New Optimization Methods for Converging Perturbative Series with a Field Cutoff

We take advantage of the fact that in lambda phi ^4 problems a large field cutoff phi_max makes perturbative series converge toward values exponentially close to the exact values, to make optimal choices of phi_max. For perturbative series terminated at even order, it is in principle possible to adjust phi_max in order to obtain the exact result. For perturbative series terminated at odd order, the error can only be minimized. It is however possible to introduce a mass shift in order to obtain the exact result. We discuss weak and strong coupling methods to determine the unknown parameters. The numerical calculations in this article have been performed with a simple integral with one variable. We give arguments indicating that the qualitative features observed should extend to quantum mechanics and quantum field theory. We found that optimization at even order is more efficient that at odd order. We compare our methods with the linear delta-expansion (LDE) (combined with the principle of minimal sensitivity) which provides an upper envelope of for the accuracy curves of various Pade and Pade-Borel approximants. Our optimization method performs better than the LDE at strong and intermediate coupling, but not at weak coupling where it appears less robust and subject to further improvements. We also show that it is possible to fix the arbitrary parameter appearing in the LDE using the strong coupling expansion, in order to get accuracies comparable to ours.Comment: 10 pages, 16 figures, uses revtex; minor typos corrected, refs. adde

Phases of Chiral Gauge Theories

We discuss the behavior of two non-supersymmetric chiral SU(N) gauge theories, involving fermions in the symmetric and antisymmetric two-index tensor representations respectively. In addition to global anomaly matching, we employ a recently proposed inequality constraint on the number of effective low energy (massless) degrees of freedom of a theory, based on the thermodynamic free energy. Several possible zero temperature phases are consistent with the constraints. A simple picture for the phase structure emerges if these theories choose the phase, consistent with global anomaly matching, that minimizes the massless degree of freedom count defined through the free energy. This idea suggests that confinement with the preservation of the global symmetries through the formation of massless composite fermions is in general not preferred. While our discussion is restricted mainly to bilinear condensate formation, higher dimensional condensates are considered for one case. We conclude by commenting briefly on two related supersymmetric chiral theories.Comment: 23 pages, 2 figures, ReVTeX, improved forma

D-type supersymmetry breaking and brane-to-brane gravity mediation

We revisit the issue of gravitational contributions to soft masses in five-dimensional sequestered models. We point out that, unlike for the case of F-type supersymmetry breaking, for D-type breaking these effects generically give positive soft masses squared for the sfermions. This drastically improves model building. We discuss the phenomenological implications of our result.Comment: 16 pages. Typos corrected, minor clarifications. To be published in Phys. Lett.

Holomorphic Quantization on the Torus and Finite Quantum Mechanics

We construct explicitly the quantization of classical linear maps of $SL(2, R)$ on toroidal phase space, of arbitrary modulus, using the holomorphic (chiral) version of the metaplectic representation. We show that Finite Quantum Mechanics (FQM) on tori of arbitrary integer discretization, is a consistent restriction of the holomorphic quantization of $SL(2, Z)$ to the subgroup $SL(2, Z)/\Gamma_l$, $\Gamma_l$ being the principal congruent subgroup mod l, on a finite dimensional Hilbert space. The generators of the ``rotation group'' mod l, $O_{l}(2)\subset SL(2,l)$, for arbitrary values of l are determined as well as their quantum mechanical eigenvalues and eigenstates.Comment: 12 pages LaTeX (needs amssymb.sty). Version as will appear in J. Phys.

B→πℓℓB\to\pi\ell\ell form factors for new-physics searches from lattice QCD

The rare decay $B\to\pi\ell^+\ell^-$ arises from $b\to d$ flavor-changing neutral currents and could be sensitive to physics beyond the Standard Model. Here, we present the first $ab$-$initio$ QCD calculation of the $B\to\pi$ tensor form factor $f_T$. Together with the vector and scalar form factors $f_+$ and $f_0$ from our companion work [J. A. Bailey $et~al.$, Phys. Rev. D 92, 014024 (2015)], these parameterize the hadronic contribution to $B\to\pi$ semileptonic decays in any extension of the Standard Model. We obtain the total branching ratio ${\text{BR}}(B^+\to\pi^+\mu^+\mu^-)=20.4(2.1)\times10^{-9}$ in the Standard Model, which is the most precise theoretical determination to date, and agrees with the recent measurement from the LHCb experiment [R. Aaij $et~al.$, JHEP 1212, 125 (2012)]. Note added: after this paper was submitted for publication, LHCb announced a new measurement of the differential decay rate for this process [T. Tekampe, talk at DPF 2015], which we now compare to the shape and normalization of the Standard-Model prediction.Comment: V3: Corrected errors in results for Standard-Model differential and total decay rates in abstract, Fig. 3, Table IV, and outlook. Added new preliminary LHCb data to Fig. 3 and brief discussion after outlook. Replaced outdated correlation matrix in Table III with correct final version. Other minor wording changes and references added. 7 pages, 4 tables, 3 figure

