We use Soft Collinear Effective Theory (SCET) to factorize the polarized Deep Inelastic Scattering (DIS) structure functions $\textit{g}$ ($\textit{x}$) and $\textit{g}$ ($\textit{x}$), and to sum Sudakov double logarithms of 1 − $\textit{x}$. The analysis is done both in terms of lightcone parton distributions and their moments. Computing $\textit{g}$ requires subleading SCET operators which contain gluons. We calculate the one-loop matching coefficients from QCD onto these subleading SCET operators, and the one-loop matching from SCET onto the parton distribution function (PDF). The PDF in SCET is given by a bilocal operator, rather than the trilocal operator used in the QCD analysis of $\textit{g}$ for generic $\textit{x}$. We compute the one-loop anomalous dimension of the PDF operator for any $\textit{x}$, and show that as $\textit{x}$ → 1, it factors into a single-variable evolution.

United States

Jaipratap Grewal

Aneesh Manohar

Jyotirmoy Roy

Polarized deep inelastic scattering as $\textit{x}$ → 1 using soft collinear effective theory

We present updated and comprehensive Standard Model predictions for the inclusive rare decay $$ B\to {X}_s\nu \overline{\nu} $$ . Using a state-of-the-art determination of the short-distance coefficient, including NLO QCD and electroweak effects, and implementing a consistent treatment of heavy-quark masses and power corrections within the kinetic scheme, we compute the total decay rate and the neutrino invariant mass spectrum. We incorporate all known perturbative contributions in the heavy quark limit up to $$ \mathcal{O}\left({\alpha}_s^3\right) $$ , evaluate non-perturbative corrections through the Heavy Quark Expansion up to $$ 1/{m}_b^3 $$ , and include estimates of four-quark operator matrix elements from HQET sum rules. We obtain the Standard Model branching ratios Br( $$ {B}^0\to {X}_s\nu \overline{\nu} $$ ) = (3.35 ± 0.10) × 10 and Br( $$ {B}^{+}\to {X}_s\nu \overline{\nu} $$ ) = (3.62 ± 0.11) × 10 , representing a significant improvement in both central value and precision compared to previous determinations. We also provide predictions for partial rates with kinematic cuts relevant to Belle II. Our results are timely in view of recent measurements of $$ B\to K\nu \overline{\nu} $$ and the first upper limits on inclusive $$ B\to {X}_s\nu \overline{\nu} $$ , and they offer a robust baseline for future searches for physics beyond the Standard Model in $$ b\to s\nu \overline{\nu} $$ transitions.

Italy

Matteo Fael

Germany

Jack Jenkins

Enrico Lunghi

Switzerland

Slovenia

Zachary Polonsky

The Standard Model prediction for the rare decay $$ B\to {X}_s\nu \overline{\nu} $$

