Soft Form Factors Research Articles

Possible solution of the puzzle for the branching ratio and CP violation in B→ππ decays with a modified perturbative QCD approach

We study $B\ensuremath{\rightarrow}\ensuremath{\pi}\ensuremath{\pi}$ decay with a modified perturbative QCD approach. The branching ratios and $CP$ violation are calculated with the transverse momenta of partons considered. Sudakov factor associated with each meson is included to suppress soft contribution in QCD. With the wave function of $B$ meson obtained in QCD-inspired relativistic potential model being used, the suppression of Sudakov factor to the soft contribution is not effective enough. Soft scale cutoff and soft form factors of $B\ensuremath{\pi}$ transition and $\ensuremath{\pi}\ensuremath{\pi}$ production have to be introduced. The main next-to-leading-order contributions of vertex correction, the quark-loop, and magnetic penguin are included. To solve the long-standing puzzle in $B\ensuremath{\rightarrow}\ensuremath{\pi}\ensuremath{\pi}$ decay, that is the theoretical prediction of the branching ratio of ${B}^{0}\ensuremath{\rightarrow}{\ensuremath{\pi}}^{0}{\ensuremath{\pi}}^{0}$ being seriously smaller than experimental data, color-octet matrix element which is of long-distance dynamics is introduced. With parameters taken with reasonable values, all the branching ratios and $CP$ violation are well consistent with experimental data.

Symmetry breaking radiative corrections to B to tensor meson form factors at large recoil

In heavy-to-light B decays, the heavy-quark/large-energy symmetry reduces the number of QCD form factors. At large final state meson energy, these form factors receive sizeable perturbative corrections. The hard-gluon vertex corrections are absorbed in the coefficients of soft-form factors, while the hard-spectator interactions generate symmetry-breaking corrections and end-point singularities. At an order of 1/m b, using the heavy-quark/large-energy symmetry, the end-point singularities can also be absorbed in the soft form factors, whereas the symmetry breaking corrections add separately to the form factors. In this work, we calculate these perturbative corrections for B → Tμ + μ − decays, with T representing the tensor mesons all having J P = 2+. We find that the values of the branching ratio (Br) and the zero-position of the forward–backward asymmetry of decay receive nearly 5% and 14% contributions, respectively, from these radiative corrections. Compared to these observables, the radiative corrections change the averaged longitudinal lepton polarization asymmetry (⟨P L⟩) by 13%. Therefore, prior to attributing any deviation from the SM predictions of these asymmetries as a hint of NP, one has to take into account the contributions of vertex and hard-spectator corrections.

An intrinsically stretchable aqueous Zn-MnO2 battery based on microcracked electrodes for self-powering wearable electronics

Stretchable batteries are indispensable energy storage devices to power emerging wearable electronics in soft form factors. In contrast to commonly employed engineering approaches to mitigate strains through structural design, the intrinsically stretchable devices naturally exhibit skin-like mechanical deformability by using all compliant building components. Currently, the intrinsically stretchable battery often shows a significant trade-off between electrochemical performances and mechanical deformability. Here, we introduce a low-cost and scalable approach to create an intrinsically stretchable aqueous battery featuring the deployment of state-of-art battery materials and binders. The compliant current collector, in the form of a bilayer silver nanowire/carbon nanotube nanocomposites, demonstrates excellent mechanical stretchability and electrochemical stability. The microcracked electrode layer retains stable charge transport and excellent electrochemical activity under large mechanical deformations through firm attachment to the bilayer current collector. A stretchable Zn-MnO2 cell in a sandwiched configuration is assembled exhibiting high specific capacity (>200 mAh g−1 at 100 mA g−1), excellent capacity retention of ∼90% over 100 cycles, large stretchability up to 100% strain, and durability against repetitive mechanical deformations. The practical suitability is demonstrated by a stand-alone electronic system conformably mounted on the wrist, in which an LED array is powered by a pair of stretchable Zn-MnO2 batteries.

