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# ITAL CONVERSATION Italian 13

UCI

GPA 3.69

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This 32 page Class Notes was uploaded by Maudie Bauch on Saturday September 12, 2015. The Class Notes belongs to Italian 13 at University of California - Irvine taught by Staff in Fall. Since its upload, it has received 43 views. For similar materials see /class/201852/italian-13-university-of-california-irvine in Italian at University of California - Irvine.

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Date Created: 09/12/15

OnShell Recursion Relations for MultiParton OneLoop Amplitudes Carola F Berger Stanford Linear Accelerator Center with Zvi Bern Lance Dixon Darren Forde David Kosower SUSYOG June 13th 2006 References 1 Z Bern L J Dixon D A Kosower Introduction Phys Rev D 71 105013 2005 hepth0501240 32 Recursion Phys Rev D 72 125003 2005 hepph0505055 W Phys Rev D 73 065013 2006 hepph0507005 One Loop 2 CFB Z Bern L J Dixon D Forde D A Kosower hepph0604195 Summary and Outlook 3 CFB Z Bern L J Dixon D Forde D A Kosower to appear 4 CFB V Del Duca L J Dixon to appear Carola F Berger SUSY06 June 13th 2006 OnShell Recursion Relations for MultiParton OneLoop Amplitudes 218 SUSY Search Missing Energy Jets SM background from Z gt w jets Introduction OSUSYSearch 39 l f39t39 39 39 i 739 39 i 39 nhk Missing EnergyJets quot OThe lnFamous m 4 Experimenters Wishlists 0 Feynman Graphs m i 0 0 Color Ordering Spinors and Twistors ntss39Ev i Gain a I39dl l IE we 8 h OnShell Recursion Relations 10 L OnShell Bootstrap at One Loop Summary and Outlook Mangano et al Red dots ALPGEN shaded histogram PYTHIA black dots SUSY signal ALPGEN based on exact LO multiparton amplitudes PYTHIA uses showeralgorithm gt discrepancy for events with many hard jets pp gt Z 4 jets needed at NLO Carola F Berger SUSYOB June 13th 2006 OnShell Recursion Relations for MultiParton OneLoop Amplitudes 318 References Introduction 0 SUSY Search Missing Energy Jets OThe lnFamous Experimenters Wishlists 0 Feynman Graphs 0 Color Ordering Spinors and Twistors OnShell Recursion Relations OnShell Bootstrap at One Loop Summary and Outlook The lnFamous Experimenters Wishlists Run II Monte Carlo Workshop 2001 Single boson Diboson Triboson Heavy flavor W S 5339 WW S 5339 WWW S 3339 tt S 3339 W bE g 33 WW bE g 33 WWW b5 g 33 t 7 g 2339 W 25 S 3339 WW 25 S 3339 WWW 11 S 3339 tt W S 2339 Z S 5339 ZZ S 5339 Z39y39y S 3339 tt Z S 2339 ZbEg3j ZZbEg3j WZZg3j tEH 2j Z ca g 3339 ZZ ca g 3339 ZZZ g 3339 tE g 2339 1 S 5339 77 S 5339 tbb 33 7b5S3j 7cES3j 7397 bb S 3339 7397 25 S 3339 WZ S 5339 WZ bE g 3339 WZ ca g 33 W7 S 3339 Z7 S 33 Carola F Berger SUSYOB June 13th 2006 OnShell Recursion Relations for MultiParton OneLoop Amplitudes 418 The lnFamous Experimenters Wishlists Les Houches 2005 References process wanted at NLO background to Introduction m V E Z9 W9 7 39Eii li f 1 pp gt V V iet tfH new physics Graphs 2 pp gt H 2 jets H production by 39 rquot s s vector boson fusion VBF OnShell Recursion 339 pp gt tfbg tfH 4 pp gt h 2 jets tfH w 5 1919 gt VVbE VBF gt H gt VV tfH new physics Summawandowook 6 pp gt VV 2 jets VBF gt H gt VV 7 pp gt V 3 jets new physics 8 pp gt VVV SUSY trilepton Carola F Berger SUSY06 June 13th 2006 OnShell Recursion Relations for MultiParton OneLoop Amplitudes 418 The lnFamous Experimenters Wishlists Les Houches 2005 nn process wanted at NLO background to m V E Z9 W9 7 223333 1 pp gt V V iet tfH new physics Graphs 2 pp gt H 2 jets H production by 39ggl i f j imrs vector boson fusion VBF OnShell Recursion 339 pp gt ttbb ttH Relations 4 pp gt 3 2 jets tfH 83332 squota39 5 1919 gt VVbE VBF gt H gt VV tfH new physics Summawandowook 6 pp gt VV l 2 jets VBF gt H gt VV 7 pp gt V 3 jets new physics 8 pp gt VVV SUSY trilepton Large number of highmultiplicity