On the Flavor Problem in Strongly Coupled Theories - THEP Mainz

More documents

Recommendations

Info

166 Chapter 4. The Asymmetry in Top Pair Production ctL ctR ˜C V uū/αs ˜C A uū/αs ˜C V d ¯ d /αs ˜C A d ¯ d /αs ˜C V tū/αs −0.46 0.11 1.00 0.035 · 10 −2 1.00 −0.070 · 10 −2 −0.009 · 10 −4 −0.47 0.50 1.19 0.081 · 10 −2 1.19 0.004 · 10 −2 −0.026 · 10 −4 −0.49 1.00 1.29 0.201 · 10 −2 1.29 −0.027 · 10 −2 0.108 · 10 −4 Table 4.1: Results for the Wilson coefficients corresponding to three different parameter points. The numbers shown correspond to the RS model with SU(2)L × U(1)Y bulk gauge symmetry and brane-localized Higgs sector. The coefficients scale as (1 TeV/MKK) 2 . Further details are given in the text. and t¯t invariant mass distribution in the SM have been computed at NLO [237] using MCFM [238], employing MSTW2008NLO PDFs along with αs(MZ) = 0.120, which corresponds to αs(mt) = 0.109 at two-loop accuracy. The given total SM errors represent the uncertainty due to the variation of the factorization scale µr = µf ∈ [mt/2, 2mt] as well as PDF errors within their 90% CL limits, after combining the two sources of error in quadrature. Notice that within errors our SM prediction for σ t¯t is in good agreement with recent theoretical calculations, that include effects of logarithmically enhanced NNLO terms [211, 239]. With all this at hand, we are now in a position to give the forward-backward asymmetry in the CM frame. Normalizing the result for σa to σs calculated at NLO, 9 we find the following expression (A t FB)RS = (4.70) � � 1 + 0.243 ˜C A uū + ˜ CV � tū − 0.26C˜ S tū + 0.034 ˜ CA 1 + 0.053 � C˜ V uū + ˜ CV � tū − 0.612C˜ S tū + 0.008 ˜ CV d ¯ d + 0.03 ˜ CV uū + 0.004 ˜ CV d ¯ d d ¯ d � �8.75 � +1.72 −1.56 % , where all coefficient functions should be evaluated at the scale mt. The central value of our SM prediction has been obtained by integrating the formulas given in [215] over the relevant phase space using (4.25), (4.27), and (4.28), weighted with MSTW2008LO PDFs with the unphysical scales fixed to mt. It is in agreement with (4.8) as well as the findings of [222]. Unlike [214], we have chosen not to include electroweak corrections to the forward-backward asymmetry in the central value of (4.70). Such effects have been found in [214, 240] to enhance the t¯t forward-backward asymmetry by around 9% to 4% depending on whether only mixed electroweak-QCD contributions or also purely electroweak corrections are included. To account for the uncertainty of our SM prediction due to electroweak effects we have added in quadrature an error of 5% to the combined scale and PDF uncertainties. In order to investigate the importance of the different contributions entering the RS predictions (4.68), (4.69) and (4.70) for the t¯t observables, we have calculated the relevant Wilson coefficients at the KK scale for three benchmark points with typical 9 Using MSTW2008 PDFs and µr = µf = mt = 173.1 GeV, we obtain in the SM the symmetric cross sections (σs)LO = 6.66 pb and (σs)NLO = 6.73 pb using MCFM. Since these results differ by only 1%, the central value of A t FB does essentially not depend on whether the LO or the NLO cross section is used to normalize (4.70).
4.5. Numerical Analysis 167 bulk mass parameters chosen from our dataset. In Table 4.1 the numerical results for the coefficient functions are presented. To keep the presentation simple, we show in the table only the values of the left- and right-handed top-quark bulk mass parameters ctL and ctR . The numerical values for the remaining bulk mass parameters and Yukawa matrices, specifying the three parameter points completely are collected in Appendix A. It should be emphasized that the magnitudes of the shown results are generic predictions in the allowed parameter space and do not reflect a specific choice of model parameters. From the numbers given in the table, we see that the ratios of magnitudes of the Wilson coefficients are given by | ˜ C A q¯q| | ˜ C V q¯q| ≈ 10−3 , | ˜ C V tū| | ˜ C V uū| ≈ 10−5 . (4.71) For what concerns the size of the corrections due to flavor-changing currents in the t channel (encoded in ˜ C V tū and ˜ C S tū), we mention that in the RS model based on an SU(2)L × U(1)Y bulk gauge group, the ratio of neutral electroweak gauge boson (Higgs-boson) to KK gluon effects is roughly 1/3 (on average 1/50). In the RS variant with extended SU(2)R symmetry and custodial protection of the ZbL ¯ bL vertex, one finds a very similar pattern. The scalar contributions are not explicitly listed but are another factor of 10 2 smaller than the ˜ C V tū coefficients. Focusing