We present a determination of the Cabibbo-Kobayashi-Maskawa matrix element <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mo stretchy="false">|</mo><msub><mi>V</mi><mrow><mi>c</mi><mi>b</mi></mrow></msub><mo stretchy="false">|</mo></math> from the decay <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>B</mi><mo stretchy="false">→</mo><mi>D</mi><mo>ℓ</mo><msub><mi>ν</mi><mo>ℓ</mo></msub></math> using a <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mn>365</mn><mtext> </mtext><mtext> </mtext><msup><mi>fb</mi><mrow><mo>−</mo><mn>1</mn></mrow></msup></math> <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><mo stretchy="false">→</mo><mi mathvariant="normal">ϒ</mi><mo stretchy="false">(</mo><mn>4</mn><mi>S</mi><mo stretchy="false">)</mo><mo stretchy="false">→</mo><mi>B</mi><mover accent="true"><mi>B</mi><mo stretchy="false">¯</mo></mover></math> data sample recorded by the Belle II experiment at the SuperKEKB collider. The semileptonic decay of one <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>B</mi></math> meson is reconstructed in the modes <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mi>B</mi><mn>0</mn></msup><mo stretchy="false">→</mo><msup><mi>D</mi><mo>−</mo></msup><mo stretchy="false">(</mo><mo stretchy="false">→</mo><msup><mi>K</mi><mo>+</mo></msup><msup><mi>π</mi><mo>−</mo></msup><msup><mi>π</mi><mo>−</mo></msup><mo stretchy="false">)</mo><msup><mo>ℓ</mo><mo>+</mo></msup><msub><mi>ν</mi><mo>ℓ</mo></msub></math> and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mi>B</mi><mo>+</mo></msup><mo stretchy="false">→</mo><msup><mover accent="true"><mi>D</mi><mo stretchy="false">¯</mo></mover><mn>0</mn></msup><mo stretchy="false">(</mo><mo stretchy="false">→</mo><msup><mi>K</mi><mo>+</mo></msup><msup><mi>π</mi><mo>−</mo></msup><mo stretchy="false">)</mo><msup><mo>ℓ</mo><mo>+</mo></msup><msub><mi>ν</mi><mo>ℓ</mo></msub></math>, where <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mo>ℓ</mo></math> denotes either an electron or a muon. Charge conjugation is implied. The second <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>B</mi></math> meson in the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi mathvariant="normal">ϒ</mi><mo stretchy="false">(</mo><mn>4</mn><mi>S</mi><mo stretchy="false">)</mo></math> event is not reconstructed explicitly. Using an inclusive reconstruction of the unobserved neutrino momentum, we determine the recoil variable <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>w</mi><mo>=</mo><msub><mi>v</mi><mi>B</mi></msub><mo>·</mo><msub><mi>v</mi><mi>D</mi></msub></math>, where <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>v</mi><mi>B</mi></msub></math> and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>v</mi><mi>D</mi></msub></math> are the four-velocities of the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>B</mi></math> and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>D</mi></math> mesons. We measure the total decay branching fractions to be <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mi mathvariant="script">B</mi><mo stretchy="false">(</mo><msup><mrow><mi>B</mi></mrow><mrow><mn>0</mn></mrow></msup><mo stretchy="false">→</mo><msup><mrow><mi>D</mi></mrow><mrow><mo>−</mo></mrow></msup><msup><mrow><mo>ℓ</mo></mrow><mrow><mo>+</mo></mrow></msup><msub><mrow><mi>ν</mi></mrow><mrow><mo>ℓ</mo></mrow></msub><mo stretchy="false">)</mo><mo>=</mo><mrow><mo stretchy="false">(</mo><mn>2.06</mn><mo>±</mo><mn>0.05</mn><mo stretchy="false">(</mo><mrow><mi>stat</mi></mrow><mo stretchy="false">)</mo><mo>±</mo><mn>0.10</mn><mo stretchy="false">(</mo><mrow><mi>sys</mi></mrow><mo stretchy="false">)</mo><mo stretchy="false">)</mo><mo>%</mo></mrow></mrow></math> and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi mathvariant="script">B</mi><mo stretchy="false">(</mo><msup><mi>B</mi><mo>+</mo></msup><mo stretchy="false">→</mo><msup><mover accent="true"><mi>D</mi><mo stretchy="false">¯</mo></mover><mn>0</mn></msup><msup><mo>ℓ</mo><mo>+</mo></msup><msub><mi>ν</mi><mo>ℓ</mo></msub><mo stretchy="false">)</mo><mo>=</mo><mrow><mo stretchy="false">(</mo><mn>2.31</mn><mo>±</mo><mn>0.04</mn><mo stretchy="false">(</mo><mrow><mi>stat</mi></mrow><mo stretchy="false">)</mo><mo>±</mo><mn>0.09</mn><mo stretchy="false">(</mo><mrow><mi>sys</mi></mrow><mo stretchy="false">)</mo><mo stretchy="false">)</mo><mo>%</mo></mrow></math>. We probe lepton flavor universality by measuring <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi mathvariant="script">B</mi><mo stretchy="false">(</mo><mi>B</mi><mo stretchy="false">→</mo><mi>D</mi><mi>e</mi><msub><mi>ν</mi><mi>e</mi></msub><mo stretchy="false">)</mo><mo>/</mo><mi mathvariant="script">B</mi><mo stretchy="false">(</mo><mi>B</mi><mo stretchy="false">→</mo><mi>D</mi><mi>μ</mi><msub><mi>ν</mi><mi>μ</mi></msub><mo stretchy="false">)</mo><mo>=</mo><mrow><mn>1.020</mn><mo>±</mo><mn>0.020</mn><mo stretchy="false">(</mo><mrow><mi>stat</mi></mrow><mo stretchy="false">)</mo><mo>±</mo><mn>0.022</mn><mo stretchy="false">(</mo><mrow><mi>sys</mi></mrow><mo stretchy="false">)</mo></mrow></math>. Fitting the partial decay branching fraction as a function of <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>w</mi></math> and using the average of lattice QCD calculations of the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>B</mi><mo stretchy="false">→</mo><mi>D</mi></math> form factor, we obtain <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mo stretchy="false">|</mo><msub><mi>V</mi><mrow><mi>c</mi><mi>b</mi></mrow></msub><mo stretchy="false">|</mo><mo>=</mo><mrow><mo stretchy="false">(</mo><mn>39.2</mn><mo>±</mo><mn>0.4</mn><mo stretchy="false">(</mo><mrow><mi>stat</mi></mrow><mo stretchy="false">)</mo><mo>±</mo><mn>0.6</mn><mo stretchy="false">(</mo><mrow><mi>sys</mi></mrow><mo stretchy="false">)</mo><mo>±</mo><mn>0.5</mn><mo stretchy="false">(</mo><mrow><mi>th</mi></mrow><mo stretchy="false">)</mo><mo stretchy="false">)</mo><mo>×</mo><msup><mn>10</mn><mrow><mo>−</mo><mn>3</mn></mrow></msup></mrow></math>.

