On the role of final-state interactions in Dalitz plot studies
Bastian Kubis, Franz Niecknig, Sebastian P. Schneider
备注：
5 pages, 5 figures; to appear in the proceedings of the International Workshop on e+e- collisions from Phi to Psi, September 19-22, 2011, Novosibirsk, Russia; partial textual overlap with arXiv:1108.5866
The study of Dalitz plots of heavy-meson decays to multi-hadron final states has received intensified interest by the possibility to gain access to precision investigations of CP violation. A thorough understanding of the hadronic final-state interactions is a prerequisite to achieve a highly sensitive, model-independent study of such Dalitz plots. We illustrate some of the theoretical tools, predominantly taken from dispersion theory, available for these and related purposes, and discuss the low-energy decays omega, phi --> 3pi in some more detail.
The decay $η\rightarrow π^+ π^- π^0$ is studied with the KLOE detector, at the DA$ϕ$NE e$^+$e$^-$ collider. Using a data sample corresponding to an integrated luminosity of $1.6$ fb$^{-1}$ a new study of the Dalitz plot is presented.
Bose symmetry and $CPT$ symmetry are two very fundamental symmetries of Nature. However, the validity of these symmetries in diverse phenomena must be verified by experiments. We propose new techniques to probe these two fundamental symmetries in the realm of mesons by using the Dalitz plot of a few three-body meson decays. Since these symmetries are very fundamental in nature, their violations, if any, are expected to be extremely small. Hence observing their violations requires study of a huge data sample. In this context we introduce a new three-dimensional plot which we refer to as the Dal…
We study the Dalitz plot of the Cabibbo-favored charmed-meson decay $D^+\to K^-π^+π^+$ using dispersion theory. The formalism respects all constraints from analyticity and unitarity, and consistently describes final-state interactions between all three decay products. We employ pion-pion and pion-kaon phase shifts as input, and fit the pertinent subtraction constants to Dalitz plot data by the CLEO and FOCUS collaborations. Phase motions of resonant as well as nonresonant amplitudes are discussed, which should provide crucial input for future studies of CP violation in similar three-body charm…
Recently, LHCb observed a double-charmed tetraquark candidate $T_{cc}^+$ and claimed its isospin to be zero due to the absence of $T_{cc}^{++}$. However, the absence of the $T_{cc}^{++}$ in LHCb may be due to their low production in $pp$ collisions, thus the isospin of $T_{cc}^+$ still needs to be clarified. We propose an efficient way to investigate the isospin property of $T_{cc}^+$ from the Dalitz plot distribution of $T_{cc}^+\to D^+D^0π^0$. This method can also be applied to other exotic candidates.
We present a new method using Dalitz plot and Bose symmetry of pions that allows the complete determination of the magnitudes and phases of weak decay amplitudes. We apply the method to process like B->K^* pi, with the subsequent decay of K^* -> K pi. Our approach enables the additional measurement of an isospin amplitude without any theoretical assumption. This advance will help in measuring weak phase and probing for new physics beyond standard model with fewer assumptions.
Charm meson decay dynamics have been studied extensively over the last decade. We describe the Dalitz-plot analysis technique which has been applied by many experiments to three-body D0, D+ and Ds decays. We discuss experimental results from Mark II, Mark III, E687, E691, ARGUS, E791, FOCUS, CLEO and BABAR. These studies probe a variety of physics including doubly-Cabibbo suppressed decays, searches for CP violation, the properties of established light mesons and the properties of pipi and Kpi S-wave states.
We resume the study of the Cabibbo-favored charmed-meson decays $D^+ \to \bar{K} ππ^+$ in a dispersive framework that satisfies unitarity, analyticity, and crossing symmetry by construction. The formalism explicitly describes the strong final-state interactions between all three decay products and relies on pion-pion and pion-kaon phase shift input. For the first time, we show that the $D^+ \to K_S π^0 π^+$ Dalitz plot obtained by the BESIII collaboration as well as the $D^+ \to K^- π^+ π^+$ Dalitz plot data by CLEO and FOCUS can be described consistently, exploiting the isospin relation betwe…
We propose a method to determine the phase motion of a complex amplitude in three body heavy meson decays. We show that the phase variation of a complex amplitude can be directly revealed through the interference observed in the Dalitz Plot region where it crosses with a well established resonant state. This method could be applied to the decays \d3pi and $D^+\to K^-π^+π^+$, to determine whether the low mass states $σ$ and $κ$, suggested by E791, have phase motions compatible with resonances.
