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Unstable-particles pair production in MPT approach in NNLO
M.L.Nekrasov
IHEP, Protvino


The problem:
A description of processes of production and decays of fundamental unstable particles for needs of colliders of next generation (ILC) must provide (i) gauge cancellations and unitarity; (ii) enough high accuracy of calculation of resonant contributions Modified perturbation theory (MPT) permits direct expansion of the cross-section in powers of the coupling constant with the aid of distribution-theory methods The gauge invariance should be maintained The accuracy of description of resonant contributions =

?

To clear up this question, I do numerical simulation in the MPT up to the NNLO (with taking into consideration universal massless-particles contributions)


Double-resonant contributions to pair production and decay of unstable particles:
e+

S
e-

s s

1 2

MPT

expansion of the cross-section in powers of


Ingredients of MPT:

·

Asymptotic expansion of BW factors in powers of

/ F.Tkachov,1998 /

Taylor in



Polinomial in


3-loop

NNLO :

·

Analytic regularization of the kinematic factor

/ M.Nekrasov,2007 /

analytic calculation of "singular" integrals

·

Conventional-perturbation-theory definition of the "test" function


Model for testing MPT :

· ·

Test function :
tree-level for e+ e-

, Z

tt

_

W+

b W -b

_

Breigt-Wigner factors :
three-loop contributions to self-energy ( = 1+ 22+ 33 )

·

Universal soft massless-particles contributions :
Flux function in leading-log approximation:

Coulomb singularities through one-gluon exchanges:


Results :

Total cross-section (s) :

Mt = 175 GeV MW = 80.4 GeV

Mb= 0

s [GeV]
500

__



[pb]



LO

NLO
0.6344

NNLO
0.6698(7)

0.6724

0.5687

100%
1000 0.2255

84.6%
0.1821

94.3%
0.2124

99.6(1)%
0.2240(2)

100%

80.8%

94.2%

99.3(1)%


Conclusion
In the case of pair production and decays of unstable particles: · MPT stably works at the energies near the maximum of the cross-section and higher · At 500-1000 GeV (the energies of ILC) MPT in NNLO provides approximately 0.5% accuracy
Comment:
· The higher precision is possible if proceeding to NNNLO

or if using NNLO of MPT for calculation of loop contributions only
(as, for instance, it is made at applying DPA)