Nuclear Physics B最新文献

{"title":"Celestial string integrands & their expansions","authors":"Daniel Bockisch","doi":"10.1016/j.nuclphysb.2025.116792","DOIUrl":"10.1016/j.nuclphysb.2025.116792","url":null,"abstract":"<div><div>We transform the one-loop four-point type I open superstring gluon amplitude to correlation functions on the celestial sphere including both the (non-)orientable planar and non-planar sector. This requires a Mellin transform with respect to the energies of the scattered strings, as well as to integrate over the open-string worldsheet moduli space. After accomplishing the former we obtain celestial string integrands with remaining worldsheet integrals <span><math><mi>Ψ</mi><mrow><mo>(</mo><mi>β</mi><mo>)</mo></mrow></math></span>, where <em>β</em> is related to the conformal scaling dimensions of the conformal primary operators under consideration. Employing an alternative approach of performing an <span><math><msup><mrow><mi>α</mi></mrow><mrow><mo>′</mo></mrow></msup></math></span>-expansion of the open superstring amplitude first and Mellin transforming afterwards, we obtain a fully integrated expression, capturing the pole structure in the <em>β</em>-plane. The same analysis is performed at tree-level yielding similar results. We conclude by solving <span><math><mi>Ψ</mi><mrow><mo>(</mo><mi>β</mi><mo>)</mo></mrow></math></span> for specific values of <em>β</em>, consistently reproducing the results of the <span><math><msup><mrow><mi>α</mi></mrow><mrow><mo>′</mo></mrow></msup></math></span>-expansion ansatz. In all approaches we find that the dependence on <span><math><msup><mrow><mi>α</mi></mrow><mrow><mo>′</mo></mrow></msup></math></span> reduces to that of a simple overall factor of <span><math><msup><mrow><mo>(</mo><msup><mrow><mi>α</mi></mrow><mrow><mo>′</mo></mrow></msup><mo>)</mo></mrow><mrow><mi>β</mi><mo>−</mo><mn>3</mn></mrow></msup></math></span> at loop and <span><math><msup><mrow><mo>(</mo><msup><mrow><mi>α</mi></mrow><mrow><mo>′</mo></mrow></msup><mo>)</mo></mrow><mrow><mi>β</mi></mrow></msup></math></span> at tree level, consistent with previous literature.</div></div>","PeriodicalId":54712,"journal":{"name":"Nuclear Physics B","volume":"1011 ","pages":"Article 116792"},"PeriodicalIF":2.5,"publicationDate":"2025-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143176941","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"A new-old approach to composite scalars with chiral fermion constituents","authors":"Christopher T. Hill","doi":"10.1016/j.nuclphysb.2024.116788","DOIUrl":"10.1016/j.nuclphysb.2024.116788","url":null,"abstract":"<div><div>We develop a dynamical, Lorentz invariant theory of composite scalars in configuration space consisting of chiral fermions, interacting by the perturbative exchange of a massive “gluon” of coupling <span><math><msub><mrow><mi>g</mi></mrow><mrow><mn>0</mn></mrow></msub></math></span> and mass <span><math><msubsup><mrow><mi>M</mi></mrow><mrow><mn>0</mn></mrow><mrow><mn>2</mn></mrow></msubsup></math></span> (the coloron model). The formalism is inspired by, but goes beyond, old ideas of Yukawa and the Nambu-Jona-Lasinio (NJL) model. It yields a non-pointlike internal wave-function of the bound state, <span><math><mi>ϕ</mi><mo>(</mo><mi>r</mi><mo>)</mo></math></span>, which satisfies a Schrödinger-Klein-Gordon (SKG) equation with eigenvalue <span><math><msup><mrow><mi>μ</mi></mrow><mrow><mn>2</mn></mrow></msup></math></span>. For super-critical coupling, <span><math><msubsup><mrow><mi>g</mi></mrow><mrow><mn>0</mn></mrow><mrow><mn>2</mn></mrow></msubsup><mo>&gt;</mo><msubsup><mrow><mi>g</mi></mrow><mrow><mn>0</mn><mi>c</mi></mrow><mrow><mn>2</mn></mrow></msubsup></math></span>, we have <span><math><msup><mrow><mi>μ</mi></mrow><mrow><mn>2</mn></mrow></msup><mo>&lt;</mo><mn>0</mn></math></span> leading