In this study, we investigate the possibility of enhancing the di-jet resonance searches by tagging the final state radiation (FSR) jet using an event-level deep neural network. It is found that solely relying on the 4-momenta of the leading three jets allows the algorithm to achieve good discriminating power that can identify the hardest FSR jet in the signal while rejecting other soft jets. Once the invariant mass is corrected with the tagged FSR jet, the mass resolution of the signal is greatly enhanced, and the sensitivity of the search is also improved by more than 10%. By crafting the input variables carefully, the algorithm introduces minimal mass sculpting for the background, and its applicability extends to a broad mass range. This work proves that FSR jet tagging can potentially enhance di-jet resonance searches, suiting various stages of the physics programmes at the Large Hadron Collider (LHC) and High-Luminosity LHC (HL-LHC).

China

Bingxuan Liu

Yuxuan Shen

Yuanshunzi Sui

Enhancing di-jet resonance searches via a final-state radiation jet tagging algorithm * Bingxuan Liu is supported by Shenzhen Campus of the Sun Yat-sen University under project 74140-12255011, and by the Young Scientists Fund (C Class) of the National Natural Science Foundation of China (12405122). Both Yuxuan Shen and Yuanshunzi Sui are supported by College Students’ Innovative Entrepreneurial Training Plan Program

Using a data sample of <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mo stretchy="false">(</mo><mn>2.712</mn><mo>±</mo><mn>0.014</mn><mo stretchy="false">)</mo><mo>×</mo><msup><mn>10</mn><mn>9</mn></msup><mtext> </mtext><mtext> </mtext><mi>ψ</mi><mo stretchy="false">(</mo><mn>3686</mn><mo stretchy="false">)</mo></math> events collected at <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msqrt><mi>s</mi></msqrt><mo>=</mo><mn>3.686</mn><mtext> </mtext><mtext> </mtext><mi>GeV</mi></math> by the BESIII detector, we search for the rare electromagnetic Dalitz decays <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>χ</mi><mrow><mi>c</mi><mi>J</mi></mrow></msub><mo stretchy="false">→</mo><msup><mi>e</mi><mo>+</mo></msup><msup><mi>e</mi><mo>−</mo></msup><mi>ϕ</mi><mo stretchy="false">(</mo><mi>J</mi><mo>=</mo><mn>0</mn><mo>,</mo><mn>1</mn><mo>,</mo><mn>2</mn><mo stretchy="false">)</mo></math> via the radiative transitions <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>ψ</mi><mo stretchy="false">(</mo><mn>3686</mn><mo stretchy="false">)</mo><mo stretchy="false">→</mo><mi>γ</mi><msub><mi>χ</mi><mrow><mi>c</mi><mi>J</mi></mrow></msub></math>. No statistically significant <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>χ</mi><mrow><mi>c</mi><mi>J</mi></mrow></msub><mo stretchy="false">→</mo><msup><mi>e</mi><mo>+</mo></msup><msup><mi>e</mi><mo>−</mo></msup><mi>ϕ</mi></math> signals are observed. The upper limits on the branching fractions of <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><msub><mrow><mi>χ</mi></mrow><mrow><mi>c</mi><mi>J</mi></mrow></msub><mo stretchy="false">→</mo><msup><mrow><mi>e</mi></mrow><mrow><mo>+</mo></mrow></msup><msup><mrow><mi>e</mi></mrow><mrow><mo>−</mo></mrow></msup><mi>ϕ</mi><mtext> </mtext><mo stretchy="false">(</mo><mi>J</mi><mo>=</mo><mn>0</mn><mo>,</mo><mn>1</mn><mo>,</mo><mn>2</mn><mo stretchy="false">)</mo></mrow></math>, excluding the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>ϕ</mi></math> resonance to <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> final states, are set to be <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mn>2.4</mn><mo>×</mo><msup><mn>10</mn><mrow><mo>−</mo><mn>7</mn></mrow></msup><mo>,</mo><mn>6.7</mn><mo>×</mo><msup><mn>10</mn><mrow><mo>−</mo><mn>7</mn></mrow></msup></math>, and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mn>4.1</mn><mo>×</mo><msup><mn>10</mn><mrow><mo>−</mo><mn>7</mn></mrow></msup></math> at the 90% confidence level, respectively. This is the first search for the electromagnetic Dalitz transition of P-wave charmonium <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>χ</mi><mrow><mi>c</mi><mi>J</mi></mrow></msub></math> states to a light vector meson.

