We suggest a new method to analyse the rare $\textit{D}$ → $\textit{Pℓ}$ $\textit{ℓ}$ decays ($\textit{P}$ = $\textit{π}$, $\textit{K}$), combining QCD light-cone sum rules (LCSR) with hadronic dispersion relations. As our main study case, we consider the $\textit{D}$ → $\textit{π}$ $\textit{ℓ}$ $\textit{ℓ}$ mode which attracts much of interest from the point of view of GIM cancellation and potential new sources of the FCNC $\textit{c}$ → $\textit{u}$ transitions. The hadronic amplitude of this decay is dominated by the combination of weak annihilation with the emission of a virtual photon. This $\textit{D}$ → $\textit{π}$ $\textit{γ}$ amplitude is calculated at spacelike photon virtualities, −$\textit{q}$ ≫ $$ {\Lambda}_{\textrm{QCD}}^2 $$ , using LCSR with pion distribution amplitudes. The LCSR results are then fitted to the hadronic dispersion relation in the variable $\textit{q}$ . The fit allows us to determine relative phases of the $\textit{ρ}$-, $\textit{ω}$- and $\textit{ϕ}$-meson terms and to estimate the contributions of heavier hadronic states. The latter are parameterized in two different ways: first, with a $\textit{z}$-expansion and second, using a model with excited vector-meson resonances. The resulting $\textit{D}$ → $\textit{π}$ $\textit{ℓ}$ $\textit{ℓ}$ width obtained from the LCSR-assisted dispersion relation is not much smaller than the current upper bound measured by LHCb collaboration. In comparison with our result for the dominant $\textit{D}$ → $\textit{π}$ $\textit{γ}$ transition, the contribution induced by the short distance $\textit{c}$ → $\textit{uℓ}$ $\textit{ℓ}$ quark transition generated by the effective $\textit{O}$ operator in Standard Model turns out to be practically invisible. To detect its effect, one readily needs an enhancement of the coefficient $\textit{C}$ from non-standard effects by many orders of magnitude. We also establish new $\textit{U}$-spin symmetry relations between the amplitudes of $\textit{D}$ → $\textit{Pℓ}$ $\textit{ℓ}$ decays and apply our method to the Cabibbo-favoured modes $$ {D}_s^{+}\to {\pi}^{+}{\ell}^{+}{\ell}^{-} $$ and $$ {D}^0\to {\overline{K}}^0{\ell}^{+}{\ell}^{-} $$ which proceed via the same weak annihilation mechanism.

Germany

Anshika Bansal

Alexander Khodjamirian

Thomas Mannel

$\textit{D}$ → $\textit{Pℓ}$

The recently developed <italic>B</italic>-Mesogenesis scenario predicts decays of <italic>B</italic> mesons into a baryon and hypothetical dark antibaryon &#936;. We suggest a method to calculate the amplitude of the simplest exclusive decay mode <math altimg='si1.svg'><msup><mrow><mi>B</mi></mrow><mrow><mo linebreak='badbreak' linebreakstyle='after'>+</mo></mrow></msup><mo stretchy='false'>&#8594;</mo><mi>p</mi><mi mathvariant='normal'>&#936;</mi></math>. Considering two models of <italic>B</italic>-Mesogenesis, we obtain the <math altimg='si2.svg'><mi>B</mi><mo stretchy='false'>&#8594;</mo><mi>p</mi></math> hadronic matrix elements by applying QCD light-cone sum rules with the proton light-cone distribution amplitudes. We estimate the <math altimg='si1.svg'><msup><mrow><mi>B</mi></mrow><mrow><mo linebreak='badbreak' linebreakstyle='after'>+</mo></mrow></msup><mo stretchy='false'>&#8594;</mo><mi>p</mi><mi mathvariant='normal'>&#936;</mi></math> decay width as a function of the mass and effective coupling of the dark antibaryon.