I. Adachi

K. Adamczyk

L. Aggarwal

H. Ahmed

Y. Ahn

H. Aihara

N. Akopov

S. Alghamdi

M. Alhakami

A. Aloisio

K. Amos

M. Angelsmark

N. Anh Ky

C. Antonioli

D.M. Asner

H. Atmacan

T. Aushev

V. Aushev

M. Aversano

R. Ayad

V. Babu

H. Bae

N.K. Baghel

S. Bahinipati

P. Bambade

Sw. Banerjee

M. Barrett

M. Bartl

J. Baudot

A. Baur

A. Beaubien

F. Becherer

J. Becker

J.V. Bennett

F.U. Bernlochner

V. Bertacchi

M. Bertemes

E. Bertholet

M. Bessner

S. Bettarini

B. Bhuyan

F. Bianchi

T. Bilka

D. Biswas

A. Bobrov

D. Bodrov

A. Bondar

G. Bonvicini

J. Borah

A. Boschetti

A. Bozek

M. Bračko

P. Branchini

R.A. Briere

T.E. Browder

A. Budano

S. Bussino

Q. Campagna

M. Campajola

L. Cao

G. Casarosa

C. Cecchi

M.C. Chang

P. Cheema

L. Chen

B.G. Cheon

K. Chilikin

J. Chin

K. Chirapatpimol

H.E. Cho

K. Cho

S.J. Cho

S.K. Choi

S. Choudhury

I. Consigny

L. Corona

J.X. Cui

E. De La Cruz-Burelo

S.A. De La Motte

G. De Pietro

R. de Sangro

M. Destefanis

A. Di Canto

J. Dingfelder

Z. Doležal

I. Domínguez Jiménez

T.V. Dong

X. Dong

K. Dugic

G. Dujany

P. Ecker

J. Eppelt

R. Farkas

P. Feichtinger

T. Ferber

T. Fillinger

C. Finck

G. Finocchiaro

F. Forti

A. Frey

Determination of <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mo stretchy="false">|</mo><msub><mi>V</mi><mrow><mi>c</mi><mi>b</mi></mrow></msub><mo stretchy="false">|</mo></math> using <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>B</mi><mo stretchy="false">→</mo><mi>D</mi><mo>ℓ</mo><msub><mi>ν</mi><mi>l</mi></msub></math> decays at Belle II

We generalize the analysis of the asymptotic higher spin symmetries developed in the first three parts of this series by considering the minimal coupling of Einstein Gravity and Yang-Mills theory. We show that there exist symmetry parameters that satisfy a collection of dual equations of motion, which allow the construction of an infinite collection of charges that are conserved in the absence of radiation. These Noether charges act on the Einstein Yang-Mills phase space canonically and non-linearly. Their action defines a symmetry algebroid which reduces to a symmetry algebra at non-radiative cuts and generalizes the celestial $\textit{sw}$ algebra. The corresponding symmetry bracket is shown to satisfy the Jacobi identity and an interesting cross-product structure, which is analyzed in details.

Canada

Nicolas Cresto

Laurent Freidel

Asymptotic higher spin symmetries. Part IV. Einstein-Yang-Mills theory

Very recently, the two-photon decay width of the <math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>η</mi><mi>b</mi></msub></math> meson was computed with lattice QCD methods. This decay has not yet been measured. The knowledge of this width allows for the calculation of the <math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>η</mi><mi>b</mi></msub></math> production cross section through photon-photon interactions in ultraperipheral (UPC) <math xmlns="http://www.w3.org/1998/Math/MathML"><mrow><mi>P</mi><mi>b</mi><mtext>−</mtext><mi>P</mi><mi>b</mi></mrow></math> collisions. In this work we present this calculation, which is the first application of the lattice result. Since UPCs are gaining increasing attention of the heavy-ion community, we take the opportunity to perform a comprehensive study of the different ways of defining ultraperipheral collisions and of the different ways to treat the equivalent photon flux.

Brazil

C.N. Azevedo

F.C. Sobrinho

F.S. Navarra

Production of <math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>η</mi><mi>b</mi></msub></math> in ultraperipheral Pb-Pb collisions

