass of the resulting lepton pair from the tau decays is
usually far from the $Z$-mass, in a region which is typical of the
signal.  Hence there is no obvious cut which can substantially reduce
this part of the $WZ$ background without at the same time reducing
signal-to-noise. On the other hand, the remaining background ($\sim
43$ fb) is reducible, since it arises from $Z\rightarrow \ell^+\ell^-$
decays.  In this case the invariant mass $m_{\ell^+\ell^-}$ of the
resulting lepton pair is equal to $p_Z^2 = (p_Z)^\mu (p_Z)_\mu$, where
$(p_Z)_\mu$ is the 4-momentum of the parent boson.  Most of the time
the $Z$ is produced nearly on-shell, $p_Z^2 \approx M_Z^2$. Hence, the
invariant mass cut $|m_{\ell^+\ell^-}-M_Z|>10$ GeV is very efficient
in removing this source of background. However, the parent can also be
off-shell, due to either the $Z$-width, or to $WZ$/$W\gamma$
interference.  In PYTHIA, where only the first effect is modeled, the
lepton pair invariant mass distribution follows a Breit-Wigner
shape. We find that roughly 10\% of the 3L background events pass the
dilepton invariant mass cut, thus bringing the reducible background
cross section down to about 4.3 fb. This is almost a factor of two
larger than the corresponding irreducible background cross section
(compare to 2.6 fb). Since ISAJET does not incorporate either $Z$-tail
effect, we find essentially no reducible background cross section from
ISAJET after the dilepton invariant mass cut is
applied\footnote{Energy smearing in the detector simulation produces a
very small background which survives the 10 GeV $Z$-mass window cut.}.
This difference between ISAJET and PYTHIA largely accounts for
the discrepancy in the backgrounds found in Refs.~\cite{Mrenna,LM} and
Refs.~\cite{3L,BPT,BK}. In what follows we use PYTHIA for our
background estimate.

We illustrate the above discussion in Fig.~\ref{inv mass}
\begin{figure}[t]
\centerline{\psfig{figure=fig_im.ps,height=3.5in}}
\begin{center}
\parbox{5.5in}{
\caption[] {\small The invariant mass distribution of any pair
opposite sign, same flavor leptons for the signal events (with
$M_0=700$ GeV, $M_{1/2}=160$ GeV, $\tan\beta=5$) and the PYTHIA $WZ$
background. We impose a set of cuts from Ref.~\cite{BK}:
$p_T(\ell)>\{11,7,5\}$ GeV, central lepton with $p_T>11$ GeV and
$|\eta|<1.0$, $\rlap{\,/}E_T>25$ GeV and $|m_{\ell^+\ell^-}-M_Z|>10$ GeV.  Each
histogram is normalized to its cross section.
\label{inv mass}}}
\end{center}
\end{figure}
where we show the invariant mass distribution of {\em any} pair of
opposite sign, same flavor leptons for both signal and $WZ$
background.  The signal point has $M_0=700$ GeV, $M_{1/2}=160$ GeV and
$\tan\beta=5$, which results in $m_{\tilde\chi_1^{\pm}}\simeq
m_{\tilde\chi_2^0}\simeq122$ GeV. The leptons are required to pass the
set of cuts from Ref.~\cite{BK}: $p_T(\ell)>\{11,7,5\}$ GeV, central
lepton with $p_T>11$ GeV and $|\eta|<1.0$, $\rlap{\,/}E_T>25$ GeV and
$|m_{\ell^+\ell^-}-M_Z|>10$ GeV.  The histograms are normalized to the
respective cross section.

Even with the modeling of the $Z$-width effect, we caution that the
$WZ$ simulation in PYTHIA is still not realistic, since the
$W\gamma^*$ contribution is neglected. It results in a peak at low
invariant mass, and the resulting distribution is markedly different
from the result shown in Fig.~\ref{inv mass}. We anticipate that it
will be necessary to cut away {\em all} events on the low-end of the
dilepton invariant mass distribution. We therefore always apply the
cut $|m_{\ell^+\ell^-}|>11$ GeV for all three channels. This cut also
helps in eliminating background lepton pairs from Drell-Yan, as well
as $J/\psi$ and $\Upsilon$ decays.

Since recent trilepton analyses of the Tevatron reach \cite{BPT,BK}
use ISAJET for the simulation, they underestimate the trilepton
background.  As a result, we find a significantly reduced Tevatron
reach. However, in some cases we can employ an invariant mass cut
which will substantially reduce the $WZ$ background with no
significant loss of signal.  The signal distribution in Fig.~\ref{inv
mass} has a sharp kinematic cut-off at around
$m_{\tilde\chi_2^0}-m_{\tilde\chi_1^0}\sim
m_{\tilde\chi^{\pm}_1}/2\sim 60$ GeV, and we can exploit this feature
to increase signal-to-noise. Indeed, by applying the more stringent
cut $m_{\ell^+\ell^-}>m_{\tilde\chi^{\pm}_1}/2 \sim 60$ GeV, we can
eliminate most of the off-shell $Z$ events, at almost no cost to
signal. This is why in addition to standard $Z$-mass window cuts we
consider four dilepton mass cuts which eliminate {\em all} events
above a given invariant mass value. Also notice that only a very small
fraction of signal events have invariant dilepton masses between 0 and
11 GeV, so that the low-end invariant mass cut $m_{\ell^+\ell^-}>11$
GeV is quite efficient in improving $S/\sqrt{B}$.  Our discussion of
the $WZ$ background can be similarly applied to the less serious, but
nevertheless non-negligible $ZZ$ background.

The second largest background to the 3L channel is from dilepton
$t\bar{t}$ events, where there happens to be a third isolated lepton
from a $b$-jet. This background is most easily suppressed by a jet
veto.

Finally, the remaining 3L background one should worry about is $Z$-jet
production. In this case part of the background is due to events where
a jet fakes a lepton. Monte Carlo simulations, especially with a
simplified detector simulation like SHW, cannot give a reliable
estimate of this background.  In order to estimate the fake rate one
has to understand the details of the detector response as well as the
jet fragmentation. Only with Run II data will one be able to obtain a
good estimate. For our study we follow a procedure which makes use of
Run I data. It was used in Ref.~\cite{JN} to study the $W+{\rm jets}$
background to the 2L channel (see the next subsection).

\subsection{Backgrounds to the like-sign dilepton channel}\label{sec:2L}

We now discuss the backgrounds to the 2L channel.  Ref.~\cite{JN}
observed that it can be advantageous to not require the odd-sign
lepton in the 3L events due to the gain in signal acceptance. At the
same time, events with two like-sign leptons are still quite rare at
the Tevatron, so the 2L channel was suggested as a possible
alternative to 3L for SUSY searches in Run I. However, the rates for
the relevant diboson backgrounds were somewhat underestimated, since
ISAJET was used for the simulation.  Here we are interested in
determining whether the 2L channel will be useful in the larger
background environment of Run II.

