Massive Quarks in Vincia. M. Ritzmann in collaboration with A. Gehrmann-De Ridder and P. Skands

Transcription

1 Massive Quarks in Vincia M. Ritzmann in collaboration with A. Gehrmann-De Ridder and P. Skands

2 Outline Introduction - Parton Showers Vincia - Principles Masses in Vincia

3 Energy Scales at a Collider Energy (log scale) 1 TeV m Z m ρ

4 Energy Scales at a Collider Energy (log scale) 1 TeV fixed order full pqcd (fixed order) few partons m Z m ρ

5 Energy Scales at a Collider Energy (log scale) 1 TeV m Z m ρ

6 Energy Scales at a Collider Energy (log scale) 1 TeV m Z m ρ

7 Energy Scales at a Collider Energy (log scale) 1 TeV m Z parton shower approximate pqcd (all orders) many partons m ρ

8 Energy Scales at a Collider Energy (log scale) 1 TeV m Z + π + n m ρ K + π + π 0

9 Energy Scales at a Collider Energy (log scale) 1 TeV m Z m ρ confined QCD phenomenological models very many hadrons

10 Energy Scales at a Collider Energy (log scale) 1 TeV fixed order full pqcd (fixed order) few partons m Z parton shower approximate pqcd (all orders) many partons m ρ confined QCD phenomenological models very many hadrons

11 Parton Showers - Questions What governs the emission pattern? How are emissions ordered? How is colour coherence accounted for?

12 Examples of Parton Showers

13 Examples of Parton Showers based on ordering coherence

14 Examples of Parton Showers Herwig++ [1] based on 1 2 Altarelli-Parisi splitting functions P q qg ordering angular ordering coherence shower evolution [1] M. Bähr, S. Gieseke, M. A. Gigg, D. Grellscheid, K. Hamilton, O. Latunde-Dada, S. Plätzer, P. Richardson, M.H. Seymour, A, Sherstnev, J. Tully, B. R. Webber arxiv:

15 Examples of Parton Showers Herwig++ [1] Sherpa [2] based on 1 2 Altarelli-Parisi splitting functions 1 2 Altarelli-Parisi splitting functions ordering coherence angular ordering particle virtuality angular ordering superimposed [2] T. Gleisberg, S. Höche, F. Krauss, M. Schönherr, S. Schumann, F. Siegert, J. Winter arxiv:

16 Examples of Parton Showers Herwig++ [1] Sherpa [2] Sherpa [3] based on 1 2 Altarelli-Parisi splitting functions 1 2 Altarelli-Parisi splitting functions 2 3 Catani-Seymour dipoles [a, b] ordering particle virtuality transverse momentum pt coherence angular ordering angular ordering superimposed pt ordering kinematics + C.-S. dipoles [a] S. Catani, M. H. Seymour arxiv: hep-ph/ [b] Z. Nagy, D. E. Soper arxiv: hep-ph/ [3] S. Schumann, F. Krauss arxiv:

17 Examples of Parton Showers Herwig++ [1] Sherpa [2] Sherpa [3] Pythia 8 [4] based on 1 2 Altarelli-Parisi splitting functions 1 2 Altarelli-Parisi splitting functions 2 3 Catani-Seymour dipoles [a, b] 1 2 A-P s. functions (2 3 kinematics) ordering particle virtuality transverse momentum pt transverse momentum pt coherence angular ordering angular ordering superimposed pt ordering kinematics + C.-S. dipoles pt ordering kinematics [4] T. Sjöstrand, S. Mrenna, P. Skands arxiv:

18 Vincia W. Giele, D. Kosower, P. Skands arxiv:

19 Vincia W. Giele, D. Kosower, P. Skands arxiv: based on 2 3 splittings (antenna cascade, as pioneered by Ariadne [1] ) [1] G. Gustafson, U. Pettersson Nucl.Phys.B306:746,1988

20 based on 2 3 splittings (antenna cascade, as pioneered by Ariadne [1] ) for other projects inspired by Ariadne, see e.g. J.-C. Winter, F. Krauss arxiv: A. J. Larkoski, M. E. Peskin arxiv: [1] G. Gustafson, U. Pettersson Nucl.Phys.B306:746,1988

21 Vincia W. Giele, D. Kosower, P. Skands arxiv: based on 2 3 splittings (antenna cascade, as pioneered by Ariadne [1] ) flexible with regards to ordering variable [1] G. Gustafson, U. Pettersson Nucl.Phys.B306:746,1988

22 Vincia W. Giele, D. Kosower, P. Skands arxiv: based on 2 3 splittings (antenna cascade, as pioneered by Ariadne [1] ) flexible with regards to ordering variable closely related to antenna subtraction [2] [1] G. Gustafson, U. Pettersson Nucl.Phys.B306:746,1988 [2] A. Gehrmann-De Ridder, T. Gehrmann, E. W. N. Glover arxiv:hep-ph/

23 Vincia W. Giele, D. Kosower, P. Skands arxiv: based on 2 3 splittings (antenna cascade, as pioneered by Ariadne [1] ) flexible with regards to ordering variable closely related to antenna subtraction [2] implemented for e + -e - collisions at present [1] G. Gustafson, U. Pettersson Nucl.Phys.B306:746,1988 [2] A. Gehrmann-De Ridder, T. Gehrmann, E. W. N. Glover arxiv:hep-ph/

24 Goals of Vincia a parton shower which improves the description of QCD radiation facilitates matching with fixed order results helps estimating its theory error can be used from within Pythia 8

25 Antenna Shower - Cartoon at what value of the ordering variable Q will each antenna emit? p I p q p K p q

26 Antenna Shower - Cartoon determined by evolution integral I A p 2 ant,q 2 start,q 2 emit p q p ant = p q + p I qg qgg qg qq q p I p ant = p I + p K gg ggg gg gq q p q p ant = p q + p K qg qgg qg qq q p K

