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.

Japan

Germany

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 investigate charge-balance functions for pion, kaon, and proton pairs in proton-proton (pp) collisions at <math xmlns="http://www.w3.org/1998/Math/MathML"><mrow><msqrt><mi>s</mi></msqrt><mo>=</mo><mn>13</mn></mrow></math> TeV using Monte Carlo models, pythia8, and epos-lhc, with transverse spherocity to classify event topology and charged-particle multiplicity to select system size. Simulations with pythia8 and epos-lhc reveal that balance-function widths in rapidity and azimuthal angle depend on multiplicity and event shape. In pythia8, widths decrease monotonically with multiplicity, consistent with local charge conservation in a fragmentation-dominated scenario. In contrast, the epos-lhc model, especially when using the core corona implementation, exhibits a more intricate response, where the combined effects of hydrodynamic radial flow and longitudinal diffusion result in narrower azimuthal correlations and broader rapidity correlations. These features are characteristic signatures of collective dynamics, similar to those observed in heavy-ion collisions. Events with low spherocity, which are jetlike in nature, exhibit significantly narrower balance-function widths compared to isotropic events with high spherocity, illustrating that event-shape selection provides clear sensitivity to the underlying dynamics of particle production in pp collisions. The species dependence and event-shape sensitivity of the balance-function widths provide information about the hadronization dynamics and collectivity in small systems. These results demonstrate that multidimensional, particle-species-dependent balance-function measurements can disentangle the underlying mechanisms of charge correlations and mediumlike behavior in high-multiplicity pp collisions.

Italy

Subash Chandra Behera

Arvind Khuntia

System-size and event-shape dependence of particle-identified balance functions in proton-proton collisions at <math xmlns="http://www.w3.org/1998/Math/MathML"><mrow><msqrt><mi>s</mi></msqrt><mo>=</mo><mn>13</mn></mrow></math> TeV using PYTHIA 8 and EPOS models

Several possible excesses around $ 95 $ GeV hint at an additional light scalar beyond the Standard Model. We examine the capability of the Circular Electron-Positron Collider (CEPC) to test this hypothesis in the Higgs-strahlung channel $ e^{+}e^{-} \to ZS $ with $ Z \to\mu^{+}\mu^{-} $ and $ S \to\tau^{+}\tau^{-} $ . A full detector simulation shows that the optimal center-of-mass energy for studying the 95 GeV light scalar is 210 GeV. A deep neural network classifier reduces the luminosity required for discovery by half. At $ L = 20\; \mathrm{ab}^{-1} $ , the $ 5\sigma $ sensitivity of the CEPC to the signal strength $ \mu_{\tau\tau}^{ZS} $ reaches 0.016 and 0.020 for $ \sqrt{s} = 210 $ GeV and 240 GeV, respectively. The corresponding thresholds for a 5% precision measurement are $ \mu_{\tau\tau}^{ZS} \gt 0.10 $ and $ \gt 0.12 $ . At $ \sqrt{s}=210 $ GeV (240 GeV), the $ 5\sigma $ coverage of all N2HDM-Flipped samples with $ \chi^2_{h_{95}} \lt 7.82 $ requires $ L=800\ \mathrm{fb}^{-1} $ (1.22 $ \mathrm{ab}^{-1} $ ). These results establish a 210 GeV run, augmented by machine-learning selection, as the most efficient strategy to confirm or refute the 95 GeV excess at future lepton colliders.

China

Yabo Dong

Manqi Ruan

Kun Wang

Haijun Yang

Jingya Zhu

Testing a 95 GeV Scalar at the CEPC with Machine Learning * This work was supported by the National Natural Science Foundation of China under Grant No. 12275066 and by the startup research funds of Henan University. The work of K. Wang was also supported by the Open Project of the Shanghai Key Laboratory of Particle Physics and Cosmology under Grant No. 22DZ2229013-3. The work of M. Ruan was also supported by the National Key Program for S&T Research and Development under Contract No. 2024YFA1610603. The work of H. Yang was also supported by the National Natural Science Foundation of China under Grant No. W2441004.

