The neutrino mass hierarchy determination (<math id="M2"><mi>ν</mi></math> MHD) is one of the main goals of the major current and future neutrino experiments. The statistical analysis usually proceeds from a standard method, a single-dimensional estimator <math id="M3"><mfenced><mrow><mn>1</mn><mtext>D</mtext><mo>−</mo><mi>Δ</mi><msup><mrow><mi>χ</mi></mrow><mrow><mn>2</mn></mrow></msup></mrow></mfenced></math> that shows some drawbacks and concerns, together with a debatable strategy. The drawbacks and considerations of the standard method will be explained through the following three main issues. The first issue corresponds to the limited power of the standard method. The <math id="M4"><mi>Δ</mi><msup><mrow><mi>χ</mi></mrow><mrow><mn>2</mn></mrow></msup></math> estimator provides us with different results when different simulation procedures were used. Regarding the second issue, when <math id="M5"><msubsup><mrow><mi>χ</mi></mrow><mrow><mi>min</mi><mfenced><mrow><mtext>NH</mtext></mrow></mfenced></mrow><mrow><mn>2</mn></mrow></msubsup></math> and <math id="M6"><msubsup><mrow><mi>χ</mi></mrow><mrow><mi>min</mi><mfenced><mrow><mtext>IH</mtext></mrow></mfenced></mrow><mrow><mn>2</mn></mrow></msubsup></math> are drawn in a 2D map, their strong positive correlation manifests <math id="M7"><msup><mrow><mi>χ</mi></mrow><mrow><mn>2</mn></mrow></msup></math> as a bidimensional variable, instead of a single-dimensional estimator. The overlapping between the <math id="M8"><msup><mrow><mi>χ</mi></mrow><mrow><mn>2</mn></mrow></msup></math> distributions of the two hypotheses leads to an experiment sensitivity reduction. The third issue corresponds to the robustness of the standard method. When the JUNO sensitivity is obtained using different procedures, either with <math id="M9"><mi>Δ</mi><msup><mrow><mi>χ</mi></mrow><mrow><mn>2</mn></mrow></msup></math> as one-dimensional or <math id="M10"><msup><mrow><mi>χ</mi></mrow><mrow><mn>2</mn></mrow></msup></math> as two-dimensional estimator, the experimental sensitivity varies with the different values of the atmospheric mass, the input parameter. We computed the oscillation of <math id="M11"><mfenced><mrow><mover><mrow><mi>Δ</mi><msup><mrow><mi>χ</mi></mrow><mrow><mn>2</mn></mrow></msup></mrow><mrow><mo>¯</mo></mrow></mover></mrow></mfenced></math> with the input parameter values, <math id="M12"><msub><mrow><mfenced><mrow><mi>Δ</mi><msup><mrow><mi>m</mi></mrow><mrow><mn>2</mn></mrow></msup></mrow></mfenced></mrow><mrow><mtext>input</mtext></mrow></msub></math>. The MH significance using the standard method, <math id="M13"><mi>Δ</mi><msup><mrow><mi>χ</mi></mrow><mrow><mn>2</mn></mrow></msup></math>, strongly depends on the values of the parameter <math id="M14"><msub><mrow><mfenced><mrow><mi>Δ</mi><msup><mrow><mi>m</mi></mrow><mrow><mn>2</mn></mrow></msup></mrow></mfenced></mrow><mrow><mtext>input</mtext></mrow></msub></math>. Consequently, the experiment sensitivity depends on the precision of the atmospheric mass. This evaluation of the standard method confirms the drawbacks.

