Two-Higgs-Doublet Model with Soft CP-violation Confronting Electric Dipole Moments and Colliders
Kingman Cheung, Adil Jueid, Ying-nan Mao, Stefano Moretti
备注：
60 pages in one column (34 pages in two columns), 14 figures, 11 tables, PRDaccepted version. Introduction and EDM parts updated with brief discussion about EW baryogenesis. Collider part updated through better selection cuts to improve the significance. References added
We analyze CP-violating effects in both Electric Dipole Moment (EDM) measurements and future analyses at the Large Hadron Collider (LHC) assuming a Two-Higgs-Doublet Model (2HDM) with "soft" CP-violation. Our analysis of EDMs and current LHC constraints shows that, in the case of a 2HDM Type II and Type III, an $\mathcal{O}(0.1)$ CP-violating phase in the Yukawa interaction between $H_1$ (the $125~\textrm{GeV}$ Higgs boson) and fermions is still allowed. For these scenarios, we study CP-violating effects in the neutron EDM and $t\bar{t}H_1$ production at the LHC. Our analysis shows that such an $\mathcal{O}(0.1)$ CP-violating phase can be easily confirmed or excluded by future neutron EDM tests, with LHC data providing a complementary cross-check.
The Inert Doublet Model (IDM) is a simple extension of the Standard Model (SM) that aims to address the naturalness problem, electroweak baryogenesis and accommodate a viable dark matter (DM) candidate, along with a rich phenomenlogy in terms of collider signatures. In this note, we address the constraints on the IDM by recasting dilepton + missing energy searches performed for Supersymmetry at LHC run-1 using Madanalysis5.
Recent study of gamma rays originating from the region of galactic centre has confirmed an anomalous $γ$-ray excess within the energy range 1-3 GeV. This can be explained as the consequence of pair annihilation of a 31-40 GeV dark matter into $b \bar b$ with thermal annihilation cross-section $σv \sim 1.4-2.0 \times 10^{-26}~\rm{cm^3/s}$. In this work we revisit the Inert Doublet Model (IDM) in order to explain this gamma ray excess. Taking the lightest inert particle (LIP) as a stable DM candidate we show that a 31-40 GeV dark matter derived from IDM will fail to satisfy experimental limits o…
A sequential fourth generation is known to be excluded because the non-decoupling contribution to $κ_g$, the Higgs coupling modifier with a gluon pair, is unacceptably large. Recently a new way to save the model was suggested in the Type-II two Higgs doublet model: if the Yukawa couplings of down-type fermions have wrong-sign, the contributions from $t'$ and $b'$ to $κ_g$ are cancelled. We study the theoretical and experimental constraints on this model, focusing on the heavy Higgs bosons. Two constraining features are pointed out. First the exact wrong-sign limit does not allow the alignment,…
The recent Fermilab measurement of the muon anomalous magnetic moment yields $4.2 σ$ deviations from the SM prediction when combined with the BNL E821 experiment results. In the Type-X two Higgs doublet model, we study the consequence of imposing the observed muon $g-2$, along with the constraints from theoretical stabilities, electroweak oblique parameters, Higgs precision data, and direct searches. For a comprehensive study, we scan the whole parameter space in two scenarios, the normal scenario where $h_{\rm SM} = h$ and the inverted scenario where $h_{\rm SM}=H$, where $h$ ($H$) is the lig…
We consider a fermionic dark matter (DM) in the left-right symmetric framework by introducing a pair of vector-like (VL) doublets in the particle spectrum. The stability of the DM is ensured through an unbroken $\mathcal{Z}_2$ symmetry. We explore the parameter space of the model compatible with the observed relic density and direct and indirect detection cross sections. The presence of charged dark fermions opens up an interesting possibility for the doubly charged Higgs signal at LHC and ILC. The signal for the doubly charged scalar decaying into the dark sector is analyzed in multilepton fi…
We perform a comprehensive analysis for the light scalar dark matter (DM)in the Inert two Higgs doublet model (i2HDM) with compressed mass spectra, small mass splittings among three $\mathbb{Z}_2$ odd particles---scalar $S$, pseudo-scalar $A$, and charged Higgs $H^\pm$. In such a case, the co-annihilation processes play a significant role to reduce DM relic density. As long as a co-annihilation governs the total interaction rate in the early universe, a small annihilation rate is expected to reach a correct DM relic density and its coupling $λ_S$ between DM pair and Higgs boson shall be tiny. …
We consider the di-photon signal arises from two bunches of collimated photon jets emitting from a pair of highly boosted scalars. Following the discussion of detecting the photon jets at the collider, we extend the two-Higgs-doublet model (2HDM) by adding a gauge singlet scalar. To explain the di-photon excess which is recently observed at the first 13 TeV run of the LHC, the mixing between the heavy doublet state and the newly added singlet is crucially needed. After the mixing, one can have a heavy Higgs state $Y_2$ at 750 GeV and a very singlet-like scalar $Y_1$ of sub-GeV, which would be …
We study the Electric Dipole moment of b quark in the general two Higgs Doublet model (model III) and three Higgs Doublet model with O(2) symmetry in the Higgs sector. We analyse the dependency of this quantity to the new phase coming from the complex Yukawa couplings and masses of charged and neutral Higgs bosons. We see that the Electric Dipole moment of b quark is at the order of 10^{-20} e cm, which is an extremely large value compared to one calculated in the SM and also two Higgs Doublet model (model II) with real Yukawa couplings.