27 Antenna Shower - Cartoon determine scales p I p q Q 1 Q 2 p q Q 3 p K

28 Antenna Shower - Cartoon determine scales p I p q Q 1 Q 2 p q Q 3 p K Q 2 >Q 1 >Q 3 split {p I,p K } {p i,p j,p k }

29 Dipole-Antenna Shower - Cartoon given Q2, determine 3-particle invariants sij, sjk y jk i k i j j 0.2 Q (s ij,s jk )=Q 2 j soft j k y ij = 2 p ip j p 2 ant

30 Dipole-Antenna Shower - Cartoon from sij, sjk, determine pi, pj, pk with momentum mapping p I p q p K p q

31 Dipole-Antenna Shower - Cartoon from sij, sjk, determine pi, pj, pk with momentum mapping p i p q p j p q p k replace

32 Dipole-Antenna Shower - Cartoon restart p i p q p j p q p k

33 Evolution Integral I A I A p 2 ant,q 2 start,q 2 emit = 1 λ Q 2 start Q 2 emit ds ij ds jk α s (s ij,s jk ) 4π C ijk A IK ijk (s ij,s jk,...) s jk Q start Q emit s ij

34 Evolution Integral I A I A p 2 ant,q 2 start,q 2 emit = 1 λ Q 2 start Q 2 emit ds ij ds jk α s (s ij,s jk ) 4π C ijk A IK ijk (s ij,s jk,...) Q : evolution variable s ij =2p i p j C ijk : colour factor A IK ijk (p 2 ant,s ij,s jk,m 2 i,m 2 j,m 2 k) : antenna function λ = λ(p 2 ant,m 2 I,m 2 K)=(2p I p K ) 2 (2m I m K ) 2

35 Evolution Variables several options implemented y jk 1.0 m D 2 min(y ij,y jk ) y jk 1.0 p T 4 y ij y jk md = y ij pt = y ij

36 Antenna Functions I A p 2 ant,q 2 start,q 2 emit = 1 λ Q 2 start Q 2 emit ds ij ds jk α s (s ij,s jk ) 4π C ijk A IK ijk (s ij,s jk,...) reproduce (quasi-)collinear splitting functions / soft eikonals in unresolved limits parts which do not contribute in unresolved limits are irrelevant for fixed order, but influence the shower handle on shower uncertainty

37 Masses - needed? secondary production of beauty and charm are highly relevant to phenomenology during the shower evolution, quark masses will become important inevitably want to be consistent with the production of heavy mesons

38 Masses - needed? s = GeV e + e B-hadron(s) + X, 1 N dn dx B PRELIMINARY SLD collaboration Phys.Rev.D65:092006,2002 Erratum-ibid.D66:079905,2002 Vincia (errors only statistical) b massless no hadronisation x B =2E B-hadron /E cm

39 Masses in Vincia A. Gehrmann-De Ridder, MR, P. Skands in preparation masses have to be implemented in phase space antenna functions [1] momentum mapping [1] A. Gehrmann-De Ridder, MR arxiv:

40 Massive Antennae: QQ QgQ massless m Q = m Q =0.15 p 2 ant y jk 1.0 y jk y jk 1.0 y jk y ij y ij 0.4 A QQ QgQ (y ij,y jk ) 0.4 A QQ QgQ (y ij,y jk ) 50 = 5 = y ij y ij

41 Massive Antennae: massless Qg Qgg m Q =0.15 p 2 ant y jk 1.0 y jk y jk 1.0 y jk y ij y ij 0.4 A Qg Qgg (y ij,y jk ) 0.4 A Qg Qgg (y ij,y jk ) = = y ij y ij

42 Massive Antennae: massless gg gqq m Q =0.15 p 2 ant y jk 1.0 y jk A gg gqq (y ij,y jk ) = A gg gqq (y ij,y jk ) = y ij y ij

43 Massive Antenna Mapping conserves four-momentum keeps all particles on-shell

44 Massive Antenna Mapping conserves four-momentum } keeps all particles on-shell one parameter remaining

45 Massive Antenna Mapping conserves four-momentum keeps all particles on-shell } one parameter remaining generalises massless antenna mapping [1] treats emitters of identical mass symmetrically [1] D. A. Kosower arxiv:hep-ph/

46 Massive Antenna Mapping {p I,p K } {p i,p j,p k }, p 2 I = M 2 I,p 2 i = m 2 i,... p I = xp i + rp j + zp k antenna mapping given by r = p2 ant + MI 2 M K 2 2 p 2 ant s 2 + IK (s min IK )2 2 p 2 ant 2 m j m k } (s jk s min jk ) (s ij s min ) ij s jk s min jk + s ij s min ij

47 1.0 y jk Mapping - Examples m i = m k =0.15 p 2 ant, m j =0 0.8 parent configuration p K p I y ij

48 Masses - needed? s = GeV e + e B-hadron(s) + X, 1 N dn dx B PRELIMINARY SLD collaboration Phys.Rev.D65:092006,2002 Erratum-ibid.D66:079905,2002 Vincia (errors only statistical) b massive no hadronisation x B =2E B-hadron /E cm

49 Masses - needed? s = GeV e + e B-hadron(s) + X, 1 N dn dx B PRELIMINARY SLD collaboration Phys.Rev.D65:092006,2002 Erratum-ibid.D66:079905,2002 Vincia (errors only statistical) b massive default Pythia 8 hadronisation x B =2E B-hadron /E cm

50 Conclusions Vincia has been extended to include quark masses in electron-positron collisions next: finish tests and tune hadronisation on LEP data next-to-next: extend to initial state partons