Renormalization-group evolution of the none-local matrix element of B-meson in QCD and B → π transition form factor

We consider the renormalization-group evolution of the matrix element of 〈0|q¯(z)β[z,0]b(0)α|B¯〉, which can be used to define the distribution amplitudes for B meson and widely applied in studies of B meson decays. The contribution to the renormalization constant of the non-local operator q¯(z)β[z,0]b(0)α is considered up to one-loop order in QCD. Since the quark fields in this operator are not directly coupled fields, momentum can not flow freely through this non-local operator. Momentum involved in this operator can be treated stringently in coordinate space. We find that the ultraviolet divergences regulated by dimensional parameter ϵ cancel with each other, and the evolution effect vanishes. The matrix element 〈0|q¯(z)β[z,0]b(0)α|B¯〉 escapes from the renormalization-group evolution. We then apply the matrix element in calculating B→π transition form factor, where the matrix element is obtained by using the B meson wave function calculated in QCD-inspired potential model. By comparing with experimental data for the semileptonic decay of B→πℓν and light-cone sum rule calculation, we analyze the perturbative and non-perturbative contributions to B→π transition form factor in the frame work of perturbative QCD approach. We find that the effectiveness of the suppression of Sudakov factor to soft contribution depends on the end-point behavior of B meson wave function, and with the B-meson wave function used in this work, soft contribution can not be well suppressed. The hard contribution to the B→π transition form factor is about 59%, and soft contribution can be as large as 41% in the naive calculation. To make the perturbative calculation reliable, a soft momentum cutoff in the calculation and soft form factor have to be introduced.

Hand Gesture Recognition Using Single Patchable Six-Axis Inertial Measurement Unit via Recurrent Neural Networks.

Recording human gestures from a wearable sensor produces valuable information to implement control gestures or in healthcare services. The wearable sensor is required to be small and easily worn. Advances in miniaturized sensor and materials research produces patchable inertial measurement units (IMUs). In this paper, a hand gesture recognition system using a single patchable six-axis IMU attached at the wrist via recurrent neural networks (RNN) is presented. The IMU comprises IC-based electronic components on a stretchable, adhesive substrate with serpentine-structured interconnections. The proposed patchable IMU with soft form-factors can be worn in close contact with the human body, comfortably adapting to skin deformations. Thus, signal distortion (i.e., motion artifacts) produced for vibration during the motion is minimized. Also, our patchable IMU has a wireless communication (i.e., Bluetooth) module to continuously send the sensed signals to any processing device. Our hand gesture recognition system was evaluated, attaching the proposed patchable six-axis IMU on the right wrist of five people to recognize three hand gestures using two models based on recurrent neural nets. The RNN-based models are trained and validated using a public database. The preliminary results show that our proposed patchable IMU have potential to continuously monitor people’s motions in remote settings for applications in mobile health, human–computer interaction, and control gestures recognition.

QCD uncertainties in the prediction of B → K⁎μ+μ− observables

The recent LHCb angular analysis of the exclusive decay B→K⁎μ+μ− has indicated significant deviations from the Standard Model expectations. In order to give precise theory predictions, it is crucial that uncertainties from non-perturbative QCD are under control and properly included. The dominant QCD uncertainties originate from the hadronic B→K⁎ form factors and from cc‾ loops. We present a systematic method to include factorisable power corrections to the form factors in the framework of QCD factorisation and study the impact of the scheme chosen to define the soft form factors. We also discuss charm-loop effects.

On the impact of power corrections in the prediction of B → K *μ+μ− observables

The recent LHCb angular analysis of the exclusive decay B->K^*mu+mu- has indicated significant deviations from the Standard Model expectations. Accurate predictions can be achieved at large K*-meson recoil for an optimised set of observables designed to have no sensitivity to hadronic input in the heavy-quark limit at leading order in alpha_s. However, hadronic uncertainties reappear through non-perturbative Lambda_QCD/m_b power corrections, which must be assessed precisely. In the framework of QCD factorisation we present a systematic method to include factorisable power corrections and point out that their impact on angular observables depends on the scheme chosen to define the soft form factors. Associated uncertainties are found to be under control, contrary to earlier claims in the literature. We also discuss the impact of possible non-factorisable power corrections, including an estimate of charm-loop effects. We provide results for angular observables at large recoil for two different sets of inputs for the form factors, spelling out the different sources of theoretical uncertainties. Finally, we comment on a recent proposal to explain the anomaly in B->K*mu+mu- observables through charm-resonance effects, and we propose strategies to test this proposal identifying observables and kinematic regions where either the charm-loop model can be disentangled from New Physics effects or the two options leave different imprints.

