Search

We analyze the neutral meson mixing by directly solving the dispersion relation obeyed by the mass and width differences of the two meson mass eigenstates. We solve for the parameters $x$ and $y$, proportional to the mass and width differences in the charm mixing, respectively, taking the box-diagram contributions to $x(s)$ and $y(s)$ at large mass squared $s$ of a fictitious $D$ meson as inputs. The SU(3) symmetry breaking is introduced through physical thresholds of different $D$ meson decay channels for $y(s)$. These threshold-dependent effects, acting like nonperturbative power corrections in QCD sum rules, stabilize the solutions of $y(s=m_D^2)$ with the $D$ meson mass $m_D$. We then calculate $x(s)$ through the dispersive integration of $y(s)$, and show that our predictions $x(m_D^2)\approx 0.21\%$ and $y(m_D^2)\approx 0.52\%$ are close to the data in both $CP$-conserving and $CP$-violating cases. It is observed that the channel containing di-kaon states provides the major source of SU(3) breaking, which enhances $x(m_D^2)$ and $y(m_D^2)$ by four orders of magnitude relative to the perturbative results. We also predict the coefficient ratio $q/p$ involved in the charm mixing with $|q/p|-1\approx 2\times 10^{-4}$ and $Arg(q/p)\approx 6\times 10^{-3}$ degrees, which can be scrutinized by precise future measurements. The formalism is extended to studies of the $B_{s(d)}$ meson mixing and the kaon mixing, and the small deviations of the obtained width differences from the perturbative inputs explain why the above mixing can be understood via short-distance dynamics. We claim that the puzzling charm mixing is attributed to the strong Glashow-Iliopoulos-Maiani suppression on perturbative contributions, instead of to breakdown of the quark-hadron duality, which occurs only at 15\% level., Journal version, 16 pages, 10 figures

We demonstrate that fermion masses in the Standard Model (SM) can be constrained by the dispersion relations obeyed by hadronic and semileptonic decay widths of a fictitious heavy quark $Q$ with an arbitrary mass. These relations, imposing stringent connections between the high-mass and low-mass behaviors of decay widths, correlate a heavy quark mass and the chiral symmetry breaking scale. Given the known input from leading-order heavy quark expansion and a hadronic threshold for decay products, we solve for a physical heavy quark decay width. It is shown that the charm (bottom) quark mass $m_c= 1.35$ GeV ($m_b= 4.0$ GeV) can be determined by the dispersion relation for the $Q\to du\bar d$ ($Q\to c\bar ud$) decay with the threshold $2m_\pi$ ($m_\pi+m_D$), where $m_\pi$ ($m_D$) denotes the pion ($D$ meson) mass. Requiring that the dispersion relation for the $Q\to su\bar d$ ($Q\to d\mu^+\nu_\mu$, $Q\to u\tau^-\bar\nu_\tau$) decay with the threshold $m_\pi+m_K$ ($m_\pi+m_\mu$, $m_\pi+m_\tau$) yields the same heavy quark mass, $m_K$ being the kaon mass, we constrain the strange quark (muon, $\tau$ lepton) mass to be $m_s= 0.12$ GeV ($m_\mu=0.11$ GeV, $m_\tau= 2.0$ GeV). Moreover, all the predicted decay widths corresponding to the above masses agree with the data. It is pointed out that our formalism is similar to QCD sum rules for probing resonance properties, and that the Pauli interference (weak annihilation) provides the higher-power effect necessary for establishing the solutions of the hadronic (semilaptonic) decay widths. This work suggests that the parameters in the SM may not be free, but arranged properly to achieve internal dynamical consistency., Comment: 20 pages, 14 figures, journal version, estimates on theoretical uncertainties included

We derive the dependence of the leading-twist pion light-cone distribution amplitude (LCDA) on a parton momentum fraction $x$ by directly solving the dispersion relations for the moments with inputs from the operator product expansion (OPE) of the corresponding correlation function. It is noticed that these dispersion relations must be organized into those for the Gegenbauer coefficients first in order to avoid the ill-posed problem appearing in the conversion from the moments to the Gegenbauer coefficients. Given the values of various condensates in the OPE, we find that a solution for the pion LCDA, which is stable in the Gegenbauer expansion, exists. Moreover, the solution from summing contributions up to 18 Gegenbauer polynomials is smooth, and can be well approximated by a function proportional to $x^p(1-x)^p$ with $p\approx 0.45$ at the scale $\mu=2$ GeV. Turning off the condensates, we get the asymptotic form, independent of the scale $\mu$, for the pion LCDA as expected. We then solve for the pion LCDA at a different scale $\mu=1.5$ GeV with the condensate inputs at this $\mu$, and demonstrate that the result is consistent with the one obtained by evolving the Gegenbauer coefficients from $\mu=2$ GeV to 1.5 GeV. That is, our formalism is compatible with the QCD evolution. The strength of the above approach that goes beyond analyses limited to only the first few moments of a LCDA in conventional QCD sum rules is highlighted. The precision of our results can be improved systematically by including higher-order and higher-power terms in the OPE., Comment: 23 pages, 12 figures, journal version, more references included