M. Ablikim

Russia

M.N. Achasov

Sweden

P. Adlarson

X.C. Ai

Germany

R. Aliberti

Italy

A. Amoroso

Q. An

Y. Bai

JINR

O. Bakina

Y. Ban

H.R. Bao

Poland

V. Batozskaya

Mongolia

K. Begzsuren

N. Berger

M. Berlowski

M. Bertani

D. Bettoni

F. Bianchi

E. Bianco

A. Bortone

I. Boyko

United States

R.A. Briere

A. Brueggemann

H. Cai

M.H. Cai

X. Cai

A. Calcaterra

G.F. Cao

N. Cao

Türkiye

S.A. Cetin

X.Y. Chai

J.F. Chang

G.R. Che

Y.Z. Che

C.H. Chen

Chao Chen

G. Chen

H.S. Chen

H.Y. Chen

M.L. Chen

S.J. Chen

S.L. Chen

S.M. Chen

T. Chen

X.R. Chen

X.T. Chen

X.Y. Chen

Y.B. Chen

Y.Q. Chen

Z. Chen

Z.J. Chen

Z.K. Chen

South Korea

S.K. Choi

X. Chu

G. Cibinetto

F. Cossio

United Kingdom

J. Cottee-Meldrum

J.J. Cui

H.L. Dai

J.P. Dai

A. Dbeyssi

R.E. de Boer

D. Dedovich

C.Q. Deng

Z.Y. Deng

A. Denig

I. Denysenko

M. Destefanis

F. De Mori

B. Ding

X.X. Ding

Y. Ding

Y.X. Ding

J. Dong

L.Y. Dong

M.Y. Dong

X. Dong

M.C. Du

S.X. Du

Y.Y. Duan

P. Egorov

G.F. Fan

J.J. Fan

Y.H. Fan

J. Fang

S.S. Fang

W.X. Fang

Y.Q. Fang

R. Farinelli

L. Fava

F. Feldbauer

G. Felici

C.Q. Feng

J.H. Feng

L. Feng

Q.X. Feng

Search for the electromagnetic Dalitz decays <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>χ</mi><mrow><mi>c</mi><mi>J</mi></mrow></msub><mo stretchy="false">→</mo><msup><mi>e</mi><mo>+</mo></msup><msup><mi>e</mi><mo>−</mo></msup><mi>ϕ</mi></math>

We propose a three-zero texture for the down-quark mass matrix within a <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>S</mi><mi>U</mi><mo stretchy="false">(</mo><mn>5</mn><mo stretchy="false">)</mo></math> grand unified theory (GUT)-inspired Standard Model, enforced by a noninvertible selection rule originating from <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi mathvariant="double-struck">Z</mi><mn>2</mn></msub></math> gauging of <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi mathvariant="double-struck">Z</mi><mi>N</mi></msub></math> symmetries. Assuming <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>C</mi><mi>P</mi></math> invariance at the high-energy scale, our framework solves the strong <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>C</mi><mi>P</mi></math> problem while reproducing a realistic quark mass matrix. The <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>C</mi><mi>P</mi></math> symmetry is spontaneously broken down at an intermediate scale via complex vacuum expectation values of new scalar fields <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>η</mi><mi>i</mi></msub></math>, which generate the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>C</mi><mi>P</mi></math> phase in the Cabibbo-Kobayashi-Maskawa matrix without inducing the quantum chromodynamics (QCD) <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mover accent="true"><mi>θ</mi><mo stretchy="false">¯</mo></mover></math> term. The present model incorporates three generations of matter, Higgs, and additional scalars with a common structure under the noninvertible symmetry, which may be naturally embedded into <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>S</mi><mi>O</mi><mo stretchy="false">(</mo><mn>10</mn><mo stretchy="false">)</mo></math> GUTs at high energies.

