We perform a detailed comparison between three formalisms used in recent studies of $\textit{DD}$ scattering at heavier-than-physical pion masses, which aim to understand the properties of the doubly-charmed tetraquark, $$ {T}_{cc}^{+}(3875) $$ . These methods are the three-particle relativistic field theory (RFT) formalism, the two-body Lippmann-Schwinger (LS) equation with chiral effective field theory potentials, and the two-particle relativistic framework proposed by Baião Raposo and Hansen (BRH approach). In a simplified single-channel setting, we derive the conditions under which the infinite-volume integral equations from the RFT and BRH approaches reduce to the LS form. We present numerical examples showing that differences between these methods can be largely removed by adjusting short-range couplings. We also address a number of technical issues in the RFT approach.

United States

Sebastian Dawid

Switzerland

Fernando Romero-López

Stephen Sharpe

Comparison of integral equations used to study $$ {T}_{cc}^{+} $$ for a stable $\textit{D}$

The photoproduction of doubly charmed tetraquark <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>T</mi><mrow><mi>c</mi><mi>c</mi></mrow></msub></math> is predicted through the resolved channel <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>γ</mi><mo>+</mo><mi>g</mi><mo stretchy="false">→</mo><mo stretchy="false">⟨</mo><mi>c</mi><mi>c</mi><mo stretchy="false">⟩</mo><mo stretchy="false">[</mo><mi>n</mi><mo stretchy="false">]</mo><mo>+</mo><mover accent="true"><mi>c</mi><mo stretchy="false">¯</mo></mover><mo>+</mo><mover accent="true"><mi>c</mi><mo stretchy="false">¯</mo></mover><mo stretchy="false">→</mo><msub><mi>T</mi><mrow><mi>c</mi><mi>c</mi></mrow></msub><mo>+</mo><mover accent="true"><mi>c</mi><mo stretchy="false">¯</mo></mover><mo>+</mo><mover accent="true"><mi>c</mi><mo stretchy="false">¯</mo></mover></math> at ILC and CLIC. At <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mi>e</mi><mo>+</mo></msup><msup><mi>e</mi><mo>−</mo></msup></math> colliders, the initial photons <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>γ</mi></math> can be produced from two primary sources, well-delineated within the Weizäcker Williams approximation (WWA) and the laser backscattering (LBS). And the initial gluon can be emitted from the photon. The spin and color quantum number [<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>n</mi></math>] of the intermediate diquark configuration can be <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mo stretchy="false">⟨</mo><mi>c</mi><mi>c</mi><mo stretchy="false">⟩</mo><mo stretchy="false">[</mo><msub><mrow><mmultiscripts><mrow><mi>S</mi></mrow><mprescripts></mprescripts><none></none><mrow><mn>3</mn></mrow></mmultiscripts></mrow><mrow><mn>1</mn></mrow></msub><msub><mrow><mo stretchy="false">]</mo></mrow><mrow><mover accent="true"><mrow><mn>3</mn></mrow><mrow><mo stretchy="false">¯</mo></mrow></mover></mrow></msub></mrow></math>. Then its nonperturbative hadronization to <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>T</mi><mrow><mi>c</mi><mi>c</mi></mrow></msub></math> was discussed in the phenomenological potential models. Finally, the differential distributions and theoretical uncertainty of the doubly charmed tetraquark <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>T</mi><mrow><mi>c</mi><mi>c</mi></mrow></msub></math> were analyzed. As the collision energy increases, the contribution of the resolved photon channel will become increasingly significant, and it may even dominate the production of <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>T</mi><mrow><mi>c</mi><mi>c</mi></mrow></msub></math> with the laser backscattering spectrum. The conclusion is that it is promising to observe <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>T</mi><mrow><mi>c</mi><mi>c</mi></mrow></msub></math> via the resolved channel of photoproduction both at the ILC and CLIC, and the results have a strong dependence on the mass of constituent charm quark <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>m</mi><mi>c</mi></msub></math> and the potential model.

