Radiative Corrections for the LHC: 1. Advanced School
Contents of the lectures at the Advanced School

Andreas Nyffeler and V. Ravindran  (2 + 2 lectures)
 
Title:  Basics of QCD corrections for hadron colliders 

  • Basics of QCD, ultraviolet (UV) divergences and dimensional regularization of UV divergent integrals, Passarino-Veltman reduction of tensorial integrals in n-dimensions.
  • UV renormalization of fields and strong coupling constant, alpha_s evolution and asymptotic freedom.
  • QCD improved parton model, soft and collinear divergences in QCD, mass factorisation.
  • Explicit computation of next to leading order QCD contributions to resonant production of a scalar particle at hadron colliders and uncertainties resulting from renormalization and factorization scales.

 
References:

  1. R.D. Field, Applications of perturbative QCD, Addison-Wesley, 1989
  2. K. Ellis, W.J. Stirling, B.R. Webber, QCD and Collider Physics, Cambridge University Press, 1991
  3. T. Muta, Foundations of Quantum Chromodynamics, World-Scientific, 1998
  4. G. Sterman, An introduction to quantum field theory, Cambridge University Press, 1993

 
Suvrat Raju  (2 lectures)
 
Title: On-shell methods in Quantum Field Theory for tree-amplitudes

  • Introduction to helicity amplitudes
  • Review on the Parke-Taylor formula for Maximally Helicity Violating (MHV) amplitudes
  • Discussion of the  Britto-Cachazo-Feng-Witten (BCFW) recursion relations that provide an elegant method of calculating tree amplitudes in gauge theories; three-point amplitudes.

 
References:

  1. Lance Dixon, "Calculating Scattering Amplitudes Efficiently", hep-ph/9601359
  2. Berger et al., "An Automated Implementation of On-Shell Methods for One-Loop Amplitudes", arxiv:0803.4180
  3. Arkani-Hamed et al., "What is the Simplest Quantum Field Theory?", arxiv:0808.1446

 
Keith Ellis   (4 lectures)

Title: Advanced methods for radiative corrections at the LHC (Part-1)

  • Analytic on-shell methods for loop diagrams
  • Forde's method and spinor integration
  • Introduction to MCFM
  • Ossola-Papadopoulos-Pittau (OPP) and n-dimensional unitarity

Rikkert Frederix  (4 lectures)

Title: Advanced methods for radiative corrections at the LHC (Part-2)

  • Subtraction procedure Catani-Seymour (CS), Frixione-Kunszt-Signer (FKS), slicing
  • Introduction to MC@NLO, Powheg
  • Phenomenological consequences
  • Parton showers, Catani-Krauss-Kuhn-Webber (CKKW) and MLM matching?

References (Part-1 and Part-2):

  1. R. K. Ellis, W. J. Stirling and B. R. Webber, QCD and collider physics, Camb. Monogr. Part. Phys. Nucl. Phys. Cosmol. 8, 1 (1996).
  2. Z. Bern, L. J. Dixon and D. A. Kosower, On-Shell Methods in Perturbative QCD, Annals Phys. 322, 1587 (2007) arXiv:0704.2798 [hep-ph].

Anuradha Misra  (2 lectures)
 
Title:  Introduction to Resummation at colliders

  • Basics of Sudakov resummation in quantum field theories. 
  • Soft gluon contributions to observables at hadron colliders to all orders in perturbation  theory. 
  • Threshold, small transverse momentum resummation and their effects. 
  • Applications to  Drell-Yan production; joint resummation.

References:

  1. G. Sterman, TASI '95 lecture notes, hep-ph/9606312
  2. E. Laenen, Pramana 63, 1225 (2004)

 
Rajesh Gopakumar (2 lectures)
 
Title: AdS/CFT and applications to scattering amplitudes in gauge theories

  • Basics of AdS/CFT: Statement of Gauge-gravity dualities. Dictionary between observables on both sides of the duality. Regimes of applicability. 
  • Applications to scattering amplitudes: Strong coupling amplitudes in N=4 Super Yang-Mills from the gravity dual. 
  • Relation to Bern-Dixon-Smirnov ansatz. Dual superconformal invariance of amplitudes and relation to momentum space Wilson loops.

 
References:

  1. "Large N field theories, string theory and gravity"- O. Aharony et.al.Phys.Rept.323:183-386,2000. e-Print: hep-th/9905111
  2. L. Alday and J. Maldacena, JHEP 0706:064,2007. e-Print:arXiv:0705.0303 [hep-th].
  3. L. Alday, R. Roiban, "Scattering Amplitudes, Wilson Loops and the String/Gauge Theory Correspondence". Phys.Rept.468:153-211,2008. e-Print:arXiv:0807.1889 [hep-th].
  4. "L. Alday, Lectures on Scattering Amplitudes via AdS/CFT.", e-Print:arXiv:0804.0951 [hep-th]