We explore the non-perturbative aspects of $\textit{c}$ = 1 string with compactified Euclidean time, its 0 + 0 dimensional matrix model duals (at self-dual radius), and 0 + 1 dimensional Matrix Quantum Mechanics (free fermion) description. We calculate the instanton normalizations, disk two-point function, and annulus one-point function in worldsheet formalism using string field theory insights. We further match them with the corresponding predictions from the matrix model descriptions. We also have some results and remarks regarding the multi ZZ instanton normalizations and the general (1, $\textit{n}$) ZZ instanton normalization for $\textit{c}$ = 1 string at both self-dual and generic radius.

India

Rishabh Kaushik

$\textit{c}$ = 1, $\textit{R}$ = 1 and $\textit{N}$ ≫ 1: ZZ instantons in 2D string theory and matrix integrals

The nucleon matrix elements (NMEs) associated with quark chromomagnetic dipole moments (cMDMs) play a crucial role in determining the <math xmlns="http://www.w3.org/1998/Math/MathML"><mrow><mi mathvariant="italic">CP</mi></mrow></math>-odd pion-nucleon couplings induced by quark chromoelectric dipole moments. In recent years, it has been argued that the NMEs of cMDMs can be related to the third moment of the nucleon's higher-twist (specifically, twist-3) parton distribution function (PDF) <math xmlns="http://www.w3.org/1998/Math/MathML"><mrow><mi>e</mi><mo>(</mo><mi>x</mi><mo>)</mo></mrow></math>, which can, in principle, be measured through dihadron production in semi-inclusive deep inelastic scattering processes. By applying the spin-flavor expansion to the cMDM operators in the large-<math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>N</mi><mi>c</mi></msub></math> limit, where <math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>N</mi><mi>c</mi></msub></math> is the number of quark colors, we show that the NMEs receive contributions not only from the twist-3 PDF <math xmlns="http://www.w3.org/1998/Math/MathML"><mrow><mi>e</mi><mo>(</mo><mi>x</mi><mo>)</mo></mrow></math> but also from an additional, previously neglected nucleon form factor. Incorporating constraints from the spin-flavor expansion, recent experimental data on <math xmlns="http://www.w3.org/1998/Math/MathML"><mrow><mi>e</mi><mo>(</mo><mi>x</mi><mo>)</mo></mrow></math>, as well as model calculations of <math xmlns="http://www.w3.org/1998/Math/MathML"><mrow><mi>e</mi><mo>(</mo><mi>x</mi><mo>)</mo></mrow></math>, we estimate the NMEs of the cMDM operators. Our analysis indicates that the NMEs are dominated by the nucleon form factors, and the cMDM contributions to pion-nucleon couplings can be comparable to those from the quark sigma terms.

United States

Shohini Bhattacharya

Kaori Fuyuto

Emanuele Mereghetti

Thomas R. Richardson

Toward the determination of <math xmlns="http://www.w3.org/1998/Math/MathML"><mrow><mi>C</mi><mi>P</mi></mrow></math>-odd pion-nucleon couplings

