<inline-formula> <mml:math display="block" id="mm799"> <mml:semantics> <mml:mrow> <mml:msup> <mml:mi>D</mml:mi> <mml:mo>*</mml:mo> </mml:msup> </mml:mrow> </mml:semantics> </mml:math> </inline-formula> Polarization as an Additional Constraint on New Physics in the <i>b</i> → <i>cτ</i><inline-formula> <mml:math display="block" id="mm610"> <mml:semantics> <mml:mrow> <mml:mover> <mml:mi>ν</mml:mi> <mml:mo stretchy="false">¯</mml:mo> </mml:mover> </mml:mrow> </mml:semantics> </mml:math> </inline-formula>_<i>τ</i> Transition

• Main Authors: Mikhail A. Ivanov, Jürgen G. Körner, Pietro Santorelli, Chien-Thang Tran
• Format: Article
• Language: English
• Published: MDPI AG 2020-03-01
• Series: Particles
• Subjects: semileptonic decay; <i>b</i> meson; lepton flavor universality; beyond standard model; form factors; covariant constituent quark model; branching fraction; polarization
• Online Access: https://www.mdpi.com/2571-712X/3/1/16

Measurements of the branching fractions of the semileptonic decays <inline-formula> <math display="inline"> <semantics> <mrow> <mi>B</mi> <mo>→</mo> <msup> <mi>D</mi> <mrow> <mo stretchy="false">(</mo> <mo>*</mo> <mo stretchy="false">)</mo> </mrow> </msup> <mi>τ</mi> <msub> <mover> <mi>ν</mi> <mo stretchy="false">¯</mo> </mover> <mi>τ</mi> </msub> </mrow> </semantics> </math> </inline-formula> and <inline-formula> <math display="inline"> <semantics> <mrow> <msub> <mi>B</mi> <mi>c</mi> </msub> <mo>→</mo> <mi>J</mi> <mo>/</mo> <mi>ψ</mi> <mi>τ</mi> <msub> <mover> <mi>ν</mi> <mo stretchy="false">¯</mo> </mover> <mi>τ</mi> </msub> </mrow> </semantics> </math> </inline-formula> systematically exceed the Standard Model predictions, pointing to possible signals of new physics that can violate lepton flavor universality. The unknown origin of new physics realized in these channels can be probed using a general effective Hamiltonian constructed from four-fermion operators and the corresponding Wilson coefficients. Previously, constraints on these Wilson coefficients were obtained mainly from the experimental data for the branching fractions. Meanwhile, polarization observables were only theoretically studied. The situation has changed with more experimental data having become available, particularly those regarding the polarization of the tau and the <inline-formula> <math display="inline"> <semantics> <msup> <mi>D</mi> <mo>*</mo> </msup> </semantics> </math> </inline-formula> meson. In this study, we discuss the implications of the new data on the overall picture. We then include them in an updated fit of the Wilson coefficients using all hadronic form factors from our covariant constituent quark model. The use of our form factors provides an analysis independent of those in the literature. Several new-physics scenarios are studied with the corresponding theoretical predictions provided, which are useful for future experimental studies. In particular, we find that under the one-dominant-operator assumption, no operator survives at <inline-formula> <math display="inline"> <semantics> <mrow> <mn>1</mn> <mi>σ</mi> </mrow> </semantics> </math> </inline-formula>. Moreover, the scalar operators <inline-formula> <math display="inline"> <semantics> <msub> <mi mathvariant="script">O</mi> <msub> <mi>S</mi> <mi>L</mi> </msub> </msub> </semantics> </math> </inline-formula> and <inline-formula> <math display="inline"> <semantics> <msub> <mi mathvariant="script">O</mi> <msub> <mi>S</mi> <mi>R</mi> </msub> </msub> </semantics> </math> </inline-formula> are ruled out at <inline-formula> <math display="inline"> <semantics> <mrow> <mn>2</mn> <mi>σ</mi> </mrow> </semantics> </math> </inline-formula> if one uses the constraint <inline-formula> <math display="inline"> <semantics> <mrow> <mi mathvariant="script">B</mi> <mo stretchy="false">(</mo> <msub> <mi>B</mi> <mi>c</mi> </msub> <mo>→</mo> <mi>τ</mi> <msub> <mi>ν</mi> <mi>τ</mi> </msub> <mo stretchy="false">)</mo> <mo>≤</mo> <mn>10</mn> <mo>%</mo> </mrow> </semantics> </math> </inline-formula>, while the more relaxed constraint <inline-formula> <math display="inline"> <semantics> <mrow> <mi mathvariant="script">B</mi> <mo