Introduction to HEP
Thursday, 6 February 1997

Problem 1 (50%)

There are 4 experimentally observed conserved global symmetry quantum numbers which are not known to couple to a local gauge symmetry boson: these are baryon number (B), electron number (Le), muon number (Lµ), and tauon number (Lt). Experimental limits on very light gauge bosons coupling to B or Le are set by "5th force" experiments comparing the gravitational attraction between materials with different ratios of nucleons and electrons (e.g., see E.G. Adelberger, et al., Ann. Rev. Nucl. Part. Sci. 41 (1991) 269). Because muons and tau leptons decay, it is more difficult to set limits on gauge bosons coupling to Lµ or Lt. Use the agreement between the observed and theoretical values of the anomalous magnetic moment of the muon to set a limit on the coupling strength (i.e. aµ) of a gauge boson coupling to muon number for an exact unbroken U(1)Lµ gauge symmetry.

Problem 2 (Also 50%, but longer^†)

The CDF experiment has reported a "Measurement of Dijet Angular Distributions by the Collider Detector at Fermilab" in Physical Review Letters 77 (1996) 5336. The highest energy dijets are dominated by elastic quark-antiquark scattering, since gluons usually have lower momentum than the valence quarks. To make things simple, you can assume the quarks that scatter are of different flavours, and that they are scattering and not annihilating.¹ This assumption means that we can analyze the data in analogy to electron-muon scattering in the high energy limit, the only difference being the scattering is dominated by the strong interaction so that a² is replaced by .²

(a) Calculate and plot the expected distribution (1/N dN/dc) for scattering of of two point particles via a 1/r potential in the ultra high energy limit. Does your theoretical distribution agree with the observed data for M>625 GeV/c² from Figure 1 of the paper?

(b) Use the M>625 GeV data to set an upper limit on the size of fuzzy ball quarks.

(b) Use the M>625 GeV/c2 data to set a limit on a contact potential. Contact interactions are typically parameterized in an Eichten-Lane-Peskin 4-fermion form, assuming a_contact=1, giving . (Note: Assuming a_weak=1 for Fermi weak interaction theory would lead to an overestimate of the weak scale, so this usual assumption is potentially misleading.)

^†Although I originally did this problem at 1am with a broken pencil, a scrap of paper, and a screaming baby, I have since tuned up my answer with Maple and Excel. Consult with me if you have problems.

¹ Table 9.1 of "Collider Physics" by Barger & Phillips gives a listing of other possible processes.

² The factor of 2/9 is my evaluation of the colour factor by comparing Sections 9.3.1 and 5.2 of Barger & Phillips. I may be wrong, but you can assume I am right.