Symmetry studies represent one of the most promising frontiers in particle physics research. This investigation focuses on exploring P and $\rm CP $ symmetries in the charm system through the measurement of asymmetry decay parameters in the three-body decay of $ \Xi_c^{+} $ . By incorporating electron and positron beam polarization effects and utilizing the helicity formalism, we characterize the decay of $ \Xi_c^{+} $ and its secondary hyperons through asymmetry decay parameters. The complete angular distribution formula for these decays is systematically derived. Our study evaluates the sensitivity of the asymmetry parameters for the $ \Xi_c^{+} \to \Xi^{-}\pi^{+}\pi^{+} $ decay channel under various data sample sizes and beam polarization scenarios. The findings establish a robust theoretical framework for future experimental studies at the Super Tau-Charm Facility, providing valuable insights for symmetry investigations in the charm sector.

China

Yunlu Wang

Yunlong Xiao

Pengcheng Hong

Ronggang Ping

Study of P and CP symmetries in ${ \boldsymbol\Xi^{\bf +}_{\boldsymbol c}\rightarrow \boldsymbol\Xi^-\boldsymbol\pi^+\boldsymbol\pi^+ }$ at electron-positron collider

An $\textit{SU}$(3) flavor projection operator technique is implemented to construct the baryon-meson scattering amplitude within the framework of the $1/N_c$ expansion of quantum chromodynamics (QCD), where $N_c$ represents the number of color charges. The operator technique is implemented to evaluate not only the lowest-order scattering amplitude but also effects from the first-order perturbative $\textit{SU}$(3) flavor symmetry breaking and strong isospin breaking. The most general expression is obtained by explicitly accounting for the effects of the decuplet-octet baryon mass difference. At order ${\cal{O}}(1/N_c^2)$ , a large number of unknown operator coefficients appear, and therefore, there is little additional predictive power unless leading and subleading terms are retained. Although the resultant expression is sufficiently general that it can be applied to any incoming and outgoing baryons and pseudo scalar mesons, provided that the Gell-Mann--Nishijima scheme is respected, results for $N\pi\to N\pi$ scattering processes are explicitly considered.

Víctor Miguel Banda Guzmán

Rubén Flores-Mendieta

Johann Hernández

Use of $\textit{SU}$(3) flavor projection operators to construct baryon-meson scattering amplitudes in the 1/ N$_{c}$ expansion * The authors are grateful to Consejo Nacional de Humanidades, Ciencias y Tecnologías (Mexico) for support through the $\textit{Ciencia de Frontera}$ project CF-2023-I-162

In this study, we investigate the isospin-violating decays of $ B_{c}(1P)^{+}\to B_{c}^{(*)+}\pi^{0} $ , which may provide additional information for the determination of the properties of $ B_{c}(1P)^{+} $ , the first orbital excitation states of the $B_c $ meson. By assuming a dual relation between the $\textit{U}$(1) anomaly soft-gluon coupling for $ B_{c}(1P)^{+}\to B_{c}^{(*)+}\pi^{0} $ and the intermediate meson loop transitions, we can quantify the isospin-violating decay effects for these four $\textit{P}$-wave states. We observe that the partial decay width of $ B_{c0}^{*+}\to B_{c}^{+}\pi^{0} $ is approximately three orders of magnitude larger than that for $ B_{c2}^{*+}\to B_{c}^{+}\pi^{0} $ . This indicates that $ B_{c0}^{*+} $ can be established in the $ B_{c}^{+}\pi^{0} $ decay channel as a single state. Meanwhile, the two axial-vector states $ B_{c1}^{+}/B_{c1}'^{+} $ can be possibly identified in $ B_{c1}^{+}/B_{c1}'^{+}\to B_{c}^{*+}\pi^{0} $ with comparable strengths. Although these isospin-violating decays are observed to be small, the theoretical predictions should be useful for guiding future experimental efforts.

