Search

Neutral triple gauge couplings (nTGCs) are manifestation of new physics beyond the Standard Model (SM), as they are absent in the SM and are first generated by dimension-8 operators in the SM Effective Field Theory (SMEFT). We study the UV completion of nTGCs in a renormalizable model with vector-like heavy fermions. We compute the one-loop heavy fermion contributions to nTGC vertices by matching them to dimension-8 operators in the low energy limit. Such fermion loops contain either heavy fermions only or mixture of heavy fermions with light SM fermions. We find that their contributions can induce dimension-8 nTGC effective operators containing two SM Higgs-doublet fields, which are formulated with a complete set of 7 dimension-8 operators generating off-shell CP-even nTGCs. We present the results in terms of SMEFT coefficients and in terms of nTGC vertices (form factors) with two on-shell gauge bosons. In the heavy-light mixing case there appear terms that cannot be accommodated by conventional parametrizations of form factors due to extra logarithmic corrections. We further discuss the implications for probing such UV dynamics via nTGCs at the high energy colliders.

We investigate cosmological constraints on the holographic dark energy (HDE) using the state-of-the-art cosmological datasets: Planck CMB angular power spectra and weak lensing power spectra, Atacama Cosmology Telescope (ACT) temperature power spectra, baryon acoustic oscillation (BAO) and redshift-space distortion (RSD) measurements from six-degree-field galaxy survey and Sloan Digital Sky Survey (DR12 & DR16) and the Cepheids-Supernovae measurement from SH0ES team (R22). We also examine the HDE model and $\Lambda$CDM with and without $N_{\rm eff}$ (effective number of relativistic species) being treated as a free parameter. We find that the HDE model can relieve the tensions of $H_0$ and $S_8$ to certain degrees. With ``Planck+ACT+BAO+RSD'' datasets, the constraints are $H_0 = 69.70 \pm 1.39\ \mathrm{km\ s^{-1} Mpc^{-1}}$ and $S_8 = 0.823 \pm 0.011$ in HDE model, which brings down the Hubble tension down to $1.92\sigma$ confidence level (C.L.) and the $S_8$ tension to $1$-$2\sigma$ C.L. By adding the R22 data, their values are improved as $H_0 = 71.86 \pm 0.93 \,\mathrm{km\ s^{-1} Mpc^{-1}}$ and $S_8 = 0.813 \pm 0.010$, which further brings the Hubble tension down to $0.85\sigma$ C.L. and relieves the $S_{8}$ tension. We also quantify the goodness-of-fit of different models with Akaike information criterion (AIC) and Bayesian information criterion (BIC), and find that the HDE agrees with the observational data better than the $\Lambda$CDM and other extended models (treating $N_{\rm eff}$ as free for fitting)., Comment: 11 pages, 7 figures, 5 tables

We study the mechanism of topological mass-generation for 3d Chern-Simons gauge theories and propose a brand-new Topological Equivalence Theorem to connect scattering amplitudes of the physical gauge boson states to that of the transverse states under high energy expansion. We prove a general energy cancellation mechanism for $N$-point physical gauge boson amplitudes, which predicts large cancellations of $E^{4-L}\to E^{(4-L)- N}$ at any $L$-loop level ($L\geqslant 0$). We extend the double-copy approach to construct massive graviton amplitudes and study their structures. We newly uncover a series of strikingly large energy cancellations $E^{12}\to E^1$ of the tree-level four-graviton scattering amplitude under high energy expansion and establish a new correspondence between the two energy cancellations in the topologically massive Yang-Mills gauge theory and the topologically massive gravity theory. We further study the scattering amplitudes of Chern-Simons gauge bosons and gravitons in the nonrelativistic limit., Comment: 8+5 pages, to match Journal Version. This Letter paper is a companion of the systematic longer paper arXiv:2110.05399 (46pp)

We study the structure of scattering amplitudes of massive Kaluza-Klein (KK) states in the compactified 5-dimensional warped gauge and gravity theories. We present systematic formulations of the gauge theory equivalence theorem (GAET) and the gravitational equivalence theorem (GRET) for warped KK theories in $R_\xi^{}$ gauge, where the GAET connects the scattering amplitudes of longitudinal KK gauge bosons to that of the corresponding KK Goldstone bosons and the GRET connects the scattering amplitudes of KK gravitons of helicity-zero (helicity-one) to that of the corresponding gravitational KK Goldstone bosons. We analyze the structure of 3-point and 4-point scattering amplitudes of massive KK gauge bosons and of massive KK gravitons as well as their corresponding Goldstone bosons. We first prove the GAET and GRET explicitly for the fundamental 3-point KK gauge/gravity scattering amplitudes. We then demonstrate that the validity of the GAET and GRET for 4-point gauge/gravity scattering amplitudes can be reduced to the validity of GAET and GRET for 3-point gauge/gravity scattering amplitudes at tree level. With these, we study the double-copy construction of KK scattering amplitudes in the warped gauge/gravity theories. We newly realize the double-copy for massive 3-point full gauge/gravity amplitudes at tree level under proper correspondences of color-kinematics and of gauge/gravity couplings, whereas we can construct the double-copy for 4-point KK gauge/gravity amplitudes to the leading order (LO) of high energy expansion. We further demonstrate that this LO double-copy construction can be extended to $N$-point KK scattering amplitudes with $N\geqslant 4$., Comment: 91 pages. Improved version, references added

Neutral triple gauge couplings (nTGCs) are absent in the Standard Model (SM) and at the dimension-6 level in the Standard Model Effective Field Theory (SMEFT), arising first from dimension-8 operators. As such, they provide a unique window for probing new physics beyond the SM. These dimension-8 operators can be mapped to nTGC form factors whose structure is consistent with the spontaneously-broken electroweak gauge symmetry of the SM. In this work, we study the probes of nTGCs in the reaction $e^+e^-\to Z\gamma$ with $Z\to\ell^+\ell^-\,(\ell =e,\mu)$ at an $e^+e^-$ collider. We perform a detector-level simulation and analysis of this reaction at the Circular Electron Positron Collider (CEPC) with collision energy $\sqrt{s} = 240$ GeV and an integrated luminosity of 20 ab$^{-1}$. We present the sensitivity limits on probing the new physics scales of dimension-8 nTGC operators via measurements of the corresponding nTGC form factors., Comment: Frontiers of Physics (in Press), 22 pages, 10 Figs and 10 Tables

