Triangle Anomalies Research Articles

String Invention, Viable 3-3-1 Model, Dark Matter Black Holes.

With our very limited memories, we provide a brief review of Paul Frampton's memories of the discovery of the Veneziano model, with this indeed being string theory, with Y. Nambu, and, secondly, his 3-3-1 theory. The latter is, indeed, a non-excluded replacement for the Standard Model with triangle anomalies being cancelled, as they must in a truly viable theory. It even needs (essentially) three as the family number! Moreover, primordial black holes as dark matter is mentioned. We end with a review of my own very speculative, utterly recent idea that for the purpose of the classical approximation, we could, using the functional integral as our rudimentary assumption taken over from quantum mechanics, obtain the equations of motion without the, in our opinion, very mysterious imaginary unit i, which usually occurs as a factor in the exponent of the functional integrand, which is this i times the action. The functional integral without the mysterious i leads to the prediction of some of the strongest features in cosmology, and also seems to argue for as few black holes as possible and for the cosmological constant being zero.

Vortical effects in Dirac fluids with vector, chiral and helical charges

Helicity of free massless Dirac fermions is a conserved, Lorentz-invariant quantity at the level of the classical equations of motion. For a generic ensemble consisting of particles and antiparticles, the helical and chiral charges are different conserved quantities. The flow of helicity can be modelled by the helicity current, which is again conserved in the absence of interactions. Similar to the axial vortical effect which generates an axial (chiral) current, the helicity current is induced by vorticity in a finite temperature medium with vector (electrical) charge imbalance via the helical vortical effects, leading to new nondissipative transport phenomena. These phenomena lead to the appearance of a new hydrodynamic excitation, the helical vortical wave. Our results suggest the existence of a new type of triangle anomalies in QED which involve the helicity currents in addition to the standard vector and axial currents. Further exploiting the conservation of the helical current, we show that a finite helical chemical potential may be used to characterise thermodynamic ensembles of fermions similarly to, but independently of, the vector charge and chirality. We derive the pressure P for fermions at finite vector, axial and helical chemical potentials and show that the quantities arising in anomalous transport, including various vortical and circular conductivities and the shear-stress coefficients, can be obtained by differentiation of P with respect to the appropriate chemical potentials. Finally, we calculate the helicity relaxation time in the quark-gluon plasma above the crossover and show that it is similar to that for the axial charge.

Possible molecular states of D¯*K* ( D*K* ) and new exotic states X0(2900) , X1(2900) , Tcs0a(2900)0 and Tcs0a(2900)++

Two iso-singlet hadron states $X_0(2900)$ and $X_1(2900)$ with $J=0$ and 1 respectively, discovered by the LHCb collaboration in 2020, were identified as molecular bound states of $\bar D^*K^*$. Recently two structures $T^a_{cs0}(2900)^0$ and $T^a_{cs0}(2900)^{++}$ have been observed at the hadron spectra, one would suspect if they also are molecular states of $D^*$ and $K^*$. As long as they were of the molecular structures of $D^*K^*$, the hadron states must be in an iso-vector, namely $T^a_{cs0}(2900)^0$ and $T^a_{cs0}(2900)^{++}$ were $I_3=-1, 1$ components of the iso-vector. If it is the case, the corresponding $T^a_{cs0}(2900)^+$ of ($I=1,I_3=0$) and $T^{'a}_{cs0}(2900)^{+}$ of $I=0,I_3=0$ so far evade experimental observation, but should be found by the future experiments. To testify this ansatz, in this paper we study the possible molecular structures of $\bar D^{*}K^{*}$ and $D^{*}K^{*}$ within the Bethe-Salpeter (B-S) framework. With reasonable input parameters it is found that $\bar D^{*}K^{*}$ iso-scalar systems with $J^P=0^+$ and $1^+$ are solutions. The result supports the ansatz of $X_0(2900)$ ($X_1(2900)$) being molecular states of $\bar D^*K^{*}$. Whereas for the system of $ D^{*}K^{*}$ with $I=1$ the corresponding B-S equation has no solution. Thus we can draw a clear conclusion that $T^a_{cs0}(2900)^0$ and $T^a_{cs0}(2900)^{++}$ should not be bound states of $ D^{*}$ and $K^{*}$. The two structures observed by the LHCb collaboration may be caused by dynamics, such as the well-recognized triangle anomalies or other mechanisms.

Quantum Anomalies (in) Matter

Over the last decade it has bee realized that triangle anomalies give rise to dissipationless transport phenomena in hot and dense relativistic matter. I will review anomalous transport theory and then discuss its applications to the quark gluon plasma and the electronics of Weyl semimetals. Finally I briefly discuss the absence of genuine chiral torsional transport.

