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    How Important Is To Know The Value Of The Top Quark Mass?
    By Tommaso Dorigo | October 1st 2010 03:18 PM | 8 comments | Print | E-mail | Track Comments
    About Tommaso

    I am an experimental particle physicist working with the CMS experiment at CERN. In my spare time I play chess, abuse the piano, and aim my dobson...

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    I will be attending next week to a conference in Split (Croatia). The conference is titled "LHC Days", and has the purpose of bringing together experimental physicists working at the main CERN experiments with theorists and experimentalists from all over the world, to discuss the current status and the future perspectives of research in particle physics, focusing of course on the Large Hadron Collider at CERN.

    I have been assigned a talk titled "Top Physics at the Tevatron", and I will therefore represent the CDF and DZERO collaborations and describe their results. It will be very interesting for me to inform my CMS colleagues about the newest experimental techniques  in use at the Tevatron to measure the properties of the top quark in hadronic collisions.

    As soon as I find some time, I will publish here a few of the slides of my talk, trying to explain them in simple terms. For the time being, let me just paste here the draft of one slide I consider important and of general interest: an explanation of why the top quark mass, now known with 0.67% accuracy thanks to the huge effort of the two experiments, may still provide additional crucial information on the fundamental theory of subatomic particles if its uncertainty is further reduced in the next few years.


    In a nutshell, the slide makes a few points about the importance of a precise measurement of the top mass. The simple-minded argument that the top mass is a decisive input in electroweak fits to Standard Model (SM) observables when the aim is a prediction of the unknown mass of the Higgs boson fails nowadays, since the top quark is already known with enough accuracy for that purpose, as compared to other SM parameters. You can observe it in the top right graph, where the horizontal axis describes the unknown Higgs boson mass, and the vertical axis the top quark mass. The blue oblong region is the area where the two parameters are bound to lay if we believe the measurement of all other electroweak observables. The green region instead includes in the fit the known value of the top mass, which is also shown as a light green horizontal band.

    As you can see, the inclusion of the top mass strongly constrains the allowed values of the top mass, precisely to lay within the two oval green regions. Note that the LEP II lower bound on the Higgs mass and the Tevatron excluded window between 156 and 173 GeV (shown in grey) significantly help reduce the extent of those regions (which would otherwise include the pink areas). Now, ask yourself the question: if we shrunk the top mass band to a narrow horizontal line, how much would the green areas shrink consequently ? The answer is, minimally! So a more precise top quark mass is not needed if all we want is to improve our indirect knowledge of the Higgs boson's mass.

    It turns out, however, that other EW parameters in the SM are still benefitting a lot from an increased precision in the mass of the top quark. This is shown in the figure on the lower right (which comes from a highly interesting, if not very recent, paper by S.Heinemeyer et al., hep-ph/0306181) which however is a bit too complicated for me to explain meaningfully in a few lines. Suffices to say that both for the Standard Model, and for most of the Beyond-the-Standard-Model scenarios, a better-known top mass remains highly desirable to this day!

    Comments

    just a quick comment: it's not the diagram with two Higgs external legs that matters for the Higgs mass.
    Rather, it's the one with four legs (hence four powers of m_{top} as you show) that corrects the quartic self-coupling that in turn fixes the Higgs mass.

    dorigo
    Thanks for the note BB. I believe you are right. If you can provide a quick source for that diagram I'll change my slide... I only have the single virtual top loop graph handy, and I am too lazy to cook up the one you mention !
    Cheers,
    T.
    Сonsider natural logarithms mass of quarks and explore them:

    Mu=1.5- 3 MeV; Md=3-7 MeV;

    lnMu=0.4-1.09; lnMd=1.09-1.94

    Ms=70-120 MeV; Mc=1160-1390 MeV;

    lnMs=4.24-4.78; lnMc=7.05-7.23

    Mb=4130-4270 MeV; Mt=170900- 177500MeV;

    lnMb=8.32-8.35; lnMt=12.04-12.08

    As we can see, natural logarithms of values of mass are as following (expressed in round numbers): 1;2;4;5;7;8;12. Note that numbers divisible by 3(3,6,9) are absent, except the last number N=12 . Why? It seems to me interesting question!
    Why log top-quark mass is an exception?

    Ratio 3:1?

    Bonny Bonobo alias Brat
    A skew in the 3 level, trigger selection system maybe?
    My latest forum article 'Australian Researchers Discover Potential Blue Green Algae Cause & Treatment of Motor Neuron Disease (MND)&(ALS)' Parkinsons's and Alzheimer's can be found at http://www.science20.com/forums/medicine
    You can live with your diagram, just assume the two extra Higgses (not shown) are at their VEVs giving the top its mass.

    Hi Verified,

    aha I see... Nice idea.
    Cheers,
    T.

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