We describe a novel use of the Dalitz plot to probe CP symmetry in three-body modes of $B$ and $D$ mesons. It is based on an observable inspired by astronomers' practice, namely the significance in the difference between corresponding Dalitz plot bins. It provides a model independent mapping of local CP asymmetries. We illustrate the method for probing CP symmetry in the complementary cases of B decays, where sizable or even large effects can be expected, yet have to be differentiated against leading Standard Model contributions, and $D$ decays, where one cannot count on sizable effects, yet h…
We claim that the non-resonant contribution to non-leptonic charm meson decays may not be constant in the phase space of the reaction. We argue that this can be relevant for any weak reaction. We discuss in detail the decay $D^+ \to K^- π^+ π^+$.
Dalitz plot studies for multi-hadron decays of heavy mesons are expected to become very important tools for precision investigations of CP violation. A thorough understanding of the hadronic final-state interactions is a prerequisite to achieve a highly sensitive, model-independent study of CP-violating phases in such processes. We illustrate the theoretical tools available, as well as still to be developed, from low-to-medium-energy hadron physics for this purpose, and the goals of the informal "Les Nabis" network studying these and related problems.
We adapt the Veneziano model to the analysis of vector charmonium decays. Starting from a set of covariant Veneziano terms we show how to construct partial waves amplitudes that receive contributions from selected Regge trajectories. The amplitudes, nevertheless retain the proper asymptotic limit. This arises from duality between directly produced resonances and cross-channel Reggeon and in practical applications helps remove uncertainties in the parametrization of backgrounds.
We present a new and sensitive method to observe direct CP violation in $D$ mesons using Bose symmetry and Dalitz plot. We apply the method to processes such as $B \to D^0\bar{D}^0 P$, where $P$ is either a $K$ or a $π$. By choosing to reconstruct $D$ mesons only through their decays into CP eigenstates, we show that any asymmetry in the Dalitz plot can arise only through direct CP violation. We further show how CP violation parameters can be determined. Since the approach involves only Bose symmetry, the method is applicable to any multi-body process that involves $D^0\bar{D}^0$ in the final …
Three body heavy meson decays allows one to extract important quantities for flavour physic, however the phenomenological analysis has some open problems to be solved in order to make possible to extract physical parameters with precision. After many years and some experience accumulated, we have learned new features and we expect to learn much more from data coming mainly from B three body decays. In this paper we address these aspects and we present a proposal to modify the Dalitz fit amplitude method in order to allow further studies.
A possible effect of direct CP violation in D->K0Spipi decay on the gamma measurement from B->DK, D->K0Spi+pi- Dalitz plot analysis is considered. Systematic uncertainty of gamma coming from the current limits on direct CP violation in D->K0Spi+pi- is estimated, and a modified model-independent procedure of B->DK, D->K0Spi+pi- Dalitz plot analysis is proposed that gives an unbiased gamma measurement even in presence of direct CP violation in charm decays. The technique is applicable to other three-body D decays such as D->K0SK+K-, D->pi+pi-pi0, etc.
We discuss properties of three-particle Dalitz distributions in coupled channel systems in presence of triangle singularities. The single channel case was discussed long ago where it was found that as a consequence of unitarity, effects of a triangle singularity seen in the Dalitz plot are not seen in Dalitz plot projections. In the coupled channel case we find the same is true for the sum of intensities of all interacting channels. Unlike the single channel case, however, triangle singularities do remain visible in Dalitz plot projections of individual channels.
