<p>We study the interaction of a neutron with the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msubsup><mover accent="true"><mi>D</mi><mo stretchy="false">¯</mo></mover><mrow><mi>s</mi><mn>0</mn></mrow><mo>*</mo></msubsup><mo stretchy="false">(</mo><mn>2317</mn><mo stretchy="false">)</mo></math> resonance and look at the amplitude below threshold and close above threshold. The study is done from the perspective that the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msubsup><mi>D</mi><mrow><mi>s</mi><mn>0</mn></mrow><mo>*</mo></msubsup><mo stretchy="false">(</mo><mn>2317</mn><mo stretchy="false">)</mo></math> resonance is a molecular state of <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>D</mi><mi>K</mi></math> in <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>I</mi><mo>=</mo><mn>0</mn></math>. To study this interaction, we use the fixed center approximation to Faddeev equations that considers the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>D</mi><mi>K</mi></math> molecule as the cluster and the neutron as the external particle. We improve the fixed center approach to implement elastic unitarity around threshold, which is needed to obtain scattering parameters and to evaluate the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>n</mi><msubsup><mover accent="true"><mi>D</mi><mo stretchy="false">¯</mo></mover><mrow><mi>s</mi><mn>0</mn></mrow><mo>*</mo></msubsup><mo stretchy="false">(</mo><mn>2317</mn><mo stretchy="false">)</mo></math> correlation function that we determine here. One interesting result of the study is the appearance of a resonant state below threshold with a binding of about 130 MeV and a width of about 80 MeV, which we suggest to look at in reactions measuring the invariant mass of <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>π</mi><mi mathvariant="normal">Σ</mi><mover accent="true"><mi>D</mi><mo stretchy="false">¯</mo></mover></math>. The ALICE collaboration has initiated studies of this type, by looking at the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>p</mi><msub><mi>f</mi><mn>1</mn></msub><mo stretchy="false">(</mo><mn>1285</mn><mo stretchy="false">)</mo></math> correlation function, and we can only encourage work in this direction, which should provide much valuable information on the nature of many resonant states.</p>

Japan

Natsumi Ikeno

China

Spain

Eulogio Oset

Correlation function for the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>n</mi><msubsup><mover accent="true"><mi>D</mi><mo stretchy="false">¯</mo></mover><mrow><mi>s</mi><mn>0</mn></mrow><mo>*</mo></msubsup><mo stretchy="false">(</mo><mn>2317</mn><mo stretchy="false">)</mo></math> interaction and the issue of elastic unitarity

We have studied the feasibility of the experimental determination of the width of a D meson in a nuclear medium by using the method of the nuclear transparency. The cross section for inclusive production of a <math><msup><mrow><mi>D</mi></mrow><mrow><mo>+</mo></mrow></msup></math> in different nuclei is evaluated, taking care of the <math><msup><mrow><mi>D</mi></mrow><mrow><mo>+</mo></mrow></msup></math> absorption in the nucleus, or equivalently, the survival probability of the <math><msup><mrow><mi>D</mi></mrow><mrow><mo>+</mo></mrow></msup></math> in its way out of the nucleus from the point of production. We use present values of the in medium width of D mesons and calculate ratios of the cross sections for different nuclei to the <math><mmultiscripts><mrow><mtext>C</mtext></mrow><mprescripts></mprescripts><none></none><mrow><mn>12</mn></mrow></mmultiscripts></math> nucleus as reference. We find ratios of the order of 0.6 for heavy nuclei, a large deviation from unity, which indicates that the method proposed is adequate to measure this relevant magnitude, so far only known theoretically.

Victor Montesinos

Miguel Albaladejo

Juan Nieves

Germany

Laura Tolos

On the determination of the Meson Width in the Nuclear Medium With the Transparency Ratio

