Baryon Operators Research Articles

Stealth dark matter spectrum using Laplacian Heaviside smearing and irreducible representations

We present nonperturbative lattice calculations in the quenched approximation of the low-lying meson and baryon spectrum of the SU(4) gauge theory with fundamental fermion constituents. This theory is one instance of stealth dark matter, a class of strongly coupled theories, where the lowest mass stable baryon is the dark matter candidate. This work constitutes the first milestone in the program to study stealth dark matter self-interactions. Here, we focus on reducing excited state contamination in the single-baryon channel by applying the Laplacian Heaviside method, as well as projecting our baryon operators onto the irreducible representations of the octahedral group. We compare our resulting spectrum to previous work involving Gaussian smeared nonprojected operators and find good agreement with reduced statistical uncertainties. We also present the spectrum of the low-lying odd-parity baryons for the first time. Published by the American Physical Society 2024

Alternative approach to baryon masses in the 1/Nc expansion of QCD

The baryon mass operator is studied within a combined expansion in 1/Nc and perturbative SU(3) flavor symmetry breaking, where Nc denotes the number of color charges. Flavor projection operators are used to classify the baryon operators involved in the expansion, which fall into the flavor representations 1, 8, 10+10¯, 27, 35+35¯, and 64. This approach allows one to incorporate up to third-order flavor symmetry breaking in the baryon mass operator in a rigorous and systematic way. Previous work on the subject is considered to validate the approach. A fit to data is performed to evaluate the free parameters in the theory and to produce some numerical values of baryon masses. Results are consistent and reaffirm the striking success of the 1/Nc expansion. Published by the American Physical Society 2024

Baryonic states in mathbf {{mathcal {N}}=1} supersymmetric SU(2) Yang–Mills theory on the lattice

We extend our analysis of bound states in {mathcal {N}}=1 supersymmetric Yang–Mills theory by the consideration of baryonic operators, which are composed of three gluino fields. The corresponding states are similar to the baryons in QCD, but due to the difference between gluino and quark fields, their properties and the fermion line contractions involved in their correlation functions are different from QCD. In this work, we first explain the derivation of these operators and the contractions needed in numerical calculations of their correlators. In contrast to QCD the correlators contain a spectacle piece, which requires methods for all-to-all propagators. We provide a first estimate of the two-point function and the mass of the lightest baryonic state in {mathcal {N}}=1 supersymmetric Yang–Mills theory.

On the search for multicenter AdS black holes from M-theory

We study the effective potentials for various probe branes surrounding AdS4 black holes with massive halos in consistent truncations of M-theory on the Sasaki-Einstein7 manifolds Q111 and M111. These probes are either M2 branes extended in spacetime or “particle-like” probes such as internally wrapped M2 branes and, upon reduction to type IIA String theory, D6 branes corresponding to baryon operators in the dual Chern-Simons theory. We find both global and local minima of the potential outside the horizon, indicating the existence of stable and metastable multicenter AdS black holes in the extreme mass ratio regime, at fixed temperature and charges. For the planar case, we also find an instability towards nucleation of spacetime-filling M2 branes. With this analysis, we address some open questions on the holographic description of glassy phases of matter.

Monopoles and dualities in 3d mathcal{N} = 2 quivers

Seiberg-like dualities in 2 + 1d quiver gauge theories with 4 supercharges are investigated. We consider quivers made of various combinations of classical gauge groups U(N), Sp(N), SO(N) and SU(N). Our main focus is the mapping of the supersymmetric monopole operators across the dual theories. There is a simple general rule that encodes the mapping of the monopoles upon dualizing a single node. This rule dictates the mapping of all the monopoles which are not dressed by baryonic operators. We also study more general situations involving baryons and baryon-monopoles, focussing on three examples: SU − Sp, SO − SO and SO − Sp quivers.

Fermions and baryons as open-string states from brane junctions

There has been recent progress towards understanding the dynamics of world-volume fermions that arise as open-string modes from brane intersections in the probe limit (Nf/Nc → 0). In this work we consider all possible BPS brane junctions in Type IIA/B supergravity theories. We study in detail the dynamics of these states by deriving their equations of motion. We show the expected degeneracy of the bosonic and fermionic fluctuations as is expected due to the preserved supersymmetry. We also give some supporting evidence and refine the notion that these states can effectively describe baryon operators in a certain regime of the field theory’s parameter space. Our piece of evidence is the demonstration of the expected scaling of the mass in the large-Nc limit of the theory for these fermionic states; M2 ∼ {N}_c^2 . Finally, we explain analytically the avoided level crossing that was observed in a previous work after the inclusion of higher dimension operators in the field theory.

Heavy baryon spectrum on the lattice with NRQCD bottom and HISQ lighter quarks

We determine the mass spectra of heavy baryons containing one or more bottom quarks along with their hyperfine splittings and various mass differences on MILC 2+1 Asqtad lattices at three different lattice spacings. NRQCD action is used for bottom quarks whereas relativistic HISQ action for the lighter up/down, strange and charm quarks. We consider all possible combinations of bottom and lighter quarks to construct the bottom baryon operators for the states $J^P=1/2^+$ and $3/2^+$.