The Circular Electron Positron Collider (CEPC) is designed to operate at key center-of-mass energies: 91.2 GeV as a $\textit{Z}$ factory for precision $\textit{Z}$ boson studies, ≈ 160 GeV at the threshold for $\textit{W}$ boson pair production, and 240 GeV as a Higgs factory for copious Higgs boson production. It can be upgraded to 360 GeV (CEPC-360 GeV) for enabling top quark-antiquark ( $ t\bar{t}$ ) pair production. Beyond enabling high-precision measurements of the Standard Model (SM), CEPC-360 GeV is uniquely positioned to perform searches for new physics beyond the SM (BSM), serving as a valuable complement to hadron colliders. This paper presents a sensitivity study on the direct pair production of staus and smuons at the CEPC with $ \sqrt{s}$ = 360 GeV, conducted via full Monte Carlo simulation. Under the assumptions of 1.0 ab$^{−1}$ integrated luminosity and a flat 5% systematic uncertainty, CEPC-360 GeV could potentially discover the combined production of left-handed and right-handed staus up to a mass of 170 GeV (if they exist) or up to 169 for pure left-handed staus and 162 GeV for pure right-handed staus. For direct smuon production, the discovery potential reaches up to 178 GeV under the same conditions.

Feng Lyu

Jiarong Yuan

Huajie Cheng

Jianxiong Wang

Rabia Hameed

Da Xu

Xuai Zhuang

Search potential for direct slepton pair production at the CEPC with ${ \sqrt{\boldsymbol s}}$ = 360 GeV * Supported by the State Key Program of National Natural Science of China (2018YFA0404000, 12135013)

Neutrino oscillation experiments have confirmed that neutrinos are massive particles and that lepton flavors are mixed. To explain the observed lepton mass spectra and flavor mixing patterns, flavor symmetry plays a crucial and unique role. In this paper, we propose a useful symmetry-breaking scheme by applying $S_{3L} \times S_{3R} \rightarrow $ $ S_{2L} \times S_{2R} \rightarrow \emptyset$ within both charged-lepton and neutrino sectors at the mass-matrix level. For the three distinct residual subgroups $S_{2L}^{(23)} \times S_{2R}^{(23)}$ , $S_{2L}^{(13)} \times S_{2R}^{(13)}$ , and $S_{2L}^{(12)} \times S_{2R}^{(12)}$ that are under consideration, we systematically analyze the various parameterizations of the lepton mass matrices. It is shown that all three scenarios are in good agreement with current neutrino oscillation data. Notably, within the latest best-fit values of neutrino oscillation parameters, the predicted values of the Dirac CP-violating phase $\textit{δ}$ are $294.6^\circ$ , $302.3^\circ$ , and $287.0^\circ$ , respectively. To further assess the viability of the model, a comprehensive numerical analysis is performed by utilizing neutrino oscillation parameters at the $3\sigma$ level. It is found that the allowed ranges of $\textit{δ}$ are $281.2^\circ \rightarrow 338.7^\circ$ , $287.0^\circ \rightarrow 342.2^\circ$ , and $282.7^\circ \rightarrow 297.0^\circ$ , which all fall within its $3\sigma$ range. These results indicate that the proposed symmetry-breaking scheme $S_{3L} \times S_{3R} \rightarrow S_{2L} \times S_{2R} \rightarrow \emptyset$ can naturally explain the realistic lepton mass hierarchy and mixing pattern, thereby providing valuable theoretical perspectives for future research.

Chang-Qi Hu

Chun-Yuan Li

Xiao Liang

Xing-Hua Yang

Dai-Xing Zhang

Further study on lepton mass spectra and flavor mixing with $\textit{S}$ 3$\textit{L}$ × $\textit{S}$ 3$\textit{R}$ flavor symmetry * Supported in part by the National Natural Science Foundation of China (12105162, 12305106), the Natural Science Foundation of Shandong Province (ZR2021QA058, ZR2021QA040) and the Youth Innovation Technology Project of Higher School in Shandong Province (2023KJ146)

