arXiv subjects

Hsiang-nan Li

Publications and source records attributed to Hsiang-nan Li.

At least 19 recordsLinked to original sources

arXiv2026

The Pion Gravitational Form Factors and the Trace Anomaly in QCD Factorization

We study the pion gravitational form factor in QCD factorization, focusing on the trace-anomaly component generated by the non-Abelian $TJJ$ vertex. The calculation combines a Sudakov-resummation-improved pion hard kernel with the anomaly form factor suggested by momentum-space conformal field theory and by the perturbative dilaton sum rule. Comparison with lattice QCD data shows a refined projection hierarchy: the isolated anomaly cancels in the form factor $A_π(Q^2)$, while the full $TJJ$ insertion lowers the leading-order curve at small momentum transfer squared $Q^2$; the anomaly is important in $D_π(Q^2)$, and it gives the dominant $TJJ$ contribution to the trace form factor.

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arXiv2026

The Gravitational Form Factor of the Pion in Perturbative QCD with a Dilaton Interaction

We investigate the pion gravitational form factors (GFFs) at intermediate and large momentum transfer within the framework of QCD factorization. Our analysis centers on the non-Abelian $TJJ$ correlator, which couples the local QCD energy-momentum tensor to two external gluon fields and explicitly encodes the perturbative effects of the trace anomaly. We demonstrate how this quantum anomaly induces a scalar, dilaton-like contribution to the hard-scattering kernel. To ensure field-theoretic consistency, a careful separation of the quark and gluon sectors is performed, accounting for the modifications introduced by gauge-fixing terms and Slavnov-Taylor identities on the off-shell gluonic structure. To obtain realistic phenomenological predictions and regulate soft-gluon endpoint divergences in the hard kernel, we implement the Sudakov resummation framework coupled with a Gaussian model for the pion's transverse-momentum-dependent wave function. We show that the resulting anomaly-induced corrections significantly modify the behavior of the pion GFFs at large momentum transfer, leaving a unique imprint on the trace sector and the $D$-term.

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arXiv2026

Lepton sourced baryon asymmetry in the fourth generation model

We demonstrate that the observed baryon asymmetry in the Universe can be accommodated in the extended Standard Model with sequential fourth generation fermions (SM4). We first construct the dimension-6 effective operators of the type $-i(Φ^\daggerΦ)\bar F_LΦf_R$ induced by fourth generation quarks, which carry the $CP$ violation (CPV) source from the $4\times 4$ Cabibbo-Kobayashi-Maskawa (CKM) matrix, $Φ$ ($F_L$, $f_R$) being a Higgs double (left-handed fermion doublet, right-handed fermion singlet). The required inputs of the fourth generation fermion masses were derived in our previous dispersive analyses on heavy quark decays and neutral meson mixing. The similar framework allows the determination of the $4\times 4$ CKM matrix elements $V_{ib'}$, $i=u$, $c$ and $t$, such that the strength of the CPV source can be evaluated unambiguously. The dimension-6 operators associated with fourth generation leptons, as implemented into the formalism for the electroweak baryogenesis in the literature, lead to the baryon-over-entropy ratio $η_B\approx 10^{-10}$.