We first do a back-of-the-envelope comparison of the $WZ$ backgrounds
for the 3L and 2L channels. After not requiring the odd-sign lepton,
one is left with the choice of {\em vetoing} that lepton. In the case
of a veto, we find for the relative size of the two backgrounds
\beq
{\sigma_{WZ}({\rm 2L}) \over \sigma_{WZ}({\rm 3L})}\simeq
{2\varepsilon_l (1-\varepsilon_l) +0.35\varepsilon_\tau \left[
0.65+0.35(1-\varepsilon_\tau) \right] \over
2\varepsilon_l^2\varepsilon_Z + 0.35^2\varepsilon^2_\tau} \sim
{1-\varepsilon_l \over\varepsilon_l\varepsilon_Z},
\label{2L/3L veto}
\eeq
where $\varepsilon_l$ is the acceptance for leptons coming directly
from $W$ or $Z$ decays, $\varepsilon_\tau$ is the acceptance for the
(usually softer) leptons coming from leptonic tau decays, and
$\varepsilon_Z$ is the efficiency of the $Z$-window invariant mass
cut: $|m_{\ell^+\ell^-}-M_Z|>10$ GeV (we have neglected its effect on
the {\em irreducible} background component). We find from Monte Carlo
that the typical Run II values for these efficiencies in $WZ$
production are $\varepsilon_l\sim 0.60$, $\varepsilon_\tau\sim 0.46$
and $\varepsilon_Z\sim 0.10$.  Plugging into Eq.~(\ref{2L/3L veto}),
we find for the ratio 6.3, which agrees reasonably well with the
result 5.8 from our full Monte Carlo simulation. For the signal point
shown in Fig.~\ref{inv mass} we find $\varepsilon_l=0.62$ and
$\varepsilon_Z=0.99$ and the corresponding ratio is \beq
{\sigma_{signal}({\rm 2L}) \over \sigma_{signal}({\rm 3L})}\simeq
{1-\varepsilon_l \over\varepsilon_l\varepsilon_Z}\sim 0.6.  \eeq This
reveals that vetoing the third lepton is definitely not a good idea.
In comparison to the 3L channel, the signal goes down, while the major
background component is increased almost 6 times!

We therefore only consider the {\em inclusive} 2L channel, where we do
not have any requirements on the third (odd-sign) lepton, just as in
Ref.~\cite{JN}. In this case, the signal acceptance is definitely
increased. Unfortunately, the corresponding increase in the background
is even larger than before: \beq {\sigma_{WZ}({\rm 2L}) \over
\sigma_{WZ}({\rm 3L})}\simeq {2\varepsilon_l
(1-\varepsilon_l+\varepsilon_l\varepsilon_Z) +0.35\varepsilon_\tau
\over 2\varepsilon_l^2\varepsilon_Z + 0.35^2\varepsilon^2_\tau} \sim
7.3
\label{2L/3L}
\eeq for the typical values of the efficiencies. We can see
immediately that the 2L channel can compete with the 3L on the basis
of $S/\sqrt{B}$ only if the lepton acceptance for the signal is less
than $1/\sqrt{7.3}\sim 37\%$. However, for typical values of the SUSY
model parameters the lepton acceptance is much higher.

To make matters worse, the 2L channel suffers from a potentially large
new source of background: $W+$jet production where the jet fakes a
lepton.  Although the rate for a jet faking a lepton is quite small,
on the order of $10^{-4}$, the large $W+$jet cross section results in
a major background for the 2L channel. As we mentioned earlier, the
best way to estimate this background is from data, since Monte Carlo
simulations are not reliable for fakes. In our analysis we shall
follow the procedure of Ref.~\cite{JN}, where the rate for observing
an isolated track which would otherwise pass the lepton cuts was
measured in the Run I $Z+$jet event sample.  This rate was then
multiplied by the probability that, given an isolated track, it would
fake a lepton. This probability was measured in Run I minimum bias
events to be $\sim 1.5\%$, independent of $p_T$ \cite{JN}. In our
study we first simulate with Monte Carlo the $p_T$ distribution of
isolated tracks in $W$ and $Z$ production, which is shown in
Fig.~\ref{pT_iso}. In this figure we plot the isolated track $p_T$
distribution corresponding to the 2L background, i.e. we combine a
real lepton with $p_T>11$ GeV and $|\eta|<2$ with a same sign isolated
track with $|\eta|<2$. Hence, the 2L background cross section is
obtained by multiplying the cross section from Fig.~\ref{pT_iso} by
the probability that an isolated track will fake a lepton. We see that
the background from fakes falls extremely fast with $p_T$, so a larger
$p_T$ requirement will substantially suppress it.
\begin{figure}[t]
\centerline{\psfig{figure=fig_pt_iso.ps,height=3.5in}}
\begin{center}
\parbox{5.5in}{
\caption[] {\small $p_T$ distribution of isolated tracks in (a)
$W+$jet production and (b) $Z+$jet production. The isolated tracks
have $I<2$ GeV and are outside the $\Delta R=0.7$ cone around any
jet. The events in the distributions potentially contribute to the 2L
background: they have one real lepton with $p_T>11$ and $|\eta|<2$ and
one same sign isolated track with $|\eta|<2$.
\label{pT_iso}}}
\end{center}
\end{figure}

We normalize the isolated track rate to data. Using the measured 1.5\%
fake rate per isolated track, we find 1.5 fb of cross section when
running the simulation at $\sqrt{s}=1800$ GeV and using the set of
cuts from Ref.~\cite{JN}. This is half the cross section found in
Ref.~\cite{JN}. Hence, to match the data to PYTHIA/SHW we need to
double the isolated track rate obtained from Monte Carlo.

\subsection{Backgrounds to the dilepton plus tau jet channel}

The largest background to the 2L1T channel is Drell-Yan \cite{LM},
where the tau jet is a fake. As it turns out, SHW does quite a good
job in simulating the fake tau rate \cite{fake taus}, so we can safely
rely on the Monte Carlo for this background.  We shall not further
discuss the backgrounds to the 2L1T channel; we refer the interested
reader to Refs.~\cite{LM,Workshop report}.  We find a marginal increase
in the background rate here, due to the larger $\eta$ coverage used in
this analysis.

