Presentation is loading. Please wait.

Presentation is loading. Please wait.

Twistor Inspired techniques in Perturbative Gauge Theories-II including work with Z. Bern, S Bidder, E Bjerrum- Bohr, L. Dixon, H Ita, W Perkins K. Risager.

Published byAmber Cunningham Modified over 8 years ago

Similar presentations

Presentation on theme: "Twistor Inspired techniques in Perturbative Gauge Theories-II including work with Z. Bern, S Bidder, E Bjerrum- Bohr, L. Dixon, H Ita, W Perkins K. Risager."— Presentation transcript:

1 Twistor Inspired techniques in Perturbative Gauge Theories-II including work with Z. Bern, S Bidder, E Bjerrum- Bohr, L. Dixon, H Ita, W Perkins K. Risager KIAS-KIAST KIAS-KIAST 2005 David Dunbar, Swansea University, Wales

2 D Dunbar, KIAS-KIAST 05 2 Seminar II Hadron Colliders, LHC Need for NLO computations Pieces of NLO computations QCD calculations

3 D Dunbar, KIAS-KIAST 05 3 Hadron Colliders LHC

4 D Dunbar, KIAS-KIAST 05 4

5 5

6 6

7 7 LHC Physics -hadron machines are DISCOVERY machines (SPS:W+Z,Tevatron: t) -LHC will “hunt the higgs” -hunt SUSY -hunt new physics

8 D Dunbar, KIAS-KIAST 05 8 Higgs Production and Decay H g g W/Z -four final state particles end-point of Higgs production -very often four jets eg

9 D Dunbar, KIAS-KIAST 05 9

10 10

11 D Dunbar, KIAS-KIAST 05 11 -most decay end-points of new physics can be simulated by background standard model processes -very important to have robust accurate predictions for background decay rates/event shapes/angular distribution based upon known physics -jets are “inclusive processess” : experimentally we cannot distinguish colour, helicity, spin.

12 D Dunbar, KIAS-KIAST 05 12

13 D Dunbar, KIAS-KIAST 05 13 Pieces of Theoretical Prediction Probability of producing final state = Structure Functions Matrix Elements Hadronisation -piece that twistors may help with

14 D Dunbar, KIAS-KIAST 05 14 Need for NLO Matrix Elements calculations for jets Consider 2g -> 2g +g 4 2 g2g2 2 2 g3g3

15 D Dunbar, KIAS-KIAST 05 15 g2g2 +g 4 +g 6 2 2 2 g3g3 g4g4 +g 5 NNLO

16 D Dunbar, KIAS-KIAST 05 16 Wny is NLO neccessary -accurancy, QCD is strong(ish) -scale dependance -cone-size dependance

17 D Dunbar, KIAS-KIAST 05 17 One-Loop Amplitudes One Loop Gluon Scattering Amplitudes in QCD -Four Point : Ellis+Sexton -Five Point : Bern, Dixon,Kosower -Six-Point and beyond--- present problem -Five and Six-Point mixed procecess n-point MHV amplitudes supersymmetric theories Bern,Dixon,Dunbar and Kosower 94/95 Six-point N=4 amplitudes

18 D Dunbar, KIAS-KIAST 05 18 General Decomposition of One- loop Amplitude Linear in loop momentum propagators n degree n in l

19 D Dunbar, KIAS-KIAST 05 19 Passerino-Veltman reduction Decomposes a n-point integral into a sum of (n-1) integral functions obtained by collaspsing a propagator k l l-k

20 D Dunbar, KIAS-KIAST 05 20 -process continues until we reach four-point integral functions with (in yang-mills up to quartic numerators) -similarly 3-> 2 also gives scalar triangles. At bubbles process ends. Quadratic bubbles can be rational functions involving no logarithms. -so in general, for massless particles Functions of a single kinematic invariant, ln(s)

21 D Dunbar, KIAS-KIAST 05 21 Supersymmetric Decomposition Supersymmetric gluon scattering amplitudes are the linear combination of QCD ones+scalar loop -this can be inverted

22 D Dunbar, KIAS-KIAST 05 22 N=4 One-Loop Amplitudes – solved! Amplitude is a a sum of scalar box functions with rational coefficients (BDDK,1994) Coefficients are ``cut-constructable’’ (BDDK,1994) Quadruple cuts turns calculus into algebra (Britto,Cachazo,Feng,2005) Box Coefficients are actually coefficients of terms like

23 D Dunbar, KIAS-KIAST 05 23 N=4 Susy In N=4 susy there are cancelations between the states of different spin circulating in the loop. Leading four-powers of loop momentum cancel (in well chosen gauges..) N=4 lie in a small subspace of the allowed possible amplitudes

24 D Dunbar, KIAS-KIAST 05 24 Basis in N=4 Theory ‘easy’ two-mass box ‘hard’ two-mass box

25 D Dunbar, KIAS-KIAST 05 25 MHV vertices at 1-loop -MHV vertices were shown to work for N=4 (and N=1) -specific computation was (repeat) of N=4 MHV amplitudes + - - + - + + + - + + + + + + + - + + - + + - - Bedford,Brandhuber, Spence and Travaglini; Qigley,Rozali

26 D Dunbar, KIAS-KIAST 05 26 -looks very much like unitary cut of amplitude -but continuing away from l i 2 =0 -is unitarity the key?