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arXiv2026

LHC di-dijet excesses as signals of fourth-generation tetraquarks

We postulate that the excesses of di-dijet events observed at the LHC are attributed to the production of four fourth-generation quarks $b'$ with a mass $m_{b'}\approx 2$ TeV at few-TeV scales. The di-dijet signals around the four-jet invariant mass $m_{4j}\approx 8$ TeV arise from a resonant $b'b'\bar b'\bar b'$ tetraquark production, where the dijet resonances of masses about 2 TeV correspond to $b'\bar b'$ first excited states (color-octet scalars with the principal quantum number $n=2$) in a Yukawa potential created by Higgs boson exchanges. Those around $m_{4j}\approx 3.6$ TeV originate from a non-resonant $b'b'\bar b'\bar b'$ production, where the dijet resonances of masses 0.95 TeV correspond to $b'\bar b'$ ground states (color-octet vectors with $n=1$). It is shown that a $b'\bar b'$ system with $m_{b'}\approx 2$ TeV in the Yukawa potential does generate the aforementioned bound state spectrum. We then illustrate that the observed excesses can be accommodated in our setup by translating the fourth-generation model to the effective theories containing color-octet scalars and vectors available in the literature. The di-dijet events at $m_{4j}= 6.6$ TeV and 5.8 TeV with dijet masses about 2 TeV can also be interpreted in the same framework. Simply speaking, our scenario can be viewed as a TeV-scale version of the search for a fully charmed tetraquark via the four-muon channels $X(6900)\to (c\bar c)(c\bar c)\to 4μ$ at a GeV scale.

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arXiv2026

Light baryon static properties in dispersive approach

We extend our dispersive analyses on meson static properties to those of light baryons. The formalism treats the dispersion relation, which a baryonic correlation function obeys, as an inverse problem, solve for the involved spectral density with available operator-product-expansion (OPE) inputs directly, and extract baryon static properties from the spectral density. We observe that the simultaneous implementation of the chiral-even and chiral-odd dispersive constraints unambiguously determines baryon masses and pole residues. A common set of quark and gluon condensates, which appear in OPE factorization and are universal, is found to accommodate the masses of a $ρ$ meson, a proton and a $Δ(1232)$ baryon. The advantage of our approach over the conventional handling of QCD sum rules is advocated. This work encourages broad applications of our nonperturbative analytical method to baryon systems.

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arXiv2025

Tomography of high-twist proton structure through $ep$ elastic scattering

We present the first high-twist study of the proton form factors $F_{1,2}(Q^2)$ in $ep$ elastic scattering based on the perturbative QCD $k_T$ factorization, $Q^2$ being momentum transfer squared. It is motivated by unexpectedly large higher-power contributions from subleading-twist light-cone distribution amplitudes (LCDAs), which are attributed to the enhancement in endpoint regions of parton momentum fractions. We highlight that the endpoint enhancement, tamed by the $k_T$ resummation effect, is crucial for accommodating the approximate scaling behavior of the $Q^4F_1(Q^2)$ data at intermediate $Q^2\sim {\cal O}(10)$ GeV$^2$. The proton LCDAs up to twist 6 are then extracted, and verified by the charge-parity asymmetries observed in hadronic heavy baryon decays. Our work provides new insights into the proton three-dimensional structure and manifests the precision requirement for reliable perturbative analyses of baryonic exclusive processes.

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arXiv2025

$CP$ violation in two-body hadronic $Λ_b$ decays in the PQCD approach

We systematically investigate the $CP$-averaged branching ratios and $CP$ violations (CPVs) for the two-body hadronic decays $Λ_b\to ph$, where $h$ runs through the mesons $π^-$, $ρ^-$, $a_1^-(1260)$, $K^-$, $K^{\ast -}$, $K_1^-(1270)$ and $K_1^-(1400)$, in the perturbative QCD approach to order $α_s^2$ in the strong coupling. Various topological amplitudes are obtained by incorporating subleading-twist hadron distribution amplitudes, which exhibit reasonable hierarchical patterns, sizable strong phases, and non-negligible higher-power corrections. The predicted direct CPVs in $Λ_b\to pπ^-,pK^-$, different from those in similar $B$ meson decays, are as small as the current data. The low CPV in $Λ_b\to pπ^-$ results from the cancellation between the $S$- and $P$-wave CPVs, while the one in $Λ_b\to pK^-$ is determined by the tiny $S$-wave CPV. However, individual partial-wave CPVs can exceed $10\%$, consistent with direct CPVs in $B$ meson decays. The CPVs in the $Λ_b\to pK_1^-(1270),pK_1^-(1400)$ channels are relatively larger. In particular, CPVs above $20\%$ appear in the up-down asymmetries associated with the final-state angular distributions of $Λ_b\to pK_1^-(1270),pK_1^-(1400)$, followed by the secondary $K_1\to Kππ$ decays. These observables offer promising prospects for firmly establishing baryon CPVs. The decay asymmetry parameters of $Λ_b\to ph$ are also predicted for future experimental confrontations.