\subsection{Summary and discussion}\label{sec:summary}

In Table~\ref{Table_BG} we summarize our results for the
different backgrounds to the three channels.
\begin{table}[t!]
\centering
\renewcommand{\arraystretch}{1.5}
\begin{tabular}{||c||c|c||c|c||c||}
\hline\hline
Process    &       3L         &  \cite{BK}
             &        2L        &  \cite{JN}
               &        2L1T        \\ \hline
           &                  &
             & $E=2$ TeV      &  $E=1.8$ TeV
               &                 \\
           &                  &
             & $|\eta(\ell)|<2$  &  $|\eta(\ell)|<1$
               &                 \\  \hline\hline
$ZZ$       & 0.21  $\pm$ 0.01 & 0.04
             & 1.836 $\pm$ 0.006 & 0.1 $\pm$ 0.01
               & 0.372 $\pm$ 0.003                  \\ \hline
$WZ$       & 1.39  $\pm$ 0.01 & 0.40
             & 8.79 $\pm$ 0.03 & 1.1 $\pm$ 0.02
               & 1.36  $\pm$ 0.01                   \\ \hline
$WW$       & 0.009 $\pm$ 0.003& ---
             & 0.002 $\pm$ 0.001 & 0   $+$ 0.02
               & 0.54  $\pm$ 0.02                   \\ \hline
$t\bar{t}$ & 0.33  $\pm$ 0.01 & 0.14
             & 0.21 $\pm$ 0.01 & 0   $+$ 0.02
               & 1.64  $\pm$ 0.03                   \\ \hline
$Z+$jet     & 0.13 $\pm$ 0.01  & ---
             & 3.58 $\pm$ 0.05 & 1.1 $\pm$ 0.1
               & 11.3 $\pm$ 0.6                         \\ \hline
$W+$jet     &        ---       & ---
             & 10.5 $\pm$ 0.2  & 3.0
               & ---                         \\ \hline\hline
total      & 2.07 $\pm$ 0.02  & 0.58
             & 24.9 $\pm$ 0.2    & 5.6
               & 15.2 $\pm$ 0.6                         \\ \hline\hline
\end{tabular}
\parbox{5.5in}{
\caption{ Background cross sections after cuts (in fb) for the three
channels, each with a set of cuts described in the text.  All errors
are statistical.  We also list the 3L background found in
Ref.~\cite{BK} and the 2L background found in Ref.~\cite{JN}.
\label{Table_BG}}}
\end{table}

The results are presented for a standard choice of cuts in each case.
For the 3L channel, we pick the set of cuts from Ref.~\cite{BK}:
$p_T(\ell)>\{11,7,5\}$ GeV, central lepton with $p_T>11$ GeV and
$|\eta|<1.0$, $\rlap{\,/}E_T>25$ GeV, $|m_{\ell^+\ell^-}-M_Z|>10$ GeV, and no
$|\Delta\varphi|$ or JV cuts.  For the 2L channel we use the following
cuts from Ref.~\cite{JN}: $p_T(\ell)>\{11,11\}$ GeV,
$|m_{\ell^+\ell^-}-M_Z|>10$ GeV, and no $\rlap{\,/}E_T,\ |\Delta\varphi|$ or JV
cuts. Here we require both leptons to have $|\eta|<2.0$, whereas
Ref.~\cite{JN} requires $|\eta|\lower.7ex\hbox{$\;\stackrel{\textstyle<}{\sim}\;$} 1$. Finally, for the 2L1T channel
we use the cuts $p_T(\tau)>15$ GeV, $|\eta(\tau)|<1.5$,
$p_T(\ell)>\{8,5\}$ GeV, $|\eta(\ell)|<2.0$,
$|m_{\ell^+\ell^-}-M_Z|>10$ GeV, $\rlap{\,/}E_T>20$ GeV, and no JV, from
Ref.~\cite{LM}. All errors in the table are statistical.

Comparing to Refs.~\cite{BK,JN} we see a significant increase in the
$WZ$ and $ZZ$ backgrounds to both the 3L and 2L channels. In the 2L
case this is in part due to the larger $\eta$ coverage that we use, as
well as the higher center-of-mass energy. The remaining difference is
due to the lack of $Z$-tail effects in the ISAJET simulation. The $WZ$
background is almost as large as $W+$jet, which is not surprising
based on the estimate in Eq.~(\ref{2L/3L}) (compare the $WZ$
backgrounds to 3L versus 2L).  We remind the reader that our 2L
$W+$jet background has been normalized to the 2L $W+$jet background
from Ref.~\cite{JN}, so the difference in the $W+$jet background
seen in the table is due solely to the different tracking coverage
and center of mass energy.

In the 3L case, we find significantly larger backgrounds than
Ref.~\cite{BK}. In fact, we surmise that the lepton efficiency is
smaller in SHW than in the ISAJET detector simulation, and if one were
to take this into account the background differences would be even
larger. Part of the difference in the $WZ$ and $ZZ$ backgrounds is due
to the fact that PYTHIA gives a $\sim15\%$ larger diboson cross
section than ISAJET. However, the largest part of the difference in
the diboson background rates is due to the $Z$-width. Notice that with
the fake rate procedure discussed in Sec.~\ref{sec:2L} we are able to
obtain an estimate of the $Z+$jet trilepton background (where the jet
fakes a lepton). This background has not been taken into account in
previous studies.

We do not trust the Monte Carlo simulation to provide a reliable
estimate for the $W+$jet and $Z+$jet backgrounds where the jet gives
rise to a real isolated lepton. We expect these backgrounds to be
small, and we ignore them.

In the next section, we present results for the Tevatron reach in the
three channels in the minimal gravity-mediated SUSY breaking model.
In our simulations we use PYTHIA for the background estimates and
ISAJET for the signal.

\section{Discovery reach for gravity-mediated models} \label{sec:SUGRA}

We next discuss the discovery potential of the upgraded Tevatron in
the mSUGRA model. There are various SUSY production processes which
give rise to the lepton signals under consideration. The dominant
source of signal in most regions of parameter space is
$\tilde\chi_1^+\tilde\chi_2^0$ production. Other chargino/neutralino
and slepton production processes also contribute. Typically these
processes constitute a small fraction of the total signal cross
section, but in some regions of parameter space (e.g. large
$\tan\beta$, small $M_0$) they can dominate. We ignore the possibility
of small contributions from squark and gluino production processes.

We first review which parts of the mSUGRA parameter space are
accessible in Run II via the 3L signature. The
$\tilde\chi_1^+\tilde\chi_2^0$ production cross section depends
primarily on the chargino mass, and scales roughly as
$M_{1/2}^{-5.5}$. Therefore, at the Tevatron we can only explore
regions with small $M_{1/2}$, where the cross section is large. The
$\tilde\chi_1^+\tilde\chi_2^0$ production proceeds predominantly via
$s$-channel $W$-boson exchange. There is also destructive interference
from $t$-channel squark exchange. As a result, the
$\tilde\chi_1^+\tilde\chi_2^0$ cross section is slightly enhanced in
case of heavy squarks (i.e. at large values of $M_0$).