We study the lepton electric dipole moments in the split fermion scenario, in the two Higgs doublet model, where the new Higgs scalars are localized around the origin in the extra dimension, with the help of the localizer field. We observe that the numerical value of the electron (muon, tau) electric dipole moment is at the order of the magnitude of 10^{-31} (10^{-24}, 10^{-22}) (e-cm) and this quantity is sensitive the new Higgs localization in the extra dimension.
We study the the effects of non-universal extra dimensions on the electric dipole moments of fermions in the two Higgs doublet model. We observe that the t quark and b quark electric dipole moments are sensitive to the extra dimensions, however, in the case of charged lepton electric dipole moments, this sensitivity is relatively weak.
We predict the charged lepton electric dipole moments in the split fermion scenario in the framework of the two Higgs doublet model. We observe that the numerical value of the muon (tau) electric dipole moment is at the order of the magnitude of $10^{-22} (e-cm)$ ($10^{-20} (e-cm)$) and there is an enhancement in the case of two extra dimensions, especially for the tau lepton electric dipole moment.
The present work introduces new scalar and fermionic degrees of freedom to the Standard Model. While the scalar sector is augmented by a complex scalar triplet and a doubly charged scalar singlet, the fermionic sector is extended by two copies of vector-like leptons. Of these, one copy is an $SU(2)_L$ singlet while the other, an $SU(2)_L$ doublet. We explain how this combination can offer a solution to the muon g-2 anomaly and also lead to non-zero neutrino masses. In addition, it is also shown that the parameter regions compliant with the two aforementioned issues can stabilise the electrowea…
The electric and weak electric dipole form factors for heavy fermions are calculated in the context of the most general two-Higgs-doublet model (2HDM). We find that the large top mass can produce a significant enhancement of the electric dipole form factor in the case of the b and c quarks. This effect can be used to distinguish between different 2HDM scenarios.
We study the electric and chromo electric dipole moment of top quark in the general two Higgs Doublet model (model III). We analyse the dependency of this quantity to the new phases coming from the complex Yukawa couplings and masses of charged and neutral Higgs bosons. We observe that the electric and chromo elecric dipole moments of top quark are at the order of 10^{-21} e cm and 10^{-20} g_s cm, which are extremely large values compared to ones calculated in the SM and also two Higgs Doublet model with real Yukawa couplings.
Current data on the signal strengths and angular spectrum of the 125.5 GeV Higgs boson still allow a CP-mixed state, namely, the pseudoscalar coupling to the top quark can be as sizable as the scalar coupling: $C_u^S \approx C_u^P =1/2$. CP violation can then arise and manifest in sizable electric dipole moments (EDMs). In the framework of two-Higgs-doublet models, we not only update the Higgs precision (Higgcision) study on the couplings with the most updated Higgs signal strength data, but also compute all the Higgs-mediated contributions from the 125.5 GeV Higgs boson to the EDMs, and confr…
We calculate the electric dipole moment of electron using the experimental result of muon electric dipole moment and upper limit of the BR(μ--> eγ) in the framework of the general two Higgs doublet model. Our prediction is 10^{-32} e-cm, which lies in the experimental current limits. Further, we obtain constraints for the Yukawa couplings \barξ^{D}_{N,τe} and \barξ^{D}_{N,τμ}. Finally we present an expression which connects the BR(τ\to μγ) and the electric dipole moment of τ-lepton and study the relation between these physical quantities.
