<p>Effects of supersymmetric threshold corrections on high-scale flavour textures</p>

1754-0410-2-2 1754-0410 Research article <p>Effects of supersymmetric threshold corrections on high-scale flavour textures</p> Çakir Altan altan.cakir@cern.ch Solmaz Levent lsolmaz@balikesir.edu.tr

Department of Physics, Izmir Institute of Technology, IZTECH, TR35430, Turkey

Balikesir University, Physics Department, TR10300, Balikesir, Turkey

PMC Physics A 1754-0410 2008 2 1 2 http://www.physmathcentral.com/1754-0410/2/2 10.1186/1754-0410-2-2 27 6 2007 07 3 2008 07 3 2008 2008 Çakir and Solmaz This is an Open Access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/2.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

Integration of superpartners out of the spectrum induces potentially large contributions to Yukawa couplings. Supersymmetric threshold corrections therefore influence the CKM matrix prediction in a non-trivial way. We study the effects of threshold corrections on high-scale flavor structures specified at the gauge coupling unification scale in supersymmetry. We first consider high-scale Yukawa textures which qualify as phenomenologically viable at tree level, and find that they are disqualified after incorporating the threshold corrections. Next, we consider Yukawa couplings, such as those with five texture zeroes, which are incapable of explaining flavor-changing processes. Incorporating threshold corrections, however, makes them phenomenologically viable textures. Therefore, supersymmetric threshold corrections are found to have an observable impact on Yukawa couplings of quarks, and any confrontation of high-scale textures with experiments at the weak scale must take into account such corrections.

PACS Codes: 12.60.Jv, 12.15.Hh

1 Introduction and motivation

Supersymmetric theories with general soft breaking terms possess a number of flavor and CP violation sources 1. In general, they are nested in the rigid and soft sectors of the theory, and bear no correlation or selection rules whatsoever. This is the case in supergravity and superstring scenarios where Kähler metric and superpotential couplings are all generic matrices in the space of fermion flavors and depend on the compactification scheme employed. This rather high degree of freedom in sources, textures and structures of the flavor mixings at GUT/string scale needs to be refined by confronting them with experimental data especially on rare processes. In general, testing high-scale flavor structures with experimental data involves three basic ingredients:

1. Specification of flavor textures in rigid and soft sectors at the messenger scale (which we take to be the MSSM gauge coupling unification scale Q = M_GUT~ 10¹⁶GeV).

2. Rescaling of lagrangian parameters to low-scale Q = M_weak~ TeV via renormalization group flow. This stage is particularly important due to (i) largeness of the logs (log M_GUT/M_weak) involved, and (ii) modifications of flavor structures because of mixings with others.

3. Integration out of the superpartners at M_weakto achieve an effective theory which comprises the SM particle spectrum with possible imprints of supersymmety in various couplings. For FCNC phenomenology this step is important as it induces flavor-nonuniversal couplings of gauge and Higgs bosons to fermions.

Any high-scale flavor structure specified in step 1 is classified to be phenomenologically viable if it agrees with experimental data after step 3. The first two steps have been widely discussed in literature by identifying flavor violation sources in general supergravity 2345 and confronting them with experimental data on fermion masses and mixings as well as various observables in kaon and beauty systems 56789.

So far analysis of the third step above has been restricted to TeV-scale supersymmetry where gauge 10 and Higgs 1112 bosons have been found to develop flavor-changing couplings to fermions. In particular, emphasis has been put on the couplings of Z 10 and Higgs 131415161718 to bs¯ MathType@MTEF@5@5@+=feaafiart1ev1aaatCvAUfKttLearuWrP9MDH5MBPbIqV92AaeXatLxBI9gBaebbnrfifHhDYfgasaacH8bkY=wiFfYlOipiY=Hhbbf9v8qqaqFr0xc9vqpe0di9q8qqpG0dHiVcFbIOFHK8Feei0lXdar=Jb9qqFfeaYRXxe9vr0=vr0=LqpWqaaeaabiGaciaacaqabeaabeqacmaaaOqaaiabdkgaIjqbdohaZzaaraaaaa@2DCB@ since mixing between second and third generation fermions exhibits a theoretically clean and experimentally wide room for new physics. These analyses have led to conclusion that flavor violation sources in sfermion sector can have a big impact on Higgs phenomenology as well as various rare processes in kaon and beauty systems 1112.

It is thus of prime phenomenological interest to know what impact the integration-out of sparticles can leave on high-scale flavor textures below M_weak. Stating more specifically, can integrating sparticles out of the spectrum render a given high-scale otherwise-viable texture inappropriate or generate CKM matrix from solely the soft sector or modify effects of Yukawa couplings on the soft sector? These are some of the questions which will be addressed in the present work.

In Sec. 2 below we briefly discuss the formalism for determining effects of supersymmetric threshold corrections. We mainly follow results of 1112 therein. In Sec. 3, we first discuss in Sec. 3.1 sensitivities of the GUT-scale CKM-ruled, hierarchic and democratic Yukawa textures to supersymmetric threshold corrections when trilinear couplings are proportional to Yukawas. In Sec. 3.2 we investigate effects of flavor mixings in squark mass-squared matrices on textures analyzed in Sec. 3.1. In Sec. 3.3, we determine effects of threshold corrections on Yukawa textures which would not qualify physical at tree level. In Sec. 4 we conclude.

2 The formalism

The superpotential of the MSSM

W _ = U _ Y u Q _ H _ u + D _ Y d Q _ H _ d + E _ Y e L _ H _ d + μ H _ u H _ d MathType@MTEF@5@5@+=feaafiart1ev1aaatCvAUfKttLearuWrP9MDH5MBPbIqV92AaeXatLxBI9gBaebbnrfifHhDYfgasaacH8bkY=MipeYlH8Hipec8Eeeu0xXdbba9frFj0xb9Lqpepeea0xd9q8qiYRWxGi6xij=hbbc9s8aq0=yqpe0xbbG8A8frFve9Fve9Fj0dmeaabaqaciGacaGaaeqabaqabeGadaaakeaadaqiaaqaaiabdEfaxbGaayPadaGaeyypa0ZaaecaaeaacqWGvbqvaiaawkWaaGqabiab=LfaznaaBaaaleaacqWF1bqDaeqaaOWaaecaaeaacqWGrbquaiaawkWaamaaHaaabaGaemisaGeacaGLcmaadaWgaaWcbaGaemyDauhabeaakiabgUcaRmaaHaaabaGaemiraqeacaGLcmaacqWFzbqwdaWgaaWcbaGae8hzaqgabeaakmaaHaaabaGaemyuaefacaGLcmaadaqiaaqaaiabdIeaibGaayPadaWaaSbaaSqaaiabdsgaKbqabaGccqGHRaWkdaqiaaqaaiabdweafbGaayPadaGae8xwaK1aaSbaaSqaaiab=vgaLbqabaGcdaqiaaqaaiabdYeambGaayPadaWaaecaaeaacqWGibasaiaawkWaamaaBaaaleaacqWGKbazaeqaaOGaey4kaSIaeqiVd02aaecaaeaacqWGibasaiaawkWaamaaBaaaleaacqWG1bqDaeqaaOWaaecaaeaacqWGibasaiaawkWaamaaBaaaleaacqWGKbazaeqaaaaa@568B@

encodes the rigid parameters μ and Yukawa couplings Y_u,d,e(of up quarks, down quarks and of leptons) each being a 3 × 3 non-hermitian matrix in the space of fermion flavors.

