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FCNC Penguin Processes in Models Beyond the SM

. Hanif Tanyildizi

Bogoliubov Laboratory of TheoreBcal Physics Joint InsBtute for Nuclear Research
qGhep 2013, St. Petersburg


MoBvaBon for this task LHCb data analysis as indirect search for physics beyond SM Measures Flavor Changing Neutral Current processes (suppressed in SM) Search deviaBons or any inconsistency in CKM matrix to observe new physics CKM analysis may prove that something beyond the standard model exists

BSM models are available a lot Need for comparison of different models Need for check contribuBon from any new model proposed Talks by Sajan Easo and Nigel Watson


h[p://feynrules.irmp.ucl.ac.be/wiki/ModelDatabaseMainPage FeynRules model database by the authors Claude Duhr, Neil Christensen, Benjamin Fuks and others ...
The Standard Model (The SM) Simple extensions of the SM Supersymmetric models Extra dimensional models Strongly coupled and effecBve field theories

The Standard Model: Standard Model of ParBcle Physics Simple extensions of the SM: Several models based on the SM that include one or more addiBonal parBcles, like a 4th generaBon, a second Higgs doublet or addiBonal colored scalars Supersymmetric Models: Various supersymmetric extensions of the SM, including the MSSM, the NMSSM and many more Extra dimensional Models: Extensions of the SM including KK excitaBons of the SM parBcles Strongly coupled and effecBve field theories: Including Technicolor, Li[le Higgs, as well as SM higher dimensional operators, vector like quarks


Buras A. J. Weak Hamiltonian, CP ViolaBon and Rare Decays hep ph/9806471v1

Base of the work Model dependence of Wilson Coefficients and Operators in effecBve hamiltonian

H

eff

GF = 2


i

i VCKM Ci ( µ)Qi

A more fundamental theory EffecBve theory

New Physics may modify C ) i(µ add Qi Wilson Coefficients CalculaBon of full amplitude CalculaBon of Matrix elements ExtracBon of Ci


The main of the package
Input data On this step, the FeynArts takes place Creates `topologies' > `generic' > `classes' > `parBcle level' Creates `amplitudes' from generic from classes or from the parBcle level FeynCalc reformulate the amplitudes in terms of funcBons of Passarino Veltman reducBon The package files include informaBon how it should separate Qi and respecBvely Ci Separated form of amplitude transfarred to the main `package'



Quark level transiBon

ElectromagneBc monopole terms

(


a

µ c +2 PL ,R bVµ ( E

)

0, c a ,b L ,R

)

(


µ c µ 2 µ c +2 PL ,R bVµ ( g q - q q )V ( E a

)

2, c a ,b L ,R

)

ElectromagneBc dipole terms

(

a

µ c +2 PL ,R b qµV ( M

)

c a ,b L ,R

)


Topology


Generic level
F F' V

S F F

F S S

V F F

F V S

F S V

1

2

3

4

5

S F F V V F F

V S V

F F

F F

F

6

7

8

9

10


Basic funcBons in Passarino Veltman reducBon
2µ) A( m 0 ) = i 2

(

2



2 Ê dnk m0 Æ = m0 Ë - Log 2 + 1Â N1 µ Ì Ü

n = 4 - 2
= 1 - E + Log( 4

[


B0 , B µ , B

µ

]

(2µ) = i 2
µ

2



d n k [1, k µ , k N1N
2
2

µ

]

µ

)

[C0,C µ ,C µ ,C


]

(2µ) = i 2


2

d n k [1, k µ , k µ , k N1N 2 N
3



]
,k
µ

[


D0 , D , D , D

µ

µ

µ

]

=

(2µ)
i
2



d n k [1, k µ , k µ , k

µ

]

N1N 2 N 3 N

4

2 N1 = k 2 - m0 + i




N 2 = ( k + p1

)

2

- m12 + i
2

N 3 = ( k + p1 + p

)

2

2 - m2 + i



N 3 = ( k + p1 + p2 + p3

)

2

2 - m3 + i




Test of package in low energy weak processes

InF = F[4,{1,o}]; d OutF = F[4,{2,o}]; s OutV = V[2]; Z

Inami and Lim, Prog. of Theor. Phys. Vol: 65, p. 297 (1981)


1 ( i) Zµ = (4

)

2

g3 * V jsV jd sL µ dL ( Cos W

i)

Checking: EL · no UV divergence in the end ER · no UV divergency in the end · no contribuBon to ER


Coefficient to the EL operator at LO

x (i ) =

mi MW




Generic level
F F' V

S F F

F S S

V F F

F V S

F S V

1

2

3

4

5

S F F V V F F

V S V

F F

F F

F

6

7

8

9

10


Classes



ParBcles' level InF = F[4, {3, c1}]; b OutF = F[4, {2, c2}]; s OutV = V[2]; Z


Quark level transiBon

ElectromagneBc monopole terms

(


a

µ c +2 PL ,R bVµ ( E

)

0, c a ,b L ,R

)

(


µ c µ 2 µ c +2 PL ,R bVµ ( g q - q q )V ( E a

)

2, c a ,b L ,R

)

ElectromagneBc dipole terms

(

a

µ c +2 PL ,R b qµV ( M

)

c a ,b L ,R

)


Next steps: To provide ability to calculate box diagrams To provide ability to calculate in any order To provide ability to control more parameters on the input level of package Use this package for the theoreBcal work which requires the analysis of H
eff

Interface with spectrum calculators, Flavour Les Houches Accord, export numerical rouBnes ...


The work in collaboraBon with Dr. Alexander V. Bednyakov and Prof. Dmitri I. Kazakov