arXiv subjects

Bryan W. Lynn

Publications and source records attributed to Bryan W. Lynn.

12 recordsLinked to original sources

arXiv2021

Nuclear matter as a liquid phase of spontaneously broken semi-classical $SU(2)_L \times SU(2)_R$ chiral perturbation theory: Static chiral nucleon liquids

We study effective field theories (EFT) of nuclear structure based on spontaneously broken global $SU(2)_L\times SU(2)_R$ chiral symmetry of QCD with two massless quarks, i.e. $SU(2)χPT$. For ground-state nuclei, this EFT enables expansion and truncation in inverse powers of $Λ_{χSB}\simeq 1 GeV$, with analytic operators renormalized to all loop orders. We derive the EFT Lagrangian to order $Λ^0_{χSB}$. We show that $SU(2)χPT$ of protons, neutrons and pions admits a semi-classical "Static Chiral Nucleon Liquid" (Static$χ$NL) phase and that "Pion-less" $SU(2)χPT$ emerges in this liquid: far-infrared pions decouple from Static$χ$NL, vastly simplifying the derivation of saturated nuclear matter (the infinite liquid phase) and of finite microscopic liquid drops (ground-state nuclides). Static$χ$NL are made entirely of nucleons with even parity, total spin zero, and even $Z$ and $N$; local expectation values for spin and momenta vanish. They explain the power of pion-less $SU(2)χPT$ to capture experimental ground-state properties of certain nuclides, this explanation following directly from the global symmetries of QCD with two massless quarks. Mean-field Static$χ$NL non-topological solitons are true solutions of $SU(2)χPT$'s semi-classical symmetries: they obey all CVC and PCAC conservation laws and they have zero internal and external pressure. The nuclear liquid-drop model and the semi-empirical mass formula emerge -- with correct nuclear density and saturation and asymmetry energies -- in an explicit Thomas-Fermi construction. We relate our work to compatible and complementary work in pionless and in halo/ cluster EFTs, also composed entirely of nucleons and applied to light ($A\leq 6$) nuclei, which might provide important (<12.5%) corrections to Static$χNL$.

hep-ph↗

arXiv2018

Nuclides as a liquid phase of $SU(2)_L \times SU(2)_R$ chiral perturbation theory I: emergence of pion-less SU(2) $χ$ PT

The Standard Model of particle physics, augmented with neutrino mixing, is at least very nearly the complete theory of interactions of known particles at energies accessible to Nature on Earth. Candidate effective theories of nuclear structure must therefore reflect SM symmetries, especially the chiral global $SU(2)_L \times SU(2)_R$ symmetry of two-massless-quark QCD. For ground-state nuclei, SU(2) chiral perturbation theory (XPT) enables perturbation in inverse powers of $Λ_{XSB}\simeq 1 GeV$, with analytic operators renormalized to all loop orders. We show that pion-less "Static Chiral Nucleon Liquids" (SXNL) emerge as a liquid phase of SU(2) XPT of protons, neutrons and 3 Nambu-Goldstone boson pions. Far-IR pions decouple from SXNL, simplifying the derivation of saturated nuclear matter and microscopic liquid drops (ground-state nuclides). We trace to the global symmetries of two-massless-quark QCD the power of pion-less SU(2) XPT to capture experimental ground-state properties of certain nuclides with even parity, spin zero, even proton number Z, and neutron number N. We derive the SXNL effective SU(2) XPT Lagrangian, including all order $Λ_{XSB},Λ^0_{XSB}$ operators. These include: all 4-nucleon operators that survive Fierz rearrangement in the non-relativistic limit, and effective Lorentz-vector iso-vector neutral "$ρ$-exchange" operators. SXNL motivate nuclear matter as non-topological solitons at zero pressure: the Nuclear Liquid Drop Model and Bethe-Weizsacker Semi-Empirical Mass Formula emerge in an explicit Thomas-Fermi construction provided in the companion paper. For chosen nuclides, nuclear Density Functional and Skyrme models are justified to order $Λ_{χSB}^0$. We conjecture that inclusion of higher order operators will result in accurate "natural" Skyrme, No-Core-Shell, and neutron star models.

