Higher-Twist Effects in Light-Cone Sum Rule for the B→πB\to\pi Form Factor

We calculate the higher-twist corrections to the QCD light-cone sum rule for the $B \to \pi$ transition form factor. The light-cone expansion of the massive quark propagator in the external gluonic field is extended to include new terms containing the derivatives of gluon-field strength. The resulting analytical expressions for the twist-5 and twist-6 contributions to the correlation function are obtained in a factorized approximation, expressed via the product of the lower-twist pion distribution amplitudes and the quark-condensate density. The numerical analysis reveals that new higher-twist effects for the $B \to \pi$ form factor are strongly suppressed. This result justifies the conventional truncation of the operator product expansion in the light-cone sum rules up to twist-4 terms.Comment: 14 pages, 2 figures, 1 tabl

Bs→KℓνℓB_{s}\to K \ell \nu_\ell and B(s)→π(K)ℓ+ℓ−B_{(s)} \to \pi (K) \ell^+\ell^- decays at large recoil and CKM matrix elements

We provide hadronic input for the $B$-meson semileptonic transitions to a light pseudoscalar meson at large recoil. The $B_s\to K$ form factor calculated from QCD light-cone sum rule is updated, to be used for a $|V_{ub}|$ determination from the $B_s\to K \ell \nu$ width. Furthermore, we calculate the hadronic input for the binned observables of $B \to \pi \ell^+ \ell^-$ and $B \to K \ell^+ \ell^-$. In addition to the form factors, the nonlocal hadronic matrix elements are obtained, combining QCD factorization and light-cone sum rules with hadronic dispersion relations. We emphasize that, due to nonlocal effects, the ratio of branching fractions of these decays is not sufficient for an accurate extraction of the $|V_{td}/V_{ts}|$ ratio. Instead, we suggest to determine the Wolfenstein parameters $A,\rho,\eta$ of the CKM matrix, combining the branching fractions of $B \to K \ell^+ \ell^-$ and $B \to \pi \ell^+ \ell^-$ with the direct $CP$-asymmetry in the latter decay. We also obtain the hadronic matrix elements for a yet unexplored channel $B_s \to K \ell^+ \ell^-$.Comment: 21 pages, 4 figures, 5 tables, a few comments and references addded, version accepted for publication in JHE

