The Standard Model calculation of $H\rightarrowγγ$ has the curious feature of being finite but regulator-dependent. While dimensional regularization yields a result which respects the electromagnetic Ward identities, additional terms which violate gauge invariance arise if the calculation is done setting $d=4$. This discrepancy between the $d=4-ε$ and $d=4$ results is recognized as a true ambiguity which must be resolved using physics input; as dimensional regularization respects gauge invariance, the $d=4-ε$ calculation is accepted as the correct SM result. However, here we point out another possibility; working in analogy with the gauge chiral anomaly, we note that it is possible that the individual diagrams do violate the electromagnetic Ward identities, but that the gauge-invariance-violating terms cancel when all contributions to $H\rightarrowγγ$, both from the SM and from new physics, are included. We thus examine the consequences of the hypothesis that the $d=4$ calculation is valid, but that such a cancellation occurs. We work in general renormalizable gauge, thus avoiding issues with momentum routing ambiguities. We point out that the gauge-invariance-violating terms in $d=4$ arise not just for the diagram containing a SM $W^{\pm}$ boson, but also for general fermion and scalar loops, and relate these terms to a lack of shift invariance in Higgs tadpole diagrams. We then derive the analogue of "anomaly cancellation conditions", and find consequences for solutions to the hierarchy problem. In particular, we find that supersymmetry obeys these conditions, even if it is softly broken at an arbitrarily high scale.
The possible role of the triangle mechanism in the $B^-$ decay into $D^{*0}π^-π^0η$ and $D^{*0}π^-π^+π^-$ is investigated. In this process, the triangle singularity appears from the decay of $B^-$ into $D^{*0}K^-K^{*0}$ followed by the decay of $K^{*0}$ into $π^-K^+$ and the fusion of the $K^+K^-$ which forms the $a_0(980)$ or $f_0(980)$ which finally decay into $π^0η$ or $π^+π^-$ respectively. The triangle mechanism from the $\bar{K}^*K\bar{K}$ loop generates a peak around 1420 MeV in the invariant mass of $π^-a_0$ or $π^-f_0$, and gives sizable branching fractions $Br(B^-\rightarrow D^{*0}π^…
We have investigated the cross section for the $π^-p\rightarrow K^0πΣ$ and $pp\rightarrow pK^+πΣ$ reactions paying attention to a mechanism that develops a triangle singularity. The triangle diagram is realized by the decay of a $N^*$ to $K^*Σ$ and the $K^*$ decay into $πK$, and the $πΣ$ finally merges into $Λ(1405)$. The mechanism is expected to produce a peak around $2140$ MeV in the $KΛ(1405)$ invariant mass. We found that a clear peak appears around $2100$ MeV in the $KΛ(1405)$ invariant mass which is about $40$ MeV lower than the expectation, and that is due to the resonance peak of a $N^…
We show the effects of a triangle singularity mechanism for the $γp \to K^+Λ(1405)$ reaction. The mechanism has a $N^*$ resonance around 2030 MeV, which decays into $K^* Σ$. The $K^*$ decays to $K^+ π$, and the $πΣ$ merge to form the $Λ(1405)$. This mechanism produces a peak around $\sqrt{s} = 2110$ MeV, and has its largest contribution around cos$θ=0$. The addition of this mechanism to other conventional ones, leads to a good reproduction of ${\rm d}σ/{\rm dcos}θ$ and the integrated cross section around this energy, providing a solution to a problem encountered in previous theoretical models.
We investigate the $Λ_b\toΛ_cπ^-f_0(980)$ production with a $f_0(980)$ decay into $π^+π^-$ via the $K^{*0}K^-K^+$ and $K^{*-}K^0\bar{K}^0$ triangle loops. These loops produce a peak around 1.42 GeV in the $π^-f_0(980)$ invariant mass distribution, which is the same mechanism as the one considered to explain the $a_1(1420)$ peak. In the $π^+π^-$ distribution obtained by fixing the $π^-f_0(980)$ invariant mass to some values, a clear peak of $f_0(980)$ is seen, and the $π^-f_0(980)$ distribution has a peak around $M_{π^-f_0}=1.42$ GeV, which is caused by the triangle mechanism of the $K^*\bar KK…
The decay of $Λ_c^+$ into $π^+π^0Λ(1405)$ with the $Λ(1405)$ decay into $π^0Σ^0$ through a triangle diagram is studied. This process is initiated by $ Λ_c^+ \to π^+ \bar{K}^*N $, then the $\bar{K}^*$ decays into $\bar{K} π$ and $\bar{K} N$ produce the $Λ(1405)$ through a triangle loop containing $\bar{K}^*N\bar{K}$ which develops a singularity around $1890$ MeV. This process is prohibited by the isospin symmetry, but the decay into this channel is enhanced by the contribution of the triangle diagram, which is sensitive to the mass of the internal particles. We find a narrow peak in the $π^0Σ^0…
In view of the observed strong hierarchy of the quark and lepton masses and of the flavor mixing angles it is argued that the description of flavor mixing must take this into account. One particular interesting way to describe the flavor mixing, which, however, is not the one used today, emerges, which is best suited for models of quark mass matrices based on flavor symmetries. We conclude that the unitarity triangle important for $B$ physics should be close to or identical to a rectangular triangle. CP violation is maximal in this sense.