We reanalyze the $$\Lambda _b\rightarrow p$$ Λ b → p transition form factors in the perturbative QCD (PQCD) approach by including higher-twist light-cone distribution amplitudes (LCDAs) of a $$\Lambda _b$$ Λ b baryon and a proton. The previous PQCD evaluation performed decades ago with only the leading-twist $$\Lambda _b$$ Λ b baryon and proton LCDAs gave the form factors, which are two orders of magnitude smaller than indicated by experimental data. We find that the twist-4 $$\Lambda _b$$ Λ b baryon LCDAs and the twist-4 and -5 proton LCDAs contribute dominantly, and the enhanced form factors become consistent with those from lattice QCD and other nonperturbative methods. The estimated branching ratios of the semileptonic decays $$\Lambda _b\rightarrow p\ell {\bar{\nu }}_\ell $$ Λ b → p ℓ ν ¯ ℓ and the hadronic decay $$\Lambda _b\rightarrow p\pi $$ Λ b → p π are also close to the data. It implies that the b quark mass is not really heavy enough, and higher-power contributions play a crucial role, similar to the observation made in analyses of B meson transition form factors. With the formalism established in this work, we are ready to study various exclusive heavy baryon decays systematically in the PQCD approach.

We reanalyze the anomalous angular distribution of lepton pairs produced in a pion-induced Drell-Yan process by taking into account the Glauber gluon effect in the $k_T$ factorization theorem. Compared to the previous study, we adopt the realistic parton distribution functions (PDFs) for a proton from the CTEQ and for a pion from the xFitter, include the QCD evolutions of the strong coupling and the PDFs, and integrate the differential cross section over the kinematic regions for the NA10, E615 and COMPASS experiments. These improvements then allow rigorous confrontations of theoretical results with the data. It is shown that the lepton angular distribution and the violation of the Lam-Tung relation measured in all the above experiments can be well accommodated with a single Glauber phase. We illustrate the Glauber effect in the geometric picture for a Drell-Yan process, and its distinction from the conventional Boer-Mulders mechanism. The observables are pointed out, which can be used to discriminate the two proposals, when data become more precise., Comment: 12 pages, 7 figures, discussion on rotational-invariant observables and more references added, journal version

The physics for beyond-limit focusing has great academic importance, particularly for light propagation with control over focal point location and spot size. Asymmetric boundary confinement for a beyond-limit focusing lens in a metallic subwavelength structure redirects the surface current at the inner edges of the interface between an upstream double slit with width much smaller than the wavelength and a downstream slit with width close to one wavelength. This induces intense localized fields and tightly squeezes spatial distributions for the wave sources and corresponding images that are critical for focusing beyond the diffraction limit, as opposed to separated sources in super-oscillatory lenses and metalenses for optically large areas. This squeezing simultaneously increases the distance between source and image peaks and reduces their distribution widths one order less than the wavelength. The corresponding spatial spectrum alters to excite an inward-propagation wave mode with strong lateral wave momentum for focusing. The radiated inward propagation wave mode can be manipulated to help the focused field tunnel through the downstream slit, such that the focal point can reach the intermediate zone. Source and image radiation confirmed that focused field propagation had good agreement with simulation results. The proposed analytical Green’s method opens new physics applications for this fundamental focusing process, offering new opportunities to further reduce spot size and tailoring the focal length for important potential plasmonic applications.

We develop an inverse matrix method to solve for resonance masses from a dispersion relation obeyed by a correlation function. Given the operator product expansion (OPE) of a correlation function in the deep Euclidean region, we obtain the nonperturbative spectral density, which exhibits resonance structures naturally. The value of the gluon condensate in the OPE is fixed by producing the $\rho$ meson mass in the formalism, and then input into the dispersion relations for the scalar, pseudoscalar and tensor glueballs. It is shown that the low-energy limit of the correlation function for the scalar glueball, derived from the spectral density, discriminates the lattice estimate for the triple-gluon condensate from the single-instanton estimate. The spectral densities for the scalar and pseudoscalar glueballs reveal a double-peak structure: the peak located at lower mass implies that the $f_0(500)$ and $f_0(980)$ ($\eta$ ad $\eta'$) mesons contain small amount of gluonium components, and should be included into scalar (pseudoscalar) mixing frameworks. Another peak determines the scalar (pseudoscalar) glueball mass around 1.50 (1.75) GeV with a broad width about 200 MeV, suggesting that the $f_0(1370)$, $f_0(1500)$ and $f_0(1710)$ ($\eta(1760)$) mesons are the glue-rich states. We also predict the topological susceptability $\chi_t^{1/4}=75$-78 MeV, deduced from the correlation function for the pseudoscalar glueball at zero momentum. Our analysis gives no resonance solution for the tensor glueball, which may be attributed to the insufficient nonperturbative condensate information in the currently available OPE., Comment: 21 pages, journal version, more references included