Different dark matter (DM) candidates could have different types of DM-lepton and/or DM-quark interactions. For direct detection experiments, this leads to diversity in the recoil spectra, where both DM-electron and DM-nucleus scatterings may contribute. Furthermore, kinematic effects such as those of the inelastic scattering can also play an important role in shaping the recoil spectra. In this work, we systematically study signatures of the light exothermic inelastic DM from the recoil spectra including both the DM-electron scattering and Migdal effect. Such inelastic DM has mass around (sub-)GeV scale and the DM mass-splitting ranges from 1keV to 30keV. We analyze the direct detection sensitivities to such light inelastic DM. For different inelastic DM masses and mass-splittings, we find that the DM-electron recoil and Migdal effect can contribute significantly and differently to the direct detection signatures. Hence, it is important to perform combined analysis to include both the DM-electron recoil and Migdal effect. We further demonstrate that this analysis has strong impacts on the cosmological and laboratory bounds for the inelastic DM., Comment: 30 pages, refined version, references added

We study probes of neutral triple gauge couplings (nTGCs) via $Z^*\gamma$ production followed by off-shell decays $Z^*\to\nu\bar{\nu}$ at the LHC and future $pp$ colliders, including both CP-conserving (CPC) and CP-violating (CPV) couplings. We present the dimension-8 SMEFT operators contributing to nTGCs and derive the correct form factor formulation for the off-shell vertices $Z^*\gamma V^*$ ($V=Z,\gamma$) by matching them with the dimension-8 SMEFT operators. Our analysis includes new contributions enhanced by the large off-shell momentum of $Z^*$, beyond those of the conventional $Z\gamma V^*$ vertices with on-shell $Z\gamma$. We analyze the sensitivity reaches for probing the CPC/CPV nTGC form factors and the new physics scales of the dimension-8 nTGC operators at the LHC and future 100TeV $pp$ colliders. We compare our new predictions with the existing LHC measurements of CPC nTGCs in the $\nu\bar\nu\gamma$ channel and demonstrate the importance of our new method., Comment: 25 pages (including supplemental material), only minor refinements, to match the version of PRD(letter)

We study the scattering amplitudes of massive Kaluza-Klein (KK) states under toroidal compactification. We present a shifting method to quantitatively derive the scattering amplitudes of massive KK gauge bosons and KK gravitons from the corresponding massless amplitudes in the noncompactified higher dimensional theories. With these we construct the massive KK scattering amplitudes by extending the double-copy relations of massless scattering amplitudes within the field theory framework, including both the BCJ and CHY methods, and build up their connections to the massive KK KLT relations. We present the massive BCJ-type double-copy construction of the $N$-point KK gauge boson/graviton scattering amplitudes, and as the applications we derive explicitly the four-point KK scattering amplitudes as well as the five-point KK scattering amplitudes. We further study the nonrelativistic limit of these massive scattering amplitudes with the heavy external KK states and discuss the impact of the compactified extra dimensions on the low energy gravitational potential. Finally, we analyze the four-point and $N$-point mass spectral conditions and newly propose a novel group theory approach to prove that only the KK theories under toroidal compactification can satisfy these conditions for directly realizing massive double-copy in the field theory framework., Comment: 73 pages, JHEP final version. Only minor refinements, references added

We analyze the structure of scattering amplitudes of the Kaluza-Klein (KK) gravitons and of the KK gravitational Goldstone bosons in the compactified 5d General Relativity (GR). Using a general $R_{\xi}$ gauge-fixing, we study the geometric Higgs mechanism for the massive spin-2 KK gravitons. We newly propose and prove a Gravitational Equivalence Theorem (GRET) to connect the scattering amplitudes of longitudinal KK gravitons to that of the KK gravitational Goldstone bosons, which formulates the geometric gravitational Higgs mechanism at the scattering $S$-matrix level. We demonstrate that the GRET provides a general energy-cancellation mechanism guaranteeing the $N$-point longitudinal KK graviton scattering amplitudes to have their leading energy dependence cancelled down by a large power factor of $E^{2N}$ ($N \geq 4$) up to any loop order. We propose an extended double-copy approach to construct the massive KK graviton (Goldstone) amplitudes from the KK gauge boson (Goldstone) amplitudes. With these we establish a new correspondence between the two types of energy cancellations in the four-point longitudinal KK amplitudes at tree level: $E^4\to E^0$ in the KK gauge theory and $E^{10} \to E^2$ in the KK GR theory., Comment: 9 pages (+Supplemental Material), including exact KK double-copy of both LO + NLO. This Letter is the companion of the recent systematic long paper in PRD 105 (2022) 084005 [arXiv:2106.04568]

The hMSSM is a special parameterization of the minimal supersymmetric extension of the Standard Model (MSSM) in which the mass of the lightest Higgs boson is automatically set to the LHC measured value, $M_h\!\!=\!\! 125$\,GeV, by adjusting the supersymmetric particle spectrum such that it provides the required amount of radiative corrections to the Higgs boson masses.\ The latter spectrum was in general assumed to be very heavy, as indicated by the present exclusion limits of the LHC, not to affect the phenomenology of the Higgs sector.\ In this work, we investigate the impact on the hMSSM by a light gaugino and higgsino sector, that is allowed by the present LHC data.\ In particular, we discuss the radiative corrections due to charginos and neutralinos to the Higgs boson masses and couplings and show that an hMSSM can still be realized in this context.\ We first describe how this scenario is implemented in the package SuSpect that generates the MSSM Higgs and supersymmetric spectra.\ We then analyze the possible impact of Higgs boson decays into these new states, as well as the reverse cascade channels with Higgs bosons in the final states, for the constraints on the MSSM Higgs sector at the LHC.\ We further explore the cosmological constraints on the hMSSM with a light gaugino--higgsino spectrum.\ We analyze the relic abundance of the lightest neutralino as a candidate of the dark matter in the Universe and the constraints on its mass and couplings by the present and future astroparticle physics experiments., Comment: 57 pages, 21 figures. Version to appear in JHEP