The flavor-changing neutral current semileptonic decays of <italic>B</italic> mesons provide an excellent platform for indirectly probing New Physics (NP) beyond the Standard Model (SM). Recent measurements of lepton flavor universality (LFU) ratios such as <italic>R<inf>K</inf></italic>, <math altimg='si22.svg'><msub><mi>R</mi><msup><mi>K</mi><mo>*</mo></msup></msub></math>, and <italic>R<inf>&#981;</inf></italic> are consistent with SM predictions, thereby reducing earlier hints of LFU violation. Nevertheless, notable tensions persist in individual branching fractions&#8212;for instance <math altimg='si38.svg'><mrow><mi mathvariant='script'>B</mi><mo>(</mo><msup><mi>B</mi><mo>+</mo></msup><mo>&#8594;</mo><msup><mi>K</mi><mo>+</mo></msup><msup><mi>&#956;</mi><mo>+</mo></msup><msup><mi>&#956;</mi><mo>&#8722;</mo></msup><mo>)</mo></mrow></math> and <math altimg='si50.svg'><mrow><mi mathvariant='script'>B</mi><mo>(</mo><msup><mi>B</mi><mo>+</mo></msup><mo>&#8594;</mo><msup><mi>K</mi><mo>+</mo></msup><msup><mi>e</mi><mo>+</mo></msup><msup><mi>e</mi><mo>&#8722;</mo></msup><mo>)</mo></mrow></math>, which deviate at the 4 <italic>&#963;</italic>&#8211;5 <italic>&#963;</italic> level in the low- <italic>q</italic> 2 region ([1.1,6] GeV 2). Similarly, the angular observable <math altimg='si10.svg'><msubsup><mi>P</mi><mn>5</mn><mo>&#8242;</mo></msubsup></math> in <math altimg='si8.svg'><mrow><mi>B</mi><mo>&#8594;</mo><msup><mi>K</mi><mo>*</mo></msup><msup><mi>&#956;</mi><mo>+</mo></msup><msup><mi>&#956;</mi><mo>&#8722;</mo></msup></mrow></math> shows a 3.3 <italic>&#963;</italic> deviation, while <math altimg='si128.svg'><mrow><mi mathvariant='script'>B</mi><mo>(</mo><msub><mi>B</mi><mi>s</mi></msub><mo>&#8594;</mo><mi>&#981;</mi><msup><mi>&#956;</mi><mo>+</mo></msup><msup><mi>&#956;</mi><mo>&#8722;</mo></msup><mo>)</mo></mrow></math> departs from the SM by 3.6 <italic>&#963;</italic>. Although such discrepancies could in principle originate from underestimated hadronic effects, they may also indicate possible NP contributions. In this work, we perform a global fit to the latest <math altimg='si16.svg'><mrow><mi>b</mi><mo>&#8594;</mo><mi>s</mi><msup><mi>&#8467;</mi><mo>+</mo></msup><msup><mi>&#8467;</mi><mo>&#8722;</mo></msup></mrow></math> data within the framework of dimension-6 SMEFT operators. Our analysis systematically incorporates hadronic uncertainties from form factors, non-factorizable corrections, and input parameters, thereby providing a balanced assessment of the NP interpretation. We allow for NP contributions not only in <math altimg='si129.svg'><mrow><mi>b</mi><mo>&#8594;</mo><mi>s</mi><msup><mi>&#956;</mi><mo>+</mo></msup><msup><mi>&#956;</mi><mo>&#8722;</mo></msup></mrow></math> transitions but also in <math altimg='si130.svg'><mrow><mi>b</mi><mo>&#8594;</mo><mi>s</mi><msup><mi>e</mi><mo>+</mo></msup><msup><mi>e</mi><mo>&#8722;</mo></msup></mrow></math> channels, thus testing both lepton flavor universal (LFU) and lepton flavor universality violating (LFUV) NP scenarios. The interplay between these possibilities yields distinctive signatures in branching fractions, angular observables, and &#916;-observables, offering a comprehensive view of the current flavor anomalies.

