Low-energy Theorems Research Articles

Nuclear quasielastic electron scattering limits nucleon off-mass shell properties

The use of quasielastic electron nucleus scattering is shown to provide significant constraints on models of the proton electromagnetic form factor of off-shell nucleons. Such models can be constructed to be consistent with constraints from current conservation and low-energy theorems, while also providing a contribution to the Lamb shift that might potentially resolve the proton radius puzzle in muonic hydrogen. However, observations of quasielastic scattering limit the overall strength of the off-shell form factors to values that correspond to small contributions to the Lamb shift.

Higgs low-energy theorem (and its corrections) in composite models

Abstract The Higgs low-energy theorem gives a simple and elegant way to estimate the couplings of the Higgs boson to massless gluons and photons induced by loops of heavy particles. We extend this theorem to take into account possible nonlinear Higgs interactions as well as new states resulting from a strong dynamics at the origin of the breaking of the electroweak symmetry. We show that, while it approximates with an accuracy of order a few percents single Higgs production, it receives corrections of order 50% for double Higgs production. A full one-loop computation of the gg → hh cross section is explicitly performed in MCHM5, the minimal composite Higgs model based on the SO(5)/SO(4) coset with the Standard Model fermions embedded into the fundamental representation of SO(5). In particular we take into account the contributions of all fermionic resonances, which give sizeable (negative) corrections to the result obtained considering only the Higgs nonlinearities. Constraints from electroweak precision and flavor data on the top partners are analyzed in detail, as well as direct searches at the LHC for these new fermions called to play a crucial role in the electroweak symmetry breaking dynamics.

The Dπ form factors from analyticity and unitarity

We study the shape parameters of the Dπ scalar and vector form factors using as input dispersion relations and unitarity for the moments of suitable heavy-light correlators evaluated with Operator Product Expansions, including O(α2s) terms in perturbative QCD. For the scalar form factor, a low energy theorem and phase information on the unitarity cut are implemented to further constrain the shape parameters. We finally determine points on the real axis and isolate regions in the complex energy plane where zeros of the form factors are excluded.

The Kπ form factors from Analyticity and Unitarity

Analyticity and unitarity techniques are employed to obtain bounds on the shape parameters of the scalar and vector form factors of semileptonic Kl3 decays. For this purpose we use vector and scalar correlators evaluated in pQCD, a low energy theorem for scalar form factor, lattice results for the ratio of kaon and pion decay constants, chiral perturbation theory calculations for the scalar form factor at the Callan-Treiman point and experimental information on the phase and modulus of Kπ form factors up to an energy tin = 1GeV2. We further derive regions on the real axis and in the complex-energy plane where the form factors cannot have zeros.

Decoupling constant for α s and the effective gluon-Higgs coupling to three loops in supersymmetric QCD

We compute the three-loop QCD corrections to the decoupling constant for $\alpha_s$ which relates the Minimal Supersymmetric Standard Model to Quantum Chromodynamics with five or six active flavours. The new results can be used to study the stability of $\alpha_s$ evaluated at a high scale from the knowledge of its value at $M_Z$. We furthermore derive a low-energy theorem which allows the calculation of the coefficient function of the effective Higgs boson-gluon operator from the decoupling constant. This constitutes the first independent check of the matching coefficient to three loops.

Low-energy theorems of QCD and bulk viscosity at finite temperature and baryon density in a magnetic field

The nonperturbative QCD vacuum at finite temperature and a finite baryon density in an external magnetic field is studied. Equations relating nonperturbative condensates to the thermodynamic pressure for $T\neq 0$, $\mu_q \neq 0$ and $H\neq 0$ are obtained, and low-energy theorems are derived. A bulk viscosity $\zeta(T, \mu, H)$ is expressed in terms of basic thermodynamical quantities describing the quark-gluon matter at $T\neq 0$, $\mu_q \neq 0$, and $H\neq 0$. Various limiting cases are also considered.

The scalar gluonium correlator: large-β 0 and beyond

The investigation of the scalar gluonium correlator is interesting because it carries the quantum numbers of the vacuum and the relevant hadronic current is related to the anomalous trace of the QCD energy-momentum tensor in the chiral limit. After reviewing the purely perturbative corrections known up to next-next-to-leading order, the behaviour of the correlator is studied to all orders by means of the large-beta_0 approximation. Similar to the QCD Adler function, the large-order behaviour is governed by the leading ultraviolet renormalon pole. The structure of infrared renormalon poles, being related to the operator product expansion are also discussed, as well as a low-energy theorem for the correlator that provides a relation to the renormalisation group invariant gluon condensate, and the vacuum matrix element of the trace of the QCD energy-momentum tensor.