We present an analysis of the processes <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>η</mi><mi mathvariant="normal">ϒ</mi><mo stretchy="false">(</mo><mn>1</mn><mi>S</mi><mo stretchy="false">)</mo></math>, <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>η</mi><mi mathvariant="normal">ϒ</mi><mo stretchy="false">(</mo><mn>2</mn><mi>S</mi><mo stretchy="false">)</mo></math>, and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>γ</mi><msub><mi>X</mi><mi>b</mi></msub></math> with <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>X</mi><mi>b</mi></msub><mo stretchy="false">→</mo><msup><mi>π</mi><mo>+</mo></msup><msup><mi>π</mi><mo>−</mo></msup><msub><mi>χ</mi><mrow><mi>b</mi><mi>J</mi></mrow></msub><mo>,</mo><msub><mi>χ</mi><mrow><mi>b</mi><mi>J</mi></mrow></msub><mo stretchy="false">→</mo><mi>γ</mi><mi mathvariant="normal">ϒ</mi><mo stretchy="false">(</mo><mn>1</mn><mi>S</mi><mo stretchy="false">)</mo></math> (<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mi>J</mi><mo>=</mo><mn>1</mn></mrow></math>, 2) reconstructed from <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mi>γ</mi><mi>γ</mi><msup><mrow><mi>π</mi></mrow><mrow><mo>+</mo></mrow></msup><msup><mrow><mi>π</mi></mrow><mrow><mo>−</mo></mrow></msup><msup><mrow><mo>ℓ</mo></mrow><mrow><mo>+</mo></mrow></msup><msup><mrow><mo>ℓ</mo></mrow><mrow><mo>−</mo></mrow></msup></mrow></math> <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mo stretchy="false">(</mo><mo>ℓ</mo><mo>=</mo><mi>e</mi><mo>,</mo><mi>μ</mi><mo stretchy="false">)</mo></mrow></math> final states in <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mn>19.6</mn><mtext> </mtext><mtext> </mtext><msup><mi>fb</mi><mrow><mo>−</mo><mn>1</mn></mrow></msup></math> of Belle II data collected at four energy points near the peak of the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi mathvariant="normal">ϒ</mi><mo stretchy="false">(</mo><mn>10753</mn><mo stretchy="false">)</mo></math> resonance. Here, <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>X</mi><mi>b</mi></msub></math> is a hypothetical bottomonium-sector partner of the <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 the process <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>η</mi><mi mathvariant="normal">ϒ</mi><mo stretchy="false">(</mo><mn>2</mn><mi>S</mi><mo stretchy="false">)</mo></math>, we observe a signal with a significance that exceeds <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mn>6.0</mn><mi>σ</mi></math> when all energy points are combined. A signal with a significance of <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mn>4.2</mn><mi>σ</mi></mrow></math> is observed at a center-of-mass energy of 10.653 GeV, close to the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mi>B</mi><mo>*</mo></msup><msup><mover accent="true"><mi>B</mi><mo stretchy="false">¯</mo></mover><mo>*</mo></msup></math> threshold. At this energy, we measure <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>σ</mi><mo stretchy="false">(</mo><mi>η</mi><mi mathvariant="normal">ϒ</mi><mo stretchy="false">(</mo><mn>2</mn><mi>S</mi><mo stretchy="false">)</mo><mo stretchy="false">)</mo><mo>/</mo><mi>σ</mi><mo stretchy="false">(</mo><msup><mi>π</mi><mo>+</mo></msup><msup><mi>π</mi><mo>−</mo></msup><mi mathvariant="normal">ϒ</mi><mo stretchy="false">(</mo><mn>2</mn><mi>S</mi><mo stretchy="false">)</mo><mo stretchy="false">)</mo><mo>&gt;</mo><mn>23</mn></math> at the 90% confidence level, indicating a strong violation of heavy-quark spin symmetry. No significant signal is observed for <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>η</mi><mi mathvariant="normal">ϒ</mi><mo stretchy="false">(</mo><mn>1</mn><mi>S</mi><mo stretchy="false">)</mo></math> or <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>γ</mi><msub><mi>X</mi><mi>b</mi></msub></math>. Upper limits on the Born cross sections for the processes <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>η</mi><mi mathvariant="normal">ϒ</mi><mo stretchy="false">(</mo><mn>1</mn><mi>S</mi><mo stretchy="false">)</mo></math> and <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>γ</mi><msub><mi>X</mi><mi>b</mi></msub></math> with <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>X</mi><mi>b</mi></msub><mo stretchy="false">→</mo><msup><mi>π</mi><mo>+</mo></msup><msup><mi>π</mi><mo>−</mo></msup><msub><mi>χ</mi><mrow><mi>b</mi><mi>J</mi></mrow></msub></math> are determined.