In this work we study the anomalous top quark-gluon couplings Chromoelectric Dipole Moment (CEDM) and Chromomagnetic Dipole Moment (CMDM) in a general THDM with CP violation. We find that this model provides an important contribution from the $Y_{tt}$ Yukawa coupling that needs to be taken into account. The CMDM and CEDM obtained are $-0.03<Δ\tilde{k} < 0.005}$ and $|Δ\tilde{d}| < 0.005$, respectively.
It is well-known that leptogenesis in low energy scale is difficult in the conventional Type-I seesaw mechanism with hierarchical right-handed neutrino masses. We show that in a class of two Higgs doublet model, where one Higgs doublet generates masses of quarks and charged leptons whereas the other Higgs doublet with a tiny vacuum expectation value generates neutrino Dirac masses, large Yukawa couplings lead to a large enough CP asymmetry of the right-handed neutrino decay. Thermal leptogenesis suitably works at low energy scale as keeping no enhancement of lepton number violating wash out ef…
The effect of the "chromo-electric" dipole moment on the electric dipole moment(EDM) of the neutron is studied in the two-Higgs-doublet model. The Weinberg's operator $O_{3g}=GG\t G$ and the operator $O_{qg}=\bar qσ\t Gq$ are both investigated in the cases of $\tan\b\gg 1$, $\tan\b\ll 1$ and $\tan\b\simeq 1$. The neutron EDM is considerably reduced due to the destructive contribution with two light Higgs scalars exchanges.
In this thorough study we focus on the indirect detection of Dark Matter (DM) through the confrontation of unexplained galactic and extragalactic $γ$-ray signatures for a low mass DM model. For this, we consider a simple Higgs-portal DM model, namely, the inert Higgs doublet model (IHDM) where the Standard Model is extended with an additional complex SU(2)$_L$ doublet scalar. The stability of the DM candidate in this model, i.e., the lightest neutral scalar component of the extra doublet, is ensured by imposing discrete $\mathbb{Z}_2$ symmetry. The reduced-$χ^2$ analysis with the theoretical, …
Almost all data collected at the LHC during the 7 and 8 TeV runs has now been analysed by the ATLAS and CMS collaborations. Its consistency with the Standard Model (SM) predictions has cornered the CP-conserving two-Higgs doublet model (2HDM) into the SM limit, sin (β-α) = 1. However, there are still allowed regions of the 2HDM parameter space away from this limit. In this work we discuss how the 2HDM is performing in view of the LHC data together with the remaining available experimental and theoretical constraints.
In the framework of a two Higgs doublet model type I and type II, we calculate limits on neutrino masses for the different types of neutrinos, by using the experimental bounds on their magnetic dipole moments. This is carried out by analyzing diagrams of Cherenkov neutrino decays with a charged Higgs into the loop, coming from the two Higgs doublet model (2HDM). Such constraints are translated into allowed regions in the free parameters of the models, for each neutrino flavor. The analysis was performed by sweeping the charged Higgs mass between (100-900)GeV and taking into account the experim…
The electroweak phase transition can be made first order by extending the Standard Model (SM) Higgs sector with extra scalars. The same new physics can explain the matter-antimatter asymmetry of the universe by supplying an extra source of CP violation and sphaleron processes. In this paper we study the existence of a strong first order electroweak phase transition (SFOEWPT) in the type-I and type-II two Higgs doublet models (2HDM). We focus on how the SFOEWPT requirement constraints the spectrum of non-SM Higgs. Through a parameter space scan, we find that SFOEWPT suggests upper limits on the…
We study the electric dipole moments(EDM) of the neutron and the electron in the two-Higgs-doublet model, in the case that $CP$ symmetry is violated maximally in the neutral Higgs sector. We take account of the Weinberg's operator $O_{3g}=GG\t G$ as well as the operator $O_{qg}=\bar qσ\tilde Gq$ for the neutron, and the Barr-Zee diagrams for the electron. It is found that the predicted neutron EDM could be considerably reduced by the destructive contribution of the two Higgs scalars to get the lower value than the experimental bound. As to the electron EDM, the predicted value is smaller in on…