We study probes of neutral triple gauge couplings (nTGCs) at the LHC and the proposed 100TeV $pp$ colliders, and compare their sensitivity reaches with those of the proposed $e^+ e^-$ colliders. The nTGCs provide a unique window to the new physics beyond the Standard Model (SM) because they can arise from SM effective field theory (SMEFT) operators that respect the full electroweak gauge group $SU(2)_L\otimes U(1)_Y$ of the SM only at the level of dimension-8 or higher. We derive the neutral triple gauge vertices (nTGVs) generated by these dimension-8 operators in the broken phase and map them onto a newly generalized form factor formulation, which takes into account only the residual U(1)$_{\rm{em}}$ gauge symmetry. Using this mapping, we derive new relations between the form factors that guarantee a truly consistent form factor formulation of the nTGVs and remove large unphysical energy-dependent terms. We then analyze the sensitivity reaches of the LHC and future 100TeV hadron colliders for probing the nTGCs via both the dimension-8 nTGC operators and the corresponding nTGC form factors in the reactions $ pp(q\bar{q})\to Z\gamma$ with $Z\to\ell^+\ell^-,\nu\bar{\nu}$. We compare their sensitivities with the existing LHC measurements of nTGCs and with those of the high-energy $e^+e^-$ colliders. In general, we find that the prospective LHC sensitivities are comparable to those of an $e^+ e^-$ collider with center-of-mass energy $\leq 1$TeV, whereas an $e^+ e^-$ collider with center-of-mass energy $(3 - 5)$TeV would have greater sensitivities, and a 100TeV $pp$ collider could provide the most sensitive probes of the nTGCs., Comment: 57 pages, 22 Figs + Tables. PRD Version [selected as Editors' Suggestion], only minor refinements, references added

We study the scattering amplitudes of massive Kaluza-Klein (KK) states of open and closed bosonic strings under toroidal compactification. We analyze the structure of vertex operators for the KK strings and derive an extended massive KLT-like relation which connects the $N$-point KK closed-string amplitude to the products of two KK open-string amplitudes at tree level. Taking the low energy field-theory limit of vanishing Regge slope, we derive double-copy construction formula of the $N$-point massive KK graviton amplitude from the sum of proper products of the corresponding KK gauge boson amplitudes. Then, using the string-based massive double-copy formula, we derive the exact tree-level four-point KK gauge boson amplitudes and KK graviton amplitudes, which fully agree with those given by the KK field-theory calculations. With these, we give an explicit prescription on constructing the exact four-point KK graviton amplitudes from the sum of proper products of the corresponding color-ordered KK gauge boson amplitudes. We further analyze the string-based double-copy construction of five-point and six-point scattering amplitudes of massive KK gauge bosons and KK gravitons., Comment: 41 pages, JHEP version, only minor refinements, references added

We study the mechanism of topological mass-generation for 3d Chern-Simons (CS) gauge theories, where the CS term can retain the gauge symmetry and make gauge boson topologically massive. Without CS term the 3d massless gauge boson has a single physical transverse polarization state, while adding the CS term converts it into a massive physical polarization state and conserves the total physical degrees of freedom. We newly formulate the mechanism of topological mass-generation at $S$-matrix level. For this, we propose and prove a new Topological Equivalence Theorem (TET) which connects the $N$-point scattering amplitude of the gauge boson's physical polarization states ($A^a_{\rm{P}}$) to that of the transverse polarization states ($A^a_{\rm{T}}$) under high energy expansion. We present a general 3d power counting method on the leading energy dependence of $N$-point scattering amplitudes in both topologically massive Yang-Mills (TMYM) and topologically massive gravity (TMG) theories. With these, we uncover a general energy cancellation mechanism for $N$-gauge boson scattering amplitudes which predicts the cancellation $E^4 \to E^{4-N}$ at tree level. Then, we compute the four-point amplitudes of $A^a_{\rm{P}}$'s and of $A^a_{\rm{T}}$'s, with which we explicitly demonstrate the TET and establish such energy cancellations. We further extend the double-copy approach and construct the four-point massive graviton amplitude of the TMG theory from the massive gauge boson amplitude of the TMYM theory. With these, we newly uncover striking large energy cancellations $E^{12}\to E^1$ in the four-graviton amplitude of the TMG, and establish its new correspondence to the leading energy cancellations $E^4 \to E^0$ in the four-gauge boson amplitude of the TMYM., Comment: 46 pages. All results and conclusions unchanged. Only minor refinements to stress the focus and new contributions of this paper. References added

We study the structure of scattering amplitudes of the Kaluza-Klein (KK) gravitons and of the gravitational KK Goldstone bosons in the compactified 5d General Relativity (GR). We analyze the geometric "Higgs" mechanism for mass-generation of KK gravitons under compactification with a general $R_\xi$ gauge-fixing, which is free from the vDVZ discontinuity. Then, we formulate the Gravitational Equivalence Theorem (GRET) to connect the longitudinal KK graviton amplitudes to the KK Goldstone amplitudes, which is a manifestation of the geometric Higgs mechanism at $S$-matrix level. We directly compute the tree-level KK Goldstone amplitudes which equal the longitudinal KK graviton amplitudes in the high energy limit. We further extend the double-copy method with color-kinematics duality to reconstruct the massive KK longitudinal graviton (Goldstone) amplitudes from the KK longitudinal gauge boson (Goldstone) amplitudes in the compactified 5d Yang-Mills (YM) theory under high energy expansion. From these, we reconstruct the GRET of the KK longitudinal graviton (Goldstone) amplitudes in the 5d GR from the KK longitudinal gauge boson (Goldstone) amplitudes in the 5d YM theory. Using either the GRET or the double-copy reconstruction, we provide a theoretical mechanism showing that the sum of all the energy-power terms [up to $O(E^{10})$] in the high-energy four longitudinal KK graviton amplitudes must cancel down to $O(E^2)$ as enforced by matching the energy-power dependence of the corresponding KK Goldstone amplitudes or by matching that of the double-copy amplitudes from the KK YM theory. With the double-copy approach, we establish a new correspondence between the two energy-cancellations: $E^4 \to E^0$ in the 5d KK YM theory and $E^{10} \to E^2$ in the 5d KK GR theory. We further analyze the structure of the residual terms in the GRET and uncover a new energy-cancellation mechanism therein., Comment: 90 pages. Final version inclulding the exact KK double-copy of NLO amplitudes. Conclusions unchanged, typos corrected and references added. Its companion Letter paper appeared in arXiv:2207.11214

