Chiral Symmetry Breaking Scale Research Articles

Dispersive constraints on fermion masses

We demonstrate that fermion masses in the Standard Model (SM) can be constrained by the dispersion relations obeyed by hadronic and semileptonic decay widths of a fictitious heavy quark $Q$ with an arbitrary mass. These relations, imposing stringent connections between the high-mass and low-mass behaviors of decay widths, correlate a heavy quark mass and the chiral symmetry breaking scale. Given the known input from leading-order heavy quark expansion and a hadronic threshold for decay products, we solve for a physical heavy quark decay width. It is shown that the charm (bottom) quark mass $m_c= 1.35$ GeV ($m_b= 4.0$ GeV) can be determined by the dispersion relation for the $Q\to du\bar d$ ($Q\to c\bar ud$) decay with the threshold $2m_\pi$ ($m_\pi+m_D$), where $m_\pi$ ($m_D$) denotes the pion ($D$ meson) mass. Requiring that the dispersion relation for the $Q\to su\bar d$ ($Q\to d\mu^+\nu_\mu$, $Q\to u\tau^-\bar\nu_\tau$) decay with the threshold $m_\pi+m_K$ ($m_\pi+m_\mu$, $m_\pi+m_\tau$) yields the same heavy quark mass, $m_K$ being the kaon mass, we constrain the strange quark (muon, $\tau$ lepton) mass to be $m_s= 0.12$ GeV ($m_\mu=0.11$ GeV, $m_\tau= 2.0$ GeV). Moreover, all the predicted decay widths corresponding to the above masses agree with the data. It is pointed out that our formalism is similar to QCD sum rules for probing resonance properties, and that the Pauli interference (weak annihilation) provides the higher-power effect necessary for establishing the solutions of the hadronic (semilaptonic) decay widths. This work suggests that the parameters in the SM may not be free, but arranged properly to achieve internal dynamical consistency.

Thermal transitions in domain wall AdS/QCD

We study thermal transitions in a Domain Wall AdS/QCD model. The model is based on the D5/probe D7 system with a discontinuous mass profile which restricts chiral fermions to 3+1 dimensional domain walls. Fluctuations on the domain wall are dual to the quark mass and condensate and reveal the relation between domain wall separation and the quark mass. The massive quarks exhibit a second order thermal, meson melting transition. Witten's multi-trace prescription can be used to interpret these configurations as having a dynamical mass from a Nambu-Jona-Lasinio interaction - here the transition is first order. Confinement can be introduced into the gauge sector by compactifying one direction of the D5. Compactification induces chiral symmetry breaking and there is a first order thermal restoration transition. If an NJL interaction is also introduced then the confinement and chiral symmetry breaking scales can be separated.

Correlations of mixed systems in confining backgrounds

We show that the entanglement of purification and the critical distance between the two mixed systems is a powerful measure in probing the phase structures of QCD and confining backgrounds, as it can distinguish the scale of chiral symmetry breaking versus the scale of confinement/deconfinement phase transitions. For two symmetric strips with equal and finite width and infinite length, and in the background of several confining geometries, we numerically calculate the critical distance between them where the mutual information vanishes and show that this quantity can probe the very rich phase structures of these backgrounds. The geometries that we study here are AdS-soliton, Witten–Sakai–Sugimoto and deformed Sakai–Sugimoto, Witten-QCD, Klebanov–Strassler, Klebanov–Tseytlin, Klebanov–Witten, Maldacena–Nunez, Nunez–Legramandi metric, and Domain-Wall QCD model. For each background we also present the relation for the entanglement of purification. Finally, we show that the Crofton forms of these geometries also behave in a universal form where a “well” is being observed around the IR wall, and therefore for all confining backgrounds, the Crofton form would also be capable of distinguishing the confining versus conformal backgrounds as it is also a tool in the reconstruction of various bulk geometries.

