Higgs-boson couplings beyond the Standard Model

The implications for Higgs decays of potential new physics beyond the Standard Model (BSM) are considered in the context of effective field theory, assuming perturbative decoupling. Using existing data to restrict which dimension-six operators can arise, it is shown that, given the existing experimental constraints, only a small number of operators can affect the decays of the Higgs: those that may be potentially-tree-generated (PTG) and modify the Higgs–fermion couplings, or those that may be loop-generated (LG) that modify the Higgs couplings to γγ, Zγ and GG  . Implications for specific branching ratios are given in terms of the coefficients of various dimension-six operators. In such a scenario, the ratios Γ(H→WW^?)/Γ(H→ZZ^?)$\Gamma (H\to W{W}^{?})/\Gamma (H\to Z{Z}^{?})$ and Γ(H→W?ν)/Γ(H→Z??)$\Gamma (H\to W?\nu )/\Gamma (H\to Z??)$ equal to their Standard Model values to an accuracy of O(1%)$O(1\text{\%})$ or less.     

Massless gauge bosons other than the photon

Gauge bosons associated with unbroken gauge symmetries, under which all standard model fields are singlets, may interact with ordinary matter via higher-dimensional operators. A complete set of dimension-six operators involving a massless U(1) field, gamma('), and standard model fields is presented. The mu-->egamma(') decay, primordial nucleosynthesis, star cooling, and other phenomena set lower limits on the scale of chirality-flip operators in the 1-15 TeV range if the operators have coefficients given by the corresponding Yukawa couplings. Simple renormalizable models induce gamma(') interactions with leptons or quarks at two loops, and may provide a cold dark matter candidate.     

Constraining the anomalous Higgs boson coupling in H+γ production

Higgs boson production in association with a photon(H+) offers a promising channel to test the Higgs boson to photon coupling at various energy scales. Its potential sensitivity to anomalous couplings of the Higgs boson has not been explored with the proton-proton collision data. In this paper, we reinterpret the latest ATLAS H+resonance search results within the Standard Model effective field theory(EFT) framework, using 36.1 fb~(-1) of protonproton collision data recorded with the ATLAS detector at s~(1/2) 13 TeV. Constraints on the Wilson coefficients of dimension-six EFT operators related to the Higgs boson to photon coupling are provided for the first time in the H+final state at the LHC.     

Effective-Lagrangian approach to γγ → WW I: Couplings and amplitudes

We consider the gauge-boson sector of a locally SU(2) × U(1) invariant effective Lagrangian with ten dimension-six operators added to the Lagrangian of the standard model. These operators induce anomalous three- and four-gauge-boson couplings and an anomalous γγH coupling. In the framework of this effective Lagrangian we calculate the helicity amplitudes and differential and total cross sections for the process γγ → WW at a photon collider. We give relations between different parts of the amplitudes that show which linear combinations of anomalous couplings are measurable in this reaction. The transformation properties of the differential cross section under CP are discussed. We find that three linear combinations of CP-conserving and of CP-violating couplings can be measured independently of the photon polarization in γγ → WW. M. Pospischil: now at CNRS UPR 2191, 1 Avenue de la Terrasse, 91198 Gif-sur-Yvette, France.     

Effective-Lagrangian approach to γγ→WW II: Results and comparison with e+e-→WW

We present a study of anomalous electroweak gauge-boson couplings that can be measured in e⁺e^- and γγ collisions at a future linear collider like ILC. We consider the gauge-boson sector of a locally SU(2)×U(1) invariant effective Lagrangian with ten dimension-six operators added to the Lagrangian of the standard model. These operators induce anomalous three-gauge-boson and four-gauge-boson couplings and an anomalous γγH coupling. We calculate the reachable sensitivity for the measurement of the anomalous couplings in γγ→WW. We compare these results with the reachable precision in the reaction e⁺e^-→WW on the one hand and with the bounds that one can obtain from high-precision observables in Z decays on the other hand. We show that one needs both the e⁺e^- and the γγ modes at an ILC to constrain the largest possible number of anomalous couplings and that the Giga-Z mode offers the best sensitivity for certain anomalous couplings.     