The breakdown of supersymmetry is parameterized by a set of soft (i.e. operators of dimension ≤ 3) terms 1

ℒ s o f t = m H u 2 H u † H u + m H d 2 H d † H d + Q ˜ † m Q 2 Q ˜ + U ˜ m U 2 U ˜ † + D ˜ m D 2 D ˜ † + L ˜ † m L 2 L ˜ + E ˜ m E 2 E ˜ † + [ U ˜ Y u A Q ˜ H u + D ˜ Y d A Q ˜ H d + E ˜ Y e A L ˜ H d + μ B H u H d + 1 2 ∑ α M α λ α λ α + h . c . ] MathType@MTEF@5@5@+=feaafiart1ev1aaatCvAUfKttLearuWrP9MDH5MBPbIqV92AaeXatLxBI9gBaebbnrfifHhDYfgasaacH8bkY=MipeYlH8Hipec8Eeeu0xXdbba9frFj0xb9Lqpepeea0xd9q8qiYRWxGi6xij=hbbc9s8aq0=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@BD33@

where trilinear couplings Yu,d,eA MathType@MTEF@5@5@+=feaafiart1ev1aaatCvAUfKttLearuWrP9MDH5MBPbIqV92AaeXatLxBI9gBaebbnrfifHhDYfgasaacH8bkY=wiFfYlOipiY=Hhbbf9v8qqaqFr0xc9vqpe0di9q8qqpG0dHiVcFbIOFHK8Feei0lXdar=Jb9qqFfeaYRXxe9vr0=vr0=LqpWqaaeaabiGaciaacaqabeaabeqacmaaaOqaaGqabiab=LfaznaaDaaaleaacqWF1bqDcqGGSaalcqWFKbazcqGGSaalcqWFLbqzaeaacqWFbbqqaaaaaa@3337@ like Yukawas themselves are non-hermitian flavor matrices whereas the sfermion mass-squareds mQ,...,E2 MathType@MTEF@5@5@+=feaafiart1ev1aaatCvAUfKttLearuWrP9MDH5MBPbIqV92AaeXatLxBI9gBaebbnrfifHhDYfgasaacH8bkY=wiFfYlOipiY=Hhbbf9v8qqaqFr0xc9vqpe0di9q8qqpG0dHiVcFbIOFHK8Feei0lXdar=Jb9qqFfeaYRXxe9vr0=vr0=LqpWqaaeaabiGaciaacaqabeaabeqacmaaaOqaaGqabiab=1gaTnaaDaaaleaacqWFrbqucqGGSaalcqGGUaGlcqGGUaGlcqGGUaGlcqGGSaalcqWFfbqraeaacqWFYaGmaaaaaa@3418@ are all hermitian. In general, all of the parameters in the second line and off-diagonal entries of the sfermion mass-squared matrices are endowed with CP-odd phases; they serve as sources of CP violation beyond the SM. The Yukawa matrices, trilinear couplings and sfermion mass-squareds facilitate flavor violation in processes mediated by sparticle loops. The MSSM possesses 21 mass parameters, 36 mixing angles and 40 CP-odd phases in addition to ones in the SM 19. Consequently, there is a 97-dimensional parameter space to be scanned in confronting theory with experiments at M_weak. In supergravity or string models the parameters of (1) and (2) are determined by compactification mechanism and structure of the internal manifold 234.

The parameters of (1) and (2) are scale- dependent. They are rescaled to Q = M_weakvia the MSSM RGEs 2021222324 with boundary conditions specified at Q = M_GUT. The RG running of model parameters is crucial. In fact, various phenomena central to supersymmetry phenomenology e.g. gauge coupling unification, radiative electroweak breaking, induction of flavor structures even for flavor-blind soft terms are pure renormalization effects. The Yukawa couplings, μ parameter and gauge couplings form a coupled closed set of observables 25 in that their scale dependencies are not affected by soft-breaking sector unless some sparticles are decoupled before reaching M_weak. On the other hand, running of the soft masses depend explicitly on rigid parameters of the theory, and they develop, among other things, novel flavor structures thanks to the Yukawa matrices. For instance, evolution of the soft mass-squared of left-handed squarks

d m Q 2 d t = m Q 2 ( Y u † Y u + Y d † Y d ) + ( Y u † Y u + Y d † Y d ) m Q 2 + 2 ( Y u † m U 2 Y u + Y d † m D 2 Y d + Y u A † Y u A + Y d A † Y d A ) + 2 ( m H u 2 Y u † Y u + m H d 2 Y d † Y d ) − 2 ( 16 3 g 3 2 | M 3 | 2 + 3 g 2 2 | M 2 | 2 + 1 15 g 1 2 | M 1 | 2 ) 1 , MathType@MTEF@5@5@+=feaafiart1ev1aaatCvAUfKttLearuWrP9MDH5MBPbIqV92AaeXatLxBI9gBaebbnrfifHhDYfgasaacH8bkY=MipeYlH8Hipec8Eeeu0xXdbba9frFj0xb9Lqpepeea0xd9q8qiYRWxGi6xij=hbbc9s8aq0=yqpe0xbbG8A8frFve9Fve9Fj0dmeaabaqaciGacaGaaeqabaqabeGadaaakeaafaqaaeabdaaaaeaajuaGdaWcaaqaaiabdsgaKHqabiab=1gaTnaaDaaabaGae8xuaefabaGae8NmaidaaaqaaiabdsgaKjabdsha0baaaOqaaiabg2da9aqaaiab=1gaTnaaDaaaleaacqWFrbquaeaacqWFYaGmaaGcdaqadaqaaiab=LfaznaaDaaaleaacqWF1bqDaeaaieaacqGFGaIHaaGccqWFzbqwdaWgaaWcbaGae8xDauhabeaakiabgUcaRiab=LfaznaaDaaaleaacqWFKbazaeaacqGFGaIHaaGccqWFzbqwdaWgaaWcbaGae8hzaqgabeaaaOGaayjkaiaawMcaaiabgUcaRmaabmaabaGae8xwaK1aa0baaSqaaiab=vha1bqaaiab+bcigcaakiab=LfaznaaBaaaleaacqWF1bqDaeqaaOGaey4kaSIae8xwaK1aa0baaSqaaiab=rgaKbqaaiab+bcigcaakiab=LfaznaaBaaaleaacqWFKbazaeqaaaGccaGLOaGaayzkaaGae8xBa02aa0baaSqaaiab=ffarbqaaiab=jdaYaaaaOqaaaqaaiabgUcaRaqaaiabikdaYmaabmaabaGae8xwaK1aa0baaSqaaiab=vha1bqaaiab+bcigcaakiab=1gaTnaaDaaaleaacqWFvbqvaeaacqWFYaGmaaGccqWFzbqwdaWgaaWcbaGae8xDauhabeaakiabgUcaRiab=LfaznaaDaaaleaacqWFKbazaeaacqGFGaIHaaGccqWFTbqBdaqhaaWcbaGae8hraqeabaGae8NmaidaaOGae8xwaK1aaSbaaSqaaiab=rgaKbqabaGccqGHRaWkcqWFzbqwdaqhaaWcbaGae8xDauhabaGae8xqaeKae4hiGyiaaOGae8xwaK1aa0baaSqaaiab=vha1bqaaiab=feabbaakiabgUcaRiab=LfaznaaDaaaleaacqWFKbazaeaacqWFbbqqcqGFGaIHaaGccqWFzbqwdaqhaaWcbaGae8hzaqgabaGae8xqaeeaaaGccaGLOaGaayzkaaaabaaabaGaey4kaScabaGaeGOmaiZaaeWaaeaacqWGTbqBdaqhaaWcbaGaemisaG0aaSbaaWqaaiabdwha1bqabaaaleaacqaIYaGmaaGccqWFzbqwdaqhaaWcbaGae8xDauhabaGae4hiGyiaaOGae8xwaK1aaSbaaSqaaiab=vha1bqabaGccqGHRaWkcqWGTbqBdaqhaaWcbaGaemisaG0aaSbaaWqaaiabdsgaKbqabaaaleaacqaIYaGmaaGccqWFzbqwdaqhaaWcbaGae8hzaqgabaGae4hiGyiaaOGae8xwaK1aaSbaaSqaaiab=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@D25A@

