Electroweak Radiation in Antenna Showers Rob Verheyen With Ronald - PowerPoint PPT Presentation

Electroweak Radiation in Antenna Showers Rob Verheyen With Ronald Kleiss

Introduction t cut Λ QCD t hard 2

Introduction Parton Showers = Resummation Photon Emission Soft and collinear logarithms Current implementations: only collinear Photon Splitting Only collinear logarithms Cast in antenna formalism Electroweak Radiation Complications due to mass and spin Follow QCD antenna shower Vincia Giele, Kosower, Skands:1102.2126 Gehrmann, Ritzmann, Skands:1108.6172 3

Photon Emission

Leading Color Gluon Emission Leading Color Gluon Emission Factorization → g 2 C P ( z ) p a k k | M ( .., p a , k, .. ) | 2 p a · k | M ( .., p a + k, .. ) | 2 − − − m 2 m 2  � 2 p a · p b k → 0 a | M ( .., p a , k, p b , .. ) | 2 → g 2 C b | M ( .., p a , p b , .. ) | 2 − − − ( p a · k )( k · p b ) − ( p a · k ) 2 − ( p b · k ) 2 5

Leading Color Gluon Emission Factorization → g 2 C P ( z ) p a k k | M ( .., p a , k, .. ) | 2 p a · k | M ( .., p a + k, .. ) | 2 − − − m 2 m 2  � 2 p a · p b k → 0 a | M ( .., p a , k, p b , .. ) | 2 → g 2 C b | M ( .., p a , p b , .. ) | 2 − − − ( p a · k )( k · p b ) − ( p a · k ) 2 − ( p b · k ) 2 | M ( .., p a , k, p b , .. ) | 2 ≈ g 2 C a QCD b , .. ) | 2 ( p a , k, p b ) | M ( .., p 0 a , p 0 e branching 2 → 3 Computing antennae = | M ( X → p a , k, p b ) | 2 a QCD e b ) | 2 | M ( X → p 0 a , p 0 6

Gluon Emission Ordering ⊥ = 16( p a · k )( p b · k ) Ordering scale t = 4 p 2 m 2 t Cutoff on t → removes singular regions Strong ordering t 1 > t 2 , t 2 > t 3 etc.. Illustration: S. Galam 7

Photon Emission Factorization P ( z ) p a k k | M ( .., p a , k, .. ) | 2 → e 2 Q 2 p a · k | M ( .., p a + k, .. ) | 2 − − − a m 2 m 2  � 2 p a · p b k → 0 → − e 2 X | M ( { p } , k ) | 2 | M ( { p } ) | 2 a b Q a Q b − − − ( p a · k )( k · p b ) − ( p a · k ) 2 − ( p b · k ) 2 [ a,b ] 8

Photon Emission Factorization P ( z ) p a k k | M ( .., p a , k, .. ) | 2 → e 2 Q 2 p a · k | M ( .., p a + k, .. ) | 2 − − − a m 2 m 2  � 2 p a · p b k → 0 → − e 2 X | M ( { p } , k ) | 2 | M ( { p } ) | 2 a b Q a Q b − − − ( p a · k )( k · p b ) − ( p a · k ) 2 − ( p b · k ) 2 [ a,b ] | M ( { p } , k ) | 2 ≈ e 2 a QED ( { p } , k ) | M ( { p 0 } ) | 2 e m 2 m 2  p a · p b X a a QED b ( { p } , k ) = − 2 Q a Q b ( p a · k )( k · p b ) − ( p a · k ) 2 − e ( p b · k ) 2 [ a,b ] 1 ✓ p a · k p b · k + p b · k ◆ � + m 2 a − m 2 abk − m 2 branching p a · k n → n + 1 b 9

Photon Emission Ordering Separate phase space into sectors branching 2 → 3 X | M ( { p } , k ) | 2 ≈ a e ( { p } , k ) θ (( p 2 b , .. ) | 2 ? ) ab ) | M ( .., p 0 a , p 0 [ a,b ] 1 if ( p 2 ⊥ ) ab is the smallest Equivalent to ordering in ✓ ( p a · k )( p b · k ) ◆ ( p 2 � � t = 4 min ⊥ ) ab = 16 min m 2 10

Matrix Element Comparison • Sample phase space uniformly using RAMBO histories a 1 ...a n − m | M m | 2 P PS • Compute matrix elements with Madgraph ME = | M n | 2 11

Comparison - DGLAP equation 12

Comparison - Coherence 13

Photon Splitting

Photon Splitting Factorization t = m 2 P s ( z ) p a k p b ab | M ( .., p a , p b ) | 2 → e 2 Q 2 | M ( .., k ) | 2 − − − − f p a · p b + m 2 = 2( p a · p b + m 2 f ) f Antenna showering → requires spectator 4( p a · q ) 2 + ( p b · q ) 2 Q 2 m 2  � f f a QED ( p a , p b , q ) = + s p a · p b + m 2 m 2 p a · p b + m 2 f abq f In QCD: Choice of spectator limited by color ordering In QED: Anything goes 15