At large values of $M_0$ ($M_0\gsim700$ GeV) the sleptons are heavy
and the gauginos decay to three-body final states dominantly via real
(at large $M_{1/2}$) or virtual (small $M_{1/2}$) $W$- or $Z$-boson
exchange. In this case the reach is determined solely by the signal
production cross section.  At smaller values of $M_0$ the off-shell
slepton mediated decays destructively interfere with the gauge
mediated decays. At small values of $M_0$ ($M_0\lower.7ex\hbox{$\;\stackrel{\textstyle<}{\sim}\;$} M_{1/2})$
sleptons become lighter than the $\tilde\chi_1^+/\tilde\chi_2^0$ and
two-body decays to lepton final states open up. This enhances the
leptonic branching ratios of the gauginos and improves the Tevatron
reach. We illustrate these features in Fig.~\ref{br_frac_lowtb} where
we show the branching ratios\footnote{When we use the term `branching
ratios' in relation to a pair of particles, we mean a sum of products
of branching ratios. For example, if the two-body decays of
$\tilde\chi_1^+$ and $\tilde\chi_2^0$ are closed,
BR$(\tilde\chi_1^+\tilde\chi_2^0 \rightarrow 3L) \equiv \left[{\rm BR}
(\tilde \chi_1^+ \rightarrow \tilde \chi_1^0\ell^+\nu_\ell) + {\rm BR}
(\tilde \chi_1^+ \rightarrow \tilde \chi_1^0 \tau^ + \nu_\tau
\rightarrow \tilde\chi_1^0\ell^+ \nu_\ell\bar \nu_\tau \nu_\tau
)\right]\left[{\rm BR} (\tilde \chi_2^0 \rightarrow \tilde
\chi_1^0\ell^+\ell^-) + {\rm BR} (\tilde \chi_2^0 \rightarrow \tilde
\chi_1^0\tau^+\tau^- \rightarrow\right.$$ \tilde \chi_1^0 $
$\ell^+ \ell^- \bar\nu_\ell$ $\nu_\ell\bar\nu_\tau$
$\left.\nu_\tau)\right]$.}  of a chargino-neutralino pair into the 3L,
2L and 2L1T channels at an mSUGRA model point with $\tan\beta=5$,
$\mu>0$, $A_0=0$ and (a) $M_{1/2}=175$ GeV or (b) $M_{1/2}=250$ GeV.
We plot versus $m_{\tilde \tau_1}$ (bottom axis) or $M_0$ (top axis).
\begin{figure}[t]
\centerline{\psfig{figure=fig_br_tb5.ps,height=3.5in}}
\begin{center}
\parbox{5.5in}{
\caption[] {\small Branching ratios of a chargino-neutralino pair into
the 3L (solid), 2L (dash) and 2L1T (dot dot dash) channels versus the
lightest stau mass (bottom axis), or alternatively, versus $M_0$ (top
axis), with mSUGRA model parameters $\tan\beta=5$, $\mu>0$, $A_0=0$
and (a) $M_{1/2}=175$ GeV or (b) $M_{1/2}=250$ GeV. The arrows
indicate the chargino threshold $m_{\tilde\chi_1^\pm}=m_{\tilde
\tau_1}$. For the range of $M_0$ values shown the chargino mass
varies from 118 to 139 GeV in (a), and from 187 to 201 GeV in (b).
\label{br_frac_lowtb}}}
\end{center}
\end{figure}
Notice that because of the rather small value of $\tan\beta$, all
slepton flavors are practically degenerate.

In Fig.~\ref{br_frac_lowtb}(a) the chargino mass
$m_{\tilde\chi_1^\pm}$ is only about 120 GeV, so the two-body decay to
the $W$-boson is closed. If $M_0>92$ GeV the chargino decays are
three-body and the 2L and 3L channels have a larger branching ratio
than the 2L1T, roughly by a factor of two.  The dip in the leptonic
branching ratios near $m_{\tilde \tau_1}\sim 260$ GeV is due to
destructive interference between the $Z$ and $\tilde\ell$-mediated
graphs \cite{BR interference}. In the region $M_0<92$ GeV the two-body
decays to sleptons are open and quickly become dominant. But notice
that while $\tilde\chi_2^0$ can decay to all slepton flavors through
its bino component, $\tilde\chi_1^\pm$ decays dominantly to a stau,
since the chargino couplings to the right-handed sleptons are
proportional to the corresponding lepton masses. Hence, the branching
fraction of the 2L1T channel dominates the region $40\lower.7ex\hbox{$\;\stackrel{\textstyle<}{\sim}\;$} M_0\lsim90$
GeV. For $M_0\lsim40$ GeV the 2L1T branching ratio rapidly drops while
the 2L and 3L branching ratios increase and become dominant again, due
to two-body decays of $\tilde\chi^\pm_1$ to sneutrinos.

In Fig.~\ref{br_frac_lowtb}(b) the mass of $\tilde\chi_1^\pm$ is near
190 GeV and it is always above the $W$-boson threshold. If $M_0$ is
greater than about 400 GeV the $\tilde\chi_2^0$ is above the $Z$-boson
threshold, and in this region the branching ratios for the three
signatures are determined by the $W$- and $Z$-boson branching ratios
to leptons. In the region $M_0<150$ GeV the sleptons are lighter than
the chargino, and the two-body decay modes to sleptons greatly enhance
the leptonic branching fractions. The 2L1T channel does not become as
dominant because the chargino decays to quarks via an on-shell
$W$-boson.  The decrease in the leptonic branching ratios below
$M_0\simeq70$ GeV is as before due to two-body decays to sneutrinos.

In Fig.~\ref{br_frac_hightb} we show similar plots of the
branching fractions, but for $\tan\beta=35$.
\begin{figure}[t]
\centerline{\psfig{figure=fig_br_tb35.ps,height=3.5in}}
\begin{center}
\parbox{5.5in}{
\caption[] {\small The same as Fig.~\ref{br_frac_lowtb}, but for
$\tan\beta=35$. This time the chargino mass varies from
126 to 140 GeV (in (a)), and from 192 to 201 GeV (in (b)).
\label{br_frac_hightb}}}
\end{center}
\end{figure}
Many of the features seen in Fig.~\ref{br_frac_lowtb} are present here
as well. For example, in Fig.~\ref{br_frac_hightb}(a) we see the broad
region ($150\lower.7ex\hbox{$\;\stackrel{\textstyle<}{\sim}\;$} m_{\tilde \tau_1}\lower.7ex\hbox{$\;\stackrel{\textstyle<}{\sim}\;$} 400$ GeV) where the
destructive $Z$-$\tilde\ell$ interference severely diminishes the
branching ratios. And again we observe the $\tilde\chi_2^0\rightarrow
\tilde\chi_1^0 Z$ threshold in Fig.~\ref{br_frac_hightb}(b), near
$m_{\tilde \tau_1}=260$ GeV.  However, in this case the tau slepton is
significantly lighter than the first two generation sleptons. Hence,
the branching ratio to the three tau final state quickly approaches
100\% below the stau threshold, and the 2L1T branching ratio is large.
We also see that the 2L channel is competitive at small values of
$M_0$, and is preferred over 3L on the basis of branching ratio by a
factor of 2.8.

