arXiv subjects

Claudio Rebbi

Publications and source records attributed to Claudio Rebbi.

At least 19 recordsLinked to original sources

arXiv2023

Stealth dark matter spectrum using LapH and Irreps

We present non-perturbative lattice calculations 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 non-projected 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.

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arXiv2022

Gradient flow step-scaling function for SU(3) with $N_f=8$ fundamental flavors

The step-scaling function, the lattice analog of the renormalization group $\beta$ function, is presented for the SU(3) gauge system with eight flavors in the fundamental representation. Our investigation is based on generating dynamical eight flavor gauge field configurations using stout-smeared M\"obius domain wall fermions and Symanzik gauge action. On these gauge field configurations we perform gradient flow measurements using the Zeuthen, Wilson, or Symanzik kernel and consider the Symanzik, Wilson plaquette, or clover operators to determine step-scaling functions for a scale change $s=2$ including large, up to $48^4$, volumes. Considering different flows and operators as well as the optional use of tree-level improvement allows us to check for possible systematic effects. Our result covers the range of renormalized coupling up to $g_c^2 \lesssim 10$. In the case of $N_f=8$ we observe that the reach in $g_c^2$ is limited due to an unphysical first order bulk phase transition caused by large ultra-violet fluctuations. We compare our findings to $N_f=4$, 6, 10 or 12 flavors results that are obtained using the same lattice action and analysis. In addition we investigate the phase structure for simulations with different number of flavors using stout-smeared M\"obius domain wall fermions and Symanzik gauge actions to shed some light on the limited reach in $g_c^2$.

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arXiv2022

Gradient flow step-scaling function for SU(3) with $N_f$ = 6 or 4 fundamental flavors

Nonperturbative determinations of the renormalization group (RG) $β$ function are crucial to understand properties of gauge-fermion systems at strong coupling and connect lattice simulations and the perturbative ultraviolet regime. Choosing well-understood, QCD-like systems with SU(3) gauge group and either six or four fundamental flavors, we investigate their step-scaling $β$ function. In both cases we push the simulations to the boundary of chiral symmetry breaking and study the regime $g^2_{GF} \lesssim 8.2$ with six, and $g^2_{GF} \lesssim 6.6$ with four flavors. We carefully consider the lattice discretization errors by comparing three different gradient flows (GF), and for each flow three operators to estimate the renormalized finite volume coupling. We also consider the tree level improvement of the coupling. Noteworthy outcome is that nonperturbatively determined $β$ functions run much slower than perturbatively predicted.

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arXiv2021

Near-conformal dynamics in a chirally broken system

Composite Higgs models must exhibit very different dynamics from quantum chromodynamics (QCD) regardless whether they describe the Higgs boson as a dilatonlike state or a pseudo-Nambu-Goldstone boson. Large separation of scales and large anomalous dimensions are frequently desired by phenomenological models. Mass-split systems are well-suited for composite Higgs models because they are governed by a conformal fixed point in the ultraviolet but are chirally broken in the infrared. In this work we use lattice field theory calculations with domain wall fermions to investigate a system with four light and six heavy flavors. We demonstrate how a nearby conformal fixed point affects the properties of the four light flavors that exhibit chiral symmetry breaking in the infrared. Specifically we describe hyperscaling of dimensionful physical quantities and determine the corresponding anomalous mass dimension. We obtain $y_m=1+γ^*= 1.47(5)$ suggesting that $N_f=10$ lies inside the conformal window. Comparing the low energy spectrum to predictions of dilaton chiral perturbation theory, we observe excellent agreement which supports the expectation that the 4+6 mass-split system exhibits near-conformal dynamics with a relatively light $0^{++}$ isosinglet scalar.

