An Effective Field Theory Look at Deep Inelastic Scattering

This talk discusses the effective field theory view of deep inelastic scattering. In such an approach, the standard factorization formula of a hard coefficient multiplied by a parton distribution function arises from matching of QCD onto an effective field theory. The DGLAP equations can then be viewed as the standard renormalization group equations that determines the cut-off dependence of the non-local operator whose forward matrix element is the parton distribution function. As an example, the non-singlet quark splitting functions is derived directly from the renormalization properties of the non-local operator itself. This approach, although discussed in the literature, does not appear to be well known to the larger high energy community. In this talk we give a pedagogical introduction to this subject.Comment: 11 pages, 1 figure, To appear in Modern Physics Letters

Nonperturbative calculation of the anomalous magnetic moment in the Yukawa model within truncated Fock space

Within the covariant formulation of light-front dynamics, we calculate the state vector of a physical fermion in the Yukawa model. The state vector is decomposed in Fock sectors and we consider the first three ones: the single constituent fermion, the constituent fermion coupled to one scalar boson, and the constituent fermion coupled to two scalar bosons. This last three-body sector generates nontrivial and nonperturbative contributions to the state vector, which are calculated numerically. Field-theoretical divergences are regularized using Pauli-Villars fermion and boson fields. Physical observables can be unambiguously deduced using a systematic renormalization scheme we have developed previously. As a first application, we consider the anomalous magnetic moment of the physical fermion.Comment: 24 pages, 16 figure

Systematic renormalization scheme in light-front dynamics with Fock space truncation

Within the framework of the covariant formulation of light-front dynamics, we develop a general non-perturbative renormalization scheme based on the Fock decomposition of the state vector and its truncation. The counterterms and bare parameters needed to renormalize the theory depend on the Fock sectors. We present a general strategy in order to calculate these quantities, as well as state vectors of physical systems, in a truncated Fock space. The explicit dependence of our formalism on the orientation of the light front plane is essential in order to analyze the structure of the counterterms. We apply our formalism to the two-body (one fermion and one boson) truncation in the Yukawa model and in QED, and to the three-body truncation in a scalar model. In QED, we recover analytically, without any perturbative expansion, the renormalization of the electric charge, according to the requirements of the Ward identity.Comment: 32 pages, 14 figures, submitted in Phys. Rev.

Induced current in the presence of magnetic flux tube of small radius

The induced current density, corresponding to the massless Dirac equation in (2+1) dimensions in a magnetic flux tube of small radius is considered. This problem is important for graphene. In the case, when an electron can not penetrate the region of nonzero magnetic field, this current is the odd periodical function of the magnetic flux. If the region inside the magnetic tube is not forbidden for penetration of electron, the induced current is not a periodical function of the magnetic flux. However in the limit $R\to 0$, where $R$ is the radius of magnetic flux tube, this function has the universal form which is independent of the magnetic field distribution inside the magnetic tube at fixed value of the magnetic flux.Comment: 5 pages, 1 figur

Cosmology With Many Light Scalar Fields: Stochastic Inflation and Loop Corrections

We explore the consequences of the existence of a very large number of light scalar degrees of freedom in the early universe. We distinguish between participator and spectator fields. The former have a small mass, and can contribute to the inflationary dynamics; the latter are either strictly massless or have a negligible VEV. In N-flation and generic assisted inflation scenarios, inflation is a co-operative phenomenon driven by N participator fields, none of which could drive inflation on their own. We review upper bounds on N, as a function of the inflationary Hubble scale H. We then consider stochastic and eternal inflation in models with N participator fields showing that individual fields may evolve stochastically while the whole ensemble behaves deterministically, and that a wide range of eternal inflationary scenarios are possible in this regime. We then compute one-loop quantum corrections to the inflationary power spectrum. These are largest with N spectator fields and a single participator field, and the resulting bound on N is always weaker than those obtained in other ways. We find that loop corrections to the N-flation power spectrum do not scale with N, and thus place no upper bound on the number of participator fields. This result also implies that, at least to leading order, the theory behaves like a composite single scalar field. In order to perform this calculation, we address a number of issues associated with loop calculations in the Schwinger-Keldysh "in-in" formalism.Comment: Typos corrected. Matches published versio

Mass of the higgs versus fourth generation masses

The predicted value of the higgs mass $m_H$ is analyzed assuming the existence of the fourth generation of leptons ($N, E$) and quarks ($U, D$). The steep and flat directions are found in the five-dimensional parameter space: $m_H$, $m_U$, $m_D$, $m_N$, $m_E$. The LEPTOP fit of the precision electroweak data is compatible (in particular) with $m_H \sim 300$ GeV, $m_N \sim 50$ GeV, $m_E \sim 100$ GeV, $m_U +m_D \sim 500$ GeV, and $|m_U -m_D| \sim 75$ GeV. The quality of fits drastically improves when the data on b- and c-quark asymmetries and new NuTeV data on deep inelastic scattering are ignored.Comment: 8 pages, 4 figure

On the Significance of the Quantity "A Squared"

We consider the gauge potential A and argue that the minimum value of the volume integral of A squared (in Euclidean space) may have physical meaning, particularly in connection with the existence of topological structures. A lattice simulation comparing compact and non-compact ``photodynamics'' shows a jump in this quantity at the phase transition, supporting this idea.Comment: 6 pages, one figur

Non-commutative SU(N) gauge theories and asymptotic freedom

In this paper we analyze the one-loop renormalization of the $\theta$-expanded $\rm SU(N)$ Yang-Mills theory. We show that the {\it freedom parameter} $a$, key to renormalization, originates from higher order non-commutative gauge interaction, represented by a higher derivative term $b h \theta^{\mu\nu}\hat F_{\mu\nu}\star\hat F_{\rho\sigma}\star\hat F^{\rho\sigma}$. The renormalization condition fixes the allowed values of the parameter $a$ to one of the two solutions: $a=1$ or $a=3$, i.e. to $b=0$ or to $b=1/2$, respectively. When the higher order interaction is switched on, ($a=3$), pure non-commutative SU(N) gauge theory at first order in $\theta$-expansion becomes one-loop renormalizable for various representations of the gauge group. We also show that, in the case $a=3$ and the adjoint representation of the gauge fields, the non-commutative deformation parameter $h$ has to be renormalized and it is asymptotically free.Comment: 16 pages, no figure

Gravitational radiative corrections from effective field theory

In this paper we construct an effective field theory (EFT) that describes long wavelength gravitational radiation from compact systems. To leading order, this EFT consists of the multipole expansion, which we describe in terms of a diffeomorphism invariant point particle Lagrangian. The EFT also systematically captures "post-Minkowskian" corrections to the multipole expansion due to non-linear terms in general relativity. Specifically, we compute long distance corrections from the coupling of the (mass) monopole moment to the quadrupole moment, including up to two mass insertions. Along the way, we encounter both logarithmic short distance (UV) and long wavelength (IR) divergences. We show that the UV divergences can be (1) absorbed into a renormalization of the multipole moments and (2) resummed via the renormalization group. The IR singularities are shown to cancel from properly defined physical observables. As a concrete example of the formalism, we use this EFT to reproduce a number of post-Newtonian corrections to the gravitational wave energy flux from non-relativistic binaries, including long distance effects up to 3PN ($v^6$) order. Our results verify that the factorization of scales proposed in the NRGR framework of Goldberger and Rothstein is consistent up to order 3PN.Comment: 37 pages, LaTeX. Published versio

Once more on extra quark-lepton generations and precision measurements

Precision measurements of $Z$-boson parameters and $W$-boson and $t$-quark masses put strong constraints on non $SU(2)\times U(1)$ singlet New Physics. We demonstrate that one extra generation passes electroweak constraints even when all new particle masses are well above their direct mass bounds.Comment: Dedicated to L.B. Okun's 80th birthda