arXiv subjects

A. N. Mitra

Publications and source records attributed to A. N. Mitra.

33 records · Page 2Linked to original sources

arXiv2001

Markov-Yukawa Transversality On Covariant Null-Plane: Baryon Form Factor And Magnetic Moments

The baryon-$qqq$ vertex function governed by the Markov-Yukawa Transversality Principle ($MYTP$), is formulated via the Covariant Null-Plane Ansatz ($CNPA$) as a 3-body generalization of the corresponding $q{\bar q}$ problem, and employed to calculate the proton e.m. form factor and baryon octet magnetic moments.The e.m. coupling scheme is specified by letting the e.m. field interact by turn with the `spectator' while the two interacting quarks fold back into the baryon. The $S_3$ symmetry of the matrix element is preserved in all d.o.f.'s together. The $CNPA$ formulation ensures, as in the $q{\bar q}$ case, that the loop integral is free from the Lorentz mismatch disease of covariant instantaneity ($CIA$), while the simple trick of `Lorentz completion'ensures a Lorentz invariant structure. The $k^{-4}$ scaling behaviour at large $k^2$ is reproduced. And with the infrared structure of the gluonic propagator attuned to spectroscopy, the charge radius of the proton comes out at $0.96 fm$. The magnetic moments of the baryon octet, also in good accord with data, are expressible as $(a+bλ)/(2+λ)$, where $a,b$ are purely geometrical numbers and $λ$ a dynamics-dependent quantity. PACS: 11.10.St ; 12.90.+b ; 13.40.Fn Key Words : Baryon-$qqq$ Vertex; Markov-Yukawa Principle (MYTP); 3D-4D Interlinkage; Covariant null-plane (CNPA); e.m.form factor;baryon magneton.

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arXiv2001

A Microscopic View of Parton $k_T$ Effects In High $p_T$ Processes

A microscopic mechanism is proposed for understanding the rather large $k_T$ effects ($ $ = $1-1.5 GeV/c$, as yet unaccounted for by hard QCD), found by the Fermilab E706 Collaboration for 530 and 800 GeV/c protons incident on light nuclear targets (mass $A$) like Be. The essential idea is that such high incident projectile momenta tend to break up the confinement barriers for the quark-partons residing in the individual nucleonic constituents of the target nucleus that fall in a tube-like zone around the projectile's path, so that these particles tend to behave as a collection of quark-partons confronting the beam. Using simple combinatorial principles, the resultant $ ^2$ value works out as $(3A_{eff}-1) β^2$, where $A_{eff}$ is the number of affected nucleons in the tube-like zone, and $β$ is a scale parameter derived from the basic quark-pair interaction. Using the previously found results of a Bethe-Salpeter model (attuned to $q{\bar q}$ and $qqq$ spectroscopy), one in which a key ingredient is the infrared part of the gluon propagator, giving $β^2= 0.068 GeV^2$, the desired $ $ range is reproduced, suggesting the persistence of $soft$ QCD effects even at high $p_T$. Keywords: Direct photon; high-$p_T$ reaction; parton $k_T$ distribution; soft-QCD effect.

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arXiv2000

Markov-Yukawa Transversality Principle And 3D-4D Interlinkage Of Bethe-Salpeter Amplitudes

This article is designed to focus attention on the Markov-Yukawa Transversality Principle (MYTP) as a novel paradigm for an exact 3D-4D interlinkage between the corresponding BSE amplitudes, with a closely parallel treatment of $q{\bar q}$ and $qqq$ systems, stemming from a common 4-fermion Lagrangian mediated by gluon (vector)-like exchange. This unique feature of MYTP owes its origin to a Lorentz- covariant 3D support to the BS kernel, which acts as a sort of `gauge principle' and distinguishes it from most other 3D approaches to strong interaction dynamics. Some of the principal approaches in the latter category are briefly reviewed so as to set the (less familiar) MYTP in their context. Two specific types of MYTP which provide 3D support to the BSE kernel, are considered: a) Covariant Instantaneity Ansatz (CIA); b) Covariant LF/NP ansatz (Cov.LF). Both lead to formaly identical 3D BSE reductions but produce sharply different 4D structures: Under CIA, the 4D loop integrals suffer from Lorentz mismatch of the vertex functions, leading to ill-defined time-like momentum integrals, but Cov LF is free from this disease. This is illustrated by the pion form factor under Cov LF. The reconstruction of the 4D $qqq$ wave function is achieved by Green's function techniques. PACS: 11.10 st ; 12.38 Lg ; 13.40.Fn. Keywords: Tamm-Dancoff, Bethe-Salpeter, Quasi-potentials, Light-front (LF), Markov-Yukawa, 3D-4D Interlinkage, CIA, Cov-LF, Spectroscopy.