We perform a global analysis of three-body charmless hadronic decays $B\to VP_3\to P_1P_2P_3$ in the perturbative QCD (PQCD) approach, where $V$ denotes an intermediate vector resonance, and $P_i$, $i=1,2,3$, denote final-state pseudoscalar mesons. Fitting the PQCD factorization formulas at leading order in the strong coupling $\alpha_s$ to measured branching ratios and direct $CP$ asymmetries, we determine the Gegenbauer moments in the two-meson distribution amplitudes (DAs) for the meson pairs $P_1P_2=\pi\pi, K\pi, KK$. The fitted Gegenbauer moments are then employed to make predictions for those observables, whose data are excluded in the fit due to larger experimental uncertainties. A general consistency between our predictions and data is achieved, which hints the validity of the PQCD formalism for the above three-body $B$ meson decays and the universality of the nonperturbative two-meson DAs. The obtained two-meson DAs can be applied to PQCD studies of other multi-body $B$ meson decays involving the same meson pairs. We also attempt to determine the dependence of the Gegenbauer moments on the meson-pair invariant mass, and demonstrate that this determination is promising, when data become more precise., Comment: 30 pages, 2 figures

Based on the flavor structure of four-quark effective operators, we develop an automatic computation program to calculate hadronic two-body B meson decay amplitudes, and apply it to their global analysis in the perturbative QCD (PQCD) approach. Fitting the PQCD factorization formulas for B→PP,VP decays at leading order in the strong coupling αs to measured branching ratios and direct CP asymmetries, we determine the Gegenbauer moments in light meson light cone distribution amplitudes (LCDAs). It is found that most of the fitted Gegenbauer moments of the twist-2 and twist-3 LCDAs for the pseudoscalar meson P (P=π, K) and vector meson V (V=ρ, K*) agree with those derived in QCD sum rules. The shape parameter for the Bs meson distribution amplitude and the weak phase ϕ3(γ)=(75.2±2.9)° consistent with the value in Particle Data Group are also obtained. It is straightforward to extend our analysis to higher orders and higher powers, when the corresponding subleading contributions are available in the PQCD approach, and to the global determination of LCDAs for other hadrons.

We suggest that the uncertain state ${f}_{X}(1500)$ observed by Belle and BABAR more than a decade ago, which has been viewed as a single scalar or a combination of several even spin resonances, is the vector ${\ensuremath{\rho}}^{0}(1450)$ reported recently by LHCb. Adopting the perturbative QCD approach, we determine the dikaon distribution amplitudes with the ${\ensuremath{\rho}}^{0}(1450)$ resonance from the LHCb data for the quasi-two-body decays ${B}^{\ifmmode\pm\else\textpm\fi{}}\ensuremath{\rightarrow}{\ensuremath{\pi}}^{\ifmmode\pm\else\textpm\fi{}}{\ensuremath{\rho}}^{0}(1450)\ensuremath{\rightarrow}{\ensuremath{\pi}}^{\ifmmode\pm\else\textpm\fi{}}{K}^{+}{K}^{\ensuremath{-}}$. It is then shown that the ${B}^{+}\ensuremath{\rightarrow}{K}^{+}{K}^{+}{K}^{\ensuremath{-}}$ decay spectrum around the invariant mass $M({K}^{+}{K}^{\ensuremath{-}})\ensuremath{\sim}1.5\text{ }\text{ }\mathrm{GeV}$ measured by BABAR can be well described by the resonant contribution from ${\ensuremath{\rho}}^{0}(1450)$. The broad structure in the ${B}^{+}\ensuremath{\rightarrow}{K}^{+}{K}_{S}{K}_{S}$ spectrum around the invariant mass 1.5 GeV of a ${K}_{S}{K}_{S}$ pair, which ${\ensuremath{\rho}}^{0}(1450)$ cannot decay into because of Bose-Einstein statistics, can be accounted for by a nonresonant $S$-wave contribution alone. The branching fractions and/or the direct $CP$ asymmetries of the ${B}^{\ifmmode\pm\else\textpm\fi{}}\ensuremath{\rightarrow}{\ensuremath{\pi}}^{\ifmmode\pm\else\textpm\fi{}}{\ensuremath{\rho}}^{0}(1450)\ensuremath{\rightarrow}{\ensuremath{\pi}}^{\ifmmode\pm\else\textpm\fi{}}{K}^{+}{K}^{\ensuremath{-}}$, ${B}^{+}\ensuremath{\rightarrow}{K}^{+}{\ensuremath{\rho}}^{0}(1450)\ensuremath{\rightarrow}{K}^{+}{K}^{+}{K}^{\ensuremath{-}}$ and ${B}^{0}\ensuremath{\rightarrow}{K}^{0}{\ensuremath{\rho}}^{0}(1450)\ensuremath{\rightarrow}{K}^{0}{K}^{+}{K}^{\ensuremath{-}}$ modes are predicted, which can be tested at the ongoing LHCb and Belle-II experiments. We encourage experimental colleagues to scrutinize our postulation by analyzing relevant data with higher precision.

