<p>The <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>S</mi><mi>U</mi><mo stretchy="false">(</mo><mn>2</mn><msub><mo stretchy="false">)</mo><mi>L</mi></msub><mo>×</mo><mi>U</mi><mo stretchy="false">(</mo><mn>1</mn><msub><mo stretchy="false">)</mo><mi>Y</mi></msub></math> invariance of the Standard Model effective field theory (SMEFT) predicts multiple restrictions in the space of Wilson coefficients of <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>U</mi><mo stretchy="false">(</mo><mn>1</mn><msub><mo stretchy="false">)</mo><mrow><mi>e</mi><mi>m</mi></mrow></msub></math> invariant effective Lagrangians such as the low-energy effective field theory (LEFT), used for low-energy flavor physics observables, or the Higgs effective field theory (HEFT) in unitary gauge, appropriate for weak-scale observables. In this work, we derive and list all such predictions for semileptonic operators up to dimension 6. These predictions can be expressed as linear relations among the HEFT/LEFT Wilson coefficients (WCs), that are completely independent of any assumptions about the alignment of the mass and flavor bases. We find seven sets of relations among the WCs of vector operators, nine sets with scalar and tensor operators, and two sets with the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>Z</mi><mo>,</mo><msup><mi>W</mi><mo>±</mo></msup></math> couplings. These correspond to 2223 linear relations among the complex WCs when the quark and lepton generation indices are included. They connect diverse experimental searches such as rare meson decays, high-<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>p</mi><mi>T</mi></msub></math> dilepton searches, top decays, <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>Z</mi></math>-pole observables, charged lepton flavor violating observables, and nonstandard neutrino interaction searches. We demonstrate how these relations can be used to derive strong indirect constraints on multiple WCs that are currently either weakly constrained from direct experiments or have no direct bound at all. They also imply, in general, that evidence for new physics in a particular search channel must be accompanied by correlated anomalies in other channels. For example, the observed excess in <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>B</mi><mo stretchy="false">→</mo><mi>K</mi><mi>ν</mi><mover accent="true"><mi>ν</mi><mo stretchy="false">¯</mo></mover></math> would imply possible anomalies in <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>B</mi><mo stretchy="false">→</mo><msup><mi>D</mi><mrow><mo stretchy="false">(</mo><mo>*</mo><mo stretchy="false">)</mo></mrow></msup><mo>ℓ</mo><msub><mi>ν</mi><mo>ℓ</mo></msub></math>, <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>B</mi><mo stretchy="false">→</mo><msup><mi>K</mi><mrow><mo stretchy="false">(</mo><mo>*</mo><mo stretchy="false">)</mo></mrow></msup><msup><mo>ℓ</mo><mo>+</mo></msup><msup><mo>ℓ</mo><mo>−</mo></msup></math>, <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>B</mi><mi>q</mi></msub><mo stretchy="false">→</mo><mi>τ</mi><msub><mi>ν</mi><mi>τ</mi></msub></math>, <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>B</mi><mi>s</mi></msub><mo stretchy="false">→</mo><msup><mi>τ</mi><mo>+</mo></msup><msup><mi>τ</mi><mo>−</mo></msup></math>, <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>D</mi><mi>s</mi></msub><mo stretchy="false">→</mo><msup><mi>τ</mi><mo>+</mo></msup><msub><mi>ν</mi><mi>τ</mi></msub></math>, <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>t</mi><mo stretchy="false">→</mo><mi>c</mi><msup><mo>ℓ</mo><mo>+</mo></msup><msup><mo>ℓ</mo><mo>−</mo></msup></math>, <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>t</mi><mo stretchy="false">→</mo><mi>u</mi><msup><mo>ℓ</mo><mo>+</mo></msup><msup><mo>ℓ</mo><mo>−</mo></msup></math>, etc., correlated according to the relations obtained in this paper.</p>

