This paper presents the first measurement of $$\psi {(2S)}$$ and $$\chi _{c1}(3872)$$ meson production within fully reconstructed jets. Each quarkonium state (tag) is reconstructed via its decay to the $${{J \hspace{-1.66656pt}/\hspace{-1.111pt}\psi }} $$ ( $$\rightarrow $$ $$\mu ^+\mu ^-$$ ) $$\pi ^+\pi ^-$$ final state in the forward region using proton-proton collision data collected by the LHCb experiment at the center-of-mass-energy of $$13\text {TeV} $$ in 2016, corresponding to an integrated luminosity of $$1.64\,\text {\,fb} ^{-1} $$ . The fragmentation function, presented as the ratio of the quarkonium-tag transverse momentum to the full jet transverse momentum ( $$p_{\textrm{T}} (\text {tag})/p_{\textrm{T}} (\text {jet})$$ ), is measured differentially in $$p_{\textrm{T}} (\text {jet})$$ and $$p_{\textrm{T}} (\text {tag})$$ bins. The distributions are separated into promptly produced quarkonia from proton-proton collisions and quarkonia produced from displaced $\textit{b}$-hadron decays. While the displaced quarkonia fragmentation functions are in general well described by parton-shower predictions, the prompt quarkonium distributions differ significantly from fixed-order non-relativistic QCD (NRQCD) predictions followed by a QCD parton shower.

Netherlands

R. Aaij

United Kingdom

A. Abdelmotteleb

Switzerland

C. Abellan Beteta

F. Abudinén

T. Ackernley

United States

A. Adefisoye

Spain

B. Adeva

M. Adinolfi

Sweden

P. Adlarson

France

C. Agapopoulou

C. Aidala

Z. Ajaltouni

S. Akar

K. Akiba

Italy

P. Albicocco

Germany

J. Albrecht

F. Alessio

M. Alexander

Z. Aliouche

P. Alvarez Cartelle

R. Amalric

Brazil

S. Amato

J. Amey

Y. Amhis

China

L. An

L. Anderlini

M. Andersson

A. Andreianov

P. Andreola

M. Andreotti

D. Andreou

A. Anelli

D. Ao

F. Archilli

M. Argenton

Costa Rica

S. Arguedas Cuendis

A. Artamonov

M. Artuso

E. Aslanides

R. Ataíde Da Silva

M. Atzeni

B. Audurier

D. Bacher

I. Bachiller Perea

S. Bachmann

M. Bachmayer

J. Back

P. Baladron Rodriguez

V. Balagura

W. Baldini

L. Balzani

H. Bao

J. Baptista de Souza Leite

C. Barbero Pretel

M. Barbetti

I. Barbosa

R. Barlow

M. Barnyakov

S. Barsuk

W. Barter

M. Bartolini

J. Bartz

J. Basels

Poland

S. Bashir

G. Bassi

B. Batsukh

P. Battista

A. Bay

A. Beck

M. Becker

F. Bedeschi

I. Bediaga

N. Behling

S. Belin

V. Bellee

K. Belous

I. Belov

I. Belyaev

G. Benane

G. Bencivenni

E. Ben-Haim

A. Berezhnoy

R. Bernet

S. Bernet Andres

A. Bertolin

C. Betancourt

F. Betti

J. Bex

Ia. Bezshyiko

J. Bhom

M. Bieker

N. Biesuz

P. Billoir

A. Biolchini

M. Birch

F. Bishop

A. Bitadze

A. Bizzeti

T. Blake

F. Blanc

Measurements of $$\psi (2S)$$ and $$\chi _{c1}(3872)$$ production within fully reconstructed jets

In recent years, the modeling of compact astrophysical objects ($\textit{COs}$) has garnered significant attention from various research groups, particularly in efforts to determine their stable structures. This interest has been further amplified by the incorporation of dark energy as an additional source within the relativistic interior geometries of these stellar objects. In this paper, we present new structural properties of anisotropic, static, and spherically symmetric compact stars, characterized by a two-fluid distribution comprising ordinary baryonic matter and dark energy, within the framework of the gravity theory $\textit{f}$($\textit{R}$). We derive a novel class of exact analytical solutions to the modified field equations by employing the well-established Tolman–Buchdahl solutions as seed ansatz for the $$g_{tt}$$ and $$g_{rr}$$ metric potentials, in conjunction with a linear dark energy equation of state. The unknown parameters involved in these seed solutions, along with the dark energy coupling factor $$\omega $$ , are determined by a smooth matching of the interior and exterior regions in the hypersurface of the boundary. To analyze the physical viability of our model, we apply it to the compact star $\textit{PSR}$ $$J1614-2230$$ , using the widely studied and cosmologically consistent $$f(R)=R+\chi \Big (R^{2}+\eta R^{3}\Big )$$ gravity model. The obtained space-time geometry is assessed on the basis of several physical constraints, including the regularity of metric components, the viability of matter variables, the validity of state parameters and energy conditions, and various stability factors. Additionally, we examine the mass-radius profile, compactness, and surface redshift to ensure the model’s physical acceptability. Notably, our analysis reveals that the maximum allowable mass and compactness of the proposed dark energy star model exceed observational data, providing strong implications within this modified gravity framework. This suggests that such a model has the potential to surpass conventional observational predictions. In conclusion, our results confirm that the proposed solutions are physically viable and realistic, effectively mimicking a stable ultra-compact dark-energy star. These findings offer new insights into the relativistic stellar framework, highlighting the intricate interplay between extended gravity theories and a two-fluid distribution.

