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

Brazil

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.

China

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>

The LHCb Collaboration has recently found a large <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>C</mi><mi>P</mi></math>-violating rate asymmetry in the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>b</mi></math>-baryon decay <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msubsup><mi mathvariant="normal">Λ</mi><mi>b</mi><mn>0</mn></msubsup><mo stretchy="false">→</mo><mi>p</mi><msup><mi>K</mi><mo>−</mo></msup><msup><mi>π</mi><mo>+</mo></msup><msup><mi>π</mi><mo>−</mo></msup></math>. This is the first observation of <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>C</mi><mi>P</mi></math> violation in baryon processes, opening a new window to test its standard model (SM) origin. Many more baryon decays are expected to exhibit observable signals of <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>C</mi><mi>P</mi></math> violation. We show that there also exists large <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>C</mi><mi>P</mi></math> violation in the U-spin partner decay mode, <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msubsup><mi mathvariant="normal">Ξ</mi><mi>b</mi><mn>0</mn></msubsup><mo stretchy="false">→</mo><msup><mi mathvariant="normal">Σ</mi><mo>+</mo></msup><msup><mi>π</mi><mo>−</mo></msup><msup><mi>K</mi><mo>+</mo></msup><msup><mi>K</mi><mo>−</mo></msup></math>, with rate asymmetry <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>A</mi><mrow><mi>C</mi><mi>P</mi></mrow></msub><mo stretchy="false">(</mo><msubsup><mi mathvariant="normal">Ξ</mi><mi>b</mi><mn>0</mn></msubsup><mo stretchy="false">→</mo><msup><mi mathvariant="normal">Σ</mi><mo>+</mo></msup><msup><mi>π</mi><mo>−</mo></msup><msup><mi>K</mi><mo>+</mo></msup><msup><mi>K</mi><mo>−</mo></msup><mo stretchy="false">)</mo><mo>=</mo><mo>−</mo><msub><mi>A</mi><mrow><mi>C</mi><mi>P</mi></mrow></msub><mo stretchy="false">(</mo><msubsup><mi mathvariant="normal">Λ</mi><mi>b</mi><mn>0</mn></msubsup><mo stretchy="false">→</mo><mi>p</mi><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><mfrac><mrow><mi>Br</mi><mo stretchy="false">(</mo><msubsup><mi mathvariant="normal">Λ</mi><mi>b</mi><mn>0</mn></msubsup><mo stretchy="false">→</mo><mi>p</mi><msup><mi>K</mi><mo stretchy="false">−</mo></msup><msup><mi>π</mi><mo stretchy="false">+</mo></msup><msup><mi>π</mi><mo stretchy="false">−</mo></msup><mo stretchy="false">)</mo></mrow><mrow><mi>Br</mi><mo stretchy="false">(</mo><msubsup><mi mathvariant="normal">Ξ</mi><mi>b</mi><mn>0</mn></msubsup><mo stretchy="false">→</mo><msup><mi mathvariant="normal">Σ</mi><mo stretchy="false">+</mo></msup><msup><mi>π</mi><mo stretchy="false">−</mo></msup><msup><mi>K</mi><mo stretchy="false">+</mo></msup><msup><mi>K</mi><mo stretchy="false">−</mo></msup><mo stretchy="false">)</mo></mrow></mfrac><mfrac><msup><mi>τ</mi><msub><mi mathvariant="normal">Ξ</mi><mi>b</mi></msub></msup><msup><mi>τ</mi><msub><mi mathvariant="normal">Λ</mi><mi>b</mi></msub></msup></mfrac></math> in the U-spin symmetry limit. By neglecting a subleading contribution in the amplitudes, <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>A</mi><mrow><mi>C</mi><mi>P</mi></mrow></msub><mo stretchy="false">(</mo><msubsup><mi mathvariant="normal">Λ</mi><mi>b</mi><mn>0</mn></msubsup><mo stretchy="false">→</mo><mi>p</mi><msup><mi>π</mi><mo>+</mo></msup><msup><mi>π</mi><mo>−</mo></msup><msup><mi>π</mi><mo>−</mo></msup><mo stretchy="false">)</mo><mo>=</mo><mo>−</mo><mo stretchy="false">(</mo><mn>12</mn><mo>±</mo><mn>6</mn><mo stretchy="false">)</mo><mo>%</mo></math>. These predictions can be tested in the near future.

Xiao-Gang He

Chia-Wei Liu

Jusak Tandean

Large <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>C</mi><mi>P</mi></math> violation in <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msubsup><mi mathvariant="normal">Λ</mi><mi>b</mi><mn>0</mn></msubsup><mo stretchy="false">→</mo><mi>p</mi><msup><mi>K</mi><mo>−</mo></msup><msup><mi>π</mi><mo>+</mo></msup><msup><mi>π</mi><mo>−</mo></msup></math> and its <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>U</mi></math>-spin partner decays

A search for the decay $\textit{B}$ $\textit{→ ϕϕ}$ is made using $\textit{pp}$ collision data collected with the LHCb detector at centre-of-mass energies of 7, 8 and 13 TeV, corresponding to an integrated luminosity of 9 fb . No significant signal is observed, and an upper limit on the branching fraction of 1$\textit{.}$3 (1$\textit{.}$4) × 10 at 90 (95)% confidence level is set. This result supersedes the previous LHCb study and improves the upper limit by a factor of two.