We investigate the Glauber divergences in nonfactorizable annihilation amplitudes for two-body hadronic heavy meson decays in the $k_T$ factorization theorem at one-loop level. These divergences can be absorbed into the Glauber factors in the dominant kinematic regions of small parton momenta, which modify the interference between a nonfactorizable annihilation amplitude and other amplitudes by rotating it with a phase. We postulate that only the Glauber effect associated with a pion is significant, due to its special role as a $q\bar q$ bound state and as a pseudo Nambu-Goldstone boson simultaneously. It is elaborated that the data of the $D\to\pi\pi$ and $\pi K$ branching ratios have revealed prominent Glauber effects. This work provides a solid theoretical ground for the factorization-assisted topological-amplitude parametrization of two-body hadronic $D$ meson decays., Comment: 10 pages, 3 figures

We construct QCD sum rules for nonperturbative studies without assuming the quark-hadron duality for the spectral density at low energy on the hadron side. Instead, both resonance and continuum contributions to the spectral density are solved with the operator-product-expansion input on the quark side by treating sum rules as an inverse problem. This new formalism does not involve the continuum threshold, does not require the Borel transformation and stability analysis, and can be extended to extract properties of excited states. Taking the two-current correlator as an example, we demonstrate that the series of $\rho$ resonances can emerge in our formalism, and the decay constants $f_{\rho(770)} (f_{\rho(1450)},f_{\rho(1700)},f_{\rho(1900)})\approx$ 0.22 (0.19, 0.14, 0.14) GeV for the masses $m_{\rho(770)} (m_{\rho(1450)},m_{\rho(1700)},m_{\rho(1900)})\approx$ 0.78 (1.46, 1.70, 1.90) GeV are determined. We also show that the decay width $\Gamma_{\rho(770)}\approx 0.17$ GeV can be obtained by substituting a Breit-Wigner parametrization for the $\rho(770)$ pole on the hadron side. It is observed that quark condensates of dimension-six on the quark side are crucial for establishing those $\rho$ resonances. Handling the conventional sum rules with the duality assumption as an inverse problem, we find that the multiple pole sum rules widely adopted in the literature do not describe the $\rho$ excitations reasonably. The precision of our theoretical outcomes can be improved systematically by including higher-order and higher-power corrections on the quark side. Broad applications of this formalism to abundant low energy QCD observables are expected., Comment: 17 pages, 14 figures, version accepted for publication in Phys. Rev. D, title is changed

We calculate the parameters $x$ and $y$ for the $D$ meson mixing in the Standard Model by considering a dispersion relation between them. The dispersion relation for a fictitious charm quark of arbitrary mass squared $s$ is turned into an inverse problem, via which the mixing parameters at low $s$ are solved with the perturbative inputs $x(s)$ and $y(s)$ from large $s$. It is shown that nontrivial solutions for $x$ and $y$ exist, whose values around the physical charm scale agree with the data in both CP-conserving and CP-violating cases. We then predict the observables $|q/p|-1\approx 2\times 10^{-4}$ and $Arg(q/p)\approx 6\times 10^{-3}$ degrees associated with the coefficient ratio for the $D$ meson mixing, which can be confronted with more precise future measurements. Our work represents the first successful quantitative attempt to explain the $D$ meson mixing parameters in the Standard Model., 7 pages, 6 figures, v2: Version accepted in PLB. References added. Fig. 5 added

We derive the fragmentation function (FF), which describes the probability for a charm quark to emit a $D$ meson with a certain momentum fraction, in the Nambu-Jona-Lasinio (NJL) model. The corresponding elementary FF is calculated with the quark-meson coupling determined in the NJL model involving charm quarks. The FF in the infinite momentum frame is constructed through the jet process governed by the elementary FF, and then evolved to the charm scale, at which it is defined. To prepare the FF suitable for an analysis of $D$ meson production at CLEO, we further match the above FF to that in the finite momentum frame at one loop in QCD. It is shown that the charm quark FF including the finite momentum effects leads to theoretical results in agreement with the CLEO data., Comment: 17 pages, 16 figures