We propose a new candidate of GeV scale inelastic dark matter (DM). Our construction has an anomaly-free $U(1)_X^{}$ gauge group with dark photon mediator, and can realize either scalar or fermionic inelastic DM. It is highly predictive and testable. We study the scattering rate of light inelastic DM with electrons in the XENON1T experiment and with nuclei in the XENON1T, CRESST-III, CDEX-1B and DarkSide-50 experiments. We resolve the recent XENON1T anomaly via electron recoil detection. Combining the XENON1T constraints from both electron recoils and nuclear recoils (including Migdal effect), we predict the inelastic DM mass $\lesssim 1.5$GeV. We further analyze the bounds by the DM relic abundance, the lifetime of the heavier DM component, and laboratory constraints, from which we identify the viable parameter space for the future probe. This provides an important benchmark for the theories and experimental tests of GeV scale inelastic DM., Comment: 14pp, PRD published version. Results and Conclusions unchanged, only minor refinements. The importance of Migdal bound on inelastic DM is stressed. References added

Neutral triple gauge couplings (nTGCs) are absent in the standard model effective theory up to dimension-6 operators, but could arise from dimension-8 effective operators. In this work, we study the pure gauge operators of dimension-8 that contribute to nTGCs and are independent of the dimension-8 operator involving the Higgs doublet. We show that the pure gauge operators generate both $Z\gamma Z^*$ and $Z\gamma\gamma^*$ vertices with rapid energy dependence $\propto E^5$, which can be probed sensitively via the reaction $e^+e^- \to Z\gamma$. We demonstrate that measuring the nTGCs via the reaction $e^+e^- \to Z\gamma$ followed by $Z \to q\bar{q}$ decays can probe the new physics scales of dimension-8 pure gauge operators up to the range $(1-5)$TeV at the CEPC, FCC-ee and ILC colliders with $\sqrt{s}=(0.25-1)$TeV, and up to the range $(10-16)$TeV at CLIC with $\sqrt{s}=(3-5)$TeV, assuming in each case an integrated luminosity of 5/ab. We compare these sensitivities with the corresponding probes of the dimension-8 nTGC operators involving Higgs doublets and the dimension-8 fermionic contact operators that contribute to the $e^+e^-Z\gamma$ vertex., Comment: 43pp, 9 Figs (32 plots) and 4 Tables. v4: refined Fig.9 by adding results of 5/ab integrated luminosity. v3: Only minor refinements to match online version in Science China, selected as "Editor's Focus" and "Cover Article"

Measuring dark matter (DM) signals via electron recoil provides an important means for direct detection of light DM particles. The recent XENON1T anomaly with electron recoil energy around $\,E_R^{}\!=\!(2-3)$keV can be naturally explained by DM inelastic scattering which injects energy to the recoiled electrons and gives a narrow peak structure in the recoil spectrum. We present an effective field theory (EFT) approach to exothermic inelastic DM signals for the Xenon electron recoil detection. For relatively heavy mediator, we fairly formulate the DM-lepton interactions by effective contact operators with two DM fields $(X,\,X')$ and two leptons. Using the XENON1T data, we fit the electron recoil spectrum and constrain the allowed scalar DM mass-splitting as $\,2.1\,\text{keV}\!<\!\Delta m\!<\!3.3\,\text{keV}$ (95%C.L.), with the best fit $\,\Delta m \!=\! 2.8$keV. We analyze the relic abundance produced by such effective DM-electron contact interaction. To provide both the DM relic abundance and the XENON1T excess, we derive new constraints on the DM mass and the UV cutoff scale of DM effective interactions. Finally, we study possible UV completions for the effective DM-lepton contact interactions., Comment: JCAP Final Version, 27 pages, only minor refinements, typos corrected and references added

Measuring high energy cosmic ray electrons/positrons (CRE) provides important means for the dark matter (DM) indirect detection and for probing the nearby galactic sources. In this work, we perform a systematic analysis of the flavor structure of DM annihilations into charged leptons based on the cosmic ray CRE spectra measured by DAMPE, Fermi-LAT, AMS-02, and CALET experiments. We study the annihilations of possible TeV scale DM particles in a nearby subhalo, which is proposed to explain the possible peak-like structure of the DAMPE CRE data. We pay special attention to the possible non-resonant excess (besides the possible peak-like structure) and demonstrate that such non-resonant excess can mainly arise from the decay of muons produced by the DM annihilations in the subhalo. With these we study the flavor composition of the lepton final states from DM annihilations $\chi\chi\to e^+e^-, \mu^+\mu^-, \tau^+\tau^-$ by fitting the CRE data. We demonstrate that decays of the final states $\mu^+ \mu^-$ and $\tau^+ \tau^-$ can provide the non-resonant excess, while the peak excess arises from the $e^+ e^-$ final state. We further analyze the constraints on the lepton flavor composition using the Fermi-LAT $\gamma$-ray measurements. We find that the flavor composition is consistent with the Fermi-LAT data at relatively low Galactic latitudes, while the fraction of the final state $\tau^\pm$ is severely bounded., Comment: Nucl.Phys.B (in Press), 36 pages, 9 Figs (21 plots), 8 Tables. All analyses + conclusions unchanged, only minor rewordings, references added

Self-interacting neutrinos that begin to free-stream at close to matter-radiation equality can reduce the physical size of photon sound horizon at last scattering surface. This mechanism can be the reason why standard $\Lambda$CDM cosmology sees a lower value of the Hubble constant than local measurements from distance ladder. We propose a new realization of self-interacting Dirac neutrinos (SID$\nu$) with light-dark-photon mediator for a viable interaction mechanism. Our model is UV completed by a Dirac seesaw with anomaly-free dark $U(1)_X^{}$ gauge group which charges the right-handed neutrinos. This model naturally generates small masses for Dirac neutrinos and induces self-scattering of right-handed neutrinos. The scattering with left-handed neutrinos is suppressed by a chirality-flip mass insertion when the neutrino energy is much larger than its mass. The resultant neutrino self-scattering is not operative for $E_{\nu}\gtrsim O(\text{keV})$, which avoids the cosmological and laboratory constraints. By evolving Boltzmann equations for left- and right-handed neutrino number densities, we show that about $2/3$ of the left-handed neutrinos are converted into right-handed neutrinos in a short epoch between the Big-Bang Nucleosynthesis and the recombination, and interact with each other efficiently afterwards. The resultant neutrino non-free-streaming is the crucial ingredient to shrink down the comoving sound horizon at drag epoch, which can reconcile the Hubble tension between early and late time measurements., Comment: 26 pages, JCAP in press. Only minor refinements, references added. (This update is much delayed due to pandemic situation.)

