arXiv subjects

Lewis C. Tunstall

Publications and source records attributed to Lewis C. Tunstall.

13 recordsLinked to original sources

arXiv2019

Crawling technicolor

We analyze the Callan-Symanzik equations when scale invariance at a nontrivial infrared (IR) fixed point $α^{}_{\mathrm{IR}}$ is realized in the Nambu-Goldstone (NG) mode. As a result, Green's functions at $α^{}_{\mathrm{IR}}$ do not scale in the same way as for the conventional Wigner-Weyl (WW) mode. This allows us to propose a new mechanism for dynamical electroweak symmetry breaking where the running coupling $α$ "crawls" towards (but does not pass) $α^{}_{\mathrm{IR}}$ in the exact IR limit. The NG mechanism at $α^{}_{\mathrm{IR}}$ implies the existence of a massless dilaton $σ$, which becomes massive for IR expansions in $ε\equiv α^{}_{\mathrm{IR}} - α$ and is identified with the Higgs boson. Unlike "dilatons" that are close to a WW-mode fixed point or associated with a Coleman-Weinberg potential, our NG-mode dilaton is genuine and hence naturally light. Its (mass)$^2$ is proportional to $εβ'(4+β')F_σ^{-2} \langle\hat{G}^2\rangle_{\text{vac}}$, where $β'$ is the (positive) slope of the beta function at $α^{}_{\mathrm{IR}}$, $F_σ$ is the dilaton decay constant and $\langle\hat{G}^2\rangle_{\text{vac}}$ is the technigluon condensate. Our effective field theory for this works because it respects Zumino's consistency condition for dilaton Lagrangians. We find a closed form of the Higgs potential with $β'$-dependent deviations from that of the Standard Model. Flavor-changing neutral currents are suppressed if the crawling region $α\lesssim α^{}_{\mathrm{IR}}$ includes a sufficiently large range of energies above the TeV scale. In Appendix A, we observe that, contrary to folklore, condensates protect fields from decoupling in the IR limit.

hep-ph↗

arXiv2019

Next-to-Minimal SOFTSUSY

We describe an extension to the SOFTSUSY program that provides for the calculation of the sparticle spectrum in the Next-to-Minimal Supersymmetric Standard Model (NMSSM), where a chiral superfield that is a singlet of the Standard Model gauge group is added to the Minimal Supersymmetric Standard Model (MSSM) fields. Often, a $\mathbb{Z}_{3}$ symmetry is imposed upon the model. SOFTSUSY can calculate the spectrum in this case as well as the case where general $\mathbb{Z}_{3}$ violating (denoted as $\,\mathbf{\backslash}\mkern-11.0mu{\mathbb{Z}}_{3}$) terms are added to the soft supersymmetry breaking terms and the superpotential. The user provides a theoretical boundary condition for the couplings and mass terms of the singlet. Radiative electroweak symmetry breaking data along with electroweak and CKM matrix data are used as weak-scale boundary conditions. The renormalisation group equations are solved numerically between the weak scale and a high energy scale using a nested iterative algorithm. This paper serves as a manual to the NMSSM mode of the program, detailing the approximations and conventions used.

hep-ph↗

arXiv2016

Dispersive treatment of $K_S\toγγ$ and $K_S\toγ\ell^+\ell^-$

We analyse the rare kaon decays $K_S \to γγ$ and $K_S \to γ\ell^+\ell^-$ $(\ell = e \mbox{ or } μ)$ in a dispersive framework in which the weak Hamiltonian carries momentum. Our analysis extends predictions from lowest order $SU(3)_L\times SU(3)_R$ chiral perturbation theory ($χ$PT$_3$) to fully account for effects from final-state interactions, and is free from ambiguities associated with extrapolating the kaon off-shell. Given input from $K_S \to ππ$ and $γγ^{(*)}\toππ$, we solve the once-subtracted dispersion relations numerically to predict the rates for $K_S \to γγ$ and $K_S \to γ\ell^+\ell^-$. In the leptonic modes, we find sizeable corrections to the $χ$PT$_3$ predictions for the integrated rates.

hep-ph↗

arXiv2016

Probing lepton flavour (universality) violation at NA62 and future kaon experiments

Recent results from the LHC's first run have revealed intriguing departures from lepton flavour universality in the semi-leptonic decays of $B$-mesons. We discuss the complementary role that rare kaon decays can provide in testing new physics explanations of these flavour anomalies. In the framework of minimal flavour violation, we relate the chiral low-energy constants involved in $K\toπ\ell\ell'$ and $K\to\ell\ell'$ ($\ell = μ\mbox{ or } e$) with the new physics Wilson coefficients of the $b\to s$ effective Hamiltonian. We comment on the determination of these low-energy constants at NA62 and future kaon experiments, as well as the required improvements in sensitivity necessary to test the $B$-physics anomalies in the kaon sector.

