carlomat, a program for automatic computation of cross sections p.1/11

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1 carloma, a program for auomaic compuaion of cross secions o lowes order of SM Karol Kołodziej Insiue of Physics, Universiy of Silesia Kaowice Kaowice, 5 June, 2007 carloma, a program for auomaic compuaion of cross secions p.1/11

2 Moivaion Increasing energy of iniial beams a paricle colliders such as LHC, or ILC carloma, a program for auomaic compuaion of cross secions p.2/11

3 Moivaion Increasing energy of iniial beams a paricle colliders such as LHC, or ILC reacions wih more and more paricles in he final sae will be measured. carloma, a program for auomaic compuaion of cross secions p.2/11

4 Moivaion Increasing energy of iniial beams a paricle colliders such as LHC, or ILC reacions wih more and more paricles in he final sae will be measured. Higher luminosiy of he colliders carloma, a program for auomaic compuaion of cross secions p.2/11

5 Moivaion Increasing energy of iniial beams a paricle colliders such as LHC, or ILC reacions wih more and more paricles in he final sae will be measured. Higher luminosiy of he colliders higher precision of he measuremens. carloma, a program for auomaic compuaion of cross secions p.2/11

6 Moivaion Increasing energy of iniial beams a paricle colliders such as LHC, or ILC reacions wih more and more paricles in he final sae will be measured. Higher luminosiy of he colliders higher precision of he measuremens. SM predicions for reacions wih several paricles in he final sae are needed. carloma, a program for auomaic compuaion of cross secions p.2/11

7 Moivaion Increasing energy of iniial beams a paricle colliders such as LHC, or ILC reacions wih more and more paricles in he final sae will be measured. Higher luminosiy of he colliders higher precision of he measuremens. SM predicions for reacions wih several paricles in he final sae are needed. SM radiaive correcions o such reacions should be included, a leas he leading ones. carloma, a program for auomaic compuaion of cross secions p.2/11

8 Examples Top quark pair producion a ILC e + e. carloma, a program for auomaic compuaion of cross secions p.3/11

9 Examples Top quark pair producion a ILC e + e. As he op and aniop decay before hey hadronize, predominanly ino bw + and bw, carloma, a program for auomaic compuaion of cross secions p.3/11

10 Examples Top quark pair producion a ILC e + e. As he op and aniop decay before hey hadronize, predominanly ino bw + and bw, and W s decay ino f f -pairs, carloma, a program for auomaic compuaion of cross secions p.3/11

11 Examples Top quark pair producion a ILC e + e. As he op and aniop decay before hey hadronize, predominanly ino bw + and bw, and W s decay ino f f -pairs, 6 fermion reacions of he form e + e b f 1 f 1 b f 2 f 2, where f 1, f 2 = ν e,ν µ,ν τ,u,c and f 1, f 2 = e,µ,τ,d,s, should be sudied wih a complee se of he Feynman diagrams, including a leas he leading radiaive correcions. carloma, a program for auomaic compuaion of cross secions p.3/11

12 e + e Examples of he Feynman diagrams of e + e b f1 f 1 b f2 f 2 (a) signal, (b) and (c) background. carloma, a program for auomaic compuaion of cross secions p.4/11

13 e + e Inclusion of he radiaive correcions is a complicaed ask as, e.g. a pure EW reacion e + e bν µ µ + bµ ν µ, receives conribuions from 452 diagrams carloma, a program for auomaic compuaion of cross secions p.5/11

14 e + e Inclusion of he radiaive correcions is a complicaed ask as, e.g. a pure EW reacion e + e bν µ µ + bµ ν µ, receives conribuions from 452 diagrams and he hadronic reacion e + e bu d bdū, from 1484 Feynman diagrams, carloma, a program for auomaic compuaion of cross secions p.5/11

15 e + e Inclusion of he radiaive correcions is a complicaed ask as, e.g. a pure EW reacion e + e bν µ µ + bµ ν µ, receives conribuions from 452 diagrams and he hadronic reacion e + e bu d bdū, from 1484 Feynman diagrams, already a he ree level of SM, in he uniary gauge, neglecing he Higgs boson couplings o fermions ligher han b. carloma, a program for auomaic compuaion of cross secions p.5/11