Egypt

Italy

Statistical Issues on the Neutrino Mass Hierarchy with

The measurements of the total cross section of the <math id="M2"><msup><mrow><mi>e</mi></mrow><mrow><mo>+</mo></mrow></msup><msup><mrow><mi>e</mi></mrow><mrow><mo>−</mo></mrow></msup><mo>⟶</mo><mi>γ</mi><mi>γ</mi><mfenced><mrow><mi>γ</mi></mrow></mfenced></math> reaction from the VENUS, TOPAS, OPAL, DELPHI, ALEPH, and L3 collaborations, collected between 1989 and 2003, are used to perform a <math id="M3"><msup><mrow><mi>χ</mi></mrow><mrow><mn>2</mn></mrow></msup></math> test to validate the current quantum electrodynamics (QED) theory and search for possible deviations with the direct contact term annihilation. By observing a deviation from the QED predictions on the total cross section of the <math id="M4"><msup><mrow><mi>e</mi></mrow><mrow><mo>+</mo></mrow></msup><msup><mrow><mi>e</mi></mrow><mrow><mo>−</mo></mrow></msup><mo>⟶</mo><mi>γ</mi><mi>γ</mi><mfenced><mrow><mi>γ</mi></mrow></mfenced></math> reaction above <math id="M5"><msqrt><mrow><mi>s</mi></mrow></msqrt><mo>=</mo><mn>180.0</mn></math> GeV, a non-QED direct contact term is introduced following the dimension 6 effective theory to explain the deviation. In the non-QED direct contact term, a threshold energy scale <math id="M6"><mi>Λ</mi></math> is included and explained to the finite interaction length in direct contact term and in consequence the size of the electron involved in the annihilation area. The experimental data of the total cross section is compared to the QED cross section by a <math id="M7"><msup><mrow><mi>χ</mi></mrow><mrow><mn>2</mn></mrow></msup></math> test, which gives a best fit of the <math id="M8"><mi>Λ</mi></math> to be <math id="M9"><mn>1576</mn><mo>±</mo><mn>202</mn></math> GeV, corresponding to a finite interaction length of <math id="M10"><msub><mrow><mi>r</mi></mrow><mrow><mi>e</mi></mrow></msub><mo>=</mo><mfenced><mrow><mn>1.25</mn><mo>±</mo><mn>0.16</mn></mrow></mfenced><mo>×</mo><mn>1</mn><msup><mrow><mn>0</mn></mrow><mrow><mo>−</mo><mn>17</mn></mrow></msup></math> (cm). In the direct contact term annihilation, this interaction length is a measure of the size of an electron <math id="M11"><msub><mrow><mi>r</mi></mrow><mrow><mi>e</mi></mrow></msub></math>. By combining all the data results from the mentioned collaborations, we have at least 2 to 3 times more statistics than every single experiment at high <math id="M12"><msqrt><mrow><mi>s</mi></mrow></msqrt></math> region. This induces the best precision on <math id="M13"><msub><mrow><mi>r</mi></mrow><mrow><mi>e</mi></mrow></msub></math> compared to the previous measurements.

China

Switzerland

Hint for a Minimal Interaction Length in Annihilation in Total Cross Section of Center-of-Mass Energies 55-207 GeV

The analytical exact iteration method (AEIM) has been widely used to calculate <math id="M4"><mi>N</mi></math>-dimensional radial Schrodinger equation with medium-modified form of Cornell potential and is generalized to the finite value of magnetic field (eB) with quasiparticle approach in hot quantum chromodynamics (QCD) medium. In <math id="M5"><mi>N</mi></math>-dimensional space, the energy eigenvalues have been calculated for any states (<math id="M6"><mi>n</mi></math>, <math id="M7"><mi>l</mi></math>). These results have been used to study the properties of quarkonium states (i.e, the binding energy and mass spectra, dissociation temperature, and thermodynamical properties in the <math id="M8"><mi>N</mi></math>-dimensional space). We have determined the binding energy of the ground states of quarkonium with magnetic field and dimensionality number. We have also determined the effects of magnetic field and dimensionality number on mass spectra for ground states of quarkonia. But the main result is quite noticeable for the values of dissociation temperature in terms of magnetic field and dimensionality number for ground states of quarkonia after using the criteria of dissociation energy. At last, we have also calculated the thermodynamical properties of QGP (i.e., pressure, energy density, and speed of sound) using the parameter eB with ideal equation of states (EoS). A preprint has previously been published (Solanki et al., 2023).

