Calibrating the Na\"ive Cornell Model with NRQCD

Along the years, the Cornell Model has been extraordinarily successful in describing hadronic phenomenology, in particular in physical situations for which an effective theory of the strong interactions such as NRQCD cannot be applied. As a consequence of its achievements, a relevant question is whether its model parameters can somehow be related to fundamental constants of QCD. We shall give a first answer in this article by comparing the predictions of both approaches. Building on results from a previous study on heavy meson spectroscopy, we calibrate the Cornell model employing NRQCD predictions for the lowest-lying bottomonium states up to N$^3$LO, in which the bottom mass is varied within a wide range. We find that the Cornell model mass parameter can be identified, within perturbative uncertainties, with the MSR mass at the scale $R = 1\,$GeV. This identification holds for any value of $\alpha_s$ or the bottom mass, and for all perturbative orders investigated. Furthermore, we show that: a) the "string tension" parameter is independent of the bottom mass, and b) the Coulomb strength $\kappa$ of the Cornell model can be related to the QCD strong coupling constant $\alpha_s$ at a characteristic non-relativistic scale. We also show how to remove the $u=1/2$ renormalon of the static QCD potential and sum-up large logs related to the renormalon subtraction by switching to the low-scale, short-distance MSR mass, and using R-evolution. Our R-improved expression for the static potential remains independent of the heavy quark mass value and agrees with lattice QCD results for values of the radius as large as $0.8\,$fm, and with the Cornell model potential at long distances. Finally we show that for moderate values of $r$, the R-improved NRQCD and Cornell static potentials are in head-on agreement.Comment: 22 pages, 13 figures, 3 table

Effective penetration length and interstitial vortex pinning in superconducting films with regular arrays of defects

In order to compare magnetic and non-magnetic pinning we have nanostructured two superconducting films with regular arrays of pinning centers: Cu (non-magnetic) dots in one case, and Py (magnetic) dots in the other. For low applied magnetic fields, when all the vortices are pinned in the artificial inclusions, magnetic dots prove to be better pinning centers, as has been generally accepted. Unexpectedly, when the magnetic field is increased and interstitial vortices appear, the results are very different: we show how the stray field generated by the magnetic dots can produce an effective reduction of the penetration length. This results in strong consequences in the transport properties, which, depending on the dot separation, can lead to an enhancement or worsening of the transport characteristics. Therefore, the election of the magnetic or non-magnetic character of the pinning sites for an effective reduction of dissipation will depend on the range of the applied magnetic field.Comment: 10 pages, 3 figure

Umuhimu na Changamoto za TEHAMA katika Ufundishaji na Ujifunzaji wa Lugha ya Kiswahili kwa Wageni