Japan

Tatsuo Kobayashi

Hajime Otsuka

Tsutomu T. Yanagida

Noninvertible symmetry as a solution to the strong <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>C</mi><mi>P</mi></math> problem in a GUT-inspired standard model

We investigate the sensitivity of a future high-luminosity <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> collider operating at <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msqrt><mi>s</mi></msqrt><mo>=</mo><mn>250</mn><mtext> </mtext><mtext> </mtext><mi>GeV</mi></math> to <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>C</mi><mi>P</mi></math>-violating and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>C</mi><mi>P</mi></math>-conserving anomalous <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>h</mi><mi>V</mi><mi>V</mi></math> interactions via the Higgsstrahlung process. The effects of new physics are parametrized in the Standard Model effective field theory (SMEFT) framework through six dimension-6 operators modifying the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>h</mi><mi>V</mi><mi>V</mi></math> vertices. Using polarized beams and exploiting polarization and spin correlation asymmetries reconstructed from Higgs decay products, we perform a comprehensive analysis across the three dominant decay modes, <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>h</mi><mo stretchy="false">→</mo><mi>b</mi><mover accent="true"><mi>b</mi><mo stretchy="false">¯</mo></mover></math>, <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>W</mi><msup><mi>W</mi><mo>⋆</mo></msup></math>, and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>Z</mi><msup><mi>Z</mi><mo>⋆</mo></msup></math>. The <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>h</mi><mo stretchy="false">→</mo><mi>W</mi><msup><mi>W</mi><mo>⋆</mo></msup></math> channel exhibits the highest sensitivity to <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi mathvariant="script">O</mi><mrow><mi>H</mi><mi>W</mi></mrow></msub></math> and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi mathvariant="script">O</mi><mrow><mi>H</mi><mover accent="true"><mi>W</mi><mo stretchy="false">˜</mo></mover></mrow></msub></math>, while the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>b</mi><mover accent="true"><mi>b</mi><mo stretchy="false">¯</mo></mover></math> mode constrains the remaining operators with high statistical precision. Sensitivity studies incorporating luminosity scaling and systematic uncertainties show that the projected bounds improve significantly with increasing integrated luminosity, but saturate once experimental systematics exceed the few-percent level. These results highlight the crucial role of spin-based observables and beam polarization in achieving subpercent precision on SMEFT coefficients at future lepton colliders.

India

Amir Subba

Subhaditya Bhattacharya

Abhik Sarkar

Probing <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>C</mi><mi>P</mi></math>-violating Higgs-gauge couplings with Higgsstrahlung 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

A potential quark model is used to search for a <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><msubsup><mrow><mi>P</mi></mrow><mrow><mi>c</mi><mover accent="true"><mrow><mi>c</mi></mrow><mrow><mo stretchy="false">¯</mo></mrow></mover><mi>s</mi></mrow><mrow><mn>0</mn></mrow></msubsup><mo>=</mo><mo stretchy="false">(</mo><mi>c</mi><mover accent="true"><mrow><mi>c</mi></mrow><mrow><mo stretchy="false">¯</mo></mrow></mover><mi>u</mi><mi>d</mi><mi>s</mi><msup><mrow><mo stretchy="false">)</mo></mrow><mrow><mn>0</mn></mrow></msup></mrow></math>, <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mi>J</mi><mi>P</mi></msup><mo>=</mo><mn>1</mn><mo>/</mo><msup><mn>2</mn><mo>−</mo></msup></math> pentaquark state that has recently been observed experimentally by LHCb Collaboration at 4338.2 MeV, with a width of 7.0 MeV and high statistical significance <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mo form="prefix">&gt;</mo><mn>15</mn><mi>σ</mi></math>. Our model Hamiltonian reproduces the masses of the low-lying charmed and strange hadrons. We use the Gaussian expansion method to solve the five-body Schrödinger equation. Employing the real scaling method, including the relevant meson-baryon thresholds explicitly, sharp resonances are distinguished from the meson-baryon scattering states. We incorporate new color states of the color-octet meson and baryon configurations as well as the color-singlet configurations for the five-quark states. We find no <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mi>J</mi><mi>P</mi></msup><mo>=</mo><mn>1</mn><mo>/</mo><msup><mn>2</mn><mo>−</mo></msup></math> resonance close to the observed state, and also none in the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mi>J</mi><mi>P</mi></msup><mo>=</mo><mn>3</mn><mo>/</mo><msup><mn>2</mn><mo>−</mo></msup></math> state. This increases the likelihood that <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msubsup><mi>P</mi><mrow><mi>c</mi><mover accent="true"><mi>c</mi><mo stretchy="false">¯</mo></mover><mi>s</mi></mrow><mn>0</mn></msubsup></math> is a <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi mathvariant="normal">Ξ</mi><mi>c</mi></msub><mover accent="true"><mi>D</mi><mo stretchy="false">¯</mo></mover></math> hadronic molecule rather than a compact state.

