We investigate the discovery potential of the $T_{bc}$ state with $J^P = 0^+$ in proton-proton ( $pp$ ) collisions at LHCb at a center-of-mass energy of $\sqrt{s} = 13~{\rm{TeV}}$ . The study focuses on the decay channel $T_{bc} \to B^- D^+$ . A phenomenological approach is employed to construct the background model based on the associated production of $\textit{B}$ and $\textit{D}$ mesons, incorporating previously published LHCb results. Background processes are simulated using ${\mathtt{MadGraph5\_aMC@NLO}}$ and ${\mathtt{Pythia8.3}}$ . We explore the parameter space of the $T_{bc}$ mass, width, production cross section, and the effective double-parton scattering cross section ( $\sigma_{{\rm{eff}}}$ ) relevant for the $B D$ meson background. The integrated luminosity required for a $5\sigma$ discovery at LHCb is evaluated under various assumptions. In particular, we consider three representative $T_{bc}$ production cross section scenarios: an optimistic estimate of $103~{\rm{nb}}$ , an intermediate value of $18~{\rm{nb}}$ obtained by scaling from the $T_{cc}^+$ production cross section, and a conservative lower bound of $0.3~{\rm{nb}}$ . We find that a $5\sigma$ observation is achievable for a production cross section of $103~{\rm{nb}}$ , which is expected to be within reach during Run4. In contrast, the more realistic cross section estimate of $18~{\rm{nb}}$ requires the full Run5 dataset ( $300~{\rm{fb}}^{-1}$ ) under the most favorable parameter choices. For the conservative scenario, no significant signal would be observable even with $300~{\rm{fb}}^{-1}$ . In addition, we estimate the minimum observable $\sigma(T_{bc}) \times {\cal{B}}(T_{bc} \to $ $ B^- D^+)$ for a $5\sigma$ discovery under different luminosity scenarios, providing guidance for future experimental searches at LHCb.

China

Mingjie Feng

Yiming Li

France

Hua-Sheng Shao

Prospects for discovering strongly decaying doubly heavy T$_{bc}$ tetraquark states at LHCb * Mingjie Feng and Yiming Li is Supported by the National Natural Science Foundation of China (NSFC) (2175245, 12188102, W2443008). Hua-Sheng Shao is Supported by the European Research Council (101041109, 'BOSON') and the French National Research Agency (grant ANR-20-CE31-0015, 'PrecisOnium')

Electroweak precision tests, expressed through the oblique parameters <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>S</mi></math>, <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>T</mi></math>, and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>U</mi></math>, impose stringent constraints on physics beyond the Standard Model. Gauge extensions of the Standard Model based on the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>S</mi><mi>U</mi><mo stretchy="false">(</mo><mn>3</mn><msub><mo stretchy="false">)</mo><mi>L</mi></msub><mo>×</mo><mi>U</mi><mo stretchy="false">(</mo><mn>1</mn><msub><mo stretchy="false">)</mo><mi>N</mi></msub></math> symmetry predict a rich scalar and gauge spectrum that contribute to these parameters. Previous studies have shown that 3-3-1 gauge bosons give negligible contributions to the oblique parameters, while the contributions of the scalar sector to these parameters have received comparatively little attention. In particular, for the version of the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>S</mi><mi>U</mi><mo stretchy="false">(</mo><mn>3</mn><msub><mo stretchy="false">)</mo><mi>L</mi></msub><mo>×</mo><mi>U</mi><mo stretchy="false">(</mo><mn>1</mn><msub><mo stretchy="false">)</mo><mi>N</mi></msub></math> model with right-handed neutrinos, the impact of the scalar sector on <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>S</mi></math>, <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>T</mi></math>, and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>U</mi></math> has not yet been addressed. In this work, we fill this gap and address systematically the scalar contributions to the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>S</mi></math>, <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>T</mi></math>, and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>U</mi></math> within this version. As main result, we show that the parameter <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>T</mi></math> puts stringent constraints on the masses and energy scales associated to the spectrum of scalars of the model.