Selecting the Spectator First attempt: Select spectator uniformly What’s causing this overcounting? 16

Ariadne factor Emission → is on-shell p K Giele, Kosower, Skands:1102.2126 Splitting → is taken off-shell Lönnblad: Comput.Phys.Commun. 71 (1992) 15-31 p K m 2 IK = ( p I + p K ) 2 is small Let’s say is collinear with p K p I → • Use p I as spectator → m 2 IK stays the same as spectator → m 2 IK becomes large • Use p J m 2 JK Ari IK = p m 2 IK + m 2 JK Probability to select p I as spectator 17

Selecting the Spectator Generalized Ariadne factor 1 /m 2 IK Ari p IK = J 1 /m 2 P JK 18

Electroweak Radiation Work in progress

Importance of EW radiation Significant corrections to many processes at high energies: Exclusive di-jet: ~ 10-30% Bell, Kuhn and Rittinger: 1004.4117 W/Z + jets: ~ 5-10% Kuhn, Kulesza, Pozzorini, Schulze: 0703.283 Bauer, Ferland: 1601.07190 20

Importance of EW radiation Chen, Han, Tweedie: 1611.00788 21

Complications for EW radiation • CP violation → forced to keep track of fermion helicities ∆ i = 2 p i · p k + m 2 • Mass effects of the gauge bosons show up V ✓ 1 = 2 g 2 ✓ ( s − ∆ a )( s − ∆ b ) ◆◆ + 1 V + ( ∆ a ∆ b − m 2 emit s ( C v − λ C a ) V ) a V ∆ 2 ∆ 2 ∆ a ∆ b a b • Electroweak decays are a natural part of an EW parton shower Z → f ¯ W → f ¯ f 0 f t → Wb • Massive fermions → Helicity becomes handedness (not Lorentz invariant) → Handedness can flip • Physical differences between transverse and longitudinal gauge bosons → Keep track of those as well 22

Amplitude level calculations Polarization vectors p a p a 1 ✏ µ u ± ( k 1 ) � µ u ± ( k 2 ) T = 2 m ¯ p k √ + L = 1 p k ✏ µ m ( k 1 − k 2 ) p b p b Spinors Vertex decides initial 1 u λ ( p ) = √ 2 k 0 · p ( / p + m ) u − λ ( k 0 ) handedness configuration 1 V = / q 1 u ρ 1 ( p A )¯ v ρ 2 ( p B ) / q 2 v λ ( p ) = √ 2 k 0 · p ( / p − m ) u − λ ( k 0 ) Write everything in terms of products of spinors → Easily calculable Future: More than two fermions → Reduction of computation times 23

Conclusion & Outlook Photon emission • Resums soft and collinear logarithms • Fully coherent Photon splitting • Resums collinear logarithms • Corrects for on-shell photon effects Electroweak radiation • Complications due to mass and helicities • Naturally incorporates electroweak decays • Amplitude level calculations 24

Extra Slides

Sudakov Veto Algorithm Set u = t start Z u ✓ ◆ Sample t from g ( t ) exp d τ g ( τ ) − t Set u = t Accept with probability f ( t ) g ( t ) Sudakov form factor Resums logarithm Z u ✓ ◆ Done t from f ( t ) exp d τ f ( τ ) − t 26

Sudakov Veto Algorithm - Competition 1 Multiple channels g i ( t ) > f i ( t ) For all channels … t 2 t 3 t 4 t 1 Select highest 0 1 Z u X X f i ( t ) exp d τ f j ( τ ) Done @ − A t i j 27

Sudakov Veto Algorithm - Competition 2 Kleiss, Verheyen: 1605.09246 0 1 Z u X X g i ( t ) exp d τ g j ( τ ) Sample t from @ − A t i j g i ( t ) Select a channel with P j g j ( t ) Set u = t Accept with probability f i ( t ) g i ( t ) 0 1 Z u X X f i ( t ) exp d τ f j ( τ ) Done @ − A t i j 28

Sudakov Veto Algorithm - Photon Emission Find an overestimate b ( t ) of a QED (simplified) ( { p } , k ) e Z u ✓ ◆ Start with fermion Sample t from N p b ( t ) exp d τ N p b ( τ ) − momenta { p } t Select a pair ( a, b ) uniformly Set u = t Construct the momenta p 0 a , p 0 b , k Check if ( p 2 ⊥ ) ab is the lowest Accept with probability a e ( { p 0 } , k ) b ( t ) 29

Introduction (old) Two approaches to QED radiation in parton showers DGLAP • Resums collinear photon logarithms • Interleaving with QCD shower • Also applicable in antenna/dipole showers YFS • Resums soft photon logarithms • Collinear logarithms can be included, but not resummed • Afterburner to add soft photons Can we resum both the soft and collinear logarithms? Follow QCD antenna shower Vincia Giele, Kosower, Skands:1102.2126 Gehrmann, Ritzmann, Skands:1108.6172 30