Cosmological Implications of Dynamical Supersymmetry Breaking

We provide a taxonomy of dynamical supersymmetry breaking theories, and discuss the cosmological implications of the various types of models. Models in which supersymmetry breaking is produced by chiral superfields which only have interactions of gravitational strength (\eg\ string theory moduli) are inconsistent with standard big bang nucleosynthesis unless the gravitino mass is greater than \CO(3) \times 10^4 GeV. This problem cannot be solved by inflation. Models in which supersymmetry is dynamically broken by renormalizable interactions in flat space have no such cosmological problems. Supersymmetry can be broken either in a hidden or the visible sector. However hidden sector models suffer from several naturalness problems and have difficulties in producing an acceptably large gluino mass.Comment: 24 pages (uses harvmac) UCSD/PTH 93-26, RU-3

Refining new-physics searches in B -> D tau nu decay with lattice QCD

The semileptonic decay channel B -> D tau nu is sensitive to the presence of a scalar current, such as that mediated by a charged-Higgs boson. Recently the BaBar experiment reported the first observation of the exclusive semileptonic decay B -> D tau nu, finding an approximately 2-sigma disagreement with the Standard-Model prediction for the ratio R(D)=BR(B->D tau nu)/BR(B->D l nu), where l=e,mu. We compute this ratio of branching fractions using hadronic form factors computed in unquenched lattice QCD and obtain R(D) = 0.316(12)(7), where the errors are statistical and total systematic, respectively. This result is the first Standard-Model calculation of R(D) from ab initio full QCD. Its error is smaller than that of previous estimates, primarily due to the reduced uncertainty in the scalar form factor f_0(q^2). Our determination of R(D) is approximately 1-sigma higher than previous estimates and, thus, reduces the tension with experiment. We also compute R(D) in models with electrically charged scalar exchange, such as the type II two-Higgs doublet model. Once again, our result is consistent with, but approximately 1-sigma higher than, previous estimates for phenomenologically relevant values of the scalar coupling in the type II model. As a byproduct of our calculation, we also present the Standard-Model prediction for the longitudinal polarization ratio P_L (D)= 0.325(4)(3).Comment: 6 pages, 3 figures, 1 table. References and text added. Fig. 3 R(D) in 2HDM II corrected and conclusions modified. Standard-Model R(D) unchange

B_s->D_s/B->D Semileptonic Form-Factor Ratios and Their Application to BR(B^0_s->\mu^+\mu^-)

We calculate form-factor ratios between the semileptonic decays \bar{B}->D^+\ell^-\bar{\nu} and \bar{B}_s->D_s^+\ell^-\bar{\nu} with lattice QCD. These ratios are a key theoretical input in a new strategy to determine the fragmentation fractions of the neutral B decays, which are needed for measurements of BR(B^0_s-> \mu^+\mu^-). We use the MILC ensembles of gauge configurations with 2+1 flavors of sea quarks at two lattice spacings of approximately 0.12 fm and 0.09 fm. We use the model-independent z-parametrization to extrapolate our simulation results at small recoil toward maximum recoil. Our results for the form-factor ratios are $f_0^{(s)}(M^2_\pi)/f_0^{(d)}(M^2_K) =1.046(44)_{stat.}(15)_{syst.}$ and $f_0^{(s)}(M^2_\pi)/f_0^{(d)}(M^2_\pi)=1.054(47)_{stat.}(17)_{syst.}$. In contrast to a QCD sum-rule calculation, no significant departure from U-spin (ds) symmetry is observed.Comment: 30 pages, 11 figures. Fig. 1 updated. Table II added. Conforms with version published in Physical Review D, except typos fixed, as in the PRD Erratum, in Table V (previously Table IV in arXiv v1). Results unchange

Bs→KℓνB_s \to K \ell\nu form factors with 2+1 flavors

Using the MILC 2+1 flavor asqtad quark action ensembles, we are calculating the form factors $f_0$ and $f_+$ for the semileptonic $B_s \rightarrow K \ell\nu$ decay. A total of six ensembles with lattice spacing from $\approx0.12$ to 0.06 fm are being used. At the coarsest and finest lattice spacings, the light quark mass $m'_l$ is one-tenth the strange quark mass $m'_s$. At the intermediate lattice spacing, the ratio $m'_l/m'_s$ ranges from 0.05 to 0.2. The valence $b$ quark is treated using the Sheikholeslami-Wohlert Wilson-clover action with the Fermilab interpretation. The other valence quarks use the asqtad action. When combined with (future) measurements from the LHCb and Belle II experiments, these calculations will provide an alternate determination of the CKM matrix element $|V_{ub}|$.Comment: 8 pages, 6 figures, to appear in the Proceedings of Lattice 2017, June 18-24, Granada, Spai