Brazil

A. Doff

C.A. de S. Pires

Scalar contributions to the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mi>S</mi></mrow></math>, <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mi>T</mi></mrow></math>, <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mi>U</mi></mrow></math> parameters in a 3-3-1 model

We investigate the spectrum of <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><msub><mrow><mi>T</mi></mrow><mrow><mi mathvariant="normal">ϒ</mi><mi mathvariant="normal">ϒ</mi></mrow></msub></mrow></math> tetraquark candidates within a coupled-channel framework. The analysis includes all <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>L</mi><mo>≤</mo><mn>2</mn></math> combinations of <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi mathvariant="normal">ϒ</mi><mo stretchy="false">(</mo><mn>1</mn><mi>S</mi><mo stretchy="false">)</mo></math>, <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi mathvariant="normal">ϒ</mi><mo stretchy="false">(</mo><mn>2</mn><mi>S</mi><mo stretchy="false">)</mo></math>, <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>η</mi><mi>b</mi></msub><mo stretchy="false">(</mo><mn>1</mn><mi>S</mi><mo stretchy="false">)</mo></math>, and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>η</mi><mi>b</mi></msub><mo stretchy="false">(</mo><mn>2</mn><mi>S</mi><mo stretchy="false">)</mo></math> in the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mi>J</mi><mi>P</mi></msup><mo>=</mo><msup><mn>0</mn><mo>±</mo></msup><mo>,</mo><msup><mn>1</mn><mo>±</mo></msup><mo>,</mo><msup><mn>2</mn><mo>±</mo></msup></math> sectors. The meson-meson interaction is derived from an underlying constituent quark model through the resonating group method, and the properties of the states are obtained from poles of the scattering matrix. We find a rich spectrum of resonant, and virtual, states distributed between the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>η</mi><mi>b</mi></msub><mo stretchy="false">(</mo><mn>1</mn><mi>S</mi><mo stretchy="false">)</mo><msub><mi>η</mi><mi>b</mi></msub><mo stretchy="false">(</mo><mn>1</mn><mi>S</mi><mo stretchy="false">)</mo></math> and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi mathvariant="normal">ϒ</mi><mo stretchy="false">(</mo><mn>2</mn><mi>S</mi><mo stretchy="false">)</mo><mi mathvariant="normal">ϒ</mi><mo stretchy="false">(</mo><mn>2</mn><mi>S</mi><mo stretchy="false">)</mo></math> thresholds. The pattern of poles exhibits approximate heavy-quark spin symmetry multiplets. Several states are dominated by a single channel and can be associated with threshold-driven structures, while higher-mass resonances show sizable mixing among channels involving radially excited bottomonia. The predicted widths range from tens to several hundred MeV. Branching ratios indicate that many states couple predominantly to final states with at least one excited bottomonium, whereas only a subset of the spectrum is expected to be visible in the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>η</mi><mi>b</mi></msub><mo stretchy="false">(</mo><mn>1</mn><mi>S</mi><mo stretchy="false">)</mo><msub><mi>η</mi><mi>b</mi></msub><mo stretchy="false">(</mo><mn>1</mn><mi>S</mi><mo stretchy="false">)</mo></math>, <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>η</mi><mi>b</mi></msub><mo stretchy="false">(</mo><mn>1</mn><mi>S</mi><mo stretchy="false">)</mo><mi mathvariant="normal">ϒ</mi><mo stretchy="false">(</mo><mn>1</mn><mi>S</mi><mo stretchy="false">)</mo></math> and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi mathvariant="normal">ϒ</mi><mo stretchy="false">(</mo><mn>1</mn><mi>S</mi><mo stretchy="false">)</mo><mi mathvariant="normal">ϒ</mi><mo stretchy="false">(</mo><mn>1</mn><mi>S</mi><mo stretchy="false">)</mo></math> channels. These results provide quantitative guidance for experimental searches of fully heavy tetraquarks and offer a test of coupled-channel dynamics and heavy-quark spin symmetry in the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>b</mi><mi>b</mi><mover accent="true"><mi>b</mi><mo stretchy="false">¯</mo></mover><mover accent="true"><mi>b</mi><mo stretchy="false">¯</mo></mover></math> sector.