Emiko Hiyama

Atsushi Hosaka

Makoto Oka

Georg Wolschin

Quark-model search for compact <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mi>c</mi><mover accent="true"><mrow><mi>c</mi></mrow><mrow><mo stretchy="false">¯</mo></mrow></mover><mi>u</mi><mi>d</mi><mi>s</mi></mrow></math> pentaquark states

We consider the resummation of large logarithmic corrections arising in the two-particle limit at next-to-next-to-leading logarithmic (NNLL) accuracy for the heavy-jet mass and <italic>C</italic>-parameter distributions in the decay of a Higgs boson to quarks and gluons: <math altimg='si2.svg'><mrow><mi>H</mi><mo>&#8594;</mo><mi>b</mi><mover accent='true'><mi>b</mi><mo>&#175;</mo></mover></mrow></math>, <math altimg='si3.svg'><mrow><mi>H</mi><mo>&#8594;</mo><mi>c</mi><mover accent='true'><mi>c</mi><mo>&#175;</mo></mover></mrow></math>, and <italic>H</italic>&#8239;&#8594;&#8239; <italic>gg</italic>. We demonstrate how the matched NNLO+NNLL results clarify the relative contributions of key hadronic Higgs-decay channels ( <math altimg='si2.svg'><mrow><mi>H</mi><mo>&#8594;</mo><mi>b</mi><mover accent='true'><mi>b</mi><mo>&#175;</mo></mover></mrow></math>, <math altimg='si3.svg'><mrow><mi>H</mi><mo>&#8594;</mo><mi>c</mi><mover accent='true'><mi>c</mi><mo>&#175;</mo></mover></mrow></math>, <italic>H</italic>&#8239;&#8594;&#8239; <italic>gg</italic>) yielding reduced uncertainties for both event-shape observables &#8211; especially for heavy-jet mass &#8211; while revealing substantial effects that shift the <italic>C</italic>-parameter peak in gluonic decays.

Elliot Fox

Switzerland

Aude Gehrmann-De Ridder

Thomas Gehrmann

Nigel Glover

Matteo Marcoli

Christian T. Preuss

NNLO+NNLL predictions for heavy-jet mass and <italic>C</italic>-parameter in Higgs decays to quarks and gluons