We study the  $$D^+ \rightarrow {\bar{K}}^0 \pi ^+ \eta $$  <math> <mrow> <msup> <mi>D</mi> <mo>+</mo> </msup> <mo>→</mo> <msup> <mrow> <mover> <mrow> <mi>K</mi> </mrow> <mrow> <mo>¯</mo> </mrow> </mover> </mrow> <mn>0</mn> </msup> <msup> <mi>π</mi> <mo>+</mo> </msup> <mi>η</mi> </mrow> </math>   reaction where the  $$a_0(980)$$  <math> <mrow> <msub> <mi>a</mi> <mn>0</mn> </msub> <mrow> <mo>(</mo> <mn>980</mn> <mo>)</mo> </mrow> </mrow> </math>   excitation plays a dominant role. We consider mechanisms of external and internal emission at the quark level, hadronize the  $$q {\bar{q}}$$  <math> <mrow> <mi>q</mi> <mover> <mrow> <mi>q</mi> </mrow> <mrow> <mo>¯</mo> </mrow> </mover> </mrow> </math>   components into two mesons and allow these mesons to undergo final state interaction where the  $$a_0(980)$$  <math> <mrow> <msub> <mi>a</mi> <mn>0</mn> </msub> <mrow> <mo>(</mo> <mn>980</mn> <mo>)</mo> </mrow> </mrow> </math>   state is generated. While the  $$a_0(980)$$  <math> <mrow> <msub> <mi>a</mi> <mn>0</mn> </msub> <mrow> <mo>(</mo> <mn>980</mn> <mo>)</mo> </mrow> </mrow> </math>   production is the dominant term, we also find other terms in the reaction that interfere with this production mode and, through interference with it, lead to a shape of the  $$a_0(980)$$  <math> <mrow> <msub> <mi>a</mi> <mn>0</mn> </msub> <mrow> <mo>(</mo> <mn>980</mn> <mo>)</mo> </mrow> </mrow> </math>   significantly different from the one observed in other experiments, with an apparently much larger width.

Jorgivan Dias

Wei-Hong Liang

$$D^+ \rightarrow K_s^0 \pi ^+ \eta $$  <math> <mrow> <msup> <mi>D</mi> <mo>+</mo> </msup> <mo>→</mo> <msubsup> <mi>K</mi> <mi>s</mi> <mn>0</mn> </msubsup> <msup> <mi>π</mi> <mo>+</mo> </msup> <mi>η</mi> </mrow> </math>   reaction and  $$a_0(980)^+$$  <math> <mrow> <msub> <mi>a</mi> <mn>0</mn> </msub> <msup> <mrow> <mo>(</mo> <mn>980</mn> <mo>)</mo> </mrow> <mo>+</mo> </msup> </mrow> </math>

We make a study of the <math><msub><mi>Ω</mi><mi>c</mi></msub><mo>(</mo><mn>3120</mn><mo>)</mo></math>, one of the five <math><msub><mi>Ω</mi><mi>c</mi></msub></math> states observed by the LHCb Collaboration, which is well reproduced as a molecular state from the <math><msubsup><mi>Ξ</mi><mi>c</mi><mo>*</mo></msubsup><mover><mi>K</mi><mo>¯</mo></mover></math> and <math><msubsup><mi>Ω</mi><mi>c</mi><mo>*</mo></msubsup><mi>η</mi></math> channels mostly. The state with <math><msup><mi>J</mi><mi>P</mi></msup><mo>=</mo><mn>3</mn><mo>/</mo><msup><mn>2</mn><mo>−</mo></msup></math> decays to <math><msub><mi>Ξ</mi><mi>c</mi></msub><mover><mi>K</mi><mo>¯</mo></mover></math> in the <math><mi>D</mi></math> wave, and we include this decay channel in our approach, as well as the effect of the <math><msubsup><mi>Ξ</mi><mi>c</mi><mo>*</mo></msubsup></math> width. With all these ingredients, we determine the fraction of the <math><msub><mi>Ω</mi><mi>c</mi></msub><mo>(</mo><mn>3120</mn><mo>)</mo></math> width that goes into <math><msub><mi>Ξ</mi><mi>c</mi></msub><mi>π</mi><mover><mi>K</mi><mo>¯</mo></mover></math>, which could be a measure of the <math><msubsup><mi>Ξ</mi><mi>c</mi><mo>*</mo></msubsup><mover><mi>K</mi><mo>¯</mo></mover></math> molecular component, but due to a relatively big binding, compared to its analogous <math><mi>Ω</mi><mo>(</mo><mn>2012</mn><mo>)</mo></math> state, we find only a small fraction of about 3%, which makes this measurement difficult with present statistics. As an alternative, we evaluate the scattering length and effective range of the <math><msubsup><mi>Ξ</mi><mi>c</mi><mo>*</mo></msubsup><mover><mi>K</mi><mo>¯</mo></mover></math> and <math><msubsup><mi>Ω</mi><mi>c</mi><mo>*</mo></msubsup><mi>η</mi></math> channels, which, together with the binding and width of the <math><msub><mi>Ω</mi><mi>c</mi></msub><mo>(</mo><mn>3120</mn><mo>)</mo></math> state, could give us an answer to the issue of the compositeness of this state when these magnitudes are determined experimentally, something feasible nowadays, for instance, measuring correlation functions.

