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QFTHEP'2010

Alexey Sukachev [*] [*]: M.V. Lomonosov Moscow State University (MSU), D.V. Skobeltsyn Scientific Institute of Nuclear Research (SINP) Alexey Sukachev and Mikhail Dubinin

Neutral mesons' mixings and rare decays in the framework of the MSSM (with an explicit CP-violation)

[*]: salex-82@yandex.ru


Model. 1-1. Feature points
· Scalar sector ­ MSSM Effective Potential: SM:
mh > 114 GeV
e + e - ZH

MS S M:
mH ± > 79.3 GeV

e+e- H + H

-

·

Yukava sector ­ THDM II (Two Higgs Doublet Model of the Second Type):

·

Radiative Corrections [1]:
­ ­ Universal trilinear couplings Higgsino mass ("Higgs mixing parameter") SUSY breaking scale: Universal phase:
[1] ­ E. N. Akhmetzyanova, M. V. Dolgopolov, and M. N. Dubinin; Phys. Rev. D. 71, P. 075008 (2005).

Mass spectrum:

h, H, A

h(1), h(2), h(3)

Main Assumptions:
· CPX scenario:

· Phase universality:


System. 2-1. -mesons. Basic expressions
Mass splitting:

Corrections and contributions: 1). 2). 3). 4). - contributions from virtual exchanges at short distances (PT); - QCD (perturbative) corrections accounting for hard gluon exchanges; - QCD (non-perturbative) corrections accounting for intermediary hadron states at short distances; - hadron boundary states at long distances.

Normalization:

Non-Direct CP-violation:


System. 2-2. K-mesons. SM.
1. GIM-mechanism [3], [4]:

3. QCD-corrections [5]:

2. Vysotsky-Inami-Lim Functions:

BK 1.0, Bd 1.4, Bs 1.4
1 = 1.3 (central value)

2 = 0.57 , 2B = 0.55 3 = 0.47
[3] ­ S.L. Glashow, J. Iliopoulos, and L. Maiani, Phys. Rev. D 2, P. 1285 (1970); [4] ­ J. Ellis, M.K. Gaillard, and D.V. Nanopoulos, Nucl. Phys. B 109, P 213 (1976); [5] ­ S. Herrlich, and U. Nierste, Nucl. Phys. B 419, P 292 (1994).


System. 2-3. K-mesons. MSSM. HW, HH HG

FOUR-FERMION APPROXIMATION


System. 2-4. K-mesons. MSSM. HW, HH HG

EXACT RESULTS


System. 2-5. K-mesons. MSSM. SP impacts

tg 5, mH ± 150 GeV m%1 5 TeV

LEADING ORDER


System. 2-6. K-mesons. MSSM. Loop Integrals

L'Hospital Rules

Sample: integration results for ­ctHW­

EXACT RESULTS


System. 2-7. K-mesons. MSSM. Integrals
Elimination of singularities strictly depends on the sort of the certain propagator
Feynman propogator for a scalar particle: Basic fermionic propagator:

Summing over all sorts of single-particle irreducable insertions:

Expressing the full width via an imaginary part of self-energy: Gauge-invariant: Breit-Wigner propogator ~ Laurent Series first sum.:

9


System. 2-8. D-mesons. MSSM. HW and HH.

ONLY FOUR-FERMION APROXIMATION (!)


System. 2-9. Rare Decays. SM. K-mesons


System. 2-9. Rare Decays. MSSM. K-mesons
s d µ µ s d µ

BOXES

µ

s

µ

s d

µ µ

s

µ µ

d

µ

d

s s

d d

s s d s d

d s

s d

d

H

0

PENGUINS


Numerical Results. -mesons
EXACT RESULTS
mH ± , GeV mH ± , GeV

mK


Numerical Results. -mesons
EXACT RESULTS (THE FUTURE IS YET TO COME)
mH ± , GeV mH ± , GeV

mK


Numerical Results. B-mesons

B
( 10

d
d

mB
-13

GeV )

(Standard designations)

mH ± , GeV

EXACT RESULTS


Numerical results. Estimates
The statistical approach has been used [6].
1. Hypotheses

2. Errors

3. Functions

[6] ­ S.I. Bityukov and N.V. Krasnikov, Nucl. Instr. And Meth., A 534, P 152 (2004)

ESTIMATE SAMPLE (K-Mesons)
Error of measurements: ± 0.006 10 Confidence level: Distinguishability: Boundaries:
-15

4. Universal method of error estimation: Uncertainty (Geometrical) Uncertainty (arithmetical)

GeV

m > 3.492 10 GeV tg < 6 mH ± > 225 GeV

appr - K LS

-15

5. Estimators: Distinguishability (in %) Confidence level (in )

FOUR-FERMION APPROXIMATION


Numerical results. Estimations
Theoretical boundaries for exact results
Excluded regions: 1. K-mesons:
> 86 %
> 1 .0 5

???

