Zooming in on the Higgs March 24, 2009Posted by dorigo in news, physics, science.
Tags: CDF, DZERO, Higgs boson, LEP, MSSM, standard model, supersymmetry, Tevatron, top quark, W boson
Yesterday Sven Heinemeyer kindly provided me with an updated version of a plot which best describes the experimental constraints on the Higgs boson mass, coming from electroweak observables measured at LEP and SLD, and from the most recent measurements of W boson and top quark masses. It is shown on the right (click to get the full-sized version).
The graph is a quite busy one, but I will try below to explain everything one bit at a time, hoping I keep things simple enough that a non-physicist can understand it.
The axes show suitable ranges of values of the top quark mass (varying on the horizontal axis) and of the W boson masses (on the vertical axis). The value of these quantities is functionally dependent (because of quantum effects connected to the propagation of the particles and their interaction with the Higgs field) on the Higgs boson mass.
The dependence, however, is really “soft”: if you were to double the Higgs mass by a factor of two from its true value, the effect on top and W masses would be only of the order of 1% or less. Because of that, only recently have the determinations of top quark and W boson masses started to provide meaningful inputs for a guess of the mass of the Higgs.
Top mass and W mass measurements are plotted in the graphs in the form of ellipses encompassing the most likely values: their size is such that the true masses should lie within their boundaries, 68% of the time. The red ellipse shows CDF results, and the blue one shows DZERO results.
There is a third measurement of the W mass shown in the plot: it is displayed as a horizontal band limited by two black lines, and it comes from the LEP II measurements. The band also encompasses the 68% most likely W masses, as ellipses do.
In addition to W and top masses, other experimental results constrain the mass of top, W, and Higgs boson. The most stringent of these results are those coming from the LEP experiment at CERN, from detailed analysis of electroweak interactions studied in the production of Z bosons. A wide band crossing the graph from left to right, with a small tilt, encompasses the most likely region for top and W masses.
So far we have described measurements. Then, there are two different physical models one should consider in order to link those measurements to the Higgs mass. The first one is the Standard Model: it dictates precisely the inter-dependence of all the parameters mentioned above. Because of the precise SM predictions, for any choice of the Higgs boson mass one can draw a curve in the top mass versus W mass plane. However, in the graph a full band is hatched instead. This correspond to allowing the Higgs boson mass to vary from a minimum of 114 GeV to 400 GeV. 114 GeV is the lower limit on the Higgs boson mass found by the LEP II experiments in their direct searches, using electron-positron collisions; while 400 GeV is just a reference value.
The boundaries of the red region show the functional dependence of Higgs mass on top and W masses: an increase of top mass, for fixed W mass, results in an increase of the Higgs mass, as is clear by starting from the 114 GeV upper boundary of the red region, since one then would move into the region, to higher Higgs masses. On the contrary, for a fixed top mass, an increase in W boson mass results in a decrease of the Higgs mass predicted by the Standard Model. Also note that the red region includes a narrow band which has been left white: it is the region corresponding to Higgs masses varying between 160 and 170 GeV, the masses that direct searches at the Tevatron have excluded at 95% confidence level.
The second area, hatched in green, is not showing a single model predictions, but rather a range of values allowed by varying arbitrarily many of the parameters describing the supersymmetric extension of the SM called “MSSM”, its “minimal” extension. Even in the minimal extension there are about a hundred additional parameters introduced in the theory, and the values of a few of those modify the interconnection between top mass and W mass in a way that makes direct functional dependencies in the graph impossible to draw. Still, the hatched green region shows a “possible range of values” of the top quark and W boson masses. The arrow pointing down only describes what is expected for W and top masses if the mass of supersymmetric particles is increased from values barely above present exclusion limits to very high values.
So, to summarize, what to get from the plot ? I think the graph describes many things in one single package, and it is not easy to get the right message from it alone. Here is a short commentary, in bits.
- All experimental results are consistent with each other (but here, I should add, a result from NuTeV which finds indirectly the W mass from the measured ratio of neutral current and charged current neutrino interactions is not shown);
- Results point to a small patch of the plane, consistent with a light Higgs boson if the Standard Model holds
- The lower part of the MSSM allowed region is favored, pointing to heavy supersymmetric particles if that theory holds
- Among experimental determinations, the most constraining are those of the top mass; but once the top mass is known to within a few GeV, it is the W mass the one which tells us more about the unknown mass of the Higgs boson
- One point to note when comparing measurements from LEP II and the Tevatron experiments: when one draws a 2-D ellipse of 68% contour, this compares unfavourably to a band, which encompasses the same probability in a 1-D distribution. This is clear if one compares the actual measurements: CDF (with 200/pb of data), DZERO (with five times more statistics), LEP II (average of four experiments). The ellipses look like they are half as precise as the black band, while they are actually only 30-40% worse. If the above is obscure to you, a simple graphical explanation is provided here.
- When averaged, CDF and DZERO will actually beat the LEP II precision measurement -and they are sitting on 25 times more data (CDF) or 5 times more (DZERO).