hep-ph↗

arXiv2020

Gradient flow step-scaling function for SU(3) with ten fundamental flavors

We calculate the step scaling function, the lattice analog of the renormalization group $β$-function, for an SU(3) gauge theory with ten fundamental flavors. We present a detailed analysis including the study of systematic effects of our extensive data set generated with ten dynamical flavors using the Symanzik gauge action and three times stout smeared Möbius domain wall fermions. Using up to $32^4$ volumes, we calculate renormalized couplings for different gradient flow schemes and determine the step-scaling $β$ function for a scale change $s=2$ on up to five different lattice volume pairs. In an accompanying paper we discuss that gradient flow can promote lattice dislocations to instanton-like objects, introducing nonperturbative lattice artifacts to the step scaling function. Motivated by the observation that Wilson flow sufficiently suppresses these artifacts, we choose Wilson flow with the Symanzik operator as our preferred analysis. We study systematic effects by calculating the step-scaling function based on alternative flows (Zeuthen or Symanzik), alternative operators (Wilson plaquette, clover), and also explore the effects of the perturbative tree-level improvement. Further we investigate the effects due to the finite value of $L_s$.

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arXiv2019

Gradient flow step-scaling function for SU(3) with twelve flavors

We calculate the step scaling function, the lattice analog of the renormalization group $β$-function, for an SU(3) gauge theory with twelve flavors. The gauge coupling of this system runs very slowly, which is reflected in a small step scaling function, making numerical simulations particularly challenging. We present a detailed analysis including the study of systematic effects of our extensive data set generated with twelve dynamical flavors using the Symanzik gauge action and three times stout smeared Möbius domain wall fermions. Using up to $32^4$ volumes, we calculate renormalized couplings for different gradient flow schemes and determine the step-scaling $β$ function for a scale change $s=2$ on up to five different lattice volume pairs. Our preferred analysis is fully $O(a^2)$ Symanzik improved and uses Zeuthen flow combined with the Symanzik operator. We find an infrared fixed point within the range $5.2 \le g_c^2 \le 6.4$ in the $c=0.250$ finite volume gradient flow scheme. We account for systematic effects by calculating the step-scaling function based on alternative flows (Wilson or Symanzik) as well as operators (Wilson plaquette, clover) and also explore the effects of the perturbative tree-level improvement.

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arXiv2019

Nonperturbative investigations of SU(3) gauge theory with eight dynamical flavors

We present our lattice studies of SU(3) gauge theory with $N_f$ = 8 degenerate fermions in the fundamental representation. Using nHYP-smeared staggered fermions we study finite-temperature transitions on lattice volumes as large as $L^3 \times N_t = 48^3 \times 24$, and the zero-temperature composite spectrum on lattice volumes up to $64^3 \times 128$. The spectrum indirectly indicates spontaneous chiral symmetry breaking, but finite-temperature transitions with fixed $N_t \leq 24$ enter a strongly coupled lattice phase as the fermion mass decreases, which prevents a direct confirmation of spontaneous chiral symmetry breaking in the chiral limit. In addition to the connected spectrum we focus on the lightest flavor-singlet scalar particle. We find it to be degenerate with the pseudo-Goldstone states down to the lightest masses reached so far by non-perturbative lattice calculations. Using the same lattice approach, we study the behavior of the composite spectrum when the number of light fermions is changed from eight to four. A heavy flavor-singlet scalar in the 4-flavor theory affirms the contrast between QCD-like dynamics and the low-energy behavior of the 8-flavor theory.

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arXiv2019

On the calculation and use of non-zero momentum correlators in lattice simulations

In lattice simulations one generally projects correlators over zero spatial momentum to calculate masses and related spectral data. The sum over space lattice points, however, discards information which may be useful especially in the calculation of disconnected diagrams. By using momentum conservation, the calculation of non-zero momentum components of disconnected diagrams and other quantities related to space convolutions can be done with little additional computational cost and may be useful in the analysis of disconnected correlators.

