Slepton NLG (Non-linear gauge) in GRACE/SUSY-loop

Transcription

1 Slepton NLG (Non-lnear gauge n GRACE/SUSY-loop M. Jbo (Speaker, T. Ishkawa and M. Kuroda 3 Chba Unversty o Coerce KEK 3 Mej GakunUnversty CPP, 3rd Coputatonal Partcle Physcs orkshop at KEK (Tsukuba, Japan, 3rd-5th Septeber

2 Contents. Motvaton. GRACE syste 3. Non-lnear gauge (NLG 4. Renoralzaton schee 5. Nuercal tests 6. Suary

3 . Motvaton SUSY s an attractve canddate or BSM. Search or SUSY partcles at LHC and ILC Experents at the ILC oer hgh-precson deternaton o SUSY paraeters. Theoretcal predctons wth the slarly hgh accuracy s requred. Contrbutons at least one-loop level should be ncluded n perturbatve calculatons o apltudes. Autoatc calculaton 3

4 . GRACE syste Generates all eynan dagras autoatcally Generates physcal apltudes autoatcally Incorporates lbrares (-pont unctons, Loop ntegral, Kneatcs, etc. Integrates the atrx eleent by the adaptve Monte Carlo ethod (BASES Does Monte Carlo event generaton (SPRING Enables varous sel-check or the results (UV cancellaton, IR cancellaton, NLG nvarance, etc. 4 Other autoatc SUSY -loop systes SloopS (. Boudjea, et al., 5, eynart/calc (T. Hahn,, 6

5 Structure o autoatc systes or loop calculaton Lagrangan Renoralzaton Process Graph generator eynan rule Apltude generator Kneatcs Source code or all graphs (wth Sybolc anpulaton Couplng const. Counter ter Renor. const. 5 Loop ntegraton -pont unc.

6 eatures o GRACE SM MSSM Tree level GRACE GRACE/SUSY -loop level GRACE-loop GRACE/SUSY-loop 6

7 eatures o GRACE Calculaton Methods SM MSSM Tree level GRACE GRACE/SUSY Helcty apltudes (CHANEL -loop level GRACE-loop GRACE/SUSY-loop Matrx eleents (REDUCE, ORM (REDUCE 7

8 eatures o GRACE Gauge-nvarance tests SM MSSM Tree level -loop level GRACE GRACE/SUSY Between covarant and untary gauge GRACE-loop GRACE/SUSY-loop Non-lnear gauge (NLG 8

9 Rearks: In general R -gauge, the longtudnal k k part o the gauge propagators, e.g. g ( k M k causes nuercal nstablty n loop calculaton. In untary gauge (, stuaton s worse. e need another gauge xng along wth t Hoot- eynan gauge ( or gauge-nvarance test. Non-lnear gauge k k M 9

10 3. Non-lnear gauge (NLG g L (gauge xng ters G ν g G ν g vg g A The NLG orals s an extenson o the lnear -gauge: R v g M v g M,

11 NLG orals: (gauge xng ters G G H h ν g gc A e H h ( ( G G H h ν g gc A e H h ( ( ( G H h v g H h NLG paraeters:,,,,,, ( H h H h SM: G. Bélanger et al., Phys. Rep. 43 (6 7 MSSM: J. ujoto et al., Nucl. Phys. (Proc. Suppl. 57 (6 57; Phys. Rev. D75 (7 3 A g L

12 (gauge xng ters G G H h ν g gc A e H h ( ( G G H h ν g gc A e H h ( ( ( G H h v g H h NLG paraeters: Extenson o NLG by ncludng blnear ors o sleptons, * * * e e c c e c g, * * * e e c c e c g,,,,,,,,, ( e H h H h c c c A g L

13 eynan rules ( g cos ( p p gc ( p p Lnear gauge + NLG (G + g M cos ( M cos gm c Lnear gauge + NLG 3 g g c g cos sn sn 4 M cos NLG Lnear gauge + g

14 4. Renoralzaton schee The renoralzaton schee or the electroweak sector n GRACE/SUSY-loop s a varaton o the on-ass-shell schee []. The on-ass-shell condton: gauge bosons (,, all erons ( all serons ( CP odd Hggs ( A the heaver CP even Hggs ( H both chargnos (, the lghtest neutralno ( 4 [] J. ujoto, T. Ishkawa, Y. Kurhara, M. Jbo, T. Kon and M. Kuroda, Phys. Rev. D75 3 (7.

15 Renoralzaton condtons n slepton sector 5 RC-I (used n [] aveuncton renoralzaton constants ntrduced n ass egenstates R L cos sn sn cos / / / / cos sn sn cos R L cos sn sn cos,, e

16 Renoralzaton condtons n RC-I (The thrd generaton o slepton sector On ass-shell condtons: Resdue condtons: Decouplng condtons: SU( relaton:,,, ( j j j j j, ( cos ( [ M ( sn ] sn cos 6 -pont unc. (dagonal ( ( ( q q q

17 RC-II aveuncton renoralzaton constants ntrduced n gauge syetrc states (The thrd generaton o slepton sector L R / LL / RL / LR / RR L R / L ( M cos 7

18 8 cos sn sn cos cos sn sn cos M R L cos sn sn cos R LR LR L M * * * * R L RR RL LR LL RR LR RL LL * R * L M M M M R L / RR / RL / LR / LL R LR LR L / RR / LR / RL / LL * R * L