We investigate the Ξ* resonances within the molecular picture, where these states are dynamically generated as poles in the unitarized scattering amplitudes arising from the coupled-channel interactions of <math altimg='si2.svg'><mrow><msup><mi>K</mi><mrow><mo>*</mo><mo>&#8722;</mo></mrow></msup><mstyle mathvariant='normal'><mi>&#923;</mi></mstyle></mrow></math>, <math altimg='si3.svg'><mrow><msup><mi>K</mi><mrow><mo>*</mo><mo>&#8722;</mo></mrow></msup><msup><mstyle mathvariant='normal'><mi>&#931;</mi></mstyle><mn>0</mn></msup></mrow></math>, <math altimg='si4.svg'><mrow><msup><mi>&#961;</mi><mo>&#8722;</mo></msup><msup><mstyle mathvariant='normal'><mi>&#926;</mi></mstyle><mn>0</mn></msup></mrow></math>, <math altimg='si5.svg'><mrow><mspace width='0.16em' /><msup><mover><mrow><mspace width='-0.16em' /><mi>K</mi></mrow><mo stretchy='true'>&#8254;</mo></mover><mrow><mo>*</mo><mn>0</mn></mrow></msup><msup><mstyle mathvariant='normal'><mi>&#931;</mi></mstyle><mo>&#8722;</mo></msup></mrow></math>, <math altimg='si6.svg'><mrow><msup><mi>&#961;</mi><mn>0</mn></msup><msup><mstyle mathvariant='normal'><mi>&#926;</mi></mstyle><mo>&#8722;</mo></msup></mrow></math>, <math altimg='si7.svg'><mrow><mi>&#969;</mi><msup><mstyle mathvariant='normal'><mi>&#926;</mi></mstyle><mo>&#8722;</mo></msup></mrow></math>, and <math altimg='si9.svg'><mrow><mi>&#981;</mi><msup><mstyle mathvariant='normal'><mi>&#926;</mi></mstyle><mo>&#8722;</mo></msup></mrow></math>. The interaction kernel is derived from the local hidden gauge formalism, while the unitarization procedure employs a hybrid method that combines cutoff and dimensional regularizations in the evaluation of the loop function. From a detailed spectroscopic analysis, we identify two <math altimg='si149.svg'><mrow><mi>S</mi><mo linebreak='goodbreak'>=</mo><mo>&#8722;</mo><mn>2</mn></mrow></math> baryon states whose properties are compatible with some of the &#926;* resonances listed in the Review of Particle Physics. To explore their possible experimental signatures, we compute the femtoscopic correlation functions for all the vector&#8211;baryon pairs considered in the present study, using realistic estimates of production weights and varying source sizes <math altimg='si150.svg'><mrow><mi>R</mi><mo linebreak='goodbreak'>=</mo><mn>1</mn><mo>,</mo><mn>1.1</mn><mo>,</mo><mn>1.2</mn><mo>,</mo><mn>1.3</mn><mo>,</mo><mn>1.5</mn></mrow></math> fm.

Spain

Jia-Xin Lin

Pablo Encarnación

Miguel Albaladejo

Albert Feijoo

Signatures of odd-parity <italic>s</italic>-wave &#926;* states in femtoscopic correlation functions

A measurement of $\textit{CP}$ asymmetry in $$ {D}^0\to {K}_{\textrm{S}}^0{K}_{\textrm{S}}^0 $$ decays is reported, based on a data sample of proton-proton collisions collected with the LHCb detector in 2024 at a centre-of-mass energy of 13.6 TeV, corresponding to an integrated luminosity of 6.2 fb . The $$ {D}^0\to {K}_{\textrm{S}}^0{\pi}^{+}{\pi}^{-} $$ decay is used as calibration channel to cancel residual detection and production asymmetries. The time-integrated $\textit{CP}$ asymmetry for the $$ {D}^0\to {K}_{\textrm{S}}^0{K}_{\textrm{S}}^0 $$ mode is measured to be