processes that need to be computed The LHC turns on in 2007 Carola F Berger SUSY06 June 13th 2006 OnShell Recursion Relations for MultiParton OneLoop Amplitudes 418 References Introduction 0 SUSY Search Missing Energy Jets OThe lnFamous Experimenters Wishlists 0 Color Ordering Spinors and Twistors OnShell Recursion Relations OnShell Bootstrap at One Loop Summary and Outlook Feynman Graphs l Feynman rules are too general not optimized do not take into account all symmetries of the theory I Vertices and propagators involve gaugedependent offshell states I Explosive growth of number of diagramsterms gluon legs tree level one loop 6 220 1034 8 34300 3017490 00 worse than 00 even worse than 00 Carola F Berger SUSYOB June 13th 2006 219 more p o OnShell Recursion Relations for MultiParton OneLoop Amplitudes 518 References Introduction 0 SUSY Search Missing Energy Jets OThe lnFamous Experimenters Wishlists 0 Color Ordering Spinors and Twistors OnShell Recursion Relations OnShell Bootstrap at One Loop Summary and Outlook Feynman Graphs l Feynman rules are too general not optimized do not take into account all symmetries of the theory I Vertices and propagators involve gaugedependent offshell states I Explosive growth of number of diagramsterms gluon legs tree level one loop 6 220 1034 8 34300 3017490 00 worse than 00 even worse than 00 Time to panic Carola F Berger SUSYOB June 13th 2006 OnShell Recursion Relations for MultiParton OneLoop Amplitudes 518 References Introduction 0 SUSY Search Missing Energy Jets OThe lnFamous Experimenters Wishlists 0 Color Ordering Spinors and Twistors OnShell Recursion Relations OnShell Bootstrap at One Loop Summary and Outlook Feynman Graphs l Feynman rules are too general not optimized do not take into account all symmetries of the theory I Vertices and propagators involve gaugedependent offshell states I Explosive growth of number of diagramsterms gluon legs tree level one loop 6 220 1034 8 34300 3017490 00 worse than 00 even worse than 00 Time to panic I SemiNumerical approaches and automatization No MadEvent ALPGEN CompHEP GRACE HELACPHEGAS Kramer Soper Nagy Ellis Giele Glover Zanderighi Binoth Ciccolini Guillet Heinrich Kauer Pilon Schubert Czakon Anastasiou Daleo Carola F Berger SUSYOB June 13th 2006 I Recursion relations OnShell Recursion Relations for MultiParton OneLoop Amplitudes 518 References Introduction 0 SUSY Search Missing Energy Jets OThe lnFamous Experimenters Wishlists 0 Feynman Graphs 0 Color Ordering Spinors and Twistors OnShell Recursion Relations OnShell Bootstrap at One Loop Summary and Outlook Carola F Berger SUSY06 June 13th 2006 Color Ordering Spinors and Twistors I Strip color information only calculate diagrams with cyclic color ordering gt 36 diagrams not 220 for 6 gluons at tree level OnShell Recursion Relations for MultiParton OneLoop Amplitudes 618 References Introduction 0 SUSY Search Missing Energy Jets OThe lnFamous Experimenters Wishlists 0 Feynman Graphs 0 Color Ordering Spinors and Twistors OnShell Recursion Relations OnShell Bootstrap at One Loop Summary and Outlook Carola F Berger SUSYOB June 13th 2006 Color Ordering Spinors and Twistors I Strip color information only calculate diagrams with cyclic color ordering gt 36 diagrams not 220 for 6 gluons at tree level I Decompose oneloop QCD amplitudes AQCD 4 Ascalar OnShell Recursion Relations for MultiParton OneLoop Amplitudes 618 References Introduction 0 SUSY Search Missing Energy Jets OThe lnFamous Experimenters Wishlists 0 Feynman Graphs 0 Color Ordering Spinors and Twistors OnShell Recursion Relations OnShell Bootstrap at One Loop Summary and Outlook Carola F Berger SUSYOB June 13th 2006 Color Ordering Spinors and Twistors I Strip color information only calculate diagrams with cyclic color ordering gt 36 diagrams not 220 for 6 gluons at tree level 39 Decompose