The light hadron states are satisfactorily described in the quark model using $SU(3)$ flavor symmetry. If the $SU(3)$ flavor symmetry relating the light hadrons were exact, one would have an exchange symmetry between these hadrons arising out of the exchange of the up, down and strange quarks. This aspect of $SU(3)$ symmetry is used extensively to relate many decay modes of heavy quarks. However, the nature of the effects of $SU(3)$ breaking in such decays is not well understood and hence, a reliable estimate of $SU(3)$ breaking effects is missing. In this work we propose a new method to quant…
The BaBar Collaboration has pointed out that $D^0 \to π^+ π^- π^0$ is dominated by an isospin-zero final state, leading to nearly complete depletion of the Dalitz plot along all three diagonals. In flavor-SU(3) approaches to charmed particle decays to a light vector and a light pseudoscalar particle, this behavior is seen, but does not appear to have a fundamental origin. Instead, it arises as a result of approximate cancellation of higher-isospin combinations of several types of amplitudes: color-favored tree, color-suppressed tree, and exchange. Interpretation in terms of a direct-channel ef…
A large CP asymmetry predicted recently in the framework of the QCD factorization model for the B+- --> K+- K+ K- decays in the range of the K+ K- invariant masses above the phi(1020) resonance has been confirmed by the LHCb Collaboration. We discuss the emergence and size of this asymmetry in an extended model involving S- and P-waves together with the contribution from the D-wave f2(1270) resonance and compare our model with the experimental data of the LHCb and BABAR Collaborations.
We present a feasibility study of a method to measure the cosine of twice the CKM Unitarity Triangle angle beta using a time-dependent Dalitz plot analysis of B0 -> D pi+ pi- decays, where the neutral D meson is reconstructed in decays to CP eigenstates. We show that this method can be used at the B factories to make a measurement of cos(2beta) that is competitive with, or more precise than, other techniques using different quark-level transitions, while sin(2beta) can be measured to an accuracy more precise than any existing measurement using b -> c ubar d transitions. Furthermore, this techn…
It is shown that it is possible to perform a model-independent extraction of the CKM Unitarity Triangle angle $γ$ using only the decays $B^0\to D K^+π^-$ with $D\to K^0_Sπ^+π^-$ and $B^0\to D K^+π^-$ with flavour-specific $D$ decays. The proposed method can also utilise the $B^0\to D K^+π^-$ data with CP-eigenstate decays of the D meson in a model-independent way.
Two of the most powerful methods currently used to determine the angle $γ$ of the CKM Unitarity Triangle exploit $B^+ \to DK^+$, $D \to K_{\rm S}^0π^+π^-$ decays and $B^0 \to DK^+π^-$, $D \to K^+K^-$, $π^+π^-$ decays. It is possible to combine the strengths of both approaches in a "double Dalitz plot" analysis of $B^0 \to DK^+π^-$, $D \to K_{\rm S}^0π^+π^-$ decays. The potential sensitivity of such an analysis is investigated in the light of recently published experimental information on the $B^0 \to DK^+π^-$ decay. The formalism is also expanded, compared to previous discussions in the litera…
Relative phases of amplitudes for $D$ meson decays to a light pseudoscalar meson $P$ and a light vector meson $V$ decaying to two pseudoscalar mesons will lead to characteristic interferences on the three-body Dalitz plot. These phases may be compared with predictions of a flavor-symmetric treatment which extracts contributing amplitudes and their relative phases from a fit to $D \to PV$ decay rates. Good agreement was found previously for the cases of $D^0 \to K^- π^+ π^0$ and $D^0 \to π^+ π^- π^0$. The present work is devoted to the decays $D^0 \to K_S π^+ π^-$ and $D^0 \to π^0 K^+ K^-$, for…
The presently available high-statistics data of the D0 --> K0S pi+ pi- processes measured by the Belle and BABAR Collaborations are analyzed within a quasi two-body QCD factorization framework. Starting from the weak effective Hamiltonian, tree and annihilation amplitudes build up the D0 --> K0S pi+ pi- decay amplitude. Two of the three final-state mesons are assumed to form a single scalar, vector or tensor state originating from a quark-antiquark pair so that the factorization hypothesis can be applied. The meson-meson final state interactions are described by K pi and pi pi scalar and vecto…