Jun Wang

Qiang Zhao

Predictions for the isospin-violating decays of ${{\boldsymbol B}_{\boldsymbol c}({\boldsymbol{1P}})^{\bf +}{\bf\to}{\boldsymbol B}_{\boldsymbol c}^{({\bf *})+}\boldsymbol\pi^{\bf 0}}$ * Supported, in part, by the National Natural Science Foundation of China (12235018), DFG and NSFC funds to the Sino-German CRC 110 'Symmetries and the Emergence of Structure in QCD' (12070131001, DFG Project-ID 196253076), National Key Basic Research Program of China (2020YFA0406300) and Strategic Priority Research Program of Chinese Academy of Sciences (XDB34030302)

Motivated by the LHCb Collaboration's observation of the doubly charmed tetraquark state <math xmlns="http://www.w3.org/1998/Math/MathML"><mrow><msub><mi>T</mi><mrow><mi>c</mi><mi>c</mi></mrow></msub><mrow><mo>(</mo><mn>3875</mn><mo>)</mo></mrow></mrow></math>, we systematically explore the potential existence of doubly charmed pentaquark states using the resonating group method within the quark delocalization color screening model framework. The effective potential of the two involved hadrons and the bound-state dynamics are included in the present work. Moreover, we have also calculated the scattering phase shifts of open channels with channel coupling, aiming to identify possible resonance states. Our estimations suggest that the existence of a bound state with quantum numbers <math xmlns="http://www.w3.org/1998/Math/MathML"><mrow><mi>I</mi><mrow><mo>(</mo><msup><mi>J</mi><mi>P</mi></msup><mo>)</mo></mrow><mo>=</mo><mfrac><mn>3</mn><mn>2</mn></mfrac><mrow><mo>(</mo><msup><mfrac><mn>5</mn><mn>2</mn></mfrac><mo>−</mo></msup><mo>)</mo></mrow></mrow></math> and a mass of approximately 4461.7 MeV. Furthermore, five resonance states are predicted through coupled-channels analysis, which are <math xmlns="http://www.w3.org/1998/Math/MathML"><mrow><msub><mi mathvariant="normal">Ξ</mi><mrow><mi>c</mi><mi>c</mi></mrow></msub><mi>ρ</mi></mrow></math> and <math xmlns="http://www.w3.org/1998/Math/MathML"><mrow><msub><mi mathvariant="normal">Σ</mi><mi>c</mi></msub><msup><mi>D</mi><mo>*</mo></msup></mrow></math> with <math xmlns="http://www.w3.org/1998/Math/MathML"><mrow><mi>I</mi><mrow><mo>(</mo><msup><mi>J</mi><mi>P</mi></msup><mo>)</mo></mrow><mo>=</mo><mfrac><mn>1</mn><mn>2</mn></mfrac><mrow><mo>(</mo><msup><mfrac><mn>1</mn><mn>2</mn></mfrac><mo>−</mo></msup><mo>)</mo></mrow></mrow><mo>,</mo><mo> </mo><mrow><msub><mi mathvariant="normal">Λ</mi><mi>c</mi></msub><msup><mi>D</mi><mo>*</mo></msup></mrow></math> and <math xmlns="http://www.w3.org/1998/Math/MathML"><mrow><msubsup><mi mathvariant="normal">Σ</mi><mrow><mi>c</mi></mrow><mo>*</mo></msubsup><msup><mi>D</mi><mo>*</mo></msup></mrow></math> with <math xmlns="http://www.w3.org/1998/Math/MathML"><mrow><mi>I</mi><mrow><mo>(</mo><msup><mi>J</mi><mi>P</mi></msup><mo>)</mo></mrow><mo>=</mo><mfrac><mn>1</mn><mn>2</mn></mfrac><mrow><mo>(</mo><msup><mfrac><mn>3</mn><mn>2</mn></mfrac><mo>−</mo></msup><mo>)</mo></mrow></mrow></math>, and <math xmlns="http://www.w3.org/1998/Math/MathML"><mrow><msub><mi mathvariant="normal">Σ</mi><mi>c</mi></msub><msup><mi>D</mi><mo>*</mo></msup></mrow></math> with <math xmlns="http://www.w3.org/1998/Math/MathML"><mrow><mi>I</mi><mrow><mo>(</mo><msup><mi>J</mi><mi>P</mi></msup><mo>)</mo></mrow><mo>=</mo><mfrac><mn>3</mn><mn>2</mn></mfrac><mrow><mo>(</mo><msup><mfrac><mn>1</mn><mn>2</mn></mfrac><mo>−</mo></msup><mo>)</mo></mrow></mrow></math>, respectively. The existence of these predicted doubly charmed pentaquark states needs to be supported by experimental measurements and discoveries. We hope future experiments will provide evidence for these states.

