Hasil untuk "Nuclear and particle physics. Atomic energy. Radioactivity"

E. Lanina, A. Sleptsov

We explore algebraic relations on Vassiliev knot invariants related with correlators in the 3-dimensional Chern–Simons theory. Vassiliev invariants form infinite-dimensional algebra. We focus on k-parametric knot families with Vassiliev invariants being polynomials in family parameters. We conjecture that such 1-parametric algebra of Vassiliev invariants is always finitely generated, while in the case of more parameters, we provide example of the knot family with infinite number of generators. Inside a knot family, there appear extra algebraic relations on Vassiliev invariants. We show that there are  ≤ k algebraically independent Vassiliev invariants for k-parametric knot family. However, in all our examples, the number of algebraically independent Vassiliev invariants is exactly k, and it is open question if there exists a k-parametric knot family with a fewer number of algebraically independent Vassiliev invariants. We also demonstrate that a complete knot invariant of some k-parametric knot families consists of k Vassiliev invariants.

Samprity Das, Prabir Rudra, Surajit Chattopadhyay

This article presents a new model for anisotropic compact stars that are confined to physical dark matter in the background of f(T) teleparallel gravity. The model is based on the equation of state (EoS) of the bag model type and the Bose-Einstein dark matter density profile. The derived solutions meet the energy conditions, the causality conditions, and the required conditions on the stability factor and adiabatic index, indicating that they are physically well-behaved and represent the physical and stable matter configuration. We also determine the maximum mass, surface redshift, and compactness parameter at the surface. Interestingly, all of these numbers fall within the specified range, supporting the physical viability of our proposal. Additionally, the various masses that are derived for varying the model parameter k correspond to five compact, realistic compact objects, including LMC X-4, Her X-1, 4U 1538-52, SAX J1808.4-3658, and Cen X-3. We have also illustrated the radially symmetric profiles of energy density and the moment of inertia for non-rotating stars.

The ATLAS collaboration, G. Aad, E. Aakvaag et al.

Abstract This article presents a search for a heavy charged Higgs boson produced in association with a top quark and a bottom quark, and decaying into a W boson and a 125 GeV Higgs boson h. The search is performed in final states with one charged lepton, missing transverse momentum, and jets using proton-proton collision data at s $$ \sqrt{s} $$ = 13 TeV recorded with the ATLAS detector during Run 2 of the LHC at CERN. This data set corresponds to a total integrated luminosity of 140 fb −1. The search is conducted by examining the reconstructed invariant mass distribution of the Wh candidates for evidence of a localised excess in the charged Higgs boson mass range from 250 GeV to 3 TeV. No significant excess of data over the expected background is observed and 95% confidence-level upper limits between 2.8 pb and 1.2 fb are placed on the production cross-section times branching ratio for charged Higgs bosons decaying into Wh.

Jock McOrist, Martin Sticka, Eirik Eik Svanes

Abstract In this article we dimensionally reduce a heterotic supergravity on a G 2 background with Minkowski spacetime using a certain cohomology as a basis for the Kaluza-Klein expansion, up to and including first order in α‵. We construct the moduli space heterotic G 2 compactifications. The α‵-correction induces a curvature correction to the Weyl-Peterson metric. In the limit in which the G 2 manifold reduces to SU(3), we recover known results.

ATLAS Collaboration

Abstract A search is presented for a heavy scalar (H) or pseudo-scalar (A) predicted by the two-Higgs-doublet models, where the H/A is produced in association with a top-quark pair $$(t\bar{t}H/A),$$ ( t t ¯ H / A ) , and with the H/A decaying into a $$t\bar{t}$$ t t ¯ pair. The full LHC Run 2 proton–proton collision data collected by the ATLAS experiment is used, corresponding to an integrated luminosity of $$139~\text {fb}^{-1}.$$ 139 fb - 1 . Events are selected requiring exactly one or two opposite-charge electrons or muons. Data-driven corrections are applied to improve the modelling of the $$t\bar{t}$$ t t ¯ +jets background in the regime with high jet and b-jet multiplicities. These include a novel multi-dimensional kinematic reweighting based on a neural network trained using data and simulations. An H/A-mass parameterised graph neural network is trained to optimise the signal-to-background discrimination. In combination with the previous search performed by the ATLAS Collaboration in the multilepton final state, the observed upper limits on the $$t\bar{t}H/A \rightarrow t\bar{t}t\bar{t}$$ t t ¯ H / A → t t ¯ t t ¯ production cross-section at 95% confidence level range between 14 fb and 5.0 fb for an H/A with mass between 400  $$\text {GeV}$$ GeV and 1000  $$\text {GeV}$$ GeV , respectively. Assuming that both the H and A contribute to the $$t\bar{t}t\bar{t}$$ t t ¯ t t ¯ cross-section, $$\tan \beta $$ tan β values below 1.7 or 0.7 are excluded for a mass of 400  $$\text {GeV}$$ GeV or 1000  $$\text {GeV}$$ GeV , respectively. The results are also used to constrain a model predicting the pair production of a colour-octet scalar, with the scalar decaying into a $$t\bar{t}$$ t t ¯ pair.