Azerbaijan

Hammad Nazar

Pakistan

Ghulam Abbas

M. Shahzad

Asifa Ashraf

Saudi Arabia

Ali Hakami

Ali Mubaraki

Exploring the stability of ultra-compact anisotropic dark energy stars with maximum allowable mass in $$R+\chi (R^{2}+\eta R^{3})$$ gravity

<p>We present two kinds of resonance soliton solutions on the ultrahyperbolic space <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi mathvariant="double-struck">U</mi></math> for the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>G</mi><mo>=</mo><mi>U</mi><mo stretchy="false">(</mo><mn>2</mn><mo stretchy="false">)</mo></math> Yang equation, which is equivalent to the anti-self-dual Yang-Mills (ASDYM) equation. We reveal and illustrate the solitonic behaviors in the four-dimensional Wess-Zumino-Witten (<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><msub><mrow><mi>WZW</mi></mrow><mrow><mn>4</mn></mrow></msub></mrow></math>) model through the sigma model action densities. The Yang equation is the equation of motion of the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><msub><mrow><mi>WZW</mi></mrow><mrow><mn>4</mn></mrow></msub></mrow></math> model. In the case of <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi mathvariant="double-struck">U</mi></math>, the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><msub><mrow><mi>WZW</mi></mrow><mrow><mn>4</mn></mrow></msub></mrow></math> model describes a string field theory action of open <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>N</mi><mo>=</mo><mn>2</mn></math> string theories. Hence, our solutions on <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi mathvariant="double-struck">U</mi></math> suggest the existence of the corresponding classical objects in the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>N</mi><mo>=</mo><mn>2</mn></math> string theories. Our solutions include multiple-pole solutions and V-shape soliton solutions. The V-shape solitons suggest annihilation and creation processes of two solitons and would be building blocks to classify the ASDYM solitons, like the role of Y-shape solitons in classification of the Kadomtsev-Petviashvili (line) solitons. We also clarify the relationship between the Cauchy matrix approach and the binary Darboux transformation in terms of quasideterminants. Our formalism can start with a simpler input data for the soliton solutions and hence might give a suitable framework for the classification of the ASDYM solitons.</p>