Hadronic effects and observables in semileptonic B-meson decays

An accurate phenomenological analysis of rare B-meson decays is important both for precise tests of the Standard Model and in the search for possible New Physics in the flavour sector. In the framework of this thesis, several semileptonic B-meson decays induced by flavour-changing quark currents are studied. The main focus is put on the analysis of the underlying hadronic input including the relevant form factors and nonlocal hadronic amplitudes. With accurate determination of the hadronic input from the QCD-based methods, various observables in inclusive and exclusive semileptonic decays of B mesons are predicted. This dissertation is written in the form of a cumulative work based on our four articles published in international peer reviewed journals. The first chapter contains a short introduction to the Standard Model and a brief discussion of theoretical methods. The chapter 2 of the thesis is dedicated to the analysis of the flavour-changing neutral current (FCNC) b --> d observed in the form of the semileptonic B --> pi ell ell decays. In the latter decays, the underlying hadronic nonlocal contributions are systematically taken into account using the operator-product expansion, QCD factorization and light-cone sum rules. Together with the B --> pi form factors derived from light-cone sum rules, these nonlocal hadronic amplitudes are used to predict various observables such as the differential rate, direct CP-asymmetry and isospin asymmetry in B --> pi ell ell decays. In addition, the total width of B --> pi nu nu decay is estimated. The third chapter of the thesis is devoted to the analysis of the higher-twist effects in the QCD light-cone sum rule for the heavy-to-light transition form factors. To this end, the light-cone expansion of the massive quark propagator in the external gluonic field is extended to include new terms containing the derivatives of gluon-field strength. The resulting analytical expressions for the twist-5 and twist-6 contributions to the correlation function are obtained in a factorized approximation, expressed via the product of the lower-twist pion distribution amplitudes and the quark-condensate density. The numerical analysis reveals a smallness of the higher twist effects justifying the conventional truncation of the operator product expansion in the light-cone sum rules up to twist 4. The chapter 4 of the thesis extends the analysis of hadronic input to other semileptonic decays including B --> K ell ell and Bs --> K ell ell. To this end, the light-cone sum rule results for the relevant form factors are updated taking into account the estimate of the higher twist effects. In addition, the corresponding nonlocal hadronic matrix elements are extracted in a systematic way. Moreover, a new way to determine the Wolfenstein parameters of the Cabibbo-Kobayashi-Maskawa matrix is suggested based on the observables in semileptonic FCNC B --> pi ell ell and B --> K ell ell decays. The prediction for the Bs --> K ell nu partial decay width provides an additional source for the determination of the CKM parameter |Vub|. The last chapter 5 of the thesis deals with the inclusive semileptonic B --> Xc tau nu decays. Using the standard techniques of heavy quark expansion, the decay width and moments of tau-lepton energy distribution are calculated including power corrections up to order Lambda_QCD^3/m_b^3. The result is compared with the sum of the predictions for the branching fractions of the exclusive semileptonic B --> (D, D*, D**) tau nu decays as well as with the relevant experimental data. In addition, the impact from physics beyond the Standard Model to the inclusive B --> Xc tau nu rate is discussed.Eine genaue phänomenologische Analyse von seltenen Zerfällen von B-Mesonen ist sowohl für präzise Tests des Standardmodells als auch für die Suche nach möglicher neuer Physik im Flavoursektor wichtig. Im Rahmen dieser Arbeit werden verschiedene semileptonische Zerfälle von B-Mesonen, die durch flavourändernde Quarkströme induziert werden, untersucht. Der Schwerpunkt liegt dabei auf der Analyse des zugrundeliegenden hadronischen Inputs, einschließlich der relevanten Formfaktoren und nichtlokalen hadronischen Amplituden. Mithilfe einer genauen Bestimmung des hadronischen Inputs, der mittels QCD-basierten Methoden gewonnen wurde, werden verschiedene Observablen von inklusiven und exklusiven semileptonischen Zerfällen von B-Mesonen, vorhergesagt. Diese Dissertation ist in Form von einer kumulativen Arbeit geschrieben und basiert auf vier Artikeln, die in internationalen, von Experten begutachteten Fachzeitschriften veröffentlicht wurden. Das erste Kapitel enthält eine kurze Einführung in das Standardmodell und eine kurze Diskussion von theoretischen Methoden. Das Kapitel 2 der Dissertation ist der Analyse des flavourändernden neutralen Stroms (FCNC) b --> d gewidmet, der in der Form von semileptonischen B --> pi ell ell Zerfällen beobachtet werden kann. In den zuletzt genannten Zerfällen, werden die zugrundeliegenden hadronischen nichtlokalen Beiträge unter Verwendung der Operatorproduktentwicklung, der QCD-Faktorisierung und den Lichtskegelsummenregeln, systematisch berücksichtigt. Diese nichtlokalen hadronischen Amplituden werden zusammen mit den aus den Lichtkegelsummenregeln abgeleiteten B --> pi Formfaktoren, zur Vorhersage verschiedener Observablen wie der differentiellen Rate, der direkten CP-Asymmetrie und der Isospin-Asymmetrie von B --> pi ell ell, verwendet. Zusätzlich wird die totale Breite des Zerfalls B --> pi nu nu abgeschätzt. Das dritte Kapitel der Dissertation ist der Analyse von Effekten höheren Twists, die in der QCD Lichtkegelsummenregel für den Übergang eines schweren Mesons in ein leichtes Meson auftauchen, gewidmet. Zu diesem Zweck wird die Lichtkegelentwicklung des massiven Quarkpropagators in einem externen gluonischen Feld ausgedehnt, um neue Terme, die Ableitungen der Gluonfeldstärke enthalten, zu berücksichtigen. Die daraus resultierenden analytischen Ausdrücke für die Beiträge vom Twist-5 und Twist-6 zu den Korrelationsfunktion, werden in einer faktorisierten Approximation, die durch ein Produkt von Pion-Verteilungsamplituden von niedrigerem Twist und der Quarkkondensatdichte ausgedrückt ist, gewonnen. Die numerische Analyse zeigt,dass die Effekte von höherem Twist klein sind, was das herkömmliche Abbrechen der Operatorproduktentwicklung in den Lichtkegelsummenregeln bei Twist-4, rechtfertigt. Das Kapitel 4 der Dissertation weitet die Analyse des hadronischen Inputs auf andere semileptonische Zerfälle, einschließlich B --> K ell ell und Bs --> K ell ell aus. Zu diesem Zweck werden die Lichtkegelsummenregel-Ergebnisse für die relevanten Formfaktoren, unter Berücksichtigung der Abschätzung der Effekte von höherem Twist, auf den aktuellen Stand gebracht. Außerdem wird ein neuer Weg vorgeschlagen, die Wolfenstein-Parameter der Cabibbo-Kobayashi-Maskawa-Matrix zu bestimmen, welcher auf den Observablen der semileptonischen FCNC Zerfälle B --> pi ell ell und B --> K ell ell basiert. Die Vorhersage für die partielle Zerfallsbreite von Bs --> K ell nu bietet eine zusätzliche Möglichkeit den CKM-Parameter |Vub| zu bestimmen. Das letzte Kapitel 5 der Dissertation beschäftigt sich mit den inklusiven semileptonischen B --> Xc tau nu Zerfällen. Unter Verwendung der Standardtechnik der Heavy-Quark-Expansion, werden die Zerfallsbreite und die Momente der Energieverteilung des tau-Leptons einschließlich der Power-Korrekturen bis zur Ordnung Lambda_QCD^3/m_b^3 berechnet. Das Ergebnis wird sowohl mit der Summe der Vorhersagen für die Verzweigungsverhältnisse der exklusiven semileptonischen B --> (D,D*,D**) tau nu Zerfälle als auch mit den relevanten experimentellen Daten verglichen. Zusätzlich wird der Effekt von Physik jenseits des Standardmodells auf die inklusive B --> Xc tau nu Zerfallsrate diskutiert