Wigner's function and other distribution functions in mock phase spaces

This review deals with the methods of associating functions with quantum mechanical operators in such a manner that these functions should furnish conveniently semiclassical approximations. We present a unified treatment of methods and results which usually appear under expressions such as Wigner's function, Weyl's association, Kirkwood's expansion, Glauber's coherent state representation, etc.; we also construct some new associations.Section 1 gives the motivation by discussing the Thomas-Fermi theory of an atom with this end in view.Section 2 introduces new operators which resemble Dirac delta functions with operator arguments, the operators being the momenta and coordinates. Reasons are given as to why this should be useful. Next we introduce the notion of an operator basis, and discuss the possibility and usefulness of writing an operator as a linear combination of the basis operators. The coefficients in the linear combination are c-numbers and the c-numbers are associated with the operator (in that particular basis). The delta function type operators introduced before can be used as a basis for the dynamical operators, and the c-numbers obtained in this manner turn out to be the c-number functions used by Wigner, Weyl, Kirkwood, Glauber, etc. New bases and associations can now be invented at will. One such new basis is presented and discussed. The reasons and motivations for choosing different bases is then explained.The copious and seemingly random mathematical relations between these functions are then nothing else but the relations between the expansion coefficients engendered by the relations between the different bases. These are shown and discussed in this light. A brief discussion is then given to possible transformation of the p, q labels.Section 3 gives examples of how the semiclassical expansions are generated for these functions and exhibits their equivalence.The mathematical paraphernalia are collected in the appendices.     

NLO inspired effective Lagrangians for Higgs physics

Either late autumn this year or latest early next year ATLAS/CMS should have results with 2–3 times the current data which might give first clues on the couplings of the light narrow resonance discovered at the LHC in July 2012, compatible with the Higgs boson of the Standard Model. A strategy for measuring deviations from the Standard Model can be based on using the “full” Standard Model, including all available QCD and electroweak higher-order corrections, and supplement it with d=6$d=6$ local operators. Their Wilson coefficients are assumed to be small enough that they can be treated at leading order. Examples of the connection of local operators with BSM Lagrangians are presented as well as a discussion of Lagrangians with/without decoupling of heavy degrees of freedom. The whole strategy is critically reviewed in the light of internal consistency and an “Effective NLO Approximation” is proposed.     

N-fold Darboux Transformation for Integrable Couplings of AKNS Equations

For the integrable couplings of Ablowitz-Kaup-Newell-Segur(ICAKNS) equations, N-fold Darboux transformation(DT) TN, which is a 4 × 4 matrix, is constructed in this paper. Each element of this matrix is expressed by a ratio of the(4N + 1)-order determinant and 4N-order determinant of eigenfunctions. By making use of these formulae,the determinant expressions of N-transformed new solutions p~([N ]), q~([N ]), r~([N ])and s~([N ])are generated by this N-fold DT.Furthermore, when the reduced conditions q =-p*and s =-r*are chosen, we obtain determinant representations of N-fold DT and N-transformed solutions for the integrable couplings of nonlinear Schr?dinger(ICNLS) equations.Starting from the zero seed solutions, one-soliton solutions are explicitly given as an example.     

Heat Kernel Coefficients for Two-Dimensional Schrödinger Operators

In this note, we compute the Hadamard coefficients of algebraically integrable Schrödinger operators in two dimensions. These operators first appeared in [BL] and [B] in connection with Huygens’ principle, and our result completes, in a sense, the investigation initiated in those papers.     

