Isospin Amplitudes Research Articles

Lellouch-Lüscher factor for the K → 3π decays

We derive an explicit expression for the Lellouch-Lüscher (LL) factor in the K → 3π decays at leading order (without derivative couplings). Several important technical details are addressed, like a proper decomposition into the isospin amplitudes, the choice of a minimal set of effective couplings and the renormalization, as well as the algorithm for the solution of the pertinent Faddeev equations in the infinite volume which is based on the contour deformation method. Most importantly, our numerical results demonstrate that the three-body force contributes very little to the LL factor. This result paves the way for the study of the K → 3π decays on the lattice.

Searching systematics for nonfactorizable contributions to and hadronic decays

The two-body weak decays / and are examined using isospin analysis to study nonfactorizable contributions. After determining strong interaction phases and obtaining factorizable contributions from spectator-quark diagrams for N c =3, we determine nonfactorizable isospin amplitudes from the experimental data for these modes. Our results support the universality of the ratio of nonfactorizable isospin reduced amplitudes for these decays within experimental errors. To demonstrate that these systematics are not coincidental, we also plot our results w. r. t. this ratio.

Timelike nucleon electromagnetic form factors: All about interference of isospin amplitudes

A striking feature of the timelike nucleon electromagnetic form factors, investigated in ${e}^{+}{e}^{\ensuremath{-}}\ensuremath{\rightarrow}N\overline{N}$ annihilation reactions, is the modulation by local structures of small magnitude and oscillatory form, showing up above the $N\overline{N}$ threshold. Starting from an isospin decomposition of the proton and neutron form factors it is shown that such structures are the natural consequence of the interference of a large and a small amplitude, resulting in a sinusoidal behavior as a function of the ``invariant energy'' if the relative phase shift varies with energy. Thus, periodic oscillations superimposed on a smooth background will be observed. In this scenario, the equal size of the modulation for neutrons and protons (discovered by recent BESIII data) implies the particular isoscalar or isovector nature of these local structures, or their orthogonal interference. Hence, it specifies their origin as excited vector mesons whose widths are tied to the modulation frequency. We clarify that the phase difference of the modulation between neutrons and protons as BESIII data found, but not the modulation itself, is the evidence of an imaginary part of the timelike nucleon electromagnetic form factors, which is associated with the rescattering processes.

Positivity and geometric function theory constraints on pion scattering

This paper presents the fascinating correspondence between the geometric function theory and the scattering amplitudes with O(N) global symmetry. A crucial ingredient to show such correspondence is a fully crossing symmetric dispersion relation in the z-variable, rather than the fixed channel dispersion relation. We have written down fully crossing symmetric dispersion relation for O(N) model in z-variable for three independent combinations of isospin amplitudes. We have presented three independent sum rules or locality constraints for the O(N) model arising from the fully crossing symmetric dispersion relations. We have derived three sets of positivity conditions. We have obtained two-sided bounds on Taylor coefficients of physical Pion amplitudes around the crossing symmetric point (for example, π+π−→ π0π0) applying the positivity conditions and the Bieberbach-Rogosinski inequalities from geometric function theory.

Dissecting the Delta I=1/2 rule at large N_c

We study the scaling of kaon decay amplitudes with the number of colours, N_c, in a theory with four degenerate flavours, N_f=4. In this scenario, two current-current operators, Q^pm , mediate Delta S=1 transitions, such as the two isospin amplitudes of non-leptonic kaon decays for Krightarrow (pi pi )_{I=0,2}, A_0 and A_2. In particular, we concentrate on the simpler Krightarrow pi amplitudes, A^pm , mediated by these two operators. A diagrammatic analysis of the large-N_c scaling of these observables is presented, which demonstrates the anticorrelation of the leading {{mathcal {O}}}(1/N_c) and {{mathcal {O}}}(N_f/N_c^2) corrections in both amplitudes. Using our new N_f=4 and previous quenched data, we confirm this expectation and show that these corrections are naturally large and may be at the origin of the Delta I=1/2 rule. The evidence for the latter is indirect, based on the matching of the amplitudes to their prediction in Chiral Perturbation Theory, from which the LO low-energy couplings of the chiral weak Hamiltonian, g^pm , can be determined. A NLO estimate of the K rightarrow (pi pi )_{I=0,2} isospin amplitudes can then be derived, which is in good agreement with the experimental value.