nucl-th↗

arXiv2018

Global $SU(2)_L \otimes$BRST symmetry and its LSS theorem: Ward-Takahashi identities governing Green's functions, on-shell T-Matrix elements, and $V_{eff}$, in the scalar-sector of certain spontaneously broken non-Abelian gauge theories

This work is dedicated to the memory of Raymond Stora (1930-2015). $SU(2)_L$ is the simplest spontaneous symmetry breaking (SSB) non-Abelian gauge theory: a complex scalar doublet $ϕ=\frac{1}{\sqrt{2}}\begin{bmatrix}H+iπ_3-π_2 +iπ_1\end{bmatrix}\equiv\frac{1}{\sqrt{2}}\tilde{H}e^{2i\tilde{t}\cdot\tilde{\vecπ}/ }\begin{bmatrix}10\end{bmatrix}$ and a vector $\vec{W}^μ$. In Landau gauge, $\vec{W}^μ$ is transverse, $\vec{\tildeπ}$ are massless derivatively coupled Nambu-Goldstone bosons (NGB). A global shift symmetry enforces $m^{2}_{\tildeπ}=0$. We observe that on-shell T-matrix elements of physical states $\vec{W}^μ$,$ϕ$ are independent of global $SU(2)_{L}$ transformations, and the associated global current is exactly conserved for amplitudes of physical states. We identify two towers of "1-soft-pion" global Ward-Takahashi Identities (WTI), which govern the $ϕ$-sector, and represent a new global symmetry, $SU(2)_L\otimes$BRST, a symmetry not of the Lagrangian but of the physical states. The first gives relations among 1-$ϕ$-I (but one $W^μ,B^μ$ reducible) off-shell Green's functions, the second governs on-shell T-matrix elements, replacing the Adler self-consistency conditions. These WTI constrain the all-loop-orders scalar-sector effective Lagrangian and guarantee IR finiteness of the theory. These on-shell WTI include a Lee-Stora-Symanzik (LSS) theorem, which enforces the condition $m_π^2=0$ (far stronger than $m_{\tildeπ}^2=0$) and causes all relevant-operator contributions to the effective Lagrangian to vanish exactly. The global $SU(2)_L$ and the BRST transformations commute in $R_ξ$ gauges. With the on-shell T-matrix constraints, the physics therefore has more symmetry than does its BRST invariant Lagrangian. We also show that the statements made above hold for the electroweak sector of the Standard Model bosons.

hep-ph↗

arXiv2018

$U(1)\otimes BRST$ symmetry, of on-shell T-matrix elements and (1-$ϕ$-I) Green's functions, determines the vacuum state of the Abelian Higgs Model from symmetry alone: minimization of the scalar-sector effective potential is unnecessary

The weak-scale $U(1)_{Y}$ Abelian Higgs Model (AHM) is the spontaneous-symmetry-breaking gauge theory of a complex scalar $ϕ= \frac{1}{\sqrt{2}}(H + i π)$ and a vector $A_μ$. Global $U(1)_{Y}\otimes BRST$ symmetry emerges: when it is realized that on-shell T-matrix elements enjoy an extra $U(1)_{Y}$ global symmetry beyond the Lagragian's BRST symmetry. The symmetries co-exist: $U(1)_{Y}$ generators $δ_{U(1)_Y}$ commute with BRST generators s and $[δ_{U(1)_Y},s]{\cal L} = 0$. Two towers of Ward Takahashi identities (WTI), which include all-loop-orders quantum corrections, emerge: a tower of relations among off-shell 1-$ϕ$-I (but 1-$A_μ$-Reducible) Green's functions; another tower of Adler-zero WTI for on-shell T-matrix elements. The T-matrix's LSS theorem forces tadpoles to automatically vanish (equivalently $m^{2}_π = 0$) by symmetry alone. We show that, when the full symmetries of Lorenz gauge AHM are enforced on the scalar-sector effective potential, the vacuum state of the theory is specified/decided by symmetry alone. We use recursive WTI relations among Green's functions to include opeators of dimension $\geq 1$. We express the fully renormalized scalar-sector effective potential in a form which shows explicitly that, for small scalar field values, the gauge-independent vacuum state of the theory $\langle H\rangle_{renormalized} = Z^{1/2}_ϕ\langle H\rangle_{bare}$ is determined by $U(1)_{Y}\otimes BRST$ symmetry alone, without minimizing the effective potential.