China

Juan-Juan Niu

Hong-Hao Ma

Photoproduction of doubly charmed tetraquark <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><msub><mrow><mi>T</mi></mrow><mrow><mi>c</mi><mi>c</mi></mrow></msub></mrow></math> via photon-gluon fusion at ILC and CLIC

We examine the structure scalars constructed from the orthogonal splitting of the Riemann tensor for the spacetime metric describing the interior of a charged matter configuration undergoing dissipative collapse in the framework of <math altimg='si1.svg'><mrow><mi>f</mi><mo>(</mo><mi>R</mi><mo>,</mo><mi>T</mi><mo>)</mo></mrow></math> gravity (where <math altimg='si2.svg'><mi>R</mi></math> and <math altimg='si3.svg'><mi>T</mi></math> are the Ricci scalar and the trace of energy-momentum tensor, respectively), and also the way these quantities influence the various physical parameters of the collapsing matter. In absence of dissipation, the energy density inhomogeneity is found to be influenced by the structure scalar <math altimg='si4.svg'><msub><mi>X</mi><mrow><mi>T</mi><mi>F</mi></mrow></msub></math> and the mass-function of the collapsing matter. Further, the presence of charge affects the structure scalars and the total mass-energy content. The dependence of the various physical parameters like heat dissipation, energy density inhomogeneity, evolution of the expansion scalar, the shear scalar, effective homogeneous energy density, and pressure anisotropy on the structure scalars, have been clearly indicated along with a discussion on the complexity factor of the collapsing configuration. The <math altimg='si1.svg'><mrow><mi>f</mi><mo>(</mo><mi>R</mi><mo>,</mo><mi>T</mi><mo>)</mo></mrow></math> junction conditions have been presented, showing the matching conditions for the matter Lagrangian and their derivatives at the boundary. The energy conditions are also presented and the possibility of violation of the Strong Energy Condition has been discussed.

India

Uttaran Ghosh

Sarbari Guha

Structure scalars for charged dissipative spherical collapse in <math altimg='si1.svg'><mrow><mi>f</mi><mo>(</mo><mi>R</mi><mo>,</mo><mi>T</mi><mo>)</mo></mrow></math> gravity

We study nonperturbative effects of torus partition function of the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>T</mi><mover accent="true"><mi>T</mi><mo stretchy="false">¯</mo></mover></math>-deformed 2D conformal field theory (CFT) by resurgence in this Letter and a companion paper. The deformed partition function can be written as an infinite series of the deformation parameter <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>λ</mi></math>. We develop highly efficient methods to compute perturbative coefficients in the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>λ</mi></math> expansion. To exemplify, the first 600 coefficients for the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>T</mi><mover accent="true"><mi>T</mi><mo stretchy="false">¯</mo></mover></math>-deformed free boson and free fermion are computed. The method can be generalized to any rational CFTs; we present the key idea in this Letter while relegating details and results to the companion paper. Equipped with the large order perturbative data, we provide convincing numerical evidence that the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>λ</mi></math> series is asymptotic and not Borel resummable. We extract the nonperturbative contribution by resurgence and propose that they originate from new complex saddle points after analytically continuing the modular parameters in the integral representation of the partition function. The proposal is checked by comparing the predicted asymptotic behavior of the coefficients and large order perturbative data, which match nicely. The implications of these nonperturbative contributions for the Stokes phenomenon, which relates the positive and negative signs of <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>λ</mi></math>, as well as possible comparisons with holography, is also discussed.

Jie Gu

Yunfeng Jiang

Huajia Wang

Resurgence of <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mi>T</mi><mover accent="true"><mrow><mi>T</mi></mrow><mrow><mo stretchy="false">¯</mo></mrow></mover></mrow></math>-Deformed Partition Function

We elaborate on the resurgence analysis on the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>T</mi><mover accent="true"><mi>T</mi><mo stretchy="false">¯</mo></mover></math>-deformed 2D conformal field theory (CFT). Writing the deformed partition function as an infinite series in the deformation parameter <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>λ</mi></math>, we develop efficient analytical methods to compute high-order terms of the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>λ</mi></math>-series. Based on the asymptotic behavior of the large-order perturbative series, we show that the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>λ</mi></math>-series is asymptotic and extract nonperturbative contributions by resurgence. This paper extends a previous Letter of the same authors to interacting rational CFTs, with Lee-Yang CFT as a concrete example. We also discuss possible implications of the resurgence results on holography.

Resurgent properties of <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>T</mi><mover accent="true"><mi>T</mi><mo stretchy="false">¯</mo></mover></math>-deformed conformal field theories

We complete the construction of canonical differential equations (DEs) for all families of Feynman integrals appearing in the two-loop leading-color QCD amplitude for top-pair production in association with a jet at hadron colliders. This allows us to obtain analytic results for all required Feynman integrals in terms of iterated integrals with closed-form kernels. To achieve this, we study the two-loop five-point integral family for which canonical DEs were previously unavailable due to the appearance of elliptic functions and nested square roots. In addition to marking a significant step toward next-to-next-to-leading-order QCD predictions for a high-priority LHC process, this is the first time that canonical DEs are obtained for Feynman integrals where elliptic functions appear in conjunction with the high algebraic complexity of a process with more than four particles. Our results also reveal a number of new interesting analytic features, such as a “duplet” structure that generalizes the even/odd parity of square roots to nested square roots.