oneloop QCD amplitudes AQCD 4 Ascalar I Use the right variables to expose more symmetries spinor helicity formalism Transformation to Penrose s twistor space half Fourier transform of spinors only lefthanded spinors transformed gt amazingly simple structure of scattering am itUdeS Witten Nair Roiban Spradlin Volovich OnShell Recursion Relations for MultiParton OneLoop Amplitudes 618 Color Ordering Spinors and Twistors I Strip color information only calculate diagrams with cyclic color ordering gt 36 diagrams not 220 for 6 gluons at tree level ls39ti39 s I Decompose oneloop QCD amplitudes Experimenters gsmit maphs AQCD AN4 Ascalar Spinors and Twistors u I Use the rIght varIables to expose more OnShell Recursion symmetries spinor helicity formalism ggffggpaootstrapat Transformation to Penrose s twistor space half Fourier transform of spinors only lefthanded spinors transformed gt amazingly simple structure of scattering Summary and Outlook am plitUdeS Witten Nair Roiban Spradlin Volovich I Recycle known amplitudes via recursion relations Berends Giele Mahlon Cachazo Svrcek Witien Britto Cachazo Feng Witten Carola F Berger SUSYOB June 13th 2006 OnShell Recursion Relations for MultiParton OneLoop Amplitudes 618 References Introduction OnShell Recursion Relations 0 Recursion Relations at Tree Level 0 OnShell Recursions OQCD at One Loop A Disaster OnShell Bootstrap at One Loop Summary and Outlook Carola F Berger SUSYOG June 13th 2006 Recursion Relations at Tree Level 219 more P216 0 Complex continue spinors and momenta gt Amplitude function of complex parameter Az Ap19 9pjz9pj19 9plz9 apn If Az gt 00 gt O Cauchy s theorem 1 d 2 Z Az 0 27m 0 z A0 is the physical amplitude OnShell Recursion Relations for MultiParton OneLoop Amplitudes 718 References Introduction OnShell Recursion Relations 0 Recursion Relations at Tree Level 0 OnShell Recursions OQCD at One Loop A Disaster OnShell Bootstrap at One Loop Summary and Outlook Carola F Berger SUSYOB June 13th 2006 Recursion Relations at Tree Level Res Az zza Z 3 A0 polesa z Z A 1 A 2 L2 R con gs Poles in 2 correspond to physical o C factorizations 1 1 P m P m z ltj Plum lk gt n 1 if 2 k 39 p20 k1 k k 1 Britto Cachazo Feng Witten OnShell Recursion Relations for MultiParton OneLoop Amplitudes 818 References Introduction OnShell Recursion Relations 0 Recursion Relations at Tree Level 0 OnShell Recursions OQCD at One Loop A Disaster OnShell Bootstrap at One Loop Summary and Outlook Carola F Berger SUSYOG June 13th 2006 OnShell Recursions Proof at tree level only relies on Cauchy s theorem and basic factorization properties See also Draggiotis Kleiss Lazopoulos Papadopoulos Vaman Yao gt Many applications at tree level I SUSY processes with massless fermions I QCD QCD is supersymmetric at tree level I Massive scalars and fermions Badger Glover Khoze Svrcek Forde Kosower Schwinn Weinzierl Ferrario Rodrigo Luo Wen Talavera I Higgs top loop integrated out I Gravity Bedford Brandhuber Spence Travaglini Cachazo Svrcek BjerrumBohr Dunbar Ita Badger Dixon Glover Khoze Perkins Risager OnShell Recursion Relations for MultiParton OneLoop Amplitudes 918 References Introduction OnShell Recursion Relations 0 Recursion Relations at Tree Level 3970 OnShell Recursions 032le at W Mm 35 OnShell Bootstrap at One Loop Summary and Outlook I Branch cuts Carola F Berger SUSY06 June 13th 2006 OnShell Recursion Relations for MultiParton OneLoop Amplitudes 1018 References Introduction OnShell Recursion Relations 0 O Recursion Relations at Tree Level 0 OnShell Recursions OQCD at One Loop A Disaster OnShell Bootstrap at One Loop Summary and Outlook I Branch cuts I Double poles unreal poles and nonstandard factorizations Carola F Berger SUSYOG June 13th 2006 OnShell Recursion Relations for MultiParton OneLoop Amplitudes 1018 QCD at One Loop A Disaster References