I. Adachi

L. Aggarwal

H. Ahmed

Y. Ahn

H. Aihara

N. Akopov

S. Alghamdi

M. Alhakami

A. Aloisio

N. Althubiti

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

S. Bansal

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

V. Bhardwaj

B. Bhuyan

F. Bianchi

T. Bilka

D. Biswas

A. Bobrov

D. Bodrov

A. Bondar

G. Bonvicini

A. Boschetti

A. Bozek

M. Bračko

P. Branchini

R.A. Briere

T.E. Browder

A. Budano

S. Bussino

Q. Campagna

L. Cao

G. Casarosa

C. Cecchi

M.C. Chang

P. Cheema

L. Chen

B.G. Cheon

C. Cheshta

H. Chetri

K. Chilikin

J. Chin

K. Chirapatpimol

H.E. Cho

K. Cho

S.J. Cho

S.K. Choi

S. Choudhury

J.A. Colorado-Caicedo

I. Consigny

L. Corona

J.X. Cui

E. De La Cruz-Burelo

S.A. De La Motte

G. de Marino

G. De Nardo

G. De Pietro

R. de Sangro

M. Destefanis

S. Dey

A. Di Canto

J. Dingfelder

Z. Doležal

I. Domínguez Jiménez

T.V. Dong

X. Dong

M. Dorigo

K. Dugic

G. Dujany

P. Ecker

D. Epifanov

J. Eppelt

Observation of <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>η</mi><mi mathvariant="normal">ϒ</mi><mo stretchy="false">(</mo><mn>2</mn><mi>S</mi><mo stretchy="false">)</mo></math> and search for <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><msup><mrow><mi>e</mi></mrow><mrow><mo>+</mo></mrow></msup><msup><mrow><mi>e</mi></mrow><mrow><mo>−</mo></mrow></msup><mo stretchy="false">→</mo><mi>η</mi><mi mathvariant="normal">ϒ</mi><mo stretchy="false">(</mo><mn>1</mn><mi>S</mi><mo stretchy="false">)</mo></mrow></math>, <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mi>γ</mi><msub><mrow><mi>X</mi></mrow><mrow><mi>b</mi></mrow></msub></mrow></math> at <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msqrt><mi>s</mi></msqrt></math> near 10.75 GeV

We revisit the calculation of the next-to-leading order (NLO) corrections to dijet production in electron-ion collisions at small $\textit{x}$. We focus on the back-to-back configuration where the relative transverse momentum $\textit{P}$ of the measured jets is much larger than both their momentum imbalance $\textit{K}$ and the target saturation momentum $\textit{Q}$ ($\textit{x}$, $\textit{A}$). In this regime, we present for the first time a complete calculation of the real NLO corrections, associated with gluon emissions outside the jet cones, at leading power in 1/$\textit{P}$ . Our result exhibits TMD factorisation, with the same hard factor as at tree-level and a NLO correction to the Weiszäcker-Williams (WW) gluon transverse momentum dependent (TMD) distribution which involves four Wilson-line operators. By studying different kinematical regimes for $\textit{K}$ and for the radiated gluon, we recover all the quantum evolutions that were previously identified for this process at NLO: the B-JIMWLK high-energy evolution and the CSS evolution of the gluon WW TMD, and the DGLAP evolution of the gluon PDF. When both $\textit{K}$ and the transverse momentum transferred by the target are large compared to $\textit{Q}$ , all the Wilson-line operators boil down to the unintegrated gluon distribution and our NLO result for the gluon TMD can be used to isolate the transverse-momentum dependent gluon splitting function.

France

Paul Caucal

Edmond Iancu

Farid Salazar

Feng Yuan

Gluon splitting at small $\textit{x}$: a unified derivation for the JIMWLK, DGLAP and CSS equations

The Belle Collaboration recently reported a potential candidate for the spin-2 $$D^*\bar{D}^*$$ partner of the $\textit{X}$(3872), denoted as $$X_2$$ , with a mass of $$(4014.3\pm 4.0\pm 1.5)$$ MeV and a width of $$(4\pm 11\pm 6)$$ MeV. Assuming the $$X_2$$ as a $$D^*\bar{D}^*$$ molecular state, we calculate its hidden charm decay $$X_2 \rightarrow \pi ^+ \pi ^- \eta _{c}$$ via box loop diagram using an effective Lagrangian approach. To investigate the dependence of the decay width on the molecular structure, we consider four different phase angles: $$\theta =0$$ , $$\pi /6$$ , $$\pi /4$$ , and $$\pi /2$$ . The decay width is found to be sensitive to the mass of the $$X_2$$ . The decay partial widths are predicted to be on the order of 1 keV. We expect that the present calculations, performed in the molecular framework, would provide useful guidance for future experimental studies.