with t = (4π)^-2log Q/M_GUT, shows explicitly how flavor structure of a given parameter, say mQ2 MathType@MTEF@5@5@+=feaafiart1ev1aaatCvAUfKttLearuWrP9MDH5MBPbIqV92AaeXatLxBI9gBaebbnrfifHhDYfgasaacH8bkY=wiFfYlOipiY=Hhbbf9v8qqaqFr0xc9vqpe0di9q8qqpG0dHiVcFbIOFHK8Feei0lXdar=Jb9qqFfeaYRXxe9vr0=vr0=LqpWqaaeaabiGaciaacaqabeaabeqacmaaaOqaaGqabiab=1gaTnaaDaaaleaacqWFrbquaeaacqWFYaGmaaaaaa@2E9D@, at a given scale Q senses those of the remaining parameters. Indeed, flavor mixings exhibited by mQ2 MathType@MTEF@5@5@+=feaafiart1ev1aaatCvAUfKttLearuWrP9MDH5MBPbIqV92AaeXatLxBI9gBaebbnrfifHhDYfgasaacH8bkY=wiFfYlOipiY=Hhbbf9v8qqaqFr0xc9vqpe0di9q8qqpG0dHiVcFbIOFHK8Feei0lXdar=Jb9qqFfeaYRXxe9vr0=vr0=LqpWqaaeaabiGaciaacaqabeaabeqacmaaaOqaaGqabiab=1gaTnaaDaaaleaacqWFrbquaeaacqWFYaGmaaaaaa@2E9D@ at Q = M_weakcan stem from mQ,U,D2 MathType@MTEF@5@5@+=feaafiart1ev1aaatCvAUfKttLearuWrP9MDH5MBPbIqV92AaeXatLxBI9gBaebbnrfifHhDYfgasaacH8bkY=wiFfYlOipiY=Hhbbf9v8qqaqFr0xc9vqpe0di9q8qqpG0dHiVcFbIOFHK8Feei0lXdar=Jb9qqFfeaYRXxe9vr0=vr0=LqpWqaaeaabiGaciaacaqabeaabeqacmaaaOqaaGqabiab=1gaTnaaDaaaleaacqWFrbqucqGGSaalcqWFvbqvcqGGSaalcqWFebaraeaacqWFYaGmaaaaaa@3299@ or Y_u,dor Yu,dA MathType@MTEF@5@5@+=feaafiart1ev1aaatCvAUfKttLearuWrP9MDH5MBPbIqV92AaeXatLxBI9gBaebbnrfifHhDYfgasaacH8bkY=wiFfYlOipiY=Hhbbf9v8qqaqFr0xc9vqpe0di9q8qqpG0dHiVcFbIOFHK8Feei0lXdar=Jb9qqFfeaYRXxe9vr0=vr0=LqpWqaaeaabiGaciaacaqabeaabeqacmaaaOqaaGqabiab=LfaznaaDaaaleaacqWF1bqDcqGGSaalcqWFKbazaeaacqWFbbqqaaaaaa@3108@ or all of them. Therefore, a given pattern of flavor mixings in, for instance, kaon system can be sourced by various flavor matrices in rigid as well as soft sectors of the theory.

The flavor structures at M_weakarising from solutions of RGEs are further rehabilitated by taking into account the decoupling of sparticles at the supersymmetric threshold. Indeed, once part of the sparticles are integrated out of the spectrum the effective theory below M_weakcan exhibit sizeable non-standard effects in certain scattering channels of the SM particles 101112131415161718. Taking the effective theory below M_weakto be two-Higgs-doublet model (2HDM) one finds

Y d e f f = Y d ( M w e a k ) − γ d + tan ⁡ β Γ d Y u e f f = Y u ( M w e a k ) − γ u + cot ⁡ β Γ u MathType@MTEF@5@5@+=feaafiart1ev1aaatCvAUfKttLearuWrP9MDH5MBPbIqV92AaeXatLxBI9gBaebbnrfifHhDYfgasaacH8bkY=MipeYlH8Hipec8Eeeu0xXdbba9frFj0xb9Lqpepeea0xd9q8qiYRWxGi6xij=hbbc9s8aq0=yqpe0xbbG8A8frFve9Fve9Fj0dmeaabaqaciGacaGaaeqabaqabeGadaaakeaafaqadeGabaaabaacbeGae8xwaK1aa0baaSqaaiab=rgaKbqaaiabdwgaLjabdAgaMjabdAgaMbaakiabg2da9iab=LfaznaaBaaaleaacqWFKbazaeqaaOGaeiikaGIaemyta00aaSbaaSqaaiabdEha3jabdwgaLjabdggaHjabdUgaRbqabaGccqGGPaqkcqGHsislcqaHZoWzdaahaaWcbeqaaiabdsgaKbaakiabgUcaRiGbcsha0jabcggaHjabc6gaUjabek7aIjabbccaGiabfo5ahnaaCaaaleqabaGaemizaqgaaaGcbaGae8xwaK1aa0baaSqaaiab=vha1bqaaiabdwgaLjabdAgaMjabdAgaMbaakiabg2da9iab=LfaznaaBaaaleaacqWF1bqDaeqaaOGaeiikaGIaemyta00aaSbaaSqaaiabdEha3jabdwgaLjabdggaHjabdUgaRbqabaGccqGGPaqkcqGHsislcqaHZoWzdaahaaWcbeqaaiabdwha1baakiabgUcaRiGbcogaJjabc+gaVjabcsha0jabek7aIjabbccaGiabfo5ahnaaCaaaleqabaGaemyDauhaaaaaaaa@6DCD@

where Y_d,u(M_weak) are solutions of the corresponding RGEs evaluated at Q = M_weak, and γ^d,uand Γ^d,uare flavor matrices arising from squark-gluino and squark-Higgsino loops. Their explicit expressions can be found in 1112.