India

Md Isha Ali

Utpal Chattopadhyay

Dilip Kumar Ghosh

N. Rajeev

Constraints on lepton flavor universal and non-universal new physics in <math altimg='si127.svg'><mrow><mi>b</mi><mspace width='0.16em' /><mo>&#8594;</mo><mspace width='0.16em' /><mi>s</mi><mspace width='0.16em' /><msup><mi>&#8467;</mi><mo>+</mo></msup><msup><mi>&#8467;</mi><mo>&#8722;</mo></msup></mrow></math> decays: A global SMEFT survey

Following the discovery of the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msubsup><mi>D</mi><mn>2</mn><mo>*</mo></msubsup><mo stretchy="false">(</mo><mn>3000</mn><mo stretchy="false">)</mo></math>, its mass and full width have been extensively studied. Yet its nature remains undetermined to date. Since it was discovered through nonleptonic decay of <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>B</mi></math> mesons and the corresponding cascade process, we therefore in this paper investigate the nonleptonic and semileptonic decays of <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>B</mi></math> meson to <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mi>J</mi><mi>P</mi></msup><mo>=</mo><msup><mn>2</mn><mo>+</mo></msup></math> charmed mesons using the Bethe-Salpeter equation approach. Our calculations on nonleptonic <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>B</mi></math> decays reveal that the unconfirmed resonance <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msubsup><mi>D</mi><mn>2</mn><mo>*</mo></msubsup><mo stretchy="false">(</mo><mn>3000</mn><mo stretchy="false">)</mo></math> aligns well with <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msubsup><mi>D</mi><mn>2</mn><mo>*</mo></msubsup><mo stretchy="false">(</mo><msup><mn>2</mn><mn>3</mn></msup><msub><mi>P</mi><mn>2</mn></msub><mo stretchy="false">)</mo></math> predictions. Other candidates, including <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msubsup><mi>D</mi><mn>2</mn><mo>*</mo></msubsup><mo stretchy="false">(</mo><msup><mn>1</mn><mn>3</mn></msup><msub><mi>F</mi><mn>2</mn></msub><mo stretchy="false">)</mo></math>, <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msubsup><mi>D</mi><mn>2</mn><mo>*</mo></msubsup><mo stretchy="false">(</mo><msup><mn>3</mn><mn>3</mn></msup><msub><mi>P</mi><mn>2</mn></msub><mo stretchy="false">)</mo></math>, and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msubsup><mi>D</mi><mn>2</mn><mo>*</mo></msubsup><mo stretchy="false">(</mo><msup><mn>2</mn><mn>3</mn></msup><msub><mi>F</mi><mn>2</mn></msub><mo stretchy="false">)</mo></math>, are excluded due to their very small branching ratios in <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>B</mi></math> decays. Considering that the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msubsup><mi>D</mi><mn>2</mn><mo>*</mo></msubsup><mo stretchy="false">(</mo><mn>1</mn><mi>F</mi><mo stretchy="false">)</mo></math>, <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msubsup><mi>D</mi><mn>2</mn><mo>*</mo></msubsup><mo stretchy="false">(</mo><mn>3</mn><mi>P</mi><mo stretchy="false">)</mo></math>, and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msubsup><mi>D</mi><mn>2</mn><mo>*</mo></msubsup><mo stretchy="false">(</mo><mn>2</mn><mi>F</mi><mo stretchy="false">)</mo></math> have not yet been experimentally observed, we investigate the feasibility of their detection in <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>B</mi></math>-meson decays.

China

Shi-Hang Zhang

Wen-Yuan Ke

Su-Yan Pei

Wei Li

Germany

Xiao-Ze Tan

Lili Zhu

Guo-Li Wang

Identification of <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msubsup><mi>D</mi><mn>2</mn><mo>*</mo></msubsup><mo stretchy="false">(</mo><mn>3000</mn><mo stretchy="false">)</mo></math> as the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msubsup><mi>D</mi><mn>2</mn><mo>*</mo></msubsup><mo stretchy="false">(</mo><msup><mn>2</mn><mn>3</mn></msup><msub><mi>P</mi><mn>2</mn></msub><mo stretchy="false">)</mo></math> and exploring potential of undiscovered <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mn>2</mn><mo>+</mo></msup></math> mesons via <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>B</mi></math> decays

