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Maciej A. Nowak

Publications and source records attributed to Maciej A. Nowak.

At least 73 records · Page 4Linked to original sources
arXiv2004

Status of chiral doublers of heavy-light hadrons in light of recent BaBar Cleo, Belle and Selex D_s states

We explain the main idea of the chiral doublers scenario, originating from simultaneous constraints of chiral symmetry and of heavy quark spin symmetry on effective theories of heavy-light hadrons. In particular we discuss chiral doublers for mesons, chiral doublers for excited mesons, chiral doublers for baryons and chiral doublers for excited baryons. We point out the arguments why new states D_s(2317) and D_s(2457) might be viewed as chiral doublers of D_s and D_s^*. Then we comment on non-strange mesons D_0(2308) and D_1'(2427) observed by Belle and Focus, and on Theta_c(3099) signal observed by H1. Finally, we point out that very recent discovery by SELEX of D_s(2632), if confirmed by other experiments and if spin-parity of this state is 1^-, may be interpreted as a signal for chiral doubler of D_{s1}(2536). Such an identification implies another narrow, spin-parity 2^- D_s state ca 37 MeV above the new 1^-, corresponding to chiral partner of D_{s2}.

hep-ph↗
arXiv2004

Chiral doublers of heavy-light baryons

We discuss the consequences of the chiral doubling scenario for baryons built of heavy and light quarks. In particular, we use the soliton description for baryons, demonstrating why each heavy-light baryon should be accompanied by the opposite parity partner. Our argumentation holds both for ordinary baryons and for exotic heavy pentaquarks which are required by the symmetries of QCD to appear in parity doublets, seperated by the mass shift of the chiral origin. Interpreting the recently observed by BaBaR, CLEO and Belle charmed mesons with assignment $(0^+,1^+)$ as the chiral partners of known $D$ and $D^*$ mesons, allows us to estimate the parameters of the mesonic effective lagrangian, and in consequence, estimate the masses of ground states and excited states of both parities. In particular, we interpret the state recently reported by the H1 experiment at HERA as a chiral partner $\tildeΘ_c^0(3099)$ of yet undiscovered ground state pentaquark $Θ_c^0(2700)$.

hep-ph↗
arXiv2004

A Novel Approach to Non-Hermitian Random Matrix Models

In this paper we propose a new method for studying spectral properties of the non-hermitian random matrix ensembles. Alike complex Green's function encodes, via discontinuities, the real spectrum of the hermitian ensembles, the proposed here quaternion extension of the Green's function leads directly to complex spectrum in case of non-hermitian ensembles and encodes additionally some spectral properties of the eigenvectors. The standard two-by-two matrix representation of the quaternions leads to generalization of so-called matrix-valued resolvent, proposed recently in the context of diagrammatic methods [1-6]. We argue that quaternion Green's function obeys Free Variables Calculus [7,8]. In particular, the quaternion functional inverse of the matrix Green's function, called after [9] Blue's function obeys simple addition law, as observed some time ago [1,3]. Using this law we derive new, general, algorithmic and efficient method to find the non-holomorphic Green's function for all non-hermitian ensembles of the form H+iH', where ensembles H and H' are independent (free in the sense of Voiculescu [7]) hermitian ensembles from arbitrary measure. We demonstrate the power of the method by a straightforward rederivation of spectral properties for several examples of non-hermitian random matrix models.

math-ph↗
arXiv2003

Infinite Products of Large Random Matrices and Matrix-valued Diffusion

We use an extension of the diagrammatic rules in random matrix theory to evaluate spectral properties of finite and infinite products of large complex matrices and large hermitian matrices. The infinite product case allows us to define a natural matrix-valued multiplicative diffusion process. In both cases of hermitian and complex matrices, we observe an emergence of "topological phase transition" in the spectrum, after some critical diffusion time $τ_{\rm crit}$ is reached. In the case of the particular product of two hermitian ensembles, we observe also an unusual localization-delocalization phase transition in the spectrum of the considered ensemble. We verify the analytical formulae obtained in this work by numerical simulation.

math-ph↗
arXiv2003

Chiral Doubling of Heavy-Light Hadrons: BaBar 2317 MeV and CLEO 2463 MeV Discoveries

We point out that the very recent discoveries of BaBar (2317) and CLEO II (2460) are consistent with the general pattern of spontaneous breaking of chiral symmetry in hadrons built of heavy and light quarks, as originally suggested by us in 1992, and independently by Bardeen and Hill in 1993. The splitting between the chiral doublers follows from a mixing between the light constituent quark mass and the velocity of the heavy quark, and vanishes for a zero constituent quark mass. The general strictures of spontaneous chiral symmetry breaking constrain the axial charges in the chiral multiplet, and yield a mass splitting between the chiral doublers of about 345 MeV when the pion coupling to the doublers is half its coupling to a free quark. The chiral corrections are small. This phenomenon is generic and extends to all heavy-light hadrons. We predict the mass splitting for the chiral doublers of the excited mesons (D1,D2). We suggest that the heavy-light doubling can be used to address issues of chiral symmetry restoration in dense and/or hot hadronic matter. In particular, the relative splitting between D and D* mesons and their chiral partners decreases in matter, with consequences on charmonium evolution at RHIC.

hep-ph↗
arXiv2002

Wishart and Anti-Wishart random matrices

We provide a compact exact representation for the distribution of the matrix elements of the Wishart-type random matrices $A^\dagger A$, for any finite number of rows and columns of $A$, without any large N approximations. In particular we treat the case when the Wishart-type random matrix contains redundant, non-random information, which is a new result. This representation is of interest for a procedure of reconstructing the redundant information hidden in Wishart matrices, with potential applications to numerous models based on biological, social and artificial intelligence networks.