hep-ph↗

arXiv2018

Global $U(1)_Y$xBRST symmetry and the LSS theorem: Ward-Takahashi identities governing Green's functions, on-shell T-Matrix elements, and the effective potential, in the spontaneously broken extended Abelian Higgs model

The weak-scale U(1) Abelian Higgs Model (AHM) is the simplest spontaneous symmetry breaking (SSB) gauge theory. The extended AHM (E-AHM) adds certain heavy scalars $Φ$ and fermions $ψ$. In Lorenz gauge, these theories have a global U(1) conserved physical current, but no conserved charge. As shown by Kibble, the Goldstone theorem applies, there is a massless derivatively coupled Nambu-Goldstone boson (NGB). Proof of all-loop-orders renormalizability and unitarity is tricky because the BRST-invariant Lagrangian is not U(1) symmetric. Nevertheless, Slavnov-Taylor identities guarantee that on-shell T-matrix elements of physical states are independent of anomaly-free gauge transformations. We observe that they are therefore also independent of the usual anomaly-free U(1) global transformations. It follows that the associated global current, is exactly conserved for amplitudes of physical states. We identify corresponding Ward-Takahashi identities (WTI). In Lorenz gauge, two towers of "1-soft-pion" global WTI govern the scalar-sector, and represent a new global U(1)xBRST symmetry not of the Lagrangian but of the physics. The first gives relations among off-shell Green's functions, the second governs on-shell T-matrix elements, replacing the Adler self-consistency conditions. These WTI constrain the all-loop-orders scalar-sector low-energy effective Lagrangian. Consequently, certain heavy CP-conserving heavy matter representations decouple completely in the $M_{Heavy}^2/m_{Weak}^2 \to \infty$ limit. SSB (E-)AHM physics therefore has more symmetry than does its BRST-invariant Lagrantian. The NGB decouples from the observable particle spectrum in the usual way, when the observable vector absorbs it, as if it were a gauge transformation, hiding both towers of WTI from observable particle physics.

hep-ph↗

arXiv2017

Global $SU(3)_C\times SU(2)_L\times U(1)_Y$ linear sigma model: axial-vector Ward Takahashi identities, and decoupling of certain heavy BSM particles due to the Goldstone theorem

Dedicated to the memory of Raymond Stora (1930-2015). In the $SU(2)_L\times SU(2)_R$ Linear Sigma Model with PCAC, towers of Ward-Takahashi Identities (WTI) have long been known to give relations among 1-Scalar-Particle-Irreducible Green's functions, and among I- Scalar-Particle-Reducible T-Matrix elements, for external scalars (i.e. the Brout-Englert-Higgs scalar and 3 pseudoscalars). We extend these WTI and the resulting relations to the $SU(3)_C\times SU(2)_L\times U(1)_Y$ Linear Sigma Model including the heaviest generation of Standard Model (SM) fermions supplemented with the minimum necessary neutrino content -- right-handed neutrinos and Yukawa-coupling-induced Dirac neutrino mass. We extract powerful constraints on the effective Lagrangian: e.g. showing that they make separate tadpole renormalization unnecessary, and guarantee infra-red finiteness. Crucially, ultra-violet quadratic divergences (UVQD) and all other relevant operators contribute only to $m_π^2$, a Nambu-Goldstone boson (NGB) mass-squared. A WTI between T-Matrix elements (i.e. the Goldstone Theorem) then enforces $ m_π^2=0$ for the true NGB in the spontaneous symmetry breaking mode of the theory. All relevant operator contributions originating to all-loop-orders from virtual scalars, quarks and leptons, vanish identically! Our regularization-scheme-independent results are unchanged by the addition of certain heavy CP-conserving matter, such as originate in certain Beyond the SM models. We demonstrate this with two examples: a heavy singlet real scalar field with $Z_2$ symmetry and no VEV; and a heavy singlet right-handed Type I See-saw Majorana neutrino. Specifically, we prove that these heavy degrees of freedom decouple completely from the low-energy effective Lagrangian, contributing only irrelevant operators after quartic-coupling renormalization.

