Andrea Linville Office of Science, SULI Program 2009 Stanford Linear Accelerator August 13, 2009

 Objective  Standard Model  What is SUSY?  What will we calculate?  Results  The Future

 Use parton-model methods to predict the stop squark production cross- section in proton-proton collisions at LHC energies.

 Fermions (spin ½)  Bosons (integer spin) = force mediators  Elusive Higgs boson ◦ Generates masses of leptons and W, Z  SM is incomplete ◦ Dark matter? ◦ Hierarchy problem? ◦ Matter/antimatter imbalance?

 Each SM particle has a superpartner ◦ difference: ½ unit of spin  SM fermions → SUSY bosons  SM bosons → SUSY fermions  SUSY is a broken symmetry  Sparticle masses depend on SUSY breaking model (unknown)

. . Parton Distribution Functions (PDFs) .

Q μ = muon charge Q e = electron charge g L = x w – ½ g R = x w (x w = weak mixing angle) α = fine structure constant G F = Fermi coupling constant M Z = mass of Z boson Γ Z = decay width of Z boson

 Modifications made to equations: ◦ Replace electron charge with quark charge ◦ Separate components for:  u, c, t quarks (+2/3 charge)  d, s, b quarks (-1/3 charge) ◦ Sum over quark flavors

 Partons: quasi-free pointlike structures that make up hadrons  PDFs describe the probability density for finding a parton with a given fraction of the total momentum

 Convenient definitions: ◦ = Q : scattering energy/invariant mass of the products ◦ : proton center-of-mass energy (“machine” energy)  The equation we integrate:  Monte Carlo integration algorithm

 3 possible initial states: ◦. ◦ Each initial state needs a separate cross-section equation…

 but…

where α s = strong coupling constant m 1, m 2 = masses of produced squarks s = scattering energy

 was calculated to be 61.6 fb  Reminder: 1 barn = cm 2  Invariant dimuon mass: 500 GeV  This is the order of magnitude expected.

∘ Greater contribution from sea quarks as scattering energy increases ∘ At low energies, the sea quarks are confined within hadrons ∘ The probability densities of b and t were exactly zero at these energies

 Resonance at 91 GeV ±0.5, ≈ M Z (91.2 GeV)  Expected: 1fb at M =500 GeV  Calculated: 0.96 fb  Data taken every 1 GeV  Machine energy: 14 TeV (LHC)

 Maximum cross- section: 0.27 nb  More difficult to produce stops with increasing stop mass  We examined only leading order (LO) Feynman diagrams

 can be used to establish a lower bound on stop mass, once we have an experimental bound on σ  Similarly, if stops are observed, σ can determine stop particle masses  Our results are useful for: ◦ Interpreting data ◦ Preparing new experimental searches for SUSY

 My mentor, JoAnne Hewett  Tom Rizzo  Michael Peskin  Theory graduate students: John Conley, Randy Cotta, and Jamie Gainer

 S. Dawson, E. Eichten, and C. Quigg. “Search for supersymmetric particles in hadron-hadron collisions,” Physical Review D, vol. 31, no. 7, pp , 1 April  W. Beenakker, M. Krämer, T. Plehn, M. Spira, and P.M. Zerwas. “Stop Production at Hadron Colliders,” Nuclear Physics B, vol. 515, pp. 3-14,  M. Schott. “Z Boson Production at LHC with First Data,” The 2007 Europhysics Conference on High Energy Physics Journal of Physics, Conference Series 110,  Elsevier publishing, Physics Letters B, vol. 667, Issues 1-5, 18 September 2008.