Hardik Bohra, Sumit R. Das, Gautam Mandal et al.

Abstract Realizations of the holographic correspondence in String/M theory typically involve spacetimes of the form AdS × Y where Y is some internal space which geometrizes an internal symmetry of the dual field theory, hereafter referred to as an “R symmetry”. It has been speculated that areas of Ryu-Takayanagi surfaces anchored on the boundary of a subregion of Y, and smeared over the base space of the dual field theory, quantify entanglement of internal degrees of freedom. A natural candidate for the corresponding operators are linear combinations of operators with definite R charge with coefficients given by the “spherical harmonics” of the internal space: this is natural when the product spaces appear as IR geometries of higher dimensional AdS spaces. We study clustering properties of such operators both for pure AdS × Y and for flow geometries, where AdS × Y arises in the IR from a different spacetime in the UV, for example higher dimensional AdS or asymptotically flat spacetime. We show, in complete generality, that the two point functions of such operators separated along the internal space obey clustering properties at scales sufficiently larger than the AdS scale. For non-compact Y, this provides a notion of approximate locality. When Y is compact, clustering happens only when the size of Y is parametrically larger than the AdS scale. This latter situation is realized in flow geometries where the product spaces arise in the IR from an asymptotically AdS geometry at UV, but not typically when they arise near black hole horizons in asymptotically flat spacetimes. We discuss the significance of this result for entanglement and comment on the role of color degrees of freedom.

Leszek Motyka, Mariusz Sadzikowski

Abstract Effects of non-linear small-x evolution of the gluon distribution given by the Balitsky–Kovchegov equation are analyzed within the collinear approximation framework. We perform a twist decomposition of the proton structure functions $$F_2$$ F 2 and $$F_{\textrm{L}}$$ F L obtained from the Balitsky–Kovchegov equation using the Mellin representation of the scattering cross-sections at high energies. In both the structure functions we find strong corrections coming from the non-linear effects in the gluon evolution at twist 2, and strongly suppressed higher twist effects. This implies that unitarization effects of high energy scattering amplitudes are mostly the leading twist effect. Furthermore we consider the double logarithmic limit of the Balitsky–Kovchegov equation for the collinear gluon distribution, and compare the result to the Gribov–Levin–Ryskin equation. We find that these two equations differ by two powers of the hard scale logarithm for the large scales.

Andrés Anabalón, Antonio Gallerati, Simon Ross et al.

Abstract We consider soliton solutions in AdS4 with a flat slicing and Wilson loops around one cycle. We study the phase structure and find the ground state and identify supersymmetric solutions as a function of the Wilson loops. We work in the context of a scalar field truncation of gauged N $$ \mathcal{N} $$ = 8 supergravity, where all the dilatons are equal and all the axions vanish in the STU model. In this theory, we construct new soliton solutions parameterized by two Wilson lines. We find that there is a degeneracy of supersymmetric solutions. We also show that, for alternate boundary conditions, there exists a non-supersymmetric soliton solution with energy lower than the supersymmetric one.