We analyze the electromagnetic current correlator at an arbitrary photon invariant mass $q^2$ by exploiting its associated dispersion relation. The dispersion relation is turned into an inverse problem, via which the involved vacuum polarization function $\Pi(q^2)$ at low $q^2$ is solved with the perturbative input of $\Pi(q^2)$ at large $q^2$. It is found that the result for $\Pi(q^2)$, including its first derivative $\Pi^\prime(q^2=0)$, agrees with those from lattice QCD, and its imaginary part accommodates the $e^+e^-$ annihilation data. The corresponding hadronic vacuum polarization contribution $a^{\rm HVP}_\mu= (641^{+65}_{-63})\times 10^{-10}$ to the muon anomalous magnetic moment $g-2$, where the uncertainty arises from the variation of the perturbative input, also agrees with those obtained in other phenomenological and theoretical approaches. We point out that our formalism is equivalent to imposing the analyticity constraint to the phenomenological approach solely relying on experimental data, and can improve the precision of the $a^{\rm HVP}_\mu$ determination in the Standard Model., Comment: 11 pages, 6 figures, version to appear in PRD

We analyze the quasi-two-body decays B → K ρ → K π π in the perturbative QCD (PQCD) approach, in which final-state interactions between the pions in the resonant regions associated with the P -wave states ρ ( 770 ) and ρ ′ ( 1450 ) are factorized into two-pion distribution amplitudes. Adopting experimental inputs for the time-like pion form factors involved in two-pion distribution amplitudes, we calculate branching ratios and direct CP asymmetries of the B → K ρ ( 770 ) , K ρ ′ ( 1450 ) → K π π modes. It is shown that agreement of theoretical results with data can be achieved, through which Gegenbauer moments of the P -wave two-pion distribution amplitudes are determined. The consistency between the three-body and two-body analyses of the B → K ρ ( 770 ) → K π π decays supports the PQCD factorization framework for exclusive hadronic B meson decays.

We find a novel mechanism for generating transverse single-spin asymmetry (SSA) in semi-inclusive deep inelastic scattering, distinct from the known ones which involve the Sivers and Collins functions, or their collinear twist-three counterparts. It is demonstrated that a phase needed for SSA can be produced purely within a parton-level cross section starting at two loops. We identify the complete set of two-loop diagrams for SSA, and discuss their gauge invariance and collinear factorization which features the $g_T$ distribution function. In the $k_T$ factorization framework, many more sources for SSA exist, and contributions from all possible two-parton transverse-momentum-dependent parton distribution functions are presented up to two loops and twist three., 21 pages, 14 figures

It was proposed recently that different chiralities of the dark matter (DM) fermion under a broken dark U(1) gauge group can lead to distinguishable signatures at the LHC through shower patterns, which may reveal the mass origin of the dark sector. We study this subject further by examining the dark shower of two simplified models, the dubbed Chiral Model and the Vector Model. We derive a more complete set of collinear splitting functions with power corrections, specifying the helicities of the initial DM fermion and including the contribution from an extra degree of freedom, the dark Higgs boson. The dark shower is then implemented with these splitting functions, and the new features resulting from its correct modelling are emphasized. It is shown that the DM fermion chirality can be differentiated by measuring dark shower patterns, especially the DM jet energy profile, which is almost independent of the DM energy., Comment: 18 pages, 6 figures

We present the differential branching fractions for the $B\ensuremath{\rightarrow}\ensuremath{\psi}\ensuremath{\pi}\ensuremath{\pi}$ decays with the charmonia $\ensuremath{\psi}=J/\ensuremath{\psi},\ensuremath{\psi}(2S)$ in the invariant mass of the $P$-wave pion pairs in the perturbative QCD approach. The two-pion distribution amplitudes (DAs) corresponding to both longitudinal and transverse polarizations are constructed to capture important final state interactions in the processes. The timelike form factors, normalizing the two-pion DAs, contain contributions from the $\ensuremath{\rho}$ resonance and radial excitations fitted to the BABAR ${e}^{+}{e}^{\ensuremath{-}}$ annihilation data. Given the hadronic parameters for the two-pion DAs associated with the longitudinal polarization which were determined in our previous study, and tuning those associated with the transverse polarization, we accommodate well the observed branching ratios and polarization fractions of the $B\ensuremath{\rightarrow}J/\ensuremath{\psi}\ensuremath{\pi}\ensuremath{\pi}$ decays. Our predictions for the $B\ensuremath{\rightarrow}\ensuremath{\psi}(2S)\ensuremath{\pi}\ensuremath{\pi}$ modes from the same set of parameters can be tested in future LHCb and BelleII experiments. We also investigate the sources of theoretical uncertainties in our calculation.