We extend previous computations of Hermitian Yang–Mills connections for bundles on complete intersection Calabi–Yau manifolds to bundles on their free quotients. Bundles on quotient manifolds are often defined by equivariant bundles on corresponding covering spaces. Combining equivariant structure and the generalized Donaldson algorithm, we develop a systematic approach to compute connections of holomorphic poly-stable bundles on quotient manifolds. With it, we construct connections of an SU(3) bundle on a <math altimg='si1.svg'><msub><mi mathvariant='double-struck'>Z</mi><mn>5</mn></msub></math> quotient of the quintic and an SU(5) bundle on a <math altimg='si4.svg'><mrow><msub><mi mathvariant='double-struck'>Z</mi><mn>3</mn></msub><mo linebreak='goodbreak'>&#215;</mo><msub><mi mathvariant='double-struck'>Z</mi><mn>3</mn></msub></mrow></math> quotient of the bi-cubic. For both examples, the algorithm converges as expected and gives a good approximation of Hermitian Yang&#8211;Mills connections, which will be important for heterotic model building in Calabi&#8211;Yau compactifications.

Wei Cui

Numerical hermitian yang-Mills connection for bundles on quotient manifold

We show that multiparticle contributions to amplitudes of weak decays of the generic topology (heavy quark hits some intermediate point of the propagator line joining the end-points from which momenta $\textit{q}$ and $$q'$$ are emitted) is given in the heavy quark limit and at the leading order in $$\alpha _s$$ by the convolution of (i) hard kernel composed of highly virtual propagators of light degrees of freedom and (ii) the $\textit{B}$-meson multiparticle wave function, $$\langle 0|\phi (x)\phi (x_1)\cdots \phi (x_n)\phi _b(0)\phi (x'_{n'})\cdots \phi (x'_1)\phi (x')|B(p)\rangle $$ , in a $\textit{double-collinear}$ light-cone configuration: the coordinates $$x,x_1,\ldots ,x_n$$ are ordered and aligned along the light-like 4-vector $$a_\mu $$ , $$a^2=0$$ , $$q_\mu \propto a_\mu $$ , while the coordinates $$x',x_1',\ldots ,x'_{n'}$$ are ordered and aligned along the light-like 4-vector $$a'_\mu $$ , $$a'^2=0$$ , $$q'_\mu \propto a'_\mu $$ , $$a'a\ne 0$$ . Corrections to this factorization formula are suppressed by powers of $$\Lambda _\textrm{QCD}/M_B$$ .

Russia

Austria

Dmitri Melikhov

Factorization of multiparticle contributions to amplitudes of $\textit{B}$-meson weak decays

We present a prescription for computing tree-level scattering amplitudes in 10D super-Yang-Mills (SYM) theory using the pure spinor worldline formalism. The pure spinor formalism has proven to be a powerful framework for studying supersymmetric field theories, providing manifestly covariant and BRST-invariant formulations of amplitudes. By incorporating the worldline approach, we construct a first-quantized representation of SYM amplitudes in 10D, where interactions are encoded through the insertion of vertex operators along the particle’s trajectory. We explicitly compute the N-point function, demonstrating an agreement with the $\textit{α}$ $\textit{→}$ 0 limit of open superstring amplitudes and confirming that the kinematic numerators satisfy the expected BRST relations. Our results establish the pure spinor worldline formalism as a tool for studying scattering amplitudes and suggest further applications to 11D supergravity.