Japan

Shangshuai Li

Masashi Hamanaka

Shan-Chi Huang

Da-Jun Zhang

Soliton resonances in four dimensional Wess-Zumino-Witten model

This study investigates the nature of the  $$X_0(2900)$$  <math> <mrow> <msub> <mi>X</mi> <mn>0</mn> </msub> <mrow> <mo>(</mo> <mn>2900</mn> <mo>)</mo> </mrow> </mrow> </math>   and  $$\chi _{c0}(3930)$$  <math> <mrow> <msub> <mi>χ</mi> <mrow> <mi>c</mi> <mn>0</mn> </mrow> </msub> <mrow> <mo>(</mo> <mn>3930</mn> <mo>)</mo> </mrow> </mrow> </math>   based on experimental results of the process  $$B^+$$  <math> <msup> <mi>B</mi> <mo>+</mo> </msup> </math>    $$\rightarrow $$  <math> <mo>→</mo> </math>    $$D^+ D^- K^+$$  <math> <mrow> <msup> <mi>D</mi> <mo>+</mo> </msup> <msup> <mi>D</mi> <mo>-</mo> </msup> <msup> <mi>K</mi> <mo>+</mo> </msup> </mrow> </math>  . We focus on the S-wave  $$D^{*-}K^{*+}$$  <math> <mrow> <mmultiscripts> <mi>D</mi> <mrow></mrow> <mrow> <mrow></mrow> <mo>∗</mo> <mo>-</mo> </mrow> </mmultiscripts> <mmultiscripts> <mi>K</mi> <mrow></mrow> <mrow> <mrow></mrow> <mo>∗</mo> <mo>+</mo> </mrow> </mmultiscripts> </mrow> </math>   and  $$D_s^+D_s^-$$  <math> <mrow> <msubsup> <mi>D</mi> <mi>s</mi> <mo>+</mo> </msubsup> <msubsup> <mi>D</mi> <mi>s</mi> <mo>-</mo> </msubsup> </mrow> </math>   molecular states, which can be related to the  $$X_0(2900)$$  <math> <mrow> <msub> <mi>X</mi> <mn>0</mn> </msub> <mrow> <mo>(</mo> <mn>2900</mn> <mo>)</mo> </mrow> </mrow> </math>   and  $$\chi _{c0}(3930)$$  <math> <mrow> <msub> <mi>χ</mi> <mrow> <mi>c</mi> <mn>0</mn> </mrow> </msub> <mrow> <mo>(</mo> <mn>3930</mn> <mo>)</mo> </mrow> </mrow> </math>  , respectively. Using effective Lagrangians, we construct the potential kernel of the  $$D^{*-}K^{*+}$$  <math> <mrow> <mmultiscripts> <mi>D</mi> <mrow></mrow> <mrow> <mrow></mrow> <mo>∗</mo> <mo>-</mo> </mrow> </mmultiscripts> <mmultiscripts> <mi>K</mi> <mrow></mrow> <mrow> <mrow></mrow> <mo>∗</mo> <mo>+</mo> </mrow> </mmultiscripts> </mrow> </math>  – $$D^{-}K^{+}$$  <math> <mrow> <msup> <mi>D</mi> <mo>-</mo> </msup> <msup> <mi>K</mi> <mo>+</mo> </msup> </mrow> </math>   and  $$D_s^+D_s^-$$  <math> <mrow> <msubsup> <mi>D</mi> <mi>s</mi> <mo>+</mo> </msubsup> <msubsup> <mi>D</mi> <mi>s</mi> <mo>-</mo> </msubsup> </mrow> </math>  – $$D^+D^-$$  <math> <mrow> <msup> <mi>D</mi> <mo>+</mo> </msup> <msup> <mi>D</mi> <mo>-</mo> </msup> </mrow> </math>   interactions with a one-boson-exchange model, and determine the scattering amplitudes and their poles through a quasipotential Bethe–Salpeter equation approach. By incorporating the potential kernel into the three-body decay process  $$B^+$$  <math> <msup> <mi>B</mi> <mo>+</mo> </msup> </math>    $$\rightarrow $$  <math> <mo>→</mo> </math>    $$D^+ D^- K^+$$  <math> <mrow> <msup> <mi>D</mi> <mo>+</mo> </msup> <msup> <mi>D</mi> <mo>-</mo> </msup> <msup> <mi>K</mi> <mo>+</mo> </msup> </mrow> </math>  , we evaluate the  $$D^-K^+$$  <math> <mrow> <msup> <mi>D</mi> <mo>-</mo> </msup> <msup> <mi>K</mi> <mo>+</mo> </msup> </mrow> </math>   and  $$D^+D^-$$  <math> <mrow> <msup> <mi>D</mi> <mo>+</mo> </msup> <msup> <mi>D</mi> <mo>-</mo> </msup> </mrow> </math>   invariant mass spectra, as well as the Dalitz plot, using Monte Carlo simulation. A satisfactory fit to the  $$D^-K^+$$  <math> <mrow> <msup> <mi>D</mi> <mo>-</mo> </msup> <msup> <mi>K</mi> <mo>+</mo> </msup> </mrow> </math>   and  $$D^+D^-$$  <math> <mrow> <msup> <mi>D</mi> <mo>+</mo> </msup> <msup> <mi>D</mi> <mo>-</mo> </msup> </mrow> </math>   invariant mass spectra is achieved after introducing additional Breit–Wigner resonances,  $$X_1(2900)$$  <math> <mrow> <msub> <mi>X</mi> <mn>1</mn> </msub> <mrow> <mo>(</mo> <mn>2900</mn> <mo>)</mo> </mrow> </mrow> </math>  ,  $$\psi (3770)$$  <math> <mrow> <mi>ψ</mi> <mo>(</mo> <mn>3770</mn> <mo>)</mo> </mrow> </math>  , and  $$\chi _{c2}(3930)$$  <math> <mrow> <msub> <mi>χ</mi> <mrow> <mi>c</mi> <mn>2</mn> </mrow> </msub> <mrow> <mo>(</mo> <mn>3930</mn> <mo>)</mo> </mrow> </mrow> </math>  . Prominent signals of the  $$X_0(2900)$$  <math> <mrow> <msub> <mi>X</mi> <mn>0</mn> </msub> <mrow> <mo>(</mo> <mn>2900</mn> <mo>)</mo> </mrow> </mrow> </math>   and  $$\chi _{c0}(3930)$$  <math> <mrow> <msub> <mi>χ</mi> <mrow> <mi>c</mi> <mn>0</mn> </mrow> </msub> <mrow> <mo>(</mo> <mn>3930</mn> <mo>)</mo> </mrow> </mrow> </math>   states appear as peaks in the  $$D^-K^+$$  <math> <mrow> <msup> <mi>D</mi> <mo>-</mo> </msup> <msup> <mi>K</mi> <mo>+</mo> </msup> </mrow> </math>   and  $$D^+D^-$$  <math> <mrow> <msup> <mi>D</mi> <mo>+</mo> </msup> <msup> <mi>D</mi> <mo>-</mo> </msup> </mrow> </math>   invariant mass spectra near 2900 and 3930 MeV, respectively. Clear event concentration from the  $$X_0(2900)$$  <math> <mrow> <msub> <mi>X</mi> <mn>0</mn> </msub> <mrow> <mo>(</mo> <mn>2900</mn> <mo>)</mo> </mrow> </mrow> </math>   and  $$\chi _0(3930)$$  <math> <mrow> <msub> <mi>χ</mi> <mn>0</mn> </msub> <mrow> <mo>(</mo> <mn>3930</mn> <mo>)</mo> </mrow> </mrow> </math>   is evident as strips in the Dalitz plot. The results suggest that both  $$X_0(2900)$$  <math> <mrow> <msub> <mi>X</mi> <mn>0</mn> </msub> <mrow> <mo>(</mo> <mn>2900</mn> <mo>)</mo> </mrow> </mrow> </math>   and  $$\chi _{c0}(3930)$$  <math> <mrow> <msub> <mi>χ</mi> <mrow> <mi>c</mi> <mn>0</mn> </mrow> </msub> <mrow> <mo>(</mo> <mn>3930</mn> <mo>)</mo> </mrow> </mrow> </math>   can be interpreted as molecular states, with the inclusion of  $$X_1(2900)$$  <math> <mrow> <msub> <mi>X</mi> <mn>1</mn> </msub> <mrow> <mo>(</mo> <mn>2900</mn> <mo>)</mo> </mrow> </mrow> </math>   and  $$\chi _2(3930)$$  <math> <mrow> <msub> <mi>χ</mi> <mn>2</mn> </msub> <mrow> <mo>(</mo> <mn>3930</mn> <mo>)</mo> </mrow> </mrow> </math>   necessary to describe structures in the  $$D^-K^+$$  <math> <mrow> <msup> <mi>D</mi> <mo>-</mo> </msup> <msup> <mi>K</mi> <mo>+</mo> </msup> </mrow> </math>   and  $$D^+D^-$$  <math> <mrow> <msup> <mi>D</mi> <mo>+</mo> </msup> <msup> <mi>D</mi> <mo>-</mo> </msup> </mrow> </math>   invariant mass spectra, respectively.