Italy

Matteo Becchetti

Germany

Christoph Dlapa

Simone Zoia

Canonical differential equations for the elliptic two-loop five-point integral family relevant to <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>t</mi><mover accent="true"><mi>t</mi><mo stretchy="false">¯</mo></mover><mo>+</mo><mtext>jet</mtext></math> production at leading color

We study six-dimensional SU($\textit{n}$) gauge models with rank-reducing discrete boundary conditions on the orbifold $\textit{T}$ /$\textit{ℤ}$ , without and with continuous Wilson line phases. For the latter case, we find that a minimal model can describe the breakdown of the electroweak symmetry based on an SU(6) gauge group. This model possesses excellent features that two Higgs doublets come from the zero modes of the extra-dimensional gauge field, and the quarks in each generation can be unified into one multiplet, without exotic quarks, as the zero modes of a bulk field in the representation of SU(6). There exists a vacuum where the electroweak symmetry is slightly broken by the Hosotani mechanism, with the addition of suitable bulk fields. Interestingly, quadratic divergences are not reintroduced into the Higgs masses from the tadpole terms of the field strength localized on fixed points, not only at one-loop level but also at higher orders.

Japan

Yoshiharu Kawamura

Eiji Kodaira

Kentaro Kojima

Toshifumi Yamashita

Models with rank-reducing discrete boundary conditions on $\textit{T}$

In this work, we explore the feasibility of realizing the Dark Dimension Scenario through T-fold compactifications on $\textit{T}$ × $\textit{S}$ , where the base of the internal space $\textit{S}$ naturally acts as the requisite mesoscopic extra dimension. Utilizing Scherk-Schwarz reduction from 5D to 4D, and applying duality twists from both elliptic and parabolic conjugacy classes of subgroups of the T-duality group associated with $\textit{T}$ , we stabilize the volume of $\textit{T}$ and several other moduli. This approach generates a potential characterized by two runaway directions, one aligned with the Scherk-Schwarz radion. Further stabilization efforts yield a decreasing potential trajectory demanded by the Dark Dimension Scenario.