We present the results of our lattice QCD computation of the hadronic matrix elements relevant to the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>h</mi><mi>c</mi></msub><mo stretchy="false">→</mo><msub><mi>η</mi><mi>c</mi></msub><mi>γ</mi></math> and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>h</mi><mi>b</mi></msub><mo stretchy="false">→</mo><msub><mi>η</mi><mi>b</mi></msub><mi>γ</mi></math> decays by using the gauge configurations produced by the Extended Twisted Mass Collaboration with <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>N</mi><mi>f</mi></msub><mo>=</mo><mn>2</mn><mo>+</mo><mn>1</mn><mo>+</mo><mn>1</mn></math> dynamical Wilson-Clover twisted mass fermions at five different lattice spacings with physical dynamical <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>u</mi></math>, <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>d</mi></math>, <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>s</mi></math> and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>c</mi></math> quark masses (except for the coarsest lattice for which the lightest sea quark corresponds to a pion with <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>m</mi><mi>π</mi></msub><mo>≃</mo><mn>175</mn><mtext> </mtext><mtext> </mtext><mi>MeV</mi></math>). While the hadronic matrix element for <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>h</mi><mi>c</mi></msub><mo stretchy="false">→</mo><msub><mi>η</mi><mi>c</mi></msub><mi>γ</mi></math> is obtained directly, the one relevant to <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>h</mi><mi>b</mi></msub><mo stretchy="false">→</mo><msub><mi>η</mi><mi>b</mi></msub><mi>γ</mi></math> is reached by working with heavy quark masses <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msubsup><mi>m</mi><mi>H</mi><mrow><mo stretchy="false">(</mo><mi>n</mi><mo stretchy="false">)</mo></mrow></msubsup><mo>=</mo><msup><mi>λ</mi><mrow><mi>n</mi><mo>−</mo><mn>1</mn></mrow></msup><msub><mi>m</mi><mi>c</mi></msub></math>, with <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>λ</mi><mo>∼</mo><mn>1.24</mn></math> and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>n</mi><mo>=</mo><mn>1</mn><mo>,</mo><mn>2</mn><mo>,</mo><mo>…</mo><mo>,</mo><mn>6</mn></math>, and then extrapolated to <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>m</mi><mi>b</mi></msub></math> by several judicious Ansätze. In the continuum limit we obtain <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi mathvariant="normal">Γ</mi><mo stretchy="false">(</mo><msub><mi>h</mi><mi>c</mi></msub><mo stretchy="false">→</mo><msub><mi>η</mi><mi>c</mi></msub><mi>γ</mi><mo stretchy="false">)</mo><mo>=</mo><mn>0.604</mn><mo stretchy="false">(</mo><mn>24</mn><mo stretchy="false">)</mo><mtext> </mtext><mtext> </mtext><mi>MeV</mi></math>, which is by a factor of 2.3 more accurate than the previous lattice estimates, and in good agreement with the experimental measurement. In the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>b</mi></math>-quark case we obtain <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi mathvariant="normal">Γ</mi><mo stretchy="false">(</mo><msub><mi>h</mi><mi>b</mi></msub><mo stretchy="false">→</mo><msub><mi>η</mi><mi>b</mi></msub><mi>γ</mi><mo stretchy="false">)</mo><mo>=</mo><mn>46.0</mn><mo stretchy="false">(</mo><mn>4.8</mn><mo stretchy="false">)</mo><mtext> </mtext><mtext> </mtext><mi>keV</mi></math>.

France

D. Bečirević

Italy

R. Di Palma

R. Frezzotti

G. Gagliardi

V. Lubicz

F. Sanfilippo

N. Tantalo

Lattice QCD determination of the radiative decay rates <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>h</mi><mi>c</mi></msub><mo stretchy="false">→</mo><msub><mi>η</mi><mi>c</mi></msub><mi>γ</mi></math> and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>h</mi><mi>b</mi></msub><mo stretchy="false">→</mo><msub><mi>η</mi><mi>b</mi></msub><mi>γ</mi></math>

We investigate new contributions to the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>H</mi><mi>Z</mi><mi>Z</mi></math> vertex from the flavor changing neutral current (FCNC) involving the Higgs and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>Z</mi></math> bosons. Our calculations reveal that the form factors <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msubsup><mi>h</mi><mn>2</mn><mi>V</mi></msubsup></math> and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msubsup><mi>h</mi><mn>3</mn><mi>V</mi></msubsup></math> (<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>V</mi><mo>=</mo><mi>H</mi></math>, <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>Z</mi></math>) can be induced through these couplings, and we present our results in terms of the Passarino-Veltman scalar functions. Using the current limits on <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>H</mi><mover accent="true"><mi>t</mi><mo stretchy="false">¯</mo></mover><mi>c</mi></math> and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>Z</mi><mover accent="true"><mi>t</mi><mo stretchy="false">¯</mo></mover><mi>c</mi></math> couplings, we determine that the new contributions to the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>C</mi><mi>P</mi></math>-conserving form factor <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msubsup><mi>h</mi><mn>2</mn><mi>V</mi></msubsup></math> are small compared to the Standard Model (SM) predictions. However, for the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>C</mi><mi>P</mi></math>-violating form factor <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msubsup><mi>h</mi><mn>3</mn><mi>V</mi></msubsup></math>, the contributions can reach values as high as <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mn>10</mn><mrow><mo>−</mo><mn>6</mn></mrow></msup></math>, 5 orders of magnitude larger than in the SM. Furthermore, we examine how these results influence the left-right asymmetries in the processes <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mi>H</mi><mo>*</mo></msup><mo stretchy="false">→</mo><mi>Z</mi><mi>Z</mi></math> and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mi>Z</mi><mo>*</mo></msup><mo stretchy="false">→</mo><mi>Z</mi><mi>H</mi></math>. Our findings suggest that significant deviations from SM predictions may occur when considering FCNC contributions.