We study the Dalitz plot of the decay D^+ --> K^- pi^+ pi^+ with a sample of 15090 events from Fermilab experiment E791. Modeling the decay amplitude as the coherent sum of known K pi resonances and a uniform nonresonant term, we do not obtain an acceptable fit. If we allow the mass and width of the K^*_0(1430) to float, we obtain values consistent with those from PDG but the chi^2 per degree of freedom of the fit is still unsatisfactory. A good fit is found when we allow for the presence of an additional scalar resonance, with mass 797 +/- 19 +/- 43 MeV/c^2 and width 410 +/- 43 +/- 87 MeV/c^2…
Recently B-factories have published new results on the $B \to K ηγ$ decays being inspired by the theoretical suggestion to search for new physics in $B \to P_1 P_2 γ$ decays. Using heavy meson chiral perturbation theory we find mechanism which governs the amplitude in parts of the Dalitz plot where either $K$ or $η$ mesons are soft. The dominant contributions in these cases are coming from the nonresonant decay modes. We discuss also $B \to K η' γ$ Dalitz plot. Our partially integrated rates are in agreement with the experimental findings.
We present a Dalitz plot analysis of charmless B+- decays to the final state pi+-pi+-pi-+ using a sample of (465+-5)x10^-6 BBbar pairs collected by the BABAR experiment at \sqrt{s} = 10.58 GeV. We measure the branching fractions BF(B+- --> pi+-pi+-pi-+) = (15.2+-0.6+-1.2+-0.4)x10^-6, BF(B+- --> rho0(770)pi+-) = (8.1+-0.7+-1.2^{+0.4}_{-1.1})x10^-6, BF(B+- --> f2(1270)pi+-) = (1.57+-0.42+-0.16^{+0.53}_{-0.19})x10^-6, and BF(B+- --> pi+-pi+-pi-+ nonresonant) = (5.3+-0.7+-0.6^{+1.1}_{-0.5})x10^-6, where the uncertainties are statistical, systematic, and model-dependent, respectively. Measurements …
We study the potential of the measurement of the transverse muon polarization P_T in the K->mu nu gamma decay with the sensitivity of δP_T ~ 10^{-4}. It is shown that the forthcoming experiment can measure the contribution of the electromagnetic final state interactions to P_T that gives a possibility to unambiguously determine the signs of the sum of the kaon form factors F_V and F_A even without fixing their difference. We also estimate the sensitivity of this experiment to the new physics, which could give rise to T-violation: multi-Higgs doublet models, supersymmetric extensions of the Sta…
We show that the presence of residual Bose-Einstein correlations may affect the resonant contribution of hadronic charm decays where two identical pions appear in the final state. The distortion of the phase space of the reaction would be visible in the dalitz plot. The decay D+ --> K- pi+ pi+ is discussed but results can be generalized to any decay with identical bosons.
This report shows the latest results on the study of the method to determine the angle phi_3 of the unitarity triangle using Dalitz plot analysis of D^0 decay from B->DK process in a model-independent way. We concentrate on the case with a limited charm data sample, which will be available from the CLEO-c collaboration in the nearest future, with the main goal to find the optimal strategy for phi_3 extraction.
We present a new technique to extract information on the Unitarity Triangle from the study of B -> K pi pi Dalitz plots. Using the sensitivity of Dalitz analyses to the absolute values and the phases of decay amplitudes and isospin symmetry, we obtain a new constraint on the elements of the CKM matrix. We discuss in detail the role of electroweak penguins and outline future prospects.
A formalism for measuring time-dependent CP violation in B_q -> J/ψh+ h- decays with J/ψ-> mu+ mu- is developed for the general case where there can be many h+ h- final states of different angular momentum present. Here h refers to any spinless meson. The decay amplitude is derived using similar considerations as those in a Daltiz like analysis of three-body spinless mesons taking into account the fact that the J/ψis spin-1, and the various interferences allowed between different final states. Implementation of this procedure can, in principle, lead to the use of a larger number of final state…
We study the possible distortion of phase-space in the decays $K \to πππ$, which may result from final state interference among the decay products. Such distortion may influence the values of slope parameters extracted from the Dalitz plot distribution of these decays. We comment on the consequences on the magnitude of violation of the $\mid ΔI \mid = 1/2$ rule in these decays.
