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  • About
  • The Global ETD Search service is a free service for researchers to find electronic theses and dissertations. This service is provided by the Networked Digital Library of Theses and Dissertations.
    Our metadata is collected from universities around the world. If you manage a university/consortium/country archive and want to be added, details can be found on the NDLTD website.
1

Rare radiative and semileptonic B meson decays

Gratrex, James January 2018 (has links)
Recent results at the LHCb and B-factory experiments have suggested that rare processes in B →Vγ and B → V ℓ¯ℓ decays, where V is a vector meson, show some deviation from Standard Model predictions. Although these anomalies are not yet at the level to constitute a formal discovery, they are certainly suggestive of potential New Physics effects in flavour-changing neutral currents. However, explanations within the Standard Model cannot yet be ruled out. This thesis contributes to the understanding of such anomalies in two ways. Firstly, the angular distribution of the B → KJ (→ Kπ)ℓ1¯ℓ2 decay is derived, for the full dimension-six effective weak Hamiltonian, using a generalisation of the helicity formalism to effective theories mediating b → sℓ1¯ℓ2 transitions. This approach sheds light on the origin of the underlying structure, and in the process extends the general angular distribution to decays in which the two leptons in the final state, ℓ1¯ℓ2, are not necessarily identical. An additional benefit of the derivation of the angular distribution presented in this manner is that it lends itself to a moments analysis of the decay. It is shown how the angular distribution changes in the presence of new operators, predicted to be vanishingly small in the Standard Model. Such operators could be sizeable in the presence of New Physics, but using a moments analysis enables the contribution of such operators to be assessed. Secondly, an analysis is presented of the three-particle vector and axial meson distribution amplitudes. It is shown that the distribution amplitudes of both particles are, up to QCD corrections, nearly identical. These results are applied to a new calculation of the long-distance charm loop contribution to radiative B → Vγ decays, and it is shown that the approximate symmetry can be exploited to provide an improved theoretical control in the search for New Physics contributions to right-handed currents in radiative decays.
2

Scalar Mesons In Radiative Phi-meson Decays Into Neutral K-meson States

Sisman Korkmaz, Canan 01 September 2006 (has links) (PDF)
Radiative Decays of the phi-meson to the scalar mesons f0(980) and a0(980) are investigated within the framework of charged kaon loop model for both point-like scalar mesons and for scalar mesons with extended structure. Then, the radiative phi-meson decay into neutral K-meson is studied via a two step mechanism in which the scalar mesons couple the final state to the phi-meson through the charged kaon loop. The branching ratio of this decay is calculated and it is shown that this reaction will not provide a significant background to the measurements of phi-meson into neutral K-meson states decay for testing CP violation.
3

Study of B0 -> K*0 gamma, Bs0 -> phi gamma and Bs0 -> K*0 gamma decays using converted photons with the LHCb detector / Étude des désintégrations B0 -> K*0 gamma, Bs0 -> phi gamma et Bs0 -> K*0 gamma à l'aide de photons convertis avec le détecteur LHCb