Twisted mathcal{N} = 1 SCFTs and their AdS3 duals

We study compactifications of an infinite family of four-dimensional mathcal{N} = 1 SCFTs on a Riemann surface in the presence of arbitrary background fluxes for global symmetries. The four-dimensional parent theories have holographic Sasaki-Einstein duals in type IIB string theory. We compute central charges and R-charges of baryonic operators in the resulting two-dimensional mathcal{N} = (0, 2) theories in three distinct ways: from the field theory side utilizing c-extremization, its recently discovered geometric dual formulation, and holographically using new AdS3 duals of two-dimensional field theories.

3d “chiral” Kutasov-Schwimmer duality

We propose a “chiral” version of Kutasov-Schwimmer duality in a 3d N=2SU(N) gauge theory with F fundamental matters, F¯ anti-fundamental matters and an adjoint matter X with a tree-level superpotential W=trXk+1. The theory exhibits a rich structure of the baryonic and (dressed) Coulomb branch operators. At first sight, the duality seems incorrect due to a mismatch of the anti-baryonic branch of the moduli space under the duality transformation. The duality well works by realizing that the anti-baryonic operators are identified with some of the dressed Coulomb branch corresponding to non-abelian monopoles. This generalizes the SU(N) “chiral” duality with (anti-)fundamental matters, which we previously proposed.

Baryon number, lepton number, and operator dimension in the SMEFT with flavor symmetries

Using group theory techniques, we investigate the mathematical relationship between baryon number, lepton number, and operator dimension in the Standard Model effective field theory (SMEFT), when flavor symmetries are present. For a large set of flavor symmetries, the lowest-dimensional baryon- or lepton-number violating operators in the SMEFT with flavor symmetry are of mass dimension 9. As a consequence, baryon- and lepton-number violating processes are further suppressed with the introduction of flavor symmetries, e.g., the allowed scale associated with proton decay is typically lowered to 105 GeV, which is significantly lower than the GUT scale. To illustrate these features, we discuss Minimal Flavor Violation for the Standard Model augmented by sterile neutrinos.

Safe glueballs and baryons

We consider a non-Abelian gauge theory with Nf fermions and discuss the possible existence of a non-trivial UV fixed point at large Nf . Specifically, we study the anomalous dimension of the (rescaled) glueball operator Tr F2 to first order in 1/Nf by relating it to the derivative of the beta function at the fixed point. At the fixed point the anomalous dimension violates its unitarity bound and so the (rescaled) glueball operator is either decoupled or the fixed point does not exist. We also study the anomalous dimensions of the two spin-1/2 baryon operators to first order in 1/Nf for an SU(3) gauge theory with fundamental fermions and find them to be relatively small and well within their associated unitarity bounds.

3d Self-dualities

We investigate self-dualities in three-dimensional N=2 supersymmetric gauge theories. The electric and magnetic theories share the same gauge group. The examples include SU(2N), SO(7) and SO(8) gauge theories with various matter contents. In some examples, the duality exchanges the role of the baryon and Coulomb branch operators. In other examples, the Coulomb branch operator becomes an elementary field on the dual side. These self-dualities in turn teach us a correct quantum structure of the Coulomb moduli space of vacua. Some dualities exhibit symmetry enhancement.

Toric geometry and the dual of c-extremization

We consider D3-brane gauge theories at an arbitrary toric Calabi-Yau 3-fold cone singularity that are then further compactified on a Riemann surface Σg, with an arbitrary partial topological twist for the global U(1) symmetries. This constitutes a rich, infinite class of two-dimensional (0, 2) theories. Under the assumption that such a theory flows to a SCFT, we show that the supergravity formulas for the central charge and R-charges of BPS baryonic operators of the dual AdS3 solution may be computed using only the toric data of the Calabi-Yau 3-fold and the topological twist parameters. We exemplify the procedure for both the Yp,q and Xp,q 3-fold singularities, along with their associated dual quiver gauge theories, showing that the new supergravity results perfectly match the field theory results obtained using c-extremization, for arbitrary twist over Σg. We furthermore conjecture that the trial central charge , which we define in gravity, matches the field theory trial c-function off-shell, and show this holds in non-trivial examples. Finally, we check our general geometric formulae against a number of explicitly known supergravity solutions.

Flavored surface defects in 4d $$\mathcal{N}=1$$ N = 1 SCFTs

We discuss supersymmetric surface defects in compactifications of six dimensional minimal conformal matter of type SU(3) and SO(8) to four dimensions. The relevant field theories in four dimensions are N=1 quiver gauge theories with SU(3) and SU(4) gauge groups respectively. The defects are engineered by giving space-time dependent vacuum expectation values to baryonic operators. We find evidence that in the case of SU(3) minimal conformal matter the defects carry SU(2) flavor symmetry which is not a symmetry of the four dimensional model. The simplest case of a model in this class is SU(3) SQCD with nine flavors and thus the results suggest that this admits natural surface defects with SU(2) flavor symmetry. We analyze the defects using the superconformal index and derive analytic difference operators introducing the defects into the index computation. The duality properties of the four dimensional theories imply that the index of the models is a kernel function for such difference operators. In turn, checking the kernel property constitutes an independent check of the dualities and the dictionary between six dimensional compactifications and four dimensional models.