The physical quark fields are obtained by rotating the original gauge eigenstate fields via the unitary matrices VR,Lu,d MathType@MTEF@5@5@+=feaafiart1ev1aaatCvAUfKttLearuWrP9MDH5MBPbIqV92AaeXatLxBI9gBaebbnrfifHhDYfgasaacH8bkY=wiFfYlOipiY=Hhbbf9v8qqaqFr0xc9vqpe0di9q8qqpG0dHiVcFbIOFHK8Feei0lXdar=Jb9qqFfeaYRXxe9vr0=vr0=LqpWqaaeaabiGaciaacaqabeaabeqacmaaaOqaaiabdAfawnaaDaaaleaacqWGsbGucqGGSaalcqWGmbataeaacqWG1bqDcqGGSaalcqWGKbazaaaaaa@332B@ that diagonalize Y_u,d^eff:

( V R d ) † Y d e f f V L d = Y d ¯ , ( V R u ) † Y u e f f V L u = Y u ¯ MathType@MTEF@5@5@+=feaafiart1ev1aaatCvAUfKttLearuWrP9MDH5MBPbIqV92AaeXatLxBI9gBaebbnrfifHhDYfgasaacH8bkY=MipeYlH8Hipec8Eeeu0xXdbba9frFj0xb9Lqpepeea0xd9q8qiYRWxGi6xij=hbbc9s8aq0=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@5684@

where Yd¯=diag.(hd¯,hs¯,hb¯) MathType@MTEF@5@5@+=feaafiart1ev1aaatCvAUfKttLearuWrP9MDH5MBPbIqV92AaeXatLxBI9gBaebbnrfifHhDYfgasaacH8bkY=wiFfYlOipiY=Hhbbf9v8qqaqFr0xc9vqpe0di9q8qqpG0dHiVcFbIOFHK8Feei0lXdar=Jb9qqFfeaYRXxe9vr0=vr0=LqpWqaaeaabiGaciaacaqabeaabeqacmaaaOqaamaanaaabaacbeGae8xwaK1aaSbaaSqaaiab=rgaKbqabaaaaOGaeyypa0JaeeizaqMaeeyAaKMaeeyyaeMaee4zaCMaeiOla4YaaeWaaeaadaqdaaqaaiabdIgaOnaaBaaaleaacqWGKbazaeqaaaaakiabcYcaSmaanaaabaGaemiAaG2aaSbaaSqaaiabdohaZbqabaaaaOGaeiilaWYaa0aaaeaacqWGObaAdaWgaaWcbaGaemOyaigabeaaaaaakiaawIcacaGLPaaaaaa@4132@ and Yu¯=diag.(hu¯,hc¯,ht¯) MathType@MTEF@5@5@+=feaafiart1ev1aaatCvAUfKttLearuWrP9MDH5MBPbIqV92AaeXatLxBI9gBaebbnrfifHhDYfgasaacH8bkY=wiFfYlOipiY=Hhbbf9v8qqaqFr0xc9vqpe0di9q8qqpG0dHiVcFbIOFHK8Feei0lXdar=Jb9qqFfeaYRXxe9vr0=vr0=LqpWqaaeaabiGaciaacaqabeaabeqacmaaaOqaamaanaaabaacbeGae8xwaK1aaSbaaSqaaiab=vha1bqabaaaaOGaeyypa0JaeeizaqMaeeyAaKMaeeyyaeMaee4zaCMaeiOla4YaaeWaaeaadaqdaaqaaiabdIgaOnaaBaaaleaacqWG1bqDaeqaaaaakiabcYcaSmaanaaabaGaemiAaG2aaSbaaSqaaiabdogaJbqabaaaaOGaeiilaWYaa0aaaeaacqWGObaAdaWgaaWcbaGaemiDaqhabeaaaaaakiaawIcacaGLPaaaaaa@417A@ are physical Yukawa matrices whose entries are directly related to running quark masses at Q = M_weak:

h u ¯ = g 2 ( M w e a k ) m u ( M w e a k ) 2 M W sin ⁡ β , h d ¯ = g 2 ( M w e a k ) m d ( M w e a k ) 2 M W cos ⁡ β MathType@MTEF@5@5@+=feaafiart1ev1aaatCvAUfKttLearuWrP9MDH5MBPbIqV92AaeXatLxBI9gBaebbnrfifHhDYfgasaacH8bkY=MipeYlH8Hipec8Eeeu0xXdbba9frFj0xb9Lqpepeea0xd9q8qiYRWxGi6xij=hbbc9s8aq0=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@736F@

with similar expressions for other generations.

In general, whatever flavor textures are adopted at M_GUT, the resulting CKM matrix, VCKMcorr≡(VLu)†VLd MathType@MTEF@5@5@+=feaafiart1ev1aaatCvAUfKttLearuWrP9MDH5MBPbIqV92AaeXatLxBI9gBaebbnrfifHhDYfgasaacH8bkY=wiFfYlOipiY=Hhbbf9v8qqaqFr0xc9vqpe0di9q8qqpG0dHiVcFbIOFHK8Feei0lXdar=Jb9qqFfeaYRXxe9vr0=vr0=LqpWqaaeaabiGaciaacaqabeaabeqacmaaaOqaaiabdAfawnaaDaaaleaacqWGdbWqcqWGlbWscqWGnbqtaeaacqWGJbWycqWGVbWBcqWGYbGCcqWGYbGCaaGccqGHHjIUdaqadaqaaiabdAfawnaaDaaaleaacqWGmbataeaacqWG1bqDaaaakiaawIcacaGLPaaadaahaaWcbeqaaGqaaiab=bcigcaakiabdAfawnaaDaaaleaacqWGmbataeaacqWGKbazaaaaaa@41F5@, must agree with the existing experimental bounds 26. Clearly, in the limit of vanishing threshold corrections Γ^u,dand γ^u,d, physical CKM matrix VCKMcorr MathType@MTEF@5@5@+=feaafiart1ev1aaatCvAUfKttLearuWrP9MDH5MBPbIqV92AaeXatLxBI9gBaebbnrfifHhDYfgasaacH8bkY=wiFfYlOipiY=Hhbbf9v8qqaqFr0xc9vqpe0di9q8qqpG0dHiVcFbIOFHK8Feei0lXdar=Jb9qqFfeaYRXxe9vr0=vr0=LqpWqaaeaabiGaciaacaqabeaabeqacmaaaOqaaiabdAfawnaaDaaaleaacqWGdbWqcqWGlbWscqWGnbqtaeaacqWGJbWycqWGVbWBcqWGYbGCcqWGYbGCaaaaaa@353A@ reduces to VCKMtree MathType@MTEF@5@5@+=feaafiart1ev1aaatCvAUfKttLearuWrP9MDH5MBPbIqV92AaeXatLxBI9gBaebbnrfifHhDYfgasaacH8bkY=wiFfYlOipiY=Hhbbf9v8qqaqFr0xc9vqpe0di9q8qqpG0dHiVcFbIOFHK8Feei0lXdar=Jb9qqFfeaYRXxe9vr0=vr0=LqpWqaaeaabiGaciaacaqabeaabeqacmaaaOqaaiabdAfawnaaDaaaleaacqWGdbWqcqWGlbWscqWGnbqtaeaacqWG0baDcqWGYbGCcqWGLbqzcqWGLbqzaaaaaa@352E@ computed by diagonalizing Y_u,d(M_weak). Reiterating, it is with comparison of the predicted CKM matrix, VCKMcorr MathType@MTEF@5@5@+=feaafiart1ev1aaatCvAUfKttLearuWrP9MDH5MBPbIqV92AaeXatLxBI9gBaebbnrfifHhDYfgasaacH8bkY=wiFfYlOipiY=Hhbbf9v8qqaqFr0xc9vqpe0di9q8qqpG0dHiVcFbIOFHK8Feei0lXdar=Jb9qqFfeaYRXxe9vr0=vr0=LqpWqaaeaabiGaciaacaqabeaabeqacmaaaOqaaiabdAfawnaaDaaaleaacqWGdbWqcqWGlbWscqWGnbqtaeaacqWGJbWycqWGVbWBcqWGYbGCcqWGYbGCaaaaaa@353A@, with experiment that one can tell if a high-scale texture, classified to be viable at tree-level by considering VCKMtree MathType@MTEF@5@5@+=feaafiart1ev1aaatCvAUfKttLearuWrP9MDH5MBPbIqV92AaeXatLxBI9gBaebbnrfifHhDYfgasaacH8bkY=wiFfYlOipiY=Hhbbf9v8qqaqFr0xc9vqpe0di9q8qqpG0dHiVcFbIOFHK8Feei0lXdar=Jb9qqFfeaYRXxe9vr0=vr0=LqpWqaaeaabiGaciaacaqabeaabeqacmaaaOqaaiabdAfawnaaDaaaleaacqWGdbWqcqWGlbWscqWGnbqtaeaacqWG0baDcqWGYbGCcqWGLbqzcqWGLbqzaaaaaa@352E@ only, is spoiled by the supersymmetric threshold corrections. The experimental bounds on the absolute magnitudes of the CKM entries (at 90% CL) read collectively as:

| V C K M e x p | = ( 0.9739 0.9751 0.2210 0.2270 0.0029 0.0045 0.2210 0.2270 0.9730 0.9744 0.0390 0.0440 0.0048 0.0140 0.0370 0.0430 0.9990 0.9992 ) MathType@MTEF@5@5@+=feaafiart1ev1aaatCvAUfKttLearuWrP9MDH5MBPbIqV92AaeXatLxBI9gBaebbnrfifHhDYfgasaacH8bkY=MipeYlH8Hipec8Eeeu0xXdbba9frFj0xb9Lqpepeea0xd9q8qiYRWxGi6xij=hbbc9s8aq0=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@A39E@

In the next section, we will compute supersymmetric threshold corrections to Yukawa couplings of quarks for certain prototype flavor textures defined at Q = M_GUT. In particular, we will evaluate radiatively corrected CKM matrix as well as couplings of the Higgs bosons to quarks to determine the impact of the decoupling of squarks out of the spectrum at M_weakon scattering processes at energies accessible to present and future colliders.

3 High-scale textures and threshold corrections

First of all, for standardization and easy comparison with literature (e.g. with the computer codes ISAJET 32 and SOFTSUSY 33) we take SPS1a' conventions for supersymmetric parameters 34

tan β = 10, m₀= 70 GeV, A₀= -300 GeV, m_1/2= 250 GeV

and completely neglect supersymmetric CP-violating phases, as mentioned before.

Instead of scanning a 97-dimensional parameter space for specifying what high-scale parameter ranges are useful for what low-energy observables, which is actually what has to be done, we simplify the analysis by focussing on certain prototype textures at high scale. In general, for any flavor matrix in any sector of the theory there exist, boldly speaking, three extremes: (i) completely diagonal, (ii) hierarchical, and (iii) democratic textures. There are, of course, a continuous infinity of textures among these extremes; however, for definiteness and clarity in our analysis we will focus on these three structures.

3.1 Flavor violation from Yukawas and trilinear couplings

In this subsection we investigate effects of superymmetric threshold corrections on high-scale textures in which Yukawa couplings exhibit non-trivial flavor mixings and so do the trilinear couplings since we take

Y u , d , e A = A 0 Y u , d , e MathType@MTEF@5@5@+=feaafiart1ev1aaatCvAUfKttLearuWrP9MDH5MBPbIqV92AaeXatLxBI9gBaebbnrfifHhDYfgasaacH8bkY=MipeYlH8Hipec8Eeeu0xXdbba9frFj0xb9Lqpepeea0xd9q8qiYRWxGi6xij=hbbc9s8aq0=yqpe0xbbG8A8frFve9Fve9Fj0dmeaabaqaciGacaGaaeqabaqabeGadaaakeaaieqacqWFzbqwdaqhaaWcbaGae8xDauNaeiilaWIae8hzaqMaeiilaWIae8xzaugabaGae8xqaeeaaOGaeyypa0Jaemyqae0aaSbaaSqaaiabicdaWaqabaGccqWFzbqwdaWgaaWcbaGae8xDauNaeiilaWIae8hzaqMaeiilaWIae8xzaugabeaaaaa@3D03@

at the GUT scale. The soft mass-squareds, on the other hand, are taken entirely flavor conserving i.e. they are strictly diagonal and universal at the GUT scale. It is with direct proportionality of trilinear couplings with Yukawas and certain ansatze for Yukawa textures that, we will study below sensitivities of certain high-scale Yukawa structures to supersymmetric threshold corrections at the TeV scale.

3.1.1 CKM-ruled texture

We take Yukawa couplings of up and down quarks to be

Y u = diag ( 3.5 10 − 6 , 1.3 10 − 3 , 0.4566 ) Y d = ( 6.2368 10 − 5 − 1.4272 10 − 5 5.9315 10 − 7 e 0.3146 i 2.4640 10 − 4 1.07074 10 − 3 − 4.0458 10 − 5 1.6495 10 − 4 e 1.047 i 1.81465 10 − 3 4.8476 10 − 2 ) MathType@MTEF@5@5@+=feaafiart1ev1aaatCvAUfKttLearuWrP9MDH5MBPbIqV92AaeXatLxBI9gBaebbnrfifHhDYfgasaacH8bkY=MipeYlH8Hipec8Eeeu0xXdbba9frFj0xb9Lqpepeea0xd9q8qiYRWxGi6xij=hbbc9s8aq0=yqpe0xbbG8A8frFve9Fve9Fj0dmeaabaqaciGacaGaaeqabaqabeGadaaakeaafaqadeGadaaabaacbeGae8xwaK1aaSbaaSqaaiab=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@C49D@

with no flavor violation in the lepton sector: Y_e= diag. (1.9 10^-5, 4 10^-3, 0.071). The flavor violation effects are entirely encoded in Y_dwhich exhibits a CKM-ruled hierarchy in similarity to Yukawa textures analyzed in 5i.e. this choice of boundary values of the Yukawas leads to correct CKM matrix 26 at M_weakupon integration of the RGEs.