We find a new $CP$-violation effect in charm decays into neutral kaons, which results from the interference between two tree (Cabibbo-favored and doubly Cabibbo-suppressed) amplitudes with the mixing of final-state mesons. This effect, estimated to be of order of $10^{-3}$, is much larger than the direct $CP$ asymmetries in these decays, but missed in the literature. If confirmed, the new effect has to be taken into account, as the above direct $CP$ asymmetries are used to search for new physics.

We study the electron-photon deep inelastic scattering at small Bjorken variable x in the framework of holographic QCD, employing the Pomeron exchange to describe the involved strong interaction. With the Brower-Polchinski-Strassler-Tan Pomeron exchange kernel and appropriate wave functions for the incident and target particles, which are defined in the five-dimensional AdS space, we obtain the photon structure functions. It is shown that our predictions agree with the experimental data measured at LEP and with those derived from a known parameterization of the photon parton distribution functions., 7 pages, 4 figures, prepared for the proceedings of the XXVI International Workshop on Deep Inelastic Scattering and Related Subjects (DIS2018)

We derive the $k_T$ resummation for doubly heavy-flavored $B_c$ meson decays by including the charm quark mass effect into the known formula for a heavy-light system. The resultant Sudakov factor is employed in the perutrbative QCD study of the "golden channel" $B_c^+ \to J/\psi \pi^+$. With a reasonable model for the $B_c$ meson distribution amplitude, which maintains approximate on-shell conditions of both the partonic bottom and charm quarks, it is observed that the imaginary piece of the $B_c \to J/\psi$ transition form factor appears to be power suppressed, and the $B_c^+ \to J/\psi \pi^+$ branching ratio is not lower than $10^{-3}$. The above improved perutrbative QCD formalism is applicable to $B_c$ meson decays to other charmonia and charmed mesons., Comment: 9 pages, 4 figures, and 1 table, references added

The factorization theorem for organizing multiple electroweak boson emissions at future colliders with energy far above the electroweak scale is formulated. Taking the inclusive muon-pair production in electron-positron collisions as an example, we argue that the summation over isospins is demanded for constructing the universal distributions of leptons and gauge bosons in an electron. These parton distributions are shown to have the same infrared structure in the phases of broken and unbroken electroweak symmetry, an observation consistent with the Goldstone equivalence theorem. The electroweak factorization of processes involving protons is sketched, with an emphasis on the subtlety of the scalar distributions. This formalism, in which electroweak shower effects are handled from the viewpoint of factorization theorem for the first time, is an adequate framework for collider physics at ultra high energy., United States. Department of Energy (Contract DE-AC52-06NA25396), National Science Foundation (U.S.) (Grant PHY-1419008)

We study the three-body radiative decays $B\to \phi(\rho) K\gamma$ induced by a flavor-changing neutral current in the perturbative QCD approach. Pseudoscalar-vector ($PV$) distribution amplitudes (DAs) are introduced for the final-state $\phi K$ ($\rho K$) pair to capture important infrared dynamics in the region with a small $PV$-pair invariant mass. The dependence of these $PV$ DAs on the parton momentum fraction is parametrized in terms of the Gegenbauer polynomials, and the dependence on the meson momentum fraction is derived through their normalizations to time-like $PV$ form factors. In addition to the dominant electromagnetic penguin, the subleading chromomagnetic penguin, quark-loop and annihilation diagrams are also calculated. After determining the $PV$ DAs from relevant branching-ratio data, the direct $CP$ asymmetries and decay spectra in the $PV$-pair invariant mass are predicted for each $B\to \phi(\rho) K\gamma$ mode.

We find a new $CP$ violating effect in charmed hadron decays into neutral kaons, which is induced by the interference between the Cabibbo-favored and doubly Cabibbo-suppressed amplitudes with the $K^{0}-\overline K^{0}$ mixing. It is estimated to be of order of $\mathcal{O}(10^{-3})$, much larger than the direct $CP$ asymmetry, but missed in the literature. To reveal this new $CP$ violation effect, we propose a new observable, the difference of the $CP$ asymmetries in the $D^{+}\to \pi^{+}K_S^0$ and $D_{s}^{+}\to K^{+} K_S^0$ modes. Once the new effect is determined by experiments, the direct $CP$ asymmetry then can be extracted and used to search for new physics., Comment: 6 pages, 3 figures. Contribution to the proceeding of The 15th International Conference on Flavor Physics & CP Violation, 5-9 June 2017, Prague, Czech Republic