16 A program ee6f v. 1.0 Cross secions of e + e 6 fermions relevan for a -pair producion and decay in he lowes order can be calculaed wih a Mone Carlo program ee6f. K. Kołodziej, Comp. Phys. Commun. 151 (2003) 339, hep-ph/ ; A. Biernacik, K. Kołodziej, Nucl. Phys. B (Proc. Suppl) 116 (2003) 33, hep-ph/ carloma, a program for auomaic compuaion of cross secions p.6/11

17 A program ee6f v. 1.0 Cross secions of e + e 6 fermions relevan for a -pair producion and decay in he lowes order can be calculaed wih a Mone Carlo program ee6f. K. Kołodziej, Comp. Phys. Commun. 151 (2003) 339, hep-ph/ ; A. Biernacik, K. Kołodziej, Nucl. Phys. B (Proc. Suppl) 116 (2003) 33, hep-ph/ I akes ino accoun boh he elecroweak and QCD lowes order conribuions. Fermion masses are no negleced cross secions can be usually calculaed wihou any kinemaical cus. carloma, a program for auomaic compuaion of cross secions p.6/11

18 A program ee6f v. 1.0 Cross secions of e + e 6 fermions relevan for a -pair producion and decay in he lowes order can be calculaed wih a Mone Carlo program ee6f. K. Kołodziej, Comp. Phys. Commun. 151 (2003) 339, hep-ph/ ; A. Biernacik, K. Kołodziej, Nucl. Phys. B (Proc. Suppl) 116 (2003) 33, hep-ph/ I akes ino accoun boh he elecroweak and QCD lowes order conribuions. Fermion masses are no negleced cross secions can be usually calculaed wihou any kinemaical cus. Some exensions of he SM, such as an anomalous Wb coupling, have been implemened, oo. carloma, a program for auomaic compuaion of cross secions p.6/11

19 A program ee6f v. 1.0 The consan widhs of unsable paricles are inroduced hrough he complex mass parameers: MV 2 = mv 2 im V Γ V, V = W,Z, MH 2 = m 2 H im H Γ H, M = m 2 im Γ, carloma, a program for auomaic compuaion of cross secions p.7/11

20 A program ee6f v. 1.0 The consan widhs of unsable paricles are inroduced hrough he complex mass parameers: MV 2 = mv 2 im V Γ V, V = W,Z, MH 2 = m 2 H im H Γ H, M = m 2 im Γ, which replace masses in he corresponding propagaors, boh in he s- and -channel Feynman diagrams, µν F (q) = F (q) = gµν + q µ q ν /MV 2 q 2 MV 2, 1 q 2 MH 2, S F (q) = /q + M q 2 M 2. Propagaors of a phoon and a gluon are aken in he Feynman gauge. carloma, a program for auomaic compuaion of cross secions p.7/11

21 A program ee6f v. 1.0 The EW mixing parameer may be defined eiher real (FWS) or complex (CMS), sin 2 θ W = 1 m2 W m 2 Z or sin 2 θ W = 1 M2 W M 2 Z. carloma, a program for auomaic compuaion of cross secions p.8/11

22 A program ee6f v. 1.0 The EW mixing parameer may be defined eiher real (FWS) or complex (CMS), sin 2 θ W = 1 m2 W m 2 Z or sin 2 θ W = 1 M2 W M 2 Z. The marix elemens are calculaed wih he heliciy ampliude mehod of K. Kołodziej, M. Zrałek, Phys. Rev. D43 (1991) 3619; F. Jegerlehner, K. Kołodziej, Eur. Phys. J. C12 (2000) 77. carloma, a program for auomaic compuaion of cross secions p.8/11

23 A program ee6f v. 1.0 The EW mixing parameer may be defined eiher real (FWS) or complex (CMS), sin 2 θ W = 1 m2 W m 2 Z or sin 2 θ W = 1 M2 W M 2 Z. The marix elemens are calculaed wih he heliciy ampliude mehod of K. Kołodziej, M. Zrałek, Phys. Rev. D43 (1991) 3619; F. Jegerlehner, K. Kołodziej, Eur. Phys. J. C12 (2000) 77. Phase space inegraions (14-dimensional) are performed wih he Mone Carlo mehod (a muli-channel approach). carloma, a program for auomaic compuaion of cross secions p.8/11