Spain

P.G. Ortega

D.R. Entem

F. Fernández

J. Segovia

Exploring <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>T</mi><mrow><mi mathvariant="normal">ϒ</mi><mi mathvariant="normal">ϒ</mi></mrow></msub></math> tetraquark candidates in a coupled-channels formalism

We present a new determination of the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mover accent="true"><mi>b</mi><mo stretchy="false">¯</mo></mover><mover accent="true"><mi>b</mi><mo stretchy="false">¯</mo></mover><mi>u</mi><mi>d</mi></math> (<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mi>J</mi><mi>P</mi></msup><mo>=</mo><msup><mn>1</mn><mo>+</mo></msup></math>, <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>I</mi><mo>=</mo><mn>0</mn></math>) tetraquark binding energy using lattice quantum chromodynamics (QCD) with domain-wall light quarks and a nonperturbatively tuned three-parameter anisotropic-clover “relativistic” action for the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>b</mi></math> quarks. We also perform a direct comparison with a reanalysis of data generated in prior work using a lattice-nonrelativistic QCD (NRQCD) action for the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>b</mi></math> quarks and otherwise identical parameters. Using the new data with relativistic <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>b</mi></math> quarks from seven different ensembles with multiple lattice spacings and pion masses, we perform combined chiral and continuum extrapolations and obtain <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mo stretchy="false">(</mo><msub><mi>m</mi><msub><mi>T</mi><mrow><mi>b</mi><mi>b</mi></mrow></msub></msub><mo>−</mo><msub><mi>m</mi><mi>B</mi></msub><mo>−</mo><msub><mi>m</mi><msup><mi>B</mi><mo>*</mo></msup></msub><msub><mo stretchy="false">)</mo><mrow><mi>RHQ</mi></mrow></msub><mo>=</mo><mo stretchy="false">(</mo><mo>−</mo><mn>76</mn><mo>±</mo><mn>23</mn><mo stretchy="false">)</mo><mtext> </mtext><mtext> </mtext><mi>MeV</mi></math>. For the NRQCD data from five ensembles, we perform chiral-only extrapolations and obtain <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mo stretchy="false">(</mo><msub><mi>m</mi><msub><mi>T</mi><mrow><mi>b</mi><mi>b</mi></mrow></msub></msub><mo>−</mo><msub><mi>m</mi><mi>B</mi></msub><mo>−</mo><msub><mi>m</mi><msup><mi>B</mi><mo>*</mo></msup></msub><msub><mo stretchy="false">)</mo><mrow><mi>NRQCD</mi></mrow></msub><mo>=</mo><mspace linebreak="goodbreak"></mspace><mo stretchy="false">(</mo><mo>−</mo><mn>74</mn><mo>±</mo><mn>17</mn><mo>±</mo><mn>10</mn><mo stretchy="false">)</mo><mtext> </mtext><mtext> </mtext><mi>MeV</mi></math>. The lower magnitude of the results obtained here, compared to the original analysis in [Phys. Rev. D 100, 014503 (2019)], is due to the use of the symmetric parts of the correlation matrices with local four-quark operators only.

Germany

Jakob Hoffmann

United States

Stefan Meinel

Binding energy of the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>T</mi><mrow><mi>b</mi><mi>b</mi></mrow></msub></math> tetraquark from lattice QCD with relativistic and nonrelativistic heavy-quark actions

We study the $$ T\overline{T} $$ deformation using its formulation as a CFT coupled to two-dimensional dynamical gravity. Working within the BRST formalism, we apply the intertwiner operator method to obtain a unitary “dressing” map between undeformed CFT operators and elements of the BRST cohomology of the deformed theory. We identify the resulting “dressed” operators corresponding to CFT primaries as the physical observables of the deformed theory and show that they arise from a field-dependent change of coordinates, in agreement with what is expected for the $$ T\overline{T} $$ deformation. We then give a non-perturbative definition of deformed correlation functions as BRST-invariant expectation values of dressed operators in the gauge theory. Finally, we verify that our construction reproduces known structural and perturbative results.