India

Siddhartha Karmakar

Amol Dighe

Rick S. Gupta

SMEFT predictions for semileptonic processes

The <math><mi>S</mi><mi>U</mi><mo>(</mo><mn>2</mn><msub><mo>)</mo><mi>L</mi></msub><mo>×</mo><mi>U</mi><mo>(</mo><mn>1</mn><msub><mo>)</mo><mi>Y</mi></msub></math> invariance of the Standard Model effective field theory (SMEFT) imposes relations among different low-energy effective field theory Wilson coefficients (WCs), any deviations from which would signal the presence of physics beyond SMEFT. In this work, we investigate two such relations (<math><msub><mi>C</mi><mi>S</mi></msub><mo>=</mo><mo>−</mo><msub><mi>C</mi><mi>P</mi></msub></math>, <math><msubsup><mi>C</mi><mi>S</mi><mo>′</mo></msubsup><mo>=</mo><msubsup><mi>C</mi><mi>P</mi><mo>′</mo></msubsup></math>) among the scalar and the pseudoscalar new physics WCs that can contribute to <math><mi>b</mi><mo>→</mo><mi>s</mi><mi>τ</mi><mi>τ</mi></math> processes. We show that, even when new physics violating these relations would not be measurable in the branching ratios of <math><msub><mi>B</mi><mi>s</mi></msub><mo>→</mo><msup><mi>τ</mi><mo>+</mo></msup><msup><mi>τ</mi><mo>−</mo></msup></math> and <math><mi>B</mi><mo>→</mo><msup><mi>K</mi><mrow><mo>(</mo><mo>*</mo><mo>)</mo></mrow></msup><msup><mi>τ</mi><mo>+</mo></msup><msup><mi>τ</mi><mo>−</mo></msup></math> at HL-LHC and FCC-ee, it can still manifest itself in the angular distribution of <math><mi>B</mi><mo>→</mo><msup><mi>K</mi><mrow><mo>*</mo><mn>0</mn></mrow></msup><msup><mi>τ</mi><mo>+</mo></msup><msup><mi>τ</mi><mo>−</mo></msup></math>. We identify the combinations of angular observables in this decay channel that are sensitive to scenarios beyond SMEFT. We find that the two observables <math><msubsup><mi>S</mi><mn>6</mn><mi>c</mi></msubsup></math> and <math><msub><mi>A</mi><mn>7</mn></msub></math>, and their combination, have the potential to identify physics beyond SMEFT.

Exploring observable effects of scalar operators beyond SMEFT in the angular distribution of <math><mi>B</mi><mo>→</mo><msup><mi>K</mi><mrow><mo>*</mo><mn>0</mn></mrow></msup><msup><mi>τ</mi><mo>+</mo></msup><msup><mi>τ</mi><mo>−</mo></msup></math>

In the Standard Model effective field theory (SMEFT), the <math><mi>S</mi><mi>U</mi><mo>(</mo><mn>2</mn><msub><mo>)</mo><mi>L</mi></msub><mo>×</mo><mi>U</mi><mo>(</mo><mn>1</mn><msub><mo>)</mo><mi>Y</mi></msub></math> symmetry of the Standard Model is linearly realized. However, it is possible that more general effective field theories, such as the Higgs effective field theory (HEFT) where this symmetry is realized nonlinearly, are needed to describe the data. Identifying physics beyond SMEFT could shed light on the nature of Higgs and the realization of the electroweak symmetry. We explore the possibility of such an identification by studying the effects of scalar and vector new physics operators on the angular distribution of <math><msub><mi>Λ</mi><mi>b</mi></msub><mo>→</mo><msub><mi>Λ</mi><mi>c</mi></msub><mo>(</mo><mo>→</mo><mi>Λ</mi><mi>π</mi><mo>)</mo><mi>τ</mi><msub><mover><mi>ν</mi><mo>¯</mo></mover><mi>τ</mi></msub></math>. This decay is sensitive to the six-dimensional effective operator <math><msubsup><mi>O</mi><mi>V</mi><mrow><mi>L</mi><mi>R</mi></mrow></msubsup><mo>≡</mo><mo>(</mo><mover><mi>τ</mi><mo>¯</mo></mover><msup><mi>γ</mi><mi>μ</mi></msup><msub><mi>P</mi><mi>L</mi></msub><msub><mi>ν</mi><mi>τ</mi></msub><mo>)</mo><mo>(</mo><mover><mi>c</mi><mo>¯</mo></mover><msub><mi>γ</mi><mi>μ</mi></msub><msub><mi>P</mi><mi>R</mi></msub><mi>b</mi><mo>)</mo></math>, which is present in HEFT but suppressed in SMEFT. We identify the angular observables that can have significant contributions from <math><msubsup><mi>O</mi><mi>V</mi><mrow><mi>L</mi><mi>R</mi></mrow></msubsup></math> and hence would be useful for probing not only beyond the Standard Model physics but also physics beyond SMEFT. We further find that constraining the branching ratio of <math><msub><mi>B</mi><mi>c</mi></msub><mo>→</mo><mi>τ</mi><msub><mover><mi>ν</mi><mo>¯</mo></mover><mi>τ</mi></msub></math> would be crucial for performing this task.

