51 research outputs found

### Exponentiation for products of Wilson lines within the generating function approach

We present the generating function approach to the perturbative
exponentiation of correlators of a product of Wilson lines and loops. The
exponentiated expression is presented in closed form as an algebraic function
of correlators of known operators, which can be seen as a generating function
for web diagrams. The expression is naturally split onto two parts: the
exponentiation kernel, which accumulates all non-trivial information about web
diagrams, and the defect of exponentiation, which reconstructs the matrix
exponent and is a function of the exponentiation kernel. The detailed
comparison of the presented approach with existing approaches to exponentiation
is presented as well. We also give examples of calculations within the
generating function exponentiation, namely, we consider different
configurations of light-like Wilson lines in the multi-gluon-exchange-webs
(MGEW) approximation. Within this approximation the corresponding correlators
can be calculated exactly at any order of perturbative expansion by only
algebraic manipulations. The MGEW approximation shows violation of the dipole
formula for infrared singularities at three-loop order.Comment: 33 pages, 5 figures; updated to match journal versio

### Leading logarithms for the nucleon mass

Within the heavy baryon chiral perturbation theory approach, we have studied
the leading logarithm behaviour of the nucleon mass up to four-loop order
exactly and we present some results up to six-loop order as well as an
all-order conjecture. The same methods allow to calculate the main logarithm
multiplying the terms with fractional powers of the quark mass. We calculate
thus the coefficients of $m^{2n+1}\log^{(n-1)}(\mu^2/m^2)$ and
$m^{2n+2}\log^n(\mu^2/m^2)$, with $m$ the lowest-order pion mass. A side result
is the leading divergence for a general heavy baryon loop integral.Comment: 24p, misprints corrected, some minor reformulation

### Leading chiral logarithms for the nucleon mass

We give a short introduction to the calculation of the leading chiral
logarithms, and present the results of the recent evaluation of the leading
logarithm series for the nucleon mass within the heavy baryon theory. The
presented results are the first example of leading logarithm calculation in the
nucleon ChPT. We also discuss some regularities observed in the leading
logarithmical series for nucleon mass. The talk has been presented at "Quark
Confinement and the Hadron Spectrum XI".Comment: 8 pages, 3 figure, proceeding of the XIth international conference on
Quark Confinement and the Hadron Spectrum, September 8-12 2014, St.Peterburg,
Russi

### A theory of baryon resonances at large N_c

At large number of colors, N_c quarks in baryons are in a mean field of
definite space and flavor symmetry. We write down the general Lorentz and
flavor structure of the mean field, and derive the Dirac equation for quarks in
that field. The resulting baryon resonances exhibit an hierarchy of scales: The
crude mass is O(N_c), the intrinsic quark excitations are O(1), and each
intrinsic quark state entails a finite band of collective excitations that are
split as O(1/N_c). We build a (new) theory of those collective excitations,
where full dynamics is represented by only a few constants. In a limiting (but
unrealistic) case when the mean field is spherically-and flavor-symmetric, our
classification of resonances reduces to the SU(6) classification of the old
non-relativistic quark model. Although in the real world N_c is only three, we
obtain a good accordance with the observed resonance spectrum up to 2 GeV.Comment: 27 pages, 4 figures, minor changes, resembles published versio

### Dynamic Speckle Interferometry of Thin Biological Objects: Theory, Experiments, and Practical Perspectives

Relation between the phase dynamics of the waves sounding thin biological object and the dynamics of the speckles in the object image plane was theoretically detected using a model dealing with interference of multiple waves with random phases. Formulas determining the dependence of time‐average intensity I ˜and temporal autocorrelation function η=η(t) of this intensity at a point of the image plane with mean value 〈x〉, mean square deviation σu, and correlation time τ0 of the difference between the optical paths ∆u of the wave pairs in the neighborhood of a conjugate point of the object plane were obtained. A relation between a normalized temporal spectral function of stationary process ∆u(t) and a temporal spectral radiation intensity fluctuation function was substantiated. An optical device relevant to the model used in the theory was developed. Good quantitative coincidence between the theory and the experiment was shown by means of dosed random variation of path difference ∆u. The calibration procedure for the device determining σu was developed; errors and the sensitivity limit of the technique were assessed. Application of value σu as a cell activity parameter on biological objects, namely, a monolayer of live cells on a transparent substrate in a thin cuvette with the nutrient solution was substantiated. It was demonstrated that the technique allows determination of herpes virus in the cells as early as 10 min from the experiment start. A necessity to continue upgrading of the technique was pointed out as well as its prospects for studying the cell reaction to toxic substances, bacteria, and viruses considered

### Correspondence between Soft and Rapidity Anomalous Dimensions

We establish a correspondence between ultraviolet singularities of soft factors for multiparticle production and rapidity singularities of soft factors for multiparton scattering. This correspondence is a consequence of the conformal mapping between scattering geometries. The correspondence is valid to all orders of perturbation theory and in this way, provides one with a proof of rapidity renormalization procedure for multiparton scattering [including the transverse momentum dependent (TMD) factorization as a special case]. As a by-product, we obtain an exact relation between the rapidity anomalous dimension and the well-known soft anomalous dimension. The three-loop expressions for TMD and a general multiparton scattering rapidity anomalous dimension are derived

### Phase transitions in spinor quantum gravity on a lattice

We construct a well-defined lattice-regularized quantum theory formulated in
terms of fundamental fermion and gauge fields, the same type of degrees of
freedom as in the Standard Model. The theory is explicitly invariant under
local Lorentz transformations and, in the continuum limit, under
diffeomorphisms. It is suitable for describing large nonperturbative and
fast-varying fluctuations of metrics. Although the quantum curved space turns
out to be on the average flat and smooth owing to the non-compressibility of
the fundamental fermions, the low-energy Einstein limit is not automatic: one
needs to ensure that composite metrics fluctuations propagate to long distances
as compared to the lattice spacing. One way to guarantee this is to stay at a
phase transition.
We develop a lattice mean field method and find that the theory typically has
several phases in the space of the dimensionless coupling constants, separated
by the second order phase transition surface. For example, there is a phase
with a spontaneous breaking of chiral symmetry. The effective low-energy
Lagrangian for the ensuing Goldstone field is explicitly
diffeomorphism-invariant. We expect that the Einstein gravitation is achieved
at the phase transition. A bonus is that the cosmological constant is probably
automatically zero.Comment: 37 pages, 12 figures Discussion of dimensions and of the
Berezinsky--Kosterlitz--Thouless phase adde

### Low-energy general relativity with torsion: a systematic derivative expansion

We attempt to build systematically the low-energy effective Lagrangian for
the Einstein--Cartan formulation of gravity theory that generally includes the
torsion field. We list all invariant action terms in certain given order; some
of the invariants are new. We show that in the leading order the fermion action
with torsion possesses additional U(1)_L x U(1)_R gauge symmetry, with 4+4
components of the torsion (out of the general 24) playing the role of Abelian
gauge bosons. The bosonic action quadratic in torsion gives masses to those
gauge bosons. Integrating out torsion one obtains a point-like 4-fermion action
of a general form containing vector-vector, axial-vector and axial-axial
interactions. We present a quantum field-theoretic method to average the
4-fermion interaction over the fermion medium, and perform the explicit
averaging for free fermions with given chemical potential and temperature. The
result is different from that following from the "spin fluid" approach used
previously. On the whole, we arrive to rather pessimistic conclusions on the
possibility to observe effects of the torsion-induced 4-fermion interaction,
although under certain circumstances it may have cosmological consequences.Comment: 33 pages, 1 figure. A new section, discussion and references added.
Final (published) versio

### Twist-2 matching of transverse momentum dependent distributions

We systematically study the large-qT (or small-b) matching of transverse momentum dependent (TMD) distributions to the twist-2 integrated parton distributions. Performing operator product expansion for a generic TMD operator at the next-to-leading order (NLO) we found the complete set of TMD distributions that match twist-2. These are unpolarized, helicity, transversity, pretzelosity and linearly polarized gluon distributions. The NLO matching coefficients for these distributions are presented. The pretzelosity matching coefficient is zero at the presented order, however, it is evident that it is non-zero in the following orders. This result offers a natural explanation of the small value of pretzelosity found in phenomenological fits. We also demonstrate that the cancellation of rapidity divergences by the leading order soft factor imposes the necessary requirement on the Lorentz structure of TMD operators, which is supported only by the TMD distributions of leading dynamical twist. Additionally, this requirement puts restrictions on the gamma(5)-definition in the dimensional regularization. (C) 2017 The Authors. Published by Elsevier B.V. This is an open access article under the CC BY license

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