By Alexander I Studenikin
This quantity of court cases bargains with a wide selection of issues — either in conception and in test — in particle physics, reminiscent of electroweak thought, checks of the normal version and past, heavy quark physics, nonperturbative QCD, neutrino physics, astroparticle physics, quantum gravity results, and physics on the destiny accelerators.
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Extra resources for Frontiers of particle physics. Proceedings of the tenth Lomonosov conference on elementary particle physics
Sample text
Produces finite answers and, in some sense, as e ~ 0, J . ~ f . Due to Bohr and Rosenfeld's (1933, 1950) classical work, we know that field operators are intrinsically singular ; therefore, any regularization must destroy some physical feature of the theory . Thus , Pauli-Villars regularization destroys hermiticity and gauge invariance for non-Abelian theories; lattice regularization destroys Poincare invariance, etc. ). Because gauge and relativistic invariance are essential for QCD , we will use dimensional regularization that only destroys scale invariance.
4c) o Here we have defined N. = l_YE + log4'17. 10 In fact, all poles in dimensional regularization appear in this combination. 3) and rearrange it to read: 2:,t/itf} = CF~ij SD~(P) = i{jI-m + g2CFL(2)} _ . 4) into 2 jI-m{I - CFg BD ~(P)} + higher orders . 5a) takes into account exactly the contribution of all the diagrams of Figure 4 and that, replacing L(2) ~ Lexa ct, is the most general form for S . As we see, there are two divergences: g2 1- CF 16'17 2 (I - ~)N. 6) which multiplies the entire S, and I +3CF - g2 - 16'17 2 N.
QeD as a Field Theory q q q ... - .. ~ ( a) k, i q ,v,b q ,~ . O (b) +-@-@--+... 1'>. -@-- + .... ~ + ~ + (c ) Figure 6. The gluon propagator. 27 The part arising from a quark loop (Figure 6b) is, for each flavor f of quark rr;:;uark ;ab = • 2 -lg a bJ dDk 4-D Tr(le"+ mf)y IL(le"+ q+ mf)y" ~ij tij~i 2 D "o ( 7T) (k 2 2) [ - mf ( k + q) 2 - mf2 ] The calculation may be carried out using standard techniques. The result is exactly the same as that for the photon vacuum polarization, apart from the factor Tr tat b • The result is, with nf the total number of quark flavors : II:" quark s;ab = l)ab X - 2T g2 2 F (- gIL q + qILq l67T 2 P 2 { "3 N,nf - 4 (' Jo{) dx· x(l - P ) nf x) ~ log /=\ mJ- x(1 2 ~ - X)q2 ) .