India

Dissociation of And Using Dissociation Energy Criteria in -Dimensional Space

We study the transverse momentum (<math id="M1"><msub><mrow><mi>p</mi></mrow><mrow><mi>T</mi></mrow></msub></math>) spectra of neutral pions and identified charged hadrons produced in proton–proton (pp), deuteron–gold (d–Au), and gold–gold (Au–Au) collisions at the center of mass energy <math id="M2"><msqrt><mrow><msub><mrow><mi>s</mi></mrow><mrow><mtext>NN</mtext></mrow></msub></mrow></msqrt><mo>=</mo><mn>200</mn></math> GeV. The study is made in the framework of a multisource thermal model used in the partonic level. It is assumed that the contribution to the <math id="M3"><msub><mrow><mi>p</mi></mrow><mrow><mi>T</mi></mrow></msub></math>-value of any hadron comes from two or three partons with an isotropic distribution of the azimuthal angle. The contribution of each parton to the <math id="M4"><msub><mrow><mi>p</mi></mrow><mrow><mi>T</mi></mrow></msub></math>-value of a given hadron is assumed to obey any one of the standard (Maxwell-Boltzmann, Fermi-Dirac, and Bose-Einstein) distributions with the kinetic freeze-out temperature and average transverse flow velocity. The <math id="M5"><msub><mrow><mi>p</mi></mrow><mrow><mi>T</mi></mrow></msub></math> spectra of the final-state hadrons can be fitted by the superposition of two or three components. The results obtained from our Monte Carlo method are used to fit the experimental results of the PHENIX and STAR Collaborations. The results of the present work serve as a suitable reference baseline for other experiments and simulation studies.

Uzbekistan

Extracting Kinetic Freeze-Out Properties in High-Energy Collisions Using a Multisource Thermal Model

We investigate wormhole solutions using the modified gravity model <math id="M2"><mi>f</mi><mfenced><mrow><mi>Q</mi><mo>,</mo><mi>T</mi></mrow></mfenced></math> with viscosity and aim to find a solution for the existence of wormholes mathematically without violating the energy conditions. We show that there is no need to define a wormhole from exotic matter and analyze the equations with numerical analysis to establish weak energy conditions. In the numerical analysis, we found that the appropriate values of the parameters can maintain the weak energy conditions without the need for exotic matter. Adjusting the parameters of the model can increase or decrease the rate of positive energy density or radial and tangential pressures. According to the numerical analysis conducted in this paper, the weak energy conditions are established in the whole space if <math id="M3"><mi>α</mi><mo>&lt;</mo><mn>0</mn></math> and <math id="M4"><mn>12.56</mn><mo>&lt;</mo><mi>β</mi><mo>&lt;</mo><mn>25.12</mn></math> or <math id="M5"><mi>α</mi><mo>&gt;</mo><mn>0</mn></math> and <math id="M6"><mi>β</mi><mo>&gt;</mo><mn>25.12</mn></math>. The analysis also showed that the supporting matter of the wormhole is near normal matter, indicating that the generalized <math id="M7"><mi>f</mi><mfenced><mrow><mi>Q</mi><mo>,</mo><mi>T</mi></mrow></mfenced></math> model with viscosity has an acceptable parameter space to describe a wormhole without the need for exotic matter.

Iran

Modified Gravity Model and Wormhole Solution

In this study, we investigated the impact of a topological defect (<math id="M1"><mi>λ</mi></math>) on the properties of heavy quarkonia using the extended Cornell potential. We solved the fractional radial Schrödinger equation (SE) using the extended Nikiforov-Uvarov (ENU) method to obtain the eigenvalues of energy, which allowed us to calculate the masses of charmonium and bottomonium. One significant observation was the splitting between nP and nD states, which attributed to the presence of the topological defect. We discovered that the excited states were divided into components corresponding to <math id="M2"><mn>2</mn><mi>l</mi><mo>+</mo><mn>1</mn></math>, indicating that the gravity field induced by the topological defect interacts with energy levels like the Zeeman effect caused by a magnetic field. Additionally, we derived the wave function and calculated the root-mean radii for charmonium and bottomonium. A comparison with the classical models was performed, resulting in better results being obtained. Furthermore, we investigated the thermodynamic properties of charmonium and bottomonium, determining quantities such as energy, partition function, free energy, mean energy, specific heat, and entropy for P-states. The obtained results were found to be consistent with experimental data and previous works. In conclusion, the fractional model used in this work proved an essential role in understanding the various properties and behaviors of heavy quarkonia in the presence of topological defects.