We discuss the production of <math altimg='si10.svg'><mrow><mi>D</mi><mover accent='true'><mi>D</mi><mo>&#175;</mo></mover></mrow></math> pairs in <math altimg='si2.svg'><mrow><msup><mi>e</mi><mo>+</mo></msup><msup><mi>e</mi><mo>&#8722;</mo></msup></mrow></math> collisions, where <italic>D</italic> refers to either <italic>D</italic> 0 or <math altimg='si30.svg'><msup><mi>D</mi><mo>+</mo></msup></math>. The continuum mechanism with the <italic>t</italic>/ <italic>u</italic>-channel vector-meson <italic>D</italic>* exchanges are considered. The results of the calculation depend on the parameter of the off-shell form-factor for the virtual <italic>D</italic>* mesons. The <italic>D</italic>* <italic>D&#947;</italic> coupling constants are found from the <italic>D</italic>*&#8239;&#8594;&#8239; <italic>D&#947;</italic> decays. We find relatively large contribution for the <math altimg='si4.svg'><mrow><msup><mi>D</mi><mn>0</mn></msup><msup><mrow><mover accent='true'><mi>D</mi><mo>&#175;</mo></mover></mrow><mn>0</mn></msup></mrow></math> channel and much smaller contribution in the <math altimg='si1.svg'><mrow><msup><mi>D</mi><mo>+</mo></msup><msup><mi>D</mi><mo>&#8722;</mo></msup></mrow></math> channel. In the second case we consider also the <italic>D</italic> &#8239;&#177;&#8239; exchanges. We conclude that the bump at <math altimg='si31.svg'><mrow><msub><mi>M</mi><mrow><msup><mi>D</mi><mn>0</mn></msup><msup><mrow><mover accent='true'><mi>D</mi><mo>&#175;</mo></mover></mrow><mn>0</mn></msup></mrow></msub><mo linebreak='goodbreak'>=</mo><mn>3.8</mn></mrow></math> GeV observed by the Belle and BaBar Collaborations has rather continuum origin than it corresponds to the broad resonance <italic>&#967;</italic> <inf><italic>c</italic>0</inf>(3860). We discuss also production of the <italic>&#967;</italic> <inf><italic>c</italic>2</inf>(3930) resonance which is a candidate for the <italic>&#967;</italic> <inf><italic>c</italic>2</inf>(2 <italic>P</italic>) state. This state can decay into both <math altimg='si10.svg'><mrow><mi>D</mi><mover accent='true'><mi>D</mi><mo>&#175;</mo></mover></mrow></math> channels, however the branching fractions are not well known at present. From a comparison of our model results to the BaBar data we find <math altimg='si32.svg'><mrow><mi>B</mi><mo>(</mo><msub><mi>&#967;</mi><mrow><mi>c</mi><mn>2</mn></mrow></msub><mrow><mo>(</mo><mn>3930</mn><mo>)</mo></mrow><mo>&#8594;</mo><mi>D</mi><mover accent='true'><mi>D</mi><mo>&#175;</mo></mover><mo>)</mo><mo>=</mo><mn>0.58</mn><mo>&#177;</mo><mn>0.13</mn></mrow></math> using the two-photon width <math altimg='si33.svg'><mrow><msub><mstyle mathvariant='normal'><mi>&#915;</mi></mstyle><mrow><mi>&#947;</mi><mi>&#947;</mi></mrow></msub><mo linebreak='goodbreak'>=</mo><mn>0.544</mn></mrow></math> keV (obtained for the Buchm&#252;ller-Tye potential) evaluated within the light-front approach (NRQCD limit). Our finding of <math altimg='si34.svg'><mrow><msub><mstyle mathvariant='normal'><mi>&#915;</mi></mstyle><mrow><mi>&#947;</mi><mi>&#947;</mi></mrow></msub><mo linebreak='goodbreak'>&#215;</mo><mi>B</mi><mrow><mo>(</mo><msub><mi>&#967;</mi><mrow><mi>c</mi><mn>2</mn></mrow></msub><mrow><mo>(</mo><mn>3930</mn><mo>)</mo></mrow><mo>&#8594;</mo><mi>D</mi><mover accent='true'><mi>D</mi><mo>&#175;</mo></mover><mo>)</mo></mrow><mo linebreak='goodbreak'>=</mo><mn>0.32</mn><mo>&#177;</mo><mn>0.07</mn></mrow></math> keV is close to the Belle and BaBar results. Realistic predictions of the differential distributions in several variables and integrated cross-sections are given for the Belle II kinematics.

Izabela Babiarz

Piotr Lebiedowicz

Wolfgang Schäfer

Antoni Szczurek

Competition of <italic>&#967;<inf>c</inf></italic>(2 <italic>P</italic>) quarkonia and continuum in <math altimg='si9.svg'><mrow><msup><mi>e</mi><mo>+</mo></msup><msup><mi>e</mi><mo>&#8722;</mo></msup><mo>&#8594;</mo><msup><mi>e</mi><mo>+</mo></msup><msup><mi>e</mi><mo>&#8722;</mo></msup><mi>D</mi><mover accent='true'><mi>D</mi><mo>&#175;</mo></mover></mrow></math>