Susobhan Chattopadhyay

Identifying physics beyond SMEFT in the angular distribution of <math><msub><mi>Λ</mi><mi>b</mi></msub><mo>→</mo><msub><mi>Λ</mi><mi>c</mi></msub><mo>(</mo><mo>→</mo><mi>Λ</mi><mi>π</mi><mo>)</mo><mi>τ</mi><msub><mover><mi>ν</mi><mo>¯</mo></mover><mi>τ</mi></msub></math> decay

The quantum nature of neutrino oscillations would be reflected in the mismatch between the neutrino survival probabilities with and without an intermediate observation. We propose this quantum mismatch as a measure of quantumness in neutrino oscillations. For two neutrino flavors, it inevitably performs better than the Leggett-Garg measure. For three flavors, we devise modified definitions of these two measures, which would be applicable for experiments that measure neutrino survival probabilities with negligible matter effects. The modified definitions can be used to probe deviations from expected classical behavior, even for systems with an unknown number of states. For neutrino experiments like DUNE, MINOS, and JUNO, we identify the energies where these modified measures can probe quantumness efficiently.

Dibya S. Chattopadhyay

Quantum mismatch: A powerful measure of quantumness in neutrino oscillations

The measurements of the Cabibbo-Kobayashi-Maskawa (CKM) elements can be contaminated by new-physics effects. We point out that purely leptonic operators at the high scale can influence semileptonic <math><mi>K</mi></math> decays and nuclear beta decay through renormalization group (RG) running, and hence can influence the measurements of <math><msub><mi>V</mi><mrow><mi>u</mi><mi>s</mi></mrow></msub></math>. Interestingly, through this mechanism, a single six-dimensional effective operator <math><msub><mi>O</mi><mrow><mo>ℓ</mo><mo>ℓ</mo></mrow></msub></math> at the high scale can alleviate the tension due to the Cabibbo angle anomaly, by generating the desired operators at the low scale through RG running. When generated as a result of a <math><msup><mi>Z</mi><mo>′</mo></msup></math> model, the nonuniversal leptonic couplings of this operator can also contribute to the lepton flavor universality violating ratios such as <math><msub><mi>R</mi><msup><mi>K</mi><mrow><mo>(</mo><mo>*</mo><mo>)</mo></mrow></msup></msub></math>, which would act as stringent constraints on such scenarios. By performing a global fit of the <math><msup><mi>Z</mi><mo>′</mo></msup></math> model, we find that it is essential to have nonuniversal couplings of such a <math><msup><mi>Z</mi><mo>′</mo></msup></math> boson to all three generations of leptons.

Ashutosh Kumar Alok

France

Shireen Gangal

Germany

Jacky Kumar

Leptonic operators for the Cabbibo angle anomaly with SMEFT RG evolution

The interior of Earth’s core can be explored using weak interactions of atmospheric neutrinos. This would complement gravitational and seismic measurements, paving the way for multimessenger tomography of Earth. Oscillations of atmospheric neutrinos passing through Earth are affected by the ambient electron density. We demonstrate that atmospheric neutrinos can probe the possible existence of dark matter inside Earth’s core in a unique way—by measuring the amount of baryonic matter using neutrino oscillations. We find that a detector like ICAL at INO with muon charge identification capability can be sensitive to dark matter with <math><mrow><mo>∼</mo><mn>5</mn><mo>%</mo><mi>–</mi><mn>6</mn><mo>%</mo></mrow></math> mass of Earth, at <math><mrow><mn>1</mn><mi>σ</mi></mrow></math> level with 500 kt yr exposure. We show that, while it will not be possible to identify the dark matter profile using neutrino oscillation experiments, the baryonic matter profile inside the core can be probed with atmospheric neutrinos.

Anuj Kumar Upadhyay

Anil Kumar

United States

Sanjib Kumar Agarwalla

Probing dark matter inside Earth using atmospheric neutrino oscillations at INO-ICAL

Precision measurements of neutrino oscillation parameters have provided a tremendous boost to the search for sub-leading effects due to several beyond the Standard Model scenarios in neutrino oscillation experiments. Among these, two of the well-studied scenarios are Lorentz violation (LV) and non-standard interactions (NSI), both of which can affect neutrino oscillations significantly. We point out that, at a long-baseline experiment where the neutrino oscillation probabilities can be well-approximated by using the line-averaged constant matter density, the effects of these two scenarios can mimic each other. This would allow the limits obtained at such an experiment on one of the above scenarios to be directly translated to the limits on the other scenario. However, for the same reason, it would be difficult to distinguish between LV and NSI at a long-baseline experiment. We show that the observations of atmospheric neutrinos, which travel a wide range of baselines and may encounter sharp density changes at the core-mantle boundary, can break this degeneracy. We observe that identifying neutrinos and antineutrinos separately, as can be done at INO-ICAL, can enhance the capability of atmospheric neutrino experiments to discriminate between these two new-physics scenarios.

