Now we study b-hadron spectra of the two schemes by comparing their MC results with MC NLO calculation generated by MC@NLO. Since NLO calculation has higher accu-racy, we expect a scheme with better description on inclusive Higgs production should have higher agreement with MC@NLO results. In general, the 4 flavour scheme results look more like MC NLO results of MC@NLO, illustrating that the 4 flavour scheme is more convergent to real solution than the 5 flavour approximation (Fig. 3.16 to Fig. 3.20).
In histogram of pT(b), MC NLO results of MC@NLO are obviously different to results of the 4 flavour and the 5 flavour schemes (Fig. 3.16). And in histogram of pseudo
rapid-3.4. COMPARISON OF TWO SCHEMES 13
Figure 3.4: Histogram to compare two b-quarks invariant mass, m(b1, b2), of PL LO result of Hb¯b + 0 jet by the 4 flavour scheme on MadGraph 5 and by MC@NLO, red is by MadGraph 5, green is by MC@NLO result.
Figure 3.5: Histogram to compare two b-quarks ∆φ of PL LO result of Hb¯b + 0 jet by the 4 flavour scheme on MadGraph 5 and by MC@NLO, red is by MadGraph 5, green is by MC@NLO result.
ity of b-hadron, we find results of the 4 flavour scheme and which of MC@NLO fit very well (Fig. 3.17). In ∆R(b1, b2), curve of the 4 flavour scheme is very close to which of MC@NLO (Fig. 3.18). In invariant mass spectrum of first two b-hadrons, an interesting result is that the 4 flavour scheme results fit well to MC@NLO’s results with only LO considered rather than NLO considered (Fig. 3.19), which shows that effects of some loop diagrams on invariant mass spectrum can not be ignored, so m(b1, b2) spectrum in LO + n jets and in NLO are different. In ∆φ(b1, b2) all results fit well except LO results of MC@NLO (Fig. 3.20).
More interesting problems arise from Fig. 3.16 to Fig. 3.20: the first problem is what’s the difference between the two schemes at LO + n jets that yields their different b-hadron spectra, and the second problem is that in Fig. 3.16 to Fig. 3.20, Hb¯b of MC LO
14 CHAPTER 3. SIMULATION
(a) plot of pT(b1) (b) plot of pT(b2)
Figure 3.6: Histogram of pT of b-hadrons for the 4 flavour scheme generated by MadGraph 5 with matching algorithm, normalized by total event number, red: LO, PDF using MSTW2008lo68cl nf4, green: LO, PDF using MSTW2008nlo68cl nf4, blue: LO + 0,1 jet, PDF using MSTW2008lo68cl nf4, purple: LO + 0,1 jet, PDF using MSTW2008nlo68cl nf4.
in MC@NLO and in MadGraph 5 both consider the configuration to Hb¯b + n jets, then why their results are so different?
About the first problem, we find that different results of the 4 flavour and the 5 flavour schemes mainly come from high pseudo rapidity of b-hadron (see Fig. 3.17). We show that many 4 flavour scheme and 5 flavour scheme plots look similar after cutting events with pseudo rapidity of the first and the second b-hadrons larger than 3 (in Fig.
3.21 to Fig. 3.25). We can see that b-hadron pseudo rapidity histogram of the 4, 5 flavour schemes different in high pseudo rapidity part, after cutting that part, b-hadron property of left events via two schemes is similar. We think this difference is due to some b-hadrons in the 5 flavour scheme actually come from parton shower. In the 5 flavour scheme, if in ME level H + n jets final state, every parton is not b-quark, then b-hadrons come from initial parton shower, which results in larger number of high pseudo rapidity b-hadrons. We also compare the 4, 5 flavour schemes MC results in MadGraph with MC NLO results in MC@NLO, with cuts of soft and near beam-direction b-hadrons (Fig. 3.26 to Fig.
3.30), which show that after cutting events with soft and near beam-direction b-hadrons, b-hadron spectra from using matching algorithm at LO + n jets processes are similar to NLO results.