Xuejie Liu

Yue Tan

Xiaoyun Chen

Dianyong Chen

Hongxia Huang

Jialun Ping

Investigation of the doubly charmed analog of the <math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>P</mi><mi>c</mi></msub></math> states

In this work, we employ the quark-meson coupling model to investigate the mass shifts of <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mn>1</mn><mi>P</mi></math>-wave charmonia <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>χ</mi><mrow><mi>c</mi><mi>J</mi></mrow></msub><mo stretchy="false">(</mo><mn>1</mn><mi>P</mi><mo stretchy="false">)</mo></math> (<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>J</mi><mo>=</mo><mn>0</mn></math>, 1, 2) in cold symmetric nuclear matter by incorporating in-medium loop contributions to the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>χ</mi><mrow><mi>c</mi><mi>J</mi></mrow></msub><mo stretchy="false">(</mo><mn>1</mn><mi>P</mi><mo stretchy="false">)</mo></math> self-energy within the unquenched picture. At normal nuclear matter density, we obtain significant mass reductions of about 60 MeV for the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>χ</mi><mrow><mi>c</mi><mi>J</mi></mrow></msub><mo stretchy="false">(</mo><mn>1</mn><mi>P</mi><mo stretchy="false">)</mo></math> states, with the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>χ</mi><mrow><mi>c</mi><mn>2</mn></mrow></msub><mo stretchy="false">(</mo><mn>1</mn><mi>P</mi><mo stretchy="false">)</mo></math> mass shift primarily arising from the vector-vector loop. Our results also indicate the absence of level crossing between the in-medium <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>χ</mi><mrow><mi>c</mi><mi>J</mi></mrow></msub><mo stretchy="false">(</mo><mn>1</mn><mi>P</mi><mo stretchy="false">)</mo></math> mass and the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>D</mi><mover accent="true"><mi>D</mi><mo stretchy="false">¯</mo></mover></math> mass threshold up to <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>ρ</mi><mi>B</mi></msub><mo>&lt;</mo><mn>3</mn><msub><mi>ρ</mi><mn>0</mn></msub></math>—a feature that could be probed in the compressed baryonic matter experiment at FAIR and the beam energy scan program at RHIC.

Ze-Hua Zhang

Xiang Liu

Medium modifications of <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mn>1</mn><mi>P</mi></math>-wave charmonia <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>χ</mi><mrow><mi>c</mi><mi>J</mi></mrow></msub><mo stretchy="false">(</mo><mn>1</mn><mi>P</mi><mo stretchy="false">)</mo></math> in cold nuclear matter

The positive and negative energy modes of a field theory in <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>κ</mi></math>-Minkowski/<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>κ</mi></math>-Poincaré noncommutative spacetime have very different symmetry properties. This can be understood geometrically by considering that they span two distinct sectors of a curved momentum space. By performing an explicit direct computation of the relativistic Noether charges and their algebra within the canonical formalism, we identify a striking consequence of this asymmetry in momentum space: charge conjugation and Poincaré invariance are incompatible. We then notice how the structure of momentum space suggests that time reversal could be deformed so that the overall <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi mathvariant="script">C</mi><mi mathvariant="script">P</mi><mi mathvariant="script">T</mi></math>-invariance is restored. We prove that this new proposal works by studying the transformation properties under deformed discrete symmetries of the new relativistic charges.

