scholarly journals Decay amplitudes to three hadrons from finite-volume matrix elements

2021 ◽  
Vol 2021 (4) ◽  
Author(s):  
Maxwell T. Hansen ◽  
Fernando Romero-López ◽  
Stephen R. Sharpe
Keyword(s):  
Finite Volume ◽  
Decay Amplitude ◽  
Weak Decay ◽  
Matrix Elements ◽  
Isospin Breaking ◽  
Final State ◽  
Identical Particles ◽  
Hadron Decay ◽  
Finite State ◽  
Particle Decays

Abstract We derive relations between finite-volume matrix elements and infinite-volume decay amplitudes, for processes with three spinless, degenerate and either identical or non-identical particles in the final state. This generalizes the Lellouch-Lüscher relation for two-particle decays and provides a strategy for extracting three-hadron decay amplitudes using lattice QCD. Unlike for two particles, even in the simplest approximation, one must solve integral equations to obtain the physical decay amplitude, a consequence of the nontrivial finite-state interactions. We first derive the result in a simplified theory with three identical particles, and then present the generalizations needed to study phenomenologically relevant three-pion decays. The specific processes we discuss are the CP-violating K → 3π weak decay, the isospin-breaking η → 3π QCD transition, and the electromagnetic γ* → 3π amplitudes that enter the calculation of the hadronic vacuum polarization contribution to muonic g − 2.

The branching fraction calculations of Bc+ → ψ(2S)π+, Bc+ → J/ψK+ and Bc+ → J/ψDs+ decays relative to that of the Bc+ → J/ψπ+ mode

2018 ◽  
Vol 33 (08) ◽  
pp. 1850044
Author(s):  
Behnam Mohammadi
Keyword(s):  
Branching Fraction ◽  
Branching Fractions ◽  
Decay Amplitude ◽  
Weak Decay ◽  
Lhcb Collaboration ◽  
Tree Level ◽  
Final State ◽  
Factorization Approximation ◽  
Weak Annihilation ◽  
First Time

The weak decay of [Formula: see text] into [Formula: see text], [Formula: see text] and [Formula: see text] mesons, observed by LHCb collaboration for the first time, are calculated in the model which takes into account the “factorizable” contributions and “nonfactorizable” corrections. The decays of [Formula: see text] mesons into charmonia and light hadrons are expected to be well described by the factorization approximation. In the standard model, [Formula: see text], [Formula: see text] decays occur through only the tree-level diagrams and so there are no CP violation in these channels. The decay [Formula: see text] is expected to proceed mainly via a [Formula: see text] transition because the [Formula: see text] decay has identical final state and similar event topology, where it is chosen as the relative branching fraction channel. The ratio of branching fractions [Formula: see text] is of particular interest since the CKM matrix element is suppressed by a factor [Formula: see text], in which the [Formula: see text] occur through [Formula: see text] transition, but the dominant amplitude of the decay [Formula: see text] is a [Formula: see text] transition. The decay [Formula: see text] is examined by color-allowed, color-suppressed spectator and weak annihilation diagrams. The weak annihilation topology, in contrast to decays of other beauty hadrons, is not suppressed and can contribute significantly to the decay amplitude. Because of the [Formula: see text], [Formula: see text] and [Formula: see text] branching fractions are calculated relative to the [Formula: see text] decay, this decay mode is estimated separately, the ratio between them are [Formula: see text], [Formula: see text] and [Formula: see text], respectively, that are compatible with the experimental data.

scholarly journals On the three-particle analog of the Lellouch-Lüscher formula

2021 ◽  
Vol 2021 (3) ◽  
Author(s):  
Fabian Müller ◽  
Akaki Rusetsky
Keyword(s):  
Field Theory ◽  
Finite Volume ◽  
Effective Field Theory ◽  
Effective Field ◽  
Infinite Volume ◽  
Leading Order ◽  
Particle Decay ◽  
Particle Decays

Abstract Using non-relativistic effective field theory, we derive a three-particle analog of the Lellouch-Lüscher formula at the leading order. This formula relates the three-particle decay amplitudes in a finite volume with their infinite-volume counterparts and, hence, can be used to study the three-particle decays on the lattice. The generalization of the approach to higher orders is briefly discussed.

scholarly journals Dual subtractions

2021 ◽  
Vol 2021 (6) ◽  
Author(s):  
Renato Maria Prisco ◽  
Francesco Tramontano
Keyword(s):  
Field Theory ◽  
Quantum Field ◽  
Matrix Elements ◽  
Leading Order ◽  
Initial State ◽  
Final State ◽  
Dual Representation ◽  
Subtraction Scheme ◽  
Theoretical Predictions ◽  
Perturbative Quantum