We study the effect of the "chromo-electric" dipole moment on the electric dipole moment(EDM) of the neutron in the two Higgs doublet model. We systematically investigate the Weinberg's operator $O_{3g}=GG\t G$ and the operator $O_{qg}=\bar qσ\t Gq$, in the cases of $\tan\b\gg 1$, $\tan\b\ll 1$ and $\tan\b\simeq 1$. It is shown that $O_{sg}$ gives the main contribution to the neutron EDM compared to the other operators, and also that the contributions of $O_{ug}$ and $O_{3g}$ cancel out each other. It is pointed out that the inclusion of second lightest neutral Higgs scalar adding to the light…
The electric dipole moment of the muon ($d_μ$) is evaluated in a two Higgs doublet model with a softly broken discrete symmetry. The leading contributions from both one loop and two loop diagrams are considered. For $\tanβ\equiv |v_2|/|v_1|$ close to one, contributions from two loop diagrams involving the $t$ quark and the $W$ boson dominate; while for $\tanβ\agt 10$, contributions from two loop diagrams involving the $b$ quark and the $τ$ lepton are dominant. In these two regions, $d_μ\approx (m_μ/m_e) d_e$. For $8 \agt \tanβ\agt 4$, significant cancellation occurs among the contributions fro…
An appended sector of two octet-colored scalars, each an electroweak doublet, is an interesting extension of the simple two Higgs doublet model motivated by the minimal flavor violation. Their rich CP violating interaction gives rise to a sizable electron electric dipole moment, besides the quark electric dipole moment via the two-loop contribution of Barr-Zee mechanism.
We update indirect constraints on Electro-Weak Dark Matter (EWDM) considering the Sommerfeld-Ramsauer-Townsend (SRT) effect for its annihilations into a pair of standard model gauge bosons assuming that EWDM accounts for the observed dark matter (DM) relic density for a given DM mass and mass gaps among the multiplet components. For the radiative or smaller mass splitting, the hypercharged triplet and higher multiplet EWDMs are ruled out up to the DM mass ~ 10 - 20 TeV by the combination of the most recent data from AMS-02 (antiproton), Fermi-LAT (gamma-ray), and HESS (gamma-line). The Majoran…
I consider contributions to the neutron electric dipole moment within Two Higgs Doublet Models which allow for small flavor changing neutral Higgs couplings. In a previous paper, I considered flavor changing interactions for the Standard Model Higgs boson to first order in the flavor changing coupling. In that paper I found that the obtained value of the neutron electric dipole moment were below the present experimental limit, given previous restrictions on such couplings. Because this was an effective theory, the result depended on an ultraviolet cut off $Λ$, parametrized as $ln(Λ^2)$. In the…
We propose a CP-violating source in the charged Higgs sector of a 3-Higgs Doublet Model (3HDM) that will contribute to three CP-asymmetry observables for low energy processes. In the context of such a 3HDM, a measurement of one of the specific asymmetry observables (i.e., $\bar{B} \to X_{s+d} γ$) could obtain up to 2.5% or more, which would give a 5$σ$ evidence for physics Beyond the SM (BSM) from the full BELLE II data set. In addition to these CP-violating observables, the current measurements of Electron Dipole Moments (EDMs) constrain the available parameter region of the CP-violating 3HDM…
We investigate the effects of the new scalars in a two-Higgs-doublet model on the weak magnetic dipole moments of the fermions at the $Z$ peak. Proportionality of the Yukawa couplings to the fermion masses, and to $\tanβ$, makes such effects more important for the third family, and potentially relevant. For the $τ$ lepton, the new diagrams are suppressed by $v_τ= 2 \sin^2 θ_W - 1/2$, or by powers of $m_τ/M_Z$, but may still be comparable to the SM electroweak contributions. In contrast, we find that the new contributions for the bottom quark may be much larger than the SM electroweak contribut…
Parton distributions can be defined in terms of the entropy of entanglement between the spatial region probed by deep inelastic scattering (DIS) and the rest of the proton. For very small $x$, the proton becomes a maximally entangled state. This approach leads to a simple relation $S = \ln N $ between the average number $N$ of color-singlet dipoles in the proton wave function and the entropy of the produced hadronic state $S$. At small $x$, the multiplicity of dipoles is given by the gluon structure function, $N = x G(x,Q^2)$. Recently, the H1 Collaboration analyzed the entropy of the produced…