We study the $J/ψ\rightarrow K^+ K^- f_0(980)(a_0(980))$ reaction and find that the mechanism to produce this decay develops a triangle singularity around $M_{\rm inv}(K^- f_0/K^- a_0) \approx 1515$~MeV. The differential width $dΓ/ dM_{\rm inv}(K^- f_0/K^- a_0)$ shows a rapid growth around the invariant mass being 1515~MeV as a consequence of the triangle singularity of this mechanism, which is directly tied to the nature of the $f_0(980)$ and $a_0(980)$ as dynamically generated resonances from the interaction of pseudoscalar mesons. The branching ratios obtained for the $J/ψ\rightarrow K^+ K^…
The BESIII Collaboration recently reported the observation of the $a_0(980)^0-f_0(980)$ mixing in the isospin breaking decay $J/ψ\to ηπ^0ϕ$. In the Dalitz plot for that decay with the $η$ reconstructed from two photons, there is a band around $1.4$~GeV on the $π^0 ϕ$ distribution. In general, this peak can be due to a resonance or a kinematic effect. In this paper, we study the effects of a set of $K^*K\bar K$ triangle diagrams, and show that due to triangle singularities such diagrams can lead to a peak around 1.4~GeV in the $π^0ϕ$ invariant mass distribution. The Dalitz plot induced by such …
We study the appearance of structures in the decay of the $B^-$ into $K^- π^- D_{s0}^+(2317)$ and $K^- π^- D_{s1}^+(2460)$ final states by forming invariant mass distributions of $π^- D_{s0}^+$ and $π^- D_{s1}^+$ pairs, respectively. The structure in the distribution is associated to the kinematical triangle singularity that appears when the $B^- \to K^- K^{*\,0} D^0$ ($B^- \to K^- K^{*\,0} D^{*\,0}$) decay process is followed by the decay of the $K^{*\,0}$ into $π^- K^+$ and the subsequent rescattering of the $K^+ D^0$ ($K^+ D^{*\,0}$) pair forming the $D_{s0}^+(2317)$ ($D_{s1}^+(2460)$) reso…
We have analyzed the singularities of a triangle loop integral in detail and derived a formula for an easy evaluation of the triangle singularity on the physical boundary. It is applied to the $Λ_b \rightarrow J/ψK^{-} p$ process via $Λ^*$-charmonium-proton intermediate states. Although the evaluation of absolute rates is not possible, we identify the $χ_{c1}$ and the $ψ(2S)$ as the relatively most relevant states among all possible charmonia up to the $ψ(2S)$. The $Λ(1890)\, χ_{c1}\, p$ loop is very special as its normal threshold and triangle singularities merge at about 4.45 GeV, generating…
We compare contributions from the triangle diagram and the $D\bar D^*$ bubble chain to the processes of $e^{+}e^{-}\rightarrow J/ψπ^{+}π^{-}$ and $e^{+}e^{-}\rightarrow (D\bar D^*)^\mpπ^{\pm}$. By fitting the $J/ψπ$ maximum spectrum and the $D\bar D^*$ spectrum, we find that the triangle diagram cannot explain the new data from BESIII Collaboration at center of mass at 4.23GeV and 4.26GeV, simultaneously. On the contrary, the molecular assignment of $Z_c(3900)$ gives a much better description.