to spontaneous symmetry breaking. The binding of chiral fermions is semiclassical, <em>not loop-level as in NJL</em>. The mass scale is determined by the interaction as in NJL. We mainly focus on the short-distance, large <span><math><msubsup><mrow><mi>M</mi></mrow><mrow><mn>0</mn></mrow><mrow><mn>2</mn></mrow></msubsup></math></span> limit, yielding an NJL pointlike interaction, but the bound state internal wave-function, <span><math><mi>ϕ</mi><mo>(</mo><mover><mrow><mi>r</mi></mrow><mrow><mo>→</mo></mrow></mover><mo>)</mo></math></span>, remains spatially extended and dilutes <span><math><mi>ϕ</mi><mo>(</mo><mn>0</mn><mo>)</mo></math></span>. This leads to power-law suppression of the induced Yukawa and quartic couplings and requires radically less fine-tuning of a hierarchy than does the NJL model. We include a discussion of loop corrections of the theory. A realistic top condensation model appears possible.</div></div>","PeriodicalId":54712,"journal":{"name":"Nuclear Physics B","volume":"1011 ","pages":"Article 116788"},"PeriodicalIF":2.5,"publicationDate":"2025-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143177373","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Charged lepton-flavor violating constraints to non-unitarity in the Linear Seesaw scheme","authors":"Jesús Miguel Celestino-Ramírez,&nbsp;O.G. Miranda","doi":"10.1016/j.nuclphysb.2025.116804","DOIUrl":"10.1016/j.nuclphysb.2025.116804","url":null,"abstract":"<div><div>We analyze the non-unitary effects in the linear seesaw mechanism using the current constraints and future sensitivity of the charged Lepton Flavor Violation (cLFV) processes. We perform a random scan confronting the non-unitary parameters with the limits to the cLFV processes. We show our results for the normal and inverted ordering of the oscillation data. We also discuss the equivalence of different parametrizations of the non-unitary mixing matrix and show our results in terms of the different parameterizations. We found that the stronger restrictions in the non-unitary parameter space come from rare muon decay searches.</div></div>","PeriodicalId":54712,"journal":{"name":"Nuclear Physics B","volume":"1011 ","pages":"Article 116804"},"PeriodicalIF":2.5,"publicationDate":"2025-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143176952","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Higher rank elliptic partition functions and multisymmetric elliptic functions","authors":"Allan John Gerrard ,&nbsp;Kohei Motegi ,&nbsp;Kazumitsu Sakai","doi":"10.1016/j.nuclphysb.2025.116805","DOIUrl":"10.1016/j.nuclphysb.2025.116805","url":null,"abstract":"<div><div>We introduce and investigate a class of <span><math><msub><mrow><mi>gl</mi></mrow><mrow><mi>M</mi><mo>+</mo><mn>1</mn></mrow></msub></math></span> partition functions which is an extension of the one introduced by Foda-Manabe. We characterize the partition functions by a nested version of Izergin-Korepin analysis, and determine the explicit forms, for each of the rational, trigonometric and elliptic versions. The resulting multisymmetric functions can be regarded as extensions of the rational, trigonometric and elliptic weight functions.