math-ph↗
arXiv2001

Lectures on Chiral Disorder in QCD

I explain the concept that light quarks diffuse in the QCD vacuum following the spontaneous breakdown of chiral symmetry. I exploit the striking analogy to disordered electrons in metals, identifying, among others, the universal regime described by random matrix theory, diffusive regime described by chiral perturbation theory and the crossover between these two domains.

hep-ph↗
arXiv2000

Pi0 -> Gamma Gamma in Dense QCD

QCD superconductors in the color-flavor-locked (CFL) phase support light excitations (generalized pions) in the form of particle-particle or hole-hole excitations. We analyze the generalized process $\tildeπ^0\to\tildeγ\tildeγ$ in the weak coupling limit and show that it is related to the recently suggested Wess-Zumino-Witten (WZW) term. In dense QCD, the radiative decay of the generalized pion is constrained by geometry and vanishes at large density.

hep-ph↗
arXiv1999

U(1) Problem at Finite Temperature

We model the effects of a large number of zero and near-zero modes in the QCD partition function by using sparse chiral matrix models with an emphasis on the quenched topological susceptibility in the choice of the measure. At finite temperature, the zero modes are not affected by temperature but are allowed to pair into topologically neutral near-zero modes which are gapped at high temperature. In equilibrium, chiral and U(1) symmetry are simultaneously restored for total pairing, evading mean-field arguments. We analyze a number of susceptibilities versus the light quark masses. At the transition point the topological susceptibility vanishes, and the dependence on the vacuum angle $θ$ drops out. Our results are briefly contrasted with recent lattice simulations.

hep-lat↗
arXiv1999

Chiral Disorder in Two-Color QCD with Abelian External Fluxes

We investigate the effects of several Abelian external fluxes $ϕ$, on the Euclidean Dirac spectrum of light quarks in QCD with two colors. Our results provide for a novel way of assessing the pion weak decay constant directly from spectral fluctuations, and discriminating a flux-rich from a flux-poor vacuum, using QCD lattice simulations.

hep-lat↗
arXiv1999

Green's Functions in Non-hermitian Random Matrix Models

We review some recent techniques for dealing with non-hermitian random matrix models based on generalized Green's functions. We introduce the diagrammatic methods in the hermitian case and generalize them to the non-hermitian case. The results are illustrated in terms of the eigenvalue distribution, eigenvector statistics and addition laws.

cond-mat.dis-nn↗
arXiv1999

$θ$ Vacuum in a Random Matrix Model

Inspired by recent lattice calculations, we model certain aspects of the $θ$-vacuum using a matrix model with gaussian weights. The vacuum energy exhibits a cusp at $θ<π$ that is sensitive to both the accuracy of the numerical analysis and the maximum density of winding modes present in a finite volume.

hep-ph↗
arXiv1999

Chiral Disorder and Diffusion in The QCD Vacuum

In this talk, which popularizes some of our recent work, we provide novel insights into the bulk properties of light chiral quarks in a fixed Euclidean volume (e.g. lattice QCD). We show that the spontaneous breakdown of chiral symmetry results into diffusing quarks with a vacuum diffusion constant $D=2F_π^2/|<\bar{q}q>|$ $\approx 0.22$ fm, in striking analogy to diffusing electrons in disordered metals in one-, two- and three-dimensions.

hep-ph↗
arXiv1999

$θ$ Vacuum: A Matrix Model

We model the effects of a large number of zero modes for $N_f$ species of quarks at finite vacuum angle $θ$, using a matrix model with gaussian weights constrained by the topological susceptibility and compressibility. The quenched free energy exhibits a cusp at $θ<π$ that is sensitive to the accuracy of the numerical analysis and the maximum density of winding modes. Our results bear much in common with recent lattice simulations by Schierholtz and others. The unquenched free energy exhibits similar sensitivities, but for small quark masses or a large density of zero modes the results are in agreement with those derived using chiral effective Lagrangians.

hep-ph↗
arXiv1998

Chiral Random Matrix Models in QCD

We review some motivation behind the introduction of chiral random matrix models in QCD, with particular emphasis on the importance of the Gell-Mann-Oakes (GOR) relation for these arguments. We show why the microscopic limit is universal in power counting, and present arguments for why the macroscopic limit is generic for a class of problems that defy power counting, examples being the strong CP and U(1) problems. Some new results are discussed in light of recent lattice simulations.

hep-ph↗
arXiv1998

Chiral Disorder and QCD Phase Transitions

If QCD is to undergo a second order phase transition, the light quark return probability is universal for large times at the critical point. We show that this behavior is distinct from the one expected at the mobility edge of a metal-insulator transition or a percolation transition in d$\leq 4$. Our results are accessible to current lattice QCD simulations.

hep-ph↗
arXiv1998

Two-Color QCD and Aharonov-Bohm Fluxes

We investigate the effects of several Abelian Aharonov-Bohm fluxes $ϕ$ on the Euclidean Dirac spectrum of light quarks in QCD with two colors. A quantitative change in the quark return probability is caused by the fluxes, resulting into a change of the spectral correlations. These changes are controlled by a universal function of $σ_L ϕ^2$ where $σ_L$ is the pertinent Ohmic conductance. The quark return probability is sensitive to Abelian flux-disorder but not to $Z_2$ flux-disorder in the ergodic and diffusive regime, and may be used as a probe for the nature of the confining fields in the QCD vacuum.

hep-ph↗