We propose to search for <math altimg='si25.svg'><msubsup><mstyle mathvariant='normal'><mi>&#926;</mi></mstyle><mrow><mi>c</mi><mi>c</mi></mrow><mo>+</mo></msubsup></math> in the decay <math altimg='si26.svg'><mrow><msub><mstyle mathvariant='normal'><mi>&#923;</mi></mstyle><mi>b</mi></msub><mo>&#8594;</mo><msubsup><mstyle mathvariant='normal'><mi>&#926;</mi></mstyle><mrow><mi>c</mi><mi>c</mi></mrow><mo>+</mo></msubsup><msup><mi>D</mi><mo>&#8722;</mo></msup></mrow></math>, which serves as a tagged and reconstructible source of <math altimg='si25.svg'><msubsup><mstyle mathvariant='normal'><mi>&#926;</mi></mstyle><mrow><mi>c</mi><mi>c</mi></mrow><mo>+</mo></msubsup></math>. A possible fully charged final state is <math altimg='si27.svg'><mrow><msub><mrow><mo>[</mo><msub><mrow><mo>(</mo><mi>p</mi><msup><mi>K</mi><mo>&#8722;</mo></msup><msup><mi>K</mi><mo>&#8722;</mo></msup><msup><mi>&#960;</mi><mo>+</mo></msup><mo>)</mo></mrow><msubsup><mstyle mathvariant='normal'><mi>&#926;</mi></mstyle><mi>c</mi><mn>0</mn></msubsup></msub><msup><mi>&#960;</mi><mo>+</mo></msup><mo>]</mo></mrow><msubsup><mstyle mathvariant='normal'><mi>&#926;</mi></mstyle><mrow><mi>c</mi><mi>c</mi></mrow><mo>+</mo></msubsup></msub><mspace width='0.16em' /><msub><mrow><mo>(</mo><msup><mi>K</mi><mo>+</mo></msup><msup><mi>&#960;</mi><mo>&#8722;</mo></msup><msup><mi>&#960;</mi><mo>&#8722;</mo></msup><mo>)</mo></mrow><msup><mi>D</mi><mo>&#8722;</mo></msup></msub></mrow></math>, where the subscripts indicate the parent hadron in the decay chain. We estimate the branching fraction to be <math altimg='si28.svg'><mrow><mi mathvariant='script'>B</mi><mrow><mo>(</mo><msub><mstyle mathvariant='normal'><mi>&#923;</mi></mstyle><mi>b</mi></msub><mo>&#8594;</mo><msubsup><mstyle mathvariant='normal'><mi>&#926;</mi></mstyle><mrow><mi>c</mi><mi>c</mi></mrow><mo>+</mo></msubsup><msup><mi>D</mi><mo>&#8722;</mo></msup><mo>)</mo></mrow><mo linebreak='goodbreak'>=</mo><mrow><mo>(</mo><mn>5.1</mn><mo>&#177;</mo><mn>3.9</mn><mo>)</mo></mrow><mo linebreak='goodbreak'>&#215;</mo><msup><mn>10</mn><mrow><mo>&#8722;</mo><mn>4</mn></mrow></msup></mrow></math>, while the fully charged final state corresponds to an effective branching fraction of order <math altimg='si29.svg'><msup><mn>10</mn><mrow><mo>&#8722;</mo><mn>8</mn></mrow></msup></math>. These results indicate that LHCb has the potential to discover <math altimg='si25.svg'><msubsup><mstyle mathvariant='normal'><mi>&#926;</mi></mstyle><mrow><mi>c</mi><mi>c</mi></mrow><mo>+</mo></msubsup></math>. The prospects for observing <math altimg='si30.svg'><msubsup><mstyle mathvariant='normal'><mi>&#937;</mi></mstyle><mrow><mi>c</mi><mi>c</mi></mrow><mo>+</mo></msubsup></math> are also briefly discussed.

Chao-Qiang Geng

Xiang-Nan Jin

Chia-Wei Liu

Xin-Yi Liu

Xiao Yu

Potential of discovering <math altimg='si25.svg'><msubsup><mstyle mathvariant='normal'><mi>&#926;</mi></mstyle><mrow><mi>c</mi><mi>c</mi></mrow><mo>+</mo></msubsup></math> in &#923; <inf><italic>b</italic></inf> decays