Beaucourt, Léo 08 December 2016 (has links)
L'étude présentée dans cette thèse est dédiée à l'analyse des désintégrations radiatives de mésons beaux, processus faisant intervenir le quark b ce dernier se désintégrant par interaction faible en un quark s avec émission d'un photon. Ce type de désintégration est interdit à l'arbre en théorie quantique des champs et doit donc s'opérer à l'aide de boucles. Ces désintégrations ont des rapports d'embranchement très faibles, de l'ordre de 10^{-5}. Dès lors, l’étude de ces processus à l'aide du détecteur LHCb permet de mesurer précisément des observables reliées à ces processus, telles que les rapports d'embranchement, les asymétries de CP ou des variables angulaires et d'hélicité comme la polarisation du photon. En comparant ces résultats expérimentaux avec les prédictions théoriques du Modèle Standard de la Physique des Particules, il devient possible de tester ce modèle et de contraindre l'existence d'une nouvelle physique au delà du Modèle Standard. L'analyse présentée dans cette thèse se concentre sur l'étude des désintégrations B0 -> K*0 gamma, Bs0 -> phi gamma et Bs0 -> K*0 gamma. Les événements utilisés sont ceux où le photon s'est converti en une paire électron-positron par interaction avec le détecteur afin de bénéficier de la bonne résolution sur l'impulsion des traces chargées des trajectographes de LHCb. Les mesures du rapport des rapports d'embranchement des désintégrations B0 -> K*0 gamma et Bs0 -> phi gamma ainsi que de l'asymétrie de CP directe dans le processus B0 -> K*0 gamma sont réalisées. La bonne résolution obtenue sur la masse du méson B0 a permis de déterminer une première limite supérieure au rapport d'embranchement de la désintégration supprimée de Cabbibo Bs0 -> K*0 gamma. / The purpose of the work presented in this thesis is to study the radiative decays of B mesons. These processes correspond to the decay of a b-quark into a s-quark through the weak interaction with a photon in the final state. This kind of decay is not allowed at tree level in the quantum field theory but only through virtual loops. These processes have small branching fractions of the order of 10^{-5}. The study of these decays with the LHCb detector provides precise measurements of related observable such as branching fractions, CP asymmetries or angular variables such as the photon polarisation. These results can be compared with the theoretical prediction of the Standard Model of Particle Physics. Therefore, it is possible to test this model and to constrain the existence of new physics behind the Standard Model. The analysis presented in this thesis focuses on the B0 → K*0 gamma, Bs0 → phi gamma and Bs0 → K*0 gamma decays. Only events where the photon has converted into a dielectron pair by interacting with the detector are used. This allows to take advantage of the good resolution on the charged tracks momentum obtained with the LHCb's tracking system. The measurements of the ratio of branching fractions of the B0 → K*0 gamma and Bs0 → phi gamma decays and of the direct CP asymmetry in the B0 → K*0 gamma process are performed. The good resolution obtained on the B meson mass allows to set the first upper limit on the branching ratio of the Cabbibo suppressed Bs0 → K*0 gamma decay.
4

Analysis of radiative decays of charged B mesons to baryonic final states

Strube, Jan, 1978- 09 1900 (has links)
xxvi, 199 p. : ill. (some col.) A print copy of this thesis is available through the UO Libraries. Search the library catalog for the location and call number. / The abundance of B mesons at B factories opens the door to the search in rare decays for physics outside of the Standard Model. Flavor-changing neutral current transitions proceed only via higher order in the Standard Model, resulting in a b [arrow right] s³y branching fraction of about 3 x 10 -4 , but hypothesized particles could alter the rate significantly. Decays of B mesons that proceed via this electroweak penguin diagram are an interesting example of flavor-changing neutral currents, due to the large number of accessible final states with observables that are sensitive to new processes. This dissertation describes the analyses of such decays B - [arrow right] p ³, B - [arrow right] £ 0 p ³, B - [arrow right] p and B - [arrow right] p using about 350 million B meson pairs recorded by the BABAR detector in the years 2001 through 2006. In addition to the decay rate, the distribution of the invariant mass of the baryon pair is presented, using a method for statistical unfolding. The analysis is the first of these decays at the BABAR experiment and lays the groundwork for future analyses of the branching fractions and angular correlations of b [arrow right] s decays containing A hyperons and other baryons at BABAR or higher luminosity B factories. / Adviser: James E. Brau
5

A search for direct and radiative decays of the neutral B meson to invisible final states using a hadronic tagging method at the BABAR detector