The Dalitz plot slope parameters g, h and k for the K- -> pi0 pi0 pi- decay have been measured using in-flight decays detected with the ISTRA+ setup operating in the 25 GeV negative secondary beam of the U-70 PS. About 252 K events with four-momenta measured for the pi- and four involved photons were used for the analysis. The values obtained g=0.627+/-0.004(stat)+/-0.010(syst), h=0.046+/-0.004(stat)+/-0.012(syst), k=0.001+/-0.001(stat)+/-0.002(syst) are consistent with the world averages dominated by K+ data, but have significantly smaller errors.
We obtain a model-independent expression for the Dalitz plot of semileptonic decays of polarized hyperons including radiative corrections to order alpha and neglecting terms of order (alpha q)/(pi M_1), where q is the four-momentum transfer and M_1 is the mass of the decaying hyperon. We specialize our results to exhibit the correlation between the charged-lepton momentum and the spin of the decaying hyperon. We present results for the three-body region of the Dalitz plot and for the complete Dalitz plot (which includes the four-body region). From these results we also obtain the corresponding…
We demonstrate that partial wave amplitudes extracted from $D^+\to K^-π^+π^+$ Dalitz plot with a unitary coupled-channel model are significantly different from those obtained with an isobar model. The unitary coupled-channel model takes account of hadronic rescattering mechanisms involving all three mesons that have been missed in conventioanl isobar model analyses. The rescattering mechanisms contribute largely, and can triplicate the $D^+\to {K}^-π^+π^+$ decay width within our analysis. These findings deliver a warning that analysis results obtained with isobar models should be looked with a…
A quasi two-body QCD factorization is used to study the D0 --> K0S pi+ pi decays. The presently available high-statistics Dalitz plot data of this process measured by the Belle and BABAR Collaborations are analyzed together with the tau- --> K0S pi- nu_tau decay data. The total experimental branching fraction is also included in the fits which show a very good overall agreement with the experimental Dalitz plot density distributions. The branching fractions of the dominant channels compare well with those of the isobar Belle or BABAR models. We show that the branching fractions corresponding t…
We study CP violation in $B\to K^* \ell^+\ell^-$ using generalized Dalitz plot asymmetries in the angular distribution. These new kind of asymmetries are constructed by adding B and ${\bar B}$ events, and do not require flavor or time tagging, nor is the presence of strong phases needed. Using this method one requires about $2 \times 10^8/η$ B's to measure the CP violating parameter $η$ in the Standard model. The two--Higgs doublet model requires only $10^7$ B's to constrain parameters better than done by the electric dipole moment of the neutron.
The $η\to 3 π$ amplitude is sensitive to the quark mass difference $m_u-m_d$ and offers a unique way to determine the quark mass ratio $Q^2 \equiv (m_s^2-m_{ud}^2)/(m_d^2-m_u^2)$ from experiment. We calculate the amplitude dispersively and fit the KLOE data on the charged mode, varying the subtraction constants in the range allowed by chiral perturbation theory. The parameter-free predictions obtained for the neutral Dalitz plot and the neutral-to-charged branching ratio are in excellent agreement with experiment. Our representation of the transition amplitude implies $Q = 22.0 \pm 0.7$.
Dalitz plot of the $η' \to ηπ^+π^-$ decay is studied using the data collected with the VES spectrometer in two different exclusive reactions. The coefficients for the matrix element squared decomposition are measured on the largest statistics of $η'$ decays reported so far.