CAO Qiong;JIANG Heyuan;DING Xiao;LU Daogang;LI Zhen;WANG Xiaotian

After the Fukushima nuclear accident, the safety of spent fuel pool has attracted much attention. Under extreme accident conditions, the spent fuel pool may lose make-up water and cooling for a long time, causing the water level in the spent fuel pool to drop, resulting in excessive temperature of spent fuel rods, even damage to fuel assemblies and leakage of radioactive substances, come into being serious safety problems. In order to avoid this safety problem, the third generation nuclear power plants, such as AP1000 and CAP1400, introduced spray cooling system. Under the condition of spraying, the liquid film flow characteristics on spent fuel rods is an important factor affecting the cooling effect, which has not been studied in detail by domestic and foreign scholars. Too large or too small spray flow rate may lead to the rupture of the liquid film on the spent fuel rod. Therefore, it is necessary to study the flow characteristics of the liquid film on the spent fuel rod. In this paper, optical method was used to study the time and space variation of liquid film thickness formed by spray cooling of single spent fuel rod at different Reynolds numbers. The liquid film image was captured by CCD camera, and the clear liquid film thickness image and good coincidence data were obtained after processing. Using the obtained data, the fluctuation images of liquid film at different Reynolds numbers at fixed positions of spent fuel rod and at different positions of spent fuel rod at fixed Reynolds numbers were drawn. In addition, the variation trend of time-averaged liquid film thickness on spent fuel rod at different Reynolds numbers was obtained. The experimental results show that when Reynolds number is in the range of 608-7 538, the maximum value of transient liquid film thickness is 2.36 mm, which occurs when Reynolds number is 7 085. With the increase of Reynolds number, the time mean liquid film thickness will increase, and the amplitude of liquid film fluctuation will also increase. Along the rod direction, with the increase of the distance from the top of the rod, the liquid film thickness will gradually decrease and become stable, and as the Reynolds number increases, the stable part will appear farther from the top of the rod. The research on the flow characteristics of single rod coolant film of spent fuel lays a foundation for determining the minimum spray flow rate with effective cooling capacity.

Sandipan Kundu

Abstract There are effective field theories that cannot be embedded in any UV complete theory. We consider scalar effective field theories, with and without dynamical gravity, in D-dimensional anti-de Sitter (AdS) spacetime with large radius and derive precise bounds (analytically) on the coupling constants of higher derivative interactions ϕ 2□ k ϕ 2 by only requiring that the dual CFT obeys the standard conformal bootstrap axioms. In particular, we show that all such coupling constants, for even k ≥ 2, must satisfy positivity, monotonicity, and log-convexity conditions in the absence of dynamical gravity. Inclusion of gravity only affects constraints involving the ϕ 2□2 ϕ 2 interaction which now can have a negative coupling constant. Our CFT setup is a Lorentzian four-point correlator in the Regge limit. We also utilize this setup to derive constraints on effective field theories of multiple scalars. We argue that similar analysis should impose nontrivial constraints on the graviton four-point scattering amplitude in AdS.