In several frameworks for leptons-sectors of two Higgs doublet models, we calculate the magnetic dipole moment for the different flavor types of neutrino. Computations are carried out by assuming a normal hierarchy for neutrino masses, and analyzing the process $ν\rightarrow νγ$ with a charged Higgs boson into the loop. The analysis was performed by sweeping the charged Higgs mass and taking into account the experimental constraints for relevant parameters in Two Higgs Doublet Models with and without flavor changing neutral currents; obtaining magnetic dipole moments close to the experimental …
We confront the indications of lepton flavor universality (LFU) violation observed in semi-tauonic $B$ meson decays with new physics (NP) searches using high $p_T$ tau leptons at the LHC. Using effective field theory arguments we correlate possible non-standard contributions to semi-tauonic charged currents with the $τ^+ τ^-$ signature at high energy hadron colliders. Several representative standard model extensions put forward to explain the anomaly are examined in detail: (i) weak triplet of color-neutral vector resonances, (ii) second Higgs doublet and (iii) scalar or (iv) vector leptoquark…
The contributions of a second Higgs doublet to the electron electric dipole moment near the heavy Higgs decoupling limit are determined within an effective field theory framework. In models that satisfy the Glashow-Weinberg condition, the leading contributions in this limit at effective dimension six are shown to come from two-loop Barr-Zee diagrams that include the Standard Model-like Higgs boson. Additional diagrams that include heavy Higgs bosons are sub-leading and contribute only at effective dimension eight near the decoupling limit. This simplification implies that to leading order in t…
The leptonic branching fractions of the tau lepton are sensitive to anomalous charged current interactions. We use recent experimental measurements to determine the weak charged current magnetic and electric dipole moments and the Michel parameter $η$ with unprecedented precision. These results are then used to constrain the tau compositeness scale and the allowed parameter space for Higgs doublet models.
The inert Zee model is an extension of the Zee model for neutrino masses to allow for a solution to the dark matter problem that involves two vector-like fields, a doublet and a singlet of $SU(2)_L$, and two scalars, also a doublet and a singlet of $SU(2)_L$, all of them being odd under an exact $Z_2$ symmetry. The introduction of the $Z_2$ guarantees one-loop neutrino masses, forbids tree-level Higgs-mediated flavor changing neutral currents and ensures the stability of the dark matter candidate. Due to the natural breaking of lepton numbers in the inert Zee model and encouraged by the ambiti…
Electric dipole moments are extremely sensitive probes for additional sources of CP violation in new physics models. Specifically, they have been argued in the past to exclude new CP-violating phases in two-Higgs-doublet models. Since recently models including such phases have been discussed widely, we revisit the available constraints in the presence of mechanisms which are typically invoked to evade flavour-changing neutral currents. To that aim, we start by assessing the necessary calculations on the hadronic, nuclear and atomic/molecular level, deriving expressions with conservative error …
We investigate a two Higgs doublet model with extra flavour depending $U(1)_X$ gauge symmetry where $Z'$ boson interactions can explain the Atomki anomaly by choosing appropriate charge assignment for the SM fermions. For parameter region explaining the Atomki anomaly we obtain light scalar boson with $\mathcal{O}(10)$ GeV mass, and we explore scalar sector to search for allowed parameter space. We then discuss anomalous magnetic dipole moment of muon and lepton flavour violating processes induced by Yukawa couplings of our model.
In the context of a Two-Higgs-Doublet Model in which Minimal Flavour Violation (MFV) is imposed, one can allow the presence of flavour-blind CP-violating phases without obtaining electric dipole moments that overcome the experimental bounds. This choice permits to accommodate the hinted large phase in the $B_s$ mixing and, at the same time, to soften the observed anomaly in the relation between $ε_K$ and $S_{ψK_S}$.
We calculate lepton flavor violating Z -> l^+ l^- decay in the framework of the general two Higgs Doublet model. In our calculations we used the constraints for the Yukawa couplings \barξ^{D}_{N,τe} and \barξ^{D}_{N,τμ} coming from the experimental result of muon electric dipole moment and upper limit of the BR(μ-> eγ). We observe that it is possible to reach the present experimental upper limits for the branching ratios of such Z decays in the model III.