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arXiv2025

Realization of electroweak baryogenesis by fourth generation fermions

We demonstrate that the electroweak baryogenesis can be realized in the extended Standard Model with sequential fourth generation fermions (SM4). The solution to the coupled Dyson-Schwinger equations for the fermion and Higgs masses indicates that fourth generation quarks $t'$ and $b'$ with the Yukawa couplings above the threshold $g_Q^c\approx 9.1$ form condensates. This critical coupling, greater than the value $g_Y^f\approx 7$ at the ultraviolet fixed point of the renormalization-group evolution in the SM4, implies the existence of an electroweak symmetric phase at a high energy. The $t'$ and $b'$ Yukawa couplings evolve as the energy decreases, and exceed $g_Q^c$ at a lower scale. The Higgs potential with the dynamical symmetry breaking effect from heavy quark condensates plus the one-loop temperature-dependent correction from the heavy scalars formed by $t'$ and $b'$ quarks allow the first-order phase transition characterized by the ratio $ϕ_c/T_c\approx 0.9$, where $ϕ_c$ is the location of the Higgs potential minimum at the critical temperature $T_c$. Together with the baryon number violating sphaleron interaction inherent in the Standard Model and the enhanced $CP$ violation source from fourth generation quarks, the baryon asymmetry in the Universe can be achieved.

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arXiv2025

Study of $B_c \to χ_{cJ}\ (P, V)$ decays in the improved perturbative QCD formalism

Motivated by the recent LHCb measurements of the ratios between the branching ratios (BRs), $R_{χ_{c2}/J/ψ} \equiv {\rm BR}(B_c^+ \to χ_{c2} π^+)/{\rm BR}(B_c^+ \to J/ψπ^+)$ and $R_{χ_{c1}/χ_{c2}} \equiv {\rm BR}(B_c^+ \to χ_{c1} π^+)/{\rm BR}(B_c^+ \to χ_{c2} π^+)$, we analyze the decays $B_c^+ \to χ_{cJ} (P, V)^+$ in the improved perturbative QCD (iPQCD) formalism, where $χ_{cJ}$ denotes the $p$-wave charmonia with $J=0, 1, 2$, and $P (V)$ denotes the pseudoscalars $π$ and $K$ (the vectors $ρ$ and $K^*$). Our results $R_{χ_{c2}/J/ψ} = 0.32 \pm 0.05$ and $R_{χ_{c1}/χ_{c2}}= 0.11 \pm 0.01$ at leading order in the strong coupling $α_s$ agree well with the data within uncertainties. The result $R_{χ_{c0}/J/ψ} \equiv {\rm BR}(B_c^+ \to χ_{c0} π^+)/{\rm BR}(B_c^+ \to J/ψπ^+) = 0.17 \pm 0.02$ is lower than $1.41^{+0.50}_{-0.45}$ inferred by the $B_c^+ \to χ_{c0} π^+$ measurement. The large longitudinal polarization fractions imply that these components dominate the $B_c^+ \to χ_{c1,c2} ρ^+$ BRs. A peculiar constructive (destructive) interference between the twist-2 and twist-3 contributions is identified in the $B_c^+\to χ_{c1} ρ^+$ ($B_c^+\to χ_{c1} π^+$) mode, but not in the corresponding ones with $χ_{c0,c2}$ mesons. Inputting the BRs of the strong decays $χ_{c0,c2} \to π^+ π^- / K^+ K^-$ and $χ_{cJ} \to π^+π^-(π^+ π^-/K^+K^-)$ reported by the BESIII Collaboration, we obtain those of $B_c^+ \to χ_{cJ} (ρ, π)^+$ followed by secondary decay chains under the narrow-width approximation. All the above iPQCD predictions can be confronted by more precise experiments in the future to deepen our understanding of QCD dynamics in $B_c\toχ_{cJ}$ transitions.