Mexico

A.I. Hernández-Juárez

R. Gaitán

<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>C</mi><mi>P</mi></math> violation in the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>H</mi><mi>Z</mi><mi>Z</mi></math> vertex and left-right asymmetries

There are only six independent types of symmetry-constrained (renormalizable) scalar potentials in the two Higgs doublet model (2HDM). For example, the scalar sector symmetry known as <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><msub><mrow><mi mathvariant="double-struck">Z</mi></mrow><mrow><mn>2</mn></mrow></msub><mo stretchy="false">⊗</mo><msub><mrow><mi mathvariant="normal">Π</mi></mrow><mrow><mn>2</mn></mrow></msub></mrow></math>, generated by the simultaneous application of two independent symmetries acting on the scalar fields, and the generalized <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>C</mi><mi>P</mi></math> symmetry known as GCP2 yield equivalent 2HDM scalar potentials. A similar situation arises for the scalar sector symmetries known as <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi mathvariant="normal">U</mi><mo stretchy="false">(</mo><mn>1</mn><mo stretchy="false">)</mo><mo stretchy="false">⊗</mo><msub><mi mathvariant="normal">Π</mi><mn>2</mn></msub></math> and GCP3, respectively. In this paper, we show that this “degeneracy” remains when the definitions of the corresponding symmetries are extended to the Yukawa sector with three quark generations. The proof involves the exploration of all possible extensions of the corresponding symmetries to the Yukawa sector, consistent with the phenomenological constraints of nonzero quark masses and a nontrivial quark mixing matrix. Moreover, we find that this result is a peculiarity of a Yukawa sector with three quark generations. In particular, with two quark generations, we find that models based on the extension of <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi mathvariant="double-struck">Z</mi><mn>2</mn></msub><mo stretchy="false">⊗</mo><msub><mi mathvariant="normal">Π</mi><mn>2</mn></msub></math> to the Yukawa sector are inequivalent with those based on GCP2.

Germany

Sergio Carrolo

Howard E. Haber

Luis Lourenco

Portugal

João P. Silva

Extending the symmetries of the generalized <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>C</mi><mi>P</mi></math>-symmetric 2HDM scalar potential to the Yukawa sector

The quantum speed limits (QSLs) set fundamental lower bounds on the time required for a quantum system to evolve from a given initial state to a final state. In this work, we investigate <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>C</mi><mi>P</mi></math> violation and the mass ordering problem of neutrino oscillations in matter using the QSL time as a key analytical tool. We examine the QSL time for the unitary evolution of two- and three-flavor neutrino states, both in vacuum and in the presence of matter. Two-flavor neutrino oscillations are used as a precursor to their three-flavor counterparts. We further compute the QSL time for neutrino state evolution and entanglement in terms of neutrino survival and oscillation probabilities, which are experimentally measurable quantities in neutrino experiments. A difference in the QSL time between the normal and inverted mass ordering scenarios, for neutrino state evolution as well as for entanglement, under the effect of a <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>C</mi><mi>P</mi></math> violation phase is observed. Our results are illustrated using the length scales and energies of ongoing long-baseline accelerator neutrino experiments such as T2K, NOvA, and the upcoming DUNE experiment. Notably, three-flavor neutrino oscillations in constant matter density exhibit faster state evolution across all these neutrino experiments in the normal mass ordering scenario. Additionally, we observe fast entanglement suppression in DUNE assuming a normal mass ordering.

Subhadip Bouri

Abhishek Kumar Jha

Subhashish Banerjee

Probing <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>C</mi><mi>P</mi></math> violation and mass ordering in neutrino oscillations in matter through quantum speed limits