Marcel Wald

<bold><italic>B</italic></bold>-meson decay into a proton and dark antibaryon from QCD light-cone sum rules

We present the first application of QCD light-cone sum rules (LCSRs) with B (s)-meson distribution amplitudes to the   <math> <msub> <mi>B</mi> <mfenced> <mi>s</mi> </mfenced> </msub> <mo>→</mo> <msubsup> <mi>D</mi> <mrow> <mfenced> <mi>s</mi> </mfenced> <mn>0</mn> </mrow> <mo>∗</mo> </msubsup> </math>  $$ {B}_{(s)}\to {D}_{(s)0}^{\ast } $$  form factors, where   <math> <msubsup> <mi>D</mi> <mrow> <mfenced> <mi>s</mi> </mfenced> <mn>0</mn> </mrow> <mo>∗</mo> </msubsup> </math>  $$ {D}_{(s)0}^{\ast } $$  is a charmed scalar meson. We consider two scenarios for the   <math> <msubsup> <mi>D</mi> <mn>0</mn> <mo>∗</mo> </msubsup> </math>  $$ {D}_0^{\ast } $$  spectrum. In the first one, we follow the Particle Data Group and consider a single broad resonance   <math> <msubsup> <mi>D</mi> <mn>0</mn> <mo>∗</mo> </msubsup> <mfenced> <mn>2300</mn> </mfenced> </math>  $$ {D}_0^{\ast }(2300) $$ . In the second one, we assume the existence of two scalar resonances,   <math> <msubsup> <mi>D</mi> <mn>0</mn> <mo>∗</mo> </msubsup> <mfenced> <mn>2105</mn> </mfenced> </math>  $$ {D}_0^{\ast }(2105) $$  and   <math> <msubsup> <mi>D</mi> <mn>0</mn> <mo>∗</mo> </msubsup> <mfenced> <mn>2451</mn> </mfenced> </math>  $$ {D}_0^{\ast }(2451) $$ , as follows from a recent theoretically motivated analysis of B → Dππ decays. The   <math> <mi>B</mi> <mo>→</mo> <msubsup> <mi>D</mi> <mn>0</mn> <mo>∗</mo> </msubsup> </math>  $$ B\to {D}_0^{\ast } $$  form factors are calculated in both scenarios, also taking into account the large total width of   <math> <msubsup> <mi>D</mi> <mn>0</mn> <mo>∗</mo> </msubsup> <mfenced> <mn>2300</mn> </mfenced> </math>  $$ {D}_0^{\ast }(2300) $$ . Furthermore, we calculate the   <math> <msub> <mi>B</mi> <mi>s</mi> </msub> <mo>→</mo> <msubsup> <mi>D</mi> <mrow> <mi>s</mi> <mn>0</mn> </mrow> <mo>∗</mo> </msubsup> </math>  $$ {B}_s\to {D}_{s0}^{\ast } $$  form factors, considering in this case only the one-resonance scenario with D  s0(2317). In this LCSRs calculation, the c-quark mass is kept finite and the s-quark mass is taken into account. We also include contributions of the two- and three-particle distribution amplitudes up to twist-four. Our predictions for semileptonic   <math> <mi>B</mi> <mo>→</mo> <msubsup> <mi>D</mi> <mn>0</mn> <mo>∗</mo> </msubsup> <mi>ℓ</mi> <msub> <mi>ν</mi> <mi>ℓ</mi> </msub> </math>  $$ B\to {D}_0^{\ast}\ell {\nu}_{\ell } $$  and   <math> <msub> <mi>B</mi> <mi>s</mi> </msub> <mo>→</mo> <msubsup> <mi>D</mi> <mrow> <mi>s</mi> <mn>0</mn> </mrow> <mo>∗</mo> </msubsup> <mi>ℓ</mi> <msub> <mi>ν</mi> <mi>ℓ</mi> </msub> </math>  $$ {B}_s\to {D}_{s0}^{\ast}\ell {\nu}_{\ell } $$  branching ratios are compared with the available data and HQET-based predictions. As a byproduct, we also obtain the   <math> <msubsup> <mi>D</mi> <mn>0</mn> <mo>∗</mo> </msubsup> </math>  $$ {D}_0^{\ast } $$ - and   <math> <msubsup> <mi>D</mi> <mrow> <mi>s</mi> <mn>0</mn> </mrow> <mo>∗</mo> </msubsup> </math>  $$ {D}_{s0}^{\ast } $$ -meson decay constants and predict the lepton flavour universality ratios   <math> <mi>R</mi> <mfenced> <msubsup> <mi>D</mi> <mn>0</mn> <mo>∗</mo> </msubsup> </mfenced> </math>  $$ R\left({D}_0^{\ast}\right) $$  and   <math> <mi>R</mi> <mfenced> <msubsup> <mi>D</mi> <mrow> <mi>s</mi> <mn>0</mn> </mrow> <mo>∗</mo> </msubsup> </mfenced> </math>  $$ R\left({D}_{s0}^{\ast}\right) $$ .

