nLab flavour (particle physics)



Fields and quanta

fields and particles in particle physics

and in the standard model of particle physics:

force field gauge bosons

scalar bosons

matter field fermions (spinors, Dirac fields)

flavors of fundamental fermions in the
standard model of particle physics:
generation of fermions1st generation2nd generation3d generation
quarks (qq)
up-typeup quark (uu)charm quark (cc)top quark (tt)
down-typedown quark (dd)strange quark (ss)bottom quark (bb)
neutralelectron neutrinomuon neutrinotau neutrino
bound states:
mesonslight mesons:
pion (udu d)
ρ-meson (udu d)
ω-meson (udu d)
ϕ-meson (ss¯s \bar s),
kaon, K*-meson (usu s, dsd s)
eta-meson (uu+dd+ssu u + d d + s s)

charmed heavy mesons:
D-meson (uc u c, dcd c, scs c)
J/ψ-meson (cc¯c \bar c)
bottom heavy mesons:
B-meson (qbq b)
ϒ-meson (bb¯b \bar b)
proton (uud)(u u d)
neutron (udd)(u d d)

(also: antiparticles)

effective particles

hadrons (bound states of the above quarks)


in grand unified theory

minimally extended supersymmetric standard model




dark matter candidates


auxiliary fields



The fermion fundamental particles in the standard model of particle physics arrange in three “generations”. Between generations, particles differ in their mass and in further properties referred to as flavor quantum numbers, but otherwise their interactions are the same, to high accuracy. Hence flavor physics refers to the phenomenology of processes that do involve or depend on flavor quantum numbers, notably when flavor changes through interactions via the weak nuclear force and Yukawa interactions.

For the leptons these flavor quantum numbers are electron number, muon number and tauon number as well as the corresponding three neutrino numbers.

For the quarks the flavor quantum numbers are isospin, charm, strange-ness, bottom-ness and top-ness.

See yotams for a good quick introduction.


The flavor problem

In the standard model of particle physics, the sector involving flavor physics – hence the Higgs boson interaction with the generations of fermions, hence the Yukawa coupling- and CKM matrix-sector in the Lagrangian density of the Einstein-Yang-Mills-Dirac-Higgs theory that defines the standard model – has some striking characteristics different from the sector that does not:

slide grabbed from Altmannshofer 14

slide grabbed from Isidori 16

(Note that Isidori’s slide collects all terms with a Higgs boson factor, including the pure Higgs terms reflecting the cosmological constant and the hierarchy problem, and hence “all the problematic terms”, while the flavor sector proper consists of those terms involving Higgs and quark factors.)

Broadly, the flavor problem (see the references below) is the fact that the nature and principles behind the flavor sector of the standard model are much less understood than those of the gauge sector (the “color sector”). More concretely, the flavor problem in models going beyond the standard model (such as GUT models and/or the MSSM) is that introducing any New Physics while satisfying observational constraints on flavor physics seems to demand a high level of fine-tuning in the flavor sector.

Moreover, all observed CP violation is related to flavor-changing interactions.

Finally, due to confinement, the flavor-changing transitions between quarks are not seen in isolation by collider experiments, but are only seen via the induced decays of the mesons and/or baryons that the quarks are bound in. This way the flavor problem is tied to the confinement problem and hence to the problem of formulating QCD non-perturbatively (e.g. via AdS/QCD).

All this suggests that the flavor sector is controlled by mechanisms that are not understood or identified yet.

Experimental “anomalies”

Due to the flavor problem, the flavor sector of the standard model of particle physics is the least well understood in detail. Indeed, thete are persistent and growing discrepancies between SM-predictions and experimental measurements in the flavor sector:

Flavor anomaly

flavor anomalies reflect a discrepancy in B-meson decays between experiment (LHCb, Belle, BaBar) and theoretical computations, which keeps being seen at a global statistical significance of 4σ\sim 4\sigma across all experiments and decay channels. If these flavour anomalies are real they signify New Physics in the flavor sector.

See at flavour anomalies for more.