Constraining electroweak penguin graph contributions in measurements of the CKM phase alpha using B→ππ and B→ρρ decays

The unitarity of the Cabibbo-Kobayashi-Maskawa (CKM) matrix has been well established by both direct and indirect measurements without any evidence of discrepancy. The CKM weak phase $\alpha$ is directly measured using an isospin analysis in $B\rightarrow \pi\pi$ and $B\to \rho\rho$ assuming that electroweak penguin contributions are ignorable. However, electroweak penguins are sensitive to NP, hence, it is important to experimentally estimate their effects. We determine the size of both electroweak penguin and isospin amplitudes, directly from $B\rightarrow \pi\pi$ and $B\to \rho\rho$ experimental data, using in addition the indirectly measured value of $\alpha$. We find that electroweak penguin contribution are indeed small and agree with SM expectations within $1\sigma$. We also find that there is a mild enhancement of the $\Delta I=\tfrac{1}{2}$ transition amplitude.

Isospin Amplitudes in Λ_{b}^{0}→J/ψΛ(Σ^{0}) and Ξ_{b}^{0}→J/ψΞ^{0}(Λ) Decays.

Ratios of isospin amplitudes in hadron decays are a useful probe of the interplay between weak and strong interactions and allow searches for physics beyond the standard model. We present the first results on isospin amplitudes in b-baryon decays, using data corresponding to an integrated luminosity of 8.5 fb^{-1}, collected with the LHCb detector in pp collisions at center of mass energies of 7, 8, and 13TeV. The isospin amplitude ratio |A_{1}(Λ_{b}^{0}→J/ψΣ^{0})/A_{0}(Λ_{b}^{0}→J/ψΛ)|, where the subscript on A indicates the final-state isospin, is measured to be less than 1/21.8 at 95%confidence level. The Cabibbo suppressed Ξ_{b}^{0}→J/ψΛ decay is observed for the first time, allowing for the measurement |A_{0}(Ξ_{b}^{0}→J/ψΛ)/A_{1/2}(Ξ_{b}^{0}→J/ψΞ^{0})|=0.37±0.06±0.02, where the uncertainties are statistical and systematic, respectively.

Measurement of ν¯μ charged-current single π− production on hydrocarbon in the few-GeV region using MINERvA

The antineutrino scattering channel $\bar{\nu}_{\mu} \,\text{CH} \rightarrow \mu^{+} \,\pi^{-} \,X$(nucleon(s)) is analyzed in the incident energy range 1.5 to 10 GeV using the MINERvA detector at Fermilab. Differential cross sections are reported as functions of $\mu^{+}$ momentum and production angle, $\pi^{-}$ kinetic energy and production angle, and antineutrino energy and squared four-momentum transfer. Distribution shapes are generally reproduced by simulations based on the GENIE, NuWro, and GiBUU event generators, however GENIE (GiBUU) overestimates (underestimates) the cross-section normalizations by 8% (10%). Comparisons of data with the GENIE-based reference simulation probe conventional treatments of cross sections and pion intranuclear rescattering. The distribution of non-track vertex energy is used to decompose the signal sample into reaction categories, and cross sections are determined for the exclusive reactions $\mu^{+} \pi^{-} n$ and $ \mu^+ \pi^{-} p$. A similar treatment applied to the published MINERvA sample $\bar{\nu}_{\mu} \,\text{CH} \rightarrow \mu^{+} \,\pi^{0} \,X$(nucleon(s)) has determined the $\mu^{+} \pi^{0} n$ cross section, and the latter is used with $\sigma(\pi^{-} n)$ and $\sigma(\pi^{-} p)$ to carry out an isospin decomposition of $\bar{\nu}_{\mu}$-induced CC($\pi$). The ratio of magnitudes and relative phase for isospin amplitudes $A_{3}$ and $A_{1}$ thereby obtained are: $R^{\bar{\nu}} = 0.99 \pm 0.19$ and $\phi^{\bar{\nu}} = 93^{\circ} \pm 7^{\circ}$. Our results are in agreement with bubble chamber measurements made four decades ago.