To summarize, we see that depending on the values of the mSUGRA
parameters, any of the three channels offers some promise to be
observed in Run II. In the rest of this section, we shall do a
comparative study of the three channels, accounting for all relevant
background processes and using a realistic detector simulation. We
shall not only update the existing 3L analyses with improved estimates
of the $WZ$, $ZZ$ and Drell-Yan background rates, but foremost we are
interested in evaluating the different prospects each channel can
offer. For example, we would like to see whether the 2L channel offers
reach beyond the 3L channel, or can cover regions where the 3L channel
is suppressed. Also, we want to determine the region of parameter
space where the 2L1T channel can offer an independent check of a
signal in one of the other channels.

The cut optimization procedure is an important ingredient in our
analysis. We show results for the reach with the optimal set of cuts,
determined independently at each point in SUSY parameter space. The
optimal set of cuts maximizes $S/\sqrt{B}$. We require the observation
of at least 5 signal events, and present our results as $3\sigma$
exclusion contours in the $M_0-M_{1/2}$ plane, for two representative
values of $\tan\beta$ -- 5 and 35. We fix $\mu>0$ and $A_0=0$.

In Fig.~\ref{m0mh_3L} we show the Tevatron reach in the 3L channel
\begin{figure}[t]
\centerline{\psfig{figure=fig_m0mh_3l.ps,height=3.5in}}
\begin{center}
\parbox{5.5in}{
\caption[] {\small Tevatron reach in the 3L channel for mSUGRA models
with $\mu>0$, $A_0=0$, and (a) $\tan\beta=5$ or (b) $\tan\beta=35$. We
show the reach with both a standard set of soft cuts \cite{BK}
(dashed, for large $M_0$ only), as well as with the optimal set of
cuts (solid) (see text).  The reach is shown for 30 ${\rm fb}^{-1}$,
10 ${\rm fb}^{-1}$ and 2 ${\rm fb}^{-1}$ total integrated luminosity
(from top to bottom).  The cross-hatched region is excluded by current
limits on the superpartner masses. The dot-dashed lines correspond to
the projected LEP-II reach for the chargino and the lightest Higgs
masses. In Fig.~(a) the left dotted line shows where
$m_{\tilde\nu_\tau}=m_{\tilde\chi_1^\pm}$ and the right dotted line
indicates $m_{\tilde\tau_1}=m_{\tilde\chi_1^\pm}$. In Fig.~(b) the
dotted lines show where $m_{\tilde e_R}=m_{\tilde\chi_1^\pm}$ (left)
and $m_{\tilde\tau_1}=m_{\tilde\chi_1^\pm}$ (right).
\label{m0mh_3L}}}
\end{center}
\end{figure}
with a standard set of soft cuts \cite{BK} (dashed lines, for large
$M_0$ only to prevent crowding), as well as with the optimal set of
cuts (solid). We show the expected reach for 2, 10 and 30 ${\rm
fb}^{-1}$ total integrated luminosity.  The cross-hatched region is
excluded by current limits on the superpartner masses and the
dot-dashed lines indicate the projected LEP-II reach for the chargino
and the lightest Higgs mass\footnote{It should be kept in mind that at
small $\tan\beta$ the Higgs mass is a sensitive function of
$\tan\beta$. For example, if the Higgs-boson is not discovered at
LEP-II, $\tan\beta=3$ will be excluded. The reach contours are much
less sensitive to $\tan\beta$.}.
In Fig.~\ref{m0mh_3L}(a) the left (right) dotted line marks the
$\tilde\nu_\tau/\tilde\chi_1^\pm$ ($\tilde\tau_1/\tilde\chi_1^\pm$)
mass threshold, while in Fig.~\ref{m0mh_3L}(b) the left (right) dotted
line marks the $\tilde e_R/\tilde\chi_1^\pm$
($\tilde\tau_1/\tilde\chi_1^\pm$) mass threshold.

Comparing to the results of Refs.~\cite{BPT,BK}, we see the Tevatron
reach indicated in Fig.~\ref{m0mh_3L} is greatly reduced, due to the
larger backgrounds found in our analysis. Even with optimized cuts our
results show a much smaller observable region. For example, using the
set of cuts of Ref.~\cite{BK} at $\tan\beta=35$ and $M_0=1$ TeV, our
results indicate that the region bounded by the 2 fb$^{-1}$ 3-$\sigma$
contour extends to $M_{1/2}=123$ GeV (or 136 GeV with optimal cuts),
whereas in Ref.~\cite{BK} the corresponding 5-$\sigma$ region extends
to 180 GeV. Similarly, their 30 fb$^{-1}$ 3-$\sigma$ contour extends
to $M_{1/2}=250$ GeV, while ours extends to $M_{1/2}=186$ GeV (198 GeV
with optimal cuts).

As expected, there is respectable reach beyond LEP-II at small values
of $M_0$ and $\tan\beta$, where the chargino and neutralino 2-body
decays to sleptons are open. As expected from
Fig.~\ref{br_frac_lowtb}(a), the Tevatron has no sensitivity beyond
LEP-II in the region $200\lower.7ex\hbox{$\;\stackrel{\textstyle<}{\sim}\;$} M_0\lsim400$ GeV. For large values of
$M_0$, where the leptonic decays of the gauginos are three-body, we
find some sensitivity for both values of $\tan\beta$. In this region
there is a clear benefit to using optimized cuts. At Run II (2
fb$^{-1}$), with the default set of cuts, only the region with small
$\tan\beta$, small $M_0$, and small $M_{1/2}$ can be explored beyond
LEP-II. With optimal cuts, we see at large $\tan\beta$ a
non-negligible region can be excluded beyond LEP-II. Looking beyond
Run II, we notice that at TeV33 (30 fb$^{-1}$) optimization can prove
equivalent to doubling and sometimes even tripling the total
integrated luminosity!  In Fig.~\ref{advantage} we
\begin{figure}[t]
\centerline{\psfig{figure=fig_del_lum.ps,height=3.5in}}
\begin{center}
\parbox{5.5in}{
\caption[] {\small The difference $\Delta L$ (in ${\rm fb}^{-1}$)
between the required total integrated luminosity for the optimal set
of cuts and the default set of cuts, for the 3L signal.  The three
(solid) contours correspond to (from top to bottom) $\Delta L = 30,
10$ and 2 ${\rm fb}^{-1}$.  The dotted lines indicate the optimal-cut
30 ${\rm fb}^{-1}$ reach contours from Fig.~\ref{m0mh_3L}.
\label{advantage}}}
\end{center}
\end{figure}
show the difference in the required luminosity when using the fixed
set of cuts from \cite{BK} and the optimized cuts.  As a guideline, we
also show the 30 ${\rm fb}^{-1}$ optimal-cut contours (dotted lines) from
Fig.~\ref{m0mh_3L}.