Netherlands

R. Aaij

United Kingdom

A. Abdelmotteleb

Switzerland

C. Abellan Beteta

F. Abudinén

T. Ackernley

United States

A. Adefisoye

B. Adeva

M. Adinolfi

Sweden

P. Adlarson

France

C. Agapopoulou

C. Aidala

Z. Ajaltouni

S. Akar

K. Akiba

Poland

M. Akthar

P. Albicocco

J. Albrecht

Lithuania

R. Aleksiejunas

F. Alessio

P. Alvarez Cartelle

R. Amalric

Brazil

S. Amato

J. Amey

Y. Amhis

L. An

L. Anderlini

M. Andersson

P. Andreola

M. Andreotti

S. Andres Estrada

A. Anelli

D. Ao

C. Arata

F. Archilli

Z. Areg

M. Argenton

Costa Rica

S. Arguedas Cuendis

L. Arnone

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

Z. Baldwin

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

S. Bashir

B. Batsukh

P. Battista

A. Bay

A. Beck

M. Becker

F. Bedeschi

I. Bediaga

N. Behling

S. Belin

A. Bellavista

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

A. Biolchini

M. Birch

F. Bishop

A. Bitadze

A. Bizzeti

Measurement of $\textit{CP}$ asymmetry in $$ {D}^0\to {K}_{\textrm{S}}^0{K}_{\textrm{S}}^0 $$ decays with Run 3 data

We propose an <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mi>AdS</mi><mo>×</mo><mi mathvariant="normal">S</mi></mrow></math> factorization formula at the level of the generating function for correlators with arbitrary Kaluza-Klein configurations and implement it in the supergravity limit of <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mi mathvariant="script">N</mi><mo>=</mo><mn>4</mn></mrow></math> supersymmetric Yang-Mills theory. By incorporating this mechanism into Mellin space bootstrap, together with an observed <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>Z</mi><mn>2</mn></msub></math> symmetry under <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mi>AdS</mi><mo stretchy="false">↔</mo><mi mathvariant="normal">S</mi></mrow></math>, we manage to simultaneously work out unified formulas both for all five-point half-BPS correlators and for all four-point correlators with one superdescendant. This <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mi>AdS</mi><mo>×</mo><mi mathvariant="normal">S</mi></mrow></math> bootstrap method is directly applicable to generic multipoint computation at tree level.

Portugal

Bruno Fernandes

Vasco Gonçalves

Zhongjie Huang

Yichao Tang

Joao Vilas Boas

Ellis Ye Yuan

<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mi>AdS</mi><mo stretchy="false">×</mo><mi mathvariant="normal">S</mi></mrow></math> Mellin Bootstrap, Hidden 10D Symmetry and Five-Point Kaluza-Klein Functions in <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mi mathvariant="script">N</mi><mo>=</mo><mn>4</mn></mrow></math> Supersymmetric Yang-Mills Theory

Recently, many new excited states of heavy mesons have been discovered in recent experiments, including radially excited states. The production processes of these states from 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></math> meson have drawn significant interest. In this paper, we use the covariant light-front approach to study the nonleptonic <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></math> meson decays to the first radially excited states <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>D</mi><mrow><mo stretchy="false">(</mo><mi>s</mi><mo stretchy="false">)</mo></mrow></msub><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"><msubsup><mi>D</mi><mrow><mo stretchy="false">(</mo><mi>s</mi><mo stretchy="false">)</mo></mrow><mo>*</mo></msubsup><mo stretchy="false">(</mo><mn>2</mn><mi>S</mi><mo stretchy="false">)</mo></math>. Our results reveal that many channels exhibit large branching ratios in the range <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mn>10</mn><mrow><mo>−</mo><mn>5</mn></mrow></msup><mi>–</mi><msup><mn>10</mn><mrow><mo>−</mo><mn>4</mn></mrow></msup></math>, even up to <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mn>10</mn><mrow><mo>−</mo><mn>3</mn></mrow></msup></math> for individual channels, which are detectable by current experiments. Our predictions for the decays <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><mo stretchy="false">(</mo><mn>2</mn><mi>S</mi><mo stretchy="false">)</mo><mo stretchy="false">(</mo><mi>π</mi><mo>,</mo><mi>ρ</mi><mo>,</mo><msup><mi>K</mi><mrow><mo stretchy="false">(</mo><mo>*</mo><mo stretchy="false">)</mo></mrow></msup><mo stretchy="false">)</mo></math> are larger than those given by the Bethe-Salpeter (BS) equation method, but agree well with the relativistic quark mode (RQM) and the relativistic independent quark model (RIQM) calculations. For comparison, we also present the branching ratios of the decays <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><mo stretchy="false">(</mo><mn>1</mn><mi>S</mi><mo stretchy="false">)</mo><mo stretchy="false">(</mo><mi>π</mi><mo>,</mo><mi>ρ</mi><mo>,</mo><msup><mi>K</mi><mrow><mo stretchy="false">(</mo><mo>*</mo><mo stretchy="false">)</mo></mrow></msup><mo stretchy="false">)</mo></math>, which are comparable with other theoretical results and the data. Although the branching ratios of the decays <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><mo>*</mo></msubsup><mo stretchy="false">(</mo><mn>1</mn><mi>S</mi><mo stretchy="false">)</mo><mo stretchy="false">(</mo><mi>ρ</mi><mo>,</mo><msup><mi>K</mi><mo>*</mo></msup><mo stretchy="false">)</mo></math> are much larger than those of the decays <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><mo>*</mo></msubsup><mo stretchy="false">(</mo><mn>2</mn><mi>S</mi><mo stretchy="false">)</mo><mo stretchy="false">(</mo><mi>ρ</mi><mo>,</mo><msup><mi>K</mi><mo>*</mo></msup><mo stretchy="false">)</mo></math>, the polarization properties between them are similar, that is, the longitudinal polarization fractions are dominant and can amount roughly to 90%.