hep-ph↗

arXiv2016

Hidden $U(1)_Y$ Ward-Takahashi identities in the spontaneously brokenAbelian Higgs model and the decoupling of certain heavy particles in its simple extensions

This work is dedicated to the memory of R. Stora. The spontaneously broken (SSB) $U(1)_Y$ Abelian Higgs model (AHM) (the gauge theory of a scalar $ϕ\propto (H+iπ)= {\tilde H}e^{i{\tilde π}/ }$ and a transverse vector A) has a massless pseudo-scalar $π$ in Lorenz gauge. Physical states have a conserved global current and Goldstone theorem (GT). $\tilde π$ becomes a Nambu-Goldstone boson (NGB). Slavnov-Taylor identities keep on-shell T-matrix elements of physical states independent of anomaly-free gauge, and global, transformations, yielding towers of $ϕ$-sector Ward-Takahashi Identities (WTI), and constraining external $ϕ$ dynamics. Ultraviolet quadratic divergences (UVQD) contribute only to $m_π^2$, forced by the GT to 0, so all UVQD vanish. Weak-scale renormalized gauge-independent Higgs pole-mass and VEV are therefore not fine-tuned. The NGB is "eaten" and decouples, hiding the $U(1)_Y$ WTI from observable particle physics. Our regularization-scheme-independent results are unchanged by the addition of certain heavy fields as the extended WTI and GT cause all relevant operators to vanish. We prove 5 SSB decoupling theorems, illustrating them with two examples: a heavy $>>m_{Weak}$ $Z_2$-symmetric singlet real scalar field with 0 VEV; and a heavy singlet right-handed type 1 see-saw Majorana neutrino. Including all loops we prove that certain heavy degrees of freedom decouple from the low-energy effective Lagrangian, contributing only irrelevant operators after renormalization. The $ν_R^{M}$ cannot completely decouple, but becomes invisible in practice. The NGB decouples, but our hidden SSB $U(1)_Y$ WTI, and a ${\tilde π}$ shift symmetry, protect the low-energy SSB AHM physics from loop contributions of heavy particles! Gauge-independent observable weak-scale $m_{H;Pole}$ and $ $ are Goldstone Exceptionally Natural, not fine-tuned.

hep-ph↗

arXiv2015

Macro Dark Matter

Dark matter is a vital component of the current best model of our universe, $Λ$CDM. There are leading candidates for what the dark matter could be (e.g. weakly-interacting massive particles, or axions), but no compelling observational or experimental evidence exists to support these particular candidates, nor any beyond-the-Standard-Model physics that might produce such candidates. This suggests that other dark matter candidates, including ones that might arise in the Standard Model, should receive increased attention. Here we consider a general class of dark matter candidates with characteristic masses and interaction cross-sections characterized in units of grams and cm$^2$, respectively -- we therefore dub these macroscopic objects as Macros. Such dark matter candidates could potentially be assembled out of Standard Model particles (quarks and leptons) in the early universe. A combination of Earth-based, astrophysical, and cosmological observations constrain a portion of the Macro parameter space. A large region of parameter space remains, most notably for nuclear-dense objects with masses in the range $55 - 10^{17}$ g and $2\times10^{20} - 4\times10^{24}$ g, although the lower mass window is closed for Macros that destabilize ordinary matter.