</div></div>","PeriodicalId":54712,"journal":{"name":"Nuclear Physics B","volume":"1011 ","pages":"Article 116805"},"PeriodicalIF":2.5,"publicationDate":"2025-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143177375","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Multiplicity dependence of ϒ production at forward rapidity in pp collisions at s=13 TeV","authors":"","doi":"10.1016/j.nuclphysb.2024.116786","DOIUrl":"10.1016/j.nuclphysb.2024.116786","url":null,"abstract":"<div><div>The measurement of ϒ(1S), ϒ(2S), and ϒ(3S) yields as a function of the charged-particle multiplicity density, <span><math><mtext>d</mtext><msub><mrow><mi>N</mi></mrow><mrow><mtext>ch</mtext></mrow></msub><mo>/</mo><mtext>d</mtext><mi>η</mi></math></span>, using the ALICE experiment at the LHC, is reported in pp collisions at <span><math><msqrt><mrow><mi>s</mi></mrow></msqrt><mo>=</mo></math></span> 13 TeV. The ϒ meson yields are measured at forward rapidity (<span><math><mn>2.5</mn><mo>&lt;</mo><mi>y</mi><mo>&lt;</mo><mn>4</mn></math></span>) in the dimuon decay channel, whereas the charged-particle multiplicity is defined at central rapidity (<span><math><mo>|</mo><mi>η</mi><mo>|</mo><mo>&lt;</mo><mn>1</mn></math></span>). Both quantities are divided by their average value in minimum bias events to compute the self-normalized quantities. The increase of the self-normalized ϒ(1S), ϒ(2S), and ϒ(3S) yields is found to be compatible with a linear scaling with the self-normalized <span><math><mtext>d</mtext><msub><mrow><mi>N</mi></mrow><mrow><mtext>ch</mtext></mrow></msub><mo>/</mo><mtext>d</mtext><mi>η</mi></math></span>, within the uncertainties. The self-normalized yield ratios of excited-to-ground ϒ states are compatible with unity within uncertainties. Similarly, the measured double ratio of the self-normalized ϒ(1S) to the self-normalized J/<em>ψ</em> yields, both measured at forward rapidity, is compatible with unity for self-normalized charged-particle multiplicities beyond one. The measurements are compared with theoretical predictions incorporating initial or final state effects.</div></div>","PeriodicalId":54712,"journal":{"name":"Nuclear Physics B","volume":"1011 ","pages":"Article 116786"},"PeriodicalIF":2.5,"publicationDate":"2025-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143178293","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Phenomenological aspects of Lee-Wick QED","authors":"Fayez Abu-Ajamieh ,&nbsp;Pratik Chattopadhyay ,&nbsp;Marco Frasca","doi":"10.1016/j.nuclphysb.2025.116799","DOIUrl":"10.1016/j.nuclphysb.2025.116799","url":null,"abstract":"<div><div>We study some phenomenological aspects of Lee-Wick (LW) QED. In particular, we show that LW QED implies charge dequantization and a flavor-dependent LW scale. We study the implications of the Weak Gravity Conjecture (WGC) in LW QED and calculate the modified electric force and potential and use the former to reformulate the WGC in LW QED. We also calculate the photon self-energy and the Uehling potential in LW QED. We show that bounds on milli-charged particles from matter neutrality experiments set stringent limits on the LW scale of fermions and of the photon.</div></div>","PeriodicalId":54712,"journal":{"name":"Nuclear Physics B","volume":"1011 ","pages":"Article 116799"},"PeriodicalIF":2.5,"publicationDate":"2025-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143176953","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Universal non-equilibrium scaling of cumulants across a critical point","authors":"Leon J. Sieke ,&nbsp;Mattis Harhoff ,&nbsp;Sören Schlichting ,&nbsp;Lorenz von Smekal","doi":"10.1016/j.nuclphysb.2025.116808","DOIUrl":"10.1016/j.nuclphysb.2025.116808","url":null,"abstract":"<div><div>We study the critical dynamics of a scalar field theory with <span><math><msub><mrow><mi>Z</mi></mrow><mrow><mn>2</mn></mrow></msub></math></span> symmetry in the dynamic universality class of Model A in two and three spatial dimensions with classical-statistical lattice simulations. In particular, we measure the non-equilibrium behavior of the system under a quench protocol in which the symmetry-breaking external field is changed at a constant rate through the critical point. Using the well-established Kibble-Zurek scaling theory we compute non-equilibrium scaling functions of cumulants of the order parameter up to fourth order. Together with the static critical exponents and the dynamic critical exponent, these fully describe the universal non-equilibrium evolution of the system near the critical point. We further extend the analysis to include finite-size effects and observe good collapse of our data onto two-dimensional universal non-equilibrium and finite-size scaling functions.