Abstract We propose a novel local subtraction scheme for the computation of Next-to-Leading Order contributions to theoretical predictions for scattering processes in perturbative Quantum Field Theory. With respect to well known schemes proposed since many years that build upon the analysis of the real radiation matrix elements, our construction starts from the loop diagrams and exploits their dual representation. Our scheme implements exact phase space factorization, handles final state as well as initial state singularities and is suitable for both massless and massive particles.

scholarly journals Another SMEFT story: Z′ facing new results on ε′/ε, ∆MK and K → $$ \pi \nu \overline{\nu} $$

2020 ◽  
Vol 2020 (12) ◽  
Author(s):  
Jason Aebischer ◽  
Andrzej J. Buras ◽  
Jacky Kumar
Keyword(s):  
Renormalization Group ◽  
Mass Difference ◽  
Branching Ratios ◽  
New Physics ◽  
Matrix Elements ◽  
Isospin Breaking ◽  
Left Handed ◽  
The Standard Model ◽  
First Time ◽  
Group Effects

Abstract Recently the RBC-UKQCD lattice QCD collaboration presented new results for the hadronic matrix elements relevant for the ratio ε′/ε in the Standard Model (SM) albeit with significant uncertainties. With the present knowledge of the Wilson coefficients and isospin breaking effects there is still a sizable room left for new physics (NP) contributions to ε′/ε which could both enhance or suppress this ratio to agree with the data. The new SM value for the K0 − $$ {\overline{K}}^0 $$ K ¯ 0 mass difference ∆MK from RBC-UKQCD is on the other hand by 2σ above the data hinting for NP required to suppress ∆MK. Simultaneously the most recent results for K+ → $$ {\pi}^{+}\nu \overline{\nu} $$ π + ν ν ¯ from NA62 and for KL → $$ {\pi}^0\nu \overline{\nu} $$ π 0 ν ν ¯ from KOTO still allow for significant NP contributions. We point out that the suppression of ∆MK by NP requires the presence of new CP-violating phases with interesting implications for K → $$ \pi \nu \overline{\nu} $$ πν ν ¯ , KS → μ+μ− and KL → π0ℓ+ℓ− decays. Considering a Z′-scenario within the SMEFT we analyze the dependence of all these observables on the size of NP still allowed by the data on ε′/ε. The hinted ∆MK anomaly together with the εK constraint implies in the presence of only left-handed (LH) or right-handed (RH) flavour-violating Z′ couplings strict correlation between K+ → $$ {\pi}^{+}\nu \overline{\nu} $$ π + ν ν ¯ and KL → $$ {\pi}^0\nu \overline{\nu} $$ π 0 ν ν ¯ branching ratios so that they are either simultaneously enhanced or suppressed relative to SM predictions. An anticorrelation can only be obtained in the presence of both LH and RH couplings. Interestingly, the NP QCD penguin scenario for ε′/ε is excluded by SMEFT renormalization group effects in εK so that NP effects in ε′/ε are governed by electroweak penguins. We also investigate for the first time whether the presence of a heavy Z′ with flavour violating couplings could generate through top Yukawa renormalization group effects FCNCs mediated by the SM Z-boson. The outcome turns out to be very interesting.

SYMMETRY DECOUPLING IN LINEAR ALGEBRAIC VARIATIONAL SCATTERING PROBLEMS

1995 ◽  
Vol 06 (01) ◽  
pp. 105-121
Author(s):  
MEISHAN ZHAO
Keyword(s):  
Angular Momentum ◽  
Variational Principle ◽  
Total Angular Momentum ◽  
Numerical Calculations ◽  
Quantum Mechanical ◽  
Matrix Elements ◽  
Scattering Problems ◽  
Identical Particles ◽  
Generalized Newton

This paper discusses the symmetry decoupling in quantum mechanical algebraic variational scattering calculations by the generalized Newton variational principle. Symmetry decoupling for collisions involving identical particles is briefly discussed. Detailed discussion is given to decoupling from evaluation of matrix elements with nonzero total angular momentum. Example numerical calculations are presented for BrH2 and DH2 systems to illustrate accuracy and efficiency.