Model of decision support system used for assessment of insurance risk

Za savremeno poslovanje u uslovima neizvesnosti, rezultati predviđanja poslovanja su od suštinskog značaja za evaluaciju buduće finansijske efikasnosti preduzeća. U radu je izložen primer predviđanja premija na osnovu ocena izvora rizika u osiguranju. Zbog neizvesnosti koja prati trenutak nastanka i iznosa štete neophodno je osigurati dovoljno sredstava za pokriće rizika. Za usklađivanje sredstava i obaveza potrebno je oceniti uticaj rizika na promenu premije po vrstama osiguranja, što čini osnovni koncept razvoja i poslovanja osiguravajućih društava. U radu je predstavljeno eksperimentalno istraživanje rangiranja rizika na osnovu projektovanog modela u sistemu za podršku odlučivanju. Sistem za podršku odlučivanju korišćen je u cilju generisanja hijerarhije uticajnih kriterijuma i alternativa u modelu za ocenu rizika kod navedenih vrsta osiguranja. Predloženi model zagovara ideju da se za vrste osiguranja kod koje se utvrdi najviši stepen rizika i na osnovu toga donesu odluke o visini premije u narednom periodu. .In order to run a modern business in uncertain times, business forcasting is very important for evaluation of company.s future financial performance. This paper shows an example of premium forecast based on the assessment of risk sources in insurance system. Due to uncertainty that is one of the characteristics of loss occurrence and indemnity amount, it is important to hold sufficient assets to cover the risk. For asset-liability matching, one should first assess the impact of risk on premium movement per insurance lines. This is the main concept of development and performance of insurance companies. This paper shows an experimental research of risk ranking based on projected model of decision support system. Decision support system is used with the aim to generate hierarchy of influential criteria and alternatives of risk assessment model for stated insurance lines. Suggested model sup- ports the idea according to which one should first determine insurance lines with the highest risk and then, on that basis, make a decision on premium amount in the following period

Model of decision support system used for assessment of insurance risk

Za savremeno poslovanje u uslovima neizvesnosti, rezultati predviđanja poslovanja su od suštinskog značaja za evaluaciju buduće finansijske efikasnosti preduzeća. U radu je izložen primer predviđanja premija na osnovu ocena izvora rizika u osiguranju. Zbog neizvesnosti koja prati trenutak nastanka i iznosa štete neophodno je osigurati dovoljno sredstava za pokriće rizika. Za usklađivanje sredstava i obaveza potrebno je oceniti uticaj rizika na promenu premije po vrstama osiguranja, što čini osnovni koncept razvoja i poslovanja osiguravajućih društava. U radu je predstavljeno eksperimentalno istraživanje rangiranja rizika na osnovu projektovanog modela u sistemu za podršku odlučivanju. Sistem za podršku odlučivanju korišćen je u cilju generisanja hijerarhije uticajnih kriterijuma i alternativa u modelu za ocenu rizika kod navedenih vrsta osiguranja. Predloženi model zagovara ideju da se za vrste osiguranja kod koje se utvrdi najviši stepen rizika i na osnovu toga donesu odluke o visini premije u narednom periodu. .In order to run a modern business in uncertain times, business forcasting is very important for evaluation of company.s future financial performance. This paper shows an example of premium forecast based on the assessment of risk sources in insurance system. Due to uncertainty that is one of the characteristics of loss occurrence and indemnity amount, it is important to hold sufficient assets to cover the risk. For asset-liability matching, one should first assess the impact of risk on premium movement per insurance lines. This is the main concept of development and performance of insurance companies. This paper shows an experimental research of risk ranking based on projected model of decision support system. Decision support system is used with the aim to generate hierarchy of influential criteria and alternatives of risk assessment model for stated insurance lines. Suggested model sup- ports the idea according to which one should first determine insurance lines with the highest risk and then, on that basis, make a decision on premium amount in the following period