Molecular nature of the <math><msub><mi>Ω</mi><mi>c</mi></msub><mo>(</mo><mn>3120</mn><mo>)</mo></math> and its analogy with the <math><mi>Ω</mi><mo>(</mo><mn>2012</mn><mo>)</mo></math>

We face the inverse problem of obtaining the interaction between coupled channels from the correlation functions of these channels. We apply the method to the interaction of the <math><msup><mrow><mi>D</mi></mrow><mrow><mn>0</mn></mrow></msup><msup><mrow><mi>K</mi></mrow><mrow><mo>+</mo></mrow></msup></math>, <math><msup><mrow><mi>D</mi></mrow><mrow><mo>+</mo></mrow></msup><msup><mrow><mi>K</mi></mrow><mrow><mn>0</mn></mrow></msup></math>, and <math><msubsup><mrow><mi>D</mi></mrow><mrow><mi>s</mi></mrow><mrow><mo>+</mo></mrow></msubsup><mi>η</mi></math> channels, from where the <math><msubsup><mrow><mi>D</mi></mrow><mrow><mi>s</mi><mn>0</mn></mrow><mrow><mo>⁎</mo></mrow></msubsup><mo>(</mo><mn>2317</mn><mo>)</mo></math> state emerges. We use synthetic data extracted from an interaction model based on the local hidden gauge approach and find that the inverse problem can determine the existence of a bound state of the system with a precision of about 20 MeV. At the same time, we can determine the isospin nature of the bound state and its compositeness in terms of the channels. Furthermore, we evaluate the scattering length and effective range of all three channels, as well as the couplings of the bound state found to all the components. Lastly, the size parameter of the source function, R, which in principle should be a magnitude provided by the experimental teams, can be obtained from a fit to the data with relatively high accuracy. These findings show the value of the correlation function to learn about the meson–meson interaction for systems which are difficult to access in other present facilities.

United States

Mexico

Genaro Toledo

Model independent analysis of femtoscopic correlation functions: An application to the