Neutrino phenomenology and dark matter in an A_4 flavour extended B-L model

We present an {mathrm{A}}_4 flavor extended {mathrm{B-L}} model for realization of eV scale sterile neutrinos, motivated by the recent experimental hints from both particle physics and cosmology. The framework considered here is a gauged {mathrm{B-L}} extension of standard model without the introduction of right-handed neutrinos, where the gauge triangle anomalies are canceled with the inclusion of three exotic neutral fermions N_{i} (i=1,2,3) with {mathrm{B-L}} charges -,4,-,4 and 5. The usual Dirac Yukawa couplings between the SM neutrinos and the exotic fermions are absent and thus, the model allows natural realization of eV scale sterile-like neutrino and its mixing with standard model neutrinos by invoking {mathrm{A}}_4 flavor symmetry. We demonstrate how the exact tri-bimaximal mixing pattern is perturbed due to active-sterile mixing by analyzing 1+3 case in detail. We also show the implication of eV scale sterile-like neutrino on various observables in neutrino oscillation experiments and the effective mass in neutrinoless double beta decay. Another interesting feature of the model is that one of three exotic fermions is required to explain eV scale phenomena, while other two fermions form stable dark matter candidates and their total relic density satisfy the observed 3sigma limit of Planck data. We constrain the gauge parameters associated with U(1) gauge extension, using relic density and collider bounds.

Type III seesaw for neutrino masses in U(1)B\u2212L model with multi-component dark matter

We propose a B − L gauged extension of the Standard Model where light neutrino masses arise from type III seesaw mechanism. Unlike the minimal B − L model with three right handed neutrinos having unit lepton number each, the model with three fermion triplets is however not anomaly free. We show that the leftover triangle anomalies can be cancelled by two neutral Dirac fermions having fractional B − L charges, both of which are naturally stable by virtue of a remnant ℤ2× {mathbb{Z}}_2^{prime } symmetry, naturally leading to a two component dark matter scenario without any ad-hoc symmetries. We constrain the model from all relevant phenomenological constraints including dark matter properties. Light neutrino mass and collider prospects are also discussed briefly. Due to additional neutral gauge bosons, the fermion triplets in type III seesaw can have enhanced production cross section in collider experiment.

Reconnection of magnetic fields in neutron stars driven by the electron mass term in the triangle anomaly

The Adler-Bell-Jackiw anomaly for massive particles is studied in an external magnetic field. The contributions of the mean spin and the pseudoscalar are accounted for in the quasiclassical approximation. The equation for the evolution of the magnetic helicity with the new quantum corrections is derived. We show that the quantum contribution to the helicity evolution can overcome the classical one in the dense degenerate matter which can be present in the core of a neutron star. The application of the obtained results for the interpretation of magnetar bursts are discussed.

Flavoured gauge extension of singlet-doublet fermionic dark matter: neutrino mass, high scale validity and collider signatures

We propose an Abelian gauged version of the singlet-doublet fermionic dark matter (DM) model where the DM, combination of a vector like fermion doublet and a fermion singlet, is naturally stabilised by the gauge symmetry without requiring any ad-hoc discrete symmetries. In order to have an enlarged parameter space for the DM, accsessible at collider experiments like the Large Hadron Collider (LHC), we consider the additional gauge symmetry to be based on the quantum B − 3Lτ. The restriction to third generation of leptons is chosen in order to have weaker bounds from the LHC on the corresponding gauge boson. The triangle anomalies arising in this model can be cancelled by the inclusion of a right handed neutrino which also takes part in generating light neutrino masses through type I seesaw mechanism. The model thus offers a potential thermal DM candidate, interesting collider signatures and correct neutrino mass along with a stable electroweak vacuum and perturbative couplings all the way up to the Planck scale. We constrain our model parameters from these requirements as well as existing relevant constraints related to DM and colliders.

Triangle anomalies and nonrelativistic Nambu-Goldstone modes of generalized global symmetries

In massless QCD coupled to QED in an external magnetic field, a photon with the linear polarization in the direction of the external magnetic field mixes with the charge neutral pion through the triangle anomaly, leading to one gapless mode with the quadratic dispersion relation $\omega \sim k^2$ and one gapped mode. We show that this gapless mode can be interpreted as the so-called type-B Nambu-Goldstone (NG) mode associated with the spontaneous breaking of generalized global symmetries and that its presence is solely dictated by the anomalous commutator in the symmetry algebra. We also argue a possible realization of such nonrelativistic NG modes in 3-dimensional Dirac semimetals.

Relationship between perception of smile esthetics and orthodontic treatment in Spanish patients.