Zuo-Ming Ding

Qi Huang

Jun He

$$X_0(2900)$$  <math> <mrow> <msub> <mi>X</mi> <mn>0</mn> </msub> <mrow> <mo>(</mo> <mn>2900</mn> <mo>)</mo> </mrow> </mrow> </math>   and  $$\chi _{c0}(3930)$$  <math> <mrow> <msub> <mi>χ</mi> <mrow> <mi>c</mi> <mn>0</mn> </mrow> </msub> <mrow> <mo>(</mo> <mn>3930</mn> <mo>)</mo> </mrow> </mrow> </math>   in process  $$B^+\rightarrow D^+ D^- K^+$$  <math> <mrow> <msup> <mi>B</mi> <mo>+</mo> </msup> <mo>→</mo> <msup> <mi>D</mi> <mo>+</mo> </msup> <msup> <mi>D</mi> <mo>-</mo> </msup> <msup> <mi>K</mi> <mo>+</mo> </msup> </mrow> </math>

The quest for supersymmetric (SUSY) particles is among the main search channels currently pursued at the LHC. Particularly, electroweak (EW) particles with masses as low as a few hundred GeV are still viable. Recent searches for the “golden channel”,  $$pp \rightarrow \tilde{\chi }_{2}^0 \tilde{\chi }_{1}^\pm \rightarrow \tilde{\chi }_{1}^0 Z^{(*)} \, \tilde{\chi }_{1}^0 W^{\pm (*)}$$  <math> <mrow> <mi>p</mi> <mi>p</mi> <mo>→</mo> <msubsup> <mover> <mi>χ</mi> <mo>~</mo> </mover> <mrow> <mn>2</mn> </mrow> <mn>0</mn> </msubsup> <msubsup> <mover> <mi>χ</mi> <mo>~</mo> </mover> <mrow> <mn>1</mn> </mrow> <mo>±</mo> </msubsup> <mo>→</mo> <msubsup> <mover> <mi>χ</mi> <mo>~</mo> </mover> <mrow> <mn>1</mn> </mrow> <mn>0</mn> </msubsup> <mmultiscripts> <mi>Z</mi> <mrow></mrow> <mrow> <mo>(</mo> <mrow></mrow> <mo>∗</mo> <mo>)</mo> </mrow> </mmultiscripts> <mspace width="0.166667em"></mspace> <msubsup> <mover> <mi>χ</mi> <mo>~</mo> </mover> <mrow> <mn>1</mn> </mrow> <mn>0</mn> </msubsup> <mmultiscripts> <mi>W</mi> <mrow></mrow> <mrow> <mo>±</mo> <mo>(</mo> <mrow></mrow> <mo>∗</mo> <mo>)</mo> </mrow> </mmultiscripts> </mrow> </math>   show consistent excesses between ATLAS and CMS in the 2 lepton, 3-lepton and mono-jet searches, assuming      and  $$\Delta m:= m_{\tilde{\chi }_{2}^0} - m_{\tilde{\chi }_{1}^0} \approx 20 \,\, \textrm{GeV}$$  <math> <mrow> <mi>Δ</mi> <mi>m</mi> <mo>:</mo> <mo>=</mo> <msub> <mi>m</mi> <msubsup> <mover> <mi>χ</mi> <mo>~</mo> </mover> <mrow> <mn>2</mn> </mrow> <mn>0</mn> </msubsup> </msub> <mo>-</mo> <msub> <mi>m</mi> <msubsup> <mover> <mi>χ</mi> <mo>~</mo> </mover> <mrow> <mn>1</mn> </mrow> <mn>0</mn> </msubsup> </msub> <mo>≈</mo> <mn>20</mn> <mspace width="0.166667em"></mspace> <mspace width="0.166667em"></mspace> <mtext>GeV</mtext> </mrow> </math>  . This mass configuration arises naturally in SUSY scenarios with wino/bino Dark Matter (DM) or higgsino DM. In these scenarios the lightest supersymmetric particle (LSP), assumed to be the lightest neutralino,  $$\tilde{\chi }_{1}^0$$  <math> <msubsup> <mover> <mi>χ</mi> <mo>~</mo> </mover> <mrow> <mn>1</mn> </mrow> <mn>0</mn> </msubsup> </math>  , as a DM candidate is in good agreement with the observed limits on the DM content of the universe, as well as with negative results from Direct Detection (DD) experiments. We analyze these two scenarios with respect to the observed excesses, taking into account all relevant experimental constraints. We show that in particular wino/bino DM with different signs of the SU(2) and U(1) soft SUSY-breaking parameters can describe well the experimental excesses, while being in agreement with all other constraints.