Blount, Nicholas L., 1979- 12 1900 (has links)
xii, 118 p. : ill. (some col.) A print copy of this thesis is available through the UO Libraries. Search the library catalog for the location and call number. / This dissertation describes a search for the decays B 0 [arrow right] invisible and B 0 [arrow right] invisible+γ, where invisible refers to a final state consisting of long lived particles with a low cross-section for interaction with matter, leading to a low probability of detection in typical particle detectors. While the branching fractions for these decays predicted by the Standard Model are far below what could be feasably measured by current experiments, new physics such as right-handed neutrinos propagating in large extra space-time dimensions or light R-parity violating neutralinos in supersymmetry could greatly enhance the branching fractions. The decays are searched for in data corresponding to 423.5 fb -1 integrated luminosity produced at the Υ(4 S ) resonance collected with the BABAR detector at the PEP-II B factory, corresponding to 2.30 × 10 8 B 0 B¯ 0 pairs. Using those events that contain a hadronically reconstructed neutral B meson, evidence for the signal decays is sought in the remainder of the event. In (5.00 ± 0.02) × 10 5 events with a fully reconstructed neutral B meson, a total of 39 events consistent with the B 0 [arrow right] invisible decay mode are seen in data with an expected background of 28.5 ± 7.8(stat.)±9.2(syst.) events, and 8 events consistent with the B 0 [arrow right] invisible+γ decay mode are seen in data mode with an expected background of 14.1 ± 5.5(stat.)±8.1(syst.) events, from which upper limits of [Special characters omitted.] ( B 0 [arrow right] invisible) < 11.7 × 10 -5 and of [Special characters omitted.] ( B 0 [arrow right] invisible+γ) < 4.3 × 10 -5 at the 90% confidence level are obtained. / Adviser: David Strom
6

The Charm of Excited Glue : Charmonium in <i>e</i><sup>+</sup><i>e</i><i>–</i> and <i>ppbar</i> collisions

Lundborg, Agnes January 2007 (has links)
<p>This thesis treats the mass range of charmonium states and excited gluonic fields in two experiments, BESII and PANDA, and outlines a phenomenological model that connects them.</p><p>In BESII, <i>e</i><sup>+</sup><i>e</i><sup>–</sup> form a charmonium initial state, which is utilised as a source for secondary particles. The analysed channels, <i>ψ</i>´→ <i>γK</i><sup>+</sup><i>K</i><sup>–</sup> and <i>ψ</i>´→ <i>γπ</i><sup>+</sup><i>π</i><sup>–</sup>, give access to intermediate scalar states such as the two glueball candidates: f<sub>0</sub>(1500) and f<sub>0</sub>(1710). The f<sub>0</sub>(1710) is indeed observed in decay into both <i>π</i><sup>+</sup><i>π</i><sup>–</sup> and <i>K</i><sup>+</sup><i>K</i><sup>–</sup> and the f<sub>0</sub>(1500) is accepted as a necessary part of the <i>π</i><sup>+</sup><i>π</i><sup>–</sup> signal at the moderate 5% level. In addition, we observe the two tensor states f<sub>2</sub>(1270) (in both channels) and f<sub>2</sub>´(1525) (in <i>K</i><sup>+</sup><i>K</i><sup>–</sup>), but the need for the f<sub>2</sub>´(1525) is not firmly established. The region around 2 GeV/<i>c</i><sup>2</sup> is fitted with an f<sub>4</sub>(2050) and an f<sub>0</sub>(2200) in <i>π</i><sup>+</sup><i>π</i><sup>–</sup>. This region is fairly flat in <i>K</i><sup>+</sup><i>K</i><sup>–</sup> with a slight peak at the f<sub>0</sub>(2200). Branching ratios for all eight channels are given. A fit to the angular distribution of ψ´→ γ f<sub>2</sub>(1270) → <i>γ π</i><sup>+</sup><i>π</i><sup>–</sup>gave two possible solutions for the relative importance of helicity projections zero, one and two.</p><p>The future <i>pp</i>bar experiment PANDA is still in the development phase; important physics goals have been defined and we are now taking on the laborious task of constructing a detector that is able to fulfil them. A simulation investigation of a theoretically preferred <i>J</i><i>PC</i>=1<sup>–+</sup> charmonium hybrid (<i>H</i><i>c</i>) is presented: <i>ppbar</i> → <i>H</i><i>c</i><i>π</i><sup>0</sup>/<i>η</i>, <i>H</i><i>c</i> → <i>χ</i><i>c</i><sub>1</sub> (<i>π</i><sup>0</sup><i>π</i><sup>0</sup>)<i>S–wave</i>, <i>χ</i><i>c</i><sub>1</sub> → <i>J</i>/<i>ψπ</i><sup>0</sup>, with a final state of seven photons and a lepton pair. To detect this channel next to full coverage of CM phase space is needed and as little material as possible before the electromagnetic calorimeter. </p><p>A second simulation study of <i>pp</i>bar → <i>η</i><i>c</i> → <i>γγ</i> at PANDA, suggests that the channel should be possible to detect with a signal-to-background ratio of 5±1 and a detection efficiency of at least 10%. </p><p>By assuming a constant matrix element we obtain a relation between the decay width for <i>ψ</i> → <i>pp</i>bar+<i>m</i>, which has been measured at BES for several cases, and the cross section for <i>pp</i>bar charmonium production in association with the same light meson, <i>m</i> (at for example PANDA). Cross sections of ~300–3000 pb were predicted for J/ψ production and ~30 pb for <i>ψ</i>' production. Isoscalars seem to be preferred to isovectors in <i>J</i>/<i>ψ</i> production, this might however be an artefact of simplifications within the model. A comparison with the only measured cross section, <i>pp</i>bar → <i>J</i>/<i>ψπ</i><sup>0</sup>, suggests that the model is useful as a first estimate.</p>
7