In this work we study the role of the <math><msub><mi>f</mi><mn>0</mn></msub><mo>(</mo><mn>980</mn><mo>)</mo></math> and <math><msub><mi>a</mi><mn>0</mn></msub><mo>(</mo><mn>980</mn><mo>)</mo></math> resonances in the low <math><msup><mi>K</mi><mo>+</mo></msup><msup><mi>K</mi><mo>−</mo></msup></math> and <math><msup><mi>K</mi><mn>0</mn></msup><msup><mover><mi>K</mi><mo>¯</mo></mover><mn>0</mn></msup></math> invariant-mass region of the <math><msup><mi>B</mi><mo>−</mo></msup><mo>→</mo><msup><mi>π</mi><mo>−</mo></msup><msup><mi>K</mi><mo>+</mo></msup><msup><mi>K</mi><mo>−</mo></msup></math> and <math><msup><mi>B</mi><mo>−</mo></msup><mo>→</mo><msup><mi>π</mi><mo>−</mo></msup><msup><mi>K</mi><mn>0</mn></msup><msup><mover><mi>K</mi><mo>¯</mo></mover><mn>0</mn></msup></math> reactions. The amplitudes are calculated by using the chiral unitary SU(3) formalism, in which these two resonances are dynamically generated from the unitary pseudoscalar-pseudoscalar coupled-channel approach. The amplitudes are then used as input in the evaluation of the mass distributions with respect to the <math><msup><mi>K</mi><mo>+</mo></msup><msup><mi>K</mi><mo>−</mo></msup></math> and <math><msup><mi>K</mi><mn>0</mn></msup><msup><mover><mi>K</mi><mo>¯</mo></mover><mn>0</mn></msup></math> invariant masses, where the contributions coming from the <math><mi>I</mi><mo>=</mo><mn>0</mn></math> and <math><mi>I</mi><mo>=</mo><mn>1</mn></math> components are explicitly assessed. Furthermore, the contribution of the <math><msup><mi>K</mi><mo>*</mo></msup><mo>(</mo><mn>892</mn><msup><mo>)</mo><mn>0</mn></msup><msup><mi>K</mi><mo>−</mo></msup></math> production and its influence on the <math><msup><mi>π</mi><mo>−</mo></msup><msup><mi>K</mi><mo>+</mo></msup></math> and <math><msup><mi>K</mi><mo>+</mo></msup><msup><mi>K</mi><mo>−</mo></msup></math> systems are also evaluated, showing that there is no significant strength for small <math><msup><mi>K</mi><mo>+</mo></msup><msup><mi>K</mi><mo>−</mo></msup></math> invariant mass. Finally, the final distributions of <math><msubsup><mi>M</mi><mrow><mi>inv</mi></mrow><mn>2</mn></msubsup><mo>(</mo><msup><mi>K</mi><mo>±</mo></msup><msup><mi>K</mi><mo>∓</mo></msup><mo>)</mo></math> for the <math><msup><mi>B</mi><mo>∓</mo></msup><mo>→</mo><msup><mi>π</mi><mo>∓</mo></msup><msup><mi>K</mi><mo>±</mo></msup><msup><mi>K</mi><mo>∓</mo></msup></math> reactions are estimated and compared with the LHCb data. Our results indicate that the <math><mi>I</mi><mo>=</mo><mn>0</mn></math> component tied to the <math><msub><mi>f</mi><mn>0</mn></msub><mo>(</mo><mn>980</mn><mo>)</mo></math> excitation generates the dominant contribution in the range of low <math><msup><mi>K</mi><mo>+</mo></msup><msup><mi>K</mi><mo>−</mo></msup></math> invariant mass.

Brazil

Luciano M. Abreu

Role of <math><msub><mi>f</mi><mn>0</mn></msub><mo>(</mo><mn>980</mn><mo>)</mo></math> and <math><msub><mi>a</mi><mn>0</mn></msub><mo>(</mo><mn>980</mn><mo>)</mo></math> in the <math><msup><mi>B</mi><mo>−</mo></msup><mo>→</mo><msup><mi>π</mi><mo>−</mo></msup><msup><mi>K</mi><mo>+</mo></msup><msup><mi>K</mi><mo>−</mo></msup></math> and <math><msup><mi>B</mi><mo>−</mo></msup><mo>→</mo><msup><mi>π</mi><mo>−</mo></msup><msup><mi>K</mi><mn>0</mn></msup><msup><mover><mi>K</mi><mo>¯</mo></mover><mn>0</mn></msup></math> reactions