General neutrino interactions with sterile neutrinos in light of coherent neutrino-nucleus scattering and meson invisible decays

In this work we study the current bounds from the CEνNS process and meson invisible decays on generic neutrino interactions with sterile neutrinos in effective field theories. The interactions between quarks and left-handed SM neutrinos and/or right-handed neutrinos are first described by the low-energy effective field theory (LNEFT) between the electroweak scale and the chiral symmetry breaking scale. We complete the independent operator basis for the LNEFT up to dimension-6 by including both the lepton-number-conserving (LNC) and lepton-number-violating (LNV) operators involving right-handed neutrinos. We translate the bounds on the LNEFT Wilson coefficients from the COHERENT observation and calculate the branching fractions of light meson invisible decays. The bounds on LNEFT are then mapped onto the SM effective field theory with sterile neutrinos (SMNEFT) to constrain new physics above the electroweak scale. We find that the meson invisible decays can provide the only sensitive probe for τ neutrino flavor component and s quark component in the quark-neutrino interactions involving two (one) active neutrinos and for the effective operators without any active neutrino fields. The CEνNS process places the most stringent bound on all other Wilson coefficients. By assuming one dominant Wilson coefficient at a time in SMNEFT and negligible sterile neutrino mass, the most stringent limits on the new physics scale are 2.7–10 TeV from corresponding dipole operator in LNEFT and 0.5–1.5 TeV from neutrino-quark operator in LNEFT.

Implication of K→πνν¯ for generic neutrino interactions in effective field theories

In this work we investigate the implication of $K\to \pi \nu \bar{\nu}$ from the recent KOTO and NA62 measurements for generic neutrino interactions and the new physics scale in effective field theories. The interactions between quarks and left-handed Standard Model (SM) neutrinos are first described by the low energy effective field theory (LEFT) below the electroweak scale. We match them to the chiral perturbation theory ($\chi$PT) at the chiral symmetry breaking scale to calculate the branching fractions of Kaon semi-invisible decays and match them up to the SM effective field theory (SMEFT) to constrain new physics above the electroweak scale. In the framework of effective field theories, we prove that the Grossman-Nir bound is valid for both dim-6 and dim-7 LEFT operators, and the dim-6 vector and scalar operators dominantly contribute to Kaon semi-invisible decays based on LEFT and chiral power counting rules. They are induced by multiple dim-6 lepton-number-conserving operators and one dim-7 lepton-number-violating operator in the SMEFT, respectively. In the lepton-number-conserving $s\to d$ transition, the $K\to \pi \nu \bar{\nu}$ decays provide the most sensitive probe for the operators with $\tau\tau$ component and point to a corresponding new physics scale of $\Lambda_{\rm NP} \in[47~\text{TeV},~72~\text{TeV}]$ associated with a single effective coefficient. The lepton-number-violating operator can also explain the observed $K\to\pi\nu\bar{\nu}$ discrepancy with the SM prediction within a narrow range $\Lambda_{\rm NP}\in [19.4~\text{TeV},~21.5~\text{TeV}]$, which is consistent with constraints from Kaon invisible decays.

On the chiral expansion of vector meson masses

We study the chiral expansion of meson masses and decay constants using a chiral Lagrangian that was constructed previously based on the hadrogenesis conjecture. The one-loop self energies of the Goldstone bosons and vector mesons are evaluated. It is illustrated that a renormalizeable effective field theory arises once specific conditions on the low-energy constants are imposed. For the case where the hadrogenesis mass gap scale Lambda_{HG} is substantially larger than the chiral symmetry breaking scale Lambda_chi a partial summation scheme is required. All terms proportional to (M/\Lambda_\chi)^n can be summed by a suitable renormalization, where M is the chiral and large-N_c limit of the vector meson masses in QCD. The size of loop effects from vector meson degrees of freedom is illustrated for physical quarks masses. Naturally sized effects are observed that have significant impact on the chiral structure of low-energy QCD with three light flavours.

Nonperturbative quark, gluon, and meson correlators of unquenched QCD

We present non-perturbative first-principle results for quark-, gluon- and meson $1$PI correlation functions of two-flavour Landau-gauge QCD in the vacuum. These correlation functions carry the full information about the theory. They are obtained by solving their Functional Renormalisation Group equations in a systematic vertex expansion, aiming at apparent convergence. This work represents a crucial prerequisite for quantitative first-principle studies of the QCD phase diagram and the hadron spectrum within this framework. In particular, we have computed the gluon, ghost, quark and scalar-pseudoscalar meson propagators, as well as gluon, ghost-gluon, quark-gluon, quark, quark-meson, and meson interactions. Our results stress the crucial importance of the quantitatively correct running of different vertices in the semi-perturbative regime for describing the phenomena and scales of confinement and spontaneous chiral symmetry breaking without phenomenological input.