Cabibbo anomaly

See at Cabibbo anomaly and V_cb puzzle.

(g2)(g-2) anomaly

See at (g-2) anomaly.

Geometric engineering on D8-branes

In geometric engineering of flavor physics in intersecting D-brane models, the flavour degrees of freedom come from open strings ending on spacetime-filling D-branes called “flavor branes” (Karch-Katz 02).

Specifically in the Sakai-Sugimoto model geometrically engineering something close to actual quantum chromodynamics (Sakai-Sugimoto 04, Sakai-Sugimoto 05), flavour is encoded in the presence of D8-branes in the model:

Here we are showing

  1. the color D4-branes;

  2. the flavor D8-branes;


    1. the 5d Chern-Simons theory on their worldvolume

    2. the corresponding 4d WZW model on the boundary

    both exhibiting the meson fields;

  3. the baryon D4-branes

    (see at WSS-model – Baryons);

  4. the Yang-Mills monopole D6-branes

    (see at D6-D8-brane bound state);

  5. the NS5-branes (often not considered here).



A good quick account is in

  • yotams, What is flavor? (pdf, pdf)

Textbook accounts:

Lecture notes:

With an emphasis on CP-violation?:

  • Antonio Pich, Flavour Dynamics and Violations of the CP Symmetry, Lectures at the 2017 and 2019 CERN - Latin-American Schools of High-Energy Physics (arXiv:1805.08597)

With an emphasis on the neutrino-sector:

  • Zhi-zhong Xing, Flavor structures of charged fermions and massive neutrinos (arXiv:1909.09610)

See also

On flavour physics and flavour anomalies seen at the LHCb experiment:

  • Niels Tuning, Recent results from LHCb, Nikhef 2020 (nikhef event:2253, pdf, pdf)

    In recent years a number of results in flavour physics have drawn some attention due to tensions with respect to Standard Model predictions. An overview of these results will be shown, together with a few recent results from this Spring, both on the flavour anomalies and ‘classical’ flavour physics

Survey and outlook:

The flavour problem

On the flavour problem:

In relation to the neutrino mass problem:

On the flavor problem in the MSSM:

Flavour anomalies

Outlook on the field of flavour physics in view of LHCb-measurement of flavour anomalies and CP violation:

See also

  • Rafael Aoude, Tobias Hurth, Sophie Renner, William Shepherd, The impact of flavour data on global fits of the MFV SMEFT (arXiv:2003.05432)

On flavour physics and potential flavour anomalies in kaon-decays:

Geometric engineering on flavor branes

The geometric engineering of flavour physics in intersecting D-brane models (flavor branes in AdS/QCD) was originally understood in

and then developed in detail for QCD on D8-branes in the Sakai-Sugimoto model:

SU(2)SU(2)-flavor symmetry on heterotic M5-branes

Emergence of SU(2) flavor-symmetry on single M5-branes in heterotic M-theory on ADE-orbifolds (in the D=6 N=(1,0) SCFT on small instantons in heterotic string theory):

Argument for this by translation under duality between M-theory and type IIA string theory to half NS5-brane/D6/D8-brane bound state systems in type I' string theory:

Reviewed in:

  • Santiago Cabrera, Amihay Hanany, Marcus Sperling, Section 2.3 of: Magnetic Quivers, Higgs Branches, and 6d 𝒩=(1,0)\mathcal{N}=(1,0) Theories, JHEP06(2019)071, JHEP07(2019)137 (arXiv:1904.12293)

The emergence of flavor in these half NS5-brane/D6/D8-brane bound state systems, due to the semi-infinite extension of the D6-branes making them act as flavor branes:

Reviewed in:

  • Fabio Apruzzi, Marco Fazzi, Section 2.1 of: AdS 7/CFT 6AdS_7/CFT_6 with orientifolds, J. High Energ. Phys. (2018) 2018: 124 (arXiv:1712.03235)

See also:

Last revised on February 20, 2024 at 09:43:44. See the history of this page for a list of all contributions to it.