Nico Gubernari

India

Rusa Mandal

<math> <mi>B</mi> <mo>→</mo> <msubsup> <mi>D</mi> <mn>0</mn> <mo>∗</mo> </msubsup> </math>  $$ B\to {D}_0^{\ast } $$  and   <math> <msub> <mi>B</mi> <mi>s</mi> </msub> <mo>→</mo> <msubsup> <mi>D</mi> <mrow> <mi>s</mi> <mn>0</mn> </mrow> <mo>∗</mo> </msubsup> </math>  $$ {B}_s\to {D}_{s0}^{\ast } $$  form factors from QCD light-cone sum rules

We derive a set of light-cone sum rules relating the S-wave B → Kπ hadronic form factors to the B-meson light-cone distribution amplitudes (LCDAs), taking into account the complete set of LCDAs up to and including twist four. These results complement the sum rules for the P-wave B → Kπ form factors obtained earlier. We then use the new sum rules to estimate the S-wave contributions to B → Kπℓℓ decays as a function of the Kπ invariant mass. We pay particular attention to the fact that the S-wave Kπ spectrum cannot be modelled by a sum of Breit-Wigner resonances, and employ a more consistent dispersive coupled-channel approach. We compare our predictions for branching ratios and angular observables with LHCb measurements in two different kinematic regions, around K ∗(892) and   <math> <msubsup> <mi>K</mi> <mn>0</mn> <mo>∗</mo> </msubsup> <mfenced> <mn>1430</mn> </mfenced> </math>  $$ {K}_0^{\ast }(1430) $$ . We observe an overall compatibility and discuss possible improvements of our model to obtain a better description of the B → Kπ form factors over a large kinematic range.

France

Sébastien Descotes-Genon

Spain

Javier Virto

Netherlands

K. Vos

Light-cone sum rules for S-wave B → Kπ form factors

Defect characterizes the depth of factorization of terms in differential (cyclotomic) expansions of knot polynomials, i.e. of the non-perturbative Wilson averages in the Chern-Simons theory. We prove the conjecture that the defect can be alternatively described as the degree in  $$q^{\pm 2}$$  <math> <msup> <mi>q</mi> <mrow> <mo>±</mo> <mn>2</mn> </mrow> </msup> </math>   of the fundamental Alexander polynomial, which formally corresponds to the case of no colors. We also pose a question if these Alexander polynomials can be arbitrary integer polynomials of a given degree. A first attempt to answer the latter question is a preliminary analysis of antiparallel descendants of the 2-strand torus knots, which provide a nice set of examples for all values of the defect. The answer turns out to be positive in the case of defect zero knots, what can be observed already in the case of twist knots. This proved conjecture also allows us to provide a complete set of C-polynomials for the symmetrically colored Alexander polynomials for defect zero. In this case, we achieve a complete separation of representation and knot variables.

