On lightest baryon and its excitations in large-N 1+1-dimensional QCD

We study baryons in multicolour 1+1D QCD via Rajeev's gauge-invariant reformulation as a non-linear classical theory of a bilocal meson field constrained to lie on a Grassmannian. It is known to reproduce 't Hooft's meson spectrum via small oscillations around the vacuum, while baryons arise as topological solitons. The lightest baryon has zero mass per colour in the chiral limit; we find its form factor. It moves at the speed of light through a family of massless states. To model excitations of this baryon, we linearize equations for motion in the tangent space to the Grassmannian, parameterized by a bilocal field U. A redundancy in U is removed and an approximation is made in lieu of a consistency condition on U. The baryon spectrum is given by an eigenvalue problem for a hermitian singular integral operator on such tangent vectors. Excited baryons are like bound states of the lightest one with a meson. Using a rank-1 ansatz for U in a variational formulation, we estimate the mass and form factor of the first excitation.Comment: 26 pages, 3 figures, shorter published version, added remarks on parit

Phase transition in matrix model with logarithmic action: Toy-model for gluons in baryons

We study the competing effects of gluon self-coupling and their interactions with quarks in a baryon, using the very simple setting of a hermitian 1-matrix model with action tr A^4 - log det(nu + A^2). The logarithmic term comes from integrating out N quarks. The model is a caricature of 2d QCD coupled to adjoint scalars, which are the transversely polarized gluons in a dimensional reduction. nu is a dimensionless ratio of quark mass to coupling constant. The model interpolates between gluons in the vacuum (nu=infinity), gluons weakly coupled to heavy quarks (large nu) and strongly coupled to light quarks in a baryon (nu to 0). It's solution in the large-N limit exhibits a phase transition from a weakly coupled 1-cut phase to a strongly coupled 2-cut phase as nu is decreased below nu_c = 0.27. Free energy and correlation functions are discontinuous in their third and second derivatives at nu_c. The transition to a two-cut phase forces eigenvalues of A away from zero, making glue-ring correlations grow as nu is decreased. In particular, they are enhanced in a baryon compared to the vacuum. This investigation is motivated by a desire to understand why half the proton's momentum is contributed by gluons.Comment: 20 pages, 7 figure

A critique of recent semi-classical spin-half quantum plasma theories

Certain recent semi-classical theories of spin-half quantum plasmas are examined with regard to their internal consistency, physical applicability and relevance to fusion, astrophysical and condensed matter plasmas. It is shown that the derivations and some of the results obtained in these theories are internally inconsistent and contradict well-established principles of quantum and statistical mechanics, especially in their treatment of fermions and spin. Claims of large semi-classical effects of spin magnetic moments that could dominate the plasma dynamics are found to be invalid both for single-particles and collectively. Larmor moments dominate at high temperature while spin moments cancel due to Pauli blocking at low temperatures. Explicit numerical estimates from a variety of plasmas are provided to demonstrate that spin effects are indeed much smaller than many neglected classical effects. The analysis presented suggests that the aforementioned `Spin Quantum Hydrodynamic' theories are not relevant to conventional laboratory or astrophysical plasmas.Comment: 11 pages, To appear in Contributions to Plasma Physics. Minor correction on page 3 to electron spin magnetic momen

Study of the profile of mucocutaneous lesions in paediatric onset systemic lupus erythematosus, the expression of Interleukin – 17 in cutaneous lesions of lupus erythematosus and the association with disease activity (SLEDAI score)