Holographic dark energy (HDE) describes the vacuum energy in a cosmic IR region whose total energy saturates the limit of avoiding the collapse into a black hole. HDE predicts that the dark energy equation of the state transiting from greater than the $-1$ regime to less than $-1$, accelerating the Universe slower at the early stage and faster at the late stage. We propose the HDE as a new {\it physical} resolution to the Hubble constant discrepancy between the cosmic microwave background (CMB) and local measurements. With Planck CMB and galaxy baryon acoustic oscillation (BAO) data, we fit the HDE prediction of the Hubble constant as $H_0^{}\!=\, 71.54\pm1.78\,\mathrm{km\,s^{-1} Mpc^{-1}}$, consistent with local $H_0^{}$ measurements by LMC Cepheid Standards (R19) at $1.4\sigma$ level. Combining Planck+BAO+R19, we find the HDE parameter $c=0.51\pm0.02$ and $H_0^{}\! = 73.12\pm 1.14\,\mathrm{km \,s^{-1} Mpc^{-1}}$, which fits cosmological data at all redshifts. Future CMB and large-scale structure surveys will further test the holographic scenario., Comment: Published version in PRD Rapid Communication, 6 pages, 5 figures, 2 tables. All results and conclusions are unchanged, only minor refinements, references added

Boson stars may consist of a new type of light singlet scalar particles with nontrivial self-interactions, and may compose a fraction of the dark matter in the Universe. In this work, we study the dynamics of boson stars with Liouville and logarithmic scalar self-interaction potentials as benchmarks. We perform a numerical analysis as well as a semi-analytic study on how the compactness and the total mass will deviate from that of the usual boson stars formed with a quartic repulsive self-interaction. We apply the recently suggested Swampland conjecture to examine whether boson stars with such benchmark potentials belong to the Landscape of a quantum gravity. Using the mass constraint on the macroscopic compact halo object (MACHO) and the cold dark matter (CDM) isocurvature mode constraint from the cosmic microwave background (CMB), we derive the allowed mass range of scalar particles which compose the boson star. We further analyze applications of the lensing of fast radio bursts (FRBs) and the gravitational wave (GW) detection to probe the presence of such boson stars and constrain the parameter space of their corresponding models. We discuss how the two types of boson star potentials can be discriminated by the FRB and GW measurements., Comment: JCAP version (in press). 38pp, 11 Figs and 2 Tables. All results/conclusions unchanged, only minor refinements

The $ZZ\gamma$ triple neutral gauge couplings are absent in the Standard Model (SM) at the tree level. They receive no contributions from dimension-6 effective operators, but can arise from effective operators of dimension-8. We study the scale of new physics associated with such dimension-8 operators that can be probed by measuring the reaction $e^+e^-\to Z\gamma$, followed by $Z \to \ell\bar{\ell},\nu\bar{\nu}$ decays, at future $e^+e^-$ colliders including the ILC, CEPC, FCC-ee and CLIC. We demonstrate how angular distributions of the final state mono-photon and leptons can play a key role in suppressing SM backgrounds. We further show that using electron/positron beam polarizations can significantly improve the signal sensitivities. We find that the dimension-8 new physics scale can be probed up to the multi-TeV region at such lepton colliders., Comment: Final Journal Version, 53 pages [12 Figs (30 plots), 7 Tables]. Extended version, all conclusions and results unchanged, clarifications & references added

The discovery of the Higgs boson with its mass around 125 GeV by the ATLAS and CMS Collaborations marked the beginning of a new era in high energy physics. The Higgs boson will be the subject of extensive studies of the ongoing LHC program. At the same time, lepton collider based Higgs factories have been proposed as a possible next step beyond the LHC, with its main goal to precisely measure the properties of the Higgs boson and probe potential new physics associated with the Higgs boson. The Circular Electron Positron Collider~(CEPC) is one of such proposed Higgs factories. The CEPC is an $e^+e^-$ circular collider proposed by and to be hosted in China. Located in a tunnel of approximately 100~km in circumference, it will operate at a center-of-mass energy of 240~GeV as the Higgs factory. In this paper, we present the first estimates on the precision of the Higgs boson property measurements achievable at the CEPC and discuss implications of these measurements., Comment: 46 pages, 37 figures

The seesaw and leptogenesis commonly depend on the masses of same particles, and thus are both realized at the same scale. In this work, we demonstrate a new possibility to realize a TeV-scale neutrino seesaw and a natural high-scale leptogenesis. We extend the standard model by two gauge-singlet scalars, a vector-like iso-doublet fermion and one iso-triplet Higgs scalar. Our model respects a softly broken lepton number and an exactly conserved $Z_2$ discrete symmetry. It can achieve three things altogether: (i) realizing a testable type-II seesaw at TeV scale with two nonzero neutrino mass-eigenvalues, (ii) providing a minimal inelastic dark matter from the new fermion doublets, and (iii) accommodating a thermal or nonthermal leptogenesis through the singlet scalar decays. We further analyze the current experimental constraints on our model and discuss the implications for the dark matter direct detections and the LHC searches., Comment: PRD final version. 20 pages and 3 figures. Only minor refinements on the presentation and discussions, all conclusions un-changed, references added

The Dark Matter Particle Explorer (DAMPE) satellite detector announced its first result for measuring the cosmic-ray electron/positron (CRE) energy spectrum up to 4.6TeV, including a tentative peak-like event excess at (1.3-1.5)TeV. In this work, we uncover a significant hidden excess in the DAMPE CRE spectrum over the energy range (0.6-1.1)TeV, which has a non-peak-like structure. We propose a new mechanism to explain this excess by a set of 1.5TeV $\mu^\pm$ events with subsequent decays into $e^\pm$ plus neutrinos. For explaining this new excess together with the peak excess around 1.4TeV, we demonstrate that the {\it flavor structure} of the original lepton final-state produced by dark matter (DM) annihilations (or other mechanism) should have a composition ratio $N_e : (N_\mu +\frac{1}{6}N_\tau) = 1 : y$, with $y \simeq 2.6-10.8$. For lepton portal DM models, this puts important constraint on the lepton-DM-mediator couplings $\lambda_e : (\lambda_\mu^4 + \frac{1}{6}\lambda_\tau^4)^{\frac{1}{4}} = 1 : y^{\frac{1}{4}}$ with a narrow range $y^{\frac{1}{4}} \simeq 1.3-1.8$., Comment: PLB journal version, 10 pages, 3 Figs and 1 Table. All conclusions un-changed, only fixed minor typos