astro-ph.CO↗

arXiv2014

The Goldstone theorem protects naturalness, and the absence of Brout-Englert-Higgs fine-tuning, in spontaneously broken SO(2)

The Gell-Mann-Levy (GML), Schwinger and Standard Models were previously shown to lack a Brout-Englert-Higgs (BEH) fine-tuning problem due to quadratic divergences, with finite Euclidean cut-off Λ, because of the symmetries obeyed by all O(Λ^2) contributions. We extend those results to finite contributions from certain M_{Heavy}^2>> m_{BEH}^2 particles in SO(2) versions of GML and Schwinger. We demonstrate explicit 1-loop physical naturalness for two SO(2) singlet examples: a heavy real scalar S and a right-handed Type 1 see-saw Majorana neutrino. We prove that for low |q^2| the heavy degrees of freedom contribute, at worst, marginal operators in spontaneously broken SO(2) Schwinger. The key GML lesson from these examples is that the pseudo Nambu-Goldstone boson (NGB) mass-squared must be properly renormalized. A true NGB value, m_3^2 = 0, is then protected by the Goldstone theorem. For the Schwinger model, two crucial observations emerge: global Ward-Takahashi identities (WTI) force all relevant operators into the pseudo-NGB mass-squared; and WTI enforce the Goldstone theorem by forbidding all relevant operator contributions in the spontaneously broken Goldstone mode, π_3 is a massless NGB there. Goldstone mode, with weak-scale m_{BEH}^2 \& ^2, is not-fine-tuned even as a low-energy effective theory with certain high-mass-scale extensions. Its "Goldstone Exceptional Naturalness (GEN)," where all relevant operators vanish, a powerful suppression of fine-tuning, is simply another (albeit un-familiar) consequence of WTI, spontaneous symmetry breaking and the Goldstone theorem. If GEN can somehow be extended to the Standard Model (SM), there should be no expectation that LHC will discover any Beyond the SM physics unrelated to neutrino mixing, i.e. the only known experimentally necessary modification of the Standard Model plus General Relativity paradigm.

hep-ph↗

arXiv2013

The "Goldstone Exception" II: Absence of a Higgs Fine-Tuning Problem in the Spontaneously Broken Limit of the Gell Mann Levy Linear Sigma Model: O(4) with PCAC and SU(2)_L with PCAC and Standard Model Quarks and Leptons

More than four decades ago, Lee and Symanzik proved that, in the Gell Mann-Levy (GML) model with partially conserved axial-vector currents (PCAC), tadpole renormalization (a Higgs Vacuum Stability Condition) forces all S-matrix ultra-violet quadratic divergences (UVQD) to be absorbed into the physical renormalized pseudo-scalar pion (pole) mass squared. We show that this includes "new" UVQD (widely unfamiliar to modern audiences). We also show that tadpole renormalization is an automatic consequence of Ward-Takahashi identities. We prove that all UVQD therefore vanish identically in the Goldstone-mode limit, where pions are Nambu-Goldstone Bosons (NGB), and where Lee and Symanzik's Goldstone Symmetry Restoration Condition (a renormalization prescription) enforces spontaneous symmetry breaking and the massless-ness of NGB. Axial-vector current conservation is restored as is SU(2)(L-R) chiral symmetry: the vanishing of UVQD is therefore achieved in the Goldstone-mode by restoration of an exact symmetry, and therefore (by definition) without fine-tuning! A weak-scale Higgs mass is therefore not UVQD fine-tuned in the spontaneously broken GML LSM. That is simply another (albeit unfamiliar) consequence of the Goldstone Theorem. Hence Goldstone-mode O(4) LSM symmetries are sufficient to ensure that the theory does not suffer from the Higgs Fine Tuning Problem. This is contrary to the widely accepted belief that UVQD in the Higgs mass lead to such problems in the O(4) LSM, which are then presumed to be inherited by the Standard Model (SM). The key observation is to regard the spontaneously broken O(4) LSM as the Goldstone-mode limit of the GML LSM. We prove this first at 1-loop then at all loop orders for the pure scalar GML model. We then break the O(4) symmetry to SU(2)L with SM Yukawa couplings, and show that the above remains true.