Sadashiv Sahoo

Discriminating between Lorentz violation and non-standard interactions using core-passing atmospheric neutrinos at INO-ICAL

Atmospheric neutrinos provide a unique avenue to explore the internal structure of Earth based on weak interactions, which is complementary to seismic studies and gravitational measurements. In this work, we demonstrate that the atmospheric neutrino oscillations in the presence of Earth matter can serve as an important tool to locate the core-mantle boundary (CMB). An atmospheric neutrino detector like the proposed 50 kt magnetized ICAL at INO can observe the core-passing neutrinos efficiently. These neutrinos would have experienced the MSW resonance and the parametric or neutrino oscillation length resonance. The net effect of these resonances on neutrino flavor conversions depends upon the location of CMB and the density jump at that radius. We quantify the capability of ICAL to measure the location of CMB in the context of multiple three-layered models of Earth. For the model where the density and the radius of core are kept flexible while the mass and radius of Earth as well as the densities of outer and inner mantle are fixed, ICAL can determine the location of CMB with a 1σ precision of about 250 km with an exposure of 1000 kt yr. With the 81-layered PREM profile, this 1σ precision would be about 350 km. The charge identification capability of ICAL plays an important role in achieving this precision.

Anuj Upadhyay

Sanjib Agarwalla

Locating the core-mantle boundary using oscillations of atmospheric neutrinos

We analytically calculate the neutrino conversion probability P  μe  in the presence of sterile neutrinos, with exact dependence on   <math> <mtext>∆</mtext> <msubsup> <mi>m</mi> <mn>41</mn> <mn>2</mn> </msubsup> </math>  $$ \Delta {m}_{41}^2 $$  and with matter effects explicitly included. Using perturbative expansion in small parameters, the terms involving the small mixing angles θ 24 and θ 34 can be separated out, with θ 34 dependence only arising due to matter effects. We express P  μe  in terms of the quantities of the form sin(x)/x, which helps in elucidating its dependence on matter effects and a wide range of   <math> <mtext>∆</mtext> <msubsup> <mi>m</mi> <mn>41</mn> <mn>2</mn> </msubsup> </math>  $$ \Delta {m}_{41}^2 $$  values. Our analytic expressions allow us to predict the effects of the sign of   <math> <mtext>∆</mtext> <msubsup> <mi>m</mi> <mn>41</mn> <mn>2</mn> </msubsup> </math>  $$ \Delta {m}_{41}^2 $$  at a long baseline experiment like DUNE. We numerically calculate the sensitivity of DUNE to the sterile mass ordering and find that this sensitivity can be significant in the range   <math> <mo>∣</mo> <mi>Δ</mi> <msubsup> <mi>m</mi> <mn>41</mn> <mn>2</mn> </msubsup> <mo>∣</mo> <mo>∼</mo> <mfenced> <mrow> <msup> <mn>10</mn> <mrow> <mo>−</mo> <mn>4</mn> </mrow> </msup> <mo>−</mo> <msup> <mn>10</mn> <mrow> <mo>−</mo> <mn>2</mn> </mrow> </msup> </mrow> </mfenced> </math>  $$ \mid \Delta {m}_{41}^2\mid \sim \left({10}^{-4}-{10}^{-2}\right) $$  eV2, for either mass ordering of active neutrinos. The dependence of this sensitivity on the value of   <math> <mtext>∆</mtext> <msubsup> <mi>m</mi> <mn>41</mn> <mn>2</mn> </msubsup> </math>  $$ \Delta {m}_{41}^2 $$  for all mass ordering combinations can be explained by investigating the resonance-like terms appearing due to the interplay between the sterile sector and matter effects.

Dibya Chattopadhyay

Moon Devi

Debajyoti Dutta

Brazil

Dipyaman Pramanik

Sushant Raut

Sterile neutrinos: propagation in matter and sensitivity to sterile mass ordering

We present compact analytic expressions for 3-flavor neutrino oscillation probabilities with invisible neutrino decay, where matter effects have been explicitly included. We take into account the possibility that the oscillation and decay components of the effective Hamiltonian do not commute. This is achieved by employing the techniques of inverse Baker-Campbell-Hausdorff (BCH) expansion and the Cayley-Hamilton theorem applied in the 3-flavor framework. If only the vacuum mass eigenstate ν 3 decays, we show that the treatment of neutrino propagation may be reduced to an effective 2-flavor analysis in the One Mass Scale Dominance (OMSD) approximation. The oscillation probabilities for P  μμ , P  ee , P  eμ  and P  μe  — relevant for reactor, long baseline and atmospheric neutrino experiments — are obtained as perturbative expansions for the case of only ν 3 decay, as well as for the more general scenario where all components of the decay matrix are non-zero. The analytic results thus obtained match the exact numerical results for constant density matter to a high precision and provide physical insights into possible effects of the decay of neutrinos as they propagate through Earth matter. We find that the effects of neutrino decay are most likely to be observable in P  μμ . We also point out that at any long baseline, the oscillation dips in P  μμ  can show higher survival probabilities in the case with decay than without decay, and explain this feature using our analytic approximations.