The Charm of Excited Glue : Charmonium in e+e– and ppbar collisions

Lundborg, Agnes January 2007 (has links)
This thesis treats the mass range of charmonium states and excited gluonic fields in two experiments, BESII and PANDA, and outlines a phenomenological model that connects them. In BESII, e+e– form a charmonium initial state, which is utilised as a source for secondary particles. The analysed channels, ψ´→ γK+K– and ψ´→ γπ+π–, give access to intermediate scalar states such as the two glueball candidates: f0(1500) and f0(1710). The f0(1710) is indeed observed in decay into both π+π– and K+K– and the f0(1500) is accepted as a necessary part of the π+π– signal at the moderate 5% level. In addition, we observe the two tensor states f2(1270) (in both channels) and f2´(1525) (in K+K–), but the need for the f2´(1525) is not firmly established. The region around 2 GeV/c2 is fitted with an f4(2050) and an f0(2200) in π+π–. This region is fairly flat in K+K– with a slight peak at the f0(2200). Branching ratios for all eight channels are given. A fit to the angular distribution of ψ´→ γ f2(1270) → γ π+π–gave two possible solutions for the relative importance of helicity projections zero, one and two. The future ppbar experiment PANDA is still in the development phase; important physics goals have been defined and we are now taking on the laborious task of constructing a detector that is able to fulfil them. A simulation investigation of a theoretically preferred JPC=1–+ charmonium hybrid (Hc) is presented: ppbar → Hcπ0/η, Hc → χc1 (π0π0)S–wave, χc1 → J/ψπ0, with a final state of seven photons and a lepton pair. To detect this channel next to full coverage of CM phase space is needed and as little material as possible before the electromagnetic calorimeter. A second simulation study of ppbar → ηc → γγ at PANDA, suggests that the channel should be possible to detect with a signal-to-background ratio of 5±1 and a detection efficiency of at least 10%. By assuming a constant matrix element we obtain a relation between the decay width for ψ → ppbar+m, which has been measured at BES for several cases, and the cross section for ppbar charmonium production in association with the same light meson, m (at for example PANDA). Cross sections of ~300–3000 pb were predicted for J/ψ production and ~30 pb for ψ' production. Isoscalars seem to be preferred to isovectors in J/ψ production, this might however be an artefact of simplifications within the model. A comparison with the only measured cross section, ppbar → J/ψπ0, suggests that the model is useful as a first estimate.
8

