* possible many new particles

1. Introduction

Automatic calculation of amplitudes

important @ HE colliders LHC & ILC

* many body final states

GRACE

CompHEP

Feyn series

MADGRAPH/MADEVENT

hep-ph/0205020, hep-ph/0111291, hep-ph/0101232

Belanger et al. MicroOmega, hep-ph/0210327

Hahn, Comput.Phys.Commun. 140 (2001) 418; 143 (2002) 54

Maltoni and Stelzer, JHEP 0302 (2003) 027

Comput.Phys.Commun. 153 (2003) 106

Prog. Theor. Phys. Suppl. 138 (2000) 18

Systems of automatic calculation

(Ours)

,

2. Tree level system (GRACE/SUSY)

Model: MSSM

Input parameters:

Higgs & Gauginos

Sfermions

M. Kuroda, Complete Langarian of MSSM, hep-ph/9902340

J. Fujimoto et al., Comput.Phys.Commun. 153 (2003) 106

Example

Input file 'in.prc'

Feynman diagrams drawn by 'gracefig'

Feynman diagrams

generated by 'grc'

Fortran codes

generated by 'grcfort'

Model=”mssm.mdl”;

Process;

ELWK=3;

QCD=0;

Initial={electron, positron};

Final ={photon,chargino1,anti-chargino1};

Kinem=”2302”

Pend;

Integration by 'bases'

Gauge invariance check

gauge, quadruple-precision at 1-point in phase space

ans1 = 0.139175455829902 covariant gauge

ans2 = 0.139175455829902 unitary gauge

ans1/ans2 - 1 = -2.220446049250313E-016

GRACE/SUSY (tree-level) system is

COMPLETED!

We have checked the gauge invariance

with quadruple-precision

SUSY processes with up to 6 external particles

582,102

processes

DONE!

http://minami-home.kek.jp/

The system can be obtained at

3. 1-loop level system (GRACE/SUSY/1LOOP)

Renormalization scheme of the MSSM

Gauge-boson sector:

Renormalization constants of wavefunctions Unmixed bare states

Mass counterterms Mixed mass eigenstates

M. Kuroda, in Research report to the Ministry of Education, Science and Culture,

Japan, the Grant-in-Aid for Scientific Research C (No.08640391), (1999) 127

T. Fritzsche and W. Hollik, Eur. Phys. J. C24 (2002) 619

(conventional approach)

Higgs-boson sector:

Renormalization constants of wavefunctions Unmixed bare states

Chargino sector and Neutralino sector:

Renormalization constants of wavefunctions Unmixed bare states

Matter-fermion sector and Sfermion sector:

Renormalization constants of wavefunctions Mixed mass eigenstates

K-I. Aoki, Z. Hioki, R. Kawabe, M. Konuma and T. Muta,

Prog. Theor. Phys. Suppl. 73 (1982) 1

On mass-shell renormalization

Example

Refs.

M. A. Diaz, S. F. King and A. Ross,

Nucl. Phys. B529 (1998) 23, hep-ph/0008117

T. Blank and W. Hollik, hep-ph/0011092

W. Oller, H. Eberl, W. Majerotto and C. Weber,

hep-ph/0304006

..

* Full Electroweak correction

1935 1-loop level diagrams 7 tree-level diagrams

Model="mssmnlg.mdl";

Process;

ELWK={4,2};

QCD=0;

Initial ={electron positron};

Final ={chargino1 anti-chargino1};

Kinem="2001";

Expand=Yes;

Block=No;

AnyCT=Yes;

Extself=Yes;

Pend;

Input file 'in.prc'

Feynman diagrams

REDUCE source codes

Fortran codes &

Executable files

'grc'

'grcred'

'make'

Feynman diagrams printed to ps-files by 'grcplot'

How you can believe the numbers

produced by an automated system?

UV finiteness

IR finiteness

gauge invariance

Check varing the UV constant ( )

Check varing the fictitious photon mass ( )

[1-loop + soft poton]

Check varing the non-linear gauge parameters

G. Belanger, F. Boudjema, J. Fujimoto, T. Ishikawa, T. Kaneko, K. Kato

and Y. Shimizu, LAPTH-982-03, KEK-CP-138 (2003) hep-ph/0308080

,

* Checking GRACE with the non-linear gauge

has already been done in the SM

(

)

Non-linear gauge in MSSM

Numerator structure is the same

as Feynman gauge (for = 1)

Vertices modified = 1 no AWG

New vertices (ghost sector) appear

Non-linear gauge fixing terms

Results of checks ( )