S. Pandit, A. Shrivastava, K. Mahata et al.

The origin of the large α particle production and incomplete fusion in reactions involving weakly-bound α+x cluster nuclei still remains unresolved. While the (two-step) process of breakup followed by capture of the “free” complementary fragment (x) is widely believed to be responsible, a few recent studies suggest the dominant role of (direct) cluster stripping. To achieve an unambiguous experimental discrimination between these two processes, a coincidence measurement between the outgoing α particles and γ rays from the heavy residues has been performed for the 7Li(α+triton)+93Nb system. Proper choice of kinematical conditions allowed for the first time a significant population of the region accessible only to the direct triton stripping process and not to breakup followed by the capture of the “free” triton (from the three-body continuum). This result, also supported by a cluster-transfer calculation, clearly establishes the dominance of the direct cluster-stripping mechanism in the large alpha production. Clustering is a general phenomenon observed over a wide range of physical scales and in diverse fields such as the aggregation of galaxies in the universe or the existence of gene clusters in complex biological systems. In nuclear physics, the enormous pairing stability in fermionic quantum systems leads to a large binding energy for the α particle and consequently α clustering is very prevalent in atomic nuclei [1]. While the α decay of radioactive nuclei was long ago adduced as direct evidence that α particles formed constituents of heavier nuclei [2], the origin and consequences of α clustering in nuclei remain the subject of intense research due to its importance in fundamental nuclear physics as well as other areas [3]. In many light nuclei, α clustering is responsible for the weak binding of α + x cluster configurations. A large α-particle yield compared to that of the complementary fragment (x) is observed in nuclear reactions involving such nuclei, e.g., 6,7Li and 7,9Be, indicating that it cannot arise solely due to simple breakup of the weakly-bound projectile in the field of the target Email address: sanat@barc.gov.in (S. K. Pandit) nucleus. Capture/transfer of the complementary fragment/cluster, also sometimes referred to as incomplete fusion (ICF), has also been observed with similar magnitudes in these reactions. Further, the measured large α production and ICF cross sections are commensurate with an observed suppression of the complete fusion (CF) process, suggesting a common origin. However, it is still debated whether the former process influences the multi-dimensional quantum tunneling of fusion in a coherent or incoherent way [4, 5]. The mechanisms responsible for the large α-particle production, ICF and fusion suppression remain unclear and the subject of current interest [6, 7, 8, 9, 10, 11, 12, 13]. Unraveling the reaction mechanisms in systems involving nuclei with clustering and weak binding, common features of many light radioactive ion beams (RIBs), is important not only from its fundamental aspect, but also as a promising tool in other areas including nuclear astrophysics [14, 15, 16] and nuclear energy applications [17, 18]. Incomplete fusion can arise due to either direct stripping of a cluster from a bound state of the projectile or fusion of one of the “free” fragments after breakup of Preprint submitted to Physics Letter B October 5, 2021 ar X iv :2 11 0. 01 02 1v 1 [ nu cl -e x] 3 O ct 2 02 1 the projectile, i.e. so-called breakup-fusion [10, 19, 20, 21, 22]. Experimentally, it is challenging to distinguish between these two mechanisms as both lead to the same final products with similar energy and angular distributions. Although a clear experimental identification of the underlying mechanism could not be achieved in earlier coincidence measurements, e.g. [10, 19, 20, 21], a dominant role of breakup-fusion was suggested by comparing the results with calculations based on a semiclassical model [10, 23] or otherwise [19]. In a recent study, a few exclusive events (<1% of the total α yields) could be identified as arising from direct stripping only and comparing the inclusive energy-angle distribution with simulations, it was concluded that direct stripping plays a dominant role in ICF [6]. Thus, a model independent experimental demonstration of the ICF mechanism is still missing. Significant theoretical effort has been invested in understanding the mechanism of the large α-particle production and ICF cross sections [8, 7, 9, 24, 25, 23, 26, 27, 28]. Recently, using a non elastic breakup model, the cluster-stripping process was shown to be the dominant mechanism for ICF [8, 7]. In other studies, fusion of the breakup fragments was considered to be the main ICF mechanism [9, 10, 24, 23]. Calculations assuming both cluster stripping [8, 7] and breakupfusion [9, 10, 24, 23] mechanisms have successfully reproduced experimental inclusive α yields and/or fusion data to a similar extent. Further, it has also been suggested that breakup-fusion and transfer to the continuum of the target are equivalent [9, 25]. It is therefore essential to have experimental data populating the bound states and the continuum with comparable magnitude to discriminate between the two widely different mechanisms. As depicted in Fig. 1, while the outgoing α particle has access to the reaction Q value in the case of direct stripping, the triton fusion (second step) Q value can not be shared with the α particle (produced in the first step) in the two-step breakup-fusion process. A suitable choice of experimental conditions could therefore allow a region which is exclusively populated by only one of these processes to be studied. This letter reports a measurement of particle-γ coincidences for the 7Li+93Nb system to identify the mechanisms responsible for the origin of the large α-particle production and ICF by exploiting the kinematical conditions illustrated in Fig. 1. Experimental observations are compared with Monte-Carlo simulations and quantum mechanical calculations based on the distorted-wave Born approximation (DWBA) for breakup and cluster transfer, respectively. The inclusive and exclusive measurements of α parFigure 1: Illustration of (a) direct cluster transfer and (b) breakup followed by fusion of one of the cluster fragments for a 7Li(α+ t)+target reaction. ticles were carried out using the 7Li beam from the BARC-TIFR Pelletron-Linac facility, Mumbai, in two separate experiments. Targets were self-supporting 93Nb foils of thickness ∼ 1.6 mg/cm2. A beam energy of 24 MeV (1.2VB) was chosen for both measurements to optimize the kinematical conditions and cross section. In the exclusive measurement, prompt γ-ray transitions were detected using the Indian National Gamma Array (INGA) [29], consisting of 18 Compton suppressed high purity germanium (HPGe) clover detectors. Three Si surface barrier telescopes (thicknesses ∆E ∼ 15-30 μm, E ∼ 300-5000 μm) were kept at 35◦, 45◦ and 70◦ for the detection of α particles around the grazing angle. One Si surface barrier detector (thickness ∼ 300 μm) was fixed at 20◦ to monitor Rutherford scattering for absolute normalization purposes. The time stamped data were collected using a digital data acquisition system with a sampling rate of 100 MHz [29]. Efficiency and energy calibration of the clover detectors were carried out using standard calibrated 152Eu and 133Ba γ-ray sources. In the inclusive measurement, angular distributions of α particles and elastically scattered 7Li were measured with three Si surface-barrier detector telescopes (thicknesses: ∆E ∼ 20-50 μm, E ∼ 450-1000 μm) mounted on a movable arm inside the scattering chamber. A typical energy correlation spectrum of prompt γ rays versus outgoing α particles, detected at an angle of 35◦, is shown in Fig. 2(a). Photo-peaks corresponding to the residues (94−96Mo) formed after triton capture (t+93Nb→ 96Mo) are identified and labeled on the projected spectrum in the same figure. Other possible sources of 94−96Mo residues are compound nuclear evaporation (αxn), d-stripping: 93Nb(7Li,5He)95Mo, and p-stripping: 93Nb(7Li,6He∗)94Mo reaction channels. In case of p-stripping, the ejectile (6He) has to be left in an excited state above its 2n emission threshold (975 keV) in order to give an α particle in coincidence with a characteristic γ-rays of 94Mo. As can be seen, γ transitions from 96Mo are mixed with intense transitions from 94Mo and 95Mo. However, after