Structure of the neutral pion and its electromagnetic transition form factor

The $\gamma^\ast \gamma \to \pi^0$ transition form factor, $G(Q^2)$, is computed on the entire domain of spacelike momenta using a continuum approach to the two valence-body bound-state problem in relativistic quantum field theory: the result agrees with data obtained by the CELLO, CLEO and Belle Collaborations. The analysis unifies this prediction with that of the pion's valence-quark parton distribution amplitude (PDA) and elastic electromagnetic form factor, and demonstrates, too, that a fully self-consistent treatment can readily connect a pion PDA that is a broad, concave function at the hadronic scale with the perturbative QCD prediction for the transition form factor in the hard photon limit. The normalisation of that limit is set by the scale of dynamical chiral symmetry breaking, which is a crucial feature of the Standard Model. Understanding of the latter will thus remain incomplete until definitive transition form factor data is available on $Q^2>10\,$GeV$^2$.

Theory and phenomenology of the elementary Goldstone Higgs boson

We show, via a careful analytical and numerical analysis, that a pseudo Goldstone nature of the Higgs is naturally embodied by an elementary realization that also serves as ultraviolet completion. Renormalizability married to perturbation theory allows to precisely determine the quantum corrections of the theory while permitting to explore the underlying parameter space. By characterising the available parameter space of the extended Higgs sector we discover that the preferred electroweak alignment angle is centred around $\theta \simeq 0.02$, corresponding to the Higgs chiral symmetry breaking scale $ f \simeq 14~$TeV. The latter is almost 60 times higher than the Standard Model electroweak scale. However, due to the perturbative nature of the theory, the spectrum of the enlarged Higgs sector remains in the few TeV energy range. We also analyse precision constraints and the relevant phenomenological aspects of the theory.

Vacuum structure of vector mesons in QCD

We study the chiral dynamics of vector mesons in two-flavor QCD in vacuum by utilizing a functional renormalization group approach. This allows us to capture the dynamical transition from the quark-gluon phase at high energies to the hadronic phase at low energies without the necessity of model parameter tuning. We use this to analyze the scaling of vector meson masses towards the chiral symmetry breaking scale, the decoupling of the mesons at high energies and the validity of vector meson dominance.

Magnetic moments ofJP=32+decuplet baryons using effective quark masses in a chiral constituent quark model

The magnetic moments of ${J}^{P}={\frac{3}{2}}^{+}$ decuplet baryons have been calculated in the chiral constituent quark model ($\ensuremath{\chi}\mathrm{CQM}$) with explicit results for the contribution coming from the valence quark polarizations, sea quark polarizations, and their orbital angular momentum. Since the ${J}^{P}={\frac{3}{2}}^{+}$ decuplet baryons have short lifetimes, the experimental information about them is limited. The $\ensuremath{\chi}\mathrm{CQM}$ has important implications for chiral symmetry breaking as well as SU(3) symmetry breaking since it works in the region between the QCD confinement scale and the chiral symmetry breaking scale. The predictions in the model not only give a satisfactory fit when compared with the experimental data but also show improvement over the other models. The effect of the confinement on quark masses has also been discussed in detail and the results of $\ensuremath{\chi}$CQM are found to improve further with the inclusion of effective quark masses.

Top seesaw with a custodial symmetry, and the 126 GeV Higgs

The composite Higgs models based on the top seesaw mechanism commonly possess an enhanced approximate chiral symmetry, which is spontaneously broken to produce the Higgs field as the pseudo-Nambu-Goldstone bosons. The minimal model with only one extra vector-like singlet quark that mixes with the top quark can naturally give rise to a 126 GeV Higgs boson. However, without having a custodial symmetry it suffers from the weak-isospin violation constraint, which pushes the chiral symmetry breaking scale above a few TeV, causing a substantial fine-tuning for the weak scale. We consider an extension to the minimal model to incorporate the custodial symmetry by adding a vector-like electroweak doublet of quarks with hypercharge +7/6. Such a setup also protects the $$ Zb\overline{b} $$ coupling which is another challenge for many composite Higgs models. With this addition, the chiral symmetry breaking scale can be lowered to around 1 TeV, making the theory much less fine-tuned. The Higgs is a pseudo-Nambu-Goldstone boson of the broken O(5) symmetry. For the Higgs mass to be 126 GeV, the hypercharge +7/6 quarks should be around or below the chiral symmetry breaking scale, and are likely to be the lightest new states. The 14 TeV LHC will significantly extend the search reach of these quarks. To probe the rest of the spectrum, on the other hand, would require a higher-energy future collider.