hep-ph↗

arXiv2016

Status of Chiral-Scale Perturbation Theory

Chiral-scale perturbation theory $χ$PT$_σ$ has been proposed as an alternative to chiral $SU(3)_L\times SU(3)_R$ perturbation theory which explains the $ΔI = 1/2$ rule for kaon decays. It is based on a low-energy expansion about an infrared fixed point in three-flavor QCD. In $χ$PT$_σ$, quark condensation $\langle\bar q q \rangle_\mathrm{vac} \neq 0$ induces nine Nambu-Goldstone bosons: $π, K, η$ and a QCD dilaton $σ$ which we identify with the $f_0(500)$ resonance. Partial conservation of the dilatation and chiral currents constrains low-energy constants which enter the effective Lagrangian of $χ$PT$_σ$. These constraints allow us to obtain new phenomenological bounds on the dilaton decay constant via the coupling of $σ/f_0$ to pions, whose value is known precisely from dispersive analyses of $ππ$ scattering. Improved predictions for $σ\to γγ$ and the $σNN$ coupling are also noted. To test $χ$PT$_σ$ for kaon decays, we revive a 1985 proposal for lattice methods to be applied to $K \to π$ on-shell.

hep-ph↗

arXiv2016

Lepton flavor (universality) violation in rare kaon decays

Recent anomalies in the decays of $B$ mesons and the Higgs boson provide hints towards lepton flavor (universality) violating physics beyond the Standard Model. We observe that four-fermion operators which can explain the $B$-physics anomalies have corresponding analogs in the kaon sector, and we analyze their impact on $K\toπ\ell \ell'$ and $K\to\ell \ell'$ decays $(\ell=μ,e)$. For these processes, we note the corresponding physics opportunities at the NA62 experiment. In particular, assuming minimal flavor violation, we comment on the required improvements in sensitivity necessary to test the $B$-physics anomalies in the kaon sector.

hep-ph↗

arXiv2016

Stop searches in flavourful supersymmetry

Natural realisations of supersymmetry require light stops ${\tilde t}_1$, making them a prime target of LHC searches for physics beyond the Standard Model. Depending on the kinematic region, the main search channels are ${\tilde t_1}\to t \tilde χ^0_1$, ${\tilde t_1}\to W b \tilde χ^0_1$ and ${\tilde t_1}\to c \tilde χ^0_1$. We first examine the interplay of these decay modes with ${\tilde c_1}\to c \tilde χ^0_1$ in a model-independent fashion, revealing the existence of large regions in parameter space which are excluded for any ${\tilde t_1}\to c \tilde χ^0_1$ branching ratio. This effect is then illustrated for scenarios with stop-scharm mixing in the right-handed sector, where it has previously been observed that the stop mass limits can be significantly weakened for large mixing. Our analysis shows that once the LHC bounds from ${\tilde c_1}\to c \tilde χ^0_1$ searches are taken into account, non-zero stop-scharm mixing leads only to a modest increase in the allowed regions of parameter space, with large areas excluded for arbitrary mixing angles.

hep-ph↗

arXiv2015

Light stops, blind spots, and isospin violation in the MSSM

In the framework of the MSSM, we examine several simplified models where only a few superpartners are light. This allows us to study WIMP--nucleus scattering in terms of a handful of MSSM parameters and thereby scrutinize their impact on dark matter direct-detection experiments. Focusing on spin-independent WIMP--nucleon scattering, we derive simplified, analytic expressions for the Wilson coefficients associated with Higgs and squark exchange. We utilize these results to study the complementarity of constraints due to direct-detection, flavor, and collider experiments. We also identify parameter configurations that produce (almost) vanishing cross sections. In the proximity of these so-called blind spots, we find that the amount of isospin violation may be much larger than typically expected in the MSSM. This feature is a generic property of parameter regions where cross sections are suppressed, and highlights the importance of a careful analysis of the nucleon matrix elements and the associated hadronic uncertainties. This becomes especially relevant once the increased sensitivity of future direct-detection experiments corners the MSSM into these regions of parameter space.

hep-ph↗

arXiv2015

Dark Matter: Connecting LHC searches to direct detection

In these proceedings we review the interplay between LHC searches for dark matter and direct detection experiments. For this purpose we consider two prime examples: the effective field theory (EFT) approach and the minimal supersymmetric standard model (MSSM). In the EFT scenario we show that for operators which do not enter directly direct detection at tree-level, but only via loop effects, LHC searches give complementary constraints. In the MSSM stop and Higgs exchange contribute to the direct detection amplitude. Therefore, LHC searches for supersymmetric particles and heavy Higgses place constraints on the same parameter space as direct detection.