UV check

(

)

+

s

Z

0

Z

0

zsum0 0 255 (-2.4238440460988892389568132161782622e-0002,

4.8670226801714368832289586855722879e-0003)

zsumc 0 255 (-2.4238440460988892389568132161777729e-0002,

4.8670226801714368832289586855722879e-0003)

(30 digits)

C

UV

= 0, 100

Total

Zall0 (-0.13714308824382200850001518957739093,

2.9534974780222292111693636042692019e-0002)

Zallc (-0.13714308824382200850001518957737294,

2.9534974780222292111693636042692019e-0002)

(31 digits)

(tree)

IR check

= 10

-18

-24

ANS = -8.482168085150522e-0002

= 10

ANS = -8.482168087342838e-0002

(for selected graphs)

(9 digits)

[Ommited e-e-scalar]

gauge invariance check

NLG parameters

alpha

--------------------------

<<selected graph>>42

--------------------------

IU no. T : @ = ^2, # = ^3

RV

| a^4 | a^3 | a^2 | a^1 | a^0

--------------------------

226V | -0.2651979e-07 | 0.2651979e-07

227V | 0.9541715e-07 | -0.9541715e-07

228V | 0.9308935e-07 | -0.9308935e-07

229V | 0.3661252e-08 | -0.3661252e-08

230V | -0.2651979e-07 | 0.2651979e-07

1931S | 0.3902432e-15 | 0.2084935e-14

1932SQ| -0.5294619e-50 | 0.1057452e-49 | 0.5338774e-50 | -0.3820339e-49 | 0.2758471e-49

----------------------------------------------------------------------

cnt 1 0 0 25

tot 0.20977e-01 0.20977e-01 0.20977e-01 0.20977e-01 0.20977e-01

sum1 0.65123e-34 -0.47138e-34 -0.32167e-33 -0.77400e-15 0.20977e-01

max 0.42898e-34 0.22914e-34 0.21894e-33 0.81660e-03 0.12824e-01

beta

--------------------------

<<selected graph>>41

--------------------------

IU no. T : @ = ^2, # = ^3

RV

| a^4 | a^3 | a^2 | a^1 | a^0

--------------------------

158V | -0.1404845e-07 | 0.2651979e-07

159V | 0.4166858e-07 | -0.9541715e-07

160V | 0.3906425e-07 | -0.9308935e-07

161V | 0.1964962e-08 | -0.3661252e-08

166V | -0.1404845e-07 | -0.4044929e-08

1931S | -0.5221061e-15 | 0.2084935e-14

1932SQ| -0.2759842e-52 | -0.1103847e-52 | 0.1159122e-51 | 0.5519367e-52 | 0.2758471e-49

----------------------------------------------------------------------

cnt 1 0 0 20

tot 0.18567e-01 0.18567e-01 0.18567e-01 0.18567e-01 0.18567e-01

sum1 -0.15159e-34 -0.41344e-34 0.67172e-34 0.10355e-14 0.18567e-01

max 0.61753e-35 0.13166e-34 0.19059e-34 0.96369e-03 0.12824e-01

epsln1

--------------------------

<<selected graph>>47

--------------------------

IU no. T : @ = ^2, # = ^3

RV

| a^4 | a^3 | a^2 | a^1 | a^0

--------------------------

132V | 0.4131154e-17 | -0.9419811e-07

133V | 0.2199380e-18 | 0.3210661e-04

150V | 0.4131154e-17 | -0.9419811e-07

151V | 0.2199380e-18 | 0.3210661e-04

276V | -0.5827019e-15 | 0.2976493e-15

1931S@ | 0.2161744e-15 | 0.5510489e-16 | 0.2084935e-14

1933S | -0.6013497e-14 | 0.7254471e-13

1934S@ | -0.3242617e-15 | 0.1240086e-13 | -0.4383777e-12

----------------------------------------------------------------------

cnt 0 0 4 43

tot 0.38631e-03 0.38631e-03 0.38631e-03 0.38631e-03 0.38631e-03

sum1 0.23510e-37 0.10777e-37 -0.10394e-36 -0.37361e-37 0.38631e-03

max 0.23510e-37 0.11755e-37 0.32426e-15 0.50786e-13 0.32229e-03

h

0

4. Outlook

More processes

decays, final 2-bodies, 3-bodies, ...

e.g.

25126 1-loop level diagrams

22 tree-level diagrams!

Masato Jimbo

2004-11-01T16:31:21

Yoshiaki Yasui