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arXiv2018

Determination of the $N_f=12$ step scaling function using Möbius domain wall fermions

We calculate the renormalized step scaling function for twelve fundamental flavors nonperturbatively by determining the gradient flow coupling on gauge field configurations generated with dynamical stout-smeared Möbius domain wall fermions and Symanzik gauge action. Using Zeuthen, Symanzik, and Wilson flow we measure the energy density with three different operators. Our updated analysis is based on up to five volume pairs ranging from L^4=8^4 up to 32^4. Predictions for the infinite volume extrapolated step scaling function based on different flows and operators are mutually consistent. Our new results confirm the previously observed significant discrepancy with staggered fermion simulations in a wide range of the renormalized coupling.

hep-lat↗

arXiv2018

Composite Higgs from mass-split models

Beyond Standard Model theories describing the electro-weak sector must exhibit a large separation of scales (or "walking") to account for a light, 125 GeV Higgs boson and the fact that so far no other resonances have been observed. Large separation of scales arises naturally and in a tunable manner in mass-split models that are built on a conformal fixed point in the ultraviolet. Splitting the fermion masses into "light" (massless) and "heavy" flavors, the system shows conformal behavior in the ultraviolet but is chirally broken in the infrared. Due to the presence of a conformal fixed point, such chirally broken systems show hyperscaling and have a highly constrained resonance spectrum that is significantly different from the QCD spectrum. We highlight most characteristic features presenting numerical data obtained from dynamical simulations of an SU(3) gauge theory with four light and eight heavy flavors. In addition, we give an outlook on ongoing work simulating an SU(3) gauge theory with four light and six heavy flavors using a set-up well suited to explore e.g. mass-generation of Standard Model fermions via four-fermion interactions or partial compositeness.

hep-ph↗

arXiv2017

Investigating BSM Models with Large Scale Separation

Mass-split systems based on a conformal infrared fixed point provide a low-energy effective description of beyond the standard model systems with large scale separation. We report results of exploratory investigations with four light and eight heavy flavors using staggered fermions, and up to five different values for the light flavor mass, five different heavy flavor masses, and two values of the bare gauge coupling.

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arXiv2017

Large scale separation and resonances within LHC range from a prototype BSM model

Many theories describing physics beyond the Standard Model rely on a large separation of scales. Large scale separation arises in models with mass-split flavors if the system is conformal in the ultraviolet but chirally broken in the infrared. Because of the conformal fixed point, these systems exhibit hyperscaling and a highly constrained resonance spectrum. We derive hyperscaling relations and investigate the realization of one such system with four light and eight heavy flavors. Our numerical simulations confirm that both light-light and heavy-heavy resonance masses show hyperscaling and depend only on the ratio of the light and heavy flavor masses. The heavy-heavy spectrum is qualitatively different from QCD and exhibits quarkonia with masses not proportional to the constituent quark mass. These resonances are only a few times heavier than the light-light ones, which would put them within reach of the LHC.

hep-ph↗

arXiv2017

Testing Fermion Universality at a Conformal Fixed Point

Universality of various fermion formulations is well established in QCD-like theories defined around the perturbative $g^2=0$ fixed point. These arguments do not apply for conformal systems that exhibit an infrared fixed point at non-vanishing $g^2$ coupling. We investigate the step scaling function for systems with 10 or 12 fundamental flavors using domain wall fermions and compare it to perturbative predictions. We test universality by contrasting our findings to results published in the literature based on staggered fermions.

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arXiv2016

Infrared properties of a prototype model for beyond-Standard Model physics

We construct a prototype BSM model based on the SU(3) color gauge group and a combination of 4 light (massless) and 8 heavy flavors. In the infrared, the SU(4) flavor chiral symmetry is spontaneously broken, while in the ultraviolet this model exhibits the properties of the $N_f=12$ conformal fixed point. Renormalization group considerations predict the spectrum of such a system to show hyperscaling, i.e. dimensionless ratios of hadron masses or decay constants are independent of the heavy mass. Hyperscaling is present for bound states of light, heavy, or a combination of heavy and light flavors and leads to a strongly predictive model. Despite chiral symmetry breaking, this system features a spectrum exhibiting a very non-QCD like behavior. Furthermore, the gauge coupling becomes an irrelevant parameter. We support these expectations by presenting numerical results based on four different values of the heavy quark mass $am_h$, up to six different values of the light quark mass $am_\ell$, and include, for the first time, preliminary data at a second value of the gauge coupling $β$. Our model can be embedded in scenarios describing the Higgs boson either as a pseudo Nambu-Goldstone boson or a dilaton-like particle.