We find a new $CP$-violation effect in charm decays into neutral kaons, which results from the interference between two tree (Cabibbo-favored and doubly Cabibbo-suppressed) amplitudes with the mixing of final-state mesons. This effect, estimated to be of an order of $10^{-3}$, is much larger than the direct $CP$ asymmetries in these decays, but missed in the literature. It can be revealed by measuring the difference of the time-dependent $CP$ asymmetries in the $D^{+}\to\pi^{+}K_S^0$ and $D_{s}^{+}\to K^{+} K_S^0$ modes, which are accessible at the LHCb and Belle II experiments. If confirmed, the new effect has to be taken into account, as the above direct $CP$ asymmetries are used to search for new physics., Comment: 5 pages, 4 figures; Accepted by Physical Review Letters

We calculate the $D^0$-$\overline{D}^0$ mixing parameter $y$ in the factorization-assisted topological-amplitude (FAT) approach, considering contributions from $D^{0}\to PP$, $PV$, and $VV$ modes, where $P$ ($V$) stands for a pseudoscalar (vector) meson. The $D^{0}\to PP$ and $PV$ decay amplitudes are extracted in the FAT approach, and the $D^{0}\to VV$ decay amplitudes with final states in the longitudinal polarization are estimated via the parameter set for $D^{0}\to PV$. It is found that the $VV$ contribution to $y$, being of order of $10^{-4}$, is negligible, and that the $PP$ and $PV$ contributions amount only up to $y_{PP+PV}=(0.21\pm0.07)\%$, a prediction more precise than those previously obtained in the literature, and much lower than the experimental data $y_{\rm exp}=(0.61\pm0.08)\%$. We conclude that $D^{0}$ meson decays into other two-body and multi-particle final states are relevant to the evaluation of $y$, so it is difficult to understand it fully in an exclusive approach., 13 pages

We revisit the proof of the perturbative QCD factorization for the exclusive processes $\rho \gamma^{\star} \to \pi(\rho)$ at the two-parton twist-3 level. It is pointed out that the residual collinear divergences observed in the literature, which break the factorization of the above processes at the considered accuracy, are attributed to the improper insertion of the Fierz identity for factorizing the fermion flow. We show that the factorization theorem indeed holds at the two-parton twist-3 level after the mishandling is corrected.

We study two-body hadronic B-s -> PT decays, with P(T) being a light pseudoscalar (tensor) meson, in the perturbative QCD approach. The CP-averaged branching ratios and the direct CP asymmetries of the Delta S = 0 modes are predicted, where Delta S is the difference between the strange numbers of final and initial states. We also define and calculate experimental observables for the Delta S = 1 modes under the B-s(0)-(B) over bar (0)(s) mixing, including CP averaged branching ratios, time-integrated CP asymmetries, and the CP observables C-f, D-f and S-f. Results are compared to the B-s -> PV ones in the literature, and to the B -> PT ones, which indicate considerable U-spin symmetry breaking. Our work provides theoretical predictions for the B-s -> PT decays for the first time, some of which will be potentially measurable at future experiments. 0 2014 The Authors. Published by Elsevier B.V.

We propose a modified definition for a quasi-parton distribution function (QPDF) with an equal-time correlator in the large momentum limit, whose two pieces of space-like Wilson links are oriented in orthogonal directions. It is explicitly shown at one-loop level that the linear divergence in the original QPDF with dipolar Wilson links, which complicates its matching to the standard light-cone parton distribution function (LPDF), is removed. The LPDF can then be extracted reliably from Euclidean lattice data for the QPDF with the non-dipolar Wilson links., 7 pages, 2 figures

We point out that the existence of Glauber gluons in the $k_T$ factorization theorem can account for the violation of the Lam-Tung relation, namely, the anomalous lepton angular distribution, observed in pion-induced Drell-Yan processes. Radiations, that balance the lepton-pair transverse momentum, cause the responsible spin-transverse-momentum correlation in the Glauber-gluon background. It is argued that the Glauber effect is significant in the pion due to its unique role of being a Nambu-Goldstone boson and a $q\bar q$ bound state simultaneously. This mechanism is compared to other resolutions in the literature by means of vacuum effects and Boer-Mulders functions. We propose to discriminate the above resolutions by measuring the $p\bar p$ Drell-Yan process at GSI and J-PARC., Comment: power counting of Glauber divergences added; more references included

We calculate the time-like pion–photon transition form factor and the pion electromagnetic form factor up to next-to-leading order (NLO) of the strong coupling constant in the leading-twist k T factorization formalism. It is found that the NLO corrections to the magnitude (phase) are lower than 30 % (30°) for the former, and lower than 25 % (10°) for the latter at large invariant mass squared Q 2 > 30 GeV 2 of the virtual photons. The increase of the strong phases with Q 2 is obtained, consistent with the tendency indicated by experimental data. This behavior is attributed to the inclusion of parton transverse momenta k T , implying that the k T factorization is an appropriate framework for analyzing complex time-like form factors. Potential extensions of our formalism to two-body and three-body hadronic B meson decays are pointed out.

