Flavor

Flavor or flavor (English for aroma or taste ) is one of the quantum numbers of elementary particles ( quarks and leptons ) in connection with the weak interaction . In the theory of the electroweak interaction , flavor is not a conservation number , and flavor- changing processes exist. In quantum chromodynamics, on the other hand, it is a global symmetry , and flavor is retained in all processes that are only subject to the strong interaction .

The flavor quantum numbers of the quarks are called isospin (for up and down quarks), charm , strangeness , topness (also truth ) and bottomness (also beauty ) after the respective quarks .

The term flavor was first used in 1968 in connection with the quark model of the hadrons . The name is said to have been invented by Murray Gell-Mann and Harald Fritzsch when they passed an ice cream parlor ( Baskin-Robbins ) on their way to lunch , which offered 31 different flavors.

Quark flavors

There are a total of six different quark flavors (two per generation ):

Surname	sym bol	Baryon number ${\ displaystyle B}$	charge ${\ displaystyle Q}$	Flavor quantum numbers					hyper- charge ${\ displaystyle Y}$
Surname	sym bol	Baryon number ${\ displaystyle B}$	charge ${\ displaystyle Q}$	${\ displaystyle I_ {3}}$	${\ displaystyle C}$	${\ displaystyle S}$	${\ displaystyle T}$	${\ displaystyle B '}$	hyper- charge ${\ displaystyle Y}$
Up	u	+1/3	+2/3	+1/2	0	0	0	0	+1/3
Down	d	+1/3	−1/3	−1/2	0	0	0	0	+1/3
Charm	c	+1/3	+2/3	0	+1	0	0	0	+4/3
Strange	s	+1/3	−1/3	0	0	−1	0	0	−2/3
Top (also truth )	t	+1/3	+2/3	0	0	0	+1	0	+4/3
Bottom (also beauty )	b	+1/3	−1/3	0	0	0	0	−1	−2/3

Here is the baryon number , the electrical charge (in units of e ), or also the third component of the isospin, the strangeness, the charm, the bottomness (the apostrophe in serves to differentiate the baryon number ), the topness and the hypercharge . ${\ displaystyle B}$ ${\ displaystyle Q}$ ${\ displaystyle I_ {3}}$ ${\ displaystyle I_ {z}}$ ${\ displaystyle S}$ ${\ displaystyle C}$ ${\ displaystyle B '}$ ${\ displaystyle B '}$ ${\ displaystyle B}$ ${\ displaystyle T}$ ${\ displaystyle Y}$

The flavor quantum numbers are defined by the numbers of the respective quarks:

{\ displaystyle {\ begin {array} {ccl} I_ {3} & = & {\ big (} (n_ {u} -n _ {\ bar {u}}) - (n_ {d} -n _ {\ bar {d}}) {\ big)} / 2 \\ C & = & n_ {c} -n _ {\ overline {c}} \\ S & = & n _ {\ overline {s}} - n_ {s} \\ T & = & n_ {t} -n _ {\ overline {t}} \\ B '& = & n _ {\ overline {b}} - n_ {b} \\\ end {array}}}

The sign convention is chosen so that for quarks of the up type (u, c, t) the respective flavor quantum number is positive, while for quarks of the down type (d, s, b) it is negative. For the antiquarks the sign is always the other way around than for the respective quark, for all other elementary particles the respective flavor is 0.

Hadrons get their flavor from the valence quarks , this is the basis of the Eightfold Way and the quark model.

The Gell-Mann-Nishijima formula applies to hadrons and quarks

{\ displaystyle Q = I_ {3} + {\ frac {Y} {2}} \ \ \ mathrm {with} \ \ Y = B + S + C + B '+ T}

.

history

Ordinary matter, which consists of protons and neutrons, is described by the isospin, or the two quark flavors Up (u) and Down (d). Strange matter later made the introduction of the s-quark and the corresponding quantum number strangeness necessary. According to the isospin symmetry, James Bjorken and Sheldon Glashow suspected in 1964 that there must be another quantum number as a partner to strangeness, which they called charm . The orthocharmonium they postulated (analogous to the orthopositronium ) was discovered in 1974 at the BNL as J and at SLAC under the name ψ ( J / ψ meson ).