In-Medium η′ Mass Reduction

In this talk, we present the reduction of the mass of η′-meson at finite temperature which leads to the enhancement of η′ contributions to the dilepton spectra from relativistic heavy ion collisions. QCD low energy theorem, together with the Witten–Veneziano formula, provides the relation of the η′ mass with gluon condensates.

Compositeness of dynamically generated states in a chiral unitary approach

The structure of dynamically generated states in the chiral unitary approach is studied from a viewpoint of their compositeness. We analyze the properties of bound states, virtual states, and resonances in a single-channel chiral unitary approach, paying attention to the energy dependence of the chiral interaction. We define the compositeness of a bound state using the field renormalization constant which is given by the overlap of the bare state and the physical state in the nonrelativistic quantum mechanics, or by the residue of the bound state propagator in the relativistic field theory. The field renormalization constant enables one to define a normalized quantitative measure of compositeness of the bound state. Applying this scheme to the chiral unitary approach, we find that the bound state generated by the energy-independent interaction is always a purely composite particle, while the energy-dependent chiral interaction introduces the elementary component, depending on the value of the cutoff parameter. This feature agrees with the analysis of the effective interaction by changing the cutoff parameter. A purely composite bound state can be realized by the chiral interaction only when the bound state lies at the threshold or when the strength of the two-body attractive interaction is infinitely large. The natural renormalization scheme, introduced by the property of the loop function and the matching with the chiral low-energy theorem, is shown to generate a bound state which is dominated by the composite structure when the binding energy is small.

The strong decays of orbitally excited [formula omitted] mesons by improved Bethe–Salpeter method

We calculate the masses and the strong decays of orbitally excited states Bs0, Bs1′, Bs1 and Bs2 by the improved Bethe–Salpeter method. The predicted masses of Bs0 and Bs1′ are MBs0=5.723±0.280 GeV, MBs1′=5.774±0.330 GeV. We calculate the isospin symmetry violating decay processes Bs0→Bsπ and Bs1′→Bs⁎π through π0–η mixing and get small widths. Considering the uncertainties of the masses, for Bs0 and Bs1′, we also calculate the OZI allowed decay channels: Bs0→BK¯ and Bs1′→B⁎K¯. For Bs1 and Bs2, the OZI allowed decay channels Bs1→B⁎K¯, Bs2→BK¯ and Bs2→B⁎K¯ are studied. In all the decay channels, the reduction formula, PCAC relation and low energy theorem are used to estimate the decay widths. We also obtain the strong coupling constants GBs0Bsπ, GBs0BK¯, GBs1′Bs⁎π, FBs1′Bs⁎π, GBs1′B⁎K¯, FBs1′B⁎K¯, GBs1B⁎K¯, FBs1B⁎K¯, GBs2BK¯ and GBs2B⁎K¯.

Implications of unitarity and analyticity for the Dπ form factors

We consider the vector and scalar form factors of the charm-changing current responsible for the semileptonic decay D\rightarrow \pi l \nu. Using as input dispersion relations and unitarity for the moments of suitable heavy-light correlators evaluated with Operator Product Expansions, including O(\alpha_s^2) terms in perturbative QCD, we constrain the shape parameters of the form factors and find exclusion regions for zeros on the real axis and in the complex plane. For the scalar form factor, a low energy theorem and phase information on the unitarity cut are also implemented to further constrain the shape parameters. We finally propose new analytic expressions for the $D\pi$ form factors, derive constraints on the relevant coefficients from unitarity and analyticity, and briefly discuss the usefulness of the new parametrizations for describing semileptonic data.

Simultaneous decoupling of bottom and charm quarks

We compute the decoupling relations for the strong coupling, the light quark masses, the gauge-fixing parameter, and the light fields in QCD with heavy charm and bottom quarks to three-loop accuracy taking into account the exact dependence on m c /m b . The application of a low-energy theorem allows the extraction of the three-loop effective Higgs-gluon coupling valid for extensions of the Standard Model with additional heavy quarks from the decoupling constant of α s .

Low-energy Theorems for Strongly Interacting W's and Z's in SU(2)L × SU(2)R × U(1)B–L

In this work, low energy theorems for gauge boson (GB) longitudinal modes of the SU(2)L × SU(2)R × U(1)B−L electroweak gauge theory are derived. These theorems are valid for energies in the domain of applicability of the Equivalence Theorem, and hold for all left-right symmetric models assuming that there are no extra contributions from light scalars to the scattering amplitudes.