Towards large volume big divisor D3/D7 “μ-split supersymmetry” and Ricci-flat Swiss-cheese metrics, and dimension-six neutrino mass operators

We show that it is possible to realize a “μ-split SUSY” scenario (Cheng and Cheng, 2005) [1] in the context of large volume limit of type IIB compactifications on Swiss-cheese Calabi-Yau orientifolds in the presence of a mobile space-time filling D3-brane and a (stack of) D7-brane(s) wrapping the “big” divisor. For this, we investigate the possibility of getting one Higgs to be light while other to be heavy in addition to a heavy higgsino mass parameter. Further, we examine the existence of long lived gluino that manifests one of the major consequences of μ-split SUSY scenario, by computing its decay width as well as lifetime corresponding to the three-body decays of the gluino into either a quark, a squark and a neutralino or a quark, squark and goldstino, as well as two-body decays of the gluino into either a neutralino and a gluon or a goldstino and a gluon. Guided by the geometric Kähler potential for ΣB obtained in Misra and Shukla (2010) [2] based on GLSM techniques, and the Donaldson?s algorithm (Barun et al., 2008) [3] for obtaining numerically a Ricci-flat metric, we give details of our calculation in Misra and Shukla (2011) [4] pertaining to our proposed metric for the full Swiss-cheese Calabi-Yau (the geometric Kähler potential being needed to be included in the full moduli space Kähler potential in the presence of the mobile space-time filling D3-brane), but for simplicity of calculation, close to the big divisor, which is Ricci-flat in the large volume limit. Also, as an application of the one-loop RG flow solution for the higgsino mass parameter, we show that the contribution to the neutrino masses at the EW scale from dimension-six operators arising from the Kähler potential, is suppressed relative to the Weinberg-type dimension-five operators.     

Bulk-boundary correlators in the hermitian matrix model and minimal Liouville gravity

We construct the one matrix model (MM) correlators corresponding to the general bulk-boundary correlation numbers of the minimal Liouville gravity (LG) on the disc. To find agreement between both discrete and continuous approach, we investigate the resonance transformation mixing boundary and bulk couplings. It leads to consider two sectors, depending on whether the matter part of the LG correlator is vanishing due to the fusion rules. In the vanishing case, we determine the explicit transformation of the boundary couplings at the first order in bulk couplings. In the non-vanishing case, no bulk-boundary resonance is involved and only the first order of pure boundary resonances have to be considered. Those are encoded in the matrix polynomials determined in our previous paper. We checked the agreement for the bulk-boundary correlators of MM and LG in several non-trivial cases. In this process, we developed an alternative method to derive the boundary resonance encoding polynomials.     

Renormalization group evolution of the non-unitary operator

Integrating out a heavy field gives rise to effective Lagrangian containing higher-dimensional operators. In the context of Type-I seesaw mechanism, integrating out the heavy right-handed neutrino field leads to unique dimension-five operator which gives the tree level neutrino mass term. Apart from these there are dimension-six operators that can have important implications. A linear combination of two such operators gives rise to the non-unitarity in the lepton mixing matrix, _UPMNS$U_{\mathrm{PMNS}}$. In this paper, we discuss the origin of non-unitarity at the high scale and its evolution through renormalization group running.     

Anomalous gauge-boson couplings and the Higgs-boson mass

We study anomalous gauge-boson couplings induced by a locally SU(2) × U(1) invariant effective Lagrangian containing ten operators of dimension six built from boson fields of the standard model (SM) before spontaneous symmetry breaking (SSB). After SSB some operators lead to new three- and four-gauge-boson interactions, some contribute to the diagonal and off-diagonal kinetic terms of the gauge bosons, to the kinetic term of the Higgs boson and to the mass terms of the W and Z bosons. This requires a renormalisation of the gauge-boson fields, which, in turn, modifies the charged- and neutral-current interactions, although none of the additional operators contain fermion fields. Also the Higgs field must be renormalised. Bounds on the anomalous couplings from electroweak precision measurements at LEP and SLC are correlated with the Higgs-boson mass m_H. Rather moderate values of anomalous couplings allow m_H up to 500 GeV. At a future linear collider the triple-gauge-boson couplings and ZWW can be measured in the reaction . We compare three approaches to anomalous gauge-boson couplings: the form-factor approach, the addition of anomalous-coupling terms to the SM Lagrangian after and, as outlined above, before SSB. The translation of the bounds on the couplings from one approach to another is not straightforward. We show that it can be done for the process by defining new effective and ZWW couplings.Received: 8 June 2004, Revised: 26 January 2005, Published online: 8 June 2005     