Scheme-independent calculations of anomalous dimensions of baryon operators in conformal field theories

We present the first analytic scheme-independent series calculations of anomalous dimensions of several types of baryon operators at an infrared fixed point (IRFP) in an asymptotically free SU(3) gauge theory with $N_f$ fermions. Separately, for an asymptotically free gauge theory with a gauge group $G$ and $N_f$ fermions in a representation $R$ of $G$, we consider physical quantities at an IRFP, including the anomalous dimension of gauge-invariant fermion bilinears and the derivative of the beta function. These quantities have been calculated in series expansions whose coefficients have been proved to be scheme-independent at each order. We illustrate the scheme independence using a variety of schemes, including the RI$^\prime$ scheme and several types of momentum subtraction (MOM) schemes.

Anomalous dimension of spin- 1/2 baryons in many-flavor QCD

The anomalous dimension of spin-$1/2$ baryon operators in QCD is derived at leading $1/{N}_{f}$ order using the minimal subtraction scheme. A residual ambiguity, originating from the presence of evanescent operators in dimensional regularization, is parametrized by a function of the renormalized coupling. Our result is shown to agree with previous two- and three-loop calculations performed in two different renormalization schemes.

Calm Multi-Baryon Operators

There are many outstanding problems in nuclear physics which require input and guidance from lattice QCD calculations of few baryons systems. However, these calculations suffer from an exponentially bad signal-to-noise problem which has prevented a controlled extrapolation to the physical point. The variational method has been applied very successfully to two-meson systems, allowing for the extraction of the two-meson states very early in Euclidean time through the use of improved single hadron operators. The sheer numerical cost of using the same techniques in two-baryon systems has so far been prohibitive. We present an alternate strategy which offers some of the same advantages as the variational method while being significantly less numerically expensive. We first use the Matrix Prony method to form an optimal linear combination of single baryon interpolating fields generated from the same source and different sink interpolating fields. Very early in Euclidean time this optimal linear combination is numerically free of excited state contamination, so we coin it a calm baryon. This calm baryon operator is then used in the construction of the two-baryon correlation functions.To test this method, we perform calculations on the WM/JLab iso-clover gauge configurations at the SU(3) flavor symmetric point with mπ~ 800 MeV — the same configurations we have previously used for the calculation of two-nucleon correlation functions. We observe the calm baryon significantly removes the excited state contamination from the two-nucleon correlation function to as early a time as the single-nucleon is improved, provided non-local (displaced nucleon) sources are used. For the local two-nucleon correlation function (where both nucleons are created from the same space-time location) there is still improvement, but there is significant excited state contamination in the region the single calm baryon displays no excited state contamination.

A dangerous irrelevant UV-completion of the composite Higgs

One of the most challenging hurdles to the construction of realistic composite Higgs models is the generation of Yukawa couplings for the Standard Model fermions. This problem can be successfully addressed in approximate conformal theories that admit a marginally relevant mixing between composite fermionic operators and the SM fermions. I argue that SU(3) gauge theories with light Dirac flavors in the fundamental representation feature all the ingredients under theoretical control, including a strongly-coupled IR fixed point, composite partners for all Standard Model fermions, absence of Landau poles at low energy, and a realistic phenomenology. These models acquire the status of compelling UV-completions of the SM if some spin-1/2 baryon operator has scaling dimension close to 2.5 within the conformal window, a possibility that can only be assessed via non-perturbative methods like lattice QCD. A distinctive collider signature is long-lived hadrons with fractional charges.Vacuum alignment is controlled by the Nambu-Goldstone bosons of the coset SU(4) × SU(4)/SU(4). With a technically natural choice of mixing for the top-quark, the exotic scalars with electro-weak charges acquire large positive masses and a compelling custodial-symmetric phenomenology is obtained. In the decoupling limit the symmetry breaking pattern effectively reduces to SU(4) → Sp(4) with a light Higgs.

Baryon superfluids in AdS/CFT with flavor

Baryonic matter is notoriously difficult to deal with in the large-N limit, as baryons become operators of very large dimension with N fields in the fundamental representation. This issue is also present in gauge/gravity duals as baryons are described by very heavy localized objects. There are however alternative large-N extrapolations of QCD where small baryonic operators exist and can be treated on an equal footing to mesons. We explore the possibility of turning on a finite density of “light” baryons in a theory with a hadronic mass gap using a gauge/gravity construction based on the D3/D7 intersection. We find a novel phase with spontaneous breaking of baryon symmetry at zero temperature.

Anomalous dimensions of conformal baryons

We determine the anomalous dimensions of baryon operators for the three color theory as function of the number of massless flavours within the conformal window to the maximum known order in perturbation theory. We show that the anomalous dimension of the baryon is controllably small, within the $\delta$-expansion, for a wide range of number of flavours. We also find that this is always smaller than the anomalous dimension of the fermion mass operator. These findings challenge the partial compositeness paradigm.