CALCULATION OF BULK VISCOSITY OF QCD AT ZERO TEMPERATURE AND FINITE CHEMICAL POTENTIAL

In this paper, based on Kubo's formula and the QCD low energy theorem, we propose a direct formula for calculating the bulk viscosity of QCD at finite chemical potential μ and zero temperature. According to this formula, the bulk viscosity at finite μ is totally determined by the dressed quark propagator at finite μ. We then use a dynamical, confining Dyson–Schwinger equation model of QCD to calculate the bulk viscosity at finite μ. It is found that no sharp peak behavior of the bulk viscosity at finite μ is observed, which is quite different from that of the bulk viscosity at finite temperature.

Low-energy theorems of hot and dense QCD in a magnetic field

The nonperturbative QCD vacuum at finite temperature and a finite baryon density in an external magnetic field is studied. Equations that relate nonperturbative condensates to the thermodynamic pressure for T ≠ 0, µq ≠ 0, and H ≠ 0 are obtained, and low-energy theorems are derived.

Chiral Random Matrix Theory and Chiral Perturbation Theory

Spontaneous breaking of chiral symmetry in QCD has traditionally been inferred indirectly through low-energy theorems and comparison with experiments. Thanks to the understanding of an unexpected connection between chiral Random Matrix Theory and chiral Perturbation Theory, the spontaneous breaking of chiral symmetry in QCD can now be shown unequivocally from first principles and lattice simulations. In these lectures I give an introduction to the subject, starting with an elementary discussion of spontaneous breaking of global symmetries.

Low-energy theorems from holography

In the context of gauge/gravity duality, we verify two types of gauge theory low-energy theorems, the dilation Ward identities and the decoupling of heavy flavor. First, we provide an analytic proof of non-trivial dilation Ward identities for a theory holographically dual to a background with gluon condensate (the self-dual Liu--Tseytlin background). In this way an important class of low-energy theorems for correlators of different operators with the trace of the energy-momentum tensor is established, which so far has been studied in field theory only. Another low-energy relationship, the so-called decoupling theorem, is numerically shown to hold universally in three holographic models involving both the quark and the gluon condensate. We show this by comparing the ratio of the quark and gluon condensates in three different examples of gravity backgrounds with non-trivial dilaton flow. As a by-product of our study, we also obtain gauge field condensate contributions to meson transport coefficients.

An asymptotics theorem for low-energy compton scattering in the degenerate case

This representation exhibits explicitly the Lorentz and gauge invariance of the S-matrix. The invariant amplitudes A and B describe the photon–target interaction dynamics. In what follows, k and k′ (p and p′) are the photon (target) initial and finite pulses, P = 1/2(p + p′), χ = 1/4(s− u), s and u are the Mandelstam variables, and eμ is the photon polarization vector. In what follows, we use the Coulomb gauge and the laboratory system of coordinates and consider scattering in the lowest perturbation order. For simplicity, we neglect higher-order effects, in particular, infrared divergences, whose contribution to the particle structure parameters was studied earlier in [2]. The low-energy theorems [3]–[6] state that, up to ω2 (ω = k0), the amplitude T can be represented as T = e ∗ e ′(αω2 − 2e) + ( e× k)( e ′ × k′) β, (1)

Nucleon polarizabilities from deuteron Compton scattering within a Green’s function hybrid approach

We examine elastic Compton scattering from the deuteron for photon energies ranging from zero to 100MeV, using state-of-the-art deuteron wave functions and NN potentials. Nucleon-nucleon rescattering between emission and absorption of the two photons is treated by Green’s functions in order to ensure gauge invariance and the correct Thomson limit. With this Green’s function hybrid approach, we fulfill the low-energy theorem of deuteron Compton scattering and there is no significant dependence on the deuteron wave function used. Concerning the nucleon structure, we use the chiral effective field theory with explicit $ \Delta$ (1232) degrees of freedom within the small-scale expansion up to leading-one-loop order. Agreement with available data is good at all energies. Our 2-parameter fit to all elastic $ \gamma$ d data leads to values for the static isoscalar dipole polarizabilities which are in excellent agreement with the isoscalar Baldin sum rule. Taking this value as additional input, we find $ \alpha_{E}^{s}$ = (11.3±0.7(stat)±0.6(Baldin)±1(theory)).10-4 fm^3 and $ \beta_{M}^{s}$ = (3.2±0.7(stat)±0.6(Baldin)±1(theory)).10-4 fm^3 and conclude by comparison to the proton numbers that neutron and proton polarizabilities are the same within rather small errors.

Pion electroproduction in a nonrelativistic theory

A nonrelativistic effective theory to describe the electroproduction reaction of a single pion on the nucleon at leading order in the electromagnetic coupling is constructed. The framework is tailored to accurately describe the cusp generated by the pion and nucleon mass differences. The S- and P-wave multipole amplitudes at two loops for all four reaction channels are provided. As an application, a new low energy theorem is discussed.