Gino Isidori, Saad Nabeebaccus, Roman Zwicky

Abstract We present a detailed analysis of QED corrections to B ¯ → K ¯ ℓ + ℓ − $$ \overline{B}\to \overline{K}{\mathrm{\ell}}^{+}{\mathrm{\ell}}^{-} $$ decays at the double-differential level. Cancellations of soft and collinear divergences are demonstrated analytically using the phase space slicing method. Whereas soft divergences are found to cancel at the differential level, the cancellation of the hard-collinear logs ln m ℓ require, besides photon-inclusiveness, a specific choice of kinematic variables. In particular, hard-collinear logs in the lepton-pair invariant mass distribution (q 2), are sizeable and need to be treated with care when comparing with experiment. Virtual and real amplitudes are evaluated using an effective mesonic Lagrangian. Crucially, we show that going beyond this approximation does not introduce any further infrared sensitive terms. All analytic computations are performed for generic charges and are therefore adaptable to semileptonic decays such as B ¯ → D ℓ ν ¯ $$ \overline{B}\to D\mathrm{\ell}\overline{\nu } $$ .

Dáfni F.Z. Marchioro, Daniel Luiz Nedel

Abstract In this work we study new issues involving the type IIB superstring in a time dependent plane wave background with a constant self-dual Ramond-Ramond 5-form and a linear dilaton in the light-like direction. We construct a unitary Bogoliubov generator which relates the asymptotically flat superstring Hilbert space to the finite time Hilbert space. The time dependent vacuum is a superposition of SU(1, 1) × SU(2) coherent states, which has a particular structure of excitation, characterized by a condensation of right and left moving supertring modes. We calculate the time dependent left/right entanglement entropy and carry out the summation over the oscillator modes of the superstring two-point function. We show that, close to the null singularity, the entanglement entropy is well- behaved. In particular, for asymptotically flat observers, the closed superstring vacuum close to the singularity appears as superstring thermal vacuum, which is unitarily inequivalent to the asymptotically flat vacuum. Actually, we show that close to the singularity the superstring thermalizes and the entanglement entropy becomes a thermodynamical entropy for a supersymmetric two-dimensional gas.

L. Andrianopoli, B.L. Cerchiai, R. D’Auria et al.

Abstract We derive a 2+1 dimensional model with unconventional supersymmetry at the boundary of an AdS4 N $$ \mathcal{N} $$ -extended supergravity, generalizing previous results. The (unconventional) extended supersymmetry of the boundary model is instrumental in describing, within a top-down approach, the electronic properties of graphene-like 2D materials at the two Dirac points, K and K′. The two valleys correspond to the two independent sectors of the OSp(p|2) × OSp(q|2) boundary model in the p = q case, which are related by a parity transformation. The Semenoff and Haldane-type masses entering the corresponding Dirac equations are identified with the torsion parameters of the substrate in the model.