To study the second problem, we notice that MC@NLO interface to HERWIG does
3.4. COMPARISON OF TWO SCHEMES 15
(a) η(b1) (b) η(b2)
Figure 3.7: Histogram of pseudo rapidity of b-hadrons for the 4 flavour scheme generated by MadGraph 5 with matching algorithm, normalized by total event number, red: LO, PDF using MSTW2008lo68cl nf4, green: LO, PDF using MSTW2008nlo68cl nf4, blue: LO + 0,1 jet, PDF using MSTW2008lo68cl nf4, purple: LO + 0,1 jet, PDF using MSTW2008nlo68cl nf4.
not reweight coupling constants and parton distribution functions as MadGraph does. We want to check whether the difference comes from the reweighting of matching algorithm.
So we compare:
1. PL results of the 4 flavour scheme with matching & with no matching algorithm by MadGraph to PL LO results by MC@NLO.
2. MC results of the 4 flavour scheme with matching & with no matching algorithm by MadGraph to MC LO results by MC@NLO.
As shown in Fig. 3.31 and Fig. 3.32 in PL and MC level, if we turn off matching al-gorithm, b-hadron (or b-quark) pT spectra of MadGraph become harder and fix well with b-hadron (or b-quark) pT spectra of MC@NLO, both for MC LO and for PL LO. This is because, when we turn on the matching algorithm in MadGraph, we turn on the reweight-ing of couplreweight-ing constants and PDFs at the same time, which increases the probability of radiating low pT particles via higher strong coupling at low energy scale. However, even if we turn off matching algorithm in MC LO level, other b-hadron spectra in MadGraph such as pseudo rapidity are not similar to MC LO results of MC@NLO (in Fig. 3.33 and Fig. 3.34). So we can conclude that the difference of b-hadron pT spectra of MC LO in MadGraph and in MC@NLO are dominated by effect of reweighting, and cause of
differ-16 CHAPTER 3. SIMULATION
Figure 3.8: Histogram of ∆R(b1, b2) for the 4 flavour scheme generated by MadGraph 5 with matching algorithm, normalized by total event number, red: LO, PDF using MSTW2008lo68cl nf4, green: LO, PDF using MSTW2008nlo68cl nf4, blue: LO + 0,1 jet, PDF using MSTW2008lo68cl nf4, purple: LO + 0,1 jet, PDF using MSTW2008nlo68cl nf4.
ence of pseudo rapidity and ∆R b-hadron spectrum (in Fig. 3.33 and Fig. 3.34) is perhaps that PYTHIA and HERWIG use different way to generate parton shower (PYTHIA: pT order parton shower, HERWIG: angular order parton shower).
3.4. COMPARISON OF TWO SCHEMES 17
Figure 3.9: Histogram of invariant mass of two b-hadrons, m(b1, b2), for the 4 flavour scheme gener-ated by MadGraph 5 with matching algorithm, normalized by total event number, red: LO, PDF using MSTW2008lo68cl nf4, green: LO, PDF using MSTW2008nlo68cl nf4, blue: LO + 0,1 jet, PDF using MSTW2008lo68cl nf4, purple: LO + 0,1 jet, PDF using MSTW2008nlo68cl nf4.
Figure 3.10: Histogram of ∆φ of two b-hadrons, Dphi(b1,b2), for the 4 flavour scheme generated by MadGraph 5 with matching algorithm, normalized by total event number, red: LO, PDF using MSTW2008lo68cl nf4, green: LO, PDF using MSTW2008nlo68cl nf4, blue: LO + 0,1 jet, PDF using MSTW2008lo68cl nf4, purple: LO + 0,1 jet, PDF using MSTW2008nlo68cl nf4.
18 CHAPTER 3. SIMULATION
(a) plot of pT(b1) (b) plot of pT(b2)
Figure 3.11: Histogram of pT of b-hadrons for the 5 flavour scheme generated by MadGraph 5 with match-ing algorithm, normalized by total event number, red: LO, PDF usmatch-ing MSTW2008lo68cl, green: LO, PDF using MSTW2008nlo68cl, blue: LO + 0,1 jet, PDF using MSTW2008lo68cl, purple: LO + 0,1 jet, PDF using MSTW2008nlo68cl.