Searching for new Higgs particle beyond the observed light Higgs boson h(125GeV) will unambiguously point to new physics beyond the standard model. We study the resonant production of a CP-even heavy Higgs state $H^0$ in the di-Higgs channel via, $gg\to H^0\to h^0h^0\to WW^*WW^*$, at the LHC Run-2 and the high luminosity LHC (HL-LHC). We analyze two types of the $4W$ decay modes, one with the same-sign di-leptons ($4W\to\ell^\pm\nu\ell^\pm\nu 4q$) and the other with tri-leptons ($4W\to\ell^\pm\nu\ell^\mp\nu\ell^\pm\nu 2q$). We perform a full simulation for the signals and backgrounds, and estimate the discovery potential of the heavy Higgs state at the LHC Run-2 and the HL-LHC, in the context of generical two-Higgs-doublet models (2HDM). We determine the viable parameter space of the 2HDM as allowed by the theoretical constraints and the current experimental limits. We systematically analyze the allowed parameter space of the 2HDM which can be effectively probed by the heavy Higgs searches of the LHC, and further compare this with the viable parameter region under the current theoretical and experimental bounds., Comment: v3: JHEP published version, 34pp, 10 Figs(36 plots) and 9 Tables. Only minor typos fixed, references added. v2: JHEP version. All results and conclusions un-changed, discussions and references added. (This update is much delayed due to author's traveling and flu.)

We show that gravitational lensing can provide a direct method to probe the nature of dark energy at astrophysical scales. For lensing system as an isolated astrophysical object, we derive the dark energy contribution to gravitational potential as a repulsive power-law term, containing a generic equation of state parameter $w$. We find that it generates $w$-dependent and position-dependent modification to the conventional light orbital equation of $w=-1$. With post-Newtonian approximation, we compute its direct effect for an isolated lensing system at astrophysical scales and find that the dark energy force can deflect the path of incident light rays. We demonstrate that the dark-energy-induced deflection angle $\Delta\alpha_{DE}^{}\propto M^{(1+\frac{1}{3w})}$ (with $1+\frac{1}{3w}>0$), which increases with the lensing mass $M$ and consistently approaches zero in the limit $M \to 0$. This effect is distinctive because dark energy tends to diffuse the rays and generates concave lensing effect. This is in contrast to the conventional convex lensing effect caused by both visible and dark matter. Measuring such concave lensing effect can directly probe the existence and nature of dark energy. We estimate this effect and show that the current gravitational lensing experiments are sensitive to the direct probe of dark energy at astrophysical scales. For the special case $w=-1$, our independent study favors the previous works that the cosmological constant can affect light bending, although our prediction qualitatively and quantitatively differ from the literature, including our consistent realization of $\Delta\alpha_{DE}\to 0$ (under $M \to 0$) at the leading order., Comment: 30pp. JCAP final version. All conclusions un-changed. Refinements and references added. (This update is delayed due to author's traveling)

The next-generation lepton colliders, such as CEPC, FCC-ee, and ILC will make precision measurement of the Higgs boson properties. We first extract the Higgs coupling precision from Higgs observables at CEPC to illustrate the potential of future lepton colliders. Depending on the related event rates, the precision can reach percentage level for most couplings. Then, we try to estimate the new physics scales that can be indirectly probed with Higgs and electroweak precision observables. The Higgs observables, together with the existing electroweak precision observables, can probe new physics up to 10TeV (40TeV for the gluon-related operator $\mathcal O_g$) at 95% C.L. Including the $Z/W$ mass measurements and $Z$-pole observables at CEPC further pushes the limit up to 35TeV. Although $Z$-pole running is originally for the purpose of machine calibration, it can be as important as the Higgs observables for probing the new physics scales indirectly. The indirect probe of new physics scales at lepton colliders can mainly cover the energy range to be explored by the following hadron colliders of pp (50-100TeV), such as SPPC and FCC-hh., Comment: 15pp. Presentation at IAS Program on HEP (Jan-2016). -- Our updated analyses and fits appeared in journal paper JHEP 1610 (2016) 007 [arXiv:1603.03385]

Leptonic unitarity triangle (LUT) provides fundamental means to geometrically describe CP violation in neutrino oscillation. In this work, we use LUT to present a new geometrical interpretation of the vacuum oscillation probability, and derive a compact new oscillation formula in terms of only 3 independent parameters of the corresponding LUT. Then, we systematically study matter effects in the geometrical formulation of neutrino oscillation with CP violation. Including nontrivial matter effects, we derive a very compact new oscillation formula by using the LUT formulation. We further demonstrate that this geometrical formula holds well for applications to neutrino oscillations in matter, including the long baseline experiments T2K, MINOS, NOvA, and DUNE., Comment: PRD Final Version (9pp, 5 Figs). All results/conclusions un-changed. Further added new Fig.5 for analysis of LBL experiment DUNE. Only minor rewording to clarify the Importance of this work

We extend our previous study of supersymmetric Higgs inflation in the context of no-scale supergravity and grand unification, to include models based on the flipped SU(5) and the Pati-Salam group. Like the previous SU(5) GUT model, these yield a class of inflation models whose inflation predictions interpolate between those of the quadratic chaotic inflation and Starobinsky-like inflation, while avoiding tension with proton decay limits. We further analyse the reheating process in these models, and derive the number of e-folds, which is independent of the reheating temperature. We derive the corresponding predictions for the scalar tilt and the tensor-to-scalar ratio in cosmic microwave background perturbations, as well as discussing the gravitino production following inflation., Comment: JCAP Final Version. 23pp, 3 Figs. Only minor refinements, references added