27 D Dunbar, KIAS-KIAST 05 27 Box-Coefficients -works for massless corners (complex momenta) S Britto,Cachazo,Feng or signature (--++) -works for non-supersymmetric Bjerrum-Bohr,Bidder,DCD,Perkins

28 D Dunbar, KIAS-KIAST 05 28 Box Coefficients-Twistor Structure Box coefficients has coplanar support for NMHV 1-loop amplitudes -true for both N=4 and QCD!!!

29 D Dunbar, KIAS-KIAST 05 29 N=1 One-Loop Amplitudes -???? Important to choose a good basis of functions A) choose chiral multiplet B) use D=6 boxes Amplitude also cut constructible -six gluon amplitudes now obtained using unitarity Bidder,Bjerrum-Bohr,Dixon, Dunbar, Perkins Britto, Buchbinder Cachazo, Feng, 04/05

30 D Dunbar, KIAS-KIAST 05 30 The Final Pieces : scalar contributions -last component of QCD amplitudes - R is rational and not cut constructible (to O(  )) cut construcible recursive? -can we avoid direct integration?

31 D Dunbar, KIAS-KIAST 05 31 Recursion for Rational terms -can we shift R and obtain it from its factorisation? 1)Function must be rational 2)Function must have simple poles 3)We must understand these poles

32 D Dunbar, KIAS-KIAST 05 32 -understanding poles -multiparticle factorisation theorems Bern,Chalmers

33 D Dunbar, KIAS-KIAST 05 33 Complication, Either R or the coefficients of integral functions may contain Spurious Singularities which are not present in the full amplitude It is important and non-trivial to find shift(s) which avoid these spurious singularities whilst still affecting the full R/coefficient

34 D Dunbar, KIAS-KIAST 05 34 Example of Spurious singularities Collinear Singularity Multi-particle pole Co-planar singularity

35 D Dunbar, KIAS-KIAST 05 35 Splitting Amplitude into C and R is not unique The integral functions can be defined to include rational pieces, e.g rather than avoids a spurious singularity as r  1 (r=s/s’) Spurious singularities spoil understanding of residues – can we avoid them?

36 D Dunbar, KIAS-KIAST 05 36 Results: It has been demonstrated, using A) (-++….+++), (+++++….++) and B) (--++++) and (--++….+++) that shifts can be found which allow calculation of rational parts recursively Bern, Dixon Kosower 1) 2) Shifts can be found which allow the integral coefficients to be computed recursively A(---..--+++…++) Bern, Bjerrum-Bohr, Dunbar, Ita Forde, Kosower

37 D Dunbar, KIAS-KIAST 05 37 State of Play Six Gluon Scattering X XX X X X X X X X X X X X X X X 2g-  4g

38 D Dunbar, KIAS-KIAST 05 38 Conclusions -Reasons for optimism in computing one-loop QCD matrix elements -Recent progress uses UNITARITY and FACTORISATION as key features of on-shell amplitudes -Inspired by Weak-Weak duality but not dependant upon it -after much progress in highly super-symmetric theories the (harder) problem of QCD beginning to yield results -first complete result for a partial 2g  ng amplitude! -NNLO is the goal for LHC -analytic vs. numerical? -fermions, masses, multi-loops,…..

Download ppt "Twistor Inspired techniques in Perturbative Gauge Theories-II including work with Z. Bern, S Bidder, E Bjerrum- Bohr, L. Dixon, H Ita, W Perkins K. Risager."

Similar presentations

Bill Spence* Oxford April 2007

Bill Spence* Oxford April 2007
Maximal Unitarity at Two Loops David A. Kosower Institut de Physique Théorique, CEA–Saclay work with Kasper Larsen & Henrik Johansson; & with Krzysztof.

Maximal Unitarity at Two Loops David A. Kosower Institut de Physique Théorique, CEA–Saclay work with Kasper Larsen & Henrik Johansson; & with Krzysztof.
N =4 Supersymmetric Gauge Theory, Twistor Space, and Dualities David A. Kosower Saclay Lectures Fall Term 2004.

N =4 Supersymmetric Gauge Theory, Twistor Space, and Dualities David A. Kosower Saclay Lectures Fall Term 2004.
1 Top Production Processes at Hadron Colliders By Paul Mellor.

1 Top Production Processes at Hadron Colliders By Paul Mellor.
Twistors and Pertubative Gravity including work (2005) with Z Bern, S Bidder, E Bjerrum-Bohr, H Ita, W Perkins, K Risager From Twistors to Amplitudes 2005.

