Short-distance Amplitude Research Articles

Production of X(3872) accompanied by a pion in B meson decay

If the $X(3872)$ is a weakly bound charm-meson molecule, it can be produced by the creation of $D^{*0} \bar{D}^0$ or $D^{0} \bar{D}^{*0}$ at short distances followed by the formation of the bound state from the charm-meson pairs. It can also be produced by the creation of $D^{*} \bar{D}^*$ at short distances followed by the rescattering of the charm mesons into $X \pi$. We use results of a previous isospin analysis of $B$ meson decays into $K D^{(*)} \bar D^{(*)}$ to estimate the short-distance amplitudes for creating $D^* \bar D^*$. We use an effective field theory for charm mesons and pions called XEFT to calculate the amplitudes for rescattering of $D^{*} \bar{D}^*$ into $X \pi$ with small relative momentum. The $X\pi$ invariant mass distribution is predicted to have a narrow peak near the $D^{*} \bar{D}^*$ threshold from a charm-meson triangle singularity. We estimate the branching fractions into the peak from the triangle singularity for the decays $B^0 \to K^+ X \pi^-$ and $B^+ \to K^0 X \pi^+$.

Impact on the decay rate of Bs→μ+μ− from the dispersive two-photon transition

We study the long-distance contribution to ${B}_{s}\ensuremath{\rightarrow}{\ensuremath{\mu}}^{+}{\ensuremath{\mu}}^{\ensuremath{-}}$ decay, which is generated by the two-photon intermediate state via the ${B}_{s}\ensuremath{\rightarrow}{\ensuremath{\gamma}}^{*}{\ensuremath{\gamma}}^{*}\ensuremath{\rightarrow}{\ensuremath{\mu}}^{+}{\ensuremath{\mu}}^{\ensuremath{-}}$ transition. It is found that the dispersive two-photon amplitude can interfere with the dominant short-distance amplitude, which gives rise to new theoretical uncertainty in the branching ratio of ${B}_{s}\ensuremath{\rightarrow}{\ensuremath{\mu}}^{+}{\ensuremath{\mu}}^{\ensuremath{-}}$. Our analysis shows that, by taking into account present experimental constraints, this uncertainty could be up to the same order of magnitude as some theoretical uncertainties of $\mathcal{B}({B}_{s}\ensuremath{\rightarrow}{\ensuremath{\mu}}^{+}{\ensuremath{\mu}}^{\ensuremath{-}})$ given in the past literature. Future precise studies of the double radiative ${B}_{s}\ensuremath{\rightarrow}\ensuremath{\gamma}\ensuremath{\gamma}$ decay, both experimentally and theoretically, may help to reduce the uncertainty. This novel effect has never been examined in ${B}_{s}\ensuremath{\rightarrow}{\ensuremath{\mu}}^{+}{\ensuremath{\mu}}^{\ensuremath{-}}$ decay.

An empirical model to determine the hadronic resonance contributions to overline{B}{} ^0 !rightarrow overline{K}{} ^{*0} mu ^+ mu ^- transitions

A method for analysing the hadronic resonance contributions in overline{B}{} ^0 !rightarrow overline{K}{} ^{*0} mu ^+ mu ^- decays is presented. This method uses an empirical model that relies on measurements of the branching fractions and polarisation amplitudes of final states involving J^{PC}=1^{--} resonances, relative to the short-distance component, across the full dimuon mass spectrum of overline{B}{} ^0 !rightarrow overline{K}{} ^{*0} mu ^+ mu ^- transitions. The model is in good agreement with existing calculations of hadronic non-local effects. The effect of this contribution to the angular observables is presented and it is demonstrated how the narrow resonances in the q^2 spectrum provide a dramatic enhancement to C!P-violating effects in the short-distance amplitude. Finally, a study of the hadronic resonance effects on lepton universality ratios, R_{K^{(*)}}, in the presence of new physics is presented.