hep-ph↗

arXiv2012

Spontaneously broken Standard Model (SM) symmetries and the Goldstone theorem protect the Higgs mass and ensure that it has no Higgs Fine Tuning Problem (HFTP)

B.W.Lee/K.Symanzik proved that Ward-Takahashi identities and tadpole renormalization force all ultra-violet quadratic divergences (UV-QD) to be absorbed into the physical renormalized pseudo-scalar pion mass in O(4)LSM (linear sigma models) across the Higgs-VEV vs. Pion-Mass-Squared half-plane. We show that all UV-QD vanish identically in the "Goldstone mode" Zero-Pion-Mass spontaneous symmetry breaking (SSB) limit. The Higgs mass is protected to all loop-orders and Goldstone-mode O(4)LSM has no Higgs fine-tuning problem (HFTP). We insist that self-consistent renormalization of the Standard Model (SM) requires that the scalar-sector UV-QD-corrected effective Lagrangians of the SM and Goldstone-mode O(4)LSM are smoothly identical in the zero-gauge-coupling limit. Lee/Symanzik's two conditions must be imposed on the SM: the Higgs cannot simply disappear into the vacuum; SM Nambu-Goldstone boson (NGB) masses (i.e. the pre-Higgs-mechanism longitudinal Wand Z masses) must vanish identically. At 1-loop, the Higgs-VEV is neither UV-QD divergent nor fine-tuned. Loop-induced-artefact NGB masses absorb all SM UV-QD, which vanish identically in the Zero-NGB-Mass limit, i.e. the SSB SM. Simply another (un-familiar) consequence of the Goldstone theorem, no fine-tuning is necessary for a weak-scale Higgs mass. Our SM results can (almost certainly) be extended to include all-orders perturbative electro-weak and QCD loops. SM symmetries (as realized by SSB and the Goldstone theorem) are sufficient to protect the Higgs mass, and ensure that the SM does not suffer a HFTP. It is un-necessary to impose any new Beyond the Standard-Model (BSM) symmetries. Mistaken belief in a 1-loop SM HFTP has historically driven an expectation that new BSM physics must appear < 14 TeV. But our results re-open the possibility that LHC discovery potential might be confined to SM physics.

hep-ph↗

arXiv2010

Liquid Phases in SU(3) Chiral Perturbation Theory: Drops of Strange Chiral Nucleon Liquid & Ordinary Chiral Heavy Nuclear Liquid

Chiral SU(3) Perturbation Theory (SU3XPT) identifies hadrons as the building blocks of strongly interacting matter at low densities and temperatures. We show that it admits two co-existing chiral nucleon liquid phases at zero external pressure with well-defined surfaces: 1) ordinary microscopic chiral heavy nuclear liquid drops (XNL) and 2) a new Strange Chiral Nucleon Liquid (SXNL) phase with both microscopic and macroscopic drop sizes. Liquid drops of both XNL and SXNL are simultaneously solutions to the SU3XPT semi-classical equations of motion and obey all relevant CVC and PCAC equations. Axial-vector currents are conserved inside macroscopic drops of SXNL, a new form of baryonic matter with zero electric charge density, which is by nature "dark". The numerical values of all SU3XPT coefficients are used to fit current scattering experiments and ordinary XNL drops (identified with the ground state of ordinary even-even spin-zero spherical closed-shell nuclei). SXNL then also emerges (i.e. without new adjustable parameters). For certain SU3XPT coefficients, finite microscopic and macroscopic drops of SXNL may be the ground state of a collection of nucleons: ordinary heavy nuclei may be meta-stable, while oceans of SXNL may force qualitative and experimentally observable changes to the neutron star equation of state.

hep-ph↗