Sweden

Max Guillen

United States

Marcelo Santos

United Kingdom

Spain

Eggon Viana

The pure spinor superparticle and 10D super-Yang-Mills amplitudes

We perform a theoretical study of the decay process <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi mathvariant="normal">ϒ</mi><mo stretchy="false">→</mo><msup><mi>D</mi><mo>−</mo></msup><msup><mover accent="true"><mi>B</mi><mo stretchy="false">¯</mo></mover><mn>0</mn></msup><msubsup><mi>D</mi><mi>s</mi><mo>+</mo></msubsup></math> in search of the doubly heavy tetraquark states <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>T</mi><mrow><mi>b</mi><mi>c</mi><mover accent="true"><mi>s</mi><mo stretchy="false">¯</mo></mover></mrow></msub></math> with quark content <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>b</mi><mi>c</mi><mover accent="true"><mi>s</mi><mo stretchy="false">¯</mo></mover><mover accent="true"><mi>d</mi><mo stretchy="false">¯</mo></mover></math>. These <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>T</mi><mrow><mi>b</mi><mi>c</mi><mover accent="true"><mi>s</mi><mo stretchy="false">¯</mo></mover></mrow></msub></math> states are assumed to be dynamically generated molecular states from the S-wave interactions between <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><mrow><mo stretchy="false">(</mo><mo>*</mo><mo stretchy="false">)</mo><mn>0</mn></mrow></msubsup><msup><mi>D</mi><mrow><mo stretchy="false">(</mo><mo>*</mo><mo stretchy="false">)</mo><mo>+</mo></mrow></msup></math> and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mover accent="true"><mi>B</mi><mo stretchy="false">¯</mo></mover><mrow><mo stretchy="false">(</mo><mo>*</mo><mo stretchy="false">)</mo><mn>0</mn></mrow></msup><msubsup><mi>D</mi><mi>s</mi><mrow><mo stretchy="false">(</mo><mo>*</mo><mo stretchy="false">)</mo><mo>+</mo></mrow></msubsup></math> meson pairs. Based on the total angular momentum and the type of the constituent mesons (pseudoscalars <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>P</mi></math> or vectors <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>V</mi></math>), they are labeled as <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msubsup><mi>T</mi><mrow><mi>b</mi><mi>c</mi><mover accent="true"><mi>s</mi><mo stretchy="false">¯</mo></mover></mrow><mrow><mn>0</mn><mo>,</mo><mi>P</mi><mi>P</mi></mrow></msubsup></math>, <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msubsup><mi>T</mi><mrow><mi>b</mi><mi>c</mi><mover accent="true"><mi>s</mi><mo stretchy="false">¯</mo></mover></mrow><mrow><mn>0</mn><mo>,</mo><mi>V</mi><mi>V</mi></mrow></msubsup></math>, and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msubsup><mi>T</mi><mrow><mi>b</mi><mi>c</mi><mover accent="true"><mi>s</mi><mo stretchy="false">¯</mo></mover></mrow><mrow><mn>2</mn><mo>,</mo><mi>V</mi><mi>V</mi></mrow></msubsup></math>, respectively. The <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mover accent="true"><mi>B</mi><mo stretchy="false">¯</mo></mover><mn>0</mn></msup><msubsup><mi>D</mi><mi>s</mi><mo>+</mo></msubsup></math> invariant mass distribution for this decay is calculated using current algebra, incorporating contributions from <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>T</mi><mrow><mi>b</mi><mi>c</mi><mover accent="true"><mi>s</mi><mo stretchy="false">¯</mo></mover></mrow></msub></math> states arising from final-state interactions. Our results reveal a clear peak structure in the 7415–7425 MeV region, which is attributed to the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msubsup><mi>T</mi><mrow><mi>b</mi><mi>c</mi><mover accent="true"><mi>s</mi><mo stretchy="false">¯</mo></mover></mrow><mrow><mn>2</mn><mo>,</mo><mi>V</mi><mi>V</mi></mrow></msubsup></math> state. Additionally, a distinct dip structure appears near the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mover accent="true"><mi>B</mi><mo stretchy="false">¯</mo></mover><mrow><mo>*</mo><mn>0</mn></mrow></msup><msubsup><mi>D</mi><mi>s</mi><mrow><mo>*</mo><mo>+</mo></mrow></msubsup></math> threshold, characteristic of the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msubsup><mi>T</mi><mrow><mi>b</mi><mi>c</mi><mover accent="true"><mi>s</mi><mo stretchy="false">¯</mo></mover></mrow><mrow><mn>2</mn><mo>,</mo><mi>V</mi><mi>V</mi></mrow></msubsup></math> as a hadronic molecular state. A near-threshold enhancement associated with the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msubsup><mi>T</mi><mrow><mi>b</mi><mi>c</mi><mover accent="true"><mi>s</mi><mo stretchy="false">¯</mo></mover></mrow><mrow><mn>0</mn><mo>,</mo><mi>P</mi><mi>P</mi></mrow></msubsup></math> state and a dip arising from the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msubsup><mi>T</mi><mrow><mi>b</mi><mi>c</mi><mover accent="true"><mi>s</mi><mo stretchy="false">¯</mo></mover></mrow><mrow><mn>0</mn><mo>,</mo><mi>V</mi><mi>V</mi></mrow></msubsup></math> state are also identified, though the manifestation of these features depends sensitively on model parameter fine-tuning. Therefore, with increased experimental statistics, the decay channel <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi mathvariant="normal">ϒ</mi><mo stretchy="false">→</mo><msup><mi>D</mi><mo>−</mo></msup><msup><mover accent="true"><mi>B</mi><mo stretchy="false">¯</mo></mover><mn>0</mn></msup><msubsup><mi>D</mi><mi>s</mi><mo>+</mo></msubsup></math> offers a promising avenue for discovering and characterizing the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>T</mi><mrow><mi>b</mi><mi>c</mi><mover accent="true"><mi>s</mi><mo stretchy="false">¯</mo></mover></mrow></msub></math> states.