CP-Violation from Spin-1 Resonances in a Left-Right Dynamical Higgs Context

New physics field content in the nature, more specifically, from spin-1 resonances sourced by the extension of the SM local gauge symmetry to the larger local group SU(2)_L ⊗ SU(2)_R U(1)_B-L, may induce CP-violation signalling NP effects from higher energy regimes. In this work we completely list and study all the CP-violating operators up to the p⁴-order in the Lagrangian expansion, for a non-linear left-right electroweak chiral context and coupled to a light dynamical Higgs. Heavy right handed fields can be integrated out from the physical spectrum, inducing thus a physical impact in the effective gauge couplings, fermionic electric dipole moment, and CP-violation in the decay h→ ZZ^* → 4l that are briefly analysed. The final relevant set of effective operators have also been identified at low energies.     

基于级联方程的量子耗散半经典方法

We present a semiclassical (SC) approach for quantum dissipative dynamics, constructed on basis of the hierarchical-equation-of-motion (HEOM) formalism. The dynamical components considered in the developed SC-HEOM are wavepackets'' phase-space moments of not only the primary reduced system density operator but also the auxiliary density operators (ADOs) of HEOM. It is a highly numerically efficient method, meanwhile taking into account the high-order effects of system-bath couplings. The SC-HEOM methodology is exemplified in this work on the hierarchical quantum master equation[J. Chem. Phys. 131, 214111 (2009)] and numerically demonstrated on linear spectra of anharmonic oscillators.     

Effective Hamiltonian approach to doubly degenerate electronic states

Effective vibronic Hamiltonian models are built for E ⊗e Jahn-Teller systems and analytical solutions are obtained through Lie algebraic methods. Although approximate, we show that these models allow in particular to recover the possible ground state crossover when quadratic couplings are present. The equivalence of E ⊗e and G' ⊗e vibronic systems in cubic symmetry is precisely established through a particular realization of the electronic operators for an orbital quadruplet. We show how this equivalence is broken by a rovibronic interaction which, for a G' ⊗e system, still gives an exactly solvable model.     

Orientation restraints in molecular dynamics simulations using time and ensemble averaging

In this article we present methodology for simulating protein dynamics while imposing restraints derived from NMR measurements on partially ordered molecules. Such measurements may include residual dipolar couplings and chemical-shift anisotropies. We define a restraint potential for use in molecular dynamics and energy minimization. The presented potential is consistent with the simultaneously optimized molecular order tensor. Restraining can be performed with time and ensemble averaging. We performed a large number of molecular dynamics simulations of the histidine containing phosphocarrier protein with restraints on backbone N-H vector orientations derived from residual dipolar couplings. From these simulations it is evident that the use of time- or ensemble-averaged restraints is essential to leave the fluctuations of the restrained vectors unaffected. Without averaging the fluctuations of the restrained vectors are reduced significantly. This also has the effect of decreasing the apparent molecular order-parameter tensor.     

P and T violating form factors of the deuteron

We calculate the electric-dipole and magnetic-quadrupole form factors of the deuteron that arise as a low-energy manifestation of parity and time-reversal violation in quark-gluon interactions. We consider the QCD vacuum angle and the dimension-six operators that originate from physics beyond the standard model: the quark electric and chromoelectric dipole moments and the gluon chromoelectric dipole moment. Within the framework of two-flavor chiral perturbation theory, we show that in combination with the nucleon electric dipole moment, the deuteron moments would allow an identification of the dominant source(s) of symmetry violation.     

Virasoro constraints and polynomial recursion for the linear Hodge integrals

The Hodge tau-function is a generating function for the linear Hodge integrals. It is also a tau-function of the KP hierarchy. In this paper, we first present the Virasoro constraints for the Hodge tau-function in the explicit form of the Virasoro equations. The expression of our Virasoro constraints is simply a linear combination of the Virasoro operators, where the coefficients are restored from a power series for the Lambert W function. Then, using this result, we deduce a simple version of the Virasoro constraints for the linear Hodge partition function, where the coefficients are restored from the Gamma function. Finally, we establish the equivalence relation between the Virasoro constraints and polynomial recursion formula for the linear Hodge integrals.