flavour (particle physics)



Fields and quanta

field (physics)

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:
mesonspion (udu d)
rho-meson (udu d)
omega-meson (udu d)
kaon (q u/dsq_{u/d} s)
eta-meson (u u + d d + s s)
B-meson (qbq b)
baryonsproton (uud)(u u d)
neutron (udd)(u d d)

(also: antiparticles)

effective particles

hadron (bound states of the above quarks)


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.

Flavor anomalies

Due to the flavor problem, the flavor sector of the standard model of particle physics is the least well understood in detail. Indeed, persistent flavor anomalies reflect a discrepancy 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.

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 (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)

Lecture notes:

See also

The flavour problem

On the flavour 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

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:

Realization in intersecting D-brane models

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

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

Last revised on March 26, 2020 at 05:43:56. See the history of this page for a list of all contributions to it.