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arXiv2025

Dispersive determination of neutrino mass ordering

We argue that the mixing phenomenon of a neutral meson formed by a fictitious massive quark will disappear, if the electroweak symmetry of the Standard Model (SM) is restored at a high energy scale. This disappearance is taken as the high-energy input for the dispersion relation, which must be obeyed by the width difference between two meson mass eigenstates. The solution to the dispersion relation at low energy, i.e., in the symmetry broken phase, then connects the Cabibbo-Kobayashi-Maskawa (CKM) matrix elements to the quark masses involved in the box diagrams responsible for meson mixing. It is demonstrated via the analysis of the $D$ meson mixing that the typical $d$, $s$ and $b$ quark masses demand the CKM matrix elements in agreement with measured values. In particular, the known numerical relation $V_{us}\approx \sqrt{m_s/m_b}$ with the $s$ ($b$) quark mass $m_s$ ($m_b$) can be derived analytically from our solution. Next we apply the same formalism to the mixing of the $μ^- e^+$ and $μ^+ e^-$ states through similar box diagrams with intermediate neutrino channels. It is shown that the neutrino masses in the normal hierarchy (NH), instead of in the inverted hierarchy or quasi-degenerate spectrum, match the observed Pontecorvo-Maki-Nakagawa-Sakata matrix elements. The lepton mixing angles larger than the quark ones are explained by means of the inequality $m_2^2/m_3^2\gg m_s^2/m_b^2$, $m_{2,3}$ being the neutrino masses in the NH. At last, the solution for the $τ^-e^+$-$τ^+e^-$ mixing specifies the mixing angle $θ_{23}\approx 45^\circ$, leading to the $μ$-$τ$ reflection symmetry. Our work suggests that the fermion masses and mixing parameters are constrained dynamically, and the neutrino mass orderings can be discriminated by the internal consistency of the SM.

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arXiv2025

Establishing CP Violation in $b$-Baryon Decays

It is a long-standing puzzle why the {\it CP} violation (CPV) in the baryon system has not yet been definitively established as in the meson one. We demonstrate that individual partial-wave CPV in the $Λ_b\to pπ^-$ and $pK^-$ decays can exceed $10\%$, but the destruction between the partial waves (the suppression by the small partial-wave weight) results in a small net direct CPV in the former (the latter) as measured currently. Our finding highlights the different dynamics responsible for CPVs in baryon and meson decays. We propose to probe the CPV observables associated with the angular distributions of the $Λ_b\to pa_1(1260)$, $pK_1(1270)$ decay products, which are large enough for being identified experimentally.

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arXiv2025

Improved global determination of two-meson distribution amplitudes from multi-body $B$ decays

We improve the perturbative QCD (PQCD) formalism for multi-body charmless hadronic $B$ meson decays, such as $B\to VP_3\to P_1P_2P_3$, by resolving the possible discrepancy in parametrizing the contribution of the $P$-wave resonance $V$ to the two-meson distribution amplitudes (DAs) associated with the pairs $P_1P_2=ππ, Kπ, KK$. The determination of the Gegenbauer moments in the two-meson DAs is then updated in the global fit of the improved PQCD factorization formulas at leading order in the strong coupling $α_s$ to available data for branching ratios and polarization fractions of three- and four-body $B$ decays. The convergence of the Gegenbauer expansion of the resultant two-meson DAs is manifest. The satisfactory quality of the fit implies the consistency of the PQCD framework for multi-body $B$ decays and the universality of the nonperturbative two-meson DAs. In particular, the predicted longitudinal polarization fraction $f_0(B_s^0\to K^{*0} {\bar K}^{*0})=28.2^{+8.8}_{-9.5} \%$ with the updated Gegenbauer moments matches well the measurement. The observable $L_{K^{*0}{\bar K}^{*0}}=7.7^{+4.9}_{-3.8}$, defined as the ratio of the longitudinal amplitudes of the two $U$-spin related channels $B_s^0\to K^{*0} {\bar K}^{*0}$ and $B^0\to K^{*0} {\bar K}^{*0}$, accommodates the current data within errors. It is found that the direct $CP$ asymmetries ${\cal A}^{0,||,\bot}_{\rm CP}$ in the polarization states of some four-body decays $B\to V_1V_2\to (P_1P_2)(P_3P_4)$ might be large, but the destruction among them result in small net $CP$ violation. Our predictions can be confronted with LHCb and Belle-II data in the future.

