arXiv subjects

Hsiang-nan Li

Publications and source records attributed to Hsiang-nan Li.

At least 37 records · Page 2Linked to original sources

arXiv2023

Dispersive constraints on fermion masses

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 $2m_π$ ($m_π+m_D$), where $m_π$ ($m_D$) denotes the pion ($D$ meson) mass. Requiring that the dispersion relation for the $Q\to su\bar d$ ($Q\to dμ^+ν_μ$, $Q\to uτ^-\barν_τ$) decay with the threshold $m_π+m_K$ ($m_π+m_μ$, $m_π+m_τ$) yields the same heavy quark mass, $m_K$ being the kaon mass, we constrain the strange quark (muon, $τ$ lepton) mass to be $m_s= 0.12$ GeV ($m_μ=0.11$ GeV, $m_τ= 2.0$ 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.

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arXiv2023

Dispersive analysis of neutral meson mixing

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.

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arXiv2022

Dispersive derivation of the pion distribution amplitude

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 $μ=2$ GeV. Turning off the condensates, we get the asymptotic form, independent of the scale $μ$, for the pion LCDA as expected. We then solve for the pion LCDA at a different scale $μ=1.5$ GeV with the condensate inputs at this $μ$, and demonstrate that the result is consistent with the one obtained by evolving the Gegenbauer coefficients from $μ=2$ 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.

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arXiv2022

$Λ_b\to p$ transition form factors in perturbative QCD

We reanalyze the $Λ_b\to p$ transition form factors in the perturbative QCD (PQCD) approach by including higher-twist light-cone distribution amplitudes (LCDAs) of a $Λ_b$ baryon and a proton. The previous PQCD evaluation performed decades ago with only the leading-twist $Λ_b$ 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 $Λ_b$ 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 $Λ_b\to p\ell\barν_\ell$ and the hadronic decay $Λ_b\to pπ$ 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.

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arXiv2022

Glauber gluons in pion-induced Drell-Yan processes revisited

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.

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arXiv2021

Global determination of two-meson distribution amplitudes from three-body $B$ decays in the perturbative QCD approach

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 $α_s$ to measured branching ratios and direct $CP$ asymmetries, we determine the Gegenbauer moments in the two-meson distribution amplitudes (DAs) for the meson pairs $P_1P_2=ππ, Kπ, KK$. 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.

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arXiv2021

Dispersive analysis of glueball masses

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 $ρ$ 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 $f_0(980)$ ($η$ ad $η'$) 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 $f_0(1710)$ ($η(1760)$) mesons are the glue-rich states. We also predict the topological susceptability $χ_t^{1/4}=75$-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.

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arXiv2021

The $g_T(x)$ contribution to single spin asymmetries in SIDIS

Motivated by a novel origin of transverse single spin asymmetry (SSA) in semi-inclusive Deep Inelastic Scattering (SIDIS) uncovered by some of us, we quantitatively investigate its impact on the theoretical understanding of the mechanism responsible for SSA. This new contribution from the quark-initiated channel first appears in two-loop perturbation theory and involves the $g_T(x)$ distribution. We point out another entirely analogous piece from the gluon-initiated channel proportional to the gluon helicity distribution $ΔG(x)$. Both contributions are solely expressed in terms of twist-two polarized parton distribution functions and twist-two fragmentation functions in the Wandzura-Wilczek approximation, such that they can be unambiguously evaluated without introducing free parameters. We make predictions for measurements of the asymmetries $A_{UT}$ at the future Electron-Ion Collider (EIC), and find that $A_{UT}$ associated with the $\sin (ϕ_h-ϕ_S)$, $\sin ϕ_S$ and $\sin (2ϕ_h-ϕ_S)$ harmonics can reach up to 1-2\% even at the top EIC energy.

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arXiv2021

Glauber gluons in annihilation amplitudes for heavy meson decays

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 $D\toππ$ and $πK$ 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.

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arXiv2021

Four-body decays $B_{(s)} \rightarrow (Kπ)_{S/P} (Kπ)_{S/P}$ in the perturbative QCD approach

We investigate the four-body decays $B_{(s)} \rightarrow (Kπ)_{S/P} (Kπ)_{S/P}$ in the $Kπ$-pair invariant mass region around the $K^*(892)$ resonance in the perturbative QCD (PQCD) approach, where $(Kπ)_{S/P}$ denotes a $S$- or $P$-wave $Kπ$ configuration. The contributions from the $P$-wave resonance $K^*(892)$ and from possible $S$-wave components are included into the parametrization of the $Kπ$ two-meson distribution amplitudes, which are the nonperturbative inputs in this formalism. We calculate the branching ratio for each resonance and observe sizable $S$-wave contributions to the $B_s$ modes, well consistent with recently available LHCb data. We also deduce the polarization fractions for the $K^*\bar{K}^*$ final states, and compare our predictions to those in previous PQCD analyses of the corresponding two-body $B\to K^*\bar{K}^*$ decays. The polarization puzzle associated with the two $U$-spin related channels $B^0\rightarrow K^{*0}\bar{K}^{*0}$ and $B^0_s\rightarrow K^{*0}\bar{K}^{*0}$ still exists. In addition to direct $CP$ asymmetries, triple-product asymmetries and $S$-wave induced direct $CP$ asymmetries originating from the interference among various helicity amplitudes, are presented. It is shown that true triple-product asymmetries are rather small, while direct $CP$ asymmetries and $S$-wave-induced direct $CP$ asymmetries are significant in some decays. Our results will be subject to stringent tests with precise data from $B$ factories in the near future.