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arXiv2000

A Dynamical Principle For The Salpeter Equation

The `Salpeter Equation' which has long been known as the 3D version of the 4D Bethe-Salpeter Equation under the Instantaneous Approximation, has a well-defined rationale that stems from the half-century old Markov-Yukawa Transversality Principle (MYTP) which not only effects an exact 3D reduction from the original (4D) BS form, but also provides an equally exact reconstruction of the 4D BS amplitude in terms of 3D ingredients. The second aspect which is new, opens up a vista of applications to transition amplitudes as 4D loop integrals. PACS: 03.65.-w ; 03.65.Co ; 11.10.Qr ; 11.10.St Keywords: Salpeter eq; Markov-Yukawa Transversality Principle (MYTP); Covariant Instantaneity; 3D-4D interlinkage; Vertex fn; 4D loop integrals

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arXiv1999

3D-4D Interlinkage Of B-S Amplitudes : Unified View Of QQbar And QQQ Dynamics

This article has a 3-fold objective: i) to provide a panoramic view of several types of 3D vs 4D approaches in Field Theory (Tamm-Dancoff, Bethe Salpeter Equation (BSE), Quasi-potentials, Light-Front Dynamics, etc) for strong interaction dunamics; ii) to focus on the role of the Markov-Yukawa Transversality Principle (MYTP) as a novel paradigm for an exact 3D-4D interlinkage between the corresponding BSE amplitudes; iii) Stress on a closely parallel treatment of $q{\bar q}$ and qqq BSE's stemming from a common 4-fermion Lagrangian mediated by gluon (vector)-like exchange. The two-way interlinkage offered by MYTP between the 3D and 4D BSE forms via a Lorentz-covariant 3D support to the BS kernel, gives it a unique status which distinguishes it from most other 3D approaches to strong interaction dynamics, which give at most a one-way connection. Two specific types of MYTP which provide 3D support to the BSE kernel, are considered: a) Covariant Instantaneity Ansatz (CIA); b) Covariant LF/NP ansatz (Cov.LF). Both lead to formaly identical 3D BSE reductions (thus ensuring common spectral predictions), but their 4D manifestations differ sharply: Under CIA, the 4D loop integrals suffer from Lorentz mismatch of the vertex functions, leading to ill-defined time-like momentum integrals, but Cov LF is free from this disease. Some practical uses of MYTP as a basis for evaluating various types of 4D loop integrals are outlined. PACS: 11.10 st ; 12.38 Lg ; 13.40.Fn Keywords: Tamm-Dancoff, Bethe-Salpeter, Quasi-potentials, Light-front (LF), Markov-Yukawa, 3D-4D Interlinkage, CIA, Cov-LF, Spectroscopy.

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arXiv1999

The Dimensions of Field Theory : From Particles to Strings

This is an editorial summary of the contents of a Book comprising a set of Articles by acknowledged experts dealing with the impact of Field Theory on major areas of physics (from elementary particles through condensed matter to strings), arranged subjectwise under six broad heads. The Book which emphasizes the conceptual, logical and formal aspects of the state of the art in these respective fields, carries a Foreword by Freeman Dyson, and is to be published by the Indian National Science Academy on the occasion of the International Mathematical Year 2000. The authors and full titles of all the Articles (33) are listed sequentially (in the order of their first appearance in the narration) under the bibliography at the end of this Summary, while a few of the individual articles to appear in the Book are already available on the LANL internet.

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arXiv1999

Soft-QCD Effects In B to gamma gamma Decay: Quark Level Form Factors

Soft-QCD effects of quark-level form factors in $γγ$ decay of $B_s$-mesons via $D{\bar D}$ intermediate states, suggested by Ellis et al, are examined in the "Salpeter" model [reinterpreted in terms of the Markov-Yukawa Transversality Principle (MYTP)] when formulated on a covariant light front (null-plane). The gluonic kernel in the infrared regime which generates the constituent mass via standard $DBχS$, is calibrated to both $q{\bar q}$ and qqq spectra, meson mass splittings, pion form factor,and other parameters. With this check, an exact evaluation of the $D{\bar D}γ$ vertex form factor $F(α)$ (normalized to F(0)=1), gives a multiplicative effect of $F^2(α)$ on the $B_s \Rightarrow γγ$ amplitude via D-meson triangle loop, where $α$ = $(p^2+M^2)/M^2$ is the off-shellness parameter of the exchanged D-meson of mass M and 4-momentum $p_μ$, and is a variables of the (internal)loop integration. Unfortunately, the $F^2(α)$ effect decreases the loop amplitude by a factor of 30 w.r.t. the point hadron value, resulting in a reduction of 3 orders of magnitude in long distance (hadronic) contributions to the $B_s \Rightarrow γγ$ decay rate, thus greatly impairing the visibility of such modes. PACS: 11.10.St ; 12.38.Lg ; 13.20.Gd ; 13.40.Hq Keywords: $B_s$ radiative decay; Soft-QCD; Vertex-Fn; Form-factor; Markov-Yukawa-Transversality Principle; Salpeter eq; Cov. light front