Zhi-Jie Sun

Yong-Jin Sun

Zhi-Qing Zhang

You-Ya Yang

Si-Yang Wang

<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>D</mi><mrow><mo stretchy="false">(</mo><mi>s</mi><mo stretchy="false">)</mo></mrow></msub><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"><msubsup><mi>D</mi><mrow><mo stretchy="false">(</mo><mi>s</mi><mo stretchy="false">)</mo></mrow><mo>*</mo></msubsup><mo stretchy="false">(</mo><mn>2</mn><mi>S</mi><mo stretchy="false">)</mo></math> production in nonleptonic <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></math> weak decays

Lorentzian gravitational path integral for the Gauss-Bonnet gravity in 4$\textit{D}$ is studied in the mini-superspace ansatz for metric. The gauge-fixed path-integral for Robin boundary choice is computed exactly using $\textit{Airy}$-functions, where the dominant contribution comes from No-boundary geometries. The lapse integral is further analysed using saddle-point methods to compare with exact results. Picard-Lefschetz methods are utilized to find the $\textit{relevant}$ complex saddles and deformed contour of integration, thereby using WKB method to compute the integral along the deformed contour in the saddle-point approximation. However, their successful application is possible only when system is devoid of degeneracies, which in present case appear in two types: $\textit{type-1}$ where the flow-lines starting from neighbouring saddles overlap leading to ambiguities in deciding the $\textit{relevance}$ of saddles, $\textit{type-2}$ where saddles merge for specific choices of boundary parameters leading to failure of WKB. Overcoming degeneracies using artificial $\textit{defects}$ introduces ambiguities due to the choice of $\textit{defects}$ involved. Corrections from quantum fluctuations of scale-factor overcome degeneracies only partially (lifts $\textit{type-2}$ completely with partial resolution of $\textit{type-1}$ ), with the residual lifted fluently by complex deformation of ($\textit{G}$ℏ). $\textit{Anti-linear}$ symmetry present in various forms in the lapse action is the reason behind all the $\textit{type-1}$ degeneracies. Any form of $\textit{defect}$ or $\textit{deformation}$ breaking anti-linearity resolves $\textit{type-1}$ degeneracies, indicating complex deformation of ($\textit{G}$ℏ) as an ideal choice. Compatibility with the KSW criterion is analyzed after symmetry breaking. Complex deformation of ($\textit{G}$ℏ) modifies the KSW criterion, imposing a strong constraint on the deformation if No-boundary geometries are required to be always KSW-allowed.

India

Manishankar Ailiga

Shubhashis Mallik

Gaurav Narain

Resolving degeneracies in complex $\textit{ℝ}$ × $\textit{S}$