United Kingdom

E. Sabbata

Italy

P. Grassi

M. Porrati

$$ T\overline{T} $$ deformations through BRST symmetry

We develop a quantization scheme for the quantum theory of a real scalar field on a class of non-commutative spacetime models collectively known as T-Minkowski. Requiring the theory to be covariant under T-Poincaré transformations, we find that for a subclass of models the Wightmann functions are equal to their commutative counterparts, and we are able to prove a Wick theorem for Wightmann functions that is structurally equivalent to the one encountered in commutative QFT. For some of these models we further extend the result to Green functions and to $\textit{N}$-point functions of interacting QFT, which we also find to be commutative, leaving no space for IR/UV mixing effects advocated in other approaches to noncommutative QFT.

Giuseppe Fabiano

Flavio Mercati

Covariant quantization of field theories on T-Minkowski noncommutative spacetimes

We study Higgs-boson production in association with a top-quark pair ( $$ t\overline{t}H $$ ) at hadron colliders and present the first matching of next-to-next-to-leading order (NNLO) QCD corrections to parton showers using the M NNLO method. For the two-loop amplitude, we employ two established approximations, based on the soft Higgs-boson and high-energy limits, respectively. For the first time, we also construct the latter in full colour and propose a pointwise combination of the two approximations across phase space. By assigning a conservative uncertainty estimate, which remains well below the perturbative uncertainties, we ensure robust and reliable differential predictions, explicitly validated at the one-loop level. Apart from the two-loop amplitude, all remaining ingredients of the M NNLO calculation are included exactly. After thorough validation, we present a series of phenomenological results illustrating the impact of NNLO corrections and parton-shower effects. We consider fiducial predictions for the Higgs-boson decay into photons and include off-shell top-quark decays with tree-level spin correlations in both the dilepton and semileptonic channels.

Switzerland

Christian Biello

Chiara Savoini

Chiara Signorile-Signorile

Marius Wiesemann

Next-to-next-to-leading order event generation for $$ t\overline{t}H $$ production with approximate two-loop amplitude

Type-IIB string theory on <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mtext>AdS</mtext><mn>3</mn></msub><mo>×</mo><msup><mi>S</mi><mn>3</mn></msup><mo>×</mo><msup><mi>T</mi><mn>4</mn></msup></math> with Ramond–Ramond flux as the near-horizon limit of the D1-D5 solution is expected to be dual to a (4, 4) supersymmetric 2D conformal field theory (CFT) parametrized by the integers <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>Q</mi><mn>1</mn></msub></math>, <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>Q</mi><mn>5</mn></msub></math>, and other moduli. It is related by T-duality to type-IIA string theory in the near-horizon limit of the D2-D4 solution, which admits an uplift to the 11D <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mtext>AdS</mtext><mn>3</mn></msub><mo>×</mo><msup><mi>S</mi><mn>3</mn></msup><mo>×</mo><msup><mi>T</mi><mn>5</mn></msup></math> background which is the near-horizon limit of the M2-M5 solution. We point out that this relation allows one to use the quantum M2-brane description to probe “nonplanar” corrections in the dual 2D CFT, in close analogy with the Aharony-Bergman-Jafferis-Maldacena (ABJM) theory case (described by M-theory on <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mtext>AdS</mtext><mn>4</mn></msub><mo>×</mo><msup><mi>S</mi><mn>7</mn></msup><mo>/</mo><msub><mi mathvariant="double-struck">Z</mi><mi>k</mi></msub></math>). We consider an analog of a supersymmetric Wilson loop (line defect) expectation value represented by a type-IIA string partition function expanded around an <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mtext>AdS</mtext><mn>2</mn></msub><mo>⊂</mo><msub><mtext>AdS</mtext><mn>3</mn></msub></math> minimal surface. Its M-theory analog is the M2-brane partition function expanded near <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mtext>AdS</mtext><mn>2</mn></msub><mo>×</mo><msup><mi>S</mi><mn>1</mn></msup></math>. We compute the one-loop contribution <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>Z</mi><mn>1</mn></msub></math> to the M2-brane partition function and find that in contrast to the ABJM case in arXiv:2303.15207 [where <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>Z</mi><mn>1</mn></msub><mo>=</mo><mo stretchy="false">(</mo><mn>2</mn><mi>sin</mi><mfrac><mrow><mn>2</mn><mi>π</mi></mrow><mi>k</mi></mfrac><msup><mo stretchy="false">)</mo><mrow><mo>−</mo><mn>1</mn></mrow></msup><mo>=</mo><mfrac><mi>k</mi><mrow><mn>4</mn><mi>π</mi></mrow></mfrac><mo>+</mo><mfrac><mi>π</mi><mrow><mn>6</mn><mi>k</mi></mrow></mfrac><mo>+</mo><mo>⋯</mo></math> contains an infinite series of higher-genera string corrections, <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mi>k</mi><mrow><mo>−</mo><mn>1</mn></mrow></msup><mo>∼</mo><mfrac><msub><mi>g</mi><mi>s</mi></msub><msqrt><mi mathvariant="normal">T</mi></msqrt></mfrac></math>], here it is given solely by the leading string theory contribution <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>Z</mi><mn>1</mn></msub><mo>=</mo><mfrac><mi>κ</mi><msqrt><mrow><mn>2</mn><mi>π</mi></mrow></msqrt></mfrac></math>, where <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>κ</mi><mo>∼</mo><msqrt><msub><mi>Q</mi><mn>5</mn></msub></msqrt></math> plays a role analogous to <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>k</mi></math>. We also discuss a generalization to the mixed-flux case which is straightforward from the 11D perspective.