Higgs mass from compositeness at a multi-TeV scale

Within composite Higgs models based on the top seesaw mechanism, we show that the Higgs field can arise as the pseudo Nambu-Goldstone boson of the broken U(3)_L chiral symmetry associated with a vector-like quark and the t-b doublet. As a result, the lightest CP-even neutral state of the composite scalar sector is lighter than the top quark, and can be identified as the newly discovered Higgs boson. Constraints on weak isospin violation push the chiral symmetry breaking scale above a few TeV, implying that other composite scalars are probably too heavy to be probed at the LHC, but may be within reach at a future hadron collider with center-of-mass energy of about 100 TeV.

Nonperturbative renormalization of the chiral nucleon-nucleon interaction up to next-to-next-to-leading order

We study the nonperturbative renormalization of the nucleon-nucleon (NN) interaction at next-to-leading order (NLO) and next-to-next-to-leading order (NNLO) of chiral effective field theory. A systematic variation of the cutoff parameter is performed for values below the chiral symmetry breaking scale of about 1 GeV. The accuracy of the predictions is determined by calculating the $\chi^2$ for the reproduction of the NN data for energy intervals below pion-production threshold. At NLO, the NN data are described well up to about 100 MeV laboratory energy and, at NNLO, up to about 200 MeV---with, essentially, cutoff independence for cutoffs between about 450 and 850 MeV.

Pion Electromagnetic Form Factor at Spacelike Momenta

A novel method is employed to compute the pion electromagnetic form factor, F(π)(Q²), on the entire domain of spacelike momentum transfer using the Dyson-Schwinger equation (DSE) framework in QCD. The DSE architecture unifies this prediction with that of the pion's valence-quark parton distribution amplitude (PDA). Using this PDA, the leading-order, leading-twist perturbative QCD result for Q²F(π)(Q²) underestimates the full computation by just 15% on Q²≳8 GeV², in stark contrast to the result obtained using the asymptotic PDA. The analysis shows that hard contributions to the pion form factor dominate for Q²≳8 GeV², but, even so, the magnitude of Q²F(π)(Q²) reflects the scale of dynamical chiral symmetry breaking, a pivotal emergent phenomenon in the standard model.

Effective multiquark interactions with explicit breaking of chiral symmetry

In a long distance Lagrangian approach to the low lying meson phenomenology we present and discuss the most general spin zero multi-quark interaction vertices of non-derivative type which include a set of effective interactions proportional to the current quark masses, breaking explicitely the chiral SU(3)_L X SU(3)_R and U_A(1) symmetries. These vertices are of the sameorder in Nc counting as the 't Hooft flavor determinant interaction and the 8 quark interactions which extend the original leading in Nc four quark interaction Lagrangian of Nambu and Jona-Lasinio. The Nc assignements match the counting rules based on arguments set by the scale of spontaneous chiral symmetry breaking. With path integral bosonization techniques which take appropriately into account the quark mass differences we derive the mesonic Lagrangian up to 3-point mesonic vertices. We demonstrate that explicit symmetry breaking effects in interactions are essential to obtain the correct empirical ordering and magnitude of the splitting of certain states such as m_K < m_eta for the pseudoscalars and m{kappa(800)} < m{a0(980)} m{f0(980)} in the scalar sector, and achieve total agreement with the empirical low lying meson mass spectra. With all parameters of the model fixed by the spectra we analyze further a bulk of two body decays at tree level of the bosonic Lagrangian: the strong decays of the scalars sigma->pi pi, f0->pi pi, kappa->pi K, a0(980)->pi eta, as well as the two photon decays of a0, f0 and sigma mesons and the anomalous decays of the pseudoscalars {pi,eta,eta'}-> 2 photons. Our results for the strong decays are within the current expectations and the pseudoscalar radiative decays are in very good agreement with data. The radiative decays of the scalars are smaller than the observed values for the f0 and the sigma, but reasonable for the a0. A detailed discussion accompanies all the results.