Lepton flavors

Leptons also occur in six flavors (two per lepton family):

Surname	sym bol	Baryon number ${\ displaystyle B}$	charge ${\ displaystyle Q}$	Flavor quantum numbers
Surname	sym bol	Baryon number ${\ displaystyle B}$	charge ${\ displaystyle Q}$	${\ displaystyle L_ {e}}$	${\ displaystyle L _ {\ mu}}$	${\ displaystyle L _ {\ tau}}$
electron	${\ displaystyle e}$	0	−1	+1	0	0
Electron neutrino	${\ displaystyle \ nu _ {\ mathrm {e}}}$	0	0	+1	0	0
Muon	${\ displaystyle \ mu}$	0	−1	0	+1	0
Muon neutrino	${\ displaystyle \ nu _ {\ mu}}$	0	0	0	+1	0
dew	${\ displaystyle \ tau}$	0	−1	0	0	+1
Tau neutrino	${\ displaystyle \ nu _ {\ tau}}$	0	0	0	0	+1

${\ displaystyle L_ {f}}$ is the respective lepton family number for the families , and . Their sum gives the number of leptons . ${\ displaystyle f = e}$ ${\ displaystyle \ mu}$ ${\ displaystyle \ tau}$ ${\ displaystyle L = L _ {\ mathrm {e}} + L _ {\ mu} + L _ {\ tau}}$

Antiparticles have opposite quantum numbers to the corresponding particles. For example, the positron (the anti-electron) has the quantum numbers and . ${\ displaystyle L _ {\ mathrm {e}} = - 1}$ ${\ displaystyle Q = + 1}$

Generations

If one regards (quark) generations and (lepton) families as basically equivalent, then the leptons can also be divided into uncharged ( neutrinos ) and electrically charged leptons. In summary, these three families or generations are each with two types of particles :

		charge ${\ displaystyle Q}$		Three generations
Quarks	${\ displaystyle B = 1/3}$	${\ displaystyle \ left ({\ begin {array} {c} + {\ frac {2} {3}} \\ - {\ frac {1} {3}} \ end {array}} \ right)}$	up-like down-like	${\ displaystyle \ left ({\ begin {array} {c} u \\ d \ end {array}} \ right)}$	${\ displaystyle \ left ({\ begin {array} {c} c \\ s \ end {array}} \ right)}$	${\ displaystyle \ left ({\ begin {array} {c} t \\ b \ end {array}} \ right)}$
Leptons	${\ displaystyle L = 1}$	${\ displaystyle \ left ({\ begin {array} {c} 0 \\ - 1 \ end {array}} \ right)}$	Neutrinos charged leptons	${\ displaystyle \ left ({\ begin {array} {c} \ nu _ {e} \\ e ^ {-} \ end {array}} \ right)}$	${\ displaystyle \ left ({\ begin {array} {c} \ nu _ {\ mu} \\\ mu ^ {-} \ end {array}} \ right)}$	${\ displaystyle \ left ({\ begin {array} {c} \ nu _ {\ tau} \\\ tau ^ {-} \ end {array}} \ right)}$

To prevent chiral anomalies , the number of families of quarks and leptons must match.

A fermion of the respective flavor is an eigenstate of the weakly interacting part of the Hamilton operator : Each particle interacts in a characteristic way with the vector bosons W ^± and Z ⁰ . On the other hand, a fermion with a certain mass (i.e. an eigenstate of the kinematic part of the Hamilton operator) is a superposition of different flavor states. It follows that the flavor state of a particle can change while it is moving freely. The transformation from the flavor base to the mass base takes place in quarks using the Cabibbo-Kobayashi-Maskawa matrix (CKM matrix). The Maki-Nakagawa-Sakata matrix (MNS matrix) also exists for leptons .

If there are three or more families, the CKM matrix allows CP invariance to be violated .

Conservation quantities

Absolutely retained z. B .:

the electric charge

{\ displaystyle Q}

the difference between the number of baryons and number of leptons : (a symmetry different from the weak hypercharge ) ${\ displaystyle BL}$ ${\ displaystyle U (1)}$

Under the strong interaction, all flavor quantum numbers are retained.

Individual evidence

↑ BJ Bjørken, SL Glashow: Elementary Particles and SU (4) . In: Phys. Lett. tape 11 , no. 3 , 1964, pp. 255-257 , doi : 10.1016 / 0031-9163 (64) 90433-0 .

[1] BJ Bjørken, SL Glashow: Elementary Particles and SU (4) . In: Phys. Lett. tape 11 , no. 3 , 1964, pp. 255-257 , doi : 10.1016 / 0031-9163 (64) 90433-0 .