Scalar Mesons In Radiative Phi-meson Decays Into Charged K-meson States

Ozturk, Fahri 01 June 2008 (has links) (PDF)
The role of $f_{0}(980)$ and $a_{0}(980)$ scalar meson intermediate states in the mechanism of radiative $phi (1020)$ meson decay into two charged $K (494)$ mesons and a photon $phirightarrow K^{+} + K^{-} + gamma$ is investigated. For the contribution of scalar meson intermediate state two models are considered. In the kaon-loop model, the scalar meson intermediate state couples the final state to the initial $phi$ meson through a charged kaon-loop. The second model, called no-structure model, consist of point-like coupling of intermediate scalar meson state to the initial state. It is found that in the kaon-loop model, scalar meson intermediate state results in a considerable modification of the pure Bremsstrahlung photon spectrum.
9

Étude des désintégrations radiatives Z →μμγ et recherches du boson de Higgs dans le canal H→γγ dans l’expérience CMS au LHC (CERN) / Study of radiative decays Z →μμγ and search for Higgs bosons in the H→γγ channel, in the CMS experiment at LHC (CERN)

Bondu, Olivier 10 October 2012 (has links)
Le Large Hadron Collider (LHC) au CERN (Organisation Européenne pour la Recherche Nucléaire) fonctionne depuis 2009 à la frontière franco-suisse. Cet accélérateur de particules a produit des quantités importantes de collisions proton-proton, à des énergies dans le centre de masse de 7 TeV (2010 et 2011), et 8 TeV (depuis avril 2012). L'un des buts de l'expérience Compact Muon Solenoid (CMS), qui enregistre et analyse ces collisions, est la recherche de bosons de Higgs. Dans le cadre du Modèle Standard, cette particule serait le quantum du champ de Higgs, qui permet d'expliquer le mécanisme de brisure de symétrie électrofaible. Un canal parmi les plus sensibles pour la recherche d'un boson de Higgs léger (c'est-à-dire pour des masses du boson de Higgs entre 90GeV/c2 et 150GeV/c2) au LHC est la désintégration en deux photons. En effet, la production de deux photons isolés de haute énergie dans l'état final constitue un signal clair en milieu hadronique, malgré le faible rapport d'embranchement. De plus, à ces masses, la largeur du pic en masse invariante reconstruite est dominée par la résolution du détecteur. Une compréhension fine de l'objet photon, tel que reconstruit par l'expérience, est donc un pré requis obligatoire. La première partie de mes travaux de thèse porte sur l'étude des désintégrations radiatives Z$^0 \rightarrow \mu\mu\gamma$ ces désintégrations sont la seule source de photons certifiés de haute pureté du Modèle Standard, pour laquelle l'impulsion transverse des photons est relativement proche de celle prévue pour des photons issus d'un boson de Higgs. L'étude de ces désintégrations a permis la détermination de l'échelle d'énergie différentielle des photons dans les données à 7 TeV. Elles ont également été utilisées dans les données à 8 TeV comme outil de validation des variables de forme de cluster pour les photons dans la simulation, ainsi que pour déterminer l'efficacité des critères de réjection des électrons. La deuxième partie de mes travaux de thèse traite de la recherche d'un boson de Higgs se désintégrant en deux photons. Cette recherche est effectuée en plusieurs classes d'évènements pour améliorer la sensibilité, et l'étude de cette procédure de séparation en classes est présentée. Enfin, une analyse de faisabilité de recherche d'un boson de Higgs se désintégrant en deux photons, produit lors de la désintégration d'un quark vecteur lourd à 14 TeV a été effectuée / The Large Hadron Collider (LHC) at CERN (European Organisation for Nuclear Research) has been in operation since 2009 at the border between France and Switzerland. This particle accelerator has provided a significant quantity of proton-proton collisions, at center of mass energies of 7 TeV (2010 and 2011) and 8 TeV (since April 2012). One of the purposes of the Compact Muon Solenoid (CMS) experiment, which records and analyses those collisions, is the search for Higgs bosons. In the Standard Model, this particle would be the quantum of the Higgs field, thought to explain the electroweak symmetry-breaking mechanism. One of the most sensitive channels for the search for a light Higgs boson (i.e. for masses between 90 GeV=c2 and 150 GeV=c2) at the LHC is through its decay into two photons. Indeed, the production of two highly energetic and isolated photons in the final state is a clean signal in hadronic collisions, despite the small branching ratio. Moreover, at these masses, the width of the reconstructed invariant mass peak is dominated by the detector resolution. Hence, a precise understanding of the photon object as reconstructed by the experiment is required. The first part of the work presented here is the study of radiative decays Z$^0 \rightarrow \mu\mu\gamma$ these decays are the only Standard Model source of high purity certified photons, for which the transverse momentum of the photon is relatively similar to the one of the photons coming from a Higgs boson decay. The study of these decays enables the determination of the differential photon energy scale in the 7 TeV data. These decays have also been used in the 8 TeV data as a validation tool of photon cluster shape variables in the simulation, and also as a way to determine the electron rejection criteria efficiency. The second part of the work concerns the search for a Higgs boson decaying into two photons. This search is done in several event classes in order to increase the sensitivity of the analysis, the study of the class separation procedure is presented. Finally, a benchmark study for the search for a Higgs boson decaying into two photons via vector-like top-partner decays at 14 TeV has been performed
10