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arXiv2016

Strongly interacting dynamics and the search for new physics at the LHC

We present results for the spectrum of a strongly interacting SU(3) gauge theory with $N_f = 8$ light fermions in the fundamental representation. Carrying out non-perturbative lattice calculations at the lightest masses and largest volumes considered to date, we confirm the existence of a remarkably light singlet scalar particle. We explore the rich resonance spectrum of the 8-flavor theory in the context of the search for new physics beyond the standard model at the Large Hadron Collider (LHC). Connecting our results to models of dynamical electroweak symmetry breaking, we estimate the vector resonance mass to be about 2 TeV with a width of roughly 450 GeV, and predict additional resonances with masses below ~3 TeV.

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arXiv2015

Stealth Dark Matter: Dark scalar baryons through the Higgs portal

We present a new model of "Stealth Dark Matter": a composite baryonic scalar of an $SU(N_D)$ strongly-coupled theory with even $N_D \geq 4$. All mass scales are technically natural, and dark matter stability is automatic without imposing an additional discrete or global symmetry. Constituent fermions transform in vector-like representations of the electroweak group that permit both electroweak-breaking and electroweak-preserving mass terms. This gives a tunable coupling of stealth dark matter to the Higgs boson independent of the dark matter mass itself. We specialize to $SU(4)$, and investigate the constraints on the model from dark meson decay, electroweak precision measurements, basic collider limits, and spin-independent direct detection scattering through Higgs exchange. We exploit our earlier lattice simulations that determined the composite spectrum as well as the effective Higgs coupling of stealth dark matter in order to place bounds from direct detection, excluding constituent fermions with dominantly electroweak-breaking masses. A lower bound on the dark baryon mass $m_B \gtrsim 300$ GeV is obtained from the indirect requirement that the lightest dark meson not be observable at LEP II. We briefly survey some intriguing properties of stealth dark matter that are worthy of future study, including: collider studies of dark meson production and decay; indirect detection signals from annihilation; relic abundance estimates for both symmetric and asymmetric mechanisms; and direct detection through electromagnetic polarizability, a detailed study of which will appear in a companion paper.

hep-ph↗

arXiv2015

Direct Detection of Stealth Dark Matter through Electromagnetic Polarizability

We calculate the spin-independent scattering cross section for direct detection that results from the electromagnetic polarizability of a composite scalar baryon dark matter candidate -- "Stealth Dark Matter", that is based on a dark SU(4) confining gauge theory. In the nonrelativistic limit, electromagnetic polarizability proceeds through a dimension-7 interaction leading to a very small scattering cross section for dark matter with weak scale masses. This represents a lower bound on the scattering cross section for composite dark matter theories with electromagnetically charged constituents. We carry out lattice calculations of the polarizability for the lightest baryons in SU(3) and SU(4) gauge theories using the background field method on quenched configurations. We find the polarizabilities of SU(3) and SU(4) to be comparable (within about 50%) normalized to the baryon mass, which is suggestive for extensions to larger SU(N) groups. The resulting scattering cross sections with a xenon target are shown to be potentially detectable in the dark matter mass range of about 200-700 GeV, where the lower bound is from the existing LUX constraint while the upper bound is the coherent neutrino background. Significant uncertainties in the cross section remain due to the more complicated interaction of the polarizablity operator with nuclear structure, however the steep dependence on the dark matter mass, $1/m_B^6$, suggests the observable dark matter mass range is not appreciably modified. We briefly highlight collider searches for the mesons in the theory as well as the indirect astrophysical effects that may also provide excellent probes of stealth dark matter.

hep-ph↗

arXiv2014

Targeting the Conformal Window: Scalars on the Lattice

The light Higgs boson of the Standard Model could arise as the consequence of the weakly broken conformal symmetry in a strongly interacting gauge theory. Here we present a novel idea to study the transition from conformal to confining behavior using an SU(3) gauge theory with four light and eight heavy flavors. This system interpolates between the 12-flavor conformal and the 4 flavor chirally broken theory as the mass of the heavy flavors are varied. We show first results on our determination of the iso-singlet 0++ state.

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