name: group:

Exercise Sheet 8 – Particle Physics – WS 2012/13

hand in: Tuesday, December 11, 2012 (after the lecture) or till 4pm at the secretariat INF 226, 3.104

8.1 tt¯ production at the Tevatron and the LHC (7 points) The Tevatron collider was running until 2011 and collided protons with antiprotons at a centre of mass energy √s = 1.96 TeV. The LHC collides proton with protons, ultimately at √s = 14 TeV. These two machines are the only ones powerful enough to produce real top - antitop quark pairs. a) Draw the leading order parton level Feynman diagrams for tt¯ production. b) What momentum fractions x1 and x2 do the partons involved in the reaction need in order to produce a tt¯ pair at rest at the Tevatron and at the LHC? c) Go to http://hepdata.cedar.ac.uk/pdf/pdf3.html and plot the parton density func- 2 2 tions at the appropriate scale (Q = (2mt ) ). (Use HERAPDF as group and HERAPDF01 as set; note that the plotted parton density function is scaled with x). d) Use the parton density functions, the different colliding particles and the x values calculated to deter- mine the two most relevant contributions amongst the various Feynman diagrams and initial partons at the Tevatron and the LHC. e) Is the tt¯ pair production cross-section higher at the LHC or at the Tevatron?

8.2 Magnetic moment of the proton and the neutron (7 points) Using the proton wave funtion from the lecture, a) Perform an ”isospin-reflection” to obtain the corresponding wave function for the neutron. b) Determine the ratio between the neutron and proton magnetic moments and compare your result with the experimental value. Hint: The magnetic moments of baryons can be obtained by combining the Dirac-moments of the involved quarks (keep in mind the quark charges). Thus all that is needed is adding the quark moments with the correct sign in the absolute-squared baryon wave function. Assume isospin symmetry (mu = md). c) Use the measured value of the proton magnetic moment to obtain an estimate of the quark mass (again assuming isospin symmetry).

8.3 Isospin (6 points) a) The isospin of a meson is defined by the isospin of its quark content. Look up the quark content of the K∗(892) meson (http://pdg.lbl.gov/2012/listings/rpp2012-list-K-star-892. + pdf) and derive its total isospin I and the third component I3. What is the I,I3 > composition of the π 0 | + and the π meson? Exploit this information to derive I,I3 > of the missing particle in the possible K | ∗ decays listed below.

1 + + K∗ ? + π → + 0 K∗ ? + π . → b) What is the ratio between the decay rates of the above channels. (Hint: Compare the Glebsh-Gordan coefficients for the possible decays)

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