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arXiv1999

MarKov-Yukawa Transversality On Covariant Null Plane: Pion Form Factor, Gauge Invariance And Lorentz Completion

The Markov-Yukawa Transversality Principle (MYTP) on a 2-body Bethe-Salpeter kernel is formulated on a covariant Null Plane (NP) to reconstruct the 4D BS wave function for 2 fermion quarks in terms of 3D entities that satisfy a 3D BSE. This result is the null-plane counterpart of a 3D-4D interconnection for the 2-body BS wave functions found earlier by imposing MYTP covariantly in the instantaneous rest frame (termed CIA) of the composite. This formulation yields a 3D BSE which is formally identical to its Covariant Instantaneity form, thus fully preserving its spectral results, while ensuring full covariance. More importantly, the reconstructed 4D vertex functions in the covariant null-plane ensure that 4D quark-loops are now free from ill-defined time-like momentum integrations (which had plagued the earlier CIA vertex functions), while a simple prescription of `Lorentz completion' in the new description yields a manifestly Lorentz-invariant result.This is illustrated for the pion and kaon form factors with full QED gauge-invariance, showing a $k^{-2}$ behaviour at large $k^2$, and `correct' slopes at small $k^2$. This method is compared with the Kadychevsky-Karmanov light-front formalism.

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arXiv1999

Baryon Self-Energy With QQQ Bethe-Salpeter Dynamics In The Non-Perturbative QCD Regime: n-p Mass Difference

A qqq BSE formalism based on DBχS of an input 4-fermion Lagrangian of `current' u,d quarks interacting pairwise via gluon-exchange-propagator in its {\it non-perturbative} regime, is employed for the calculation of baryon self-energy via quark-loop integrals. To that end the baryon-qqq vertex function is derived under Covariant Instantaneity Ansatz (CIA), using Green's function techniques. This is a 3-body extension of an earlier q{\bar q} (2-body) result on the exact 3D-4D interconnection for the respective BS wave functions under 3D kernel support, precalibrated to both q{\bar q} and qqq spectra plus other observables. The quark loop integrals for the neutron (n) - proton (p) mass difference receive contributions from : i) the strong SU(2) effect arising from the d-u mass difference (4 MeV); ii) the e.m. effect of the respective quark charges. The resultant n-p difference comes dominantly from d-u effect (+1.71 Mev), which is mildly offset by e.m.effect (-0.44), subject to gauge corrections. To that end, a general method for QED gauge corrections to an arbitrary momentum dependent vertex function is outlined, and on on a proportionate basis from the (two-body) kaon case, the net n-p difference works out at just above 1 MeV. A critical comparison is given with QCD sum rules results.

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arXiv1999

QCD-Motivated BSE-SDE Framework For Quark-Dynamics Under Markov-Yukawa Transversality

This article aims at an integrated formulation of BSE's for 2- and 3-quark hadrons under the Markov-Yukawa Transversality Principle (MYTP) which provides a deep interconnection between the 3D and 4D BSE forms, and hence offers a unified treatment of 3D spectroscopy with 4D quark-loop integrals for hadronic transitions. For the actual dynamics, an NJL-type realization of DBchiS is achieved via the interplay of Bethe-Salpeter (BSE) and Schwinger-Dyson (SDE) equations, which are simultaneously derivable from a chiral Lagrangian with a gluonic (Vector-exchange) 4-fermion interaction of `current' uds quarks, specifically addressing the non-perturbative regime. A prior critique of the literature on various aspects of the non-perturbative QCD problem, on the basis of some standard criteria, helps converge on a BSE-SDE framework with a 3D-4D interconnection based on MYTP. This framework is then employed for a systematic self-contained presentation of 2- and 3-quark dynamics on the lines of MYTP-governed DBchiS, with enough calculational details illustrating the techniques involved. Specific topics include: 3D-4D interconnection of qbar q and qqq wave functions by Green's Function methods; pion form factor; 3-hadron form factors with unequal mass loops; SU(2) mass splittings; Vacuum condensates (direct and induced); Complex H.O. techniques and SO(2,1) algebras for Baryon Spectroscopy; plus others. PACS: 12.90.+b ; 11.10.St ; 12.70.+q ; 12.38.Lg

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arXiv1998

3D-4D Interlinkage Of qqq Wave Functions Under 3D Support For Pairwise Bethe-Salpeter Kernels