Based on <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> collision data corresponding to an integrated luminosity of about <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mn>4.5</mn><mtext> </mtext><mtext> </mtext><msup><mi>fb</mi><mrow><mo>−</mo><mn>1</mn></mrow></msup></math> collected at center-of-mass energies between 4599.53 and 4698.82 MeV with the BESIII detector, the absolute branching fraction of the Cabibbo-favored decay <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msubsup><mi mathvariant="normal">Λ</mi><mi>c</mi><mo>+</mo></msubsup><mo stretchy="false">→</mo><mi mathvariant="normal">Λ</mi><msubsup><mi>K</mi><mi>S</mi><mn>0</mn></msubsup><msup><mi>K</mi><mo>+</mo></msup></math> is measured to be <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mo stretchy="false">(</mo><mn>3.12</mn><mo>±</mo><mn>0.46</mn><mo>±</mo><mspace linebreak="goodbreak"></mspace><mn>0.15</mn><mo stretchy="false">)</mo><mo>×</mo><msup><mn>10</mn><mrow><mo>−</mo><mn>3</mn></mrow></msup></math>. Combined with a previous measurement from the BESIII Collaboration, the branching fraction of the decay <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msubsup><mi mathvariant="normal">Λ</mi><mi>c</mi><mo>+</mo></msubsup><mo stretchy="false">→</mo><mi mathvariant="normal">Λ</mi><msubsup><mi>K</mi><mi>S</mi><mn>0</mn></msubsup><msup><mi>K</mi><mo>+</mo></msup></math> is calculated to be <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mo stretchy="false">(</mo><mn>3.07</mn><mo>±</mo><mn>0.26</mn><mo>±</mo><mn>0.13</mn><mo stretchy="false">)</mo><mo>×</mo><msup><mn>10</mn><mrow><mo>−</mo><mn>3</mn></mrow></msup></math>. The decay <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msubsup><mi mathvariant="normal">Λ</mi><mi>c</mi><mo>+</mo></msubsup><mo stretchy="false">→</mo><msup><mi mathvariant="normal">Ξ</mi><mn>0</mn></msup><msubsup><mi>K</mi><mi>S</mi><mn>0</mn></msubsup><msup><mi>π</mi><mo>+</mo></msup></math> is observed for the first time with a statistical significance of <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mn>6.6</mn><mi>σ</mi></math>, and its branching fraction is determined to be <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mo stretchy="false">(</mo><mn>3.70</mn><mo>±</mo><mn>0.60</mn><mo>±</mo><mn>0.21</mn><mo stretchy="false">)</mo><mo>×</mo><msup><mn>10</mn><mrow><mo>−</mo><mn>3</mn></mrow></msup></math>. In addition, a search for the decay <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msubsup><mi mathvariant="normal">Λ</mi><mi>c</mi><mo>+</mo></msubsup><mo stretchy="false">→</mo><msup><mi mathvariant="normal">Σ</mi><mn>0</mn></msup><msubsup><mi>K</mi><mi>S</mi><mn>0</mn></msubsup><msup><mi>K</mi><mo>+</mo></msup></math> is performed, and its branching fraction is determined to be <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mo stretchy="false">(</mo><mn>0.8</mn><msubsup><mn>0</mn><mrow><mo>−</mo><mn>0.24</mn></mrow><mrow><mo>+</mo><mn>0.28</mn></mrow></msubsup><mo>±</mo><mn>0.16</mn><mo stretchy="false">)</mo><mo>×</mo><msup><mn>10</mn><mrow><mo>−</mo><mn>3</mn></mrow></msup></math>, corresponding to an upper limit of <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mn>1.28</mn><mo>×</mo><msup><mn>10</mn><mrow><mo>−</mo><mn>3</mn></mrow></msup></math> at a 90% confidence level. These measurements provide new information that can be used to distinguish between theoretical models.

China

M. Ablikim

Russia

M.N. Achasov

Sweden

P. Adlarson

X.C. Ai

R. Aliberti

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

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

G. Chelkov

C. Chen

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

Y.B. Chen

Y.Q. Chen

Z.J. Chen

South Korea

S.K. Choi

X. Chu

G. Cibinetto

F. Cossio

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

Z.H. 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

Y.T. Feng

M. Fritsch

C.D. Fu

J.L. Fu

Y.W. Fu

Measurement of the branching fractions of the Cabibbo-favored decays <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msubsup><mi mathvariant="normal">Λ</mi><mi>c</mi><mo>+</mo></msubsup><mo stretchy="false">→</mo><mi mathvariant="normal">Λ</mi><msubsup><mi>K</mi><mi>S</mi><mn>0</mn></msubsup><msup><mi>K</mi><mo>+</mo></msup></math> and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><msubsup><mrow><mi mathvariant="normal">Λ</mi></mrow><mrow><mi>c</mi></mrow><mrow><mo>+</mo></mrow></msubsup><mo stretchy="false">→</mo><msup><mrow><mi mathvariant="normal">Ξ</mi></mrow><mrow><mn>0</mn></mrow></msup><msubsup><mrow><mi>K</mi></mrow><mrow><mi>S</mi></mrow><mrow><mn>0</mn></mrow></msubsup><msup><mrow><mi>π</mi></mrow><mrow><mo>+</mo></mrow></msup></mrow></math> and search for <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msubsup><mi mathvariant="normal">Λ</mi><mi>c</mi><mo>+</mo></msubsup><mo stretchy="false">→</mo><msup><mi mathvariant="normal">Σ</mi><mn>0</mn></msup><msubsup><mi>K</mi><mi>S</mi><mn>0</mn></msubsup><msup><mi>K</mi><mo>+</mo></msup></math>

