Scalar Mass Universality, “Anomalous”U(1) andRSymmetries

Abstract

When the supersymmetric theory contains the "anomalous" U(1) gauge symmetry with Green-Schwarz anomaly cancellation mechanism in four dimensions, Fayet-Iliopoulos D-term generates generically non-universal scalar masses and the positive cosmological constant after the supersymmetry breaking. Both give the new contributions to the known results obtained from F-term. Our mechanism is naturally realized in many string models and in some cases, leads to remarkable cancellations between F-and D-term contributions, providing the universal scalar mass and vanishing cosmological constant. We illustrate how such a possibility can arise by taking a simple orbifold example. §1. Introduction Supersymmetry (SUSY) provides us with an attractive picture for the physics above the weak scale mz up to the Planck scale Mp. Despite the beautiful structure, we have no convincing evidence yet that such an idea is realized in Nature. This is primarily due to our lack of satisfactory mechanism for dynamical supersymmetry breaking. It should explain the origin of the mass hierarchy mz « Mp and the reason why the cosmological constant A vanishes after the supersymmetry breaking. It should also lead to the predictive low-energy theory to be experimentally checked; without it, we are faced with general set of soft supersymmetry breaking parameters.Here we have little to say about the supersymmetry-breaking mechanism itself. We assume that some mechanism primordially generates the observable supersymmetrybreaking scale m 3 ; 2 "' mz. Actually we work in the conventional scenario of hiddensector gaugino condensation. 2 ) It was argued 3 ), 4 ) that combined with the stringy symmetry, target-space duality, 5 ) the nonperturbative superpotential is generated to break the supersymmetry in F-term sector. Soft breaking parameters were also calcu- lated. 6 )-B)Low-energy phenomenology requires to some extent the "universality" (or degeneracy) of soft-breaking scalar masses. Motivated by "minimal" supergravity, many phenomenological analyses assumed that the scalar masses are all equal at Mp, and deal only with the radiative corrections which invalidate the equality at lower scale. However, being not the logical consequence of local supersymmetry, such an assumption may well be violated. Actually, many string-model calculations 7 ) show that the universality is violated by "moduli-dependent" contributions to scalar masses.So far, much effort has concentr~ted on F-term sector. After early attempts, 9 ), 10 ) little attention has been paid to D-term sector. Our purpose here is to address its possible role in the phenomenological issue related to scalar masses and also in the cosmological constant problem. We would like to argue that if the theory contains an •) The present paper is partially based on the preprint.

Net-baryon number fluctuations across the chiral phase transition at finite density in strong-coupling lattice QCD

“…[44,48,54,55] We obtain the effective action of the auxiliary fields, S AF eff , after the following three steps. First, by integrating out spatial link variables [50,51,52,53,54,55,56,59,60] in the leading order of the strong coupling and 1/d (large-dimensional) expansion [51], one finds a convenient expression for the effective action,…”

“…In the second step, we transform the effective action to the fermion-bilinear form by using the extended Hubbard-Stratonovich (eHS) transformation [59,60],…”

“…One of the possible alternative ways to attack the finite density region is the strong coupling approach of LQCD with fermions [44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61]. The strong coupling approach with fermions could reduce the severity of the sign problem and is applied to investigate the chiral phase transition.…”

Path optimization method for the sign problem

“…In order to attack the sign problem, there have been many attempts such as the Taylor expansion around zero density [6], the analytic continuation from the imaginary chemical potential [7,8], the canonical method based on calculations at imaginary chemical potential [9,10] and the strong coupling expansion in the mean field treatment [11][12][13][14][15][16][17][18] or with the Monte-Carlo calculation [19][20][21][22][23]. Recent developments in the sign problem include the complex Langevin method (CLM) [24][25][26], the Lefschetz thimble method (LTM) [27][28][29], and the generalized Lefschetz thimble method (GLTM) [30,31].…”

Auxiliary field Monte Carlo simulation of strong-coupling lattice QCD for QCD phase diagram

“…Second, we can obtain insight into the QCD phase diagram from the mean-field studies at strong coupling. The chiral transition has systematically and analytically been studied in the strong coupling expansion (1/g 2 expansion) under the mean-field approximation: the strong coupling limit (leading order, O(1/g 0 )) [10][11][12][13][14][15][16][17][18][19], the next-to-leading order (NLO, O(1/g 2 )) [13][14][15][16][17][18][19], and the next-to-next-to-leading order (NNLO, O(1/g 4 )) [16,19] with staggered fermion.…”