</div></div>","PeriodicalId":54712,"journal":{"name":"Nuclear Physics B","volume":"1011 ","pages":"Article 116808"},"PeriodicalIF":2.5,"publicationDate":"2025-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143177376","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Study of texture zero neutrino models with vanishing sub-trace and their flavor structures","authors":"Sangeeta Dey,&nbsp;Mahadev Patgiri","doi":"10.1016/j.nuclphysb.2024.116789","DOIUrl":"10.1016/j.nuclphysb.2024.116789","url":null,"abstract":"<div><div>In this work, we carry out a systematic investigation of thirty six possible structures of neutrino mass matrix, <span><math><msub><mrow><mi>M</mi></mrow><mrow><mi>ν</mi></mrow></msub></math></span> having textures of one zero element and one vanishing sub-trace taking the latest 3<em>σ</em> neutrino data. Correlation plots of the ratio of solar to atmospheric mass splittings, <span><math><msub><mrow><mi>R</mi></mrow><mrow><mi>ν</mi></mrow></msub></math></span> and the Dirac CP phase, <em>δ</em> for each texture are examined and found only fourteen textures phenomenologically viable with 3<em>σ</em> range. The restricted ranges of <em>δ</em> for allowed textures are used to predict theoretically the Majorana CP Phases (<em>α</em> and <em>β</em>) which are yet to be measured experimentally. With these results, we also calculate the Majorana mass term, <span><math><mo>|</mo><msub><mrow><mi>m</mi></mrow><mrow><mi>e</mi><mi>e</mi></mrow></msub><mo>|</mo></math></span> on which the neutrinoless double beta decay rate depends, and the Jarlskog invariant, <span><math><msub><mrow><mi>J</mi></mrow><mrow><mi>c</mi><mi>p</mi></mrow></msub></math></span> for the strength of CP violation and also study the correlations between the CP phases and the mixing angle <span><math><msub><mrow><mi>θ</mi></mrow><mrow><mn>23</mn></mrow></msub></math></span>. Besides them, we also checked the experimental compatibilities for the parameters effective electron neutrino mass <span><math><msub><mrow><mi>m</mi></mrow><mrow><msub><mrow><mi>ν</mi></mrow><mrow><mi>e</mi></mrow></msub></mrow></msub></math></span>, total ‘sum’ of neutrino masses, <span><math><msub><mrow><mi>Σ</mi></mrow><mrow><mi>ν</mi></mrow></msub></math></span>. The consistency of mass orderings of textures is checked with <span><math><mfrac><mrow><msub><mrow><mi>m</mi></mrow><mrow><mn>3</mn></mrow></msub></mrow><mrow><msub><mrow><mi>m</mi></mrow><mrow><mn>1</mn></mrow></msub></mrow></mfrac></math></span>, and phenomenological identification of textures having no octant degeneracy for <span><math><msub><mrow><mi>θ</mi></mrow><mrow><mn>23</mn></mrow></msub></math></span> is done. Finally, the flavor symmetry realization of textures is done under the symmetry group, <span><math><msub><mrow><mi>S</mi></mrow><mrow><mn>3</mn></mrow></msub><mo>×</mo><msub><mrow><mi>Z</mi></mrow><mrow><mn>4</mn></mrow></msub></math></span> in Type II seesaw mechanism.