The processes $D^0\to K^0 K^-π^+$ and $D^0\to\ok K^+π^-$ involve intermediate vector resonances whose amplitudes and phases are related to each other via flavor-SU(3) symmetry. Dalitz plots for these two processes can shed light on the usefulness of this symmetry in studying charm decays. Until this year the only available data on this process came from a conference report in 2002 by the BaBar Collaboration, but now an independent data sample of higher statistics has become available from the CLEO Collaboration. The goal is to predict Dalitz plot amplitudes and phases assuming flavor-SU(3) sym…
Analytical radiative corrections of order (α/π)(q/M_1) are calculated for the four-body region of the Dalitz plot of baryon semileptonic decays when the s_1 \cdot p_2 correlation is present. Once the final result is available, it is possible to exhibit it in terms of the corresponding final result of the three-body region following a set of simple changes in the latter. We cover two cases, a charged and a neutral polarized decaying baryon.
A model-independent expression for the Dalitz plot of semileptonic decays of neutral kaons, K_{l3}^0, including radiative corrections to order (α/π)(q/M_1), where q is the momentum transfer and M_1 is the mass of the kaon, is presented. The model dependence of radiative corrections is kept in a general form within this approximation, which is suitable for model-independent experimental analyses. Expressions for bremsstrahlung radiative corrections are presented in two forms: one with the triple integral over the kinematical variables of the photon ready to be performed numerically and the othe…
Analytical radiative corrections of order (alpha/pi)(q/M) are calculated for the four-body region of the Dalitz plot of baryon semileptonic decays when the s1.l correlation is present. Once the final result is available, it is possible to exhibit it in terms of the corresponding final result of the three-body region following a set of simple changes in the latter, except for a few exceptions. We cover two cases, a charged and a neutral polarized decaying baryon.
We complement the results for the radiative corrections to the s2.l angular correlation of baryon semileptonic decays of Ref. [1] with the final results in the rest frame of the decaying baryon.
High statistics Dalitz-plot distribution of $η\to π^+π^-π^0$ decay obtained recently by KLOE collaboration \cite{kloe} is fitted to the results of corresponding theoretical calculations in Chiral Perturbation Theory (ChPT) with unitarity corrections taken into account. The quark mass ratio $Q = \sqrt{(m^2_s - (m_d + m_u)^2/4)/(m^2_d - m^2_u)} $ can be otained from this analysis. We get $Q= 22.8\pm 0.4$ which differs from the value $Q_{DT} = 24.2$ that follows from Dashen's theorem and agrees with recently calculated electromagnetic kaon mass difference.
A violation of mirror symmetry in the $η\toπ^+π^-π^0$ Dalitz plot has long been recognized as a signal of C and CP violation. Here we show how the isospin of the underlying C- and CP-violating structures can be reconstructed from their kinematic representation in the Dalitz plot. Our analysis of the most recent experimental data reveals, for the first time, that the C- and CP-violating amplitude with total isospin $I=2$ is much more severely suppressed than that with total isospin $I=0$.
We have calculated the radiative corrections to the Dalitz plot of baryon semileptonic decays with angular correlation between polarized emitted baryons and charged leptons. This work covers both charged and neutral decaying baryons and is restricted to the so-called three-body region of the Dalitz plot. Also it is specialized at the center-of-mass frame of the emitted baryon. We have considered terms up to order (alpha/pi)(q/M_1)^0, where q is the momentum-transfer and M_1 is the mass of the decaying baryon, and neglected terms of order (alpha/pi)(q/M_1)^n$ for n >= 1. The expressions display…
Very accurate analytical expressions for the radiative corrections of unpolarized hyperons semileptonic decays of charged and neutral baryons have been obtained in the recent past. Some of these formulas contain logarithmic singularities at the edges of the Dalitz plot for the three- and four-body decays. These singularities are analyzed and integrated analytically to obtain new divergentless formulas for the energy spectrum of the produced beta particle. The new equations contain terms of the order alpha times the momentum transfer, are applicable to any beta decay process and are suitable fo…