CP Violation and Strong Pion-Pion Interactions in the Weak $${B^\pm \to \pi^\pm \pi^\mp \pi^\pm}$$ Decays

An analysis of $${B^\pm \to \pi^\pm \pi^\mp \pi^\pm}$$ decay data in a quasi two-body B ± → π ± [π + π −] S, P, D QCD factorization framework is performed. The short distance amplitudes are calculated including next-to-leading order in α s vertex and penguin corrections. The long distance amplitudes due to the [π + π −] S, P, D final state interactions are described by the pion non-strange scalar and vector form factors for the [π + π −] S S-wave state and [π + π −] P P-wave state, respectively and by a relativistic Breit–Wigner formula for the[π + π −] D D-wave state. We achieve a good fit of the data with only three parameters for the S wave, one for the P wave and one for the D wave. Our model gives a unified unitary description of the three scalar resonances, f 0(600), f 0(980) and f 0(1400) in terms of the pion scalar form factor. We predict for the B to f 2(1270) transition form factor, $${F^{Bf_2}(m_\pi^2)=0.098\pm0.007}$$ .

Exclusive production of theX(3872)inBmeson decay

If the recently discovered charmoniumlike state $X(3872)$ is a loosely bound $S$-wave molecule of the charm mesons ${D}^{0}{\overline{D}}^{*0}$ or ${D}^{*0}{\overline{D}}^{0}$, it can be produced through the weak decay of the $B$ meson into ${D}^{0}{\overline{D}}^{*0}K$ or ${D}^{*0}{\overline{D}}^{0}K$ followed by the coalescence of the charm mesons at a long-distance scale set by the scattering length of the charm mesons. The long-distance factors in the amplitude for the decay $B\ensuremath{\rightarrow}XK$ are determined by the binding energy of $X$, while the short-distance factors are essentially determined by the amplitudes for $B\ensuremath{\rightarrow}{D}^{0}{\overline{D}}^{*0}K$ and $B\ensuremath{\rightarrow}{D}^{*0}{\overline{D}}^{0}K$ near the thresholds for the charm mesons. We obtain a crude determination of the short-distance amplitudes by analyzing data from the BABAR Collaboration on the branching fractions for $B\ensuremath{\rightarrow}{\overline{D}}^{(*)}{D}^{(*)}K$ using a factorization assumption, heavy-quark symmetry, and isospin symmetry. The resulting order-of-magnitude estimate of the branching fraction for ${B}^{+}\ensuremath{\rightarrow}X{K}^{+}$ is compatible with observations provided that $J/\ensuremath{\psi}{\ensuremath{\pi}}^{+}{\ensuremath{\pi}}^{\ensuremath{-}}$ is a major decay mode of the $X$. The branching fraction for ${B}^{0}\ensuremath{\rightarrow}X{K}^{0}$ is predicted to be suppressed by more than an order of magnitude compared to that for ${B}^{+}\ensuremath{\rightarrow}X{K}^{+}$.

Inelastic Final State Interactions in [formula omitted] Decays

A method parametrizing all inelastic final state interactions (FSI) in $B\to PP$ decays is presented ($P$ - pseudoscalar meson). The method explicitly shows how rescattering leads to the replacement of the short-distance amplitudes with the effective quark diagram amplitudes, and how it affects the extraction of the unitarity triangle angle $\gamma $ from the data. It is furthermore pointed out that the size of FSI effects cannot be determined from $B^0_d \to K^+ K^-$ decays in a satisfactory way. The case of SU(3)-violating FSI is also discussed. When fits to the branching ratios of all $B \to PP$ decays are performed with all inelastic FSI included, the extracted value of $ \gamma $ is shifted down by some $20^o-30^o$ when compared to the no-FSI analyses, and becomes consistent with the Standard Model value of $ 65^o \pm 7^o$.

Exclusive rareB→K*ℓ+ℓ−decays at low recoil: Controlling the long-distance effects

We present a model-independent description of the exclusive rare decays $\overline{B}\ensuremath{\rightarrow}{K}^{*}{e}^{+}{e}^{\ensuremath{-}}$ in the low recoil region (large lepton invariant mass ${q}^{2}\ensuremath{\sim}{m}_{b}^{2}$). In this region the long-distance effects from quark loops can be computed with the help of an operator product expansion in $1/Q$, with $Q={{m}_{b},\sqrt{{q}^{2}}}$. Nonperturbative effects up to and including terms suppressed by $\ensuremath{\Lambda}/Q$ and ${m}_{c}^{2}/{m}_{b}^{2}$ relative to the short-distance amplitude can be included in a model-independent way. Based on these results, we propose an improved method for determining the Cabibbo-Kobayashi-Maskawa matrix element $|{V}_{ub}|$ from a combination of rare and semileptonic $B$ and $D$ decays near the zero recoil point. The residual theoretical uncertainty from long-distance effects in this $|{V}_{ub}|$ determination comes from terms in the operator product expansion of order ${\ensuremath{\alpha}}_{s}(Q)\ensuremath{\Lambda}/{m}_{b}$, ${\ensuremath{\alpha}}_{s}^{2}(Q)$, ${m}_{c}^{4}/{m}_{b}^{4}$, and duality violations, and is estimated to be below 10%.