Implications from clean observables for the binned analysis of B → K ∗ μ + μ − at large recoil

AbstractWe perform a frequentist analysis ofq2-dependentB→K∗(→Kπ)ℓ+ℓ−angular observables at large recoil, aiming at bridging the gap between current theoretical analyses and the actual experimental measurements. We focus on the most appropriate set of observables to measure and on the role of theq2-binning. We highlight the importance of the observablesPiexhibiting a limited sensitivity to soft form factors for the search for New Physics contributions. We compute predictions for these binned observables in the Standard Model, and we compare them with their experimental determination extracted from recent LHCb data. Analysingb→sandb→sℓ+ℓ−transitions within four different New Physics scenarios, we identify several New Physics benchmark points which can be discriminated through the measurement ofPiobservables with a fineq2-binning. We emphasise the importance (and risks) of using observables with (un)suppressed dependence on soft form factors for the search of New Physics, which we illustrate by the different size of hadronic uncertainties attached to two related observables (P1andS3). We illustrate how theq2-dependent angular observables measured in several bins can help to unravel New Physics contributions toB→K∗(→Kπ)ℓ+ℓ−, and show the extraordinary constraining power that the clean observables will have in the near future. We provide semi-numerical expressions for these observables as functions of the relevant Wilson coefficients at the low scale.

Form factors forΛb→Λtransitions in the soft-collinear effective theory

We present a systematic discussion of Lambda_b -> Lambda transition form factors in the framework of soft-collinear effective theory (SCET). The universal soft form factor, which enters the symmetry relations in the limit of large recoil energy, is calculated from a sum-rule analysis of a suitable SCET correlation function. The same method is applied to derive the leading corrections from hard-collinear gluon exchange at first order in the strong coupling constant. We present numerical estimates for form factors and form-factor ratios and their impact on decay observables in Lambda_b -> Lambda mu^+ mu^- decays.

Heavy-to-light baryonic form factors at large recoil

We analyze heavy-to-light baryonic form factors at large recoil and derive the scaling behavior of these form factors in the heavy quark limit. It is shown that only one universal form factor is needed to parameterize Lambda_b to p and Lambda_b to Lambda matrix elements in the large recoil limit of light baryons, while hadronic matrix elements of Lambda_b to Sigma transition vanish in the large energy limit of Sigma baryon due to the space-time parity symmetry. The scaling law of the soft form factor eta(P^{\prime} \cdot v), P^{\prime} and v being the momentum of nucleon and the velocity of Lambda_b baryon, responsible for Lambda_b to p transitions is also derived using the nucleon distribution amplitudes in leading conformal spin. In particular, we verify that this scaling behavior is in full agreement with that from light-cone sum rule approach in the heavy-quark limit. With these form factors, we further investigate the Lambda baryon polarization asymmetry alpha in Lambda_b to Lambda gamma and the forward-backward asymmetry A_{FB} in Lambda_b to Lambda l^{+} l^{-}. Both two observables (alpha and A_{FB}) are independent of hadronic form factors in leading power of 1/m_b and in leading order of alpha_s. We also extend the analysis of hadronic matrix elements for Omega_b to Omega transitions to rare Omega_b to Omega gamma and Omega_b to Omega l^{+} l^{-} decays and find that radiative Omega_b to Omega gamma decay is probably the most promising FCNC b to s radiative baryonic decay channel. In addition, it is interesting to notice that the zero-point of forward-backward asymmetry of Omega_b to Omega l^{+} l^{-} is the same as the one for Lambda_b to Lambda l^{+} l^{-} to leading order accuracy provided that the form factors \bar{\zeta}_i (i=3, 4, 5) are numerically as small as indicated from the quark model.

On the new physics reach of the decay mode $ {\bar{B}_d} \to {\bar{K}^{*0}}{\ell^{+} }{\ell^{-} } $

We present a complete method to construct QCD-protected observables based on the exclusive 4-body $B$-meson decay $\bar{B} \to \bar{K}^{*0}\ell^+\ell^-$ in the low dilepton mass region. The core of the method is the requirement that the constructed quantities should fulfil the symmetries of the angular distribution. We have identified all symmetries of the angular distribution in the limit of massless leptons and explore: a new non-trivial relation between the coefficients of the angular distribution, the possibility to fully solve the system for the $K^{*}$ amplitudes, and the construction of non-trivial observables. We also present a phenomenological analysis of the new physics sensitivity of angular observables in the decay based on QCD factorisation. We further analyse the CP-conserving observables, $A_{T}^{(2)}$, $A_{T}^{(3)}$ and $A_{T}^{(4)}$. They are practically free of theoretical uncertainties due to the soft form factors for the full range of dilepton masses rather than just at a single point as for $A_{FB}$. They also have a higher sensitivity to specific new physics scenarios compared to observables such as $A_{FB}$. Moreover, we critically examine the new physics reach of CP-violating observables via a complete error analysis due to scale dependences, form factors and $\Lambda/m_b$ corrections. We have developed an ensemble method to evaluate the error on observables from $\Lambda/m_b$ corrections. Finally, we explore the experimental prospects of CP-violating observables and find that they are rather limited. Indeed, the CP-conserving (averaged) observables $A_{T}^{(i)}$ (with $i=2,3,4$) will offer a better sensitivity to large CP phases and may be more suitable for experimental analysis.