stretchy="false">(</mo> <msub> <mi>B</mi> <mi>c</mi> </msub> <mo>→</mo> <mi>τ</mi> <msub> <mi>ν</mi> <mi>τ</mi> </msub> <mo stretchy="false">)</mo> <mo>≤</mo> <mn>30</mn> <mo>%</mo> </mrow> </semantics> </math> </inline-formula> still allows these operators at <inline-formula> <math display="inline"> <semantics> <mrow> <mn>2</mn> <mi>σ</mi> </mrow> </semantics> </math> </inline-formula>, but only minimally. The inclusion of the new data for the <inline-formula> <math display="inline"> <semantics> <msup> <mi>D</mi> <mo>*</mo> </msup> </semantics> </math> </inline-formula> polarization fraction <inline-formula> <math display="inline"> <semantics> <msubsup> <mi>F</mi> <mi>L</mi> <msup> <mi>D</mi> <mo>*</mo> </msup> </msubsup> </semantics> </math> </inline-formula> reduces the likelihood of the right-handed vector operator <inline-formula> <math display="inline"> <semantics> <msub> <mi mathvariant="script">O</mi> <msub> <mi>V</mi> <mi>R</mi> </msub> </msub> </semantics> </math> </inline-formula> and significantly constrains the tensor operator <inline-formula> <math display="inline"> <semantics> <msub> <mi mathvariant="script">O</mi> <msub> <mi>T</mi> <mi>L</mi> </msub> </msub> </semantics> </math> </inline-formula>. Specifically, the <inline-formula> <math display="inline"> <semantics> <msubsup> <mi>F</mi> <mi>L</mi> <msup> <mi>D</mi> <mo>*</mo> </msup> </msubsup> </semantics> </math> </inline-formula> alone rules out <inline-formula> <math display="inline"> <semantics> <msub> <mi mathvariant="script">O</mi> <msub> <mi>T</mi> <mi>L</mi> </msub> </msub> </semantics> </math> </inline-formula> at <inline-formula> <math display="inline"> <semantics> <mrow> <mn>1</mn> <mi>σ</mi> </mrow> </semantics> </math> </inline-formula>. Finally, we show that the longitudinal polarization <inline-formula> <math display="inline"> <semantics> <msubsup> <mi>P</mi> <mi>L</mi> <mi>τ</mi> </msubsup> </semantics> </math> </inline-formula> of the tau in the decays <inline-formula> <math display="inline"> <semantics> <mrow> <mi>B</mi> <mo>→</mo> <msup> <mi>D</mi> <mo>*</mo> </msup> <mi>τ</mi> <msub> <mover> <mi>ν</mi> <mo stretchy="false">¯</mo> </mover> <mi>τ</mi> </msub> </mrow> </semantics> </math> </inline-formula> and <inline-formula> <math display="inline"> <semantics> <mrow> <msub> <mi>B</mi> <mi>c</mi> </msub> <mo>→</mo> <mi>J</mi> <mo>/</mo> <mi>ψ</mi> <mi>τ</mi> <msub> <mover> <mi>ν</mi> <mo stretchy="false">¯</mo> </mover> <mi>τ</mi> </msub> </mrow> </semantics> </math> </inline-formula> is extremely sensitive to the tensor operator. Within the <inline-formula> <math display="inline"> <semantics> <mrow> <mn>2</mn> <mi>σ</mi> </mrow> </semantics> </math> </inline-formula> allowed region, the best-fit value <inline-formula> <math display="inline"> <semantics> <mrow> <msub> <mi>T</mi> <mi>L</mi> </msub> <mo>=</mo> <mn>0.04</mn> <mo>+</mo> <mi>i</mi> <mn>0.17</mn> </mrow> </semantics> </math> </inline-formula> predicts <inline-formula> <math display="inline"> <semantics> <mrow> <msubsup> <mi>P</mi> <mi>L</mi> <mi>τ</mi> </msubsup> <mrow> <mo stretchy="false">(</mo> <msup> <mi>D</mi> <mo>*</mo> </msup> <mo stretchy="false">)</mo> </mrow> <mo>=</mo> <mo>−</mo> <mn>0.33</mn> </mrow> </semantics> </math> </inline-formula> and <inline-formula> <math display="inline"> <semantics> <mrow> <msubsup> <mi>P</mi> <mi>L</mi> <mi>τ</mi> </msubsup> <mrow> <mo stretchy="false">(</mo> <mi>J</mi> <mo>/</mo> <mi>ψ</mi> <mo stretchy="false">)</mo> </mrow> <mo>=</mo> <mo>−</mo> <mn>0.34</mn> </mrow> </semantics> </math> </inline-formula>, which are at about 33% larger than the Standard Model (SM) prediction <inline-formula> <math display="inline"> <semantics> <mrow> <msubsup> <mi>P</mi> <mi>L</mi> <mi>τ</mi> </msubsup> <mrow> <mo stretchy="false">(</mo> <msup> <mi>D</mi> <mo>*</mo> </msup> <mo stretchy="false">)</mo> </mrow> <mo>=</mo> <mo>−</mo> <mn>0.50</mn> </mrow> </semantics> </math> </inline-formula> and <inline-formula> <math display="inline"> <semantics> <mrow> <msubsup> <mi>P</mi> <mi>L</mi> <mi>τ</mi> </msubsup> <mrow> <mo stretchy="false">(</mo> <mi>J</mi> <mo>/</mo> <mi>ψ</mi> <mo stretchy="false">)</mo> </mrow> <mo>=</mo> <mo>−</mo> <mn>0.51</mn> </mrow> </semantics> </math> </inline-formula>.