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    What Is An Inverse Femtobarn?
    By Hank Campbell | May 27th 2011 11:56 AM | 3 comments | Print | E-mail | Track Comments
    About Hank

    I'm the founder of Science 2.0® and co-author of "Science Left Behind".

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    Since Science 2.0 first came online, we have been excited about the Tevatron in Illinois because, statistically, by 2011 the famous Fermi experiment in Batavia,IL would have accumulated 10 inverse femtobarns of data and that means the Higgs, if it exists, would be somewhere in there.  If it could be found.
     
    It was less of a big deal then because the LHC hype machine was still in full swing even though it had already been delayed.  Everyone expected that with its much greater luminosity the LHC would find the eponymous "God particle" (since, as Peter Higgs said, no one around him would allow it to be called "that God damn particle") before it mattered what the Tevatron found.   But things don't always go as planned, the LHC has suffered some setbacks, and Fermi is still in the running.

    Earlier this week, dual-experimental (both Fermi and the LHC) physicist Tommaso Dorigo posted a celebratory picture because they reached 11 inverse femtobarns at Fermi, and that just shortly after reaching 10 fb-1 in December, as Tommaso also discussed.    It led to the question again from people I talk with about just what an inverse femtobarn is.

    The story goes that in the early days of World War II, progress was moving steadily in nuclear research and two physicists needed to be able to describe the atomic nucleus of uranium.  The atomic nucleus of uranium is big - really big - compared to other atomic nuclei, maybe even 'as big as a barn' in the minds of zany scientists.   Regardless of their motivation, by 1943 'barn' entered the science lexicon and never left.

    But big in this case means small.   The cross-section of the uranium nucleus, that 'barn' unit, is 10−28 m2  and 'femto' means 10-15, a a thousandth of a millionth of a millionth.  So a femtobarn is 10-43 m2 (if meters are too big to use for such small numbers, try 10-39 cm2, but I doubt that helps) and inverse femtobarns are another exotic twist on an already arcane concept.

    The inverse femtobarn is how many particle collision events per femtobarn.    So if you want to run your experiment for a year, and your cross-sectional area is one femtobarn, you can get at least some basis for understanding these giant numbers.   The 'luminosity' of the collisions measured over this time is directly related to the collisions and luminosity is the number of particles for each area (let's say 1 femtobarn) per unit time (let's say 1 year)  times the opacity of the target, usually expressed in cm−2 s−1.    Luminosity is essentially number of collisions per cm2 and per second.

    Kate Metropolis at Stanford did a great example which stays in our barn motif:

    Imagine you throw enough tomatoes at a barn to get an average of two tomato hits per square foot. If the barn door is 10 feet by 15 feet, then the cross section for tomato-barn door interactions is 150 square feet, and the number of tomatoes that splat on the door is given by: 

    150 square feet x 2 tomatoes per square foot = 300 tomato interactions.

    In this case, what physicists call the integrated luminosity is 2 tomatoes per square foot (or, in physics jargon, 2 "inverse square feet").

    When Tommaso described the results of 10 inverse femtobarns in December, he wrote
    A mile-long stretch of sand, extending 100 meters into the land and with a depth of one meter, contains roughly the same number of sand grains as that number of collisions.
    and then also "the total mass of annihilated protons would just make a picogram of matter" so even small things can mean a big number - in this case some 160,000,000 collisions.

    If the Higgs boson exists and the Standard Model is correct and the Higgs has a mass of 120 GeV then, as he noted by example, 20,000 of those particles have already been created inside the Tevatron.   

    Finding them with a high degree of confidence is another matter and that is one of the reasons the LHC was created.

    Comments

    Thanks. I've always wondered what an inverse femtobarn was.

    The Stand-Up Physicist
    A femtobarn, the area, sounds huge to my ear. The Planck area used to make this expression dimensionless,

    turns out to be 2.6x10-70 m2. It takes another 27 orders of magnitude smaller play in my house. I gotta find really tiny cups to server anybody here.
    very interesting, would like to go on with this ......