We investigate the possibilities offered by the long baseline experiments T2K, No$ν$a, LBNE and LAGUNA for the evaluation of the neutrino mass hierarchy and CP violating phase $δ_{CP}$. We consider a neutrino and antineutrino energy in the interval [0.5,12] GeV. It is found that the clearest possible distinction between the two hierarchy signatures is provided by LAGUNA for an (anti)neutrino energy $E_{(\barν)ν}\simeq 0.5$ GeV in the $(\barν_μ \rightarrow \barν_μ) ν_μ\rightarrow ν_μ$ disappearance channel. For LBNE at $E_{\barν}\simeq 1$ GeV the $\barν_μ\rightarrow \barν_μ$ channel may also pr…
In the framework of a left-right model containing mirror fermions with gauge group SU(3)$_{C} \otimes SU(2)_{L} \otimes SU(2)_{R} \otimes U(1)_{Y^\prime}$, we estimate the neutrino masses, which are found to be consistent with their experimental bounds and hierarchy. We evaluate the decay rates of the Lepton Flavor Violation (LFV) processes $μ\rightarrow e γ$, $τ\rightarrow μγ$ and $τ\rightarrow eγ$. We obtain upper limits for the flavor-changing branching ratios in agreement with their present experimental bounds. We also estimate the decay rates of heavy Majorana neutrinos in the channels $N…
In view of the observed strong hierarchy of the quark and lepton masses and of the flavor mixing angles it is argued that the description of flavor mixing must take this into account. One particular interesting way to describe the flavor mixing, which, however, is not the one used today, emerges, which is particularly suited for models of quark mass matrices based on flavor symmetries. We conclude that the unitarity triangle important for B physics should be close to or identical to a rectangular triangle. CP violation is maximal in this sense.
We consider QCD corrections to two loops for the polarized amplitudes of $q{\bar q}\to Z +$ Higgs boson. First we show how the polarized amplitudes of $b \bar{b} \rightarrow Z h$ associated with a non-vanishing $b$-quark Yukawa coupling and a scalar or pseudoscalar Higgs boson $h$ can be built up solely from vector form factors (FF) of properly grouped classes of diagrams, bypassing completely the need of explicitly manipulating $γ_5$ in dimensional regularization (up to a few "anomalous", i.e., triangle diagrams). We determine the contributions of the triangle diagrams in the heavy top limit.…
In view of the observed strong hierarchy of the quark and lepton masses and of the flavor mixing angles, it is argued that the description of flavor mixing must take this into account. One particularly interesting way to describe the flavor mixing, which, however, is not the one used today, emerges, which is particularly suited for models of quark mass matrices based on flavor symmetries. We conclude that the unitarity triangle important for B physics should be close to or identical to a rectangular triangle. CP violation is maximal in this sense.
In view of the observed strong hierarchy of quark masses, we propose a new description of flavor mixing which is particularly suited for models of quark mass matrices based on flavor symmetries. The necessary and sufficient conditions for CP violation are clarified. The emergence of CP violation is primarily linked to a large phase difference (near 90^{\circ}) in the light quark sector. The unitarity triangle is determined by the mass ratios of the light quarks. We conclude that the unitarity triangle should be close or identical to a rectangular triangle, and CP violation is maximal in this s…
THREE TYPES OF FERMION MIXING AND POSSIBLE MANIFESTATIONS OF A PATI--SALAM LEPTOQUARK IN THE LOW--ENERGY PROCESSES
我报告了最近的研究\cite{1,2}的低能量表现的最小扩展的标准模型的基础上的夸克-轻子对称$SU(4)_V \otimes SU(2)_L \otimes G_R$的Pati-Salam型。考虑到这种对称性，在$SU(4)_V$轻夸克与夸克和轻子的相互作用中，第三种类型的混合是必需的。原则上，混合参数的额外任意性可以显著降低源自低能稀有过程的矢量轻夸克质量的下限。分析了通过矢量轻夸克衰变的$μ\rightarrow e γ$、$μ\rightarrow e γγ$和$μ\rightarrow e e \bar e$，证明了衰变概率$Γ(μ\rightarrow e e \bar e) \gg Γ(μ\rightarrow e γγ) \gg Γ(μ\rightarrow e γ)$的特定等级的存在。建立了$μ\rightarrow e γγ$衰变在$10^{-18}$水平和$μ\rightarrow e e \bar e$衰变在$10^{-15}$水平的分支比的上限。
The Daya Bay, RENO, and Double Chooz experiments have discovered a large non-zero value for $θ_{13}$. We present a global analysis that includes these three experiments, Chooz, the Super-K atmospheric data, and the $ν_μ\rightarrow ν_e$ T2K and MINOS experiments that are sensitive to the hierarchy and the sign of $θ_{13}$. We report preliminary results in which we fix the mixing parameters other than $θ_{13}$ to those from a recent global analysis. Given there is no evidence for a non-zero CP violation, we assume $δ=0$. T2K and MINOS lie in a region of $L/E$ where there is a hierarchy degenerac…
The $η'$ meson is associated with the U(1) anomaly. In this paper, a successful effective chiral theory of mesons has been applied to study the anomalous decay of $η'\rightarrow π^+π^-π^{+(0)}π^{-(0)}$. In this study, the contributions of triangle and box anomalies are calculated. It is shown that the contribution of box diagrams is important in this process. We predict branching ratios of $Br(η' \rightarrow π^+ π^- π^+ π^-)={1 \over 2}Br(η' \rightarrow π^+ π^- π^0 π^0) = (8.3 \pm 1.2) \times 10^{-5}$, which is in good agreement with BESIII measurement.