Introduction OnShell Recursion Relations O Recursion Relations at Tree Level O OnShell Recursions OQCD at One Loop A Disaster OnShell Bootstrap at One Loop 0 Summary and Outlook I Branch cuts I Double poles unreal poles and nonstandard factorizations lAz gtoo750 Carola F Berger SUSYOG June 13th 2006 OnShell Recursion Relations for MultiParton OneLoop Amplitudes 1018 Flelerences Introduction Dn Shell Recursion Relations Dn Shell Bootstrap at Dne Lou ODn Shell Bootstrap Method CL Pans OOH Shell Recursion lur Rational Pans Summary and Dutluuk Carola F Berger SUSYUG June 13th 2006 OnShell Bootstrap Method znlcle Aiscussinn e39y timsnaue39 llrsll murmured mum he Wiwpedm runwig Bootstrap model me Wiklpzdia the free eammpema mm r lheuvy mnl I 4 in n lnlh m unes See ceumy Chew derived byims method Here very general consistency criteria I Cuts unitarity I Poles factorization 4 Az CZ Rz OnShell quot 39 quot 39 39 for quotultiParton 0ne 39 quot quot 1118 References Introduction OnShell Recursion Relations OnShell Bootstrap at One Loop 0 OnShell Bootstrap M O OnShell Recursion for Rational Parts 0 NonStandard Factorizations O Largez Contributions OThe Bootstrap Formalism Summary and Outlook Carola F Berger SUSY06 June 13th 2006 OnShell Recursion Relations for MultiParton OneLoop Amplitudes 1218 References Introduction OnShell Recursion Relations OnShell Bootstrap at One Loop 0 OnShell Bootstrap Method 0 OnShell Recursion for Rational Parts 0 NonStandard Factorizations O Largez Contributions OT he Bootstrap Formalism Summary and Outlook Carola F Berger SUSYOG June 13th 2006 Cut Parts m21gt 99 C l l k quot11 Ill ml0 W CO contains only Li In 772 cutconstructible via generalized unitarity l2Atree l1 m1 m2 l2Atree l2 Til21 m1 1l1 Trees recycled into loops Bern Dixon Dunbar Kosower Bedtord Brandhuber McNamara Spence Travaglini Quigley Rozali Britto Buchbinder Cachazo Feng Mastrolia Bern Bidder BjerrumBohr Dixon Dunbar lta Perkins O39nShell Recursion Relations for MultiParton OneLoop Amplitudes 1218 References Introduction OnShell Recursion Relations OnShell Bootstrap at One Loop 0 OnShell Bootstrap Method 0 Cut Parts for Rational Parts 0 NonStandard Factorizations O Largez Contributions OThe Bootstrap Formalism Summary and Outlook Carola F Berger SUSYOB June 13th 2006 OnShell Recursion for Rational Parts Az A0 1 dz 277i 02 Rz CZ Res RZ zzza z 00 InfR Z poles a 1 00 InfR Z ALPz AR BW con gs con gs lm Loops recycled into loops ignoring slight subtleties with spurious singularities Bern Dixon Kosower OnShell Recursion Relations for MultiParton OneLoop Amplitudes 1318 References Introduction OnShell Recursion Relations OnShell Bootstrap at One Loop 0 OnShell Bootstrap Method 0 Cut Parts 0 OnShell Recursion for Rational Pa Qmmm mgar mfme O Largez Contributions 0 The Bootstrap Formalism Summary and Outlook Carola F Berger SUSY06 June 13th 2006 Res E zzza z poles a OnShell Recursion Relations for MultiParton OneLoop Amplitudes 1418 References Introduction OnShell Recursion Relations OnShell Bootstrap at One Loop 0 OnShell Bootstrap Method 0 Cut Parts 0 OnShell Recursion for Rational Parts 0 NonStandard Factorizations O Largez Contributions OThe Bootstrap Formalism Summary and Outlook Carola F Berger SUSY06 June 13th 2006 C 2 con gs zzzza z OnShell Recursion Relations for MultiParton OneLoop Amplitudes 1418 References Introduction OnShell Recursion Relations OnShell Bootstrap at One Loop 0 OnShell Bootstrap Method 0 Cut Parts 0 OnShell Recursion for Rational Parts Factorizations O Largez Contributions OThe Bootstrap Formalism Summary and Outlook Carola F Berger SUSYOB June 13th 2006 NonStandard Factorizations Res Rz zzza z 9 A0 C0 Inf RZ poles a quot 3939argez W 0 x N double pole ratl gtlt tree rational gtlt tree Factorization properties unclear at one loop OnShell Recursion Relations for MultiParton