Manimala Chakraborti

Sven Heinemeyer

India

Ipsita Saha

Consistent excesses in the search for  $$\varvec{\tilde{\chi }_{2}^0\tilde{\chi }_{1}^\pm :}$$  <math> <mrow> <msubsup> <mover> <mi>χ</mi> <mo>~</mo> </mover> <mrow> <mn>2</mn> </mrow> <mn>0</mn> </msubsup> <msubsup> <mover> <mi>χ</mi> <mo>~</mo> </mover> <mrow> <mn>1</mn> </mrow> <mo>±</mo> </msubsup> <mo>:</mo> </mrow> </math>   wino/bino vs. Higgsino dark matter

A study of   <math> <msubsup> <mi>B</mi> <mi>c</mi> <mo>+</mo> </msubsup> <mo>→</mo> <msub> <mi>χ</mi> <mi>c</mi> </msub> <msup> <mi>π</mi> <mo>+</mo> </msup> </math>  $$ {B}_c^{+}\to {\chi}_c{\pi}^{+} $$  decays is reported using proton-proton collision data, collected with the LHCb detector at centre-of-mass energies of 7, 8, and 13 TeV, corresponding to an integrated luminosity of 9 fb −1. The decay   <math> <msubsup> <mi>B</mi> <mi>c</mi> <mo>+</mo> </msubsup> <mo>→</mo> <msub> <mi>χ</mi> <mrow> <mi>c</mi> <mn>2</mn> </mrow> </msub> <msup> <mi>π</mi> <mo>+</mo> </msup> </math>  $$ {B}_c^{+}\to {\chi}_{c2}{\pi}^{+} $$  is observed for the first time, with a significance exceeding seven standard deviations. The relative branching fraction with respect to the   <math> <msubsup> <mi>B</mi> <mi>c</mi> <mo>+</mo> </msubsup> <mo>→</mo> <mi>J</mi> <mo>/</mo> <mi>ψ</mi> <msup> <mi>π</mi> <mo>+</mo> </msup> </math>  $$ {B}_c^{+}\to J/\psi {\pi}^{+} $$  decay is measured to be  <math> <mfrac> <msub> <mi>B</mi> <mrow> <msubsup> <mi>B</mi> <mi>c</mi> <mo>+</mo> </msubsup> <mo>→</mo> <msub> <mi>χ</mi> <mrow> <mi>c</mi> <mn>2</mn> </mrow> </msub> <msup> <mi>π</mi> <mo>+</mo> </msup> </mrow> </msub> <msub> <mi>B</mi> <mrow> <msubsup> <mi>B</mi> <mi>c</mi> <mo>+</mo> </msubsup> <mo>→</mo> <mi>J</mi> <mo>/</mo> <mi>ψ</mi> <msup> <mi>π</mi> <mo>+</mo> </msup> </mrow> </msub> </mfrac> <mo>=</mo> <mn>0.37</mn> <mo>±</mo> <mn>0.06</mn> <mo>±</mo> <mn>0.02</mn> <mo>±</mo> <mn>0.01</mn> <mo>,</mo> </math>  $$ \frac{{\mathcal{B}}_{B_c^{+}\to {\chi}_{c2}{\pi}^{+}}}{{\mathcal{B}}_{B_c^{+}\to J/\psi {\pi}^{+}}}=0.37\pm 0.06\pm 0.02\pm 0.01, $$