Poland

Tadeusz Adach

Andrea Bevilacqua

Jerzy Kowalski-Glikman

Italy

Giacomo Rosati

Asymmetry in momentum space: Restoring <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi mathvariant="script">C</mi><mi mathvariant="script">P</mi><mi mathvariant="script">T</mi></math> invariance of <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>κ</mi></math>-field theory

This paper describes a measurement of the $$ {\Lambda}_b^0\to J/\psi \Lambda $$ branching fraction using data collected with the LHCb experiment in proton-proton collisions from 2016 to 2018. The dataset corresponds to an integrated luminosity of 5$\textit{.}$4 fb . The branching fraction is determined relative to that of $$ {B}^0\to J/\psi {K}_{\textrm{S}}^0 $$ decays,

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

M. Akthar

P. Albicocco

Germany

J. Albrecht

Lithuania

R. Aleksiejunas

F. Alessio

P. Alvarez Cartelle

R. Amalric

Brazil

S. Amato

J. Amey

Y. Amhis

L. An

L. Anderlini

M. Andersson

P. Andreola

M. Andreotti

S. Andres Estrada

A. Anelli

D. Ao

C. Arata

F. Archilli

Z. Areg

M. Argenton

Costa Rica

S. Arguedas Cuendis

L. Arnone

A. Artamonov

M. Artuso

E. Aslanides

R. Ataíde Da Silva

M. Atzeni

B. Audurier

J. Authier

D. Bacher

I. Bachiller Perea

S. Bachmann

M. Bachmayer

J. Back

P. Baladron Rodriguez

V. Balagura

A. Balboni

W. Baldini

Z. Baldwin

L. Balzani

H. Bao

J. Baptista de Souza Leite

C. Barbero Pretel

M. Barbetti

I. Barbosa

R. Barlow

M. Barnyakov

S. Barsuk

W. Barter

J. Bartz

S. Bashir

B. Batsukh

P. Battista

A. Bay

A. Beck

M. Becker

F. Bedeschi

I. Bediaga

N. Behling

S. Belin

A. Bellavista

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

Ukraine

O. Bezshyyko

J. Bhom

M. Bieker

N. Biesuz

A. Biolchini

M. Birch

F. Bishop

A. Bitadze

A. Bizzeti

Measurement of the branching fraction of the $$ {\Lambda}_b^0\to J/\psi \Lambda $$ decay and isospin asymmetry of $\textit{B → J/ψK}$ decays

This paper reports world averages of measurements of <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>b</mi></math>-hadron, <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>c</mi></math>-hadron, and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>τ</mi></math>-lepton properties obtained by the Heavy Flavor Averaging Group using results available before October 2023. In rare cases, significant results obtained several months later are also used. For the averaging, common input parameters used in the various analyses are adjusted (rescaled) to common values, and known correlations are taken into account. The averages include branching fractions, lifetimes, neutral meson mixing parameters, <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>C</mi><mi>P</mi></math> violation parameters, parameters of semileptonic decays, and Cabibbo-Kobayashi-Maskawa matrix elements.

Sw. Banerjee

F. Bernlochner

E. Bertholet

M. Bona

A. Bozek

C. Bozzi

J. Brodzicka

V. Chobanova

M. Chrzaszcz

U. Egede

M. Gersabeck

P. Goldenzweig

N. Gharbi

L. Grillo

K. Hayasaka

T. Humair

D. Johnson

T. Kuhr

O. Leroy

A. Lusiani

H.L. Ma

M. Margoni

R. Mizuk

P. Naik

T. Nanut Petric

A. Pereiro Castro

M. Prim

M. Roney

M. Rotondo

O. Schneider

C. Schwanda

A.J. Schwartz

J. Serrano

B Schwartz

A. Soffer

M. Whitehead

J. Yelton

Averages of <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>b</mi></math>-hadron, <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>c</mi></math>-hadron, and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>τ</mi></math>-lepton properties as of 2023