scholarly journals Finding Cut-Offs in Leaderless Rendez-Vous Protocols is Easy

2021 ◽  
pp. 42-61
Author(s):  
A. R. Balasubramanian ◽  
Javier Esparza ◽  
Mikhail Raskin
Keyword(s):  
Lower Bounds ◽  
Petri Net ◽  
Special Class ◽  
Upper Bounds ◽  
Initial State ◽  
Reachability Problem ◽  
Final State ◽  
Final Configuration ◽  
Finite State ◽  
State Agents

AbstractIn rendez-vous protocols an arbitrarily large number of indistinguishable finite-state agents interact in pairs. The cut-off problem asks if there exists a number B such that all initial configurations of the protocol with at least B agents in a given initial state can reach a final configuration with all agents in a given final state. In a recent paper [17], Horn and Sangnier prove that the cut-off problem is equivalent to the Petri net reachability problem for protocols with a leader, and in "Image missing" for leaderless protocols. Further, for the special class of symmetric protocols they reduce these bounds to "Image missing" and "Image missing" , respectively. The problem of lowering these upper bounds or finding matching lower bounds is left open. We show that the cut-off problem is "Image missing" -complete for leaderless protocols, "Image missing" -complete for symmetric protocols with a leader, and in "Image missing" for leaderless symmetric protocols, thereby solving all the problems left open in [17].

scholarly journals Diagonal finite volume matrix elements in the sinh-Gordon model

2019 ◽  
Vol 945 ◽  
pp. 114664 ◽  
Author(s):  
Zoltan Bajnok ◽  
Fedor Smirnov
Keyword(s):  
Finite Volume ◽  
Matrix Elements

scholarly journals Weak decays of heavy hadrons into dynamically generated resonances

2016 ◽  
Vol 25 (01) ◽  
pp. 1630001 ◽  
Author(s):  
Eulogio Oset ◽  
Wei-Hong Liang ◽  
Melahat Bayar ◽  
Ju-Jun Xie ◽  
Lian Rong Dai ◽  
...  
Keyword(s):  
Weak Interaction ◽  
Weak Decay ◽  
Final State ◽  
Hadron Interaction ◽  
Heavy Mesons ◽  
Weak Decays ◽  
Quantum Numbers ◽  
Unitary Approach ◽  
Chiral Unitary Approach ◽  
Interpretation Of Results

In this paper, we present a review of recent works on weak decay of heavy mesons and baryons with two mesons, or a meson and a baryon, interacting strongly in the final state. The aim is to learn about the interaction of hadrons and how some particular resonances are produced in the reactions. It is shown that these reactions have peculiar features and act as filters for some quantum numbers which allow to identify easily some resonances and learn about their nature. The combination of basic elements of the weak interaction with the framework of the chiral unitary approach allow for an interpretation of results of many reactions and add a novel information to different aspects of the hadron interaction and the properties of dynamically generated resonances.

scholarly journals RESONANCES AND WEAK INTERACTIONS IN D+→ π+π−π+ DECAYS

2007 ◽  
Vol 16 (09) ◽  
pp. 2876-2879 ◽  
Author(s):  
DIOGO R. BOITO ◽  
BRUNO EL-BENNICH ◽  
BENOÎT LOISEAU ◽  
OLIVIER LEITNER
Keyword(s):  
Weak Interactions ◽  
Decay Amplitude ◽  
D Meson ◽  
Final State ◽  
Meson Decays ◽  
Factorization Approximation ◽  
Weak Part ◽  
Unitary Model ◽  
Final State Interactions ◽  
Three Body

We describe the ππS-wave in D+→ π+π−π+ decays using a unitary model for the ππ Final State Interactions (FSI). The three body decay is treated as a quasi two-body process where, at the weak vertex, the D meson decays into a resonance and a pion. The weak part of the decay amplitude is evaluated using the effective weak Hamiltonian within the factorization approximation.

scholarly journals DALITZ ANALYSES: A TOOL FOR PHYSICS WITHIN AND BEYOND THE STANDARD MODEL

2006 ◽  
Vol 21 (27) ◽  
pp. 5503-5512 ◽  
Author(s):  
M. R. PENNINGTON
Keyword(s):  
Standard Model ◽  
Strong Coupling Regime ◽  
Hadronic Decays ◽  
Beyond The Standard Model ◽  
Final States ◽  
Matrix Elements ◽  
Final State ◽  
Ckm Matrix ◽  
The Standard Model ◽  
Final State Interactions

Dalitz analyses are introduced as the method for studying hadronic decays. An accurate description of hadron final states is critical not only to an understanding of the strong coupling regime of QCD, but also to the precision extraction of CKM matrix elements. The relation of such final state interactions to scattering processes is discussed.

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