Hadronic production of a Higgs boson in association with two jets at ...

More documents

Recommendations

Info

2.1. Unitarity 33four dimensional cuts are only sensitive to terms of the form c 0 I 0 . The missingpieces, which are of higher order in ǫ in the coefficient contribute finite pieces whenmultiplying the pole pieces of the integral. This is why they can be thought of ashaving no discontinuities in the kinematic invariants (but can still be detected byD-dimensional cuts).The separation into rational and cut-constructible pieces leads to divide andconquer strategies for methods which rely on four-dimensional cuts. Unitarity techniquescan be used to calculate the cut-constructible pieces leaving the rationalpieces to be determined by some other method. For amplitudes in N = 4 andN = 1 supersymmetric Yang-Mills (SYM) theories, no additional methods areneeded, since these amplitudes are completely determined by their four-dimensionalcuts [110,111]. This realisation has led to many calculations of amplitudes in thesetheories [110–116]. In addition to being interesting in their own right, these amplitudescan be used to construct gluonic amplitudes. If one combines one N = 4multiplet (which contains one gluon four fermions and three complex scalars), withfour N = 1 chiral multiplets (each one containing one fermion and one complexscalar) one finds thatA gluonn = A N=4n − 4A N=1n + An N=0,scalar(2.3)Here the gluon loop is represented in terms of two pieces which are cut-constructibleand one piece which contains a complex scalar. This last piece, although not cutconstructiblein four-dimensions, is simpler than the initial gluon loop. Importantly,the rational pieces can be thought of arising from diagrams which contain scalars,rather than gluons, circulating around the loop. The piece of gluon amplitudes whicharises from a fermion loop (and is proportional to the number of light flavours N F )has a similar breakdown.A gluon,N Fn = A N=1n − An N=0,scalar(2.4)So that the rational parts of pure gluonic amplitudes are always proportional to(1 − N F /N C ) (which will be useful in later chapters).The unitarity method as described above (with various techniques to determine
2.2. Quadruple cuts 34the rational part) was used to calculate several phenomenologically important processes[117–119]. The main drawback of the method being that for a given cut onewould find multiple basis integrals (for example a cut could contain box, triangle andbubble contributions and all can enter simultaneously) and the appearance of termsin the reduction of tensors which do not contain the appropriate cut propagators.In 2004 unitarity methods were reinvigorated by several developments in onshelltechniques. New methods for generating compact helicity expressions werediscovered, the BCFW recursion relations, and the MHV rules. At the same timethe idea of using multiple cuts was established as a useful technique, known asgeneralised unitarity.2.2 Quadruple cuts2.2.1 The quadruple cut methodAs discussed previously, massless one-loop amplitudes can be written in the followingbasis,A (1)n= ∑ i(c 4;i I 4,i + c 3;i I 3;i + c 2;i I 2;i ) + R n , (2.5)where I i;j is a basis integral with i propagators with a topology denoted by j (inthe above equation the summation is over the various allowed topologies given theexternal momenta). Since the basis is process independent, the calculation of oneloopamplitudes is essentially reduced to extracting the coefficients of each basisintegral as efficiently as possible. With this in mind it was proposed [120] that onecould isolate a given box coefficient by applying four (rather than two) cuts. Sinceonly the box terms in eq. (2.5) contain four propagators each four-cut should isolatean individual box,∫d 4 l4∏i=1δ(l 2 i)A (0)1 (l 1 , l 2 )A (0)2 (l 2 , l 3 )A (0)3 (l 3 , l 4 )A (0)4 (l 4 , l 1 )= c 4,{P }∫d 4 l4∏δ(l 2 i) (2.6)i=1
Page 7 and 8: Contentsvii1.4.1 Effective Lagrangi
Page 9 and 10: Contentsix4 One-loop Higgs plus fou
Page 11: ContentsxiB.2 Box Integral Function
Page 18 and 19: 1.1. The Standard Model of Particle
Page 20: 1.1. The Standard Model of Particle
Page 27 and 28: 1.2. Electroweak Symmetry Breaking