Motivated by the recently obtained Hadrons to Atomic nuclei from Lattice QCD potentials for the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mi>N</mi><mtext>−</mtext><mi>ϕ</mi></mrow></math>, <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mi>N</mi><mtext>−</mtext><mi>J</mi><mo>/</mo><mi>ψ</mi></mrow></math>, and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mi>N</mi><mtext>−</mtext><msub><mrow><mi>η</mi></mrow><mrow><mi>c</mi></mrow></msub></mrow></math> interactions, we investigate the structure of the exotic nuclei <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mmultiscripts><mrow><mi>Be</mi></mrow><mprescripts></mprescripts><mrow><mi>ϕ</mi></mrow><mrow><mn>8</mn></mrow></mmultiscripts></mrow></math>, <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mmultiscripts><mrow><mi>Be</mi></mrow><mprescripts></mprescripts><mrow><mi>J</mi><mo>/</mo><mi>ψ</mi></mrow><mrow><mn>8</mn></mrow></mmultiscripts></math>, and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mmultiscripts><mrow><mi>Be</mi></mrow><mprescripts></mprescripts><msub><mi>η</mi><mi>c</mi></msub><mrow><mn>8</mn></mrow></mmultiscripts></mrow></math> as <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>α</mi><mo>+</mo><mi>α</mi><mo>+</mo><mi>M</mi></math> three-body systems (<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>M</mi></math> denotes the meson). The bound and resonant states are calculated consistently using the Gaussian expansion method, with resonances identified via the complex scaling method. For the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>α</mi><mi>ϕ</mi></math> and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>α</mi></math>-charmonium interactions, a folding potential is constructed based on the Hadrons to Atomic nuclei from Lattice (HAL) QCD potentials and fitted to a Woods-Saxon form. We find that the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>ϕ</mi></math> meson exhibits a strong “gluelike” effect, binding the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msubsup><mn>0</mn><mn>1</mn><mo>+</mo></msubsup></math>, <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msubsup><mn>2</mn><mn>1</mn><mo>+</mo></msubsup></math>, and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msubsup><mn>4</mn><mn>1</mn><mo>+</mo></msubsup></math> resonant states of <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mmultiscripts><mrow><mi>Be</mi></mrow><mprescripts></mprescripts><none></none><mrow><mn>8</mn></mrow></mmultiscripts></mrow></math> into stable states and significantly reducing the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mi>α</mi><mtext>−</mtext><mi>α</mi></mrow></math> distance. In contrast, the interactions of <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>J</mi><mo>/</mo><mi>ψ</mi></math> and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>η</mi><mi>c</mi></msub></math> with the nucleus are weaker, forming only shallow bound states with the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msubsup><mn>0</mn><mn>1</mn><mo>+</mo></msubsup></math> state of <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mmultiscripts><mrow><mi>Be</mi></mrow><mprescripts></mprescripts><none></none><mrow><mn>8</mn></mrow></mmultiscripts></mrow></math> and even increasing the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mi>α</mi><mtext>−</mtext><mi>α</mi></mrow></math> separation. Notably, our analysis predicts weakly bound <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mi>α</mi><mtext>−</mtext><mi>J</mi><mo>/</mo><mi>ψ</mi></mrow></math> states in the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mrow><mmultiscripts><mrow><mi>S</mi></mrow><mprescripts></mprescripts><none></none><mrow><mn>4</mn></mrow></mmultiscripts></mrow><mrow><mn>3</mn><mo>/</mo><mn>2</mn></mrow></msub></math> and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mrow><mmultiscripts><mrow><mi>S</mi></mrow><mprescripts></mprescripts><none></none><mrow><mn>2</mn></mrow></mmultiscripts></mrow><mrow><mn>1</mn><mo>/</mo><mn>2</mn></mrow></msub></math> channels, a result not reported in prior studies, which suggests that <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mmultiscripts><mrow><mi>Be</mi></mrow><mprescripts></mprescripts><mrow><mi>J</mi><mo>/</mo><mi>ψ</mi></mrow><mrow><mn>8</mn></mrow></mmultiscripts></math> may not be a Borromean nucleus. The sensitivity of the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mmultiscripts><mrow><mi>Be</mi></mrow><mprescripts></mprescripts><mrow><mi>ϕ</mi></mrow><mrow><mn>8</mn></mrow></mmultiscripts></mrow><mo stretchy="false">(</mo><msubsup><mn>4</mn><mn>1</mn><mo>+</mo></msubsup><mo stretchy="false">)</mo></math> state—transitioning from bound to resonant depending on the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>α</mi></math>-particle radius—highlights the subtle dynamics at play. These results provide a systematic theoretical comparison of how different vector mesons modify nuclear clustering, offering critical predictions for future experimental searches of such exotic hadron-nucleus systems.