The Return of Kaon Flavour Physics

Kaon flavour physics has played in the 1960s and 1970s a very important role in the construction of the Standard Model (SM) and in the 1980s and 1990s in SM tests with the help of CP violation in $K_L\to\pi\pi$ decays represented by $\varepsilon_K$ and the ratio $\varepsilon'/\varepsilon$. In this millennium this role has been taken over by $B_{s,d}$ and $D$ mesons. However there is no doubt that in the coming years we will witness the return of kaon flavour physics with the highlights being the measurements of the theoretically clean branching ratios for the rare decays $K^+\rightarrow \pi^+\nu\bar\nu$ and $K_{L}\rightarrow\pi^0\nu\bar\nu$ and the improved SM predictions for the ratio $\varepsilon'/\varepsilon$, for $\varepsilon_K$ and the $K^0-\bar K^0$ mixing mass difference $\Delta M_K$. Theoretical progress on the decays $K_{L,S}\to\mu^+\mu^-$ and $K_L\to\pi^0\ell^+\ell^-$ is also expected. They all are very sensitive to new physics (NP) contributions and the correlations between them should help us to identify new dynamics at very short distance scales. These studies will be enriched when theory on the $K\to\pi\pi$ isospin amplitudes ${\rm Re} A_0$ and ${\rm Re} A_2$ improves. This talk summarizes several aspects of this exciting field. In particular we emphasize the role of the Dual QCD approach in getting the insight into the numerical Lattice QCD results on $K^0-\bar K^0$ mixing and $K\to\pi\pi$ decays.

Isospin analysis of [formula omitted] and the absence of the Zc(3900) in B decays

We study the isospin amplitudes in the exclusive B to D⁎D¯K decay process and fit the available D⁎0D¯0 invariant mass distributions near threshold. The analysis demonstrates that the production of the isospin triplet D⁎D¯ state is highly suppressed compared to the isospin singlet one. That explains why the Zc(3900) has not been found in B decays. In addition, the production of the negative charge-parity state might be further suppressed in the heavy quark limit. These two reasons which are based on the molecular assumption offer the first explanation why the Zc(3900) is absent in B decays. Further studies of the absence from both the experimental and the theoretical side is extremely important for understanding the nature of the X(3872) and the Zc(3900).

Constraints on the S=-1 meson-baryon interaction at NLO

This work contains a study of the meson-baryon interaction in the S = −1 sector by means of a chiral SU (3) Lagrangian up to next-to-leading order (NLO) and implementing unitarization in coupled channels. In order to get more reliable values of the parameters which are present in the model, we performed several fits which take a large set of experimental scattering data in different two-body channels, threshold branching ratios, and the precise SIDDHARTA values of the energy shift and width of kaonic hidrogen into consideration. In previous studies, we had shown that the K − p → K Ξ reactions are especially sensitive to the next to Weinberg-Tomozawa (WT) corrections in the hierarchy. In addition, we pointed out the need to employ processes which are described by pure isospin amplitudes as a tool to discern which models are more realistic among those which give small values for the χ 2 in the fits. Following the former suggestion, we present results which include data from K − p → η Λ, η Σ reactions which have pure isospin I = 0 and I = 1 component respectively. Finally, to check the goodness of the new obtained parametrization of the model, we present a prediction for another process that filters the I = 1 isospin component: the pure I = 1 reaction which could be measured at the proposed secondary K 0 L beam at Jlab.

Isospin amplitudes of B → Kππ decays

We obtain two isospin amplitude decompositions of the B→Kππ decays. We use the method of addition of three isospin vectors, and prove the equivalency of the two isospin amplitude decompositions obtained. We only have considered contributions of the Hamiltonian to the transitions with change of isospin ΔI=0 and ΔI=1. The symmetry of isospin allows to relate the charged B+→K+π+π−, B+→K+π0π0, and B+→K0π0π+ channels with the neutral B0→K0π+π−, B0→K0π0π0, and B0→K+π0π− channels. Additionally, we obtain equivalent triangular relations in the charged and neutral channels.

Formula: see text] rule, [Formula: see text] and [Formula: see text] in [Formula: see text] and [Formula: see text] models with FCNC quark couplings.