We derive gluon fragmentation functions in the Nambu-Jona-Lasinio (NJL) model by treating a gluon as a pair of color lines formed by fictitious quark and anti-quark ($q\bar q$). Gluon elementary fragmentation functions are obtained from the quark and anti-quark elementary fragmentation functions for emitting specific mesons in the NJL model under the requirement that the $q\bar q$ pair maintains in the flavor-singlet state after meson emissions. An integral equation, which iterates the gluon elementary fragmentation functions to all orders, is then solved to yield the gluon fragmentation functions at a model scale. It is observed that these solutions are stable with respect to variation of relevant model parameters, especially after QCD evolution to a higher scale is implemented. We show that the inclusion of the gluon fragmentation functions into the theoretical predictions from only the quark fragmentation functions greatly improves the agreement with the SLD data for the pion and kaon productions in $e^+e^-$ annihilation. Our proposal provides a plausible construct for the gluon fragmentation functions, which are supposed to be null in the NJL model., 26 pages, 23 figures

We extend the perturbative QCD formalism including the Glauber gluons, which has been shown to accommodate the measured $B \to \pi \pi$ and $B^0\to\rho^0 \rho^0$ branching ratios simultaneously, to the analysis of the $B \to K \pi$ and $K \bar K$ decays. It is observed that the convolution of the universal Glauber phase factors with the transverse-momentum-dependent kaon wave function reveals weaker (stronger) Glauber effects than in the pion ($\rho$ meson) case as expected. Our predictions for the branching ratios and the direct CP asymmetries of the $B \to K \pi$ and $K \bar K$ modes at next-to-leading-order accuracy agree well with data. In particular, the predicted difference of the $B^\pm \to K^\pm \pi^0$ and $B^0 \to K^\pm \pi^\mp$ direct CP asymmetries, $\Delta A_{K\pi}\equiv A_{\rm CP}^{\rm dir}(K^\pm \pi^0)[0.021 \pm 0.016] - A_{\rm CP}^{\rm dir}(K^\pm \pi^\mp)[-0.081 \pm 0.017] = 0.102 \pm 0.023$, is consistent with the measured $\Delta A_{K\pi} = 0.119 \pm 0.022$ within uncertainties, and the known $B \to K\pi$ puzzle is resolved. The above $B \to \pi \pi$, $K\pi$ and $K \bar K$ studies confirm that the Glauber gluons associated with pseudo-Nambu-Goldstone bosons enhance the color-suppressed tree amplitude significantly, but have a small impact on other topological amplitudes.

We calculate the three-parton twist-3 contribution to the B → π transition form factors in the k T factorization theorem. Since different mesons are involved in the initial and final states, two(three)-parton-to-three(two)-parton amplitudes do not vanish. It is found that the dominant contribution arises from the diagrams with the additional valence gluon attaching to the leading-order hard gluon. Employing the three-parton meson distribution amplitudes from QCD sum rules, we show that this subleading piece amounts only up to few percents of the form factors at large recoil of the pion. The framework for analyzing three-parton contributions to B meson decays in the k T factorization is established.

We investigate the photon structure functions at small Bjorken variable $x$ in the framework of the holographic QCD, assuming dominance of the Pomeron exchange. The quasi-real photon structure functions are expressed as convolution of the Brower-Polchinski-Strassler-Tan (BPST) Pomeron kernel and the known wave functions of the U(1) vector field in the five-dimensional AdS space, in which the involved parameters in the BPST kernel have been fixed in previous studies of the nucleon structure functions. The predicted photon structure functions, as confronted with data, provide a clean test of the BPST kernel. The agreement between theoretical predictions and data is demonstrated, which supports applications of holographic QCD to hadronic processes in the nonperturbative region. Our results are also consistent with those derived from the parton distribution functions of the photon proposed by Gl\"uck, Reya, and Schienbein, implying realization of the vector meson dominance in the present model setup., Comment: 6 pages, 5 figures; v2: version accepted for publication in Phys. Lett. B, Fig. 2 and clarifications added to Section 3

We point out mistakes made in the one-loop calculation of some diagrams for the process π γ ∗ → γ in the preprint arXiv:0807.0296 , and present correct results. Especially, we have difficulty to understand their argument that a highly off-shell gluon generates a light-cone (infrared) singularity. It is shown by means of the Ward identity that the gauge-dependent light-cone singularity found in arXiv:0807.0296 does not exist. It is then shown that a hard kernel derived in the k T factorization of exclusive processes is gauge invariant and free of the light-cone singularity.