2. D-mesons (?):

3. B(d)-mesons:

4. B(s)-mesons:

>5 5. COMBINED FIT (SOFT): > 1.0% 86


Conclusions
· It's shown that HW-, HH- and HG- contributions are tiny in comparison with those of the SM in the largest region of the MSSM parameter plane as they also decrease with the increase of tan and m H ± for K-mesons and Bmesons as well. · An entire set of Vysotsky-Inami-Lim analogues are shown to have common low-energy approximation, where it's during loop integration while using the analogue functions is obtained. VIL limits with the results of four-fermion meant that one fixes a cutoff constant latter.

· An estimation of possible constraints of the MSSM parameters space has been performed with the use of Bityukov-Krasnikov statistical approach. A region of low tan ~ 5 -10 is found, where roots of the PBSM can be discovered with distuingishability > 86% and confidence level > 1.05 at modest mH < 325 GeV Excluded regions are found with somewhat stricter bounds on . and . It's shown for the first time (based on Bs0 ­mesons studies) that considerable deviations from the SM do exist in the region of large and low values of the charged Higgs mass mH < 150 GeV .
±

±


Prospects
1. Mass splitting and non-direct CP-violation effects in neutral mesons due to chargino-stop exchanges can be large on the outskirts of the MSSM parameter plane.

2. Evaluation of penguin and box diagrams with charged higgs and charginos for direct CP-violation quantities and asymmetries.

3. Box and penguin diagrams for rare decays in B-, K- and D-meson systems with scalar bosons and superpartners.

4. Finite temperature effects and corresponding constraints for the MSSM parameters space (based on "CP Violation Evidence and Phase Transition in Extended Higgs Sector" by Mikhail Dolgopolov, Elsa Rykova and Mikhail Dubinin).


Thanks for Your Attention!



BACKUP SLIDES


Highlights - R

1. Model and motivation: what are the main boundary conditions for MSSM basic parameters?

2. System: evaluation of main mixing parameters for various neutral meson systems ( K 0 , D 0 , Bd0,s ) -> direct applications to purely leptonic rare decays.

3. Numerical results: full-fledged comparison of evaluated observables with experimental data -> bounding MSSM parameter space.

4. Future prospects and conclusions


Model. R-1. Details
h, H , A
CP
|| aij
CP

h( 1) , h( 2) , h( 3)
||

, mA = m A ( = 0) [2]


Model. R-2. Details
Main Assumptions: · CPX scenario[2]: · Phase universality: , .

LEP2 limits
SM: mh > 114 GeV
e + e - ZH

MSSM: mH > 79.3 GeV
±

e+e- H + H

-

GeV

GeV

Pl. 1: Charged Higgs under the certain assumptions: (a) mh1 > 0 , (b) mh1 = 40 GeV as a function of tg = v2 / v1 . varies from zero (the lowest outline) to 180 degrees (the highest outline) with 10 degree increment with each selected outline. CPX scenario is used. Below the certain outline the lightest neutral Higgs possesses either a negative mass or one, which is lower than 40 GeV. [2] ­ M. Carena et. al., Nucl. Phys., B 659, P. 145 (2003);

Pl. 2: Charged Higgs Boson in the model with: mh1 ~ 50 GeV at large values of tg . (a) (b)


System. R-1. Neutral K-mesons
% CP | K 0 >=| K 0 >, % CP | K 0 >=| K 0 >
CP eigenstates 1). Mass splitting

% % m = m1 - m2 = < K | H | K > + < K | H | K >

% K0 + K0 , CP | K10 >= + | K10 >, K= 2 % K0 - K0 0 0 0 , C P | K 2 >= - | K 2 > K2 = 2
0 1

Cronin, Fitch ­ 1964 ­ -violation

2). CP violation
0 KL =

1 1+ | |2 1 1+ | |2

| K > | K10 0 % 0 > | K 2 |K
0

> | K > > | K >
0 S 0 L

0 ( K 2 + K10 ),

K=

0 s

0 ( K10 + K 2 )


System. R-2. -mesons. QCD Corrections
1). Perturbative

2). Non-perturbative

3). Long-distance contributions:


System. R-3. -mesons. QCD corrections
References
1. Perturbative QCD Corrections:

2. Non-Perturbative QCD Corrections:

3. Long-Distance Contributions:


System. R-4. K-mesons. MSSM. Loop Integrals
FOUR-FERMION APPROXIMATION
Basic Integrals


System. R-5. K-mesons. MSSM. Integrals

asymptotics

Dimensional variables

Dimentionless variables

EXACT RESULTS


System. R-6. K-mesons. MSSM. Integrals
Loop integrand's singularities ­ SM

Loop integrand's singularities ­ MSSM

L'Hospital Rules

EXACT RESULTS


Numerical Results. R-1. -mesons
FOUR-FERMION APPROXIMATION

mK



K

Mass Splitting

CP-Violation


Numerical Results. R-2. -mesons
FOUR-FERMION APPROXIMATION (FUTURE IS YET TO COME)

mK



K

Mass Splitting

CP-Violation


Numerical Results. R-3. B-mesons

Bd

( 10

-1 3

)

Bs

mBs

( 10

-1 2

)

FOUR-FERMION APPROXIMATION


Numerical results. R-4. D-mesons

ONLY FOUR-FERMION APPROXIMATION