China

Hao-Dong Cai

Gang Li

Shi-Dong Liu

Hidden charmed decays of spin-2 partner of $\textit{X}$(3872) within $$D^*\bar{D}^*$$ molecular framework

Tensor-polarized twist-3 parton distribution functions (PDFs) <italic>f<inf>LT</inf></italic>( <italic>x</italic>) are calculated for the spin-1 deuteron by using twist-2 relations, which are similar to the Wandzura-Wilczek relation and the Burkhardt-Cottingham sum rule in the spin-1/2 nucleon, together with tensor-polarized twist-2 PDFs <italic>f</italic> <inf>1<italic>LL</italic></inf>( <italic>x</italic>). The PDFs are shown for <italic>f<inf>LT</inf></italic>( <italic>x</italic>) at <math altimg='si1.svg'><mrow><msup><mi>Q</mi><mn>2</mn></msup><mo linebreak='goodbreak'>=</mo><mn>2.5</mn></mrow></math>&#8239;GeV 2, where the tensor-polarized PDFs <italic>f</italic> <inf>1<italic>LL</italic></inf>( <italic>x</italic>) are provided. The <italic>x</italic>-dependence of <italic>f<inf>LT</inf></italic>( <italic>x</italic>) is similar to <italic>f</italic> <inf>1<italic>LL</italic></inf>( <italic>x</italic>), and the magnitude of <italic>f<inf>LT</inf></italic>( <italic>x</italic>) is roughly of the order of <italic>f</italic> <inf>1<italic>LL</italic></inf>( <italic>x</italic>). In experiments at the Thomas Jefferson National Accelerator Facility (JLab), higher-twist effects could be sizable because <italic>Q</italic> 2 values are not very large in comparison with the hadronic scale of 1&#8239;GeV 2. Therefore, the JLab experiments could provide a good opportunity to investigate the twist-3 distributions <italic>f<inf>LT</inf></italic>( <italic>x</italic>) in addition to the twist-2 ones <italic>f</italic> <inf>1<italic>LL</italic></inf>( <italic>x</italic>). Furthermore, these tensor-polarized PDFs could be investigated at future Electron-Ion Colliders (EICs) and hadron accelerator facilities such as the Fermi National Accelerator Laboratory (Fermilab), the Nuclotron-based Ion Collider fAcility (NICA), and the Large Hadron Collider (LHC).

Japan

S. Kumano

Kenshi Kuroki

Tensor-polarized twist-3 parton distribution functions <italic>f<inf>LT</inf></italic>( <italic>x</italic>) for the spin-1 deuteron by using twist-2 relations

In this paper, we propose the analysis of the heavy quark photoproduction associated with a leading neutron in hadronic collisions at the LHC as an alternative to probe the pion gluon distribution in a kinematical range not covered by previous experiments. We perform an exploratory study of the charm and bottom photoproduction associated with a leading neutron in proton-proton (<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>p</mi><mi>p</mi></math>) and proton-lead (<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>p</mi><mi>P</mi><mi>b</mi></math>) collisions, and present calculations for the rapidity distributions and cross sections. Our predictions indicate that experimental studies of these processes are feasible, and that a future measurement of this final state will be useful to constrain the pion gluon distribution at small values of the Bjorken <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>x</mi></math> variable and to improve our understanding of the pion structure.