Page 33 and 34: 1.3. Higgs searches at colliders 18
Page 39 and 40: 1.4. Effective coupling between glu
Page 41 and 42: 1.4. Effective coupling between glu
Page 43 and 44: 1.5. Higgs plus two jets: Its pheno
Page 45 and 46: 1.5. Higgs plus two jets: Its pheno
Page 47: 2.1. Unitarity 32of two tree level
Page 51 and 52: 2.2. Quadruple cuts 360000000111111
Page 53 and 54: 2.2. Quadruple cuts 38We now must s
Page 55 and 56: 2.3. Forde’s Laurent expansion me
Page 61 and 62: 2.4. Spinor integration 46Here we h
Page 63 and 64: 2.4. Spinor integration 48The expli
Page 65 and 66: 2.4. Spinor integration 50with F z
Page 67 and 68: 2.5. MHV rules and BCFW recursion r
Page 69 and 70: 2.5. MHV rules and BCFW recursion r
Page 71 and 72: 2.6. The unitarity-bootstrap 56Next
Page 73 and 74: 2.6. The unitarity-bootstrap 58Figu
Page 75 and 76: 2.6. The unitarity-bootstrap 60of o
Page 77 and 78: 2.6. The unitarity-bootstrap 62rati
Page 79 and 80: 2.6. The unitarity-bootstrap 64Afte
Page 81 and 82: 2.8. Recent progress: One-loop auto
Page 83 and 84: 2.9. Summary 68cluding the recent c
Page 85 and 86: 3.2. The cut-constructible parts 70
Page 87 and 88: eplacemen3.2. The cut-constructible
Page 99 and 100:
3.2. The cut-constructible parts 84
Page 101 and 102:
Page 103 and 104:
Page 105 and 106:
Page 107 and 108:
Page 109 and 110:
Page 111 and 112:
Page 113 and 114:
3.3. The rational pieces 98m−1∑
Page 115 and 116:
3.3. The rational pieces 100+m−1
Page 117 and 118:
3.3. The rational pieces 102+R(4 +
Page 119 and 120:
3.3. The rational pieces 104The cal
Page 121 and 122:
3.4. Cross Checks and Limits 1063.4
Page 123 and 124:
3.4. Cross Checks and Limits 108The
Page 125 and 126:
3.4. Cross Checks and Limits 110The
Page 127 and 128:
3.4. Cross Checks and Limits 112−
Page 129 and 130:
3.5. Summary 114The rational terms
Page 131 and 132:
Chapter 4One-loop Higgs plus four-g
Page 133 and 134:
4.2. Cut-Constructible Contribution
Page 135 and 136:
Page 137 and 138:
Page 139 and 140:
4.3. Rational Terms 124contains two
Page 141 and 142:
4.4. Higgs plus four gluon amplitud
Page 143 and 144:
4.4. Higgs plus four gluon amplitud
Page 145 and 146:
4.6. Summary 130p µ 2 = (+0.344450
Page 147 and 148:
Chapter 5The φqqgg- NMHV amplitude
Page 149 and 150:
5.1. Introduction 134Figure 5.1: Sa
Page 151 and 152:
5.1. Introduction 136H amplitude φ
Page 153 and 154:
5.2. One-loop results 138A L 4 (φ,
Page 155 and 156:
5.2. One-loop results 140with K 1 =
Page 157 and 158:
5.2. One-loop results 142Relation f
Page 159 and 160:
5.2. One-loop results 144+ 1s 123[
Page 161 and 162:
5.4. Summary 146(φ, 1 −¯q , 2 +
Page 163 and 164:
6.2. Improvements from the semi-num
Page 165 and 166:
6.4. Tevatron results 150The W mass
Page 167 and 168:
6.4. Tevatron results 152m H [GeV]
Page 169 and 170:
6.5. LHC results 154Eq. (6.11) and
Page 171 and 172:
6.5. LHC results 156m H [GeV] 120 1
Page 173 and 174:
6.5. LHC results 158Figure 6.3: The
Page 175 and 176:
6.5. LHC results 160of describing T
Page 177 and 178:
6.5. LHC results 162Figure 6.6: p T
Page 179 and 180:
6.6. Summary 164at LO and the effec
Page 181 and 182:
6.6. Summary 166of Higgs masses, 15
Page 183 and 184:
Chapter 7. Conclusions 168one can d
Page 185 and 186:
Appendix ASpinor Helicity Formalism
Page 187 and 188:
A.1. Spinor Helicity Formalism nota
Page 189 and 190:
A.3. Pure QCD amplitudes 174Further
Page 191 and 192:
Appendix BOne-loop Basis IntegralsI
Page 193 and 194:
B.2. Box Integral Functions 178boxe
Page 195 and 196:
B.2. Box Integral Functions 180L 2
Page 197 and 198:
Bibliography 182[10] R. Feynman, Ma
Page 199 and 200:
Bibliography 184[36] M. Bahr et. al
Page 201 and 202:
Bibliography 186[63] M. Shifman, A.
Page 203 and 204:
Bibliography 188[85] R. V. Harlande
Page 205 and 206:
Bibliography 190[104] R. K. Ellis,
Page 207 and 208:
Bibliography 192[125] G. Ossola, C.
Page 209 and 210:
Bibliography 194[148] R. Boels and
Page 211 and 212:
Bibliography 196[170] Z. Bern and A
Page 213 and 214:
Bibliography 198anti-t + 2 jets at
Page 215:
Bibliography 200[214] C. Anastasiou
show all

Hadronic production of a Higgs boson in association with two jets at ...

You also want an ePaper? Increase the reach of your titles

Delete template?

Save as template?