New physics beyond the standard model (SM) can be model-independently formulated via dimension-6 effective operators, whose coefficients (cutoffs) characterize the scales of new physics. We study the probe of new physics scales from the electroweak precision observables (EWPO) and the Higgs observables (HO) at the future $e^+e^-$ Higgs factory (such as CEPC). To optimize constraints of new physics from all available observables, we establish a scheme-independent approach. With this formulation, we treat the SM electroweak parameters and the coefficients of dimension-6 operators on equal footing, which can be fitted simultaneously by the same $\chi^2$ function. As deviations from the SM are generally small, we can expand the new physics parameters up to linear order and perform an analytical $\chi^2$ fit to derive the potential reach of the new physics scales. We find that the HO from both Higgs produnction and decay rates can probe the new physics scales up to 10TeV (and to 44TeV for the case of gluon-involved operator $\mathcal{O}_g$), and the new physics scales of Yukawa-type operators can be probed by the precision Higgs coupling measurements up to (13-25)TeV. Further including the EWPO can push the limit up to 35TeV. From this prospect, we demonstrate that the EWPO measured in the early phase of a Higgs factory can be as important as the Higgs observables. These indirect probes of new physics scales at the Higgs factory can mainly cover the energy range to be directly explored by the next generation hadron colliders of pp(50-100TeV), such as the SPPC and FCC-hh., Comment: JHEP Final Version, 43 pages, 10 Tables, 6 Figs, using jheppub.sty format, only minor refinements

LHC Run-2 has provided intriguing di-photon signals of a new resonance around 750GeV, which, if not due to statistical fluctuations, must call for new physics beyond the standard model (SM) at TeV scale. We propose a minimal extension of the SM with a complex singlet scalar $\mathcal{S}$ and a doublet of vector-like quarks. The scalar sector respects CP symmetry, with its CP-odd imaginary component $\chi$ providing a natural dark matter (DM) candidate. The real component of $\mathcal{S}$ serves as the new resonance (750GeV) and explains the diphoton excess of the LHC Run-2. The new scalar degrees of freedom of $\mathcal{S}$ help to stabilize the Higgs vacuum, and can realize the Higgs inflation around GUT scale, consistent with the current cosmology observations. We construct two representative samples A and B of our model for demonstration. We study the mono-jet signals of the DM production from invisible decays Re$(\mathcal{S}) \to \chi\chi$ at the LHC Run-2. We further derive the DM relic density bound, and analyze the constraints from direct and indirect DM detections., Comment: Phys.Lett.B Final Version. 16pp (7 Figs + 2 Tables). Only minor text refinements, references added

Current data from neutrino oscillation experiments are in good agreement with $\delta =-\frac{\pi}{2}$ and $\theta_{23}^{} = \frac{\pi}{4}$. We define the notion of "constrained maximal CP violation" (CMCPV) for predicting these features and study their origin in flavor symmetry. We derive the parametrization-independent solution of CMCPV and give a set of equivalent definitions for it. We further present a theorem on how the CMCPV can be realized. This theorem takes advantage of residual symmetries in the neutrino and charged lepton mass matrices, and states that, up to a few minor exceptions, $(|\delta |, \theta_{23}) =(\frac{\pi}{2}, \frac{\pi}{4})$ is generated when those symmetries are real. The often considered $\mu$-$\tau$ reflection symmetry, as well as specific discrete subgroups of O(3), are special cases of our theorem., Comment: Phys.Lett.B Final Version, 13pp. All conclusions unchanged, only minor improvement to stress the parametrization-independence of our CMCPV

The LHC discovery of a light Higgs particle $h^0$ (125GeV) opens up new prospect for searching heavier Higgs boson(s) at the LHC Run-2, which will unambiguously point to new physics beyond the standard model (SM). We study the detection of a heavier neutral Higgs boson $H^0$ via di-Higgs production channel at the LHC (14TeV), $H^0 \to h^0h^0 \to WW^*\gamma\gamma$. This directly probes the $Hhh$ cubic Higgs interaction, which exists in most extensions of the SM Higgs sector. For the decay products of final states $WW^*$, we include both pure leptonic mode $WW^* \to \ell\bar{\nu}\bar{\ell}\nu$ and semi-leptonic mode $WW^* \to q\bar{q}'\ell\nu$. We analyze signals and backgrounds by performing fast detector simulation for the full processes $pp \to H \to hh \to WW^*\gamma\gamma \to \ell\bar{\nu}\bar{\ell}\nu\gamma\gamma$ and $pp \to H \to hh \to WW^*\gamma\gamma \to \ell\nu q\bar{q}'\gamma\gamma$, over the mass range $M_H=250-600$GeV. For generic two-Higgs-doublet models (2HDM), we present the discovery reach of the heavier Higgs boson at the LHC Run-2, and compare it with the current Higgs global fit of the 2HDM parameter space., Comment: Phys.Lett.B Final Version. 16pp (9 Figs + 4 Tables). Only minor refinements, references added

Despite the discovery of a Higgs boson h(125GeV) at the LHC Run-1, its self-interaction has fully evaded direct experimental probe so far. Such self-interaction is vital for electroweak symmetry breaking, vacuum stability and electroweak phase transition, and Higgs inflation. It is a most likely place to encode new physics beyond the standard model. We parametrize such new physics by model-independent dimension-6 effective operators, and study their tests via Higgs pair production at hadron colliders. We analyze three major di-Higgs production channels at parton level, and compare the parameter-dependence of total cross sections and kinematic distributions at the LHC(14TeV) and pp(100TeV) hadron collider. We further perform full simulations for the di-Higgs production channel $gg\to hh \to b\bar{b}\gamma\gamma$ and its backgrounds at the pp(100TeV) hadron collider. We construct four kinds of benchmark points, and study the sensitivities to probing different regions of the parameter space of cubic Higgs interactions. We find that for one-parameter analysis and with a 3/ab (30/ab) integrated luminosity, the $gg\to hh \to b\bar{b}\gamma\gamma$ channel can measure the SM cubic Higgs coupling and the derivative cubic Higgs coupling to an accuracy of about 13% (4.2%) and 5% (1.6%), respectively., Comment: 35pp (13 Figs, 2 Tables), PRD Journal Version, all results unchanged, only minor refinements, references added

Higgs inflation is attractive because it identifies the inflaton with the electroweak Higgs boson. In this work, we construct a new class of supersymmetric Higgs inflationary models in the no-scale supergravity with an SU(5) GUT group. Extending the no-scale Kahler potential and SU(5) GUT superpotential, we derive a generic potential for Higgs inflation that includes the quadratic monomial potential and a Starobinsky-type potential as special limits. This type of models can accommodate a wide range of the tensor-to-scalar ratio $r = O(10^{-3}-10^{-1})$, as well as a scalar spectral index $n_s \sim 0.96$., Comment: PRD-Rapid Communication, final version, 6pp, only minor rewordings and Refs added