At the weak scale the Yukawa matrices, trilinear couplings and squark soft mass-squareds serve as sources of flavor violation. The trilinear couplings, under two-loop RG running 2021222324 with boundary conditions (9), attain the flavor structures

Y u A = ( − 7.2 10 − 3 0 0 1.70 10 − 6 e 0.5641 i − 2.67 2.9 10 − 4 6.24 e 1.047 i 10 − 3 6.8 10 − 2 − 532.7 ) Y d A = ( − 0.204 − 0.191 − 0.138 e − 1.039 i − 0.567 − 3.495 − 1.436 − 0.384 e 1.046 i − 4.19 − 134.24 ) MathType@MTEF@5@5@+=feaafiart1ev1aaatCvAUfKttLearuWrP9MDH5MBPbIqV92AaeXatLxBI9gBaebbnrfifHhDYfgasaacH8bkY=MipeYlH8Hipec8Eeeu0xXdbba9frFj0xb9Lqpepeea0xd9q8qiYRWxGi6xij=hbbc9s8aq0=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@C285@

both measured in GeV at M_weak= 1 TeV. Clearly, YuA MathType@MTEF@5@5@+=feaafiart1ev1aaatCvAUfKttLearuWrP9MDH5MBPbIqV92AaeXatLxBI9gBaebbnrfifHhDYfgasaacH8bkY=wiFfYlOipiY=Hhbbf9v8qqaqFr0xc9vqpe0di9q8qqpG0dHiVcFbIOFHK8Feei0lXdar=Jb9qqFfeaYRXxe9vr0=vr0=LqpWqaaeaabiGaciaacaqabeaabeqacmaaaOqaaGqabiab=LfaznaaDaaaleaacqWF1bqDaeaacqWFbbqqaaaaaa@2EDB@ is essentially diagonal whereas (2, 3), (3, 2) and (2, 2) entries of YdA MathType@MTEF@5@5@+=feaafiart1ev1aaatCvAUfKttLearuWrP9MDH5MBPbIqV92AaeXatLxBI9gBaebbnrfifHhDYfgasaacH8bkY=wiFfYlOipiY=Hhbbf9v8qqaqFr0xc9vqpe0di9q8qqpG0dHiVcFbIOFHK8Feei0lXdar=Jb9qqFfeaYRXxe9vr0=vr0=LqpWqaaeaabiGaciaacaqabeaabeqacmaaaOqaaGqabiab=LfaznaaDaaaleaacqWFKbazaeaacqWFbbqqaaaaaa@2EB9@ are of the same size.

Though they start with completely diagonal and universal boundary values, the squark soft squared masses develop flavor-changing entries at M_weak= 1 TeV:

m Q 2 = ( 533.67 GeV ) 2 ( 1.07 0.0 0.0 0.0 1.07 − 2.2 10 − 4 0.0 − 2.2 10 − 4 0.86 ) m D 2 = ( 530.76 GeV ) 2 ( 1.01 0.0 0.0 0.0 1.01 − 1.5 10 − 4 0.0 − 1.5 10 − 5 0.99 ) MathType@MTEF@5@5@+=feaafiart1ev1aaatCvAUfKttLearuWrP9MDH5MBPbIqV92AaeXatLxBI9gBaebbnrfifHhDYfgasaacH8bkY=MipeYlH8Hipec8Eeeu0xXdbba9frFj0xb9Lqpepeea0xd9q8qiYRWxGi6xij=hbbc9s8aq0=yqpe0xbbG8A8frFve9Fve9Fj0dmeaabaqaciGacaGaaeqabaqabeGadaaakeaafaqabeGadaaabaacbeGae8xBa02aa0baaSqaaiab=ffarbqaaiab=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@9ED9@

with mU2 MathType@MTEF@5@5@+=feaafiart1ev1aaatCvAUfKttLearuWrP9MDH5MBPbIqV92AaeXatLxBI9gBaebbnrfifHhDYfgasaacH8bkY=wiFfYlOipiY=Hhbbf9v8qqaqFr0xc9vqpe0di9q8qqpG0dHiVcFbIOFHK8Feei0lXdar=Jb9qqFfeaYRXxe9vr0=vr0=LqpWqaaeaabiGaciaacaqabeaabeqacmaaaOqaaGqabiab=1gaTnaaDaaaleaacqWFvbqvaeaacqWFYaGmaaaaaa@2EA5@ = (497.11 GeV)²diag. (1.15, 1.15, 0.69). The numerical values of the parameters above exhibit good agreement with well-known codes like ISAJET 32 and SOFTSUSY 33.

The presence of flavor violation in the soft sector of the low-energy theory gives rise to non-trivial corrections to Yukawa couplings and in turn to the CKM matrix. Indeed, use of (11) and (12) in 1112 introduces certain corrections to the tree-level Yukawa matrices Y_u,d(M_weak) to generate Yu,deff MathType@MTEF@5@5@+=feaafiart1ev1aaatCvAUfKttLearuWrP9MDH5MBPbIqV92AaeXatLxBI9gBaebbnrfifHhDYfgasaacH8bkY=wiFfYlOipiY=Hhbbf9v8qqaqFr0xc9vqpe0di9q8qqpG0dHiVcFbIOFHK8Feei0lXdar=Jb9qqFfeaYRXxe9vr0=vr0=LqpWqaaeaabiGaciaacaqabeaabeqacmaaaOqaaGqabiab=LfaznaaDaaaleaacqWF1bqDcqGGSaalcqWFKbazaeaacqWFLbqzcqWFMbGzcqWFMbGzaaaaaa@33F2@ in (4). In fact, VCKMtree MathType@MTEF@5@5@+=feaafiart1ev1aaatCvAUfKttLearuWrP9MDH5MBPbIqV92AaeXatLxBI9gBaebbnrfifHhDYfgasaacH8bkY=wiFfYlOipiY=Hhbbf9v8qqaqFr0xc9vqpe0di9q8qqpG0dHiVcFbIOFHK8Feei0lXdar=Jb9qqFfeaYRXxe9vr0=vr0=LqpWqaaeaabiGaciaacaqabeaabeqacmaaaOqaaiabdAfawnaaDaaaleaacqWGdbWqcqWGlbWscqWGnbqtaeaacqWG0baDcqWGYbGCcqWGLbqzcqWGLbqzaaaaaa@352E@ (obtained from Y_u,d(M_weak)) and VCKMcorr MathType@MTEF@5@5@+=feaafiart1ev1aaatCvAUfKttLearuWrP9MDH5MBPbIqV92AaeXatLxBI9gBaebbnrfifHhDYfgasaacH8bkY=wiFfYlOipiY=Hhbbf9v8qqaqFr0xc9vqpe0di9q8qqpG0dHiVcFbIOFHK8Feei0lXdar=Jb9qqFfeaYRXxe9vr0=vr0=LqpWqaaeaabiGaciaacaqabeaabeqacmaaaOqaaiabdAfawnaaDaaaleaacqWGdbWqcqWGlbWscqWGnbqtaeaacqWGJbWycqWGVbWBcqWGYbGCcqWGYbGCaaaaaa@353A@ (obtained from Y_u,d^eff) compare to exhibit spectacular differences:

| V C K M t r e e | | V C K M c o r r | = ( 0.9746 0.9795 0.2241 0.2015 0.0037 0.0034 0.2240 0.2014 0.9737 0.9788 0.0406 0.0375 0.0079 0.0066 0.0400 0.0371 0.99917 0.9993 ) MathType@MTEF@5@5@+=feaafiart1ev1aaatCvAUfKttLearuWrP9MDH5MBPbIqV92AaeXatLxBI9gBaebbnrfifHhDYfgasaacH8bkY=MipeYlH8Hipec8Eeeu0xXdbba9frFj0xb9Lqpepeea0xd9q8qiYRWxGi6xij=hbbc9s8aq0=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@B408@