Glueball spectrum in a gauge theory with two dynamical scales

We investigate the glueball spectrum of a strongly coupled gauge theory with two dynamical scales. The main tool is the use of the gauge/gravity duality. The model we study has a known graviational dual, which arises from a type IIB D-brane configuration. It exhibits two dynamical scales, separated by a nearly conformal region. Thus, it is of great interest for the study of walking in gauge theories. By using the gravitational description, we are able to compute analytically the glueball mass spectrum in a certain range of the parameter space of the theory. Within that range, we do not find a light state that could be associated with a slight breaking of conformal invariance. Finally, we show that in this model there can be an order of magnitude hierarchy between the scale of confinement, given by the lowest glueball mass, and the scale of chiral symmetry breaking, determined by the lowest vector-meson mass.

Chiral polarization scale of QCD vacuum and spontaneous chiral symmetry breaking

It has recently been found that dynamics of pure glue QCD supports the low energy band of Dirac modes with local chiral properties qualitatively different from that of a bulk: while bulk modes suppress chirality relative to statistical independence between left and right, the band modes enhance it. The width of such chirally polarized zone – chiral polarization scale ∧ch – has been shown to be finite in the continuum limit at fixed physical volume. Here we present evidence that ∧ch remains non-zero also in the infinite volume, and is therefore a dynamical scale in the theory. Our experiments in Nf = 2+1 QCD support the proposition that the same holds in the massless limit, connecting ∧ch to spontaneous chiral symmetry breaking. In addition, our results suggest that thermal agitation in quenched QCD destroys both chiral polarization and condensation of Dirac modes at the same temperature Tch > Tc.

Role of Current Quark Mass Dependent Multi-quark Interactions in Low Lying Meson Mass Spectra

We call attention to a class of current-quark mass dependent multi-quark interaction terms which break explicitly the chiral $SU(3)_L\times SU(3)_R$ and $U_A(1)$ symmetries. They complete the set of effective quark interactions that contribute at the same order in $N_c$ as the 't Hooft flavor determinant interaction and the eight quark interactions in the phase of spontaneously broken chiral symmetry. The $N_c$ classification scheme matches the counting rules based on arguments set by the scale of spontaneous chiral symmetry breaking. Together with the leading in $N_c$ four quark Nambu-Jona-Lasinio Lagrangian and current quark mass matrix, the model is apt to account for the correct empirical ordering and magnitude of the splitting of states in the low lying mass spectra of spin zero mesons. The new terms turn out to be essential for the ordering $m_K < m_\eta$ in the pseudoscalar sector and $m_{\kappa_0} < m_{a_0}\sim m_{f0}$ for the scalars.

Intrinsic transverse momentum and parton correlations from dynamical chiral symmetry breaking

The dynamical breaking of chiral symmetry in QCD is caused by nonperturbative interactions on a scale rho ~ 0.3 fm, much smaller than the hadronic size R ~ 1 fm. These short-distance interactions influence the intrinsic transverse momentum distributions of partons and their correlations at a low normalization point. We study this phenomenon in an effective description of low-energy dynamics based on chiral constituent quark degrees of freedom, which refers to the large-N_c limit of QCD. The nucleon is obtained as a system of constituent quarks and antiquarks moving in a self-consistent classical chiral field (chiral quark-soliton model). The calculated distributions of constituent quarks/antiquarks are matched with QCD partons at the scale rho^{-2}. The p_T distribution of valence quarks is localized at p_T^2 ~ R^{-2} and roughly of Gaussian shape. The sea quark distribution exhibits a would-be power-like tail ~1/p_T^2 extending up to the chiral symmetry-breaking scale. Such behavior is seen in the flavor-singlet unpolarized and nonsinglet polarized sea. The high-momentum tails are the result of short-range correlations between sea quarks in the nucleon's light-cone wave function, analogous to NN correlations in nuclei. The nucleon wave function contains correlated pairs of transverse size rho << R with sigma- and pi-like quantum numbers, whose internal wave functions become identical at p_T^2 ~ rho^{-2} (restoration of chiral symmetry). These features are model-independent and represent an effect of dynamical chiral symmetry breaking on the nucleon's partonic structure. Our results have numerous implications for the P_T distributions of particles produced in hard scattering processes. The nonperturbative parton correlations predicted here could be observed in particle correlations between the current and target fragmentation regions of DIS.