INTRODUCTION: Systemic lupus erythematosus (SLE) is a chronic, heterogeneous, multifactorial autoimmune disease involving multiple organ systems, the definite aetiology of which remains unknown. It can present with a vast variety of symptoms and clinical manifestations due to which, SLE has often been referred to as „the great mimicker‟ in the past. SLE is the commonest collagen vascular disease occurring in children. About 15% of all patients with SLE develop the disease prior to their sixteenth birthday. The disease can occur at any age and its onset in childhood is not uncommon. The clinical course and manifestations of paediatric SLE (pSLE) is known to be different from that in adults and so do the mucocutaneous features associated with SLE. Systemic Lupus Erythematosus Disease Activity Index (SLEDAI) (Annexure I) is one of the tools used for measuring disease activity, which aids in the follow up of patients and taking decisions with regard to change of therapy. The discovery of TH17 cells and interleukin-17/interleukin-23 (IL-17/IL-23) axis has provided new openings in understanding the pathogenesis of SLE and also suggests a potential therapeutic target. Evident from the several animal and human studies on TH17/IL-17 in the last decade, the role of IL-17 in a variety of diseases including SLE has become the new arena of research activities. pSLE is not a well researched subject in the sub-continent and studies on cutaneous manifestations of pSLE are limited. Till date, there have been no studies from India on the expression of IL-17 in cutaneous lupus erythematosus. OBJECTIVES: Primary objective: To study the profile of mucocutaneous lesions in Psle. Secondary objectives: To the study of the association of skin lesions and IL-17 in skin biopsies with SLEDAI score METHODS: A hospital based cross-sectional study was conducted over a period of 27 months on patients with onset of SLE ≤ 16 years. Demographic and clinical data including mucocutaneous features were recorded and disease activity was calculated using SLEDAI-2K. Immunohistochemistry staining with anti-IL-17 antibody was done on lesional skin biopsies of patients with active LE-related skin lesions who were willing for biopsy. Data on skin lesions was expressed in numbers and percentages. Association of SLEDAI score with mucocutaneous lesions was studied using t-test and Kendall’s tau statistics. Correlation between IL-17 expression and SLEDAI score was done using Spearman’s Rho correlation coefficient. RESULTS: Over 27 months, 140 patients with pSLE were seen and 77.9% of them had mucocutaneous lesions. Non-scarring alopecia, oral ulcers, ACLE and cutaneous vascular disease were among the most frequent mucocutaneous features noted. Mucocutaneous lesions in SLE were found to have a prognostic significance and the presence of LE-related lesions was associated with higher disease activity (p<0.001). A linear correlation was found to exist between IL-17 expression in lupus non-specific lesions with SLEDAI score (R=0.487) but no such correlation existed in case of lupus specific lesions. CONCLUSIONS: In our study done on 140 patients with pSLE, we found that the demographic features and prevalence of mucocutaneous features in our patients were similar to that previously reported. The relative prevalence of most of the individual mucocutaneous features was found to be similar to previous studies done in dermatological and non-dermatological settings. However, the prevalence of malar rash was relatively lower in our study. ACLE (47.8%) was the commonest lupus specific lesion and alopecia (64.2%) was the most frequent non-specific lesion. Oral ulcers were seen in 54.3% patients while 32.9% patients had photosensitivity. Lupus nephritis (54.3%) and arthritis (26.4%) were the commonest forms of systemic involvement. The mean SLEDAI score in our patients was 8.79 ± 7.14 and the median SLEDAI (inter-quartile range) score was 8 (2-14) was comparable to previous data. LE related lesions were found to have a prognostic significance and the presence of either lupus specific or non-specific lesion was associated with higher SLEDAI score (p <0.001). The SLEDAI score was higher in the presence of both lupus specific and non-specific lesions concomitantly than with presence of either lesion alone (p<0.001). Lupus non-specific lesions were found to be associated with higher SLEDAI score than lupus specific lesions but this was not statistically significant (p = 0.32). Lupus non-specific lesions were found to be associated with higher mean IL-17 expression than lupus specific lesions but this was not found to be statistically significant (p = 0.83). Among lupus specific lesions, there was no statistical difference in IL-17 expression between ACLE and DLE (p = 0.39) but the mean IL-17 expression was higher in case of patients with SCLE than with ACLE (p = 0.01) or DLE (p <0.01). A linear correlation was found to exist between IL-17 expression in lupus non-specific lesions with SLEDAI score (R = 0.487) but the number of observations were small. There was no significant linear correlation between the IL-17 expression in lupus specific lesions and SLEDAI score (R = -0.235)