where left (right) window of MathType@MTEF@5@5@+=feaafiart1ev1aaatCvAUfKttLearuWrP9MDH5MBPbIqV92AaeXatLxBI9gBaebbnrfifHhDYfgasaacH8bkY=wiFfYlOipiY=Hhbbf9v8qqaqFr0xc9vqpe0di9q8qqpG0dHiVcFbIOFHK8Feei0lXdar=Jb9qqFfeaYRXxe9vr0=vr0=LqpWqaaeaabiGaciaacaqabeaabeqacmaaaOqaamaaL4babaaaamaaL4babaaaaaaa@2B85@ in (i, j)-th entry refers to |VCKMtree(i,j)|(|VCKMcorr(i,j)|) MathType@MTEF@5@5@+=feaafiart1ev1aaatCvAUfKttLearuWrP9MDH5MBPbIqV92AaeXatLxBI9gBaebbnrfifHhDYfgasaacH8bkY=wiFfYlOipiY=Hhbbf9v8qqaqFr0xc9vqpe0di9q8qqpG0dHiVcFbIOFHK8Feei0lXdar=Jb9qqFfeaYRXxe9vr0=vr0=LqpWqaaeaabiGaciaacaqabeaabeqacmaaaOqaaiabcYha8jabdAfawnaaDaaaleaacqWGdbWqcqWGlbWscqWGnbqtaeaacqWG0baDcqWGYbGCcqWGLbqzcqWGLbqzaaGccqGGOaakcqWGPbqAcqGGSaalcqWGQbGAcqGGPaqkcqGG8baFcqGGOaakcqGG8baFcqWGwbGvdaqhaaWcbaGaem4qamKaem4saSKaemyta0eabaGaem4yamMaem4Ba8MaemOCaiNaemOCaihaaOGaeiikaGIaemyAaKMaeiilaWIaemOAaOMaeiykaKIaeiiFaWNaeiykaKcaaa@51CB@. Clearly, |VCKMtree MathType@MTEF@5@5@+=feaafiart1ev1aaatCvAUfKttLearuWrP9MDH5MBPbIqV92AaeXatLxBI9gBaebbnrfifHhDYfgasaacH8bkY=wiFfYlOipiY=Hhbbf9v8qqaqFr0xc9vqpe0di9q8qqpG0dHiVcFbIOFHK8Feei0lXdar=Jb9qqFfeaYRXxe9vr0=vr0=LqpWqaaeaabiGaciaacaqabeaabeqacmaaaOqaaiabdAfawnaaDaaaleaacqWGdbWqcqWGlbWscqWGnbqtaeaacqWG0baDcqWGYbGCcqWGLbqzcqWGLbqzaaaaaa@352E@| agrees very well with |VCKMexp MathType@MTEF@5@5@+=feaafiart1ev1aaatCvAUfKttLearuWrP9MDH5MBPbIqV92AaeXatLxBI9gBaebbnrfifHhDYfgasaacH8bkY=wiFfYlOipiY=Hhbbf9v8qqaqFr0xc9vqpe0di9q8qqpG0dHiVcFbIOFHK8Feei0lXdar=Jb9qqFfeaYRXxe9vr0=vr0=LqpWqaaeaabiGaciaacaqabeaabeqacmaaaOqaaiabdAfawnaaDaaaleaacqWGdbWqcqWGlbWscqWGnbqtaeaacqWGLbqzcqWG4baEcqWGWbaCaaaaaa@33DF@| in (7) entry by entry. This qualifies (10) to be the correct high-scale texture given experimental FCNC bounds at Q = M_Z. However, radiative corrections induced by decoupling of squarks, gluinos and Higgsinos at the supersymmetric threshold M_weak= 1 TeV is seen to leave a rather strong impact on the CKM entries. Consider for instance (1, 1) entries of VCKMexp MathType@MTEF@5@5@+=feaafiart1ev1aaatCvAUfKttLearuWrP9MDH5MBPbIqV92AaeXatLxBI9gBaebbnrfifHhDYfgasaacH8bkY=wiFfYlOipiY=Hhbbf9v8qqaqFr0xc9vqpe0di9q8qqpG0dHiVcFbIOFHK8Feei0lXdar=Jb9qqFfeaYRXxe9vr0=vr0=LqpWqaaeaabiGaciaacaqabeaabeqacmaaaOqaaiabdAfawnaaDaaaleaacqWGdbWqcqWGlbWscqWGnbqtaeaacqWGLbqzcqWG4baEcqWGWbaCaaaaaa@33DF@, VCKMtree MathType@MTEF@5@5@+=feaafiart1ev1aaatCvAUfKttLearuWrP9MDH5MBPbIqV92AaeXatLxBI9gBaebbnrfifHhDYfgasaacH8bkY=wiFfYlOipiY=Hhbbf9v8qqaqFr0xc9vqpe0di9q8qqpG0dHiVcFbIOFHK8Feei0lXdar=Jb9qqFfeaYRXxe9vr0=vr0=LqpWqaaeaabiGaciaacaqabeaabeqacmaaaOqaaiabdAfawnaaDaaaleaacqWGdbWqcqWGlbWscqWGnbqtaeaacqWG0baDcqWGYbGCcqWGLbqzcqWGLbqzaaaaaa@352E@ and VCKMcorr MathType@MTEF@5@5@+=feaafiart1ev1aaatCvAUfKttLearuWrP9MDH5MBPbIqV92AaeXatLxBI9gBaebbnrfifHhDYfgasaacH8bkY=wiFfYlOipiY=Hhbbf9v8qqaqFr0xc9vqpe0di9q8qqpG0dHiVcFbIOFHK8Feei0lXdar=Jb9qqFfeaYRXxe9vr0=vr0=LqpWqaaeaabiGaciaacaqabeaabeqacmaaaOqaaiabdAfawnaaDaaaleaacqWGdbWqcqWGlbWscqWGnbqtaeaacqWGJbWycqWGVbWBcqWGYbGCcqWGYbGCaaaaaa@353A@. Present experiments provide a 1.64σ significance to |VCKMexp MathType@MTEF@5@5@+=feaafiart1ev1aaatCvAUfKttLearuWrP9MDH5MBPbIqV92AaeXatLxBI9gBaebbnrfifHhDYfgasaacH8bkY=wiFfYlOipiY=Hhbbf9v8qqaqFr0xc9vqpe0di9q8qqpG0dHiVcFbIOFHK8Feei0lXdar=Jb9qqFfeaYRXxe9vr0=vr0=LqpWqaaeaabiGaciaacaqabeaabeqacmaaaOqaaiabdAfawnaaDaaaleaacqWGdbWqcqWGlbWscqWGnbqtaeaacqWGLbqzcqWG4baEcqWGWbaCaaaaaa@33DF@(1, 1)| around a mean value of 0.745 as is seen from (7). The tree-level prediction, |VCKMtree MathType@MTEF@5@5@+=feaafiart1ev1aaatCvAUfKttLearuWrP9MDH5MBPbIqV92AaeXatLxBI9gBaebbnrfifHhDYfgasaacH8bkY=wiFfYlOipiY=Hhbbf9v8qqaqFr0xc9vqpe0di9q8qqpG0dHiVcFbIOFHK8Feei0lXdar=Jb9qqFfeaYRXxe9vr0=vr0=LqpWqaaeaabiGaciaacaqabeaabeqacmaaaOqaaiabdAfawnaaDaaaleaacqWGdbWqcqWGlbWscqWGnbqtaeaacqWG0baDcqWGYbGCcqWGLbqzcqWGLbqzaaaaaa@352E@(1, 