19 Renoralzaton condtons n RC-II On ass-shell condtons: ( [cos LL cos sn ( LR RL sn RR] ( [sn LL cos sn ( LR RL cos RR] ( Resdue condtons: ( [cos LL cos sn ( LR RL sn RR] ( [sn LL cos sn ( LR RL cos RR] ( 9

20 Decouplng condtons: ( [sn ( LL RR cos ( LR RL] ( [sn ( RR LL cos ( LR RL] SU( relaton: L M cos cos ( M cos sn M cos L cos sn cos LL LL LR RL ( M cos

21 5. Nuercal tests our knds o decay processes: h 3 4 Two knds o scatterng processes: * * Two knds o renoralzaton condtons: RC-I RC-II NLG nput-paraeter: g * νg g c * * Kneatcally allowed settngs or SUSY paraeters

22 Decay Process Loop + CT 34 dagras

23 CUV part Process Coecents o n ANS(CUV= - ANS(CUV= c n Lnear gauge RC-I Graph no. n= n= 6.77E E E E E E E E+4 su.449e-.6699e-7 ax.844e E+4 RC-II Graph no. n= n= 6.77E E E E E E E E+4 su.4489e-.6473e-7 ax.844e E+4 3

24 nte part Process Coecents o n ANS(CUV= c n 4 RC-I RC-II Graph no. n= n= E E E E E E E E E E E E E E E E+ su.55e E-4 ax.546e E+ Graph no. n= n= E E E E E E E E E E E E E E E E+ su.55e E-4 ax.546e E+

25 Process h Loop + CT 5 dagras 5

26 CUV part Process Coecents o n ANS(CUV= - ANS(CUV= c n 6 RC-I RC-II Graph no. n= n= E E E E E E E E E E+ 35.E E E E E E+3 su -6.34E E-7 ax.3668e E+3 Graph no. n= n= E E E E E E E E E E+ 35.E E E E E E+3 su -6.34E E-7 ax.3668e E+3

27 nte part Process Coecents o n ANS(CUV= c n RC-I Graph no. n= n=.43358e E E E+ 4.97E E E E E E E E E E E E- 35.E E E E E E+ su -.738E E- ax e E+ 7

28 nte part Process Coecents o n ANS(CUV= c n RC-II Graph no. n= n=.43358e E E E+ 4.97E E E E E E E E E E E E- 35.E E E E E E+ su -.738E E- ax e E+ 8

29 Process 3 Loop + CT dagras 9

30 CUV part Process 3 Coecents o n ANS(CUV= - ANS(CUV= c n 3 RC-I RC-II Graph no. n= n= 8.374E E E E E+5.838E E E E E E E+5 su E E-6 ax 5.36E+5.838E+5 Graph no. n= n= 8.374E E E E E+5.838E E E E E E E+5 su E E-6 ax 5.36E+5.838E+5

31 nte part Process 3 Coecents o n ANS(CUV= c n RC-I Graph no. n= n= E E E E E+ -.84E E+.7573E E E E E- 9.9E+3.84E E E E E E E E E E E E E E E E E E E E E+3 su E E-8 ax.9486e e+3 3

32 nte part Process 3 Coecents o n ANS(CUV= c n 3 RC-II Graph no. n= n= E E E E E+ -.84E E+.7573E E E E E- 9.9E+3.84E E E E E E E E E E E E E E E E E E E E E+3 su E E-8 ax.9486e e+3

33 Process 4 Loop + CT 56 dagras 33

34 CUV part Process 4 Coecents o n ANS(CUV= - ANS(CUV= c n RC-I RC-II Graph no. n= n= E E E E E E E E E E+3 su E E-6 ax.3546e E+3 Graph no. n= n= E E E E E E E E E E+3 su E E-6 ax.3546e E+3 34

35 nte part Process 4 Coecents o n ANS(CUV= RC-I c n Graph no. n= n= E E E E E+.58E E E E E E E E E E E E E+ su.469e E-4 ax E E+ 35 RC-II Graph no. n= n= E E E E E+.58E E E E E E E E E E E E E+ su.469e E-4 ax E E+

36 Scatterng Process [Loop+CT: 388 dagras] [Tree: dagras] Coecents o c (n,,,3,4 n ANS(CUV= ANS(CUV= canceled aong 49 dagras. n * n= n= n= n=3 n=4 su -.858E E E E E-38 ax.77758e+.94e E E-.6676E- * Coecents o c aong 43 dagras. n (n,,3,4 n ANS(CUV= canceled n= n= n= n=3 n=4 su.86445e E E E E-9 ax E E E E-3.3E-3 36

37 CUV part * * Graph no. n= n= n= n=3 n= E E E E E E E E E E E E E E E E E E E E E E E E E E E E+ su -.858E E E E E-38 ax.77758e+.94e E E-.6676E- 37

38 Process [Loop+CT: 47 dagras] * * [Tree: 9 dagras] Coecents o c (n,,,3,4 n ANS(CUV= ANS(CUV= canceled aong 69 dagras. n n= n= n= n=3 n=4 su E E E E E-34 ax 5.739E E- 4.79E E-.8445E- Coecents o c aong 5 dagras. n (n,,3,4 n ANS(CUV= canceled n= n= n= n=3 n=4 su E E E E E-36 ax.688e e e e E-5 38

39 6. Suary e have conred the NLG nvarance o our decay processes and two scatterng processes by ntroducng the gauge xng ters o blnear ors o sleptons, n two knd o renoralzaton condtons usng GRACE/SUSY-loop. 39