Z. Liu, Q. Yue, L. Yang et al.

Christoph Borschensky, Gabriele Coniglio, Barbara Jäger

Abstract We study the quantitative features of dark matter pair production at the LHC in simplified dark matter models and in the MSSM taking next-to-leading order QCD corrections and parton-shower effects fully into account. Among the large space of dark matter models, we focus on two particular models where a fermionic dark matter candidate interacts with the Standard Model via the exchange of either a vector mediator in the s-channel or coloured scalar mediators in the t-channel. We find that the simplified models are capable of reproducing the predictions of the MSSM to some extent in simplified supersymmetric scenarios, but lack the complexity to describe the complete theory over the full supersymmetric parameter space.

Muneto Nitta, Shin Sasaki, Ryo Yokokura

Abstract Spatial modulation has been studied for a long time in condensed matter, nuclear matter and quark matter, where the manifest Lorentz invariance is lost due to the finite density/temperature effects and so on. In this paper, spatially modulated vacua at zero temperature and zero density are studied in Lorentz invariant field theories. We first propose an adaptation of the Nambu–Goldstone theorem to higher derivative theories under the assumption of the absence of ghosts: when a global symmetry is spontaneously broken due to vacuum expectation values of space-time derivatives of fields, a Nambu–Goldstone (NG) boson appears without a canonical kinetic (quadratic derivative) term with a quartic derivative term in the modulated direction while a Higgs boson appears with a canonical kinetic term. We demonstrate this in a simple model allowing (meta)stable modulated vacuum of a phase modulation (Fulde–Ferrell state), where an NG mode associated with spontaneously broken translational and U(1) symmetries appears.

Lucas Hackl, Robert C. Myers

Abstract We study circuit complexity for free fermionic field theories and Gaussian states. Our definition of circuit complexity is based on the notion of geodesic distance on the Lie group of special orthogonal transformations equipped with a right-invariant metric. After analyzing the differences and similarities to bosonic circuit complexity, we develop a comprehensive mathematical framework to compute circuit complexity between arbitrary fermionic Gaussian states. We apply this framework to the free Dirac field in four dimensions where we compute the circuit complexity of the Dirac ground state with respect to several classes of spatially unentangled reference states. Moreover, we show that our methods can also be applied to compute the complexity of excited energy eigenstates of the free Dirac field. Finally, we discuss the relation of our results to alternative approaches based on the Fubini-Study metric, the relevance to holography and possible extensions.

J. Alvarez-Jimenez, I. Cortese, J. Antonio García et al.

Abstract Starting from N = 4 $$ \mathcal{N}=4 $$ SYM and using an appropriate Higgs mechanism we reconsider the construction of a scalar field theory non-minimally coupled to a Coulomb potential with a relativistic SO(4) symmetry and check for scalar field consistency conditions. This scalar field theory can also be obtained from a relativistic particle Lagrangian with a proper implementation of the non-minimal coupling. We provide the generalization of the non-relativistic construction of the Runge-Lenz vector to the relativistic case and show explicitly that this new vector generates the SO(4) algebra. Using the power of the SO(4) symmetry, we calculate the relativistic hydrogen atom spectrum. We provide a generalization of the Kustaanheimo-Stiefel transformation to the relativistic case and relate our results with the corresponding relativistic oscillator. Finally, in the light of these results, we reconsider the calculation of the hydrogen atom spectrum from the cusp anomalous dimension given in [2].

Zhen Liu, Pei-Hong Gu

We extend some two Higgs doublet models, where the Yukawa couplings for the charged fermion mass generation only involve one Higgs doublet, by two singlet scalars respectively carrying a singly electric charge and a doubly electric charge. The doublet and singlet scalars together can mediate a two-loop diagram to generate a tiny Majorana mass matrix of the standard model neutrinos. Remarkably, the structure of the neutrino mass matrix is fully determined by the symmetric Yukawa couplings of the doubly charged scalar to the right-handed leptons. Meanwhile, a one-loop induced neutrinoless double beta decay can arrive at a testable level even if the electron neutrino has an extremely small Majorana mass. We also study other experimental constraints and implications including some rare processes and Higgs phenomenology.