1)|, takes the value of 0.9746 which is rather close to the center of the experimental interval. However, once supersymmetric threshold corrections are included this tree-level prediction gets modified to |VCKMcorr MathType@MTEF@5@5@+=feaafiart1ev1aaatCvAUfKttLearuWrP9MDH5MBPbIqV92AaeXatLxBI9gBaebbnrfifHhDYfgasaacH8bkY=wiFfYlOipiY=Hhbbf9v8qqaqFr0xc9vqpe0di9q8qqpG0dHiVcFbIOFHK8Feei0lXdar=Jb9qqFfeaYRXxe9vr0=vr0=LqpWqaaeaabiGaciaacaqabeaabeqacmaaaOqaaiabdAfawnaaDaaaleaacqWGdbWqcqWGlbWscqWGnbqtaeaacqWGJbWycqWGVbWBcqWGYbGCcqWGYbGCaaaaaa@353A@(1, 1)| = 0.9795. This value is obviously far beyond the existing experimental limits as it is a 13.39σ effect. Similarly, |VCKMcorr MathType@MTEF@5@5@+=feaafiart1ev1aaatCvAUfKttLearuWrP9MDH5MBPbIqV92AaeXatLxBI9gBaebbnrfifHhDYfgasaacH8bkY=wiFfYlOipiY=Hhbbf9v8qqaqFr0xc9vqpe0di9q8qqpG0dHiVcFbIOFHK8Feei0lXdar=Jb9qqFfeaYRXxe9vr0=vr0=LqpWqaaeaabiGaciaacaqabeaabeqacmaaaOqaaiabdAfawnaaDaaaleaacqWGdbWqcqWGlbWscqWGnbqtaeaacqWGJbWycqWGVbWBcqWGYbGCcqWGYbGCaaaaaa@353A@(1, 2)|, |VCKMcorr MathType@MTEF@5@5@+=feaafiart1ev1aaatCvAUfKttLearuWrP9MDH5MBPbIqV92AaeXatLxBI9gBaebbnrfifHhDYfgasaacH8bkY=wiFfYlOipiY=Hhbbf9v8qqaqFr0xc9vqpe0di9q8qqpG0dHiVcFbIOFHK8Feei0lXdar=Jb9qqFfeaYRXxe9vr0=vr0=LqpWqaaeaabiGaciaacaqabeaabeqacmaaaOqaaiabdAfawnaaDaaaleaacqWGdbWqcqWGlbWscqWGnbqtaeaacqWGJbWycqWGVbWBcqWGYbGCcqWGYbGCaaaaaa@353A@(2, 1)|, |VCKMcorr MathType@MTEF@5@5@+=feaafiart1ev1aaatCvAUfKttLearuWrP9MDH5MBPbIqV92AaeXatLxBI9gBaebbnrfifHhDYfgasaacH8bkY=wiFfYlOipiY=Hhbbf9v8qqaqFr0xc9vqpe0di9q8qqpG0dHiVcFbIOFHK8Feei0lXdar=Jb9qqFfeaYRXxe9vr0=vr0=LqpWqaaeaabiGaciaacaqabeaabeqacmaaaOqaaiabdAfawnaaDaaaleaacqWGdbWqcqWGlbWscqWGnbqtaeaacqWGJbWycqWGVbWBcqWGYbGCcqWGYbGCaaaaaa@353A@(2, 2)| and |VCKMcorr MathType@MTEF@5@5@+=feaafiart1ev1aaatCvAUfKttLearuWrP9MDH5MBPbIqV92AaeXatLxBI9gBaebbnrfifHhDYfgasaacH8bkY=wiFfYlOipiY=Hhbbf9v8qqaqFr0xc9vqpe0di9q8qqpG0dHiVcFbIOFHK8Feei0lXdar=Jb9qqFfeaYRXxe9vr0=vr0=LqpWqaaeaabiGaciaacaqabeaabeqacmaaaOqaaiabdAfawnaaDaaaleaacqWGdbWqcqWGlbWscqWGnbqtaeaacqWGJbWycqWGVbWBcqWGYbGCcqWGYbGCaaaaaa@353A@(3, 3)| are, respectively, 12.36σ, 12.36σ, 11.95σ and 2.30σ effects. Obviously, deviation of |VCKMcorr MathType@MTEF@5@5@+=feaafiart1ev1aaatCvAUfKttLearuWrP9MDH5MBPbIqV92AaeXatLxBI9gBaebbnrfifHhDYfgasaacH8bkY=wiFfYlOipiY=Hhbbf9v8qqaqFr0xc9vqpe0di9q8qqpG0dHiVcFbIOFHK8Feei0lXdar=Jb9qqFfeaYRXxe9vr0=vr0=LqpWqaaeaabiGaciaacaqabeaabeqacmaaaOqaaiabdAfawnaaDaaaleaacqWGdbWqcqWGlbWscqWGnbqtaeaacqWGJbWycqWGVbWBcqWGYbGCcqWGYbGCaaaaaa@353A@(i, j)| from |VCKMtree MathType@MTEF@5@5@+=feaafiart1ev1aaatCvAUfKttLearuWrP9MDH5MBPbIqV92AaeXatLxBI9gBaebbnrfifHhDYfgasaacH8bkY=wiFfYlOipiY=Hhbbf9v8qqaqFr0xc9vqpe0di9q8qqpG0dHiVcFbIOFHK8Feei0lXdar=Jb9qqFfeaYRXxe9vr0=vr0=LqpWqaaeaabiGaciaacaqabeaabeqacmaaaOqaaiabdAfawnaaDaaaleaacqWGdbWqcqWGlbWscqWGnbqtaeaacqWG0baDcqWGYbGCcqWGLbqzcqWGLbqzaaaaaa@352E@(i, j|) (comparison with experiments at Q = M_Zis meaningful especially for (i, j) = (1, 1), (1, 2), (2, 1), (3, 3) entries whose scale dependencies are known to be rather mild 293031), when the latter falls well inside the experimentally allowed range, obviously violates existing experimental bounds in (7) by several standard deviations. Consequently, supersymmetric threshold corrections entirely disqualify the high-scale texture (10) being the correct texture to reproduce the FCNC measurements at the weak scale. This case study, based on numerical values for Yukawa entries in (10), manifestly shows the impact of supersymmetric threshold corrections on high-scale textures which qualify viable at tree level.

The physical quark fields, which arise after the unitary rotations (5), acquire the masses

M u ¯ ( M w e a k ) = diag . ( ≃ 0 , 0.545 , 149.45 ) , M d ¯ ( M w e a k ) = diag . ( 3.35 10