Using <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> collision data collected with the BESIII detector operating at the Beijing electron positron collider, the cross section of <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><msup><mrow><mi>π</mi></mrow><mrow><mo>+</mo></mrow></msup><msup><mrow><mi>π</mi></mrow><mrow><mo>−</mo></mrow></msup><msub><mrow><mi>h</mi></mrow><mrow><mi>c</mi></mrow></msub></mrow></math> is measured at 59 points with center-of-mass energy <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msqrt><mi>s</mi></msqrt></math> ranging from 4.009 to 4.950 GeV with a total integrated luminosity of <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mn>22.2</mn><mtext> </mtext><mtext> </mtext><msup><mi>fb</mi><mrow><mo>−</mo><mn>1</mn></mrow></msup></math>. The cross section between 4.3 and 4.45 GeV exhibits a plateaulike shape and drops sharply around 4.5 GeV, which cannot be described by two resonances only. Three coherent Breit-Wigner functions are used to parametrize the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msqrt><mi>s</mi></msqrt></math>-dependent cross section line shape. The masses and widths are determined to be <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><msub><mrow><mi>M</mi></mrow><mrow><mn>1</mn></mrow></msub><mo>=</mo><mspace linebreak="goodbreak"></mspace><mo stretchy="false">(</mo><msubsup><mrow><mn>4223.6</mn></mrow><mrow><mo>−</mo><mn>3.7</mn><mo>−</mo><mn>2.9</mn></mrow><mrow><mo>+</mo><mn>3.6</mn><mo>+</mo><mn>2.6</mn></mrow></msubsup><mo stretchy="false">)</mo><mtext> </mtext><mtext> </mtext><mi>MeV</mi><mo>/</mo><msup><mrow><mi>c</mi></mrow><mrow><mn>2</mn></mrow></msup></mrow></math>, <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><msub><mrow><mi mathvariant="normal">Γ</mi></mrow><mrow><mn>1</mn></mrow></msub><mo>=</mo><mo stretchy="false">(</mo><msubsup><mrow><mn>58.5</mn></mrow><mrow><mo>−</mo><mn>11.4</mn><mo>−</mo><mn>6.5</mn></mrow><mrow><mo>+</mo><mn>10.8</mn><mo>+</mo><mn>6.7</mn></mrow></msubsup><mo stretchy="false">)</mo><mtext> </mtext><mtext> </mtext><mi>MeV</mi></mrow></math>, <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><msub><mrow><mi>M</mi></mrow><mrow><mn>2</mn></mrow></msub><mo>=</mo><mo stretchy="false">(</mo><msubsup><mrow><mn>4327.4</mn></mrow><mrow><mo>−</mo><mn>18.8</mn><mo>−</mo><mn>9.3</mn></mrow><mrow><mo>+</mo><mn>20.1</mn><mo>+</mo><mn>10.7</mn></mrow></msubsup><mo stretchy="false">)</mo><mtext> </mtext><mtext> </mtext><mi>MeV</mi><mo>/</mo><msup><mrow><mi>c</mi></mrow><mrow><mn>2</mn></mrow></msup></mrow></math>, <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi mathvariant="normal">Γ</mi><mn>2</mn></msub><mo>=</mo><mspace linebreak="goodbreak"></mspace><mo stretchy="false">(</mo><msubsup><mn>244.1</mn><mrow><mo>−</mo><mn>27.1</mn><mo>−</mo><mn>18.3</mn></mrow><mrow><mo>+</mo><mn>34.0</mn><mo>+</mo><mn>24.2</mn></mrow></msubsup><mo stretchy="false">)</mo><mtext> </mtext><mtext> </mtext><mi>MeV</mi></math>, and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>M</mi><mn>3</mn></msub><mo>=</mo><mo stretchy="false">(</mo><msubsup><mn>4467.4</mn><mrow><mo>−</mo><mn>5.4</mn><mo>−</mo><mn>2.7</mn></mrow><mrow><mo>+</mo><mn>7.2</mn><mo>+</mo><mn>3.2</mn></mrow></msubsup><mo stretchy="false">)</mo><mtext> </mtext><mtext> </mtext><mi>MeV</mi><mo>/</mo><msup><mi>c</mi><mn>2</mn></msup></math>, and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi mathvariant="normal">Γ</mi><mn>3</mn></msub><mo>=</mo><mo stretchy="false">(</mo><msubsup><mn>62.8</mn><mrow><mo>−</mo><mn>14.4</mn><mo>−</mo><mn>7.0</mn></mrow><mrow><mo>+</mo><mn>19.2</mn><mo>+</mo><mn>9.9</mn></mrow></msubsup><mo stretchy="false">)</mo><mtext> </mtext><mtext> </mtext><mi>MeV</mi></math>. The first uncertainties are statistical and the second are systematic. The inclusion of the relatively narrower third component proves crucial for reproducing the drop at around 4.5 GeV. The statistical significance of the three-resonance assumption over the two-resonance assumption is greater than <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mn>5</mn><mi>σ</mi></math>.

