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we may need to expand buffer if the resulting string will not fit Second, we must be careful to handle aliasing Omitting the alias test for operator+= could create a stale pointer (ie, a pointer to memory that has already been deleted) for str+=str if a resize of buffer is required The use of operator+= is time consuming if a sequence of concatenations that cause resizing are present To avoid this problem, we sacrifice space and make the new buffer twice as large as it needs to be This logic is the same as that used in array-doubling (see Section 123) The array indexing operators are shown in Figure 225 If the index is out of bounds, a StringIndexOutOfBounds exception object is thrown This class is one of many exception classes provided in the online code, and we discuss its design at various points in Section 42 The main issue for the array indexing operator is the return type We know that operator [ I should return an entity of type charShould we use return by value, by reference, or by constant reference Immediately we eliminate return by constant reference because the returned entity is a primitive type and thus is small Thus we are down to return by reference or by value Let us consider the following method (ignore the possibility of aliasing or incompatible sizes, neither of which affects the algorithm)

the divergence of the sum is more gentle:

fromsize(

to = from; for( int i = 0 ; i < len; i++ ) to[ i ] = from[ len - 1 - i 1 ;

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36

Even after introducing similar diagrams with ZO exchange, the sum of all diagrams still diverges as s/M~. Heavy leptons cannot help us, so the only solution is to introduce a scalar particle which cancels these residual divergences through diagrams of the type

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This says that the estimated regression line passes through the point (X, y), which can be regarded as the center of the cloud of data points. This is a good property for a line that is intended to "fit" the data. The formula for ~ can be rewritten as

ostream & operator<<( ostream & out, const string i return out << strc-str( ) ;

char ch; str = in >> ch;

)-----(

' I " ;

if( !infail(

(Xi - X)2

str += ch; inget( ch ) ; while ( !in fail (

I \ \

! isspace (

if( isspace( ch ) ) / / put whitespace back on stream inputback( ch i ;

Here, h is just the Higgs particle If we had not previously introduced it to generate the heavy boson masses, we would have been forced to invent it now to guarantee renormalizability A detailed investigation of this point would reveal that the Higgs couplings are proportional to masSes, a result we are also familiar with Finally, we reiterate that Higgs particles have so far eluded experimental searches This may be because we have not used the right experimental probes or because they are too heavy to be produced by existing accelerators Alternatively, one might speculate that they do not exist as elementary fields, and the Higgs "particle" we have introduced actually corresponds to a more complex object, for example, a bound state of other particles which have yet to be incorporated in the theory.

L( Xi - X)2

return in;

char ch; str = ,

) &&

The interested student is encouraged to perform this and previous calculations explicitly; for assistance, see, for example, Llewellyn Smith (1974), Abers and Lee (1973), and Bernstein (1974) It is clear from the few examples mentioned that the various couplings must be closely related to ensure the "conspiratorial" cancellations of various divergences Any electroweak theory must therefore meet the dual requirements that (1) it reproduces the phenomenology of s 12 and 13, and (2) it has the correct relation between various couplings to ensure a desirable high-energy behavior The Weinberg-Salam model (1540) is the simplest model that achieves these ends In fact, 't Hooft has shown that for a theory to be renormalizable, it must be a Yang-Mills theory, that is, a theory with a local gauge invariance Only if we have such a high degree of symmetry can we obtain the systematic cancellations of divergences order by order 15.

while( inget ( ch str += ch; return in;

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