Wen-Ying Liu

Hua-Xing Chen

<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>T</mi><mrow><mi>b</mi><mi>c</mi><mover accent="true"><mi>s</mi><mo stretchy="false">¯</mo></mover></mrow></msub></math> states in the process <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi mathvariant="normal">ϒ</mi><mo stretchy="false">→</mo><msup><mi>D</mi><mo>−</mo></msup><msup><mover accent="true"><mi>B</mi><mo stretchy="false">¯</mo></mover><mn>0</mn></msup><msubsup><mi>D</mi><mi>s</mi><mo>+</mo></msubsup></math>

Under chiral effective field theory, we study the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>S</mi></math>-wave <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>D</mi><msup><mi>D</mi><mo>*</mo></msup></math> interactions up to second chiral order at one-loop level, which contain full contact, one-pion-exchange (OPE) and two-pion-exchange (TPE) contributions. Here, we adopt a new subtraction scheme of the two-particle-reducible contributions and attempt different regularization schemes uniquely for the TPE contributions since they are highly divergent on the momentum transfer. Under these schemes, we conclude that, in the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>I</mi><mo>=</mo><mn>0</mn></math> channel, the TPE contribution is repulsive, then the competition between this powerful repulsing TPE and the other two (contact and OPE) results in a quite weak attraction. This explains why <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> has an extremely small binding energy if treated as the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>I</mi><mo>=</mo><mn>0</mn></math> <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>D</mi><msup><mi>D</mi><mo>*</mo></msup></math> bound state. This feature resembles that of hidden charm <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>D</mi><msup><mover accent="true"><mi>D</mi><mo stretchy="false">¯</mo></mover><mo>*</mo></msup></math> as we investigated in previous work [<a href="http://dx.doi.org/10.1103/PhysRevD.105.034013">Phys. Rev. D 105, 034013 (2022)</a>], which also interpreted the extremely near-threshold phenomenon of <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>X</mi><mo stretchy="false">(</mo><mn>3872</mn><mo stretchy="false">)</mo></math>. In addition, we also solve the Bethe-Salpeter equation with the chiral interactions for a consistency check.

Hao Xu

Li-Xiang Ren

Investigating the two-pion exchange of the double charm <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>D</mi><msup><mi>D</mi><mo>*</mo></msup></math> chiral interactions and <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>