Properties and Behaviors of Heavy Quarkonia: Insights through Fractional Model and Topological Defects

The phase diagram of quantum chromodynamics (QCD) and its associated thermodynamic properties of quark-gluon plasma (QGP) are studied in the presence of time-dependent magnetic field. The study plays a pivotal role in the field of cosmology, astrophysics, and heavy-ion collisions. In order to explore the structure of quark-gluon plasma to deal with the dynamics of quarks and gluons, we investigate the equation of state (EoS) not only in the environment of static magnetic field but also in the presence of time-varying magnetic fields. So, for determining the equation of state of QGP at nonzero magnetic fields, we revisited our earlier model where the effect of time-varying magnetic field was not taken into consideration. Using the phenomenological model, some appealing features are noticed depending upon the three different scales: effective mass of quark, temperature, and time-independent and time-dependent magnetic fields. Earlier the effective mass of quark was incorporated in our calculations, and in the current work, it is modified for static and time-varying magnetic fields. Thermodynamic observables including pressure, energy density, and entropy are calculated for a wide range of temperature- and time-dependent as well as time-independent magnetic fields. Finally, we claim that the EoS are highly affected in the presence of a magnetic field. Our results are notable compared to other approaches and found to be advantageous for the measurement of QGP equation of state. These crucial findings with and without time-varying magnetic field could have phenomenological implications in various sectors of high-energy physics.

Role of Time-Varying Magnetic Field on QGP Equation of State

We analyze the radiative stability of the next-to-tribimaximal mixings (NTBM) with the variation of the SUSY breaking scale (<math id="M1"><msub><mrow><mi>m</mi></mrow><mrow><mi>S</mi></mrow></msub></math>) in MSSM, for both normal ordering (NO) and inverted ordering (IO) at the fixed input value of the seesaw scale <math id="M2"><msub><mrow><mi>M</mi></mrow><mrow><mi>R</mi></mrow></msub><mo>=</mo><mn>1</mn><msup><mrow><mn>0</mn></mrow><mrow><mn>15</mn></mrow></msup></math> GeV and two different values of <math id="M3"><mi>tan</mi><mi>β</mi></math>. All the neutrino oscillation parameters receive varying radiative corrections irrespective of the <math id="M4"><msub><mrow><mi>m</mi></mrow><mrow><mi>S</mi></mrow></msub></math> values at the electroweak scale, which are all within the <math id="M5"><mn>3</mn><mi>σ</mi></math> range of the latest global fit data at a low value of <math id="M6"><mi>tan</mi><mi>β</mi></math>. NO is found to be more stable than IO for all four different NTBM mixing patterns.

Stability of the Next-to-Tribimaximal Mixings under Radiative Corrections with the Variation of the SUSY Breaking Scale in MSSM

Neutrino masses are yet unknown. We discuss the present state of effective electron antineutrino mass from <math id="M1"><mi>β</mi></math> decay experiments; effective Majorana neutrino mass from neutrinoless double-beta decay experiments; neutrino mass squared differences from neutrino oscillation: solar, atmospheric, reactor, and accelerator-based experiments; sum of neutrino masses from cosmological observations. Current experimental challenges in the determination of neutrino masses are briefly discussed. The main focus is devoted to contemporary experiments.

United States

Theoretical and Experimental Challenges in the Measurement of Neutrino Mass

In this paper, we study the effects of the widths of unstable particles on the one-loop electroweak corrections for the <math id="M2"><mtext>pp</mtext><mo>⟶</mo><mtext>WW</mtext></math> process at the TeV scale within the framework of the complex mass scheme. We also investigate, for this same process, the unitarity of the theory at high energies.