It is instructive to examine the optimized sets of cuts.  In
Fig.~\ref{best cuts 1} (Fig.~\ref{best cuts 2}) we show the optimal
sets of cuts for the 3L channel in the $M_0$, $M_{1/2}$ plane, for
$\tan\beta=5$ ($\tan\beta=35$).
\begin{figure}[t]
\centerline{\psfig{figure=fig_bc_3t5.ps,height=4.5in}}
\begin{center}
\parbox{5.5in}{
\caption[] {\small The optimal sets of 3L cuts in the $M_0,\ M_{1/2}$
plane, for $\tan\beta=5$.  The key indicates which symbols correspond
to which cuts (central lepton rapidity, $\rlap{\,/}E_T$, invariant mass,
$\Delta\varphi$, and $P_T$ cuts) (see text). The dotted line indicates
the optimal-cut 30 ${\rm fb}^{-1}$ reach contours from
Fig.~\ref{m0mh_3L}.
\label{best cuts 1}}}
\end{center}
\end{figure}
\begin{figure}[t]
\centerline{\psfig{figure=fig_bc_3t35.ps,height=4.5in}}
\begin{center}
\parbox{5.5in}{
\caption[] {\small Same as Fig.~\ref{best cuts 1}, with $\tan\beta=35$.
\label{best cuts 2}}}
\end{center}
\end{figure}
We use the following notation to describe the set of cuts at each
point. The central symbol is the number of the $p_T$ cut according to
Table~\ref{pt cuts}.  The left superscript indicates which central
lepton $\eta$ cut was chosen, either $|\eta|<1.0$ (labeled ``10'') or
$|\eta|<1.5$ (``15''). A left subscript denotes the type of
$|\Delta\varphi|$ cut: for the two highest $p_T$ opposite sign, same
flavor leptons the $|\Delta\varphi|<2.5$ cut is indicated by ``2'',
the $|\Delta\varphi|<3.0$ cut by ``3'', and no symbol indicates no
$|\Delta\varphi|$ cut. The cut $|\Delta\varphi|<2.5$ for {\em any}
pair of opposite sign, same flavor leptons is indicated by ``a''.  The
right superscript shows the $\rlap{\,/}E_T$ cut: $\rlap{\,/}E_T>\{15,20,25\}$ GeV
(``15'',``20'',``25''), or no cut (no symbol).  A right subscript
denotes the dilepton invariant mass cut:
$|m_{\ell^+\ell^-}-M_Z|>\{10,15\}$ GeV (``10'',``15'') or
$|m_{\ell^+\ell^-}|<\{50,60,70,80\}$ GeV
(``50'',``60'',``70'',``80''). And finally, a tilde over the central
symbol indicates that the luminosity limit came from requiring 5
signal events rather than $3\sigma$ exclusion.

The jet veto cut is not indicated on the figures. However, except for
one point at large $\tan\beta$ the jet veto was never selected as an
optimal cut. Indeed, the major 3L background events (from WZ) are just
as likely to contain extra jets as the signal.

There are several lessons to be drawn from Figs.~\ref{best cuts 1} and
\ref{best cuts 2}. As expected, in those cases where the signal is
strong and dominates over the background (typically for small
$M_{1/2}$ or small $M_0$), softer cuts are beneficial.  Indeed, the
majority of the points which can be discovered with 5 signal events,
have selected $p_T$ cut ``1'', which is the most lenient set of $p_T$
cuts. For larger values of $M_{1/2}$, where the background is more
important, harder cuts on the lepton $p_T$'s are preferred. In fact,
we see that in the region of interest for TeV 33 at large $M_0$, the
hardest $p_T$ cuts we consider (from Ref.~\cite{BPT}, indicated by
``5''), often work best.

Figs.~\ref{best cuts 1} and \ref{best cuts 2} clearly indicate the
advantage of the invariant mass cuts introduced in
Section~\ref{sec:analysis}. Of all the points on the plots where the
background is an issue, there are only a few at which a conventional
$Z$-mass window cut is optimal. In all other cases it is advantageous
to cut all events with invariant dilepton masses above a certain
threshold.  Notice also how the value of the threshold tends to
increase with increasing $M_{1/2}$. This is expected because the sharp
edge in the signal distribution is roughly at $0.4\cdot M_{1/2}$
(see Fig.~\ref{inv mass}).

We also see from the figures that a missing $E_T$ cut is preferred
essentially everywhere in parameter space. However, a soft $\rlap{\,/}E_T$ cut
($\rlap{\,/}E_T>15$ GeV) often gives the better reach. The latest trilepton
analyses \cite{BPT,BK} have chosen to {\em increase} the $\rlap{\,/}E_T$ cut
from its nominal Run I value of 20 GeV to 25 GeV.  Our results suggest
that in the off-line analysis one is better off with a lower $\rlap{\,/}E_T$
cut. However, more work is needed to conclusively determine what the
best $\rlap{\,/}E_T$ cut will be in the actual analysis. For example, triggering
and energy mismeasurement issues will have to be carefully taken into
account.

Lastly, in the great majority of parameter space it is better not to
require a $\varphi$ cut.

Looking back at Fig.~\ref{m0mh_3L}(a), we observe that near the
slepton-chargino mass thresholds the reach becomes diluted. This
effect can easily be overlooked, since it only shows up very close to
threshold.  We find that it is entirely due to the suppressed signal
acceptance.  Indeed, although the branching ratio is increased
immediately below threshold, the lepton resulting from the
$\tilde\chi_2^0\rightarrow \tilde \ell^\pm \ell^\mp$ decay tends to be
very soft and it can fail the analysis cuts.