Netherlands

Guo-En Nian

Stefan Vandoren

Towards a string realization of the Dark Dimension via T-folds

This study explores the structure of compact stars using an extended theory of gravity known as <math altimg='si1.svg'><mi>f</mi><mo stretchy='false'>(</mo><mi mathvariant='script'>R</mi><mo>,</mo><mi mathvariant='script'>G</mi><mo>,</mo><mi mathvariant='script'>T</mi><mo stretchy='false'>)</mo></math> gravity, where <math altimg='si3.svg'><mi mathvariant='script'>R</mi></math>, is the Ricci scalar, <math altimg='si4.svg'><mi mathvariant='script'>G</mi></math>, the Gauss-Bonnet invariant, and <math altimg='si5.svg'><mi mathvariant='script'>T</mi></math> the trace of the energy-momentum tensor. Focusing on massive radio pulsars, specifically neutron stars with masses greater than 1.8 solar masses, utilize these extreme astrophysical environments to test gravity in regimes unreachable by Earth-based experiments. We adopt a linear form of the theory, <math altimg='si18.svg'><mi>f</mi><mo stretchy='false'>(</mo><mrow><mi mathvariant='script'>R</mi><mo>,</mo><mi mathvariant='script'>G</mi><mo>,</mo><mi mathvariant='script'>T</mi></mrow><mo stretchy='false'>)</mo><mo linebreak='goodbreak' linebreakstyle='after'>=</mo><mi mathvariant='script'>R</mi><mo linebreak='goodbreak' linebreakstyle='after'>+</mo><mi>&#945;</mi><mi mathvariant='script'>G</mi><mo linebreak='goodbreak' linebreakstyle='after'>+</mo><mi>&#946;</mi><mi mathvariant='script'>T</mi></math>, with <italic>&#945;</italic>, <cross-ref refid='fn0010' id='crf0390'>1</cross-ref> and <italic>&#946;</italic> are dimensional constants, and derive an exact analytical solution for anisotropic perfect fluid spheres in hydrostatic equilibrium. This model incorporates the compactness factor <math altimg='si7.svg'><mi>C</mi><mo linebreak='goodbreak' linebreakstyle='after'>=</mo><mfrac><mrow><mn>2</mn><mi>G</mi><mi>M</mi></mrow><mrow><mi>R</mi><msup><mrow><mi>c</mi></mrow><mrow><mn>2</mn></mrow></msup></mrow></mfrac></math>, to describe all physical properties within the stellar interior. To constrain the model, we employ observational data from the pulsar <italic>U</italic>1724, using its mass and radius to fix the parameters at their upper bounds: <math altimg='si8.svg'><msub><mrow><mi>&#945;</mi></mrow><mrow><mn>1</mn></mrow></msub><mo linebreak='goodbreak' linebreakstyle='after'>=</mo><mfrac><mrow><mi>&#945;</mi></mrow><mrow><msup><mrow><mi>R</mi></mrow><mrow><mn>2</mn></mrow></msup></mrow></mfrac><mo linebreak='goodbreak' linebreakstyle='after'>=</mo><mo>&#177;</mo><mn>0.023</mn></math> and <math altimg='si9.svg'><msub><mrow><mi>&#946;</mi></mrow><mrow><mn>1</mn></mrow></msub><mo linebreak='goodbreak' linebreakstyle='after'>=</mo><mfrac><mrow><mi>&#946;</mi></mrow><mrow><msup><mrow><mi>&#954;</mi></mrow><mrow><mn>2</mn></mrow></msup></mrow></mfrac><mo linebreak='goodbreak' linebreakstyle='after'>=</mo><mo>&#177;</mo><mn>0.001</mn></math>. The resulting model is consistent with physical viability and observational constraints. Notably, the squared sound speed in this framework remains below the theoretical limit ( <math altimg='si10.svg'><mmultiscripts><mrow><mtext mathvariant='normal'>c</mtext></mrow><mrow><mi>s</mi></mrow><none /><none /><mrow><mn>2</mn></mrow></mmultiscripts><mo linebreak='goodbreak' linebreakstyle='after'>&lt;</mo><msup><mrow><mi>c</mi></mrow><mrow><mn>2</mn></mrow></msup><mo stretchy='false'>/</mo><mn>3</mn></math>), contrasting with general relativity results. Without assuming a specific equation of state, the model exhibits linear behavior and predicts a core density several times higher than nuclear saturation density ( <math altimg='si11.svg'><msub><mrow><mi>&#961;</mi></mrow><mrow><mtext>nuc</mtext></mrow></msub><mo linebreak='goodbreak' linebreakstyle='after'>=</mo><mn>2.6</mn><mo>&#215;</mo><msup><mrow><mn>10</mn></mrow><mrow><mn>14</mn></mrow></msup></math> g/cm 3), with surface density <math altimg='si12.svg'><msub><mrow><mi>&#961;</mi></mrow><mrow><mi>s</mi></mrow></msub></math>, also exceeding this threshold. Additionally, the derived mass-radius relation agrees well with existing astrophysical observations.

Egypt

South Africa

G.G.L. Nashed

Constraining linear form of <math altimg='si1.svg'><mi>f</mi><mo stretchy='false'>(</mo><mrow><mi mathvariant='script'>R</mi><mo>,</mo><mi mathvariant='script'>G</mi><mo>,</mo><mi mathvariant='script'>T</mi></mrow><mo stretchy='false'>)</mo></math> gravity from astrophysical observations of the Pulsar U1724

The arrival time of electromagnetic signals traveling in chiral cosmic media is investigated in the context of Maxwell-Carroll-Field-Jackiw electrodynamics. Considering the interstellar medium (ISM) as a cold, ionized, chiral plasma, we derive the time delay between two traveling signals, expressed in terms of a modified dispersion measure (DM) which receives additional contribution from the chiral parameters. Faraday rotation angle is also addressed in this chiral plasma scenario, yielding modified rotation measures (RM). Using DMs data from five pulsars, we establish constraints on the chiral parameter magnitude at the order of <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><msup><mrow><mn>10</mn></mrow><mrow><mo>−</mo><mn>23</mn></mrow></msup><mi>–</mi><msup><mrow><mn>10</mn></mrow><mrow><mo>−</mo><mn>22</mn></mrow></msup><mtext> </mtext><mtext> </mtext><mi>GeV</mi></mrow></math>. On the other hand, the Faraday rotation retrieved from RM measurements implied upper constraints as tight as <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mn>10</mn><mrow><mo>−</mo><mn>36</mn></mrow></msup><mtext> </mtext><mtext> </mtext><mi>GeV</mi></math>.

Brazil

Filipe S. Ribeiro

Pedro D.S. Silva

Manoel M. Ferreira

Constraining <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mi>C</mi><mi>P</mi><mi>T</mi></mrow></math>-odd electromagnetic chiral parameters with pulsar timing