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arXiv2021

Is $f_X(1500)$ observed in the $B\to π(K)KK$ decays $ρ^0(1450)$?

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 $ρ^0(1450)$ reported recently by LHCb. Adopting the perturbative QCD approach, we determine the di-kaon distribution amplitudes with the $ρ^0(1450)$ resonance from the LHCb data for the quasi-two-body decays $B^{\pm}\to π^{\pm}ρ^0(1450)\toπ^{\pm}K^+K^-$. It is then shown that the $B^+ \to K^+K^+K^-$ decay spectrum around the invariant mass $M(K^+K^-)\sim 1.5~\rm GeV$ measured by BaBar can be well described by the resonant contribution from $ρ^0(1450)$. The broad structure in the $B^{+}\to K^{+} K_SK_S$ spectrum around the invariant mass $1.5~\rm GeV$ of a $K_SK_S$ pair, which $ρ^0(1450)$ 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 $B^{\pm}\to π^{\pm}ρ^0(1450)\toπ^{\pm}K^+K^-$, $B^{+}\to K^{+}ρ^0(1450)\to K^+K^+K^-$ and $B^{0}\to K^{0}ρ^0(1450)\to K^0K^+K^-$ 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.

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arXiv2021

Global Analysis of hadronic two-body B decays in the perturbative QCD approach

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 $B\to PP,VP$ decays at leading order in the strong coupling $α_s$ 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 $B_s$ meson distribution amplitude and the weak phase $ϕ_3(γ)=(75.1\pm2.9)^\circ$ consistent with the value in Particle Data Group are also obtained. It is straightforward to extend our analysis to higher orders and higher powers in the PQCD approach, and to the global determination of LCDAs for other hadrons.

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arXiv2020

QCD sum rules with spectral densities solved in inverse problems

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 $ρ$ resonances can emerge in our formalism, and the decay constants $f_{ρ(770)} (f_{ρ(1450)},f_{ρ(1700)},f_{ρ(1900)})\approx$ 0.22 (0.19, 0.14, 0.14) GeV for the masses $m_{ρ(770)} (m_{ρ(1450)},m_{ρ(1700)},m_{ρ(1900)})\approx$ 0.78 (1.46, 1.70, 1.90) GeV are determined. We also show that the decay width $Γ_{ρ(770)}\approx 0.17$ GeV can be obtained by substituting a Breit-Wigner parametrization for the $ρ(770)$ pole on the hadron side. It is observed that quark condensates of dimension-six on the quark side are crucial for establishing those $ρ$ 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 $ρ$ 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.

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arXiv2020

Next-to-leading-logarithm $k_T$ resummation for $B_c\to J/ψ$ decays

We derive the $k_T$ resummation for a transverse-momentum-dependent charmonium wave function, which involves the bottom quark mass $m_b$, the charm quark mass $m_c$, and the charm quark transverse momentum $k_T$, up to the next-to-leading-logarithm (NLL) accuracy under the hierarchy $m_b\gg m_c \gg k_T$. The resultant Sudakov factor is employed in the perutrbative QCD (PQCD) approach to the $B_c\to J/ψ$ transition form factor $A_0^{B_c \to J/ψ}(0)$ and the $B_c^+ \to J/ψπ^+$ decay. We compare the NLL resummation effect on these processes with the leading-logarithm one in the literature, and find a $(5-10)\%$ enhancement to the form factor $A_0^{B_c \to J/ψ}(0)$ and a $(10-20)\%$ enhancement to the decay rate ${\rm BR}(B_c^+ \to J/ψπ^+)$. The improved $k_T$ resummation formalism is applicable to the PQCD analysis of heavy meson decays to other charmonia.

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arXiv2020

Vacuum polarization contribution to muon $g-2$ as an inverse problem

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 $Π(q^2)$ at low $q^2$ is solved with the perturbative input of $Π(q^2)$ at large $q^2$. It is found that the result for $Π(q^2)$, including its first derivative $Π^\prime(q^2=0)$, agrees with those from lattice QCD, and its imaginary part accommodates the $e^+e^-$ annihilation data. The corresponding hadronic vacuum polarization contribution $a^{\rm HVP}_μ= (641^{+65}_{-63})\times 10^{-10}$ 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 $a^{\rm HVP}_μ$ determination in the Standard Model.

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arXiv2020

$D$ meson mixing as an inverse problem

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.

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arXiv2020

Next-to-Leading-logarithm threshold resummation for exclusive $B$ meson decays

We extend the threshold resummation of the large logarithms $\ln x$ which appear in factorization formulas for exclusive $B$ meson decays, $x$ being a spectator momentum fraction, to the next-to-leading-logarithm (NLL) accuracy. It is shown that the NLL resummation effect provides suppression in the end-point region with $x\sim 0$ stronger than the leading-logarithm (LL) one, and thus improves perturbative analyses of the above processes. We revisit the $B\to Kπ$ decays under the NLL resummation, and find that it induces 20-25\% variation of the direct CP asymmetries compared to those from the LL resummation. Our way to avoid the Landau singularity in the inverse Mellin transformation causes little theoretical uncertainty.

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arXiv2020

Charm fragmentation functions in the Nambu-Jona-Lasinio model

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.

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