OneLoop Amplitudes 1418 References Introduction OnShell Recursion Relations OnShell Bootstrap at One Loop 0 OnShell Bootstrap Method 0 Cut Parts 0 OnShell Recursion for Rational Parts 0 NonStandard Factorizations O Largez Contributions OThe Bootstrap Formalism Summary and Outlook Largez Contributions Can pick continuations to avoid either nonstandard factorizations or z gt 0 contributions but in general not both I Continuation j l avoids nonstandard factorizations 5 Carola F Berger SUSYOB June 13th 2006 recurs A0 2 00 Inf R RWgt m OnShell Recursion Relations for MultiParton OneLoop Amplitudes 1518 References Introduction OnShell Recursion Relations OnShell Bootstrap at One Loop 0 OnShell Bootstrap Method 0 Cut Parts 0 OnShell Recursion for Rational Parts 0 NonStandard Factorizations OThe Bootstrap Formalism Summary and Outlook Carola F Berger SUSYOB June 13th 2006 Largez Contributions Can pick continuations to avoid either nonstandard factorizations or z gt 0 contributions but in general not both I Continuation j l avoids nonstandard factorizations 5 A0 00 RUJ 37 recurs I Continuation a b has no largeparameter contributions A0 2 C0Rrfgt nonstandard channelsa7bgt 6 OnShell Recursion Relations for MultiParton OneLoop Amplitudes 1518 References Introduction OnShell Recursion Relations OnShell Bootstrap at One Loop 0 OnShell Bootstrap Method 0 Cut Parts 0 OnShell Recursion for Rational Parts 0 NonStandard Factorizations O Largez Contributions OThe Bootstrap Formalism Summary and Outlook Carola F Berger SUSYOB June 13th 2006 The Bootstrap Formalism Solution gt use two continuations Extract largeparameter contributions of primary continuation from auxiliary relation 6 7A0 00 Rig nonstandard bgt 77 Inf R Inf Brigg U71 371 8 if Inf nonstandard channelsa bgt 0 30 OnShell Recursion Relations for MultiParton OneLoop Amplitudes 1618 References Introduction OnShell Recursion Relations OnShell Bootstrap at One Loop 0 OnShell Bootstrap Method 0 Cut Parts 0 OnShell Recursion for Rational Parts 0 NonStandard Factorizations O Largez Contributions OThe Bootstrap Formalism Summary and Outlook Carola F Berger SUSYOB June 13th 2006 The Bootstrap Formalism Solution gt use two continuations Extract largeparameter contributions of primary continuation from auxiliary relation 6 7A0 00 Rig nonstandard bgt 77 Inf R Inf Brigg U71 371 8 if Inf nonstandard channels 7bgt 0 W The complete bootstrap AO 00 leyl Inf Rab 331 I ch I S I ch I S Passes all nontrivial checks CFB Berna Dixon Forde Kosower OnShell Recursion Relations for MultiParton OneLoop Amplitudes 1618 Results References U Allmultiplicity formulae for nereeueuen oneloop gluon amplitudes also with a fermion pair OnShell Recursion BernI Dixon1 Kosower Relations U Allmultiplicity formulae for OnShell Bootstrap at OneLoop H oneloop gluon W amplitudes Forde Kosower CFB Bern ixon Forde Kosower 39T 39 st U Allmultiplicity formulae for one3900P gluon amplitudes CFB Bern Dixon Fordee Kosower U Some allmultiplicity results for parts of Higgs plus gluons and fermion pair at NNLO effective theory top loop integrated out CFB Del Duca Dixon All of the above ltlt 00 pages U Working algorithm for all other configurations of oneloop gluon amplitudes CFB Bern Dixon Forde Kosower Carola F Berger SUSYOB June 13th 2006 OnShell Recursion Relations for MultiParton OneLoop Amplitudes 1718 ToDo List References Introduction OnShell Recursion Relations OnShell Bootstrap at One Loop Summary and Outlook 0 Results 0 ToDo List Carola F Berger SUSYOB June 13th 2006 El Understand complex factorization at one loop and beyond connection to Lagrangian El Higher loops El Massive partons external fermions scalars El Automatization El Attack the wishlists OnShell Recursion Relations for MultiParton OneLoop Amplitudes 1818

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