hep-ph↗

arXiv2015

$ΔI=1/2$ rule for kaon decays derived from QCD infrared fixed point

This article gives details of our proposal to replace ordinary chiral $SU(3)_L\times SU(3)_R$ perturbation theory $χ$PT$_3$ by 3-flavor chiral-scale perturbation theory $χ$PT$_σ$. In $χ$PT$_σ$, amplitudes are expanded at low energies and small $u,d,s$ quark masses about an infrared fixed point $α^{}_\mathrm{IR}$ of 3-flavor QCD. At $α^{}_\mathrm{IR}$, the quark condensate $\langle \bar{q}q\rangle_{\mathrm{vac}} \not= 0$ induces nine Nambu-Goldstone bosons: $π, K, η$ and a $0^{++}$ QCD dilaton $σ$. Physically, $σ$ appears as the $f_{0}(500)$ resonance, a pole at a complex mass with real part $\lesssim m_K$. The $ΔI=1/2$ rule for nonleptonic $K$-decays is then a consequence of $χ$PT$_σ$, with a $K_Sσ$ coupling fixed by data for $γγ\rightarrowππ$ and $K_{S} \to γγ$. We estimate $R_\mathrm{IR} \approx 5$ for the nonperturbative Drell-Yan ratio $R = σ(e^{+}e^{-}\rightarrow\mathrm{hadrons})/ σ(e^{+}e^{-}\rightarrowμ^{+}μ^{-})$ at $α^{}_\mathrm{IR}$, and show that, in the many-color limit, $σ/f_0$ becomes a narrow $q\bar{q}$ state with planar-gluon corrections. Rules for the order of terms in $χ$PT$_σ$ loop expansions are derived in Appendix A, and extended in Appendix B to include inverse-power Li-Pagels singularities due to external operators. This relates to an observation that, for $γγ$ channels, partial conservation of the dilatation current is not equivalent to $σ$-pole dominance.

hep-ph↗

arXiv2014

Chiral-Scale Perturbation Theory About an Infrared Fixed Point

We review the failure of lowest order chiral $SU(3)_L \times SU(3)_R$ perturbation theory $χ$PT$_3$ to account for amplitudes involving the $f_0(500)$ resonance and $O(m_K)$ extrapolations in momenta. We summarize our proposal to replace $χ$PT$_3$ with a new effective theory $χ$PT$_σ$ based on a low-energy expansion about an infrared fixed point in 3-flavour QCD. At the fixed point, the quark condensate $\langle\bar{q}q\rangle_\mathrm{vac}\neq 0$ induces nine Nambu-Goldstone bosons: $π, K, η$ and a QCD dilaton $σ$ which we identify with the $f_0(500)$ resonance. We discuss the construction of the $χ$PT$_σ$ Lagrangian and its implications for meson phenomenology at low-energies. Our main results include a simple explanation for the $ΔI = 1/2$ rule in $K$-decays and an estimate for the Drell-Yan ratio in the infrared limit.

hep-ph↗

arXiv2013

Infrared Fixed Point in the Strong Running Coupling: Unraveling the ΔI=1/2 puzzle in K-Decays

In this talk, we present an explanation for the Delta I = 1/2 rule in K-decays based on the premise of an infrared fixed point alpha_IR in the running coupling alpha_s of quantum chromodynamics (QCD) for three light quarks u,d,s. At the fixed point, the quark condensate spontaneously breaks scale and chiral SU(3)_L x SU(3)_R symmetry. Consequently, the low-lying spectrum contains nine Nambu-Goldstone bosons: pi,K,eta and a QCD dilaton sigma. We identify sigma as the f_0(500) resonance and construct a chiral-scale perturbation theory CHPT_sigma for low-energy amplitudes expanded in alpha_s about alpha_IR. The Delta I = 1/2 rule emerges in the leading order of CHPT_sigma through a sigma-pole term K_S --> sigma --> 2 pi, with a K_S-sigma coupling fixed by data on 2 gamma --> 2 pi^0 and K_S --> 2 gamma. We also determine R_IR ~ 5 for the nonperturbative Drell-Yan ratio at alpha_IR.

hep-ph↗

arXiv2012

Origin of ΔI=1/2 Rule for Kaon Decays: QCD Infrared Fixed Point

We replace ordinary chiral SU(3)_L * SU(3)_R perturbation theory CHPT_3 by a new theory CHPT_sigma based on a low-energy expansion about an infrared fixed point alpha_IR for 3-flavor QCD. At alpha_IR, the quark condensate _vac =\= 0 induces nine Nambu-Goldstone bosons: pi, K, eta and a 0++ QCD dilaton sigma. Physically, sigma appears as the f_0(500) resonance, a pole at a complex mass with real part < m_K. The ΔI = 1/2 rule for nonleptonic K-decays is then a consequence of CHPT_sigma, with a K_S-sigma coupling fixed by data for K_S^0 --> gamma gamma and gamma gamma --> pi pi. We estimate R_IR ~ 5 for the nonperturbative Drell-Yan ratio R = sigma(e+e- --> hadrons)/sigma(e+e- --> mu+mu-) at alpha_IR.

hep-ph↗