X.Y. Chen

Z.K. Chen

United Kingdom

J. Cottee-Meldrum

L. Feng

Q.X. Feng

Observation of Three Resonant Structures in the Cross Section 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><msup><mi>π</mi><mo>+</mo></msup><msup><mi>π</mi><mo>−</mo></msup><msub><mi>h</mi><mi>c</mi></msub></math>

Motivated by the deviations observed between the experimental measurements and the Standard Model (SM) predictions of the branching ratios of <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><mn>0</mn></msubsup><mo stretchy="false">→</mo><msubsup><mi>D</mi><mi>s</mi><mo>+</mo></msubsup><msup><mi>π</mi><mo>−</mo></msup></math> and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msubsup><mover accent="true"><mi>B</mi><mo stretchy="false">¯</mo></mover><mi>d</mi><mn>0</mn></msubsup><mo stretchy="false">→</mo><msup><mi>D</mi><mo>+</mo></msup><msup><mi>K</mi><mo>−</mo></msup></math> decays, we revisit the two-body hadronic <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msubsup><mi>B</mi><mi>c</mi><mo>−</mo></msubsup><mo stretchy="false">→</mo><mi>J</mi><mo>/</mo><mi>ψ</mi><mo stretchy="false">(</mo><msub><mi>η</mi><mi>c</mi></msub><mo stretchy="false">)</mo><msup><mi>L</mi><mo>−</mo></msup></math> decays, with <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>L</mi><mo>=</mo><mi>π</mi><mo>,</mo><msup><mi>K</mi><mrow><mo stretchy="false">(</mo><mo>*</mo><mo stretchy="false">)</mo></mrow></msup><mo>,</mo><mi>ρ</mi></math>, both within the SM and beyond. Since these processes are also mediated by the quark-level <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>b</mi><mo stretchy="false">→</mo><mi>c</mi><mover accent="true"><mi>u</mi><mo stretchy="false">¯</mo></mover><mi>d</mi><mo stretchy="false">(</mo><mi>s</mi><mo stretchy="false">)</mo></math> transitions and hence dominated by the color-allowed tree topology, the QCD factorization is generally expected to hold in the heavy-quark limit. First, we update the SM predictions of the observables of these decays by including the nonfactorizable vertex corrections to the hadronic matrix elements of the SM four-quark operators up to the next-to-next-to-leading order (NNLO) in <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>α</mi><mi>s</mi></msub></math>. It is found that, relative to the leading-order results, the branching ratios of these decays up to the next-to-leading-order (NLO) and NNLO corrections are always enhanced, with a relative amount given by <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>δ</mi><mi>NLO</mi></msub><mo>=</mo><mo stretchy="false">(</mo><msup><mi mathvariant="script">B</mi><mi>NLO</mi></msup><mo>−</mo><msup><mi mathvariant="script">B</mi><mi>LO</mi></msup><mo stretchy="false">)</mo><mo>/</mo><msup><mi mathvariant="script">B</mi><mi>LO</mi></msup><mo>≈</mo><mo>+</mo><mn>6</mn><mo>%</mo></math> and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>δ</mi><mrow><mi>NNLO</mi></mrow></msub><mo>=</mo><mo stretchy="false">(</mo><msup><mi mathvariant="script">B</mi><mrow><mi>NNLO</mi></mrow></msup><mo>−</mo><msup><mi mathvariant="script">B</mi><mi>LO</mi></msup><mo stretchy="false">)</mo><mo>/</mo><msup><mi mathvariant="script">B</mi><mi>LO</mi></msup><mo>≈</mo><mo>+</mo><mn>9</mn><mo>%</mo></math>, respectively. To minimize the uncertainties brought by the Cabibbo-Kobayashi-Maskawa matrix element <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>V</mi><mrow><mi>c</mi><mi>b</mi></mrow></msub></math> as well as the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>B</mi><mi>c</mi></msub><mo stretchy="false">→</mo><mi>J</mi><mo>/</mo><mi>ψ</mi><mo stretchy="false">(</mo><msub><mi>η</mi><mi>c</mi></msub><mo stretchy="false">)</mo></math> and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>B</mi><mrow><mo stretchy="false">(</mo><mi>s</mi><mo stretchy="false">)</mo></mrow></msub><mo stretchy="false">→</mo><msubsup><mi>D</mi><mrow><mo stretchy="false">(</mo><mi>s</mi><mo stretchy="false">)</mo></mrow><mrow><mo stretchy="false">(</mo><mo>*</mo><mo stretchy="false">)</mo></mrow></msubsup></math> transition form factors, we construct ratios of the nonleptonic decay rates with respect to the corresponding differential semileptonic decay rates evaluated at <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mi>q</mi><mn>2</mn></msup><mo>=</mo><msubsup><mi>m</mi><mi>L</mi><mn>2</mn></msubsup></math> (for <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>R</mi><mrow><mi>J</mi><mo>/</mo><mi>ψ</mi><mo stretchy="false">(</mo><msub><mi>η</mi><mi>c</mi></msub><mo stretchy="false">)</mo><mi>L</mi></mrow></msub></math> and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msubsup><mi>R</mi><mrow><mo stretchy="false">(</mo><mi>s</mi><mo stretchy="false">)</mo><mi>L</mi></mrow><mrow><mo stretchy="false">(</mo><mo>*</mo><mo stretchy="false">)</mo></mrow></msubsup></math>) or integrated over the whole <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mi>q</mi><mn>2</mn></msup></math> range (for <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>R</mi><mrow><mi>π</mi><mo>/</mo><mi>μ</mi><msub><mi>ν</mi><mi>μ</mi></msub></mrow></msub></math>), which are then used to constrain the model-independent new physics (NP) Wilson coefficients. After considering the latest Belle data on <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><mo stretchy="false">→</mo><msup><mi>D</mi><mrow><mo stretchy="false">(</mo><mo>*</mo><mo stretchy="false">)</mo><mo>+</mo></mrow></msup><mi>π</mi><mo stretchy="false">(</mo><mi>K</mi><msup><mo stretchy="false">)</mo><mo>−</mo></msup></math> decays and the updated fitting results of the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>B</mi><mrow><mo stretchy="false">(</mo><mi>s</mi><mo stretchy="false">)</mo></mrow></msub><mo stretchy="false">→</mo><msubsup><mi>D</mi><mrow><mo stretchy="false">(</mo><mi>s</mi><mo stretchy="false">)</mo></mrow><mrow><mo stretchy="false">(</mo><mo>*</mo><mo stretchy="false">)</mo></mrow></msubsup></math> transition form factors, we find that the deviations can still be explained by the NP four-quark operators with <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mo stretchy="false">(</mo><mn>1</mn><mo>+</mo><msub><mi>γ</mi><mn>5</mn></msub><mo stretchy="false">)</mo><mo stretchy="false">⊗</mo><mo stretchy="false">(</mo><mn>1</mn><mo>−</mo><msub><mi>γ</mi><mn>5</mn></msub><mo stretchy="false">)</mo></math> and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mo stretchy="false">(</mo><mn>1</mn><mo>+</mo><msub><mi>γ</mi><mn>5</mn></msub><mo stretchy="false">)</mo><mo stretchy="false">⊗</mo><mo stretchy="false">(</mo><mn>1</mn><mo>+</mo><msub><mi>γ</mi><mn>5</mn></msub><mo stretchy="false">)</mo></math> structures, while the solution with <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mi>γ</mi><mi>μ</mi></msup><mo stretchy="false">(</mo><mn>1</mn><mo>+</mo><msub><mi>γ</mi><mn>5</mn></msub><mo stretchy="false">)</mo><mo stretchy="false">⊗</mo><msub><mi>γ</mi><mi>μ</mi></msub><mo stretchy="false">(</mo><mn>1</mn><mo>−</mo><msub><mi>γ</mi><mn>5</mn></msub><mo stretchy="false">)</mo></math> structure does not work anymore, under the combined constraints from the ratios <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msubsup><mi>R</mi><mrow><mo stretchy="false">(</mo><mi>s</mi><mo stretchy="false">)</mo><mi>L</mi></mrow><mrow><mo stretchy="false">(</mo><mo>*</mo><mo stretchy="false">)</mo></mrow></msubsup></math> at the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mn>2</mn><mi>σ</mi></math> level. Furthermore, the ratio <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>R</mi><mrow><mi>π</mi><mo>/</mo><mi>μ</mi><msub><mi>ν</mi><mi>μ</mi></msub></mrow></msub></math>, once measured precisely, could provide complementary constraint on these NP Wilson coefficients allowed by <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msubsup><mi>R</mi><mrow><mo stretchy="false">(</mo><mi>s</mi><mo stretchy="false">)</mo><mi>L</mi></mrow><mrow><mo stretchy="false">(</mo><mo>*</mo><mo stretchy="false">)</mo></mrow></msubsup></math>. With the large <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>B</mi><mi>c</mi></msub></math> events expected at the Large Hadron Collider, we hope to obtain more precise measurements of these observables, which can be exploited to discriminate the different NP scenarios responsible for the deviations observed in the two-body nonleptonic <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>B</mi></math>-meson decays.