Brazil

Victor P. Gonçalves

Juciene T. de Souza

Diego Spiering

Probing the pion-gluon distribution at small <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>x</mi></math> in photon-induced interactions at the LHC

Motivated by the interpretation of <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mi>X</mi><mo stretchy="false">(</mo><mn>3872</mn><mo stretchy="false">)</mo></mrow></math> as a <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mi>D</mi><mover accent="true"><mrow><mi>D</mi></mrow><mrow><mo stretchy="false">¯</mo></mrow></mover><msup><mrow><mtext> </mtext></mrow><mrow><mo>*</mo></mrow></msup></mrow></math> molecular state, heavy-quark spin symmetry predicts a spin-2 partner, <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>X</mi><mn>2</mn></msub><mo stretchy="false">(</mo><mn>4013</mn><mo stretchy="false">)</mo></math>, which can be regarded as a <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><msup><mrow><mi>D</mi></mrow><mrow><mo>*</mo></mrow></msup><mover accent="true"><mrow><mi>D</mi></mrow><mrow><mo stretchy="false">¯</mo></mrow></mover><msup><mrow><mtext> </mtext></mrow><mrow><mo>*</mo></mrow></msup></mrow></math> molecule with quantum numbers <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>2</mn><mrow><mo>+</mo><mo>+</mo></mrow></msup></math>. Its experimental confirmation, however, remains elusive. In this work, we investigate the production mechanisms of <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>X</mi><mn>2</mn></msub><mo stretchy="false">(</mo><mn>4013</mn><mo stretchy="false">)</mo></math> in the reactions <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><msup><mrow><mi>K</mi></mrow><mrow><mo>−</mo></mrow></msup><mi>p</mi><mo stretchy="false">→</mo><msubsup><mrow><mi>D</mi></mrow><mrow><mi>s</mi></mrow><mrow><mo>−</mo></mrow></msubsup><msubsup><mrow><mi mathvariant="normal">Λ</mi></mrow><mrow><mi>c</mi></mrow><mrow><mo>+</mo></mrow></msubsup><msub><mrow><mi>X</mi></mrow><mrow><mn>2</mn></mrow></msub><mo stretchy="false">(</mo><mn>4013</mn><mo stretchy="false">)</mo></mrow></math> and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>p</mi><mi>p</mi><mo stretchy="false">→</mo><msubsup><mi mathvariant="normal">Λ</mi><mi>c</mi><mo>+</mo></msubsup><msubsup><mi mathvariant="normal">Λ</mi><mi>c</mi><mo>+</mo></msubsup><msub><mi>X</mi><mn>2</mn></msub><mo stretchy="false">(</mo><mn>4013</mn><mo stretchy="false">)</mo></math> within an effective Lagrangian framework. The production processes are modeled via <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>t</mi></math>-channel <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><msup><mrow><mi>D</mi></mrow><mrow><mo>*</mo></mrow></msup><mo>/</mo><mover accent="true"><mrow><mi>D</mi></mrow><mrow><mo stretchy="false">¯</mo></mrow></mover><msup><mrow><mtext> </mtext></mrow><mrow><mo>*</mo></mrow></msup></mrow></math> meson exchanges, while initial-state interactions (ISIs) mediated by Pomeron and Reggeon exchanges are also taken into account. Our calculations indicate that the total cross sections can reach the pb level, suggesting that <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>X</mi><mn>2</mn></msub><mo stretchy="false">(</mo><mn>4013</mn><mo stretchy="false">)</mo></math> may be accessible at current and future experiments such as AMBER@CERN and LHCb. Inclusion of ISIs enhances the cross sections by nearly 1 order of magnitude. The differential distributions show distinct angular behaviors for the two reactions: the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mi>K</mi><mo>−</mo></msup><mi>p</mi></math> reaction exhibits a forward-peaked distribution, whereas the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>p</mi><mi>p</mi></math> reaction shows a dip near central angles. This study provides a quantitative theoretical benchmark for future experimental searches of <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>X</mi><mn>2</mn></msub><mo stretchy="false">(</mo><mn>4013</mn><mo stretchy="false">)</mo></math> and highlights the importance of ISIs in high-energy particle investigations.