We next discuss the prospects for the 2L channel. In
Fig.~\ref{m0mh_2L} we show the 2L channel reach for the Tevatron.
\begin{figure}[t]
\centerline{\psfig{figure=fig_m0mh_2l.ps,height=3.5in}}
\begin{center}
\parbox{5.5in}{
\caption[] {\small The same as Fig.~\ref{m0mh_3L}, for the 2L channel.
The dashed lines correspond to a set of cuts from Ref.~\cite{JN}.
The 2, 10 and 30 fb$^{-1}$ reach contours are plotted.
\label{m0mh_2L}}}
\end{center}
\end{figure}
Due to the much larger background the reach in the 2L channel is not
as great as in the 3L channel.
There is one important exception, however -- the 2L channel does not
lose sensitivity near the chargino-charged slepton threshold.  Indeed,
because of the Majorana nature of the neutralinos, in 50\% of the
events the lost soft lepton in the $\tilde\chi_2^0\rightarrow \tilde
\ell^\pm \ell^\mp$ decay is of the {\em opposite} sign as the charged
lepton from the chargino decay. The remaining two hard leptons are
then of the same sign and they are readily reconstructed. Therefore,
near the $\tilde\ell/\tilde\chi_1^\pm$ mass threshold, the 2L
channel may prove to be a valuable alternative to 3L.

Fig.~\ref{m0mh_3L}(b) reveals that at large $\tan\beta$ one starts to
lose 3L sensitivity in the small $M_0$ region, since the decays to tau
final states dominate.  In fact, for $M_0\lower.7ex\hbox{$\;\stackrel{\textstyle<}{\sim}\;$} 300$ GeV and
$\tan\beta=35$, we find no 3L reach in Run II beyond LEP-II. Only with
multiple years of running and collecting soft lepton events will the
Tevatron be able to start improving on the LEP mSUGRA bounds. One can
improve this situation by considering alternative signatures with tau
jets \cite{LM}. Of those, the 2L1T channel is singled out on the basis
of both sensitivity and statistical importance.

In Fig.~\ref{m0mh_2L1T} we show the Tevatron reach in the 2L1T channel.
\begin{figure}[t]
\centerline{\psfig{figure=fig_m0mh_2l1t.ps,height=3.5in}}
\begin{center}
\parbox{5.5in}{
\caption[] {\small The same as Fig.~\ref{m0mh_3L}, for the 2L1T
channel. In this case the optimal cuts yield very little improvement
relative to a default set of cuts from Ref.~\cite{LM} (listed in
Sec.~\ref{sec:summary}), so the contours corresponding to the default
cuts are not shown.
\label{m0mh_2L1T}}}
\end{center}
\end{figure}
In this case we compare the optimal reach to a set of cuts from
Ref.~\cite{LM} (listed in Sec.~\ref{sec:summary}). We find very little
difference between this fixed set of cuts and the optimal set, so we
do not show the fixed cut lines in the figure.

The 2L1T channel has no reach in the large $M_0$ region. However, when
the two-body decays to staus open up the 2L1T branching fraction is
larger than the other two channels, leading to some sensitivity. While
the region accessible in the 2L1T channel at small $\tan\beta$ is not
competitive with the 3L and 2L reach, it can improve the statistical
significance in case of exclusion, or it can serve as an important
confirmation and provide unique information about the model
parameters in case of discovery.  This channel offers the greatest
reach at large $\tan\beta$ (together with the related much cleaner
signature of two like-sign leptons plus a tau jet \cite{LM}) in the
small $M_0$ region.

\section{Conclusions} \label{sec:conclusions}

In this paper we studied three of the cleanest and most promising
channels for SUSY discovery at the Tevatron in Run II.  We revisited
the trilepton and like-sign dilepton analyses, improving them in
several key aspects. For example, we used a more realistic simulation
of the major backgrounds. We found larger backgrounds than previous
analyses. We used a procedure relying on Run I data to estimate
backgrounds involving fake leptons. And we introduced an invariant
mass cut which took advantage of a sharp edge in the signal dilepton
invariant mass distribution. This cut was generally more effective in
increasing signal-to-noise than the standard invariant mass cuts.
Also, we varied the cuts at each point in the supersymmetric parameter
space, and determined at each point the set of cuts which yields the
largest reach. We found that this cut optimization can significantly
enhance the Tevatron reach.  Lastly, we analyzed the reach of the 2L1T
channel.

If nature is supersymmetric at low energies, and the superpartners (in
particular the gauginos) are light, there is a good chance that the
Tevatron will discover them in its upcoming runs. However, the 3L
signature has limited reach, and we can improve the reach by
optimizing cuts and considering alternative clean signatures.

\section*{Acknowledgments}

We thank J.~Campbell, R.K.~Ellis, J.~Lykken, J.~Nachtman and F.~Paige
for useful discussions.  K.T.M. (D.M.P.) is supported by Department of
Energy contract DE-AC02-76CH03000 (DE-AC02-98CH10886).

{\em Note added:} We thank H.~Baer for providing us with a preliminary
version of a preprint by H.~Baer, M.~Drees, F.~Paige, P.~Quintana and
X.~Tata. This paper is an update of their previous study \cite{BPT} of
the reach of the Tevatron in the 3L channel. Part of the improvement
is the inclusion of the $Z$-width in the $WZ$ background determination.

\newpage

redpajama_set_name: RedPajamaArXiv


text:
Cleveland ist der Name folgender Townships in den Vereinigten Staaten:

in Arkansas:
 Cleveland Township (Clay County, Arkansas)
 Cleveland Township (Fulton County, Arkansas)
 Cleveland Township (Little River County, Arkansas)
 Cleveland Township (Lonoke County, Arkansas)
 Cleveland Township (Miller County, Arkansas)
 Cleveland Township (Ouachita County, Arkansas)
 Cleveland Township (Phillips County, Arkansas)
 Cleveland Township (White County, Arkansas)

in Indiana:
 Cleveland Township (Elkhart County, Indiana)
 Cleveland Township (Whitley County, Indiana)

in Iowa:
 Cleveland Township (Davis County, Iowa)
 Cleveland Township (Lyon County, Iowa)

in Kansas:
 Cleveland Township (Barton County, Kansas)
 Cleveland Township (Marshall County, Kansas)
 Cleveland Township (Stafford County, Kansas)

in Michigan:
 Cleveland Township (Michigan)

in Minnesota:
 Cleveland Township (Minnesota)

in Missouri:
 Cleveland Township (Missouri)

in Nebraska:
 Cleveland Township (Cuming County, Nebraska)
 Cleveland Township (Holt County, Nebraska)
 Cleveland Township (Knox County, Nebraska)

in North Carolina:
 Cleveland Township (Johnston County, North Carolina)
 Cleveland Township (Rowan County, North Carolina)

in North Dakota:
 Cleveland Township (North Dakota)

in Pennsylvania:
 Cleveland Township (Pennsylvania)

in South Dakota:
 Cleveland Township (Brule County, South Dakota)
 Cleveland Township (Edmunds County, South Dakota)
 Cleveland Township (Hamlin County, South Dakota)

redpajama_set_name: RedPajamaWikipedia


Tax slips were available for pick up at daycare as of February 11th. The remaining slips were mailed out the last week of February to all families who were unable to pick up their slip.
Our next PD day is on Friday, March 29th. A cultural grant has paid for us to have Leo Brooks from Treefrog Percussion come to teach us about drumming. We will have two workshops, Intro to Percussion and a Djembe Workshop. Registration forms will go out after March Break and the deadline to register will be March 22nd.