We present a mechanism for <math><msub><mi>Ω</mi><mi>c</mi></msub><mo>→</mo><msup><mi>π</mi><mo>+</mo></msup><mi>Ω</mi><mo>(</mo><mn>2012</mn><mo>)</mo></math> production through an external emission Cabibbo favored weak decay mode, where the <math><mi>Ω</mi><mo>(</mo><mn>2012</mn><mo>)</mo></math> is dynamically generated from the interaction of <math><mover><mi>K</mi><mo>¯</mo></mover><msup><mi>Ξ</mi><mo>*</mo></msup><mo>(</mo><mn>1530</mn><mo>)</mo></math> and <math><mi>η</mi><mi>Ω</mi></math>, with <math><mover><mi>K</mi><mo>¯</mo></mover><mi>Ξ</mi></math> as the main decay channel. The <math><mi>Ω</mi><mo>(</mo><mn>2012</mn><mo>)</mo></math> decays later to <math><mover><mi>K</mi><mo>¯</mo></mover><mi>Ξ</mi></math> in this picture, with results compatible with Belle data. As a consequence, one can evaluate the direct decay <math><msubsup><mi>Ω</mi><mi>c</mi><mn>0</mn></msubsup><mo>→</mo><msup><mi>π</mi><mo>+</mo></msup><msup><mi>K</mi><mo>−</mo></msup><msup><mi>Ξ</mi><mn>0</mn></msup></math> and the decay <math><msubsup><mi>Ω</mi><mi>c</mi><mn>0</mn></msubsup><mo>→</mo><msup><mi>π</mi><mo>+</mo></msup><mover><mi>K</mi><mo>¯</mo></mover><msup><mi>Ξ</mi><mo>*</mo></msup></math>, <math><msup><mi>π</mi><mo>+</mo></msup><mi>η</mi><mi>Ω</mi></math> with direct couplings of <math><mover><mi>K</mi><mo>¯</mo></mover><msup><mi>Ξ</mi><mo>*</mo></msup></math> and <math><mi>η</mi><mi>Ω</mi></math> to <math><msup><mi>K</mi><mo>−</mo></msup><msup><mi>Ξ</mi><mn>0</mn></msup></math>. We show that, within uncertainties and using data from a recent Belle measurement, all three channels account for about (12–20)% of the total <math><msub><mi>Ω</mi><mi>c</mi></msub><mo>→</mo><msup><mi>π</mi><mo>+</mo></msup><msup><mi>K</mi><mo>−</mo></msup><msup><mi>Ξ</mi><mn>0</mn></msup></math> decay rate. The consistency of the molecular picture with all the data is established by showing that <math><msub><mi>Ω</mi><mi>c</mi></msub><mo>→</mo><msup><mi>Ξ</mi><mn>0</mn></msup><msup><mover><mi>K</mi><mo>¯</mo></mover><mrow><mo>*</mo><mn>0</mn></mrow></msup><mo>→</mo><msup><mi>Ξ</mi><mn>0</mn></msup><msup><mi>K</mi><mo>−</mo></msup><msup><mi>π</mi><mo>+</mo></msup></math> and <math><msub><mi>Ω</mi><mi>c</mi></msub><mo>→</mo><msup><mi>π</mi><mo>+</mo></msup><msup><mi>Ω</mi><mo>*</mo></msup><mo>→</mo><msup><mi>π</mi><mo>+</mo></msup><msup><mi>K</mi><mo>−</mo></msup><msup><mi>Ξ</mi><mn>0</mn></msup></math> account for about 85% of the total <math><msub><mi>Ω</mi><mi>c</mi></msub><mo>→</mo><msup><mi>π</mi><mo>+</mo></msup><msup><mi>K</mi><mo>−</mo></msup><msup><mi>Ξ</mi><mn>0</mn></msup></math>.

Interpretation of the <math><msub><mi>Ω</mi><mi>c</mi></msub><mo>→</mo><msup><mi>π</mi><mo>+</mo></msup><mi>Ω</mi><mo>(</mo><mn>2012</mn><mo>)</mo><mo>→</mo><msup><mi>π</mi><mo>+</mo></msup><mo>(</mo><mover><mi>K</mi><mo>¯</mo></mover><mi>Ξ</mi><mo>)</mo></math> relative to <math><msub><mi>Ω</mi><mi>c</mi></msub><mo>→</mo><msup><mi>π</mi><mo>+</mo></msup><mover><mi>K</mi><mo>¯</mo></mover><mi>Ξ</mi></math> from the <math><mi>Ω</mi><mo>(</mo><mn>2012</mn><mo>)</mo></math> molecular perspective