Min Yuan

Bo Nan Zhang

Yin Huang

Search for the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><msup><mrow><mi>D</mi></mrow><mrow><mo>*</mo></mrow></msup><mover accent="true"><mrow><mi>D</mi></mrow><mrow><mo stretchy="false">¯</mo></mrow></mover><msup><mrow><mtext> </mtext></mrow><mrow><mo>*</mo></mrow></msup></mrow></math> molecular state <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>X</mi><mn>2</mn></msub><mo stretchy="false">(</mo><mn>4013</mn><mo stretchy="false">)</mo></math> in <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mi>K</mi><mo>−</mo></msup><mi>p</mi></math> and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>p</mi><mi>p</mi></math> collisions

We perform a unified description of the experimental data of the $$\pi ^+\pi ^-$$ invariant mass spectra of $$B_s^0 \rightarrow \psi (2S) \pi ^+\pi ^-$$ , the $$\pi ^+\pi ^-$$ and $$K^+ K^-$$ invariant mass spectra of $$B_s^0 \rightarrow X(3872) \pi ^+\pi ^- (K^+ K^-)$$ , and the ratio of branch fractions $$\mathcal {B}[B_s^0 \rightarrow X(3872)(K^+K^-)_{\mathrm{non-}\phi }]/ \mathcal {B}[B_s^0 \rightarrow X(3872)\pi ^+ \pi ^-]$$ . The strong final state interactions between the two pseudoscalars are taken into account using a parametrization fulfilling unitarity and analyticity. We find that there is universality in the coupling constants for $$B_s^0 \rightarrow \psi (2S) \pi ^+\pi ^-$$ and $$B_s^0 \rightarrow J/\psi \pi ^+\pi ^-$$ processes. While the couplings of $$B_s^0 \rightarrow X(3872) \pi ^+\pi ^-$$ are about half of magnitude smaller than the couplings of $$B_s^0 \rightarrow \psi (2S) \pi ^+\pi ^-$$ , which indicates that the $\textit{X}$(3872) is different from a pure charmonium state. Furthermore, we find that the $$f_0(1500)$$ plays an important role in the $$B_s^0 \rightarrow \psi (2S) \pi ^+\pi ^-$$ and the $$B_s^0 \rightarrow X(3872) \pi ^+\pi ^- (K^+ K^-)$$ processes, though the phase space of $$B_s^0 \rightarrow X(3872) f_0(1500)$$ is small. Also we predict the ratio of branch fractions $$\mathcal {B}[B_s^0 \rightarrow \psi (2S)(K^+K^-)_{\mathrm{non-}\phi }]/ \mathcal {B}[B_s^0 \rightarrow \psi (2S)\pi ^+ \pi ^-]$$ and the $$K^+ K^-$$ invariant mass distribution of $$B_s^0 \rightarrow \psi (2S)K^+K^-$$ .

Yun-Hua Chen

Unified study of $$B_s^0 \rightarrow X(3872) \pi ^+\pi ^- (K^+ K^-)$$ and $$B_s^0 \rightarrow \psi (2S) \pi ^+\pi ^- (K^+ K^-)$$ processes

We consider the differential cross-section for single-inclusive jet production with transverse momentum <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>P</mi><mo>⊥</mo></msub></math> in deep inelastic scattering at small Bjorken <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>x</mi><mtext>Bj</mtext></msub></math>, mediated by a virtual photon with virtuality <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mi>Q</mi><mn>2</mn></msup></math>. Unlike most studies at small <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>x</mi></math>, which focus on particle production in the current fragmentation region, we investigate the kinematic regime where the jet is produced in the target fragmentation hemisphere of the Breit frame, and with <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>P</mi><mo>⊥</mo></msub><mo>≪</mo><mi>Q</mi></math>. For a longitudinally polarized photon, we demonstrate that this cross section is not power suppressed in <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>P</mi><mo>⊥</mo></msub><mo>/</mo><mi>Q</mi></math> and we derive a factorized expression in terms of extended quark and gluon jet fracture functions. Our formula, valid at next-to-leading order in <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>α</mi><mi>s</mi></msub></math> at small <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>x</mi></math>, is akin to the Altarelli-Martinelli identity for the longitudinal DIS structure function. Numerical estimates show that the extended quark jet fracture function is the most sensitive to saturation effects in large nuclei.

Small-<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>x</mi></math> Factorization in the Target Fragmentation Region