text:
Q: Back button url depending of previous page I have a single post page on wordpress which can be accessible from two archive page.
I put a back button on this single post page and I would like to change the url of the back button depending of the previous page. Also I would like to change the url to one of the two archive if the single post is open in a new window.
Any idea is welcome.
Thank you
Thomas

A: You could try this:
HTML:

PHP:
<?php
    if($_GET['button'] == "back"){
         header('Location: ' . $_SERVER['HTTP_REFERER']);
    }
?>

A: Thanks for your answer.
It works almost, I just have a problem with the English language when comes from the regular archive page, it always return the French page. Here my code :

         <?php $id = icl_object_id($post->ID, 'page',
false,ICL_LANGUAGE_CODE);

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if($_SERVER['HTTP_REFERER'] ==
"http://tmp.thomasdesnoyers.com/en/client/"):?>

            <input class="back-button"></input>

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elseif($_SERVER['HTTP_REFERER'] ==
"http://tmp.thomasdesnoyers.com/client/"):?>

            <input class="back-button"></input>

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elseif($_SERVER['HTTP_REFERER'] ==
"http://tmp.thomasdesnoyers.com/en/"):?>
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else:?>
    <a href="/#post-<?php echo $id; ?>">
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<?php endif; ?>

redpajama_set_name: RedPajamaStackExchange


text:
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Ocean Colour Remote Sensing in Polar Seas
Home » Groups » Ocean Colour Remote Sensing in Polar Seas
Dr. Marcel Babin
Canada Excellence Research Chair in "Remote Sensing of Canada's New Arctic Frontier"
Joint International Laboratory (Université Laval, Canada & CNRS, France), "Takuvik" (UMI 3376)
Université Laval, Québec, Canada
Email: marcel.babin@takuvik.ulaval.ca
Dr. Kevin Arrigo
Stanford University, CA
Email: arrigo@stanford.edu
Dr. Simon Bélanger
Université du Québec à Rimouski,
Email: simon_belanger@uqar.qc.ca
Scientific and programmatic background and rationale
Ocean colour remote sensing has often been used to study polar seas, especially in Antarctica where the optical properties of the upper ocean are not as complex as they are in the Arctic (e.g. Comiso et al. 1990, 1993, Sullivan et al. 1993, Arrigo et al. 1998, Stramski et al. 1999, Arrigo et al. 2008a). These data suggest that primary production in Antarctic waters has changed little over the last 14 years (Arrigo et al. 2008a). In contrast, spectacular impacts of climate change have been observed recently in the Arctic Ocean, including the receding of the summer ice cover by 30% over the last 3 decades (Comiso et al. 2008). It is predicted that it will disappear almost completely by the end of the current century (Holland et al. 2006, Serreze et al. 2007) and perhaps much earlier (Wand and Overland 2009). As a consequence of perennial ice receding, the pan-Arctic primary production, as well as the photooxidation of colored dissolved organic matter, seem to be increasing (Bélanger et al. 2006, Pabi et al. 2008, Arrigo et al. 2008b). The annual maximum phytoplankton biomass is now reached earlier in several Arctic seas (Kahru et al. 2010). As the extent of the seasonal ice zone will increase (difference between the annual maximum and minimum extents), ice-edge blooms may play an increasing role (Perrette et al. 2010).
The ongoing changes within the context of accelerating climate change call for a vastly improved understanding of the polar ecosystems based on an intensive observation program. In situ observations from ships are however inherently sparse in space and time, especially in the inaccessible Arctic Ocean. Ocean colour remote sensing is certainly one of the most appropriate tools to extensively monitor marine ecosystems, and it provides recurrent pan-Arctic and pan-Antarctic observations at relatively low cost.
The use of ocean colour remote sensing in polar regions is, however, impeded by a number of difficulties and intrinsic limitations including the prevailing low solar elevations, the impact of ice on remotely-sensed reflectance, the deep chlorophyll maximum (DCM), the peculiar phytoplankton photosynthetic parameters, the optical complexity of seawater especially over the Arctic shelves and, persistence of clouds and fog (click here for further details).
Minutes 1st WG Meeting (Nov 2011)
Minutes 2nd WG Meeting (Aug 2012)
Marcel Babin (Co-Chair) Université Laval, Quebec, Canada
Kevin Arrigo (Co-Chair) Stanford University, USA
Simon Bélanger (Co-Chair) Université du Québec à Rimouski, Canada
Joey Comiso NASA Goddard Space Flight Center, USA
Robert Frouin Scripps Institution of Oceanography, USA
Victoria Hill Old Dominion University, USA
Greg Mitchell Scripps Institution of Oceanography, USA
Don Perovich ERDC-CRREL, USA
Rick Reynolds Scripps Institution of Oceanography USA
Kai Sørensen Norwegian Institute for Water Research, Norway
Knut Stamnes Stevens Institute of Technology, USA
Menghua Wang NOAA NESDIS, USA
Toru Hirawake Hokkaido University, Japan
Review the current literature for the Arctic and Antarctic Oceans including: inherent and apparent optical properties, current ocean colour algorithms, photosynthetic parameters & primary production models, as well as impact of low Sun elevation, cloudiness and sea ice contamination on ocean colour remote sensing.
(Re)assess current ocean colour algorithms through intercomparisons, as well as the impact of the deep Chl maximum on primary production estimates though sensitivity analysis, the impact of cloudiness on products, and the current atmospheric correction schemes.
Document algorithms which can be successfully used in high latitude waters.
Make recommendations to space agencies and the scientific community on algorithm development and future research avenues.
Summarize the results and recommendations in an IOCCG report on the topic.
Ocean Colour Remote Sensing in Polar Seas2016-03-302017-04-25https://ioccg.org/wp-content/uploads/2016/05/logo-ioccg-website.pngIOCCGhttps://ioccg.org/wp-content/uploads/2016/05/logo-ioccg-website.png200px200px
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Fourth International Ocean Colour Science Meeting
The fourth International Ocean Colour Science (IOCS) meeting took place in Busan, South Korea from 9 to 12 April 2019, and was convened by the International Ocean Colour Coordinating Group (IOCCG), in partnership with, and thanks to sponsorship from the Korea Institute of Ocean Science and Technology (KIOST).
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Ocean-Colour News
This bulletin includes an announcement of the 2020 IOCCG Summer Lecture Series, new CDOM protocols, news from JAXA, NASA and NOAA, and new peer-reviewed publications.
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Calibration of Satellite Ocean-Colour Sensors