CERN

A. Alfonso Albero

F. Baryshnikov

A. Battig

A. Beiter

C. Bertella

J. Blank

S. Blusk

V. Bocharnikov

Study of   <math> <msubsup> <mi>B</mi> <mi>c</mi> <mo>+</mo> </msubsup> <mo>→</mo> <msub> <mi>χ</mi> <mi>c</mi> </msub> <msup> <mi>π</mi> <mo>+</mo> </msup> </math>  $$ {B}_c^{+}\to {\chi}_c{\pi}^{+} $$  decays

We explore the first radial excitation  $$X_{\textrm{4c}}^{*}$$  <math> <msubsup> <mi>X</mi> <mrow> <mtext>4c</mtext> </mrow> <mrow> <mrow></mrow> <mo>∗</mo> </mrow> </msubsup> </math>   of the fully charmed diquark-antidiquark state  $$X_{\textrm{4c}}=cc{\overline{c}}{\overline{c}} $$  <math> <mrow> <msub> <mi>X</mi> <mtext>4c</mtext> </msub> <mo>=</mo> <mi>c</mi> <mi>c</mi> <mover> <mi>c</mi> <mo>¯</mo> </mover> <mover> <mi>c</mi> <mo>¯</mo> </mover> </mrow> </math>   built of axial-vector components, and the hadronic molecule  $${\mathcal {M}} =\chi _{c1}\chi _{c1}$$  <math> <mrow> <mi>M</mi> <mo>=</mo> <msub> <mi>χ</mi> <mrow> <mi>c</mi> <mn>1</mn> </mrow> </msub> <msub> <mi>χ</mi> <mrow> <mi>c</mi> <mn>1</mn> </mrow> </msub> </mrow> </math>  . The masses and current couplings of these scalar states are calculated in the context of the QCD two-point sum rule approach. The full widths of  $$X_{\textrm{4c}}^{*}$$  <math> <msubsup> <mi>X</mi> <mrow> <mtext>4c</mtext> </mrow> <mrow> <mrow></mrow> <mo>∗</mo> </mrow> </msubsup> </math>   and  $${\mathcal {M}}$$  <math> <mi>M</mi> </math>   are evaluated by taking into account their kinematically allowed decay channels. We find partial widths of these processes using the strong couplings  $$g_i^{*}$$  <math> <msubsup> <mi>g</mi> <mi>i</mi> <mrow> <mrow></mrow> <mo>∗</mo> </mrow> </msubsup> </math>   and  $$G_i^{(*)}$$  <math> <msubsup> <mi>G</mi> <mi>i</mi> <mrow> <mo>(</mo> <mrow></mrow> <mo>∗</mo> <mo>)</mo> </mrow> </msubsup> </math>   at the  $$X_{\textrm{4c}}^{*}$$  <math> <msubsup> <mi>X</mi> <mrow> <mtext>4c</mtext> </mrow> <mrow> <mrow></mrow> <mo>∗</mo> </mrow> </msubsup> </math>  ( $${\mathcal {M}}$$  <math> <mi>M</mi> </math>   )-conventional mesons vertices computed by means of the QCD three-point sum rule method. The predictions obtained for the parameters  $$m=(7235 \pm 75)~ \textrm{MeV}$$  <math> <mrow> <mi>m</mi> <mo>=</mo> <mo>(</mo> <mn>7235</mn> <mo>±</mo> <mn>75</mn> <mo>)</mo> <mspace width="3.33333pt"></mspace> <mtext>MeV</mtext> </mrow> </math>  ,  $$\Gamma =(144 \pm 18)~\textrm{MeV}$$  <math> <mrow> <mi>Γ</mi> <mo>=</mo> <mo>(</mo> <mn>144</mn> <mo>±</mo> <mn>18</mn> <mo>)</mo> <mspace width="3.33333pt"></mspace> <mtext>MeV</mtext> </mrow> </math>   and  $${\widetilde{m}}=(7180 \pm 120)~\textrm{MeV}$$  <math> <mrow> <mover> <mi>m</mi> <mo>~</mo> </mover> <mo>=</mo> <mrow> <mo>(</mo> <mn>7180</mn> <mo>±</mo> <mn>120</mn> <mo>)</mo> </mrow> <mspace width="3.33333pt"></mspace> <mtext>MeV</mtext> </mrow> </math>  ,  $${\widetilde{\Gamma }}=(169 \pm 21)~\textrm{MeV}$$  <math> <mrow> <mover> <mi>Γ</mi> <mo>~</mo> </mover> <mo>=</mo> <mrow> <mo>(</mo> <mn>169</mn> <mo>±</mo> <mn>21</mn> <mo>)</mo> </mrow> <mspace width="3.33333pt"></mspace> <mtext>MeV</mtext> </mrow> </math>   of these structures, are compared with the experimental data of the CMS and ATLAS Collaborations. In accordance to these results, within existing errors of measurements and uncertainties of the theoretical calculations, both the excited tetraquark and hadronic molecule may be considered as candidates to the resonance X(7300). Detailed analysis, however, demonstrates that the preferable model for X(7300) is an admixture of the molecule  $${\mathcal {M}}$$  <math> <mi>M</mi> </math>   and sizeable part of  $$X_{\textrm{4c}}^{*}$$  <math> <msubsup> <mi>X</mi> <mrow> <mtext>4c</mtext> </mrow> <mrow> <mrow></mrow> <mo>∗</mo> </mrow> </msubsup> </math>  .