The process of <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msubsup><mi mathvariant="normal">Ξ</mi><mrow><mi>b</mi><mi>c</mi></mrow><mo>+</mo></msubsup><mo stretchy="false">→</mo><msubsup><mi mathvariant="normal">Ξ</mi><mi>c</mi><mo>+</mo></msubsup><mi>J</mi><mo>/</mo><mi>ψ</mi></math> is among the most favored modes for searching for bottom-charm baryons. However, its branching fraction has never been studied in theory. In this work, we investigate the branching fraction of <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msubsup><mi mathvariant="normal">Ξ</mi><mrow><mi>b</mi><mi>c</mi></mrow><mo>+</mo></msubsup><mo stretchy="false">→</mo><msubsup><mi mathvariant="normal">Ξ</mi><mi>c</mi><mo>+</mo></msubsup><mi>J</mi><mo>/</mo><mi>ψ</mi></math> in the final-state-interaction approach, as it is dominated by the color-suppressed nonfactorizable contributions. A similar process, <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><msup><mi mathvariant="normal">Λ</mi><mn>0</mn></msup><mi>J</mi><mo>/</mo><mi>ψ</mi></math>, is used as a control mode to fix the model parameter. Consequently, the branching fraction of <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msubsup><mi mathvariant="normal">Ξ</mi><mrow><mi>b</mi><mi>c</mi></mrow><mo>+</mo></msubsup><mo stretchy="false">→</mo><msubsup><mi mathvariant="normal">Ξ</mi><mi>c</mi><mo>+</mo></msubsup><mi>J</mi><mo>/</mo><mi>ψ</mi></math> is predicted to be <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mo stretchy="false">(</mo><mn>1.5</mn><msubsup><mn>5</mn><mrow><mo>−</mo><mn>0.42</mn></mrow><mrow><mo>+</mo><mn>0.50</mn></mrow></msubsup><mo stretchy="false">)</mo><mo>×</mo><msup><mn>10</mn><mrow><mo>−</mo><mn>4</mn></mrow></msup></math>. With the production rate of bottom-charm baryons and the detection efficiencies of the final states, it is expected for considerable signal events to observe <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msubsup><mi mathvariant="normal">Ξ</mi><mrow><mi>b</mi><mi>c</mi></mrow><mo>+</mo></msubsup></math> in the near future.

Xiao-Hui Hu

Cai-Ping Jia

Ye Xing

Fu-Sheng Yu

Branching fraction of <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msubsup><mi mathvariant="normal">Ξ</mi><mrow><mi>b</mi><mi>c</mi></mrow><mo>+</mo></msubsup><mo stretchy="false">→</mo><msubsup><mi mathvariant="normal">Ξ</mi><mi>c</mi><mo>+</mo></msubsup><mi>J</mi><mo>/</mo><mi>ψ</mi></math> in the final-state-interaction approach

Obtaining hadronic two-point functions is a central step in spectroscopy calculations in lattice QCD. This requires solving the Dirac equation repeatedly, which is computationally demanding. The distillation method addresses this difficulty by using the lowest eigenvectors of the spatial Laplacian to construct a subspace in which the Dirac operator can be fully inverted. This approach is efficient for nonlocal operators such as meson-meson and baryon-baryon operators. However, local multiquark operators with four or more (anti)quarks are computationally expensive in this framework: the cost of contractions scales with a high power of the number of Laplacian eigenvectors. We present a position-space sampling method within distillation that reduces this cost scaling by performing the momentum projection only over sparse grids rather than the full spatial lattice. We demonstrate the efficiency of this unbiased estimator for single-meson, single-baryon and local tetraquark operators. Using Wilson-clover fermions at the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>S</mi><mi>U</mi><mo stretchy="false">(</mo><mn>3</mn><mo stretchy="false">)</mo></math>-flavor-symmetric point, we apply this method to study the importance of local tetraquark operators for extracting the finite-volume <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>T</mi><mrow><mi>c</mi><mi>c</mi></mrow></msub><mo stretchy="false">(</mo><mn>3875</mn><msup><mo stretchy="false">)</mo><mo>+</mo></msup></math> spectrum. To this end, we extend a large basis of bilocal <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>D</mi><msup><mi>D</mi><mo>*</mo></msup></math> and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mi>D</mi><mo>*</mo></msup><msup><mi>D</mi><mo>*</mo></msup></math> scattering operators by including local tetraquark operators. The inclusion of local operators leads to significant shifts in the estimates of several energy levels. Finally, we show the effect of these shifts on the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>D</mi><msup><mi>D</mi><mo>*</mo></msup></math> scattering phase shift from a single-channel <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>s</mi></math>-wave Lüscher analysis.

Andres Stump

Jeremy R. Green

Position-space sampling for local multiquark operators in lattice QCD using distillation and the importance of tetraquark operators for <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>T</mi><mrow><mi>c</mi><mi>c</mi></mrow></msub><mo stretchy="false">(</mo><mn>3875</mn><msup><mo stretchy="false">)</mo><mo>+</mo></msup></math>