Using the method of Green's functions within a Bethe-Salpeter framework characterized by a pairwise qq interaction with a Lorentz-covariant 3D support to its kernel, the 4D BS wave function for a system of 3 identical relativistic spinless quarks is reconstructed from the corresponding 3D form which satisfies a fully connected 3D BSE. This result is a 3-body generalization of a similar 2-body result found earlier under identical conditions of a 3D support to the corresponding qq-bar BS kernel under Covariant Instaneity (CIA for short). (The generalization from spinless to fermion quarks is straightforward). To set the CIA with 3D BS kernel support ansatz in the context of contemporary approaches to the qqq baryon problem, a model scalar 4D qqq BSE with pairwise contact interactions to simulate the NJL-Faddeev equations is worked out fully, and a comparison of both vertex functions shows that the CIA vertex reduces exactly to the NJL form in the limit of zero spatial range. This consistency check on the CIA vertex function is part of a fuller accounting for its mathematical structure whose physical motivation is traceable to the role of `spectroscopy' as an integral part of the dynamics.

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arXiv1998

On Simulating Liouvillian Flow From Quantum Mechanics Via Wigner Functions

The interconnection between quantum mechanics and probabilistic classical mechanics for a free relativistic particle is derived in terms of Wigner functions (WF) for both Dirac and Klein-Gordon (K-G) equations. Construction of WF is achieved by first defining a bilocal 4-current and then taking its Fourier transform w.r.t. the relative 4-coordinate. The K-G and Proca cases also lend themselves to a closely parallel treatment provided the Kemmer- Duffin beta-matrix formalism is employed for the former. Calculation of WF is carried out in a Lorentz-covariant fashion by standard `trace' techniques. The results are compared with a recent derivation due to Bosanac.

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arXiv1997

Three-Quark Bethe-Salpeter Vertex Function Under Pairwise Gluon-Exchange-Like Interaction : Application to n-p Mass Difference

A qqq BSE formalism based on an input 4-fermion Lagrangian of `current' u,d quarks, is employed for the construction of a relativistic qqq-wave function) via the BSE. Chiral invariance is ensured by the vector character of the gluonic propagator in the infrared regime, while the `constituent' masses are the low momentum limits of the dynamicalmass function generated by standard DBχ. The Covariant Instantaneity Ansatz (CIA) gives an exact 3D reduction of the BSE for baryon spectroscopy, while the reconstructed 4D form identifies the baryon quark vertex function reconstructed through a reversal of steps offered by the CIA structure. It is employed for the quark loop integrals for the neutron - proton mass difference which receives contributions from two sources : i) the strong SU(2) effect arising from the $u-d$ mass difference (4 MeV); ii) the e.m. effect of the respective quark charges. The resultant n-p difference works out at 1.28 MeV (vs. 1.29 expt), with only two free parameters characterizing the infrared structure of the gluonic propagator, precalibrated via a common fit to meson and baryonspectra plus several other observable amplitudes. (PACS : 11.10 st ; 12.35 Ht ; 12.70 + q)

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arXiv1996

Interlinked 3D and 4D 3-Quark Wave Functions in a Bethe-Salpeter Model

Using the method of Green's functions within the framework of a Bethe-Salpeter formalism characterized by a pairwise $qq$ interaction with a 3D support to its kernel (expressed in a Lorentz-covariant manner), the 4D BS wave function for a system of three identical relativistic spinless quarks is reconstructed from the corresponding 3D form which satisfies a {\it fully connected} 3D BSE. This result is a 3-body generalization of a similar interconnection between the 3D and 4D 2-body wave functions that had been found earlier under identical conditions of a 3D support to the corresponding BS kernel, using the ansatz of Covariant Instaneity for the pairwise $q\bar q$ interaction. The generalization from spinless to fermion quarks is straightforward.

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arXiv1994

Off-Shell Rho-Omega Mixing Through Quark Loops With Non-Perturbative Meson Vertex And Quark Mass Functions

The momemtum dependence of the off-shell $ρ$-$ω$ mixing amplitude is calculated through a two-quark loop diagram, using non-perturbative meson-quark vertex functions for the $ρ$ and $ω$ mesons, as well as non-perturbative quark propagators. Both these quantities are generated self-consistently through an interlinked BSE-cum-SDE approach with a 3D support for the BSE kernel with two basic constants which are pre- checked against a wide cross section of both meson and baryon spectra within a common structural framework for their respective 3D BSE's. With this pre-calibration, the on-shell strength works out at -2.434$δ(m_q^2)$ in units of the change in "constituent mass squared", which is consistent with the $e^+e^-$ to $π^+π^-$ data for a u-d mass difference of ~4 MeV ,while the relative off-shell strength (0.99 $\pm$ 0.01) lies midway between quark-loop and QCD-SR results. We also calculate the photon-mediated $ρ$-$ω$ propagator whose off-shell structure has an additional pole at $q^2$=0. The implications of these results vis-a-vis related investigations are discussed.

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