Arkady A. Tseytlin

Zihan Wang

Wilson loop in <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><msub><mrow><mi>AdS</mi></mrow><mrow><mn>3</mn></mrow></msub><mo>×</mo><msup><mi>S</mi><mn>3</mn></msup><mo>×</mo><msup><mi>T</mi><mn>4</mn></msup></mrow></math> from quantum M2 brane

The present study analyzes anisotropic compact objects coupled with the electromagnetic field within the context of <italic>f</italic>( <italic>R, T</italic>) gravity. We obtain two novel solutions of modified field equations for a static charged spacetime. To simplify the system, we employ two different assumptions for the radial metric component and specific anisotropic pressure profiles, and obtain exact analytical solutions. The governing field equations in both models yield differential equations whose general solutions contain undetermined constants. These constants are evaluated through the junction conditions between the interior and the exterior Reissner-Nordstr&#246;m spacetimes across the boundary surface. In this regard, we also impose the condition that the radial pressure drops to zero on the star&#8217;s interface. Furthermore, we examine the fundamental prerequisites that must be fulfilled for physical existence of compact objects. For graphical analysis, we consider the observed data of two stars, LMC X-4 and SMC X-4, together with multiple parametric values. Our findings demonstrate that both resulting solutions satisfy the essential physical requirements under the considered modified gravitational framework for certain values of the charge and model parameter.

Pakistan

Hira Shadab

Azerbaijan

M. Sharif

Tayyab Naseer

Role of electric charge in the construction of relativistic stellar solutions in <italic>f</italic>( <italic>R, T</italic>) gravity

Recent studies suggest that applying the Buscher rules to the dimensional reduction of ten-dimensional, one-loop effective actions generate “purely stringy” couplings in nine dimensions that cannot be lifted to a local, covariant form in ten dimensions. We investigate this phenomenon at order $$\alpha '^3$$ in type IIA string theory. By computing the circular reduction of the one-loop Chern–Simons term and pure-gravity couplings in type IIA theory and applying the T-duality transformation to the resulting couplings, we derive their counterparts in the type IIB effective action. We demonstrate that the resulting nine-dimensional type IIB couplings are invariant under S-duality without requiring contributions from the tree-level effective action or non-perturbative effects. As a consistency check, we show that the nine-dimensional type IIB couplings, when reduced on a K3 surface, reproduce the known heterotic string couplings on $$ T^5 $$ at order $$ \alpha ' $$ , via the duality between the two theories.

Iran

Mohammad Garousi

The emergence of inherently 9-dimensional one-loop effective action from T-duality