rpp2010-rev-quark-model

rpp2010-rev-quark-model - 14. Quark model 1 14. QUARK MODEL...

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14. Quark model 1 14. QUARK MODEL Revised September 2009 by C. Amsler (University of Z¨urich), T. DeGrand (University of Colorado, Boulder), and B. Krusche (University of Basel). 14.1. Quantum numbers of the quarks Quarks are strongly interacting fermions with spin 1/2 and, by convention, positive parity. Antiquarks have negative parity. Quarks have the additive baryon number 1/3, antiquarks -1/3. Table 14.1 gives the other additive quantum numbers (flavors) for the three generations of quarks. They are related to the charge Q (in units of the elementary charge e ) through the generalized Gell-Mann-Nishijima formula Q = I z + B + S + C + B + T 2 , (14 . 1) where B is the baryon number. The convention is that the favor of a quark ( I z , S , C , B ,or T )has thesames ignasits charge Q . With this convention, any flavor carried by a charged meson has the same sign as its charge, e.g. , the strangeness of the K + is +1, the bottomness of the B + is +1, and the charm and strangeness of the D s are each 1. Antiquarks have the opposite flavor signs. Table 14.1: Additive quantum numbers of the quarks. Property - Quark d u s c b t Q – electric charge 1 3 + 2 3 1 3 + 2 3 1 3 + 2 3 I – isospin 1 2 1 2 0 0 0 0 I z – isospin z -component 1 2 + 1 2 0 0 0 0 S – strangeness 0 0 1 0 0 0 C –charm 0 0 0 +1 0 0 B – bottomness 0 0 0 0 1 0 T – topness 0 0 0 0 0 +1 14.2. Mesons Mesons have baryon number B = 0. In the quark model, they are q q ± bound states of quarks q and antiquarks q ± (the flavors of q and q ± may be diFerent). If the orbital angular momentum of the q q ± state is ± , then the parity P is ( 1) ± +1 . The meson spin J is given by the usual relation | ± s |≤ J ≤| ± + s | ,where s is 0 (antiparallel quark spins) or 1 (parallel quark spins). The charge conjugation, or C -parity C =( 1) ± + s , is de±ned only for the q ¯ q states made of quarks and their own antiquarks. The C -parity can be generalized to the G -parity G 1) I + ± + s for mesons made of quarks and their own antiquarks (isospin I z = 0), and for the charged u ¯ d and d ¯ u states (isospin I =1) . K. Nakamura et al. ,JPG 37 , 075021 (2010) (http://pdg.lbl.gov) July 30, 2010 14:36
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2 14. Quark model The mesons are classifed in J PC multiplets. The ± = 0 states are the pseudoscalars (0 + ) and the vectors (1 −− ). The orbital excitations ± = 1 are the scalars (0 ++ ), the axial vectors (1 ++ )and(1 + ), and the tensors (2 ++ ). Assignments For many oF the known mesons are given in Tables 14.2 and 14.3. Radial excitations are denoted by the principal quantum number n .Th e very short liFetime oF the t quark makes it likely that bound-state hadrons containing t quarks and/or antiquarks do not exist. States in the natural spin-parity series P =( 1) J must, according to the above, have s =1 and hence, CP = +1. Thus, mesons with natural spin-parity and = 1(0 + ,1 + ,2 + , 3 + , etc. ) are Forbidden in the q ¯ q ± model. The J =0 −− state is Forbidden as well. Mesons with such exotic quantum numbers may exist, but would lie outside the q ¯ q ± model (see section below on exotic mesons).
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This note was uploaded on 06/07/2011 for the course PHYS 4132 taught by Professor Kutter during the Spring '11 term at University of Florida.

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rpp2010-rev-quark-model - 14. Quark model 1 14. QUARK MODEL...

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