Ulimwengu wa utandawazi umesababisha kusambaa kwa matumizi ya Teknolojia ya Habari na Mawasiliano (TEHAMA), hususani matumizi ya kompyuta na viambata vyake. Kwa hali hiyo, maendeleo yamesababisha kuenea kwa lugha zinazotumika katika teknolojia hiyo kama vile Kiingereza na lugha nyingine za Kimagharibi, na kwa kiasi kidogo, lugha za Kiafrika kama vile Kiswahili. Hata hivyo, TEHAMA imekuwa ikitumiwa na walimu na wanafunzi katika kufundishia na kujifunzia lugha za kigeni hasa Kiingereza kama inavyoelezwa na Lopez (2016), Bostina (2016), Bilyalova (2016). Aidha, zipo tafiti chache zilizozungumzia changamoto za kutumia Kiswahili katika TEHAMA, kwa ujumla, bila kuzungumzia namna Kiswahili kinavyoweza kutumika kiteknolojia katika ufundishaji na ujifunzaji kwa wageni. Kwa hiyo, makala haya yamejadili suala hilo na yanajikita katika kufafanua umuhimu na changamoto za TEHAMA katika ufundishaji na ujifunzaji wa Kiswahili kwa wageni. Aidha, makala haya yametoa mapendekezo ya nini cha kufanya ili kukabiliana na changamoto zinazojitokeza katika ufundishaji na ujifunzaji huo. Data zilizotumika katika makala haya zimepatikana kwa njia ya dodoso. Mkabala wa kitaamuli umetumika katika kuchambua data. Matokeo yamebaini kuwa kuna umuhimu wa kutumia TEHAMA katika kufundishia na kujifunzia Kiswahili kwa wageni kwani inarahisisha ufundishaji kwa maana ya kutumia muda mfupi kufundisha mambo mengi. Pia, inamfanya mwanafunzi afurahie somo bila kuchoka na kupunguza gharama za ujifunzaji. Pamoja na umuhimu huo, zimebainika changamoto katika matumizi ya TEHAMA, yaani wakati mwingine wanafunzi wanapata shida kutumia matini zilizo mtandaoni kutokana na kukosa mwingiliano wa moja kwa moja na mwalimu, kukosekana kwa matini za kutosha na zilizoandikwa kwa usahihi mitandaoni, kukosekana kwa vifaa kama projekta na kompyuta na baadhi ya walimu na wanafunzi kutokuwa na maarifa ya kutosha ya matumizi ya vifaa hivyo. Kwa ujumla, makala yanahitimisha kwamba upo umuhimu wa kupendekeza mbinu zinazoweza kukabiliana na changamoto hizo kama vile kuwa na semina za mara kwa mara za kufundisha namna ya kutumia vifaa vinavyohusiana na TEHAMA, kuwa na vifaa vya kutosha na vinavyokidhi mahitaji y

Dispersion Relation Bounds for pi pi Scattering

Axiomatic principles such as analyticity, unitarity and crossing symmetry constrain the second derivative of the pi pi scattering amplitudes in some channels to be positive in a region of the Mandelstam plane. Since this region lies in the domain of validity of chiral perturbation theory, we can use these positivity conditions to bound linear combinations of \bar{l}_1 and \bar{l}_2. We compare our predictions with those derived previously in the literature using similar methods. We compute the one-loop pi pi scattering amplitude in the linear sigma model (LSM) using the MS-bar scheme, a result hitherto absent in the literature. The LSM values for \bar{l}_1 and \bar{l}_2 violate the bounds for small values of m_sigma/m_pi. We show how this can occur, while still being consistent with the axiomatic principles.Comment: 12 pages, 8 figures. Two references added, a few minor changes. Published versio

Green functions and the Dirichlet spectrum

This article has results of four types. We show that the firsteigenvalueλ1(Ω) of the weighted Laplacian of a bounded domain withsmooth boundary can be obtained by S. Sato’s iteration scheme of theGreen operator, taking the limitλ1(Ω) = limk→∞‖Gk(f)‖L2/‖Gk+1(f)‖L2for anyf∈L2(Ω,μ),f >0, (Theorems 2.1 & 2.2). Then, we study theL1(Ω,μ)-moment spectrum of Ω in terms of iterates of the Green oper-atorG, (Theorem 3.2), extendind the work of MacDonald-Meyers [29]to the weighted setting. As corollary, we obtain the first eigenvalue ofa weighted bounded domain in terms of theL1(Ω,μ)-moment spectrum,generalizing the work of Hurtado-Markvorsen-Palmer [25]. Finally, westudy the radial spectrumσrad(Bh(o,r)) of rotationally invariant geodesicballsBh(o,r) of model manifolds. In Theorems 5.4 & 5.6, we prove anidentity relating the radial eigenvalues ofσrad(Bh(o,r)) to an isoperimet-ric quotient, i.e.∑1/λradi=∫V(s)/S(s)ds,V(s) = vol(Bh(o,s)) andS(s) = vol(∂Bh(o,s)). We then consider a proper minimal surfaceM⊂R3and the extrinsic ball Ω =M∩BR3(o,r). We obtain upper and lower es-timates for the series∑λ−2i(Ω) in terms of the volume vol(Ω) and theradiusrof the extrinsic ball Ω, (Theorem 6.1)