Twistors and Pertubative Gravity including work (2005) with Z Bern, S Bidder, E Bjerrum-Bohr, H Ita, W Perkins, K Risager From Twistors to Amplitudes 2005.
Maximal Unitarity at Two Loops David A. Kosower Institut de Physique Théorique, CEA–Saclay work with Kasper Larsen & Henrik Johansson; & work of Simon.

Maximal Unitarity at Two Loops David A. Kosower Institut de Physique Théorique, CEA–Saclay work with Kasper Larsen & Henrik Johansson; & work of Simon.
Introduction to On-Shell Methods in Quantum Field Theory David A. Kosower Institut de Physique Théorique, CEA–Saclay Orsay Summer School, Correlations.

Introduction to On-Shell Methods in Quantum Field Theory David A. Kosower Institut de Physique Théorique, CEA–Saclay Orsay Summer School, Correlations.
Maximal Unitarity at Two Loops David A. Kosower Institut de Physique Théorique, CEA–Saclay work with Kasper Larsen & Henrik Johansson; & work of Simon.

Maximal Unitarity at Two Loops David A. Kosower Institut de Physique Théorique, CEA–Saclay work with Kasper Larsen & Henrik Johansson; & work of Simon.
Maximal Unitarity at Two Loops David A. Kosower Institut de Physique Théorique, CEA–Saclay work with Kasper Larsen; & with Krzysztof Kajda & Janusz Gluza.

Maximal Unitarity at Two Loops David A. Kosower Institut de Physique Théorique, CEA–Saclay work with Kasper Larsen; & with Krzysztof Kajda & Janusz Gluza.
Maximal Unitarity at Two Loops David A. Kosower Institut de Physique Théorique, CEA–Saclay work with Kasper Larsen & Henrik Johansson; & work of Simon.

Maximal Unitarity at Two Loops David A. Kosower Institut de Physique Théorique, CEA–Saclay work with Kasper Larsen & Henrik Johansson; & work of Simon.
Maximal Unitarity at Two Loops David A. Kosower Institut de Physique Théorique, CEA–Saclay work with Kasper Larsen & Henrik Johansson; & work of Simon.

Maximal Unitarity at Two Loops David A. Kosower Institut de Physique Théorique, CEA–Saclay work with Kasper Larsen & Henrik Johansson; & work of Simon.
QCD at the LHC: What needs to be done? West Coast LHC Meeting Zvi Bern, UCLA Part 2: Higher Order QCD.

QCD at the LHC: What needs to be done? West Coast LHC Meeting Zvi Bern, UCLA Part 2: Higher Order QCD.
On-Shell Methods in Field Theory David A. Kosower International School of Theoretical Physics, Parma, September 10-15, 2006 Lecture IV.

On-Shell Methods in Field Theory David A. Kosower International School of Theoretical Physics, Parma, September 10-15, 2006 Lecture IV.
On-Shell Methods in Field Theory David A. Kosower International School of Theoretical Physics, Parma, September 10-15, 2006 Lecture II.

On-Shell Methods in Field Theory David A. Kosower International School of Theoretical Physics, Parma, September 10-15, 2006 Lecture II.
On-Shell Methods in Field Theory David A. Kosower International School of Theoretical Physics, Parma, September 10-15, 2006 Lecture V.

On-Shell Methods in Field Theory David A. Kosower International School of Theoretical Physics, Parma, September 10-15, 2006 Lecture V.
On-Shell Methods in Field Theory David A. Kosower International School of Theoretical Physics, Parma, September 10-15, 2006 Lecture III.

On-Shell Methods in Field Theory David A. Kosower International School of Theoretical Physics, Parma, September 10-15, 2006 Lecture III.
Structure of Amplitudes in Gravity I Lagrangian Formulation of Gravity, Tree amplitudes, Helicity Formalism, Amplitudes in Twistor Space, New techniques.

Structure of Amplitudes in Gravity I Lagrangian Formulation of Gravity, Tree amplitudes, Helicity Formalism, Amplitudes in Twistor Space, New techniques.
Structure of Amplitudes in Gravity III Symmetries of Loop and Tree amplitudes, No- Triangle Property, Gravity amplitudes from String Theory Playing with.

Structure of Amplitudes in Gravity III Symmetries of Loop and Tree amplitudes, No- Triangle Property, Gravity amplitudes from String Theory Playing with.
On-Shell Methods in Field Theory David A. Kosower International School of Theoretical Physics, Parma, September 10-15, 2006 Lecture I.

On-Shell Methods in Field Theory David A. Kosower International School of Theoretical Physics, Parma, September 10-15, 2006 Lecture I.
Structure of Amplitudes in Gravity II Unitarity cuts, Loops, Inherited properties from Trees, Symmetries Playing with Gravity - 24 th Nordic Meeting Gronningen.

Structure of Amplitudes in Gravity II Unitarity cuts, Loops, Inherited properties from Trees, Symmetries Playing with Gravity - 24 th Nordic Meeting Gronningen.

Similar presentations

Ads by Google