Russia

E. Lanina

A. Morozov

Defect and degree of the Alexander polynomial

We perform the first calculation of form factors in the semileptonic decays B → D 1(2420)ℓν  ℓ  and B →   <math> <msubsup> <mi>D</mi> <mn>1</mn> <mo>′</mo> </msubsup> </math>  $$ {D}_1^{\prime } $$ (2430)ℓν  ℓ  using QCD light-cone sum rules (LCSRs) with B-meson distribution amplitudes. In this calculation the c-quark mass is finite. Analytical expressions for two-particle contributions up to twist four are obtained. To disentangle the D 1 and   <math> <msubsup> <mi>D</mi> <mn>1</mn> <mo>′</mo> </msubsup> </math>  $$ {D}_1^{\prime } $$  contributions in the LCSRs, we suggest a novel approach that introduces a combination of two interpolating currents for these charmed mesons. To fix all the parameters in the LCSRs, we use the two-point QCD sum rules for the decay constants of D 1 and   <math> <msubsup> <mi>D</mi> <mn>1</mn> <mo>′</mo> </msubsup> </math>  $$ {D}_1^{\prime } $$  mesons augmented by a single experimental input, that is the B → D 1(2420)ℓν  ℓ  decay width. We provide numerical results for all B → D 1 and B →   <math> <msubsup> <mi>D</mi> <mn>1</mn> <mo>′</mo> </msubsup> </math>  $$ {D}_1^{\prime } $$  form factors. As a byproduct, we also obtain the D 1- and   <math> <msubsup> <mi>D</mi> <mn>1</mn> <mo>′</mo> </msubsup> </math>  $$ {D}_1^{\prime } $$ -meson decay constants and predict the lepton-flavour universality ratios R(D 1) and R(  <math> <msubsup> <mi>D</mi> <mn>1</mn> <mo>′</mo> </msubsup> </math>  $$ {D}_1^{\prime } $$ ).

B → D1(2420) and B →   <math> <msubsup> <mi>D</mi> <mn>1</mn> <mo>′</mo> </msubsup> </math>  $$ {\mathrm{D}}_1^{\prime } $$ (2430) form factors from QCD light-cone sum rules

In this paper we study the group theoretic structures of colored HOMFLY polynomials in a specific limit. The group structures arise in the perturbative expansion of <math><mi>S</mi><mi>U</mi><mo>(</mo><mi>N</mi><mo>)</mo></math> Chern-Simons Wilson loops, while the limit is <math><mi>N</mi><mo>→</mo><mn>0</mn></math>. The result of the paper is twofold. First, we explain the emergence of Kadomsev-Petviashvily (KP) τ-functions. This result is an extension of what we did in [1], where a symbolic correspondence between KP equations and group factors was established. In this paper we prove that integrability of the colored Alexander polynomial is due to it's relation to soliton τ-functions. Mainly, the colored Alexander polynomial is embedded in the action of the KP generating function on the soliton τ-function. Secondly, we use this correspondence to provide a rather simple combinatoric description of the group factors in term of Young diagrams, which is otherwise described in terms of chord diagrams, where no simple description is known. This is a first step providing an explicit description of the group theoretic data of Wilson loops, which would effectively reduce them to a purely topological quantity, mainly to a collection of Vassiliev invariants.

V. Mishnyakov

A. Sleptsov

Perturbative analysis of the colored Alexander polynomial and KP soliton -functions

We revisit the calculation of the strong couplings D ∗ Dπ and B ∗ Bπ from the QCD light-cone sum rules using the pion light-cone distribution amplitudes. The accuracy of the correlation function, calculated from the operator product expansion near the light-cone, is upgraded by taking into account the gluon radiative corrections to the twist-3 terms. The double spectral density of the correlation function, including the twist-2, 3 terms at   <math> <mi>O</mi> <mfenced> <msub> <mi>α</mi> <mi>s</mi> </msub> </mfenced> </math>  $$ \mathcal{O}\left({\alpha}_s\right) $$  and the twist-4 LO terms, is presented in an analytical form for the first time. This form allows us to use various versions of the quark-hadron duality regions in the double dispersion relation underlying the sum rules. We predict   <math> <msub> <mi>g</mi> <mrow> <msup> <mi>D</mi> <mo>∗</mo> </msup> <mi>Dπ</mi> </mrow> </msub> <mo>=</mo> <msubsup> <mn>14.1</mn> <mrow> <mo>−</mo> <mn>1.2</mn> </mrow> <mrow> <mo>+</mo> <mn>1.3</mn> </mrow> </msubsup> </math>  $$ {g}_{D^{\ast } D\pi}={14.1}_{-1.2}^{+1.3} $$  and   <math> <msub> <mi>g</mi> <mrow> <msup> <mi>B</mi> <mo>∗</mo> </msup> <mi>Bπ</mi> </mrow> </msub> <mo>=</mo> <msubsup> <mn>30.0</mn> <mrow> <mo>−</mo> <mn>2.4</mn> </mrow> <mrow> <mo>+</mo> <mn>2.6</mn> </mrow> </msubsup> </math>  $$ {g}_{B^{\ast } B\pi}={30.0}_{-2.4}^{+2.6} $$  when the decay constants of heavy mesons entering the light-cone sum rule are taken from lattice QCD results. We compare our results with the experimental value for the charmed meson coupling and with the lattice QCD calculations.