S. Agaev

Iran

Türkiye

K. Azizi

B. Barsbay

H. Sundu

Resonance X(7300): excited 2S tetraquark or hadronic molecule  $$\chi _{c1}\chi _{c1}$$  <math> <mrow> <msub> <mi>χ</mi> <mrow> <mi>c</mi> <mn>1</mn> </mrow> </msub> <msub> <mi>χ</mi> <mrow> <mi>c</mi> <mn>1</mn> </mrow> </msub> </mrow> </math>  ?

In this work, a study of the  $$D_s{\bar{D}}_s$$  <math> <mrow> <msub> <mi>D</mi> <mi>s</mi> </msub> <msub> <mover> <mrow> <mi>D</mi> </mrow> <mrow> <mo>¯</mo> </mrow> </mover> <mi>s</mi> </msub> </mrow> </math>   interaction and its couplings to the channels  $$D{\bar{D}}$$  <math> <mrow> <mi>D</mi> <mover> <mrow> <mi>D</mi> </mrow> <mrow> <mo>¯</mo> </mrow> </mover> </mrow> </math>   and  $$J/\psi \phi $$  <math> <mrow> <mi>J</mi> <mo>/</mo> <mi>ψ</mi> <mi>ϕ</mi> </mrow> </math>   is performed in a quasipotential Bethe–Salpeter equation approach. The  $$D_s^+{D}_s^-$$  <math> <mrow> <msubsup> <mi>D</mi> <mi>s</mi> <mo>+</mo> </msubsup> <msubsup> <mi>D</mi> <mi>s</mi> <mo>-</mo> </msubsup> </mrow> </math>   and  $$D^+{D}^-$$  <math> <mrow> <msup> <mi>D</mi> <mo>+</mo> </msup> <msup> <mrow> <mi>D</mi> </mrow> <mo>-</mo> </msup> </mrow> </math>   invariant mass spectra in three-body B decays are investigated in order to understand the origin of X(3960),  $$\chi _{c0}(3930)$$  <math> <mrow> <msub> <mi>χ</mi> <mrow> <mi>c</mi> <mn>0</mn> </mrow> </msub> <mrow> <mo>(</mo> <mn>3930</mn> <mo>)</mo> </mrow> </mrow> </math>  , and  $$X_0(4140)$$  <math> <mrow> <msub> <mi>X</mi> <mn>0</mn> </msub> <mrow> <mo>(</mo> <mn>4140</mn> <mo>)</mo> </mrow> </mrow> </math>   structures reported at LHCb. With the help of effective Lagrangians, the potential kernel can be constructed with meson exchanges, from which the scattering amplitudes can be obtained. By inserting it into the three-body decay processes, the invariant mass spectra can be calculated with an additional Breit–Wigner resonance introduced. The  $$D_s^+{D}_s^-$$  <math> <mrow> <msubsup> <mi>D</mi> <mi>s</mi> <mo>+</mo> </msubsup> <msubsup> <mi>D</mi> <mi>s</mi> <mo>-</mo> </msubsup> </mrow> </math>   invariant mass spectrum in the decay process  $$B^+\rightarrow D^+_sD^-_sK^+$$  <math> <mrow> <msup> <mi>B</mi> <mo>+</mo> </msup> <mo>→</mo> <msubsup> <mi>D</mi> <mi>s</mi> <mo>+</mo> </msubsup> <msubsup> <mi>D</mi> <mi>s</mi> <mo>-</mo> </msubsup> <msup> <mi>K</mi> <mo>+</mo> </msup> </mrow> </math>   is well reproduced, and the X(3960) structure can be explained as a molecular state from the  $$D_s{\bar{D}}_s$$  <math> <mrow> <msub> <mi>D</mi> <mi>s</mi> </msub> <msub> <mover> <mrow> <mi>D</mi> </mrow> <mrow> <mo>¯</mo> </mrow> </mover> <mi>s</mi> </msub> </mrow> </math>   interaction. The state also exhibits as a peak in the  $$D^+{D}^-$$  <math> <mrow> <msup> <mi>D</mi> <mo>+</mo> </msup> <msup> <mrow> <mi>D</mi> </mrow> <mo>-</mo> </msup> </mrow> </math>   invariant mass spectrum in the decay  $$B^+\rightarrow D^+D^-K^+$$  <math> <mrow> <msup> <mi>B</mi> <mo>+</mo> </msup> <mo>→</mo> <msup> <mi>D</mi> <mo>+</mo> </msup> <msup> <mi>D</mi> <mo>-</mo> </msup> <msup> <mi>K</mi> <mo>+</mo> </msup> </mrow> </math>  , however, it is too narrow to reproduce the experimental structure around 3930 MeV. The dip around 4140 MeV in the  $$D_s^+{D}_s^-$$  <math> <mrow> <msubsup> <mi>D</mi> <mi>s</mi> <mo>+</mo> </msubsup> <msubsup> <mi>D</mi> <mi>s</mi> <mo>-</mo> </msubsup> </mrow> </math>   invariant mass spectrum can be reproduced by the additional resonance with interference effect. However, a small bump instead of a dip is produced from the  $$D_s{\bar{D}}_s-J/\psi \phi $$  <math> <mrow> <msub> <mi>D</mi> <mi>s</mi> </msub> <msub> <mover> <mrow> <mi>D</mi> </mrow> <mrow> <mo>¯</mo> </mrow> </mover> <mi>s</mi> </msub> <mo>-</mo> <mi>J</mi> <mo>/</mo> <mi>ψ</mi> <mi>ϕ</mi> </mrow> </math>   coupled-channel effect, which suggests that the  $$X_0(4140)$$  <math> <mrow> <msub> <mi>X</mi> <mn>0</mn> </msub> <mrow> <mo>(</mo> <mn>4140</mn> <mo>)</mo> </mrow> </mrow> </math>   cannot be interpreted as the  $$D_s{\bar{D}}_s-J/\psi \phi $$  <math> <mrow> <msub> <mi>D</mi> <mi>s</mi> </msub> <msub> <mover> <mrow> <mi>D</mi> </mrow> <mrow> <mo>¯</mo> </mrow> </mover> <mi>s</mi> </msub> <mo>-</mo> <mi>J</mi> <mo>/</mo> <mi>ψ</mi> <mi>ϕ</mi> </mrow> </math>   coupling in the current model.