Phénoménologie des mésons B à la recherche d'un signal au-delà du modèle standard / B Mesons Phenomenology to the Search of a Signal Beyond the Standard Model

Hebinger, Jeremy 18 September 2017 (has links)
Durant les dernières décennies, la désintégration induite par une boucle $b o sgamma$, a attiré beaucoup d'attention à cause de sa sensibilité potentielle à la nouvelle physique. Dans le model standard, les transitions $b o sgamma_{L(R)}$ et $overline{b} o overline{s}gamma_{R(L)}$ sont proportionnelles aux coefficients de Wilson $C_7(C'_7)$.La désintégration $B o Kpipigamma$ offre à travers l'analyse angulaire un observable P impaire ($lambda$) et à traversle mélange $B-overline{B}$ un observable CP impaire ($S_{ho Kgamma}$) tous deux étants sensibles au rapport $C'_7/C_7approx m_s/m_b$. La difficulté principale étant que $lambda$ et $S_{ho Kgamma}$ sont accompagnés par un facteur de dilution provenant de la désintégration forte. Ce travail est centré sur l'éstimation et la modélisation de ces facteurs de dilution. La transition $B o Kpipigamma$ se produit en tant quetrois désintégrations successives.La transition faible $B o K_{res}gamma$ est suivie par la désintégration forte en trois corps de la résonance kaonic $K_{res} o Kpipi$ via trois états intermediaires distincts $ho K$, $K^*pi$ et $kappapi$.L'observable $S_{ho Kgamma}$ est accessible avec l'état final $K^0pi^+pi^-gamma$, mais la présence de $K^{*pm}pi^mp$ et $kappa^pmpi^mp$, n'étants pas état propre de CP, induit le facteur de dilution $D$.Pour résoudre ce problème, nous dérivons l'expression de $D$ en fonction des ondes partielles $ho K$, $K^*pi$ et $kappapi$ et en incluant les résonances kaonic $K_1(1270/1400), K^*(1410)$ et $K_2^*(1430)$. Afin de calculer le facteur de dilution, les ondes partielles peuvent être extraites avec l'état final $K^{pm}pi^{mp}pi^{pm}gamma$, où la sensibilité expérimentale est plus élevée. Ensuite, nous proposons une nouvelle méthode, indépendante du model, pour déterminer $D$, qui consiste a extraire le facteur de dilution independamment de $S_{ho Kgamma}$ en utilisant des états finaux avec un pion neutre tels que $K^+pi^-pi^0gamma$. En exploitant des données existantes avec $m_{Kpipi} <1.8;$GeV$/c^2$, nous obtenons $D=0.92pm0.17$.Lorsque l'on considère juste $K_1(1270/1400)$ et $K^*(1410)$, $lambda$ peut être extrait de la distribution angulaire and de Dalitz avec une précision de l'ordre de $pm 10%$ pour un echantillon de $5.10^3$ évènements générés à l'aide de la méthode Monté Carlo. Mais cela demande une bonne connaissance de différentes quantités importantes pour la désintégration forte telles que l'angle de mélange de $K_1$, les rapports de branchement individuel $B o K_{res}gamma$ et les phases relatives. Nous montrons que certains de ces paramètres et $lambda$ peuvent être simultanément ajustés avec une perte de précision de