Croatia

Blaženka Melić

China

Yu-Ming Wang

Yan-Bing Wei

The D ∗ Dπ and B ∗ Bπ couplings from light-cone sum rules

We suggest to probe the pion light-cone distribution amplitude, applying a dispersion relation for the pion electromagnetic form factor. Instead of the standard dispersion relation, we use the equation between the spacelike form factor <math><msub><mi>F</mi><mi>π</mi></msub><mo>(</mo><msup><mi>Q</mi><mn>2</mn></msup><mo>)</mo></math> and the integrated modulus of the timelike form factor. For <math><msub><mi>F</mi><mi>π</mi></msub><mo>(</mo><msup><mi>Q</mi><mn>2</mn></msup><mo>)</mo></math>, the QCD light-cone sum rule with a dominant twist-2 term is used. Adopting for the pion twist-2 distribution amplitude a certain combination of the first few Gegenbauer polynomials, it is possible to fit their coefficients <math><msub><mi>a</mi><mrow><mn>2</mn><mo>,</mo><mn>4</mn><mo>,</mo><mn>6</mn><mo>,</mo><mo>.</mo><mo>.</mo></mrow></msub></math>. (Gegenbauer moments) from this equation, employing the measured pion timelike form factor. For the exploratory fit we use the data of the BABAR collaboration. The results definitely exclude the asymptotic twist-2 distribution amplitude. Also the model with a single <math><msub><mi>a</mi><mn>2</mn></msub><mo>≠</mo><mn>0</mn></math> is disfavored by the fit. Considering the models with <math><msub><mi>a</mi><mrow><mi>n</mi><mo>&gt;</mo><mn>2</mn></mrow></msub><mo>≠</mo><mn>0</mn></math>, we find that the fitted values of the second and fourth Gegenbauer moments cover the intervals <math><mrow><msub><mrow><mi>a</mi></mrow><mrow><mn>2</mn></mrow></msub><mo>(</mo><mn>1</mn><mtext> </mtext><mtext> </mtext><mi>GeV</mi><mo>)</mo><mo>=</mo><mo>(</mo><mn>0.22</mn><mi>–</mi><mn>0.33</mn><mo>)</mo></mrow></math>, <math><mrow><msub><mrow><mi>a</mi></mrow><mrow><mn>4</mn></mrow></msub><mo>(</mo><mn>1</mn><mtext> </mtext><mtext> </mtext><mi>GeV</mi><mo>)</mo><mo>=</mo><mo>(</mo><mn>0.12</mn><mi>–</mi><mn>0.25</mn><mo>)</mo></mrow></math>. The higher moments starting from <math><msub><mi>a</mi><mn>8</mn></msub></math> are consistent with zero, albeit with large uncertainties. The spacelike pion form factor obtained in two different ways, from the dispersion relation and from the light-cone sum rule, agrees, within uncertainties, with the measurement by the Jefferson Lab <math><msub><mi>F</mi><mi>π</mi></msub></math> collaboration.

Shan Cheng

United Kingdom

Aleksey V. Rusov

Pion light-cone distribution amplitude from the pion electromagnetic form factor

We derive a QCD sum rule for the inverse moment of the B  s -meson light-cone distribution amplitude in HQET. Within this method, the SU(3) f l  symmetry violation is traced to the strange quark mass and to the difference between strange and nonstrange quark condensate densities. We predict the ratio of inverse moments λ  Bs  /λ  B  = 1.19 ± 0.14 which can be used in various applications of these distribution amplitudes to the analyses of B  s -meson decays, provided an accurate value of λ  B  is available from other sources, such as the B → ℓν  ℓ  γ decay.