Wei-Jun Deng

Fang-Min Cai

Xin-Qiang Li

Yan Shi

Ya-Dong Yang

Revisiting <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msubsup><mi>B</mi><mi>c</mi><mo>−</mo></msubsup><mo stretchy="false">→</mo><mi>J</mi><mo>/</mo><mi>ψ</mi><mo stretchy="false">(</mo><msub><mi>η</mi><mi>c</mi></msub><mo stretchy="false">)</mo><msup><mi>L</mi><mo>−</mo></msup></math> decays within the SM and beyond in QCD factorization

We present an update of HPQCD’s lattice quantum chromodynamics (QCD) determination of the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>B</mi><mi>c</mi></msub><mo stretchy="false">→</mo><mi>J</mi><mo>/</mo><mi>ψ</mi></math> vector and axial-vector form factors, and provide new results for the tensor form factors. We use the highly improved staggered quark (HISQ) action for all valence quarks, together with the second generation MILC <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>n</mi><mi>f</mi></msub><mo>=</mo><mn>2</mn><mo>+</mo><mn>1</mn><mo>+</mo><mn>1</mn></math> HISQ gluon field configurations. This calculation includes two additional ensembles, one with physically light up and down quarks and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>a</mi><mo>≈</mo><mn>0.06</mn><mtext> </mtext><mtext> </mtext><mi>fm</mi></math> and one with <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>a</mi><mo>≈</mo><mn>0.03</mn><mtext> </mtext><mtext> </mtext><mi>fm</mi></math> on which we are able to reach the physical bottom quark mass. Our calculation uses nonperturbatively renormalized current operators and covers the full kinematical range of the decay. We use our recent results for the heavy-charm susceptibilities, as a function of <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>u</mi><mo>=</mo><msub><mi>m</mi><mi>c</mi></msub><mo>/</mo><msub><mi>m</mi><mi>h</mi></msub></math>, in order to employ the full dispersive parametrization for <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>B</mi><mi>c</mi></msub><mo stretchy="false">→</mo><mi>J</mi><mo>/</mo><mi>ψ</mi></math> in our physical-continuum extrapolation. We give updated Standard Model (SM) predictions <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>R</mi><mo stretchy="false">(</mo><mi>J</mi><mo>/</mo><mi>ψ</mi><mo stretchy="false">)</mo><mo>=</mo><mn>0.2597</mn><mo stretchy="false">(</mo><mn>27</mn><mo stretchy="false">)</mo></math>, <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>A</mi><msub><mi>λ</mi><mi>τ</mi></msub></msub><mo>=</mo><mn>0.5093</mn><mo stretchy="false">(</mo><mn>42</mn><mo stretchy="false">)</mo></math>, <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msubsup><mi>F</mi><mi>L</mi><mrow><mi>J</mi><mo>/</mo><mi>ψ</mi></mrow></msubsup><mo>=</mo><mn>0.4421</mn><mo stretchy="false">(</mo><mn>55</mn><mo stretchy="false">)</mo></math>, and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi mathvariant="script">A</mi><mi>FB</mi></msub><mo>=</mo><mo>−</mo><mn>0.0567</mn><mo stretchy="false">(</mo><mn>61</mn><mo stretchy="false">)</mo></math>, reducing uncertainties by 29%, 45%, 40%, and 50% respectively. Since our lattice form factors cover the full kinematic range we can use them to test extrapolations using data in a truncated range, at low-recoil. We investigate different physical continuum parametrization schemes, with lattice results in the first <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mn>1</mn><mo>/</mo><mn>3</mn></math> of the kinematic range near <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msubsup><mi>q</mi><mi>max</mi><mn>2</mn></msubsup></math>. We find that unexpectedly large systematic uncertainties near <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mi>q</mi><mn>2</mn></msup><mo>=</mo><mn>0</mn></math> can emerge when extrapolating synthetic data in the high-<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mi>q</mi><mn>2</mn></msup></math> region if higher order kinematical terms are omitted from the physical continuum extrapolation. This suggests a potentially underestimated systematic uncertainty entering extrapolations of synthetic lattice QCD data for the related <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>B</mi><mo stretchy="false">→</mo><msup><mi>D</mi><mo>*</mo></msup><mo>ℓ</mo><mover accent="true"><mi>ν</mi><mo stretchy="false">¯</mo></mover></math> decay from the high-<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mi>q</mi><mn>2</mn></msup></math> region into the low-<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mi>q</mi><mn>2</mn></msup></math> region.

Judd Harrison

Improved lattice QCD <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><msub><mrow><mi>B</mi></mrow><mrow><mi>c</mi></mrow></msub><mo stretchy="false">→</mo><mi>J</mi><mo>/</mo><mi>ψ</mi></mrow></math> vector, axial-vector, and tensor form factors