juste quelques pourcents. Puis nous dérivons comment, en utilisant seulement la distribution angulaire, il est possible d'annuler partiellement les contributions provenants de la désintégration forte afin d'obtenir une limite inférieure pour $|lambda|$. / Over the last decades, the loop induced decay $b o sgamma$ has attracted a considerable amount of attention due to its potential sensitivity to new physics. In the standard model, the processes $b o sgamma_{L(R)}$ and $overline{b} o overline{s}gamma_{R(L)}$ are proportional to the Wilson coefficients $C_7(C'_7)$. The decay $B o Kpipigamma$ provides via angular analysis a parity odd observable ($lambda$) and via $B-overline{B}$ mixing a CP odd observable ($S_{ho Kgamma}$) both sensitive to the ratio $C'_7/C_7approx m_s/m_b$. The main issue is that both $lambda$ and $S_{ho Kgamma}$ are accompanied by a dilution factor originating from the strong decay. This work is focused on the estimation and modelisation of those dilution factors.The transition $B o Kpipigamma$ occurs as three subsequent decays. The weak process $B o K_{res}gamma$ is followed by the strong 3-body decay of the kaonic resonance $K_{res} o Kpipi$ via three distinct intermediate states $ho K$, $K^*pi$ and $kappapi$.The observable $S_{ho Kgamma}$ is accessible with the final state $K^0pi^+pi^-gamma$, but the presence of non CP eigenstates $K^{*pm}pi^mp$ and $kappa^pmpi^mp$ induce the dilution factor $D$.To deal with this inconvenience, we derive the expression of $D$ in terms of the partial waves $ho K$, $K^*pi$ and $kappapi$ and including the koanic resonances $K_1(1270/1400), K^*(1410)$ and $K_2^*(1430)$. The partial waves can then be fitted using the final state $K^{pm}pi^{mp}pi^{pm}gamma$, where the experimental sensitivity is higher, in order the compute the dilution factor. Then we propose a new model independent method to determine $D$, which consist in extracting the dilution factor independently of $S_{ho Kgamma}$ using final states with one neutral pion such as $K^+pi^-pi^0gamma$. Exploiting existing data with $m_{Kpipi} <1.8;$GeV$/c^2$, we obtained $D=0.92pm0.17$.When considering only $K_1(1270/1400)$ and $K^*(1410)$, fitting the angular and Dalitz plot distribution allows to extract $lambda$ with an accuracy of the order of $pm 10%$ for a sample of $5.10^3$ Monte Carlo generated events. But this require a good knowledge of different quantities of importance in the strong decay such as the $K_1$ mixing angle, individual $B o K_{res}gamma$ branching ratios and relative phases. We show that some of those parameters can simultaneously fitted with $lambda$ with a loss of accuracy of just a few percent. We derive how, using only the angular distribution, one can partially cancel contribution from the strong decay and obtain a lower bound on $|lambda|$.

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