</div></div>","PeriodicalId":54712,"journal":{"name":"Nuclear Physics B","volume":"1011 ","pages":"Article 116789"},"PeriodicalIF":2.5,"publicationDate":"2025-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143177401","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Quasinormal modes and GUP-corrected Hawking radiation of BTZ black holes within modified gravity frameworks","authors":"Faizuddin Ahmed ,&nbsp;Ahmad Al-Badawi ,&nbsp;İzzet Sakallı ,&nbsp;Abdelmalek Bouzenada","doi":"10.1016/j.nuclphysb.2025.116806","DOIUrl":"10.1016/j.nuclphysb.2025.116806","url":null,"abstract":"<div><div>This paper aims to explore the quasinormal modes (QNMs) and effective potential profiles of massless and rotating BTZ black holes within the frameworks of <span><math><mi>f</mi><mo>(</mo><mi>R</mi><mo>)</mo></math></span> and Ricci-Inverse (<span><math><mi>RI</mi></math></span>) modified gravity theories, which, while producing similar space-time structures, exhibit variations due to distinct cosmological constants, <span><math><msub><mrow><mi>Λ</mi></mrow><mrow><mi>m</mi></mrow></msub></math></span>. We derive wave equations for these black hole perturbations and analyze the behavior of the effective potential <span><math><msub><mrow><mi>V</mi></mrow><mrow><mtext>eff</mtext></mrow></msub><mo>(</mo><mi>r</mi><mo>)</mo></math></span> under different values of mass <em>m</em>, cosmological constant <span><math><msub><mrow><mi>Λ</mi></mrow><mrow><mi>m</mi></mrow></msub></math></span>, and modified gravity parameters <span><math><msub><mrow><mi>α</mi></mrow><mrow><mn>1</mn></mrow></msub></math></span>, <span><math><msub><mrow><mi>α</mi></mrow><mrow><mn>2</mn></mrow></msub></math></span>, <span><math><msub><mrow><mi>β</mi></mrow><mrow><mn>1</mn></mrow></msub></math></span>, <span><math><msub><mrow><mi>β</mi></mrow><mrow><mn>2</mn></mrow></msub></math></span>, and <em>γ</em>. The findings indicate that increasing mass and parameter values results in a raised potential barrier, implying stronger confinement of perturbations and impacting black hole stability. Incorporating the generalized uncertainty principle, we also study its effect on the thermodynamics of rotating BTZ black holes, demonstrating how GUP modifies black hole radiation, potentially observable in QNM decay rates. Additionally, we investigate the motion of particles through null and timelike geodesics in static BTZ space-time, observing asymptotic behaviors for null geodesics and parameter-dependent shifts in potential for timelike paths. The study concludes that modified gravity parameters significantly influence QNM frequencies and effective potential profiles, offering insights into black hole stability and suggesting that these theoretical predictions may be tested through gravitational wave observations.</div></div>","PeriodicalId":54712,"journal":{"name":"Nuclear Physics B","volume":"1011 ","pages":"Article 116806"},"PeriodicalIF":2.5,"publicationDate":"2025-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143176938","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"n−n‾ oscillation in S1/Z2×Z2′ orbifold SU(5) GUT","authors":"Ankit Das ,&nbsp;Sarthak Duary ,&nbsp;Utpal Sarkar","doi":"10.1016/j.nuclphysb.2025.116802","DOIUrl":"10.1016/j.nuclphysb.2025.116802","url":null,"abstract":"<div><div>We explore the possibility of <em>B</em> and <span><math><mi>B</mi><mo>−</mo><mi>L</mi></math></span> violating processes, specifically proton decay and neutron-antineutron oscillation, using explicit realization of operators in the <span><math><mi>S</mi><mi>U</mi><mo>(</mo><mn>5</mn><mo>)</mo></math></span> grand unified theory with an <span><math><msup><mrow><mi>S</mi></mrow><mrow><mn>1</mn></mrow></msup><mo>/</mo><msub><mrow><mi>Z</mi></mrow><mrow><mn>2</mn></mrow></msub><mo>×</mo><msubsup><mrow><mi>Z</mi></mrow><mrow><mn>2</mn></mrow><mrow><mo>′</mo></mrow></msubsup></math></span> orbifold space.</div></div>","PeriodicalId":54712,"journal":{"name":"Nuclear Physics B","volume":"1011 ","pages":"Article 116802"},"PeriodicalIF":2.5,"publicationDate":"2025-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143177402","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}