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arXiv2024

Dispersive determination of the fourth generation lepton masses

We continue our previous determination of the masses of the sequential fourth generation quarks in an extension of the Standard Model, and predict the mass $m_4$ ($m_L$) of the fourth generation neutrino $ν_4$ (charged lepton $L$) by solving the dispersion relation associated with heavy fermion decays. The results $m_4\approx 170$ GeV and $m_L\approx 270$ GeV are extracted from the dispersive analyses of the $t\to d e^+ν_4$ and $L^-\to ν_1 \bar t d$ decay widths, respectively, where $t$ ($d$, $e^+$, $ν_1$) denotes a top quark (down quark, positron, light neutrino). The predictions are cross-checked by examining the $L^-\to ν_4 \bar u d$ decay, $\bar u$ being an anti-up quark. It is shown that the fourth generation leptons with the above masses survive the current experimental bounds from Higgs boson decays into photon pairs and from the oblique parameters. We also revisit how the existence of the fourth generation leptons impacts the dispersive constraints on the neutrino masses and the Pontecorvo-Maki-Nakagawa-Sakata (PMNS) matrix elements. It is found that the unitarity of the $3\times 3$ PMNS matrix holds well up to corrections of $O(m_ν^2/m_W^2)$, $m_ν$ ($m_W$) being a light neutrino (the $W$ boson) mass, whose mixing angles and $CP$ phase prefer the values $θ_{12}\approx 34^\circ$, $θ_{23}\approx 47^\circ$, $θ_{13}\approx 5^\circ$ and $δ\approx 200^\circ$ in the normal-ordering scenario for neutrino masses.

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arXiv2024

Understanding small neutrino mass and its implication

We have derived previously the relations between the neutrino masses and mixing angles in a dispersive analysis on the mixing of neutral leptonic states. The only involved assumption is that the electroweak symmetry of the Standard Model (SM) is restored at a high energy scale in some new physics scenario, which diminishes the box diagrams responsible for the mixing. Here we include corrections to the analysis up to three loops, arising from exchanges of additional neutral and charged scalars in the electroweak symmetric phase. The solution to the dispersion relation for the $μ^-e^+$-$μ^+e^-$ mixing generates a typical neutrino mass $m_ν\sim O(1)$ eV in the SM unambiguously. The solution also favors the normal ordering of the neutrino masses over the inverted one, and links the large electroweak symmetry restoration, i.e., new physics scale to the small neutrino mass.

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arXiv2024

Dispersive analysis of excited glueball states

Motivated by the determination for the spin-parity quantum numbers of the $X(2370)$ meson at BESIII, we extend our dispersive analysis on hadronic ground states to excited states. The idea is to start with the dispersion relation which a correlation function obeys, and subtract the known ground-state contribution from the involved spectral density. Solving the resultant dispersion relation as an inverse problem with available operator-product-expansion inputs, we extract excited-state masses from the subtracted spectral density. This formalism is verified by means of the application to the series of $ρ$ resonances, which establishes the $ρ(770)$, $ρ(1450)$ and $ρ(1700)$ mesons one by one under the sequential subtraction procedure. Our previous study has suggested the admixture of the $f_0(1370)$, $f_0(1500)$ and $f_0(1710)$ mesons (the $η(1760)$ meson) to be the lightest scalar (pseudoscalar) glueball. The present work predicts that the $f_0(2200)$ ($X(2370)$) meson is the first excited scalar (pseudoscalar) glueball.