24 A program ee6f v. 1.0 The EW mixing parameer may be defined eiher real (FWS) or complex (CMS), sin 2 θ W = 1 m2 W m 2 Z or sin 2 θ W = 1 M2 W M 2 Z. The marix elemens are calculaed wih he heliciy ampliude mehod of K. Kołodziej, M. Zrałek, Phys. Rev. D43 (1991) 3619; F. Jegerlehner, K. Kołodziej, Eur. Phys. J. C12 (2000) 77. Phase space inegraions (14-dimensional) are performed wih he Mone Carlo mehod (a muli-channel approach). Resuls agree nicely wih resuls of oher exising programs, see e.g. S. Dimaier, Exended ECFA/DESY Workshop, hep-ph/ carloma, a program for auomaic compuaion of cross secions p.8/11

25 EW radiaive correcions o e + e b f 1 f 1 b f 2 f 2 carloma, a program for auomaic compuaion of cross secions p.9/11

26 EW radiaive correcions o e + e b f 1 f 1 b f 2 f 2 K. Kołodziej, A. Saroń, A. Lorca, T. Riemann, Eur. Phys. J. C 46 (2006) 357. carloma, a program for auomaic compuaion of cross secions p.9/11

27 EW radiaive correcions o e + e b f1 f 1 b f2 f 2 K. Kołodziej, A. Saroń, A. Lorca, T. Riemann, Eur. Phys. J. C 46 (2006) 357. carloma, a program for auomaic compuaion of cross secions p.9/11

28 EW radiaive correcions o e + e b f1 f 1 b f2 f 2 K. Kołodziej, A. Saroń, A. Lorca, T. Riemann, Eur. Phys. J. C 46 (2006) 357. (a) is calculaed wih a subrouine based on opfi, by T. Riemann, e al., (b) (e) wih subrouines wrien by A. Saroń. carloma, a program for auomaic compuaion of cross secions p.9/11

29 e + e H If he Higgs boson has mass below he hreshold, m H < 2m, hen H Yukawa coupling can be bes deermined from his reacion [Djouadi, Kalinowski, Zerwas]. carloma, a program for auomaic compuaion of cross secions p.10/11

30 e + e H If he Higgs boson has mass below he hreshold, m H < 2m, hen H Yukawa coupling can be bes deermined from his reacion [Djouadi, Kalinowski, Zerwas]. e + e H γ, Z e + e (a) (b) γ, Z H e + e H Z Z (c) carloma, a program for auomaic compuaion of cross secions p.10/11

31 e + e H If he Higgs boson has mass below he hreshold, m H < 2m, hen H Yukawa coupling can be bes deermined from his reacion [Djouadi, Kalinowski, Zerwas]. e + e H γ, Z e + e (a) (b) γ, Z H e + e H Z Z Diagrams (a) i (b) dominae he cross secion g 2 H. (c) carloma, a program for auomaic compuaion of cross secions p.10/11

32 e + e 8 fermions Taking ino accoun decays of unsable paricles we ge, e.g., he process carloma, a program for auomaic compuaion of cross secions p.11/11

33 e + e 8 fermions Taking ino accoun decays of unsable paricles we ge, e.g., he process e + e bu d bµ ν µ b b. carloma, a program for auomaic compuaion of cross secions p.11/11

34 e + e 8 fermions Taking ino accoun decays of unsable paricles we ge, e.g., he process e + e bu d bµ ν µ b b. e + e γ, Z (a) H W b W + d u b b µ ν µ b e + e γ, Z (b) H W + b b b W b u d ν µ µ e + e H Z Z (c) W + W b b b b d u ν µ µ carloma, a program for auomaic compuaion of cross secions p.11/11

35 e + e 8 fermions Taking ino accoun decays of unsable paricles we ge, e.g., he process e + e bu d bµ ν µ b b. e + e γ, Z (a) H W b W + d u b b µ ν µ b e + e γ, Z (b) H W + b b b W b u d ν µ µ e + e H Z Z (c) W + W b b b b d u ν µ µ In he uniary gauge, here is Feynman diagrams! carloma, a program for auomaic compuaion of cross secions p.11/11

36 e + e 8 fermions Taking ino accoun decays of unsable paricles we ge, e.g., he process e + e bu d bµ ν µ b b. e + e γ, Z (a) H W b W + d u b b µ ν µ b e + e γ, Z (b) H W + b b b W b u d ν µ µ e + e H Z Z (c) W + W b b b b d u ν µ µ In he uniary gauge, here is Feynman diagrams! A srong need for a complee auomaizaion of he cross secion compuaion. Do i wih carloma! carloma, a program for auomaic compuaion of cross secions p.11/11