Electroweak Radiation in Antenna Showers

Transcription

1 Electroweak Radiation in Antenna Showers Rob Verheyen With Ronald Kleiss

2 Introduction t cut Λ QCD t hard 2

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

4 Photon Emission

5 Leading Color Gluon Emission Factorization M(.., p a,k,..) 2 M(.., p a,k,p b,..) 2 p akk! g 2 C P (z) p M(.., p a + k,..) 2 apple a k k!0! g 2 2p a p b m 2 a m 2 b C (p a k)(k p b ) (p a k) 2 (p b k) 2 M(.., p a,p b,..) 2 5

6 Leading Color Gluon Emission Factorization M(.., p a,k,..) 2 M(.., p a,k,p b,..) 2 p akk! g 2 C P (z) p M(.., p a + k,..) 2 apple a k k!0! g 2 2p a p b m 2 a m 2 b C (p a k)(k p b ) (p a k) 2 (p b k) 2 M(.., p a,p b,..) 2 M(.., p a,k,p b,..) 2 g 2 Ca QCD e (p a,k,p b ) M(.., p 0 a,p 0 b,..) 2 2! 3 branching Computing antennae a QCD e = M(X! p a,k,p b ) 2 M(X! p 0 a,p 0 b ) 2 6

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

8 Photon Emission Factorization M(.., p a,k,..) 2 M({p},k) 2 k!0! e 2 X [a,b] Q a Q b apple p akk! e 2 Q 2 a 2p a p b (p a k)(k p b ) P (z) p a k M(.., p a + k,..) 2 m 2 a (p a k) 2 m 2 b (p b k) 2 M({p}) 2 8

9 Photon Emission Factorization M(.., p a,k,..) 2 M({p},k) 2 k!0! e 2 X [a,b] Q a Q b apple p akk! e 2 Q 2 a 2p a p b (p a k)(k p b ) P (z) p a k M(.., p a + k,..) 2 m 2 a (p a k) 2 m 2 b (p b k) 2 M({p}) 2 M({p},k) 2 e 2 a QED e ({p},k) M({p 0 }) 2 a QED e ({p},k)= X p a p b m Q a Q b apple2 2 a m 2 b (p [a,b] a k)(k p b ) (p a k) 2 (p b k) 2 1 pa k + m 2 abk m 2 a m 2 b p + p b k n! n +1branching b k p a k 9

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

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

12 12 Comparison - DGLAP equation

13 13 Comparison - Coherence

14 Photon Splitting

15 Factorization Photon Splitting M(.., p a,p b ) 2 p akp b! e 2 Q 2 f P s (z) p a p b + m 2 f M(.., k) 2 t = m 2 ab =2(p a p b + m 2 f ) Antenna showering! requires spectator a QED s (p a,p b,q)= Q 2 f p a p b + m 2 f apple4 (p a q) 2 +(p b q) 2 m 2 abq + m 2 f p a p b + m 2 f In QCD: Choice of spectator limited by color ordering In QED: Anything goes 15

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

17 Emission! Splitting! p K p K is on-shell is taken off-shell Ariadne factor Giele, Kosower, Skands: Lönnblad: Comput.Phys.Commun. 71 (1992) Let s say p K is collinear with p I! m 2 IK =(p I + p K ) 2 is small Use p I as spectator! m 2 IK Use p J as spectator! m 2 IK stays the same becomes large p Ari IK = m 2 JK m 2 IK + m2 JK Probability to select p I as spectator 17

18 Selecting the Spectator Generalized Ariadne factor p Ari IK = 1/m2 IK P J 1/m2 JK 18

19 Electroweak Radiation Work in progress

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

21 Importance of EW radiation Chen, Han, Tweedie:

22 Complications for EW radiation CP violation! forced to keep track of fermion helicities Mass effects of the gauge bosons show up a emit V = 2g2 V s (C v C a ) (s a)(s b) Electroweak decays are a natural part of an EW parton shower t! Wb Z! f f W! f f 0 a b i =2p i p k + m 2 V 1 +( a b m 2 V ) a b 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

23 Amplitude level calculations p a p k + p a Polarization vectors µ T = 1 p 2m ū ± (k 1 ) µ u ± (k 2 ) p b p k p b µ L = 1 m (k 1 k 2 ) Vertex decides initial handedness configuration V = /q 1 u 1 (p A ) v 2 (p B )/q 2 u (p) = v (p) = Spinors 1 p 2k0 p ( /p + m)u (k 0 ) 1 p 2k0 p ( /p m)u (k 0 ) Write everything in terms of products of spinors! Easily calculable Future: More than two fermions! Reduction of computation times 23

24 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

25 Extra Slides

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

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

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

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

30 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: Gehrmann, Ritzmann, Skands: