arXiv subjects

Vyacheslav S. Rychkov

Publications and source records attributed to Vyacheslav S. Rychkov.

At least 19 recordsLinked to original sources

arXiv2021

Some weighted Hardy-type inequalities and applications

We study the two-weighted estimate \[ \bigg\|\sum_{k=0}^na_k(x)\int_0^xt^kf(t)dt|L_{q,v}(0,\infty)\bigg\|\leq c\|f|L_{p,u}(0,\infty)\|,\tag{$*$} \] where the functions $a_k(x)$ are not assumed to be positive. It is shown that for $1<p\leq q\leq\infty$, provided that the weight $u$ satisfies the certain conditions, the estimate $(*)$ holds if and only if the estimate \[ \sum_{k=0}^n\bigg\|a_k(x)\int_0^xt^kf(t)dt|L_{q,v}(0,\infty)\bigg\| \leq c\|f|L_{p,u}(0,\infty)\|.\tag{$**$} \] is fulfilled. The necessary and sufficient conditions for $(**)$ to be valid are well-known. The obtained result can be applied to the estimates of differential operators with variable coefficients in some weighted Sobolev spaces.

math.CA↗

arXiv2020

Splitting of Volterra Integral Operators with Degenerate Kernels

Volterra integral operators with non-sign-definite degenerate kernels $A(x,t)= \sum_{k=0}^n A_k(x,t)$, $A_k(x,t)= a_k (x) t^k$, are studied acting from one weighted $L_2$ space on $(0,+\infty)$ to another. Imposing an integral doubling condition on one of the weights, it is shown that the operator with the kernel $A(x,t)$ is bounded if and only $n+1$ operators with kernels $A_k(x,t)$ are all bounded. We apply this result to describe spaces of pointwise multipliers in weighted Sobolev spaces on $(0,+\infty)$.

math.CA↗

arXiv2009

Multi-muon events at the Tevatron: a hidden sector from hadronic collisions

Intrigued by some features of a small but significant fraction of the multi-muon events recently published by the CDF collaboration, we show an explicit attempt to describe them in terms of a light scalar singlet $ϕ$ which communicates with the standard quarks either through a heavy scalar or a heavy fermion exchange. As suggested in arXiv:0810.7530, the singlet $ϕ$ has a chain decay into a final state made of four $τ\barτ$ pairs. We can simulate most of the muon properties of the selected sample of events. Some of these properties adhere rather well to the already published data; others should allow a decisive test of the proposed interpretation. Assuming that the test is positively passed, we show how the PAMELA excess can be fitted by the annihilation of a TeV Dark Matter particle that communicates with the Standard Model via the new light singlet(s).

hep-ph↗

arXiv2009

Universal Constraints on Conformal Operator Dimensions

We continue the study of model-independent constraints on the unitary Conformal Field Theories in 4-Dimensions, initiated in arXiv:0807.0004. Our main result is an improved upper bound on the dimension Δof the leading scalar operator appearing in the OPE of two identical scalars of dimension d. In the interval 1<d<1.7 this universal bound takes the form Δ<2+0.7(d-1)^{1/2}+2.1(d-1)+0.43(d-1)^{3/2}. The proof is based on prime principles of CFT: unitarity, crossing symmetry, OPE, and conformal block decomposition. We also discuss possible applications to particle phenomenology and, via a 2-D analogue, to string theory.

hep-th↗

arXiv2008

Bounding scalar operator dimensions in 4D CFT

In an arbitrary unitary 4D CFT we consider a scalar operator ϕ, and the operator ϕ^2 defined as the lowest dimension scalar which appears in the OPE ϕ\timesϕwith a nonzero coefficient. Using general considerations of OPE, conformal block decomposition, and crossing symmetry, we derive a theory-independent inequality [ϕ^2] \leq f([ϕ]) for the dimensions of these two operators. The function f(d) entering this bound is computed numerically. For d->1 we have f(d)=2+O(\sqrt{d-1}), which shows that the free theory limit is approached continuously. We perform some checks of our bound. We find that the bound is satisfied by all weakly coupled 4D conformal fixed points that we are able to construct. The Wilson-Fischer fixed points violate the bound by a constant O(1) factor, which must be due to the subtleties of extrapolating to 4-εdimensions. We use our method to derive an analogous bound in 2D, and check that the Minimal Models satisfy the bound, with the Ising model nearly-saturating it. Derivation of an analogous bound in 3D is currently not feasible because the explicit conformal blocks are not known in odd dimensions. We also discuss the main phenomenological motivation for studying this set of questions: constructing models of dynamical ElectroWeak Symmetry Breaking without flavor problems.

hep-th↗

arXiv2008

Higgs doublet as a Goldstone boson in perturbative extensions of the Standard Model

We investigate the idea of the Higgs doublet as a pseudo-Goldstone boson in perturbative extensions of the Standard Model, motivated by the desire to ameliorate its hierarchy problem without conflict with the electroweak precision data. Two realistic supersymmetric models with global SU(3) symmetry are proposed, one for large and another for small values of tanβ. The two models demonstrate two different mechanisms for EWSB and the Higgs mass generation. Their experimental signatures are quite different. Our constructions show that a pseudo-Goldstone Higgs doublet in perturbative extensions is just as plausible as in non-perturbative ones.

hep-ph↗

arXiv2008

Heavy Vectors in Higgs-less models

One or more heavy spin-1 fields may replace the Higgs boson in keeping perturbative unitarity up to a few TeV. By means of two prototype chiral models for the heavy spin-1 bosons, a "composite" model or a "gauge" model, we discuss if and how the sole exchange of the same fields can also account for the ElectroWeak Precision Tests. While this proves impossible in the gauge model, the composite model hints to a positive solution, which we exploit to constrain the phenomenological properties of the heavy vectors.

hep-ph↗

arXiv2008

An alternative NMSSM phenomenology with manifest perturbative unification

Can supersymmetric models with a moderate stop mass be made consistent with the negative Higgs boson searches at LEP, while keeping perturbative unification manifest? The NMSSM achieves this rather easily, but only if extra matter multiplets filling complete SU(5) representations are present at intermediate energies. As a concrete example which makes use of this feature, we give an analytic description of the phenomenology of a constrained NMSSM close to a Peccei-Quinn symmetry point. The related pseudo-Goldstone boson appears in decays of the Higgs bosons and possibly of the lightest neutralino, and itself decays into (b anti-b) and (tau anti-tau).

hep-ph↗

arXiv2007

Gravitational corrections to Standard Model vacuum decay

We refine and update the metastability constraint on the Standard Model top and Higgs masses, by analytically including gravitational corrections to the vacuum decay rate. Present best-fit ranges of the top and Higgs masses mostly lie in the narrow metastable region. Furthermore, we show that the SM potential can be fine-tuned in order to be made suitable for inflation. However, SM inflation results in a power spectrum of cosmological perturbations not consistent with observations.

hep-ph↗

arXiv2007

Supersymmetry without a light Higgs boson at the LHC

We analyze the LHC phenomenology of lambdaSUSY - a version of NMSSM with a largish SH1H2 coupling. The scalar spectrum of the model contains a 200-300 GeV Higgs boson h with Standard-Model like properties, and heavy CP-even and CP-odd Higgs bosons H and A with masses in 500-800 GeV range. We study the discovery potential of H and A in the decay chains H->hh->4V->2l6j and A->Zh->Z2V->2l4j. The dominant backgrounds are the diffuse Z6j and Z4j productions, which can be suppressed by demanding reconstruction of V's and h's in intermediate states. The excess of signal events allows for a discovery of both H and A with over 5sigma significance for 100 inverse fb of integrated luminosity.

hep-ph↗

arXiv2007

The Higgs boson from an extended symmetry

The variety of ideas put forward in the context of a "composite" picture for the Higgs boson calls for a simple and effective description of the related phenomenology. Such a description is given here by means of a "minimal" model and is explicitly applied to the example of a Higgs-top sector from an SO(5) symmetry. We discuss the spectrum, the ElectroWeak Precision Tests, B-physics and naturalness. We show the difficulty to comply with the different constraints. The extended gauge sector relative to the standard SU(2)xU(1), if there is any, has little or no impact on these considerations. We also discuss the relation of the "minimal" model with its "little Higgs" or "holographic" extensions based on the same symmetry.

hep-ph↗

arXiv2007

Thermal production of gravitinos

We reconsider thermal production of gravitinos in the early universe, adding to previously considered 2 -> 2 gauge scatterings: a) production via 1 -> 2 decays, allowed by thermal masses; b) the effect of the top Yukawa coupling; c) a proper treatment of the reheating process. Our final result behaves physically (larger couplings give a larger rate) and is twice larger than previous results, implying e.g. a twice stronger constraint on the reheating temperature. Accessory results about (supersymmetric) theories at finite temperature and gravitino couplings might have some interest.

hep-ph↗

arXiv2006

Supersymmetry without a Light Higgs Boson

Motivated by the absence, so far, of any direct signal of conventional low-energy supersymmetry, we explore the consequences of making the lightest Higgs boson in supersymmetry relatively heavy, up to about 300 GeV, in the most straightforward way, i.e. via the introduction of a chiral singlet S with a superpotential interaction with the Higgs doublets, λS H_1 H_2. The coupling λdominates over all the other couplings and, to maintain the successful perturbative analysis of the ElectroWeak Precision Tests, is only restricted to remain perturbative up to about 10 TeV. The general features of this "λSUSY" framework, which deviates significantly from the MSSM or the standard NMSSM, are analyzed in different areas: ElectroWeak Precision Tests, Dark Matter, naturalness bounds on superparticle masses, and LHC signals. There is a rich Higgs/Higgsino sector in the (200-700)GeV mass region, which may include LSP Higgsino dark matter. All other superpartners, apart from the top squarks, may naturally be heavier than 1-2 TeV. This picture can be made consistent with gauge coupling unification.

hep-ph↗

arXiv2006

Improved Naturalness with a Heavy Higgs: An Alternative Road to LHC Physics

The quadratic divergences of the Higgs mass may be cancelled either accidentally or by the exchange of some new particles. Alternatively its impact on naturalness may be weakened by raising the Higgs mass, which requires changing the Standard Model below its natural cut-off. We show in detail how this can be achieved, while preserving perturbativity and consistency with the electroweak precision tests, by extending the Standard Model to include a second Higgs doublet that has neither a vev nor couplings to quarks and leptons. This Inert Doublet Model yields a perturbative and completely natural description of electroweak physics at all energies up to 1.5 TeV. The discrete symmetry that yields the Inert Doublet is unbroken, so that Dark Matter may be composed of neutral inert Higgs bosons, which may have escaped detection at LEP2. Predictions are given for multilepton events with missing transverse energy at the Large Hadron Collider, and for the direct detection of dark matter.

hep-ph↗

arXiv2005

Geometry Quantization from Supergravity: the case of "Bubbling AdS"

We consider the moduli space of 1/2 BPS configurations of type IIB SUGRA found by Lin, Lunin and Maldacena (hep-th/0409174), and quantize it directly from the supergravity action, around any point in the moduli space. This quantization is done using the Crnkovic-Witten-Zuckerman covariant method. We make some remarks on the applicability and validity of this general on-shell quantization method. We then obtain an expression for the symplectic form on the moduli space of LLM configurations, and show that it exactly coincides with the one expected from the dual fermion picture. This equivalence is shown for any shape and topology of the droplets and for any number of droplets. This work therefore generalizes the previous work (hep-th/0505079) and resolves the puzzle encountered there.

hep-th↗

arXiv2005

Minisuperspace Quantization of "Bubbling AdS" and Free Fermion Droplets

We quantize the space of 1/2 BPS configurations of Type IIB SUGRA found by Lin, Lunin and Maldacena (hep-th/0409174), directly in supergravity. We use the Crnkovic-Witten-Zuckerman covariant quantization method to write down the expression for the symplectic structure on this entire space of solutions. We find the symplectic form explicitly around AdS_5 x S^5 and obtain a U(1) Kac-Moody algebra, in precise agreement with the quantization of a system of N free fermions in a harmonic oscillator potential, as expected from AdS/CFT. As a cross check, we also perform the quantization around AdS_5 x S^5 by another method, using the known spectrum of physical perturbations around this background and find precise agreement with our previous calculation.

hep-th↗

arXiv2005

Improved analysis of black hole formation in high-energy particle collisions

We investigate formation of an apparent horizon (AH) in high-energy particle collisions in four- and higher-dimensional general relativity, motivated by TeV-scale gravity scenarios. The goal is to estimate the prefactor in the geometric cross section formula for the black hole production. We numerically construct AHs on the future light cone of the collision plane. Since this slice lies to the future of the slice used previously by Eardley and Giddings (gr-qc/0201034) and by one of us and Nambu (gr-qc/0209003), we are able to improve the prefactor estimates. The black hole production cross section increases by 40-70% in the higher-dimensional cases, indicating larger black hole production rates in future-planned accelerators than previously estimated. We also determine the mass and the angular momentum of the final black hole state, as allowed by the area theorem.

hep-th↗

arXiv2005

Topics in Black Hole Production

We revisit Voloshin's model of multiple black hole production in trans-Planckian elementary particle collisions in D=4. Our revised computation shows that the cross section to produce N additional black holes is suppressed by 1/s, rather than being enhanced as was originally found. We also review the semiclassical gravity picture of black hole production from hep-th/0409131, making additional comments about the meaning of wavepacket subdivision.

hep-th↗