We calculate the model-independent radiative corrections to the Dalitz plot of K_{l3}^\pm decays to order (α/π)(q/M_1), where q is the momentum transfer and M_1 is the mass of the kaon. The final results are presented, first, with the triple integration over the variables of the bremsstrahlung photon ready to be performed numerically and, second, in an analytical form. These two forms are useful to crosscheck on one another and with other calculations. This paper is organized to make it accessible and reliable in the analysis of the Dalitz plot of precision experiments and is not compromised t…
Dalitz-plot analyses of $B\rightarrow Kππ$ decays provide direct access to decay amplitudes, and thereby weak and strong phases can be disentangled by resolving the interference patterns in phase space between intermediate resonant states. A phenomenological isospin analysis of $B\rightarrow K^*(\rightarrow Kπ)π$ decay amplitudes is presented exploiting available amplitude analyses performed at the Babar, Belle and LHCb experiments. A first application consists in constraining the CKM parameters thanks to an external hadronic input. A method, proposed some time ago by two different groups and …
In this master thesis I discuss how the weak three-body decay B^+ --> pi^- pi^+ K^+ is related to the strong interactions between the final-state particles. Current issues in hadron spectroscopy define a region of interest in a Dalitz plot of this decay. This region is roughly characterized by energies from 0 to 1.6 GeV of the pi^- pi^+ and the pi^- K^+ system, and energies from 3 to 5 GeV of the pi^+ K^+ system. Therefore I propose to use for the former two systems elastic unitarity (Watson's theorem) as an approximate ansatz, and a non-vanishing forward-peaked amplitude for the latter system…
The four-body contribution of the model-independent radiative corrections to the Dalitz plot of the semileptonic decays of neutral kaons are computed to order (α/π)(q/M_1), where q is the momentum transfer and M_1 is the kaon mass. The final result is presented in two forms. The first one is given in terms of the triple integration of the bremsstrahlung photon ready to be performed numerically; the second one is a fully analytical expression. This paper is organized to make it accessible and reliable in the analysis of the Dalitz plot of precision experiments involving kaons and is not comprom…
We study CP-violation in resonant three-body B -> DPP decays, where PP stands for either Dpi, DK_S, pipi or piK_S. Analogously to the B -> 3pi channel and the extraction of 2alpha, the first three channels are shown to measure cos(2beta) in addition to sin(2beta), thus allowing to resolve the beta -> pi/2 -beta ambiguity, while the DpiK_S final state leads to a measurement of 2beta+gamma. The B0(t) -> D+D-pi0 channel via the interference between D** orbitally excited resonances is taken as an example, although this Cabibbo-suppressed decay suffers from irreducible penguin uncertainties. Then t…
We give a simple expression in linear and quadratic Dalitz--plot slopes which does not depend on the charge combination of the $3π$ state $(K^\pm \to π^{\pm}π^{+}π^{-}$ or $π^{\pm}π^{0}π^{0}$ and $K_L^{0} \to π^{+}π^{-}π^{0}$ or $π^{0}π^{0}π^{0})$, if all phases between final states are negligible. After investigating the influence of radiative corrections, it is shown how new measurements, especially of quadratic slopes in the $π^{\pm} π^{0} π^{0}$ channel, could help to test theoretical predictions more stringently. A FORTRAN code for the radiatiative corrections is available on request.
We analyze the Dalitz plot parameters of eta to 3 pion decay in the framework of resummed chiral perturbation theory. This approach allows us to keep the uncertainties in the NNLO and higher orders under better control and estimate their influence. We cannot confirm the suspected discrepancy in the case of the charged decay parameter b, where even small uncertainties in higher orders could accommodate the difference. On the other hand, we find the experimental value of the neutral decay parameter alpha incompatible with an assumption of good convergence properties in the center of the Dalitz p…
We calculate the radiative corrections to the Dalitz plot of K_{l3}^\pm decays to order (alpha/pi)(q/M_1), where q is the momentum transfer and M_1 is the mass of the kaon. We restrict the analysis to the so-called four-body region, which arises when no discrimination of real photons is made either kinematically or experimentally. We present our results in two ways: the first one with the triple integration over the photon kinematical variables ready to be performed numerically and the second one in a fully analytical form. Our results can be useful in experimental analyses of the Dalitz plot,…
