Recently, the experimental measurements of the branching ratios and different polarization asymmetries for processes occurring through flavor-changing-charged current   $ (b\rightarrow c\tau\overline{\nu}_{\tau}) $  transitions by BABAR, Belle, and LHCb have revealed some significant differences from the corresponding Standard Model (SM) predictions. This has triggered an interest to search for physics beyond the SM in the context of various new physics (NP) models and using the model-independent weak effective Hamiltonian (WEH). Assuming left-handed neutrinos, we add the dimension-six vector, (pseudo-)scalar, and tensor operators with complex Wilson coefficients (WCs) to the SM WEH. Using 60%, 30%, and 10% constraints resulting from the branching ratio of   $ (b\rightarrow c\tau\overline{\nu}_{\tau}) $  , we reassess the parametric space of these new physics WCs accommodating the current anomalies based on the most recent HFLAV data of   $ (b\rightarrow c\tau\overline{\nu}_{\tau}) $   and   $ (b\rightarrow c\tau\overline{\nu}_{\tau}) $   and Belle data of   $ (b\rightarrow c\tau\overline{\nu}_{\tau}) $   and   $ (b\rightarrow c\tau\overline{\nu}_{\tau}) $  . We find that the allowed parametric region of left-handed scalar couplings strongly depends on the constraints of the   $ (b\rightarrow c\tau\overline{\nu}_{\tau}) $   branching ratio, and the maximum pull from the SM predictions results from the &lt;60% branching ratio limit. Also, the parametric region changes significantly if we extend the analysis by adding LHCb data of   $ (b\rightarrow c\tau\overline{\nu}_{\tau}) $   and   $ (b\rightarrow c\tau\overline{\nu}_{\tau}) $  . Furthermore, due to the large uncertainties in the measurements of   $ (b\rightarrow c\tau\overline{\nu}_{\tau}) $   and   $ (b\rightarrow c\tau\overline{\nu}_{\tau}) $  , we derive the sum rules which complement them with   $ (b\rightarrow c\tau\overline{\nu}_{\tau}) $   and   $ (b\rightarrow c\tau\overline{\nu}_{\tau}) $  . Using the best-fit points of the new complex WCs along with the latest measurements of   $ (b\rightarrow c\tau\overline{\nu}_{\tau}) $  , we predict the numerical values of the observable   $ (b\rightarrow c\tau\overline{\nu}_{\tau}) $  ,   $ (b\rightarrow c\tau\overline{\nu}_{\tau}) $   , and   $ (b\rightarrow c\tau\overline{\nu}_{\tau}) $   from the sum rules. The simultaneous dependence of abovementioned physical observables on the NP WCs is established by plotting their correlation with   $ (b\rightarrow c\tau\overline{\nu}_{\tau}) $   and   $ (b\rightarrow c\tau\overline{\nu}_{\tau}) $  , which are useful to discriminate between various NP scenarios. We find that the most significant impact of NP results from the WC   $ (b\rightarrow c\tau\overline{\nu}_{\tau}) $  . Finally, we study the impact of these NP couplings on various angular and   $ (b\rightarrow c\tau\overline{\nu}_{\tau}) $   triple product asymmetries that could be measured in some ongoing and future experiments. The precise measurements of these observables are important to check the SM and extract the possible NP.

Pakistan

Muhammad Arslan

Tahira Yasmeen

Saba Shafaq

Ishtiaq Ahmed

Muhammad Jamil Aslam

Analysis of anomalies using weak effective Hamiltonian with complex couplings and their impact on various physical observables

Abstract Experimental studies of the observables associated with  transitions in semileptonic B-meson decays at BaBar, Belle, and LHCb have shown some deviations from the Standard Model predictions, consequently providing a handy tool to probe the possible new physics (NP). In this context, we first revisit the impact of recent measurements of  and  on the parametric space of the NP scenarios. In addition, we include the  data in the analysis and find that their influence on the best-fit point and the parametric space is mild. Using the recent HFLAV data, after validating the well established sum rule of , we derive a similar sum rule for . Furthermore, according to the updated data, we modify the correlation among the different observables, giving us their interesting interdependence. Finally, to discriminate the various NP scenarios, we plot the different angular observables and their ratios for  against the transfer momentum square , using the  and  parametric space of considered NP scenarios. By implementing the collider bounds on NP Wilson coefficients (WCs), we find that the parametric space of some NP WCs is significantly restrained. To see the clear influence of NP on the amplitude of the angular observables, we also calculate their numerical values in different  bins and show them through bar plots. We hope that their precise measurements will help to discriminate various NP scenarios.