Covariant and self-consistent vertex corrections for pions and isobars in nuclear matter

We evaluate the pion and isobar propagators in cold nuclear matter self-consistently applying a covariant form of the isobar-hole model. Migdal's vertex correction effects are considered systematically in the absence of phenomenological soft form factors. Saturated nuclear matter is modeled by scalar and vector mean fields for the nucleon. It is shown that the short-range dressing of the {pi}N{delta} vertex has a significant effect on the pion and isobar properties. Using realistic parameters sets we predict a downward shift of about 50 MeV for the {delta} resonance at nuclear saturation density. The pionic soft modes are much less pronounced than in previous studies.

B→K*ℓ+ℓ- decay in soft-collinear effective theory

We study the rare B decay $B \to K^* \ell^+ \ell^-$ using soft-collinear effective theory (SCET). At leading power in $1/m_b$, a factorization formula is obtained valid to all orders in $\alpha_s$. For phenomenological application, we calculate the decay amplitude including order $\alpha_s$ corrections, and resum the logarithms by evolving the matching coefficients from the hard scale ${\cal O}(m_b)$ down to the scale $\sqrt{m_b \Lambda_h}$. The branching ratio for $B \to K^* \ell^+ \ell^-$ is uncertain due to the imprecise knowledge of the soft form factors $\zeta_\perp (q^2)$ and $\zeta_\parallel (q^2)$. Constraining the soft form factor $\zeta_\perp (q^2=0)$ from data on $B \to K^* \gamma$ yields $\zeta_\perp (q^2=0)=0.32 \pm 0.02$. Using this input, together with the light-cone sum rules to determine the $q^2$dependence of $\zeta_\perp (q^2)$ and the other soft form factor $\zeta_\parallel (q^2)$, we eastimate the partially integrated branching ratio in the range $1~{GeV}^2 \le q^2 \le 7~{GeV}^2$ to be $(2.92^{+0.67}_{-0.61}) \times 10^{-7}$. We discuss how to reduce the form factor related uncertainty by combining data on $B \to \rho (\to \pi \pi) \ell \nu_\ell$ and $B\to K^* (\to K\pi) \ell^+\ell^-$. The forward-backward asymmetry is less sensitive to the input parameters. In particular, for the zero-point of the forward backward asymmetry in the standard model, we get $q_0^2=(4.07^{+0.13}_{-0.12})~{GeV}^2$. The scale dependence of $q_0^2$ is discussed in detail.

SCET sum rules for heavy-to-light form factors

We consider a sum rule for heavy-to-light form factors in soft-collinear effective theory (SCET). Using the correlation function given by the time-ordered product of a heavy-to-light current and its hermitian conjugate, the heavy-to-light soft form factor ζP can be related to the leading-order B meson shape function. Using the scaling behavior of the heavy-to-light form factor in ΛQCD/mb, we put a constraint on the behavior of the B meson shape function near the endpoint. We employ the sum rule to estimate the size of ζP with the model for the shape function and find that it ranges from 0.01 to 0.07.

Self consistent and covariant propagation of pions, nucleon and isobar resonances in cold nuclear matter

We evaluate the in-medium spectral functions for pions, nucleon and isobar resonances in a self consistent and covariant manner. The calculations are based on a recently developed formulation which leads to predictions in terms of the pion–nucleon scattering phase shifts and a set of Migdal parameters describing important short range correlation effects. We do not observe significant softening of pion modes if we insist on reasonable isobar resonance properties but predict a considerable broadening of the N ( 1440 ) and N ( 1520 ) resonances in nuclear matter. Contrasted results are obtained for the s-wave N ( 1535 ) and N ( 1650 ) resonances which are affected by a nuclear environment very little. The properties of slowly moving isobar's in nuclear matter are found to depend very sensitively on a soft form factor in the π N N vertex, which is not controlled by the πN scattering data.