on the numerical dominant corrections arising from s channel KK gluon exchange, we see from Table 4.1 that ˜ C V uū and ˜ C A uū are comparable in size to their counterparts involving down quarks. Since the latter coefficients are suppressed in the total cross section relative to the coefficients involving up quarks by the small ratio of quark luminosities ff d ¯ d (0.04) /ffuū (0.04) ≈ 1/5 , the numerical impact of ˜ C V d ¯ d in (4.70) is negligible. In practice, we find that the relevant ratio (0.008 ˜ C V d ¯ d )/(0.053 ˜ C V uū) amounts to less than 2.3% for the considered parameter points. For the last bin of the t¯t invariant mass spectrum, the picture is similar. The quark luminosity ratio is ff d ¯ d (0.17) /ffuū (0.17) ≈ 1/15, which results in a ratio (0.02 ˜ C V d ¯ d )/(0.33 ˜ C V uū) which is a 1.0% effect for our benchmark points. It is therefore sensible to restrict our attention to the coefficients ˜ C V,A uū that render by far the largest contributions to the t¯t observables in the RS model. Note however, that this situation is significantly changed at the LHC, where the luminosities give a ratio of ff pp d ¯ d corresponding CM energy of s = √ 7 TeV, compare Figure 4.4. (0.003) /ff pp uū (0.003) ≈ 2/3 at a These results, which hold true for all new physics models which try to explain the forward backward asymmetry through s channel exchanges of new resonances can be illustrated by a combined fit to the latest measurements of the asymmetry At FB , the total inclusive cross section σt¯t and the last bin of the invariant mass spectrum, as shown in Figure 4.7. In addition to the 99%, 95% and 68% CL ellipses in the � CV uū− � CA uū plane, the best fit point is indicated by a black cross as well as the prediction of the SM, which is indicated by a black point. The dashed lines denote the region of parameter space in which significant changes to the cross section as well as to the forward backward asymmetry are expected. From Table 4.1, one can clearly see that the RS corrections are expected to be nowhere near the right size in order to explain the asymmetry.
Page 1 and 2:
On the Flavor Problem in Strongly C
Page 3 and 4:
UNIVERSITY OF MAINZ ABSTRACT THEORE
Page 5 and 6:
Contents Acknowledgements vii Prefa
Page 7:
Acknowledgements First and foremost
Page 10 and 11:
x One of the most fascinating insig
Page 12 and 13:
2 Chapter 1. Introduction: Problems
Page 14 and 15:
Page 16 and 17:
Page 18 and 19:
Page 20 and 21:
10 Chapter 1. Introduction: Problem
Page 22 and 23:
Page 24 and 25:
Page 26 and 27:
Page 28 and 29:
Page 30 and 31:
Page 32 and 33:
Page 34 and 35:
Page 36 and 37:
Page 38 and 39:
Page 40 and 41:
Page 42 and 43:
Page 44 and 45:
Page 46 and 47:
36 Chapter 2. The Randall Sundrum M
Page 48 and 49:
Page 50 and 51:
Page 52 and 53:
Page 54 and 55:
Page 56 and 57:
Page 58 and 59:
Page 60 and 61:
Page 62 and 63:
Page 64 and 65:
Page 66 and 67:
Page 68 and 69:
Page 70 and 71:
Page 72 and 73:
Page 74 and 75:
Page 76 and 77:
Page 78 and 79:
Page 80 and 81:
Page 82 and 83:
Page 84 and 85:
Page 86 and 87:
Page 88 and 89:
Page 90 and 91:
Page 92 and 93:
Page 94 and 95:
Page 96 and 97:
Page 98 and 99:
Page 100 and 101:
Page 102 and 103:
92 Chapter 3. Solving the Flavor Pr
Page 104 and 105:
Page 106 and 107:
Page 108 and 109:
Page 110 and 111:
100 Chapter 3. Solving the Flavor P
Page 112 and 113:
Page 114 and 115:
Page 116 and 117:
Page 118 and 119:
Page 120 and 121:
Page 122 and 123:
Page 124 and 125:
Page 126 and 127: 116 Chapter 3. Solving the Flavor P
Page 156 and 157: 146 Chapter 4. The Asymmetry in Top
Page 186 and 187: 176 Chapter 5. Conclusions describe
Page 188 and 189: 178 Appendix A. Generating Paramete
Page 190 and 191: 180 Appendix A. Generating Paramete
Page 192 and 193: 182 Appendix B. Neutral Meson Mixin
Page 194 and 195: 184 Appendix B. Neutral Meson Mixin
Page 197 and 198: C Input Parameters This appendix is
Page 199: Parameter Value ± Error Reference
Page 202 and 203: 192 Appendix D. Higgs Potential for
Page 204 and 205: 194 Bibliography [13] S. Dimopoulos
Page 206 and 207: 196 Bibliography [43] G. Nordström
Page 208 and 209: 198 Bibliography [72] K. S. Babu,
Page 210 and 211: 200 Bibliography [104] R. Contino a
Page 212 and 213: 202 Bibliography [133] M. Baak, M.
Page 214 and 215: 204 Bibliography [160] J. Charles,
Page 216 and 217: 206 Bibliography [185] C. Csaki, G.
Page 218 and 219: 208 Bibliography [213] E. Thomson e
Page 220: 210 Bibliography [239] V. Ahrens, A
show all

On the Flavor Problem in Strongly Coupled Theories - THEP Mainz

Create successful ePaper yourself

Delete template?

Save as template?