We study the <math><mrow><msubsup><mrow><mi>D</mi></mrow><mrow><mi>s</mi></mrow><mrow><mo>*</mo></mrow></msubsup><msup><mrow><mover><mrow><mi>D</mi></mrow><mrow><mo>¯</mo></mrow></mover></mrow><mrow><mo>*</mo></mrow></msup></mrow></math> system in connection with the <math><mi>J</mi><mo>/</mo><mi>ψ</mi><msup><mi>K</mi><mo>*</mo></msup></math> in coupled channels and observe that, within reasonable values of the cutoff used to regularize the loops, the system does not develop a bound state. However, the <math><msup><mi>J</mi><mi>P</mi></msup><mo>=</mo><msup><mn>2</mn><mo>+</mo></msup></math> channel has enough attraction to create a strong cusp structure that shows up in the <math><mi>J</mi><mo>/</mo><mi>ψ</mi><msup><mi>K</mi><mo>+</mo></msup></math> invariant mass distribution in the <math><msup><mi>B</mi><mo>+</mo></msup><mo>→</mo><mi>J</mi><mo>/</mo><mi>ψ</mi><mi>ϕ</mi><msup><mi>K</mi><mo>+</mo></msup></math> decay at the <math><msubsup><mi>D</mi><mi>s</mi><mo>*</mo></msubsup><msup><mover><mi>D</mi><mo>¯</mo></mover><mo>*</mo></msup></math> threshold. Such structure is visible in the experimental <math><msup><mi>B</mi><mo>+</mo></msup><mo>→</mo><mi>J</mi><mo>/</mo><mi>ψ</mi><mi>ϕ</mi><msup><mi>K</mi><mo>+</mo></msup></math> and <math><msup><mover><mi>B</mi><mo>¯</mo></mover><mn>0</mn></msup><mo>→</mo><mi>J</mi><mo>/</mo><mi>ψ</mi><msup><mi>K</mi><mo>+</mo></msup><msup><mi>K</mi><mo>−</mo></msup></math> decays, with small statistics, and our results should stimulate further measurements around this region, given the fact that cusp effects provide as valuable information on hadron dynamics as resonances themselves.

Raquel Molina

<math><msub><mi>Z</mi><mrow><mi>c</mi><mi>s</mi></mrow></msub></math> states from the <math><msubsup><mi>D</mi><mi>s</mi><mo>*</mo></msubsup><msup><mover><mi>D</mi><mo>¯</mo></mover><mo>*</mo></msup></math> and <math><mi>J</mi><mo>/</mo><mi>ψ</mi><msup><mi>K</mi><mo>*</mo></msup></math> coupled channels: Signal in <math><msup><mi>B</mi><mo>+</mo></msup><mo>→</mo><mi>J</mi><mo>/</mo><mi>ψ</mi><mi>ϕ</mi><msup><mi>K</mi><mo>+</mo></msup></math> decay

We study the  $$D^+ \rightarrow \pi ^+ \eta \eta $$  <math> <mrow> <msup> <mi>D</mi> <mo>+</mo> </msup> <mo>→</mo> <msup> <mi>π</mi> <mo>+</mo> </msup> <mi>η</mi> <mi>η</mi> </mrow> </math>   and  $$D^+ \rightarrow \pi ^+ \pi ^0 \eta $$  <math> <mrow> <msup> <mi>D</mi> <mo>+</mo> </msup> <mo>→</mo> <msup> <mi>π</mi> <mo>+</mo> </msup> <msup> <mi>π</mi> <mn>0</mn> </msup> <mi>η</mi> </mrow> </math>   reactions, which are single Cabibbo suppressed and can proceed both through internal and external emission. The primary mechanisms at quark level are considered, followed by hadronization to produce three mesons in the  $$D^+$$  <math> <msup> <mi>D</mi> <mo>+</mo> </msup> </math>   decay, and after that the final state interaction of these mesons leads to the production of the  $$a_0(980)$$  <math> <mrow> <msub> <mi>a</mi> <mn>0</mn> </msub> <mrow> <mo>(</mo> <mn>980</mn> <mo>)</mo> </mrow> </mrow> </math>   resonance, seen in the  $$\pi ^+ \eta $$  <math> <mrow> <msup> <mi>π</mi> <mo>+</mo> </msup> <mi>η</mi> </mrow> </math>  ,  $$\pi ^0 \eta $$  <math> <mrow> <msup> <mi>π</mi> <mn>0</mn> </msup> <mi>η</mi> </mrow> </math>   mass distributions. The theory has three unknown parameters to determine the shape of the distributions and the ratio between the  $$D^+ \rightarrow \pi ^+ \eta \eta $$  <math> <mrow> <msup> <mi>D</mi> <mo>+</mo> </msup> <mo>→</mo> <msup> <mi>π</mi> <mo>+</mo> </msup> <mi>η</mi> <mi>η</mi> </mrow> </math>   and  $$D^+ \rightarrow \pi ^+ \pi ^0 \eta $$  <math> <mrow> <msup> <mi>D</mi> <mo>+</mo> </msup> <mo>→</mo> <msup> <mi>π</mi> <mo>+</mo> </msup> <msup> <mi>π</mi> <mn>0</mn> </msup> <mi>η</mi> </mrow> </math>   rates. This ratio restricts much the sets of parameters but there is still much freedom leading to different shapes in the mass distributions. We call for a measurement of these mass distributions that will settle the reaction mechanism, while at the same time provide relevant information on the way that the  $$a_0(980)$$  <math> <mrow> <msub> <mi>a</mi> <mn>0</mn> </msub> <mrow> <mo>(</mo> <mn>980</mn> <mo>)</mo> </mrow> </mrow> </math>   resonance is produced in the reactions.