Hao Zhou

Three-body resonances of <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>α</mi><mi>α</mi><mi>M</mi></math> clusters (<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>M</mi><mo>=</mo><mi>ϕ</mi></math>, <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>J</mi><mo>/</mo><mi>ψ</mi></math>, <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>η</mi><mi>c</mi></msub></math>) in <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mmultiscripts><mrow><mi>Be</mi></mrow><mprescripts></mprescripts><mrow><mi>M</mi></mrow><mrow><mn>8</mn></mrow></mmultiscripts></mrow></math> nuclei

A four-dimensional gauge–gravity unification based on the local <math altimg='si1.svg'><mrow><mtext>SL</mtext><mo>(</mo><mn>2</mn><mi>N</mi><mo>,</mo><mi mathvariant='double-struck'>C</mi><mo>)</mo></mrow></math> symmetry is developed in a universal Yang&#8211;Mills type setting. The accompanying tetrads are promoted to dynamical fields whose invertibility condition is interpreted as a nonlinear sigma-model type length constraint. This triggers tetrad condensation and spontaneously breaks <math altimg='si1.svg'><mrow><mtext>SL</mtext><mo>(</mo><mn>2</mn><mi>N</mi><mo>,</mo><mi mathvariant='double-struck'>C</mi><mo>)</mo></mrow></math> down to <math altimg='si2.svg'><mrow><mtext>SL</mtext><mo>(</mo><mn>2</mn><mo>,</mo><mi mathvariant='double-struck'>C</mi><mo>)</mo><mo>&#215;</mo><mtext>SU</mtext><mo>(</mo><mi>N</mi><mo>)</mo></mrow></math>, effectively filtering out unobserved non-compact directions. A special ghost-free curvature-squared Lagrangian provides a consistent quadratic sector for all gauge fields involved, while an Einstein &#226;&#8364; &#8220;Cartan linear curvature term is shown to arise radiatively from fermion loops. The matter sector clearly points to a deeper elementarity of <math altimg='si1.svg'><mrow><mtext>SL</mtext><mo>(</mo><mn>2</mn><mi>N</mi><mo>,</mo><mi mathvariant='double-struck'>C</mi><mo>)</mo></mrow></math> spinors, which can be identified with preon constituents whose bound states form the observed quarks and leptons. Anomaly matching between preons and composites singles out <math altimg='si3.svg'><mrow><mtext>SL</mtext><mo>(</mo><mn>16</mn><mo>,</mo><mi mathvariant='double-struck'>C</mi><mo>)</mo></mrow></math>, accommodating precisely three composite quark-lepton families. The theory links noncompact unification, induced gravity, and fermion family structure in a single framework.

Georgia

J.L. Chkareuli

<math altimg='si1.svg'><mrow><mtext>SL</mtext><mo>(</mo><mn>2</mn><mi>N</mi><mo>,</mo><mi mathvariant='double-struck'>C</mi><mo>)</mo></mrow></math> Hyperunification: Dynamical tetrads, induced gravity and composite families