We calculate the new physics effects on the anomalous magnetic moment of the muon in the framework of the two Higgs doublet model. We predict an upper bound for the lepton flavor violating coupling, which is responsible for the point like interaction between muon and tau, by using the uncertainty in the experimental result of the muon anomalous magnetic moment. We show that the upper bound predicted is more stringent compared to the one which is obtained by using the experimental result of the muon electric dipole moment
A two Higgs doublet model with special Yukawa interactions for the top quark and a softly broken discrete symmetry in the Higgs potential is proposed. In this model, the top quark is much heavier than the other quarks and leptons because it couples to a Higgs doublet with a much larger vacuum expectation value. The electric dipole moment (EDM) of the electron is evaluated with loop diagrams of the third generation fermions as well as the charm quark. The electron EDM is significantly enhanced for a naturally large $\tanβ\equiv |v_2|/|v_1|$.
We study CP violation in a multi-Higgs doublet model based on a $S_3 \times Z_3$ horizontal symmetry. We consider two mechanisms for CP violation in this model: a) CP violation due to complex Yukawa couplings; and b) CP violation due to scalar-pseudoscalar mixings. We find that the predictions for $ε'/ε$, CP violation in B decays and the electric dipole moments of neutron and electron are different between these two mechanisms. These predictions are also dramatically different from the minimal Standard Model predictions.
The two principles of spontaneous CP violation and natural flavor conservation can be realized in the $SU(2)_{L}\times U(1)_{Y}$ model with two Higgs doublets. In particular, this model provides a consistent application to the CP violating parameters $ε$ and $ε'/ε$ in kaon decay and the neutron electric dipole moment. The masses of the exotic scalars are unconstrained in this model and probing these exotic scalars must be valuable at the present energy scales. Large CP violations may also occur in the heavy quark and lepton sectors.
We study the complete one-loop contributions to the chromagnetic dipole moment $Δκ$ of the top quark in the Standard Model, two Higgs doublet models, topcolor assited technicolor models (TC2), 331 models and extended models with a single extra dimension. We find that the SM predicts $Δκ= - 0.056$ and that the predictions of the other models are also consitent with the constraints imposed on $Δκ$ by low-energy precision measurements.
We revisit the minimal Nambu-Goldstone (NG) Higgs supersymmetric (SUSY) SU(5) grand unified model and study its phenomenological implications. The Higgs sector of the model possesses a global SU(6) symmetry, which is spontaneously broken and results in the Higgs doublets of the minimal SUSY Standard Model (MSSM) as NG chiral superfields. Therefore, the model naturally leads to light Higgs doublets and solves the doublet-triplet splitting problem. Because of the SU(6) symmetry, the couplings of the Higgs sector are tightly restricted, and thus the model is more predictive than the minimal SUSY …
We give explicit formulae for the anomalous chromomagnetic dipole moment of the top quark in the framework of the standard model, the two higgs doublet model and the minimal supersymmetric standard model. Finally, we compare the results for this coupling with the bound -0.03 <= Delta kappa <= 0.01 coming from analysis of b --> s gamma process whith an on-shell gluon.
We examine the one loop contributions arising in the Two-Higgs-Doublet Model (THDM) to the W-boson anomalous magnetic dipole and electric quadrupole form factors for both photon and Z couplings relevant at collider energies. While the model parameter and $q^2$-dependencies of these form factors are found to be significant, the corresponding size of these corrections are relatively small in comparison to unity. They are, however, found to be comparable in magnitude to the usual Standard Model loop corrections. Radiative corrections to the Higgs particle masses and couplings due to heavy top-qua…
Updated Constraints from Electric Dipole Moments in the MSSM with R-Parity Violation
Santa Cruz Institute for Particle Physics and Department of Physics, University of California Santa Cruz（加州大学圣克鲁兹分校物理系及粒子物理研究所）；Department of Physics and McDonnell Center for the Space Sciences, Washington University（华盛顿大学物理系及麦克唐纳空间科学中心）；PRISMA + Cluster of Excellence & Mainz Institute for Theoretical Physics, Johannes Gutenberg-Universität Mainz（约翰内斯·古腾堡美因茨大学美因茨理论物理研究所及PRISMA+卓越集群）；Physics Department, Brookhaven National Laboratory（布鲁克海文国家实验室物理系）；Department of Physics, Center for Field Theory and Particle Physics, Fudan University（复旦大学物理系及场论与粒子物理中心）