Stokes vector of photon in the decays B0→ρ0γ and [formula omitted

We consider a model for the decay B0→ρ0γ in which the short-distance amplitude determined by the Hamiltonian describing b→dγ is combined with a typical long-distance contribution B0→D+D−→ρ0γ. The latter possesses a significant dynamical phase which induces a CP-violating asymmetry ACP, as well as an important modification of the Stokes vector of the photon. The components S1 and S3 of the Stokes vector S→=(S1,S2,S3) can be measured in the decay B0→ρ0γ∗→π+π−e+e− where they produce a characteristic effect in the angular distribution dΓ/dφ, φ being the angle between the π+π− and e+e− planes. A similar analysis is carried out for the decays B0→K∗γ and B0→K∗γ∗→π+K−e+e−.

Zweig-rule-satisfying inelastic rescattering inBdecays to pseudoscalar mesons

We discuss all contributions from Zweig-rule-satisfying SU(3)-symmetric inelastic FSI-induced corrections in B decays to $\pi \pi$, $\pi K$, $K\bar{K}$, $\pi \eta (\eta ')$, and $K \eta (\eta ')$ . It is shown how all of these FSI corrections lead to a simple redefinition of the amplitudes, permitting the use of a simple diagram-based description, in which, however, weak phases may enter in a modified way. The inclusion of FSI corrections admitted by the present data allows an arbitrary relative phase between the penguin and tree short-distance amplitudes. The FSI-induced error of the method, in which the value of the weak phase $\gamma $ is to be determined by combining future results from $B^+,B^0_d,B^0_s$ decays to $K\pi$, is estimated to be of the order of $5^o$ for $\gamma \approx 50^o-60^o$.

On the dispersive two-photon $K_L\rightarrow \mu^+ \mu^-$ amplitude

We present a full account of the two-loop electroweak, two-photon mediated short-distance dispersive $K_L \to\mu^+\mu^-$ decay amplitude. QCD corrections change the sign of this amplitude and reduce it by an order of magnitude. Thus, the QCD-corrected two-loop amplitude represents only a small fraction (with the central value of 5 %) of the one-loop weak short-distance contribution, and has the same sign. In combination with a recent measurement, the standard-model prediction of the short-distance amplitude, completed in this paper, provides a constraint on the otherwise uncertain long-distance dispersive amplitude.

Critical behavior near a symmetry-breaking surface and the stress tensor.

The critical behavior near a surface that breaks the order parameter symmetry is analyzed with field-theoretic renormalization-group methods. We study the short-distance expansions of the order parameter and the energy density about the surface and investigate various density profiles and correlation functions in the half-space and film geometries. Our results confirm Cardy's conjecture that the stress-energy tensor appears as the leading surface density. Its universal prefactor $C$ in the expansions determines several physical properties of interest in the critical adsorption of fluids: In a film at the bulk critical temperature ${T}_{c}$, $C$ determines the amplitude ratio of the Fisher-de Gennes distant-wall correction to the order-parameter profile and the Casimir correction to the free energy. In the half-space close to ${T}_{c}$, $C$ determines the amplitude ratio of the ${(\frac{z}{\ensuremath{\xi}})}^{d}$ term in the order parameter profile to the Ferer-Stauffer-Wortis term in the bulk free energy. Here $z$ is the distance from the surface and $\ensuremath{\xi}$ the bulk correlation length. In the half-space at ${T}_{c}$, $C$ also determines the universal short-distance amplitudes of layer susceptibilities, which should be observable in computer experiments. We calculate $C$ to second order in $\ensuremath{\epsilon}=4\ensuremath{-}d$ and estimate its value for $d=3$. $C$ is closely related to the stress-stress correlation in a half-space, for which we obtain the bulk to surface crossover. We present a simple argument showing why this crossover depends, in general, on the surface universality class except in two dimensions.