The experimental value for the isospin amplitude mathrm{Re}A_2 in Krightarrow pi pi decays has been successfully explained within the standard model (SM), both within the large N approach to QCD and by QCD lattice calculations. On the other hand within the large N approach the value of mathrm{Re}A_0 is by at least 30,% below the data. While this deficit could be the result of theoretical uncertainties in this approach and could be removed by future precise QCD lattice calculations, it cannot be excluded that the missing piece in mathrm{Re}A_0 comes from new physics (NP). We demonstrate that this deficit can be significantly softened by tree-level FCNC transitions mediated by a heavy colourless Z^prime gauge boson with a flavour-violating left-handed coupling Delta ^{sd}_L(Z^prime ) and an approximately universal flavour diagonal right-handed coupling Delta ^{qq}_R(Z^prime ) to the quarks. The approximate flavour universality of the latter coupling assures negligible NP contributions to mathrm{Re}A_2. This property, together with the breakdown of the GIM mechanisms at tree level, allows one to enhance significantly the contribution of the leading QCD-penguin operator Q_6 to mathrm{Re}A_0. A large fraction of the missing piece in the Delta I=1/2 rule can be explained in this manner for M_{Z^prime } in the reach of the LHC, while satisfying the constraints from varepsilon _K, varepsilon '/varepsilon , Delta M_K, LEP-II and the LHC. The presence of a small right-handed flavour-violating coupling Delta ^{sd}_R(Z^prime )ll Delta ^{sd}_L(Z^prime ) and of enhanced matrix elements of Delta S=2 left–right operators allows one to satisfy simultaneously the constraints from mathrm{Re}A_0 and Delta M_K, although this requires some fine-tuning. We identify the quartic correlation between Z^prime contributions to mathrm{Re}A_0, varepsilon '/varepsilon , varepsilon _K and Delta M_K. The tests of this proposal will require much improved evaluations of mathrm{Re}A_0 and Delta M_K within the SM, of langle Q_6 rangle _0 as well as precise tree-level determinations of |V_{ub}| and |V_{cb}|. We present correlations between varepsilon '/varepsilon , K^+rightarrow pi ^+nu bar{nu } and K_{L}rightarrow pi ^0nu bar{nu } with and without the Delta I=1/2 rule constraint and generalise the whole analysis to Z^prime with colour (G^prime ) and Z with FCNC couplings. In the latter case no improvement on mathrm{Re}A_0 can be achieved without destroying the agreement of the SM with the data on mathrm{Re}A_2. Moreover, this scenario is very tightly constrained by varepsilon '/varepsilon . On the other hand, in the context of the Delta I=1/2 rule G^prime is even more effective than Z^prime : it provides the missing piece in mathrm{Re}A_0 for M_{G^prime }=(3.5–4.0), mathrm{TeV}.

MEASUREMENT OF EXCITED HYPERONS IN PHOTOPRODUCTION AT CLAS

Measurement results of photoproduced excited hyperon states using the CLAS detector at Jefferson Lab are shown. The invariant mass distribution of the Λ(1405) has recently been shown to be different for each of the three Σπ channels that it decays to, showing that there is prominent interference between the isospin I = 0 and I = 1 isospin amplitudes. Measurements of the differential and total cross sections of the three hyperons Λ(1405), Σ0(1385), and Λ(1520) are presented and compared. Prospects of future studies using a 12 GeV beam with the GlueX detector are briefly given.

Measurement of theΣπphotoproduction line shapes near theΛ(1405)

The reaction gamma + p -> K+ + Sigma + pi was used to determine the invariant mass distributions or "line shapes" of the Sigma+ pi-, Sigma- pi+ and Sigma0 pi0 final states, from threshold at 1328 MeV/c^2 through the mass range of the Lambda(1405) and the Lambda(1520). The measurements were made with the CLAS system at Jefferson Lab using tagged real photons, for center-of-mass energies 1.95 < W < 2.85 GeV. The three mass distributions differ strongly in the vicinity of the I=0 \Lambda(1405), indicating the presence of substantial I=1 strength in the reaction. Background contributions to the data from the Sigma0(1385) and from K^* Sigma production were studied and shown to have negligible influence. To separate the isospin amplitudes, Breit-Wigner model fits were made that included channel-coupling distortions due to the NKbar threshold. A best fit to all the data was obtained after including a phenomenological I=1, J^P = 1/2^- amplitude with a centroid at 1394\pm20 MeV/c^2 and a second I=1 amplitude at 1413\pm10 MeV/c^2. The centroid of the I=0 Lambda(1405) strength was found at the Sigma pi threshold, with the observed shape determined largely by channel-coupling, leading to an apparent overall peak near 1405 MeV/c^2.