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arXiv2024

Dispersive determination of fourth generation quark masses

We determine the masses of the sequential fourth generation quarks $b'$ and $t'$ in the extension of the Standard Model by solving the dispersion relations associated with the mixing between the neutral states $Q\bar q$ and $\bar Qq$, $Q$ ($q$) being a heavy (light) quark. The box diagrams responsible for the mixing, which provide the perturbative inputs to the dispersion relations, involve multiple intermediate channels, i.e., the $ut$ and $ct$ channels, $u$ ($c$, $t$) being an up (charm, top) quark, in the $b'$ case, and the $db'$, $sb'$ and $bb'$ ones, $d$ ($s$, $b$) being a down (strange, bottom) quark, in the $t'$ case. The common solutions for the above channels lead to the masses $m_{b'}=(2.7\pm 0.1)$ TeV and $m_{t'}\approx 200$ TeV unambiguously. We show that these superheavy quarks, forming bound states in a Yukawa potential, barely contribute to Higgs boson production via gluon fusion and decay to photon pairs, and bypass current experimental constraints. The mass of the $\bar b'b'$ ground state is estimated to be about 3.2 TeV. It is thus worthwhile to continue the search for $b'$ quarks or $\bar b'b'$ resonances at the (high-luminosity) large hadron collider.

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arXiv2024

Perturbative QCD contribution to transverse single spin asymmetries in Drell-Yan and SIDIS

In a previous publication [Beni\' c et al., Phys. Rev. D104 (2021) 094027], we have computed the perturbative QCD contribution to transverse single spin asymmetries (SSAs) in semi-inclusive Deep Inelastic Scattering (SIDIS) involving the $g_T(x)$ distribution. In this paper, we first present a more efficient derivation of the asymmetries which is applicable to both transverse and longitudinal SSAs, and correct some inconsistencies in our previous calculation. We then adapt the method to compute transverse SSAs in Drell-Yan proportional to $g_T(x)$ and its gluonic counterpart, and discuss the crossing symmetry between the results for SIDIS and Drell-Yan. Finally, we present numerical results for various asymmetries measurable at the EIC, RHIC, COMPASS and Fermilab (SpinQuest), including also part of the genuine twist-three corrections to $g_T(x)$ from a recent global analysis. We find that the asymmetries can reach percent-level magnitude, if the kinematics predominantly probes the large-$x$ (valence) region of the polarized proton, but remain at sub-percent levels otherwise.

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arXiv2023

Dispersive determination of electroweak-scale masses

We demonstrate that the Higgs boson mass can be extracted from the dispersion relation obeyed by the correlation function of two $b$-quark scalar currents. The solution to the dispersion relation with the input from the perturbative evaluation of the correlation function up to next-to-leading order in QCD and with the $b$ quark mass $m_b=4.43$ GeV demands a specific Higgs mass 114 GeV. Our observation offers an alternative resolution to the long-standing fine-tuning problem of the Standard Model (SM): the Higgs mass is determined dynamically for the internal consistency of the SM. The similar formalism, as applied to the correlation function of two $b$-quark vector currents with the same $m_b$, leads to the $Z$ boson mass 90.8 GeV. This solution exists only when the $Z$ and $W$ boson masses are proportionate, conforming to the Higgs mechanism of the electroweak symmetry breaking. We then consider the mixing between the $Q\bar u$ and $\bar Qu$ states for a fictitious heavy quark $Q$ and a $u$ quark through the $b\bar b$ channel, inspired by our earlier analysis of neutral meson mixing. Its dispersion relation, given the perturbative input from the responsible box diagrams and the same $m_b$, fixes the top quark mass 176 GeV. It is highly nontrivial to predict the above electroweak-scale masses with at most 9\% deviation from their measured values using the single parameter $m_b$. More accurate results are expected, as more precise perturbative inputs are adopted.

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