So far all evidences of dark matter (DM) come from astrophysical and cosmological observations, due to gravitational interactions of the DM. It is possible that the true DM particle in the universe joins gravitational interactions only, but nothing else. Such a Gravitational DM (GDM) acts as a weakly interacting massive particle (WIMP), which is conceptually simple and attractive. In this work, we explore this direction by constructing the simplest scalar GDM particle $\chi_s$. It is a $Z_2$ odd singlet under the standard model (SM) gauge group, and naturally joins the unique dimension-4 interaction with Ricci curvature, $\xi_s \chi_s^2 R$, where $\xi_s$ is the dimensionless nonminimal coupling. We demonstrate that this gravitational interaction $\xi_s \chi_s^2 R$, together with Higgs-curvature nonminimal coupling term $\xi_h H^\dag H R$, induces effective couplings between $\chi_s^2$ and SM fields which can account for the observed DM thermal relic abundance. We analyze the annihilation cross sections of GDM particles and derive the viable parameter space for realizing the DM thermal relic density. We further study the direct/indirect detections and the collider signatures of such a scalar GDM. These turn out to be highly predictive and testable., Comment: 33pp, JCAP Final Version. Only minor rewordings, references added

We construct a new inflation model in which the standard model Higgs boson couples minimally to gravity and acts as the inflaton. Our construction of Higgs inflation incorporates the standard model with Einstein gravity which exhibits asymptotic safety in the ultraviolet region. The slow roll condition is satisfied at large field value due to the asymptotically safe behavior of Higgs self-coupling at high energies. We find that this minimal construction is highly predictive, and is consistent with both cosmological observations and collider experiments., Comment: 16pp, to match JCAP Final Version, only minor refinements, references added

The recent IceCube observation of ultra-high-energy astrophysical neutrinos has begun the era of neutrino astronomy. In this work, using the unitarity of leptonic mixing matrix, we derive nontrivial unitarity constraints on the flavor composition of astrophysical neutrinos detected by IceCube. Applying leptonic unitarity triangles, we deduce these unitarity bounds from geometrical conditions, such as triangular inequalities. These new bounds generally hold for three flavor neutrinos, and are independent of any experimental input or the pattern of leptonic mixing. We apply our unitarity bounds to derive general constraints on the flavor compositions for three types of astrophysical neutrino sources (and their general mixture), and compare them with the IceCube measurements. Furthermore, we prove that for any sources without $\nu_\tau$ neutrinos, a detected $\nu_\mu$ flux ratio $< 1/4$ will require the initial flavor composition with more $\nu_e$ neutrinos than $\nu_\mu$ neutrinos., Comment: JCAP Final Version. 24pp. Only minor refinements, references added

Higgs inflation is among the most economical and predictive inflation models, although the original Higgs inflation requires tuning the Higgs or top mass away from its current experimental value by more than $2\sigma$ deviations, and generally gives a negligible tensor-to-scalar ratio $r \sim 10^{-3}$ (if away from the vicinity of critical point). In this work, we construct a minimal extension of Higgs inflation, by adding only two new weak-singlet particles at TeV scale, a vector-quark $T$ and a real scalar $S$. The presence of singlets $(T, S)$ significantly impact the renormalization group running of the Higgs boson self-coupling. With this, our model provides a wider range of the tensor-to-scalar ratio $r = O(0.1 - 10^{-3})$, consistent with the favored $r$ values by either BICEP2 or Planck data, while keeping the successful prediction of the spectral index $ n_s \simeq 0.96 $. It further allows the Higgs and top masses to fully fit the collider measurements. We also discuss implications for searching the predicted TeV-scale vector-quark $T$ and scalar $S$ at the LHC and future high energy pp colliders., Comment: 20pp, to match JCAP Final Version

We study gravitational interaction of Higgs boson through the unique dimension-4 operator $\xi H^\dag H R$, with $H$ the Higgs doublet and $R$ the Ricci scalar curvature. We analyze the effect of this dimensionless nonminimal coupling $\xi$ on weak gauge boson scattering in both Jordan and Einstein frames. We explicitly establish the longitudinal-Goldstone boson equivalence theorem with nonzero $\xi$ coupling in both frames, and analyze the unitarity constraints. We study the $\xi$-induced weak boson scattering cross sections at O(1-30)TeV scales, and propose to probe the Higgs-gravity coupling via weak boson scattering experiments at the LHC(14TeV) and the next generation pp colliders (50-100TeV). We further extend our study to Higgs inflation, and quantitatively derive the perturbative unitarity bounds via coupled channel analysis, under large field background at the inflation scale. We analyze the unitarity constraints on the parameter space in both the conventional Higgs inflation and the improved models in light of the recent BICEP2 data., Comment: 40pp, JCAP Final Version. Use jcappub.sty, only minor rewordings, references added

Leptonic unitarity triangle (LUT) provides a geometric description of CP violations in the lepton-neutrino sector and is directly measurable in principle. In this work, we reveal that the angles in the LUT have definite physical meaning, and demonstrate the exact connection of the LUT to neutrino oscillations. For the first time, we prove that these leptonic angles act as phase shifts in neutrino oscillations, by shifting \Delta m^{2}L/2E to \Delta m^{2}L/2E + \alpha, where (L, E, \alpha) denote the baseline length, neutrino energy and corresponding angle of the LUT. Each LUT has three independent parameters and contains only partial information of the PMNS matrix. We demonstrate that the partial information in each LUT can describe the corresponding neutrino oscillation. Hence, for the first time, we uncover that any given kind of neutrino oscillations contain at most three (rather than four) independent degrees of freedom from the PMNS matrix. This may provide a cleaner way for fitting the corresponding oscillation data., Comment: Phys.Rev.D published version. All results/conclusions un-changed. Only minor refinement to clarify the Importance of this work. (Used latest neutrino data.)

Under conventional Legendre transformation, systems with a non-convex Lagrangian will result in a multi-valued Hamiltonian as a function of conjugate momentum. This causes problems such as non-unitary time evolution of quantum state and non-determined motion of classical particles, and is physically unacceptable. In this work, we propose a new construction of single-valued Hamiltonian by applying Legendre-Fenchel transformation, which is a mathematically rigorous generalization of conventional Legendre transformation, valid for non-convex Lagrangian systems, but not yet widely known to the physics community. With the new single-valued Hamiltonian, we study spontaneous breaking of time translation symmetry and derive its vacuum state. Applications to theories of cosmology and gravitation are discussed., Comment: Journal Version, 16pp. All results + conclusions un-changed, only minor refinements to clarify the importance of our new LFT method and its physics applications; references added