Zuo-ming Ding

Combined analysis on nature of X(3960),  $$\chi _{c0}(3930)$$  <math> <mrow> <msub> <mi>χ</mi> <mrow> <mi>c</mi> <mn>0</mn> </mrow> </msub> <mrow> <mo>(</mo> <mn>3930</mn> <mo>)</mo> </mrow> </mrow> </math>  , and  $$X_0(4140)$$  <math> <mrow> <msub> <mi>X</mi> <mn>0</mn> </msub> <mrow> <mo>(</mo> <mn>4140</mn> <mo>)</mo> </mrow> </mrow> </math>

Abstract The open N = 2 string theory is defined on the 4D space-time with the split signature (+, +, −, −). The string field theory action of the open N = 2 string theory is described by the 4D Wess–Zumino–Witten (WZW$_{4}$) model. The equation of motion of the WZW$_{4}$ model is the Yang equation, which is equivalent to the anti-self-dual Yang–Mills equation. In this paper, we study soliton-type classical solutions of the WZW$_{4}$ model in the split signature by calculating the action density of the WZW$_{4}$ model. We find that the action density of the one-soliton solutions is localized on a 3D hyperplane. This shows that there would be codimension-one-solitonic objects, or equivalently some kind of three-branes in the open N = 2 string theory. We also prove that, in the asymptotic region of the space-time, the action density of the n-soliton solutions is a “non-linear superposition” of n one-solitons. This suggests the existence of n intersecting three-branes in the N = 2 strings. Finally we make a reduction to a (1 + 2)D real space-time to calculate the energy densities of the soliton solutions. We can successfully evaluate the energy distribution for the two-soliton solutions and find that there is no singularity in the interacting region. This implies the existence of smooth intersecting codimension-one branes in the whole region. Soliton solutions in the Euclidean signature are also discussed.

Hiroaki Kanno

Solitons in open = 2 String Theory Kahler-Chen-Simons theory A tour through N=2 strings On soliton solutions of the anti-self-dual Yang-Mills equations from the perspective of integrable systems Soliton solutions in an integrable chiral model in 2+1 dimensions On the space-time monopole equation A review on tachyon condensation in open string field theories Soliton equations as dynamical systems on infinite dimensional Grassmann manifold

We study dynamics of multi-soliton solutions of anti-self-dual Yang-Mills equations for G = GL(2, ℂ) in four-dimensional spaces. The one-soliton solution can be interpreted as a codimension-one soliton in four-dimensional spaces because the principal peak of action density localizes on a three-dimensional hyperplane. We call it the soliton wall. We prove that in the asymptotic region, the n-soliton solution possesses n isolated localized lumps of action density, and interpret it as n intersecting soliton walls. More precisely, each action density lump is essentially the same as a soliton wall because it preserves its shape and “velocity” except for a position shift of principal peak in the scattering process. The position shift results from the nonlinear interactions of the multi-solitons and is called the phase shift. We calculate the phase shift factors explicitly and find that the action densities can be real-valued in three kind of signatures. Finally, we show that the gauge group can be G = SU(2) in the Ultrahyperbolic space 𝕌 (the split signature (+, +, −, −)). This implies that the intersecting soliton walls could be realized in all region in N=2 string theories. It is remarkable that quasideterminants dramatically simplify the calculations and proofs.

Multi-soliton dynamics of anti-self-dual gauge fields