One of the main objectives of orthodontic treatment is to achieve an esthetic smile. This study set out to analyze differences in the perception of smile esthetics among patients before and after receiving orthodontic treatment. 250 Spanish patients analyzed a single photograph in which, by means of computer software, midline diastema, black triangle, gingival margin of the left central incisor, and gingival (“gummy”) smile were altered. Each patient analyzed these images before and after undergoing orthodontic treatment. Patients scored the photographs on a scale from 1 to 10. Statistical analyses of each group’s level of perception were carried out, identifying significant differences in evaluations before and after treatment, and in relation to subjects’ gender and age. Patients presented significant differences in the esthetic perception of midline diastema and gummy smile anomalies after they had completed orthodontic treatment. Gender influenced the perception of smile esthetics, whereby women were significantly more critical of midline diastema, black triangle and gingival margin of the upper central incisor than men. The age variable also showed significant differences in the perception of midline diastema and black triangle anomalies. The perception of smile esthetics of some dental anomalies changes as a result of orthodontic treatment. Gender influences the perception of some of the dental anomalies studied.

Decay rates f1(1285)→ρ0π+π− and a1(1260)→ωπ+π− in the Nambu–Jona-Lasinio model

The anomalous decays $f_1(1285)\to\rho^0\pi^+\pi^-$ and $a_1(1260)\to\omega\pi^+\pi^-$ violating natural parity for vectors and axial-vectors are studied in the framework of the Nambu -- Jona-Lasinio model. We consider the Lagrangian with $U(2)_L\times U(2)_R$ chiral symmetric four quark interactions. The theory is bosonized and corresponding effective meson vertices are obtained in the leading order of $1/N_c$ and derivative expansions. The uncertainties related with the surface terms of anomalous quark triangle diagrams are fixed by the corresponding symmetry requirements. We make a numerical estimate of the decay widths $\Gamma (f_1(1285)\to\rho^0\pi^+\pi^-)=2.78\, \mbox{MeV}$ and $\Gamma (a_1(1260)\to\omega\pi^+\pi^-)=87\, \mbox{keV}$. Our result on the $f_1(1285)\to\rho^0\pi^+\pi^-$ decay rate is in a good agreement with experiment. It is shown that a strong suppression of the $a_1(1260)\to\omega \pi\pi$ decay is a direct consequence of destructive interference between box and triangle anomalies.

Anomaly-free models for flavour anomalies

We explore the constraints imposed by the cancellation of triangle anomalies on models in which the flavour anomalies reported by LHCb and other experiments are due to an extra U(1)^prime gauge boson Z^prime . We assume universal and rational U(1)^prime charges for the first two generations of left-handed quarks and of right-handed up-type quarks but allow different charges for their third-generation counterparts. If the right-handed charges vanish, cancellation of the triangle anomalies requires all the quark U(1)^prime charges to vanish, if there are either no exotic fermions or there is only one Standard Model singlet dark matter (DM) fermion. There are non-trivial anomaly-free models with more than one such ‘dark’ fermion, or with a single DM fermion if right-handed up-type quarks have non-zero U(1)^prime charges. In some of the latter models the U(1)^prime couplings of the first- and second-generation quarks all vanish, weakening the LHC Z^prime constraint, and in some other models the DM particle has purely axial couplings, weakening the direct DM scattering constraint. We also consider models in which anomalies are cancelled via extra vector-like leptons, showing how the prospective LHC Z^prime constraint may be weakened because the Z^prime rightarrow mu ^+ mu ^- branching ratio is suppressed relative to other decay modes.

The Spin‐Charge‐Family Theory Offers Understanding of the Triangle Anomalies Cancellation in the Standard Model

The standard model has for massless quarks and leptons “miraculously” no triangle anomalies due to the fact that the sum of all possible traces T r[τAi τBj τCk] — where , τAi τBj and τCk are the generators of one, of two or of three of the groups SU(3), SU(2) and U(1) — over the representations of one family of the left handed fermions and anti‐fermions (and separately of the right handed fermions and anti‐fermions), contributing to the triangle currents, is equal to zero. It is demonstrated in this paper that this cancellation of the standard model triangle anomaly follows straightforwardly if the SO(3, 1), SU(2), U(1) and SU(3) are the subgroups of the orthogonal group SO(13,1), as it is in the spin‐charge‐family theory. The authors comment on the SO(10) anomaly cancellation, which works if handedness and charges are related “by hand”.