Composite vertices that lead to soft form factors.

The momentum-space cut-off parameter $\Lambda$ of hadronic vertex functions is studied in this paper. We use a composite model where we can measure the contributions of intermediate particle propagations to $\Lambda$. We show that in many cases a composite vertex function has a much smaller cut-off than its constituent vertices, particularly when light constituents such as pions are present in the intermediate state. This suggests that composite meson-baryon-baryon vertex functions are rather soft, i.e., they have \Lambda considerably less than 1 GeV. We discuss the origin of this softening of form factors as well as the implications of our findings on the modeling of nuclear reactions.

Nucleon-nucleon interaction with consistently soft form factors for one and two pion exchange.

It has recently proven possible to construct an acceptable one-boson-exchange potential in which the [ital NN][pi] form factor is quite soft. In order to do so it was necessary to add an effective [pi][prime] meson which increased the short-range tensor force. It is much less obvious that one can use such soft form factors if the two-pion-exchange diagrams are calculated explicitly rather than being parametrized as scalar meson exchange. Here we show that it is indeed possible to construct a model which describes nucleon-nucleon data with comparable quality as the original full Bonn potential, but in which the two pion exchange is included explicitly with consistently soft [ital NN][pi] and [Delta][ital N][pi] vertices.

Separable Representation of N Scattering Amplitudes

Separable representations of the S and P wave amplitudes are presented for the pion incident energy-range in the laboratory system: TL=0-400 MeV. We make separable potentials in rank one or two form and in one or multi-channel form, depending on the eigenstates. The relationship between the form factor of Pn potential and the 11NN vertex form factor in the one-pion-exchange potential is seriously taken into account. The potentials are made by fitting the two empirical partial wave amplitudes by Koch and Pietarinen and by Arndt, Ford and Roper. in a separable form with respect to the initial and final relative momenta. This makes the three-body calculation considerably tractable and transparent. Therefore the separable form of the potentials are very significant for the study of· the TCNN system. So far the separable TCN potentials have been presented in fitting the TCN phase shifts by various groups. 4 >.s> Among all, the Pu potential is relatively complicated. This eigenstate has the nucleon pole as well as the Roper resonance and requires the separable representation in a rank two form at least. Furthermore the form factor of the separable potential should relate with the TCNN vertex form factor appearing in the one-pion-exchange potential for nuclear forces. So far, however, this interrela­ tion is not so seriously taken into account. In this paper we put the strong condition that the form factor for the nucleon pole part of the Pu potential is the same with the TCNN vertex form factor for the one-pion-exchange potential. This should provide more realistic condition for the off-shell structure of the potential than the so far presented versions. The form factor of the TCNN vertex has been studied by various groups, since Ueda and Green introduced it into the one-boson-exchange potential in 1967. 6 > They used the size parameter A in the dipole parametrization as large as A=2-3 GeV. Although Bonn group made the search of a smaller value to be consistent with the values from subhadronic models: A~0.7-0.8 GeV, they find A~1.3 GeV. 7 > More recently Ueda has proposed that the one-pion-exchange with the TCNN form factor with A=2-3 GeV is interpreted as the sum of the one-pion-exchange with a soft form factor of A~0.9 GeV and the 1=1, r=o- part of the correlated three-pion­ exchange.2>.s>-lo) The latter is effectively represented by an isovector and pseudo­

Role of vector mesons in high-Q2 lepton-nucleon scattering.

The possible role played by vector mesons in inclusive deep inelastic lepton-nucleon scattering is investigated. In the context of the convolution model, we calculate self-consistently the scaling contribution to the nucleon structure function using the formalism of time-ordered perturbation theory in the infinite momentum frame. Our results indicate potentially significant effects only when the vector meson---nucleon form factor is very hard. Agreement with the experimental antiquark distributions, however, requires relatively soft form factors for the $\pi N$, $\rho N$ and $\omega N$ vertices.

Nucleon-nucleon pion-exchange tested in three-body reactions.

Variants of a one-boson-exchange potential are applied to elastic nucleon-deuteron and electron-deuteron scattering. The models differ with respect to the treatment of the pion-nucleon vertex, where either a small coupling constant or a soft form factor is employed. We find that these variations do not affect [ital Nd] observables, but that they have a sizable effect on [ital ed] quantities via exchange currents of the pion. Taking into account also exchange currents of the [pi][prime] reduces the effect to a large extent.