Probing New Physics in Light of Recent Developments in → Transitions

Based on the expectations that the lowest-lying doubly-bottom tetraquark <math><msub><mrow><mi>T</mi></mrow><mrow><mi>b</mi><mi>b</mi><mover><mrow><mi>u</mi></mrow><mrow><mo>¯</mo></mrow></mover><mover><mrow><mi>d</mi></mrow><mrow><mo>¯</mo></mrow></mover></mrow></msub></math> (<math><msup><mrow><mi>J</mi></mrow><mrow><mi>P</mi></mrow></msup><mo>=</mo><msup><mrow><mn>1</mn></mrow><mrow><mo>+</mo></mrow></msup></math>) and the bottom-charm tetraquark <math><msub><mrow><mi>T</mi></mrow><mrow><mi>b</mi><mi>c</mi><mover><mrow><mi>u</mi></mrow><mrow><mo>¯</mo></mrow></mover><mover><mrow><mi>d</mi></mrow><mrow><mo>¯</mo></mrow></mover></mrow></msub></math> (<math><msup><mrow><mi>J</mi></mrow><mrow><mi>P</mi></mrow></msup><mo>=</mo><msup><mrow><mn>0</mn></mrow><mrow><mo>+</mo></mrow></msup></math>) are stable against strong and electromagnetic decays, we work out a number of semileptonic and non-leptonic weak decays of these hadrons, making use of the heavy quark symmetry. In doing this, we concentrate on the exclusive decays involving also tetraquarks in the final states, i.e., transitions such as <math><msub><mrow><mi>T</mi></mrow><mrow><mi>b</mi><mi>b</mi><mover><mrow><mi>u</mi></mrow><mrow><mo>¯</mo></mrow></mover><mover><mrow><mi>d</mi></mrow><mrow><mo>¯</mo></mrow></mover></mrow></msub><mo>→</mo><msub><mrow><mi>T</mi></mrow><mrow><mi>b</mi><mi>c</mi><mover><mrow><mi>u</mi></mrow><mrow><mo>¯</mo></mrow></mover><mover><mrow><mi>d</mi></mrow><mrow><mo>¯</mo></mrow></mover></mrow></msub><mspace width="0.2em"></mspace><mo>(</mo><msup><mrow><mi>ℓ</mi></mrow><mrow><mo>−</mo></mrow></msup><msub><mrow><mi>ν</mi></mrow><mrow><mi>ℓ</mi></mrow></msub><mo>,</mo><mspace width="0.2em"></mspace><msup><mrow><mi>h</mi></mrow><mrow><mo>−</mo></mrow></msup><mo>)</mo></math> and <math><msub><mrow><mi>T</mi></mrow><mrow><mi>b</mi><mi>c</mi><mover><mrow><mi>u</mi></mrow><mrow><mo>¯</mo></mrow></mover><mover><mrow><mi>d</mi></mrow><mrow><mo>¯</mo></mrow></mover></mrow></msub><mo>→</mo><msub><mrow><mi>T</mi></mrow><mrow><mi>c</mi><mi>c</mi><mover><mrow><mi>u</mi></mrow><mrow><mo>¯</mo></mrow></mover><mover><mrow><mi>d</mi></mrow><mrow><mo>¯</mo></mrow></mover></mrow></msub><mspace width="0.2em"></mspace><mo>(</mo><msup><mrow><mi>ℓ</mi></mrow><mrow><mo>−</mo></mrow></msup><msub><mrow><mi>ν</mi></mrow><mrow><mi>ℓ</mi></mrow></msub><mo>,</mo><mspace width="0.2em"></mspace><msup><mrow><mi>h</mi></mrow><mrow><mo>−</mo></mrow></msup><mo>)</mo></math>, where <math><msup><mrow><mi>h</mi></mrow><mrow><mo>−</mo></mrow></msup><mo>=</mo><msup><mrow><mi>π</mi></mrow><mrow><mo>−</mo></mrow></msup><mo>,</mo><msup><mrow><mi>ρ</mi></mrow><mrow><mo>−</mo></mrow></msup><mo>,</mo><msubsup><mrow><mi>a</mi></mrow><mrow><mn>1</mn></mrow><mrow><mo>−</mo></mrow></msubsup><mo>,</mo><msubsup><mrow><mi>D</mi></mrow><mrow><mi>s</mi></mrow><mrow><mo>−</mo></mrow></msubsup><mo>,</mo><msubsup><mrow><mi>D</mi></mrow><mrow><mi>s</mi></mrow><mrow><mo>⁎</mo><mo>−</mo></mrow></msubsup></math>. So far, only the <math><msup><mrow><mi>J</mi></mrow><mrow><mi>P</mi></mrow></msup><mo>=</mo><msup><mrow><mn>1</mn></mrow><mrow><mo>+</mo></mrow></msup></math> tetraquark <math><msub><mrow><mi>T</mi></mrow><mrow><mi>c</mi><mi>c</mi><mover><mrow><mi>u</mi></mrow><mrow><mo>¯</mo></mrow></mover><mover><mrow><mi>d</mi></mrow><mrow><mo>¯</mo></mrow></mover></mrow></msub></math> has been discovered, which we identify with the <math><mi>I</mi><mo>=</mo><mn>0</mn></math> <math><msubsup><mrow><mi>T</mi></mrow><mrow><mi>c</mi><mi>c</mi></mrow><mrow><mo>+</mo></mrow></msubsup></math> object, compatible with <math><msup><mrow><mi>J</mi></mrow><mrow><mi>P</mi></mrow></msup><mo>=</mo><msup><mrow><mn>1</mn></mrow><mrow><mo>+</mo></mrow></msup></math> and having the pole mass relative to the <math><msup><mrow><mi>D</mi></mrow><mrow><mo>⁎</mo><mo>+</mo></mrow></msup><msup><mrow><mi>D</mi></mrow><mrow><mn>0</mn></mrow></msup></math> mass threshold and decay widths <math><mi>δ</mi><mi>m</mi><mo>=</mo><mi>M</mi><mo>(</mo><msubsup><mrow><mi>T</mi></mrow><mrow><mi>c</mi><mi>c</mi></mrow><mrow><mo>+</mo></mrow></msubsup><mo>)</mo><mo>−</mo><mo>(</mo><mi>M</mi><mo>(</mo><msup><mrow><mi>D</mi></mrow><mrow><mo>⁎</mo><mo>+</mo></mrow></msup><mo>)</mo><mo>+</mo><mi>M</mi><mo>(</mo><msup><mrow><mi>D</mi></mrow><mrow><mn>0</mn></mrow></msup><mo>)</mo><mo>)</mo><mo>=</mo><mo>−</mo><mn>360</mn><mo>±</mo><msubsup><mrow><mn>40</mn></mrow><mrow><mo>−</mo><mn>0</mn></mrow><mrow><mo>+</mo><mn>4</mn></mrow></msubsup></math> keV and <math><mi>Γ</mi><mo>(</mo><msubsup><mrow><mi>T</mi></mrow><mrow><mi>c</mi><mi>c</mi></mrow><mrow><mo>+</mo></mrow></msubsup><mo>)</mo><mo>=</mo><msubsup><mrow><mn>48</mn></mrow><mrow><mo>−</mo><mn>14</mn></mrow><mrow><mo>+</mo><mn>2</mn></mrow></msubsup></math> keV. Experimental discoveries of the transitions worked out here, and related ones involving doubly-heavy baryons, will quantify the diquark-antidiquark component of these tetraquarks.