(a) η(b1) (b) η(b2)
Figure 3.12: Histogram of pseudo rapidity of b-hadrons for the 5 flavour scheme generated by MadGraph 5 with matching algorithm, normalized by total event number, red: LO, PDF using MSTW2008lo68cl, green:
LO, PDF using MSTW2008nlo68cl, blue: LO + 0,1 jet, PDF using MSTW2008lo68cl, purple: LO + 0,1 jet, PDF using MSTW2008nlo68cl.
3.4. COMPARISON OF TWO SCHEMES 19
Figure 3.13: Histogram of ∆R(b1, b2) for the 5 flavour scheme generated by MadGraph 5 with matching algorithm, normalized by total event number, red: LO, PDF using MSTW2008lo68cl nf4, green: LO, PDF using MSTW2008nlo68cl nf4, blue: LO + 0,1 jet, PDF using MSTW2008lo68cl nf4, purple: LO + 0,1 jet, PDF using MSTW2008nlo68cl nf4.
Figure 3.14: Histogram of invariant mass of two b-hadrons, m(b1, b2), for the 5 flavour scheme gen-erated by MadGraph 5 with matching algorithm, normalized by total event number, red: LO, PDF us-ing MSTW2008lo68cl, green: LO, PDF usus-ing MSTW2008nlo68cl, blue: LO + 0,1 jet, PDF usus-ing MSTW2008lo68cl, purple: LO + 0,1 jet, PDF using MSTW2008nlo68cl.
20 CHAPTER 3. SIMULATION
Figure 3.15: Histogram of ∆φ of two b-hadrons, Dphi(b1,b2), for the 5 flavour scheme gener-ated by MadGraph 5 with matching algorithm, normalized by total event number, red: LO, PDF us-ing MSTW2008lo68cl, green: LO, PDF usus-ing MSTW2008nlo68cl, blue: LO + 0,1 jet, PDF usus-ing MSTW2008lo68cl, purple: LO + 0,1 jet, PDF using MSTW2008nlo68cl.
(a) plot of pT(b1) (b) plot of pT(b2)
Figure 3.16: Histogram of pT of b-hadron by the 4 flavour scheme, the 5 flavour scheme by MadGraph 5 with matching algorithm and by MC@NLO MC LO & MC NLO, red is the 4 flavour scheme, PDF using MSTW2008nlo68cl nf4, LO + 0,1 jet, green is the 5 flavour scheme, PDF using MSTW2008nlo68cl, LO + 0,1 jet, blue is by MC@NLO MC LO, purple is by MC@NLO MC NLO.
3.4. COMPARISON OF TWO SCHEMES 21
(a) η(b1) (b) η(b2)
Figure 3.17: Histogram of pseudo rapidity of b-hadron by the 4 flavour scheme, the 5 flavour scheme by MadGraph 5 with matching algorithm and by MC@NLO MC LO & MC NLO, red is the 4 flavour scheme, PDF using MSTW2008nlo68cl nf4, LO + 0,1 jet, green is the 5 flavour scheme, PDF using MSTW2008nlo68cl, LO + 0,1 jet, blue is by MC@NLO MC LO, purple is by MC@NLO MC NLO.
Figure 3.18: Histogram of ∆R(b1, b2) by the 4 flavour scheme, the 5 flavour scheme by MadGraph 5 with matching algorithm and by MC@NLO MC LO & MC NLO, red is the 4 flavour scheme, PDF using MSTW2008nlo68cl nf4, LO + 0,1 jet, green is the 5 flavour scheme, PDF using MSTW2008nlo68cl, LO + 0,1 jet, blue is by MC@NLO MC LO, purple is by MC@NLO MC NLO.