Determination of Weak Amplitudes Using Bose Symmetry and Dalitz Plots

We present a new method using Dalitz plots and Bose symmetry of pions that allows the complete determination of the magnitudes and phases of weak decay amplitudes. We apply the method to processes such as B→K*π, with the subsequent decay of K*→Kπ. Our approach enables the additional measurement of an isospin amplitude without any theoretical assumption. This advance will help in measuring the weak phase and probing for new physics beyond the standard model with fewer assumptions.

A precise isospin analysis of [formula omitted] decays

We present a precise isospin analysis of the B→D¯(⁎)D(⁎)K decays using new recent experimental measurements on these final states. The decays B→D¯(⁎)D(⁎)K, originating from b→cc¯s transitions, are linked by a rich set of isospin properties. The isospin relations that connect the decay modes are presented and a fit is performed to obtain the isospin amplitudes and phases. We discuss the results of the fit and present a new measurement of the ratio of branching fractions B(ϒ(4S)→B+B−) and B(ϒ(4S)→B0B¯0). We finally discuss the implications of our findings for the measurement of the unitarity matrix parameters sin(2β) and cos(2β) using these decays.

Amplitude analysis ofB0→K+π−π0and evidence of directCPviolation inB→K*πdecays

We analyze the decay B0-->K+ pi- pi0 with a sample of 454 million B Bbar events collected by the BaBar detector at the PEP-II asymmetric-energy B factory at SLAC, and extract the complex amplitudes of seven interfering resonances over the Dalitz plot. These results are combined with amplitudes measured in B0-->K_S pi+ pi- decays to construct isospin amplitudes from B0-->K* pi and B0-->rho K decays. We measure the phase of the isospin amplitude Phi_3/2, useful in constraining the CKM unitarity triangle angle gamma and evaluate a CP rate asymmetry sum rule sensitive to the presence of new physics operators. We measure direct CP violation in B0-->K*+ pi- decays at the level of 3 sigma when measurements from both B0-->K+ pi- pi0 and B0-->K_S pi+ pi- decays are combined.

Production of $ \eta$ and 3$ \pi$ mesons in the pd $ \rightarrow$ 3HeX reaction at 1360 and 1450 MeV

The cross sections of the pd -> 3He eta, pd -> 3He pi0 pi0 pi0 and pd -> 3He pi+ pi- pi0 reactions have been measured at beam kinetic energies T_p= 1360 MeV and T_p= 1450 MeV using the CELSIUS/WASA detector setup. At both energies, the differential cross section dsigma/dOmega of the eta meson in the pd -> 3He eta reaction shows a strong forward-backward asymmetry in the CMS. The ratio between the pd -> 3He pi+ pi- pi0 and the pd -> 3He pi0 pi0 pi0 cross sections has been analysed in terms of isospin amplitudes. The reconstructed invariant mass distributions of the pi-pi, 3He-pi and 3He-2pi systems provide hints on the role of nucleon resonances in the 3pi production process.

Expected accuracy in a measurement of the CKM angle α using a Dalitz plot analysis of B 0 → ρπ decays in the BTeV project

A precise measurement of the angle {alpha} in the CKM triangle is very important for a complete test of Standard Model. A theoretically clean method to extract {alpha} is provided by B{sup 0} {yields} {rho}{pi} decays. Monte Carlo simulations to obtain the BTeV reconstruction efficiency and to estimate the signal to background ratio for these decays were performed. Finally the time-dependent Dalitz plot analysis, using the isospin amplitude formalism for tre and penguin contributions, was carried out. It was shown that in one year of data taking BTeV could achieve an accuracy on {alpha} better than 5{sup o}.