(I) The B ^- meson is a bu quark combination. ( a ) Show that this is consistent for all qua

(I) The B ^- meson is a bu quark combination. ( a ) Show...

Key Concepts

Quark Model of Mesons

In the quark model, mesons are bound states of one quark and one antiquark. This framework explains how the quantum numbers of mesons, such as electric charge, baryon number, and flavor, are determined by the intrinsic properties of their constituent particles. Understanding this model is fundamental to analyzing meson composition and behavior.

Quantum Number Conservation

Quantum numbers like electric charge and baryon number must be conserved when forming composite particles. When combining a quark with an antiquark to form a meson, the sum of their individual quantum numbers (including charge and other flavor-related numbers) must match the observed quantum numbers of the meson, ensuring consistency with the laws of conservation that govern particle interactions.

Properties of Antiquarks

Antiquarks possess quantum numbers that are the opposites of their corresponding quarks. This concept is critical because when an antiquark is paired with a quark in a meson, its negative charge and reversed flavor quantum numbers can cancel or modify those of the quark, leading to the overall quantum number assignments seen in meson systems.

Fractional Charge and Charge Calculation

Quarks carry fractional electric charges, and the total charge of a meson is the algebraic sum of the charges of its quark and antiquark. For example, knowing the charges of the bottom quark and the up quark (or their antiparticles) and how these add together allows one to verify that the meson’s charge is consistent with its designation (e.g., B? having a charge of -1).

Flavor Composition of B Mesons

Different B meson types are distinguished by their light quark or antiquark partners when paired with a bottom or anti-bottom quark. Recognizing the appropriate pairings—such as pairing a bottom quark with an anti-up quark for one state and a bottom quark with an anti-down quark for another—is essential for understanding the properties and classification of B mesons like B?, B?, and B?.

Transcript

00:01 All right, so problem number 36 wants us to figure out if you're given the b -mazon, a cork combination as b -minus is equal to be a bottom cork and an anti -up cork.

00:23 So we need to verify that this is actually a physical combination.

00:29 So to do that, we need to verify all the conservation.

00:31 Rules.

00:32 So first let's look at charge.

00:37 So for charge, we have a minus one for the b -mazon is equal to.

00:43 Now, corks are kind of weird.

00:45 They carry one -third charge or one -third or two -third charges instead of one -half and one charges, basically, or instead of integer charges.

00:56 So they carry a third -third or so for a bottom quark, it's a minus one -third plus an upcork, an anti -upcourt.

01:08 One, upcork carries a plus two -thirds charge.

01:11 So an anti -upcork carries a minus two -thirds charge.

01:15 So this is concerned.

01:20 Okay, so now we've got the baryon number.

01:27 So for the beryon number, we've got zero for the b -mazon is equal to.

01:34 Now the barion numbers for quarks are, again, and they're weird.

01:39 They're a third.

01:40 So one -third for the bottom cork plus the upcork would be one -third, and the anti -up quark is minus one -third.

01:50 So minus one -third, one -third plus one -third is equal to zero, so that's conserved.

01:57 Now let's look at strangeness.

02:05 Strangeness, so the strangeness of a b -mazon is zero, and the strangeness of the bottom and upcorks are both zero.