In the present work, we investigate the long-distance contributions to light hadrons and radiative decays of <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>η</mi><mi>c</mi></msub></math>, where the long-distance contribution is phenomenologically described by the meson loops. Our estimations indicate that the branching fractions of <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><msub><mrow><mi>η</mi></mrow><mrow><mi>c</mi></mrow></msub><mo stretchy="false">→</mo><mrow><mi mathvariant="script">V</mi><mi mathvariant="script">V</mi></mrow><mo>,</mo><mi mathvariant="script">V</mi><mo>=</mo><mo stretchy="false">(</mo><mi>ρ</mi><mo>,</mo><mi>ω</mi><mo>,</mo><mi>ϕ</mi><mo stretchy="false">)</mo></mrow></math>, can be roughly reproduced in the range <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mn>1.4</mn><mo>&lt;</mo><mi>α</mi><mo>&lt;</mo><mn>1.6</mn></math>, while the parameter range for <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>η</mi><mi>c</mi></msub><mo stretchy="false">→</mo><mi>γ</mi><mi mathvariant="script">V</mi></math> is determined by the similarity of <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>η</mi><mi>c</mi></msub><mo stretchy="false">→</mo><mi>γ</mi><mi mathvariant="script">V</mi><mo>/</mo><mrow><mi mathvariant="script">V</mi><mi mathvariant="script">V</mi></mrow></math> and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>χ</mi><mrow><mi>c</mi><mn>1</mn></mrow></msub><mo stretchy="false">→</mo><mi>γ</mi><mi mathvariant="script">V</mi><mo>/</mo><mrow><mi mathvariant="script">V</mi><mi mathvariant="script">V</mi></mrow></math>. In this parameter range, our estimations indicate that the branching fractions for the processes <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>η</mi><mi>c</mi></msub><mo stretchy="false">→</mo><mi>γ</mi><msup><mi>ρ</mi><mn>0</mn></msup></math> and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>η</mi><mi>c</mi></msub><mo stretchy="false">→</mo><mi>γ</mi><mi>ω</mi></math> are of the order of <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mn>10</mn><mrow><mo>−</mo><mn>4</mn></mrow></msup></math>, while the one for the process <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>η</mi><mi>c</mi></msub><mo stretchy="false">→</mo><mi>γ</mi><mi>ϕ</mi></math> is of the order of <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mn>10</mn><mrow><mo>−</mo><mn>5</mn></mrow></msup></math>. The estimations in the present work are expected to be accessible by future experiments at BESIII and Belle II.

China

Xiao-Yu Qi

Qi Wu

Dian-Yong Chen

Long-distance contributions to light vector mesons and radiative decays of <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>η</mi><mi>c</mi></msub></math>

The LHCb Collaboration has recently reported the first observation of the decay $${\bar{B}}_s^0\rightarrow \Lambda _c^+\bar{\Lambda }_c^-$$ , along with measurements of the branching fractions for both $${\bar{B}}^0\rightarrow \Lambda _c^+\bar{\Lambda }_c^-$$ and $${\bar{B}}_s^0\rightarrow \Lambda _c^+\bar{\Lambda }_c^-$$ . In this work, we investigate these two decays within the framework of final state re-scattering. Our results show that the predicted branching fractions are consistent with the experimental measurements, which indicates the significant role of long-distance final-state interactions in such baryonic $\textit{B}$ decays. Furthermore, we present predictions for the direct CP asymmetries and the asymmetry parameters. Numerically, both decays exhibit nearly vanishing direct CP asymmetries and suppressed longitudinal polarizations $$\alpha $$ , whereas the sizable values of $$\beta $$ and $$\gamma $$ reflect strong interference between the two helicity amplitudes and provide sensitive probes of the decay dynamics.

Zhu-Ding Duan

Xiao Huang

Dong-Hao Li

Run-Hui Li

Germany

Jian-Peng Wang

Fu-Sheng Yu

Final-state rescattering in $$\bar{B}^{0}_{(s)}\rightarrow \Lambda ^{+}_{c}\bar{\Lambda }^{-}_{c}$$ decays

Where does the Standard Model’s internal structure come from? Treating <math altimg='si18.svg'><mrow><mi mathvariant='double-struck'>O</mi><mo>&#8853;</mo><mi mathvariant='double-struck'>H</mi><mo>&#8853;</mo><mi mathvariant='double-struck'>C</mi><mo>&#8853;</mo><mi mathvariant='double-struck'>R</mi></mrow></math> as a module for its own multiplication algebra enables a particular origin story for the Standard Model&#8217;s pre-Higgs, <math altimg='si19.svg'><mrow><msub><mi mathvariant='fraktur'>g</mi><mtext>SM</mtext></msub><mo>:</mo><mo>=</mo><mi mathvariant='fraktur'>su</mi><msub><mrow><mo>(</mo><mn>3</mn><mo>)</mo></mrow><mi>C</mi></msub><mo>&#8853;</mo><mi mathvariant='fraktur'>su</mi><msub><mrow><mo>(</mo><mn>2</mn><mo>)</mo></mrow><mi>L</mi></msub><mo>&#8853;</mo><mi mathvariant='fraktur'>u</mi><msub><mrow><mo>(</mo><mn>1</mn><mo>)</mo></mrow><mi>Y</mi></msub><mo>,</mo></mrow></math> and low energy post-Higgs, <math altimg='si20.svg'><mrow><msub><mi mathvariant='fraktur'>g</mi><mtext>LE</mtext></msub><mo>:</mo><mo>=</mo><mi mathvariant='fraktur'>su</mi><msub><mrow><mo>(</mo><mn>3</mn><mo>)</mo></mrow><mi>C</mi></msub><mo>&#8853;</mo><mi mathvariant='fraktur'>u</mi><msub><mrow><mo>(</mo><mn>1</mn><mo>)</mo></mrow><mi>Q</mi></msub><mo>,</mo></mrow></math> symmetries. In this model, weak hypercharge and electric charge operators, <italic>Y</italic> and <italic>Q</italic>, take on a remarkably simple form: <math altimg='si21.svg'><mrow><mo>&#8721;</mo><mfrac><mn>1</mn><mi>n</mi></mfrac><msub><mi mathvariant='double-struck'>I</mi><mrow><mi>n</mi><mo>&#215;</mo><mi>n</mi></mrow></msub></mrow></math>.

Poland

N. Furey

Standard model symmetries and the nested embeddings of <math altimg='si17.svg'><mrow><mi mathvariant='double-struck'>R</mi><mo>&#8834;</mo><mi mathvariant='double-struck'>C</mi><mo>&#8834;</mo><mi mathvariant='double-struck'>H</mi><mo>&#8834;</mo><mi mathvariant='double-struck'>O</mi></mrow></math>

We study a family of genuinely exotic five-flavor molecular pentaquark states containing the five quark flavors <italic>u, d, s, c, b</italic> that form experimentally accessible hadrons. We construct the meson-baryon interaction from the local hidden gauge symmetry combined with heavy-quark spin symmetry, following the chiral unitary description that reproduces the LHCb hidden-charm strange pentaquarks. Heavy-quark flavor symmetry allows us to obtain the <math altimg='si16.svg'><mrow><mi>u</mi><mi>d</mi><mi>s</mi><mi>c</mi><mover accent='true'><mi>b</mi><mo>&#175;</mo></mover></mrow></math> sector by replacing the anti-charm quark in the meson with an anti-bottom quark while keeping the charm quark in the baryon. As a result, we obtain ten threshold-associated isoscalar poles with <math altimg='si56.svg'><mrow><msup><mi>J</mi><mi>P</mi></msup><mo linebreak='goodbreak'>=</mo><mn>1</mn><mo linebreak='goodbreak'>/</mo><msup><mn>2</mn><mo>&#8722;</mo></msup><mo>,</mo><mn>3</mn><mo linebreak='goodbreak'>/</mo><msup><mn>2</mn><mo>&#8722;</mo></msup><mo>,</mo><mn>5</mn><mo linebreak='goodbreak'>/</mo><msup><mn>2</mn><mo>&#8722;</mo></msup></mrow></math> in the range 7.72 to 7.96 GeV. They are narrow and organized into heavy-quark spin multiplets with predicted near-degeneracies. The loop subtraction constant, the single scheme parameter, is not adjusted by hand. Requiring the loop function at threshold to be independent of the heavy flavor fixes <math altimg='si57.svg'><mrow><mi>a</mi><mo>&#8771;</mo><mo>&#8722;</mo><mn>3.2</mn></mrow></math> to <math altimg='si58.svg'><mrow><mo>&#8722;</mo><mn>3.4</mn></mrow></math> from the charm sector, consistent with the value <math altimg='si14.svg'><mrow><mi>a</mi><mo linebreak='goodbreak'>=</mo><mo>&#8722;</mo><mn>3.1</mn></mrow></math> used in the earlier two-sector study, and the predicted masses move by several tens of MeV when <italic>a</italic> varies between <math altimg='si46.svg'><mrow><mo>&#8722;</mo><mn>2.9</mn></mrow></math> and <math altimg='si49.svg'><mrow><mo>&#8722;</mo><mn>3.2</mn></mrow></math>. There are four states that overlap with the earlier two-sector study in the literature to about 2 MeV, which shows that the separate-sector treatment is recovered as a limit of this work. Moreover, the strongly coupled <italic>B</italic>*&#926; <inf><italic>c</italic></inf> and <math altimg='si6.svg'><mrow><msubsup><mi>B</mi><mi>s</mi><mo>*</mo></msubsup><msub><mstyle mathvariant='normal'><mi>&#923;</mi></mstyle><mi>c</mi></msub></mrow></math> channels support additional deeply bound poles. We show that their number and positions depend on the regularization scheme, and we quantify this dependence by comparing dimensional regularization with a cutoff scheme. The resulting states provide a signal that can be searched for at LHCb in the <italic>B<inf>c</inf></italic>&#923; and <math altimg='si6.svg'><mrow><msubsup><mi>B</mi><mi>s</mi><mo>*</mo></msubsup><msub><mstyle mathvariant='normal'><mi>&#923;</mi></mstyle><mi>c</mi></msub></mrow></math> invariant mass spectra in the window 7.60 to 7.77 GeV.

Thailand

Ratirat Suntharawirat

Nongnapat Ponkhuha

Daris Samart

Five-flavor <math altimg='si16.svg'><mrow><mi>u</mi><mi>d</mi><mi>s</mi><mi>c</mi><mover accent='true'><mi>b</mi><mo>&#175;</mo></mover></mrow></math> molecular pentaquarks from heavy-quark and local hidden gauge symmetries

We perform a systematic QCD sum rule study of light tetraquark states with <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mi>J</mi><mrow><mi>P</mi><mi>C</mi></mrow></msup><mo>=</mo><msup><mn>1</mn><mrow><mo>−</mo><mo>−</mo></mrow></msup></math> in the diquark-antidiquark picture. A complete set of local interpolating currents is constructed and projected onto six flavor-isospin configurations (<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>q</mi><mo>=</mo><mi>u</mi><mo>/</mo><mi>d</mi></math>): the isoscalar <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>q</mi><mi>q</mi><mover accent="true"><mi>q</mi><mo stretchy="false">¯</mo></mover><mover accent="true"><mi>q</mi><mo stretchy="false">¯</mo></mover></math>, <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>q</mi><mi>s</mi><mover accent="true"><mi>q</mi><mo stretchy="false">¯</mo></mover><mover accent="true"><mi>s</mi><mo stretchy="false">¯</mo></mover></math>, and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>s</mi><mi>s</mi><mover accent="true"><mi>s</mi><mo stretchy="false">¯</mo></mover><mover accent="true"><mi>s</mi><mo stretchy="false">¯</mo></mover></math> sectors, the isovector <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>q</mi><mi>q</mi><mover accent="true"><mi>q</mi><mo stretchy="false">¯</mo></mover><mover accent="true"><mi>q</mi><mo stretchy="false">¯</mo></mover></math> and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>q</mi><mi>s</mi><mover accent="true"><mi>q</mi><mo stretchy="false">¯</mo></mover><mover accent="true"><mi>s</mi><mo stretchy="false">¯</mo></mover></math> sectors, and the isotensor <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>q</mi><mi>q</mi><mover accent="true"><mi>q</mi><mo stretchy="false">¯</mo></mover><mover accent="true"><mi>q</mi><mo stretchy="false">¯</mo></mover></math> sector. From the nonderivative currents studied in the present work, the extracted masses of the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>q</mi><mi>q</mi><mover accent="true"><mi>q</mi><mo stretchy="false">¯</mo></mover><mover accent="true"><mi>q</mi><mo stretchy="false">¯</mo></mover></math>, <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>q</mi><mi>s</mi><mover accent="true"><mi>q</mi><mo stretchy="false">¯</mo></mover><mover accent="true"><mi>s</mi><mo stretchy="false">¯</mo></mover></math>, and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>s</mi><mi>s</mi><mover accent="true"><mi>s</mi><mo stretchy="false">¯</mo></mover><mover accent="true"><mi>s</mi><mo stretchy="false">¯</mo></mover></math> configurations lie in the ranges 1.53–2.37 GeV, 1.86–2.51 GeV, and 2.46–2.60 GeV, respectively. For the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>s</mi><mi>s</mi><mover accent="true"><mi>s</mi><mo stretchy="false">¯</mo></mover><mover accent="true"><mi>s</mi><mo stretchy="false">¯</mo></mover></math> vector sector, we also quote the previous derivative-current result <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msubsup><mn>2.34</mn><mrow><mo>−</mo><mn>0.30</mn></mrow><mrow><mo>+</mo><mn>0.23</mn></mrow></msubsup><mtext> </mtext><mtext> </mtext><mi>GeV</mi></math> as a complementary benchmark. We further compare the present <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mn>1</mn><mrow><mo>−</mo><mo>−</mo></mrow></msup></math> tetraquark spectrum with previous QCD sum rule results for the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mn>1</mn><mrow><mo>−</mo><mo>+</mo></mrow></msup></math> tetraquark and hybrid states [N. Su, E.-L. Cui, Y.-W. Jiang, and H.-X. Chen, <a href="http://dx.doi.org/10.1140/epjc/s10052-026-15939-y">Eur. Phys. J. C 86, 724 (2026)</a>.], aiming to provide useful information for distinguishing tetraquark and hybrid configurations in the light hadron spectrum. As an additional improvement, we complete the previously missing isotensor <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mn>1</mn><mrow><mo>−</mo><mo>+</mo></mrow></msup></math> tetraquark entry and obtain its lowest mass to be <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>M</mi><mo>=</mo><mn>2.1</mn><msubsup><mn>9</mn><mrow><mo>−</mo><mn>0.24</mn></mrow><mrow><mo>+</mo><mn>0.26</mn></mrow></msubsup><mtext> </mtext><mtext> </mtext><mi>GeV</mi></math>, which is included in the spectral comparison.

Yi-Wei Jiang

Hua-Xing Chen

Er-Liang Cui

Ding-Kun Lian

Wen-Ying Liu

Niu Su

Light tetraquark states with <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mi>J</mi><mrow><mi>P</mi><mi>C</mi></mrow></msup><mo>=</mo><msup><mn>1</mn><mrow><mo>−</mo><mo>−</mo></mrow></msup></math> from QCD sum rules

The topological susceptibility of the QCD vacuum provides an understanding of <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>θ</mi></math> vacua as vacua of a Chern-Simons gauge theory. In this way, it gives an immediate proof of the physicality of the boundary <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>θ</mi></math>-term. This makes the essence of the strong-<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>C</mi><mi>P</mi></math> puzzle very transparent and offers a solution in form of the gauge axion, which has exact quality. This axion represents an intrinsic part of the QCD gauge redundancy without any reference to an anomalous global symmetry. It is a two-form transforming under the QCD gauge symmetry. Because of its pure-gauge nature, the gauge axion represents a powerful tool to monitor physics of <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>θ</mi></math> vacua in various regimes. Unlike the ordinary Peccei-Quinn axion, which is UV completed into a Goldstone phase of a complex scalar and thereby suffers from the quality problem, the gauge axion is UV completed directly into a fundamental theory of gravity. We study the domain wall and string structure of the gauge axion and show that the strings sourcing it must be a part of this fundamental theory. We thus observe that the absence of the axion quality problem motivates the presence of fundamental strings. This provides a new argument for a connection between the axion and gravity.

Gia Dvali

Lucy Komisel

Otari Sakhelashvili

United States

Anja Wachowitz

Strong <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>C</mi><mi>P</mi></math> problem and its gauge axion solution as evidence for fundamental strings

We consider the photon-energy spectrum of the inclusive radiative decay $\textit{B}$ → $\textit{X}$ $\textit{γ}$, induced by the electromagnetic dipole operator $\textit{O}$ , to next-to-next-to-next-to-leading order and calculate the complete corrections for light fermions, for the contributions with two closed massive fermion loops, and for the limit of large QCD colour factors $\textit{N}$ in the remaining part. We discuss the integrated decay rate both without and with a cut on the photon energy. In addition to the on-shell renormalization of the bottom-quark mass, we also consider the kinetic mass and the MSR mass schemes. The latter two lead to an improved perturbative behaviour of the decay rate.

Italy

Matteo Fael

Switzerland

Fabian Lange

Kay Schönwald

Matthias Steinhauser

The photon-energy spectrum in $\textit{B}$ → $\textit{X}$ $\textit{s}$ $\textit{γ}$ to N3LO: light-fermion and large-$\textit{N}$ c corrections

We point out several algebraic and dimensional inconsistencies in the derivation of the teleparallel double-wall dynamics and of the axial torsion coupling bound published in this Journal [Eur. Phys. J. C (2026) 86: 785]. Recomputing the torsion two-forms from the tetrads with vanishing spin connection, we obtain expressions that differ from those used in the paper. Consequently, the equations for the wall separation function do not lead to the reported solution, and the approximation $$h^2\ll z^2$$ does not restore the polynomial form adopted there. We also show that the proposed wave equation for the wall separation and the corresponding gravitational-wave interpretation require rederivation. In the fermionic sector, the zero-mode solutions and the scalar Dirac bilinear must be distinguished from the positive density $$\varPsi ^\dagger \varPsi $$ . With the corrected solutions, the effective coefficient $$A=eB+g_T S$$ determines a localization length $$\ell _{\textrm{loc}}\sim |A|^{-1/2}$$ , so that estimating $$g_T$$ requires specifying an additional physical scale rather than imposing $$A=0$$ . Hence the claimed constant condensate and the bound $$g_T\sim 10^{-4}$$ are not established by the calculations presented.

Brazil

Luis Castro

Comment on “Einstein–Cartan fermion condensates trapped in double walls induce axial torsion coupling bounds [Eur. Phys. J. C (2026) 86: 785]”

Motivated by the recent observation of the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msubsup><mi>B</mi><mi>c</mi><mo>*</mo></msubsup></math> meson by the ATLAS Collaboration and its promising discovery potential at future high-luminosity colliders, we investigate the semileptonic decays <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msubsup><mover accent="true"><mi>B</mi><mo stretchy="false">¯</mo></mover><mi>c</mi><mo>*</mo></msubsup><mo stretchy="false">→</mo><mo stretchy="false">(</mo><mi>P</mi><mo>,</mo><mi>V</mi><mo stretchy="false">)</mo><msup><mo>ℓ</mo><mo>−</mo></msup><msub><mover accent="true"><mi>ν</mi><mo stretchy="false">¯</mo></mover><mo>ℓ</mo></msub></math> (<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>P</mi><mo>=</mo><mi>D</mi></math>, <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>B</mi><mrow><mi>d</mi><mo>,</mo><mi>s</mi></mrow></msub></math>, <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>η</mi><mi>c</mi></msub><mo stretchy="false">(</mo><mn>1</mn><mi>S</mi><mo>,</mo><mn>2</mn><mi>S</mi><mo>,</mo><mn>3</mn><mi>S</mi><mo stretchy="false">)</mo></math>; <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>V</mi><mo>=</mo><msup><mi>D</mi><mo>*</mo></msup></math>, <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msubsup><mi>B</mi><mrow><mi>d</mi><mo>,</mo><mi>s</mi></mrow><mo>*</mo></msubsup></math>, <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>ψ</mi><mo stretchy="false">(</mo><mn>1</mn><mi>S</mi><mo>,</mo><mn>2</mn><mi>S</mi><mo>,</mo><mn>3</mn><mi>S</mi><mo stretchy="false">)</mo></math>) in the Standard Model. Using the relevant form factors obtained in the self-consistent covariant light-front quark model, we present theoretical predictions for several physical observables, including the branching fraction, the ratios of branching fractions <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>R</mi><mrow><mo stretchy="false">(</mo><mi>L</mi><mo stretchy="false">)</mo></mrow></msub></math>, the longitudinal polarization fraction of the daughter vector meson, the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>τ</mi></math> lepton spin asymmetry, and the forward-backward asymmetry. It is found that the branching fractions for the Cabibbo-favored <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msubsup><mover accent="true"><mi>B</mi><mo stretchy="false">¯</mo></mover><mi>c</mi><mo>*</mo></msubsup><mo stretchy="false">→</mo><msubsup><mover accent="true"><mi>B</mi><mo stretchy="false">¯</mo></mover><mi>s</mi><mo>*</mo></msubsup><msup><mi>e</mi><mo>−</mo></msup><msub><mover accent="true"><mi>ν</mi><mo stretchy="false">¯</mo></mover><mi>e</mi></msub></math> and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msubsup><mover accent="true"><mi>B</mi><mo stretchy="false">¯</mo></mover><mi>s</mi><mo>*</mo></msubsup><msup><mi>μ</mi><mo>−</mo></msup><msub><mover accent="true"><mi>ν</mi><mo stretchy="false">¯</mo></mover><mi>μ</mi></msub></math> decays reach the order of <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi mathvariant="script">O</mi><mo stretchy="false">(</mo><msup><mn>10</mn><mrow><mo>−</mo><mn>6</mn></mrow></msup><mo stretchy="false">)</mo></math>, which might be firstly observed at the future high-luminosity Large Hadron Collider.

Qin Chang

Jianying Qian

Liting Wang

Xiaolin Wang

Shuai Xu

Jie Zhu

Semileptonic <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msubsup><mover accent="true"><mi>B</mi><mo stretchy="false">¯</mo></mover><mi>c</mi><mo>*</mo></msubsup><mo stretchy="false">→</mo><mo stretchy="false">(</mo><mi>P</mi><mo>,</mo><mi>V</mi><mo stretchy="false">)</mo><msup><mo>ℓ</mo><mo>−</mo></msup><msub><mover accent="true"><mi>ν</mi><mo stretchy="false">¯</mo></mover><mo>ℓ</mo></msub></math> decays within the self-consistent light-front quark model

The double-logarithmic series of non-relativistic $\textit{B}$ → $\textit{η}$ form factors at large recoil is governed by a coupled set of integral equations, reflecting an intricate interplay between arbitrarily many soft-quark and soft-gluon exchanges. Whereas we previously derived these integral equations with diagrammatic resummation techniques, we analyze the form factors with methods from Soft-Collinear Effective Theory (SCET) in this work. Although the resulting factorization theorem for the so-called soft-overlap contribution is known to be spoilt by endpoint divergences, it can still be used at the level of bare (regularized) quantities at any fixed order in perturbation theory. By calculating the required ingredients, we show that the SCET analysis confirms the predictions of the integral equations up to three-loop order. We also argue that the iterative structure and the intertwined soft-quark and soft-gluon effects can be derived from standard renormalization-group equations of the $\textit{B}$ -meson light-cone distribution amplitudes, provided their inverse moments are regularized with an appropriate cutoff.

Guido Bell

Philipp Böer

Thorsten Feldmann

Dennis Horstmann

Vladyslav Shtabovenko

$\textit{B}$ $\textit{c}$ $\textit{ → η}$ $\textit{c}$ form factors at large recoil: SCET analysis and a three-loop consistency check