Advantages of unity with SU(4)-color: Reflections through neutrino oscillations, baryogenesis and proton decay

Advantages of unity with SU(4)-color: Reflections through neutrino oscillations, baryogenesis and proton decay

Realistic implementation of chiral magnetic wave in heavy ion collisions

A chiral magnetic wave (CMW) is a gapless collective excitation of chiral charges along the direction of magnetic field in the quark-gluon plasma that arises from the triangle anomaly of QCD. We perform a reliable study of the CMW in a realistic simulation of heavy ion collisions, and find that the CMW contributions to the charge-dependent elliptic flow of pions, $\ensuremath{\Delta}{v}_{2}\ensuremath{\equiv}{v}_{2}({\ensuremath{\pi}}^{\ensuremath{-}})\ensuremath{-}{v}_{2}({\ensuremath{\pi}}^{+})$, linearly depending on the net charge asymmetry ${A}_{\ifmmode\pm\else\textpm\fi{}}\ensuremath{\equiv}({N}_{+}\ensuremath{-}{N}_{\ensuremath{-}})/({N}_{+}+{N}_{\ensuremath{-}})$ with a positive slope $r$, is comparable to the recent experimental results from the Relativistic Heavy Ion Collider (RHIC). We identify a ``freeze-out hole effect,'' which is a direct consequence of the propagation of the CMW during the realistic evolution of the fireball, as the dominant physics effect responsible for a sizable contribution from the CMW to the slope parameter $r$, and emphasize that a proper treatment of the freeze-out condition is crucial in any reliable computation of the CMW contribution to the slope parameter $r$. We also implement a chiral phase transition effect in our study, which illustrates the sensitivity of the results to chiral phase transition temperature, and suggest that the CMW can be an important probe of the QCD chiral phase transition. Our results on the impact parameter dependence compare well with the RHIC experiments. We also give predictions for the Large Hadron Collider (LHC) energy.

Triangle anomaly in Weyl semimetals

Weyl semimetals possess massless chiral quasiparticles, and they are thus affected by the triangle anomalies. We discuss the features of the chiral magnetic and chiral vortical effects specific to Weyl semimetals, and then propose three phenomena caused by the triangle anomalies in this material: (i) anomaly cooling; (ii) charge transport by soliton waves as described by Burgers' equation, and (iii) the shift of the Berezinskii-Kosterlitz-Thouless phase transition of superfluid vortices coupled to Weyl fermions. In addition, we establish the conditions under which the chiral magnetic current exists in real materials.

Spin polarized photons and dileptons from axially charged plasma

Axial charge in a QCD plasma is P- and CP-odd. We propose and study P- and CP-odd observables in photon and di-lepton emissions from an axially charged QCD plasma, which may provide possible experimental evidences of axial charge fluctuation and triangle anomaly in the plasma created in heavy-ion collisions. Our observables measure spin alignments of the emitted photons and di-leptons, and are shown to be related to the imaginary part of chiral magnetic conductivity at finite frequency-momentum, which ultimately arises from the underlying triangle anomaly of the QCD plasma with a finite axial charge density. We present an exemplar computation of these observables in strongly coupled regime using AdS/CFT correspondence.

Flows and polarization of early photons with magnetic field at strong coupling

Recent experimental results from RHIC and LHC on hard photon emission rates in heavy-ion collisions indicate a large azimuthal asymmetry of photon emission rate parameterized by the elliptic flow v_2. Motivated by a recent proposal that the early magnetic field created by two colliding heavy-ions may be responsible for this large azimuthal asymmetry of photon emission rate, we compute the azimuthal dependence of the photon emission rate from a strongly coupled finite temperature plasma with magnetic field in the framework of gauge/gravity correspondence. We also propose and compute a new observable, "in/out-plane polarization asymmetry", constructed from the polarization dependence of the photon emission rates. We observe that both the azimuthal and polarization asymmetry of photon emissions are strongly affected by the triangle anomaly (chiral anomaly) for low frequency regime below 1 GeV.

Kinetic theory with Berry curvature from quantum field theories

A kinetic theory can be modified to incorporate triangle anomalies and the chiral magnetic effect by taking into account the Berry curvature flux through the Fermi surface. We show how such a kinetic theory can be derived from underlying quantum field theories. Using the new kinetic theory, we also compute the parity-odd correlation function that is found to be identical to the result in the perturbation theory in the next-to-leading order hard dense loop approximation.

Calot's triangle

Calot's triangle is an anatomical landmark of special value in cholecystectomy. First described by Jean-François Calot as an "isosceles" triangle in his doctoral thesis in 1891, this anatomical space requires careful dissection before the ligation and division of the cystic artery and cystic duct during cholecystectomy. The modern definition of the boundaries of Calot's triangle varies from Calot's original description, although the exact timing of this change is not entirely clear. The structures within Calot's triangle and their anatomical relationships can present the surgeon with difficulties, particularly when anatomical variations are encountered. Sound knowledge of the normal anatomy of the extrahepatic biliary tract and vasculature, as well as understanding of congenital variation, is thus essential in the prevention of iatrogenic injury. The authors describe the normal anatomy of Calot's triangle and common anatomical anomalies. The incidence of structural injury is discussed, and new techniques in surgery for enhancing the visualisation of Calot's triangle are reviewed. © .