Netherlands

R. Aaij

A. Abdelmotteleb

Switzerland

C. Abellan Beteta

F. Abudinén

T. Ackernley

A. Adefisoye

B. Adeva

M. Adinolfi

P. Adlarson

France

C. Agapopoulou

C. Aidala

Z. Ajaltouni

S. Akar

K. Akiba

Italy

P. Albicocco

Germany

J. Albrecht

Lithuania

R. Aleksiejunas

F. Alessio

Z. Aliouche

P. Alvarez Cartelle

R. Amalric

S. Amato

J. Amey

Y. Amhis

L. An

L. Anderlini

M. Andersson

P. Andreola

M. Andreotti

S. Andres Estrada

A. Anelli

D. Ao

F. Archilli

Z. Areg

M. Argenton

Costa Rica

S. Arguedas Cuendis

A. Artamonov

M. Artuso

E. Aslanides

R. Ataíde Da Silva

M. Atzeni

B. Audurier

J. Authier

D. Bacher

I. Bachiller Perea

S. Bachmann

M. Bachmayer

J. Back

P. Baladron Rodriguez

V. Balagura

A. Balboni

W. Baldini

L. Balzani

H. Bao

J. Baptista de Souza Leite

C. Barbero Pretel

M. Barbetti

I. Barbosa

R. Barlow

M. Barnyakov

S. Barsuk

W. Barter

J. Bartz

Poland

S. Bashir

B. Batsukh

P. Battista

A. Bay

A. Beck

M. Becker

F. Bedeschi

I. Bediaga

N. Behling

S. Belin

K. Belous

I. Belov

I. Belyaev

G. Benane

G. Bencivenni

E. Ben-Haim

A. Berezhnoy

R. Bernet

S. Bernet Andres

A. Bertolin

C. Betancourt

F. Betti

J. Bex

Ia. Bezshyiko

Ukraine

O. Bezshyyko

J. Bhom

M. Bieker

N. Biesuz

P. Billoir

A. Biolchini

M. Birch

F. Bishop

A. Bitadze

A. Bizzeti

Canada

T. Blake

F. Blanc

J. Blank

Search for the decay $\textit{B}$

The first measurement at midrapidity (|$\textit{y}$|$\textit{ <}$ 0$\textit{.}$5) of the production yield of the strange-charm baryons $${\Xi }_{\text{c}}^{+}$$ and $${\Xi }_{\text{c}}^{0}$$ as a function of transverse momentum ($\textit{p}$ ) in different charged-particle multiplicity classes in proton-proton collisions at $$\sqrt{s}=13$$ TeV with the ALICE experiment at the LHC is reported. The $${\Xi }_{\text{c}}^{+}$$ baryon is reconstructed via the $${\Xi }_{\text{c}}^{+}\to {\Xi }^{-}{\pi }^{+}{\pi }^{+}$$ decay channel in the range 4 $\textit{< p}$ $\textit{<}$ 12 GeV$\textit{/c}$, while the $${\Xi }_{\text{c}}^{0}$$ baryon is reconstructed via both the $${\Xi}_{\text{c}}^{0}\to {\Xi}^{-}{\pi }^{+}$$ and $${\Xi}_{\text{c}}^{0}\to {\Xi}^{-}{\text{e}}^{+}{\nu }_{\text{e}}$$ decay channels in the range 2 $\textit{< p}$ $\textit{<}$ 12 GeV$\textit{/c}$. The baryon-to-meson $$\left({\Xi}_{\text{c}}^{0,+}/{\text{D}}^{0}\right)$$ and the baryon-to-baryon $$\left({\Xi}_{\text{c}}^{0,+}/{\Lambda}_{\text{c}}^{+}\right)$$ production yield ratios show no significant dependence on multiplicity. In addition, the observed yield ratios are not described by theoretical predictions that model charm-quark fragmentation based on measurements at e e and e p colliders, indicating differences in the charm-baryon production mechanism in pp collisions. A comparison with different event generators and tunings, including different modelling of the hadronisation process, is also discussed. Moreover, the branching-fraction ratio of $${\text{BR}}\left({\Xi}_{\text{c}}^{0}\to {\Xi }^{-}{\text{e}}^{+}{\nu }_{\text{e}}\right)/{\text{BR}}\left({\Xi}_{\text{c}}^{0}\to {\Xi }^{-}{\pi }^{+}\right)$$ is measured as 0.825 ± 0.094 (stat.) ± 0.081 (syst.). This value supersedes the previous ALICE measurement, improving the statistical precision by a factor of 1.6.

I. Abualrob

S. Acharya

G. Aglieri Rinella

L. Aglietta

M. Agnello

N. Agrawal

India

Z. Ahammed

S. Ahmad

Slovakia

I. Ahuja

Indonesia

ZUL. Akbar

A. Akindinov

V. Akishina

M. Al-Turany

D. Aleksandrov

B. Alessandro

H. Alfanda

Mexico

R. Alfaro Molina

B. Ali

A. Alici

South Korea

A. Alkin

Norway

J. Alme

G. Alocco

T. Alt

A. Altamura

I. Altsybeev

Romania

C. Andrei

N. Andreou

A. Andronic

E. Andronov

V. Anguelov

F. Antinori

P. Antonioli

N. Apadula

H. Appelshäuser

S. Arcelli

R. Arnaldi

J. Arneiro

I. Arsene

M. Arslandok

A. Augustinus

R. Averbeck

M. Azmi

Japan

H. Baba

A. Babu

A. Badalà

J. Bae

Y. Bae

Y. Baek

X. Bai

R. Bailhache

Y. Bailung

R. Bala

A. Baldisseri

B. Balis

S. Bangalia

Z. Banoo

Multiplicity dependence of $${\Xi }_{\text{c}}^{+}$$ and $${\Xi }_{\text{c}}^{0}$$ production in pp collisions at $$\sqrt{s}=13$$ TeV