We attempt to simultaneously explain the neutrino oscillation data and the observed $(g-2)_{e,μ}$ in a hidden gauge $U(1)_X$ model where all the Standard Model(SM) fields are $U(1)_X$ singlets. The minimal version of this model calls for four exotic scalars and two pairs of vector fermions, and all are charged under $U(1)_X$. We carefully consider the experimental limits on charge lepton flavor violation without assuming any flavor symmetry and explore the viable model parameter space. The model can accommodate the neutrino oscillation data for both the normal and the inverted mass ordering wh…
The flavor problem, neutrino physics and the fermion mass hierarchy are important motivations to extend the Standard Model into the TeV scale. A new family non-universal extension is presented with three Higgs doublets, one Higgs singlet and one scalar dark matter candidate. Exotic fermions are included in order to cancel chiral anomalies and to allow family non-universal $\mathrm{U(1)}_{X}$ charges. By implementing an additional $\mathbb{Z}_{2}$ symmetry the Yukawa coupling terms are suited in such a way that the fermion mass hierarchy is obtained without fine-tuning. The neutrino sector incl…
Tension between the Standard Model (SM) and data concerning $b \rightarrow s$ processes has become apparent. Most notoriously, concerning the $R_K$ ratio, which probes lepton non-universality in $b$ decays, and measurements involving the decays $B \rightarrow K^* μ^+ μ^-$ and $B_s \rightarrow ϕμ^+ μ^-$. Careful analysis of a wide range of $b \rightarrow s$ data shows that certain kinds of new physics can significantly ameliorate agreement with experiment. Here, we show that these $b \rightarrow s$ anomalies can be naturally accommodated in the context of Natural Scherk-Schwarz Theories of the …
The light hadron decay processes of $Z_b(10610)/Z_b(10650)$ provide us a way to study their nature and decay mechanism. In this work, we evaluate the branching ratios of $Z_b(10610)/Z_b(10650) \to VP$ ($V$ and $P$ stand for light vector and pseudoscalar mesons, respectively) using an effective Lagrangian approach, in which the contributions of intermediate bottomed meson triangle loops are considered. In our calculations, the $Z_b(10610)$ and $Z_b(10650)$ are regarded as $B\bar{B}^*+c.c.$ and $B^*\bar{B}^*$ molecular states, respectively. The predicted branching ratios of $Z_b(10610)\rightarro…
讨论了$3\times 3$ Cabibbo-Kobayashi-Maskawa（CKM）矩阵的酉三角形和特征可测性.在$3\times 3$ CKM方案之外，我们对Gronau-Wyler-Dunietz方法进行了重定相不变推广，以确定$B^{\pm}_u\rightarrow D K^{\pm}$或$B^0_d\rightarrow D K^{*0}$ vs $\bar{B}^0_d\rightarrow D \bar{K}^{*0}$中的弱相移，这只对$D^0-\bar{D}^0$混合中的潜在新物理敏感。我们还表明，弱角$γ\equiv \arg (-V^*_{ub}V^*_{cd}V_{ud}V_{cb})$是可能的一些$B_d$衰变的$CP$的不对称性确定，即使在一个非标准模型与扩展夸克部门。对$3\times 3$ CKM矩阵的么正性检验作了简要评述。
We report on a new analysis of neutrino oscillations in MINOS using the complete set of accelerator and atmospheric data. The analysis combines the $ν_μ$ disappearance and $ν_{e}$ appearance data using the three-flavor formalism. We measure $|Δm^{2}_{32}|=[2.28-2.46]\times10^{-3}\mbox{\,eV}^{2}$ (68% C.L.) and $\sin^{2}θ_{23}=0.35-0.65$ (90% C.L.) in the normal hierarchy, and $|Δm^{2}_{32}|=[2.32-2.53]\times10^{-3}\mbox{\,eV}^{2}$ (68% C.L.) and $\sin^{2}θ_{23}=0.34-0.67$ (90% C.L.) in the inverted hierarchy. The data also constrain $δ_{CP}$, the $θ_{23}$ octant degeneracy and the mass hierarc…