Türkiye

Melahat Bayar

Combined theoretical study of the  $$D^+ \rightarrow \pi ^+ \eta \eta $$  <math> <mrow> <msup> <mi>D</mi> <mo>+</mo> </msup> <mo>→</mo> <msup> <mi>π</mi> <mo>+</mo> </msup> <mi>η</mi> <mi>η</mi> </mrow> </math>   and  $$D^+ \rightarrow \pi ^+ \pi ^0 \eta $$  <math> <mrow> <msup> <mi>D</mi> <mo>+</mo> </msup> <mo>→</mo> <msup> <mi>π</mi> <mo>+</mo> </msup> <msup> <mi>π</mi> <mn>0</mn> </msup> <mi>η</mi> </mrow> </math>   reactions

We develop a model to study the  $$D^0 \rightarrow K^- \pi ^+ \eta $$  <math> <mrow> <msup> <mi>D</mi> <mn>0</mn> </msup> <mo>→</mo> <msup> <mi>K</mi> <mo>-</mo> </msup> <msup> <mi>π</mi> <mo>+</mo> </msup> <mi>η</mi> </mrow> </math>   weak decay, starting with the color favored external emission and Cabibbo favored mode at the quark level. A less favored internal emission decay mode is also studied as a source of small corrections. Some pairs of quarks are allowed to hadronize producing two pseudoscalar mesons, which posteriorly are allowed to interact to finally provide the  $$K^- \pi ^+ \eta $$  <math> <mrow> <msup> <mi>K</mi> <mo>-</mo> </msup> <msup> <mi>π</mi> <mo>+</mo> </msup> <mi>η</mi> </mrow> </math>   state. The chiral unitary approach is used to take into account the final state interaction of pairs of mesons, which has as a consequence the production of the  $$\kappa $$  <math> <mi>κ</mi> </math>   ( $$K^*_0(700)$$  <math> <mrow> <msubsup> <mi>K</mi> <mn>0</mn> <mo>∗</mo> </msubsup> <mrow> <mo>(</mo> <mn>700</mn> <mo>)</mo> </mrow> </mrow> </math>  ) and the  $$a_0(980)$$  <math> <mrow> <msub> <mi>a</mi> <mn>0</mn> </msub> <mrow> <mo>(</mo> <mn>980</mn> <mo>)</mo> </mrow> </mrow> </math>   resonances, well visible in the invariant mass distributions. We also introduce the  $$\bar{K}^{*0} \eta $$  <math> <mrow> <msup> <mrow> <mover> <mrow> <mi>K</mi> </mrow> <mrow> <mo>¯</mo> </mrow> </mover> </mrow> <mrow> <mrow></mrow> <mo>∗</mo> <mn>0</mn> </mrow> </msup> <mi>η</mi> </mrow> </math>   production in a phenomenological way and show that the s-wave pseudoscalar interaction together with this vector excitation mode are sufficient to provide a fair reproduction of the experimental data. The model provides the relative weight of the  $$a_0(980)$$  <math> <mrow> <msub> <mi>a</mi> <mn>0</mn> </msub> <mrow> <mo>(</mo> <mn>980</mn> <mo>)</mo> </mrow> </mrow> </math>   to the  $$\kappa $$  <math> <mi>κ</mi> </math>   excitation, and their strength is clearly visible in the low energy part of the  $$K \pi $$  <math> <mrow> <mi>K</mi> <mi>π</mi> </mrow> </math>   spectrum.

Theoretical study of the  $$D^0 \rightarrow K^- \pi ^+ \eta $$  <math> <mrow> <msup> <mi>D</mi> <mn>0</mn> </msup> <mo>→</mo> <msup> <mi>K</mi> <mo>-</mo> </msup> <msup> <mi>π</mi> <mo>+</mo> </msup> <mi>η</mi> </mrow> </math>   reaction