Problem sets Physics 245A winter 2006 ============================================= Note: the most recent is listed first. ============================================= ============================================= Problem set 6 This has two parts. Part one: due in class Tuesday Mar. 14 This is a little project to be done in your groups, i.e. there will be three instances of this. Select one physics question to which you would like to know the answer. Define the question as sharply as you can. Check that the answer is not already known! Outline your ideas for a research program (experimental, theoretical, or both) that could (in your lifetime) make progress toward an answer. Prepare a ten minute informal presentation to be made at our last class meeting. (Don't panic. I'm lot looking for or expecting something formal, elaborate, or polished---just some ideas to stimulate thinking and discussion.) Part two: Due 5 pm, Wednesday, Mar. 15 in my office. If I am not there, you can slide it under the door. Consider a plot (http://lifshitz.physics.ucdavis.edu/kiskis/phy245a_06/prob_jet.pdf) of d sigma/d E_T vs. E_T in various rapidity bins. This is from hep-ex/0011036. Carefully explain why the cross section falls with increasing rapidity at fixed p_T. This is not trivial. It involves kinematics and the qualitative features of the parton distribution functions. ============================================= Problem set 5 due Tuesday, Mar. 7 Consider an eP scattering experiment. The e beam has a fixed energy E_lab = 50 Gev. The hydrogen (proton) target is at rest in the lab. The scattered e's are detected in a spectrometer at a fixed lab angle theta=10 deg. Consider the counting rate as a function of the scattered e energy E'. Consider three cases: a) Imaginary point proton b) Imaginary soft proton with elastic scattering only c) Real proton with elastic and inelastic scattering In each case, make a plot of the counting rate vs. E' that is qualitatively correct. Explain the plots you draw. Show how each plot will change as theta is increased. (To do this problem, you will need to do or refer to actual calculations.) ============================================= Problem set 4 due at start of class Thursday, Feb. 23 1) A possible c \bar{c} wave function is ^1P_1 ("one P one"). What is the J^{PC} of this state? Roughly what do you expect for its mass relative to psi, chi, and psi'? What is the experimental status of this state? 2) What is the ILC and how does it relate to existing and planned high energy physics research program? 3) For e^+ e^- annihilation in colliding beam machines, the luminosity must be increased as $E_{cm}$ is increased. Explain. If a machine with E_{cm}=2 Tev were built, what would the luminosity have to be to keep the counting rate for off-resonance events proceeding via a virtual photon at LEP levels? 4) In the static limit (q_0 = 0), do the 3-dimensional fourier transform of the dipole form factor of eP elastic scattering to get the charge distribution. 5) Answer questions 10 and 11 from the questions for lecture 11. ============================================= Problem set 3 due at start of class Tuesday, Feb. 7 1) Give the color-flavor-spin wave function for the Sigma^{*-}(1385) J=3/2, J_3=1/2 2) Work out a prediction for the magnetic moment of the Sigma^{*-} in the J_3=3/2 state. Will this be difficult to measure? 3) Work out the Sigma-Lambda mass splitting. Give a physical explanation of the sign of the result. (Hint: What would happen if m_u=m_d=m_s?) This is a sensitive test of the quark model. Why is the Sigma_c - \Lambda_c$ splitting larger than the Sigma - Lambda splitting? ============================================= Problem set 2 due at start of class Tuesday, Jan. 31 Seven problems from other books on the sheet in the usual envelop. Also: An electric dipole moment 3-vector D is associated with a term -E.D in the Hamiltonian. E is the 3-vector of the electric field. In discussions of electric dipole moments in particle physics, it is usually assumed that D is proportional to the spin S. The justification is at the "What else could it be?" level. Does this really make sense? Does a classical electric dipole moment transform the same way under rotations and inversions (spatial O(3)) as angular momentum? Let |JM> be a state of definite J^2 and J_3 in the usual way. Assume that the electric dipole operator D transforms the same as a classical electric dipole. Use the transformation properties of the vector operator D and of the states |JM> under rotations and time reversal to show that = 0. (Note: In my method at least, this is a bit tricky.) Optional problems, recommended but not actually assigned: O1 Is a fun problem. You will meet few people who know the answer. O1) What is the Noether current associated with the boosts? What is the charge? What new information (i.e. in addition to what you know from symmetry under translations and rotations) is in the conservation of the associated charge? To keep this from getting to be a tedious mess, you can work it out for just a free, massive, scalar field. It comes out nice if expressed in terms of the stress energy tensor. O2) Questions 4, 5, and 6 of Lecture 4. ============================================= Problem set 1 due at start of class Tuesday, Jan. 24 Select one of the archives at www.arxiv.org (hep-th, hep-ph, hep-ex, or hep-lat) and send me an email with the identifier (e.g. hep-ex/0601001) of a paper that looks interesting to you. Include a couple sentences saying what you find interesting about it. Ho-Kim and Pham: problem 4.1 Martin and Shaw (handout): problems 3.2, 3.5 Considering just the effect of track curvature in the CMS detector magnetic field, about what is the minimum transverse momentum p_T that a particle needs to reach the muon chambers in the central part of the detector? A Higgs with mass 200 GeV is produced at rest in the CMS detector. It decays into two Zs that make an angle of pi/4 with the beam axis. One of the Zs decays into a muon pair with the muons parallel and anti-parallel to the direction of the parent Z. Consider the muon with the lower lab energy. What is its p_T in the lab? As projected on a plane perpendicular to the beam axis, what is its radius of curvature? Will that present any problem for the muon reaching the muon chambers? Very roughly what fraction of its energy does this muon lose in passing through the CMS hadron calorimeter? Clearly I'm not telling you everything you need to know about CMS. Part of the problem is to find the needed info. You will have to look it up or ask around. What is the decomposition of spin-1 X spin-1? In this decomposition, what is the state J=1 M=0? (include proper normalization.) Two spinless particles A and B scatter through the process A + B -> C -> A + B. What is the angular distribution for A in the final state if the spin of C is 0? 1? 2? What is the rank of SU(5)? How many generators does SU(5) have in addition to those of its SU(3)XSU(2)XU(1) subgroup? =============================================