22 CHAPTER 3. SIMULATION
Figure 3.19: Histogram of invariant mass, m(b1, b2), by the 4 flavour scheme, the 5 flavour scheme by MadGraph 5 with matching algorithm and by MC@NLO MC LO & MC NLO, red is the 4 flavour scheme, PDF using MSTW2008nlo68cl nf4, LO + 0,1 jet, green is the 5 flavour scheme, PDF using MSTW2008nlo68cl, LO + 0,1 jet, blue is by MC@NLO MC LO, purple is by MC@NLO MC NLO.
3.4. COMPARISON OF TWO SCHEMES 23
Figure 3.20: Histogram of ∆φ of two b-hadrons, Dphi(b1,b2), by the 4 flavour scheme, the 5 flavour scheme by MadGraph 5 with matching algorithm and by MC@NLO MC LO & MC NLO, red is the 4 flavour scheme, PDF using MSTW2008nlo68cl nf4, LO + 0,1 jet, green is the 5 flavour scheme, PDF using MSTW2008nlo68cl, LO + 0,1 jet, blue is by MC@NLO MC LO, purple is by MC@NLO MC NLO.
(a) plot of pT(b1) (b) plot of pT(b2)
Figure 3.21: Histogram of comparing pT of b-hadron of the 4, 5 flavour schemes by MadGraph 5 with matching algorithm, cutting |η(b1)| > 3 and |η(b2)| > 3 events, red is the 4 flavour result, green is the 5 flavour result.
24 CHAPTER 3. SIMULATION
(a) plot of η(b1) (b) plot of η(b2)
Figure 3.22: Histogram of comparing pseudo rapidity of b-hadron of the 4, 5 flavour schemes by MadGraph 5 with matching algorithm, cutting |η(b1)| > 3 and |η(b2)| > 3 events, red is the 4 flavour result, green is the 5 flavour result.
Figure 3.23: Histogram of ∆R(b1, b2) by the 4, 5 flavour schemes by MadGraph 5 with matching algo-rithm, cutting |η(b1)| > 3 and |η(b2)| > 3 events, red is the 4 flavour result, green is the 5 flavour result.
3.4. COMPARISON OF TWO SCHEMES 25
Figure 3.24: Histogram of invariant mass, m(b1, b2), by the 4, 5 flavour schemes by MadGraph 5 with matching algorithm, cutting |η(b1)| > 3 and |η(b2)| > 3 events, red is the 4 flavour result, green is the 5 flavour result.
Figure 3.25: Histogram of ∆φ of two b-hadrons, Dphi(b1,b2), by the 4, 5 flavour schemes by MadGraph 5 with matching algorithm, cutting |η(b1)| > 3 and |η(b2)| > 3 events, red is the 4 flavour result, green is the 5 flavour result.
26 CHAPTER 3. SIMULATION
(a) plot of pT(b1) (b) plot of pT(b2)
Figure 3.26: Histogram of comparing pT of b-hadron of the 4, 5 flavour schemes by MadGraph 5 with matching algorithm to MC NLO result by MC@NLO, cutting |η(b1)| > 3, |η(b2)| > 3, pT(b1) < 10 GeV and pT(b2) < 10 GeV events, red is the 4 flavour result, green is the 5 flavour result, blue is MC NLO result by MC@NLO.
(a) plot of η(b1) (b) plot of η(b2)
Figure 3.27: Histogram of comparing pseudo rapidity of b-hadron of the 4, 5 flavour schemes by MadGraph 5 with matching algorithm to MC NLO result by MC@NLO, cutting |η(b1)| > 3, |η(b2)| > 3, pT(b1) < 10 GeV and pT(b2) < 10 GeV events, red is the 4 flavour result, green is the 5 flavour result, blue is MC NLO result by MC@NLO.
3.4. COMPARISON OF TWO SCHEMES 27
Figure 3.28: Histogram of ∆R(b1, b2) by the 4, 5 flavour schemes by MadGraph 5 with matching algorithm to MC NLO result by MC@NLO, cutting |η(b1)| > 3, |η(b2)| > 3, pT(b1) < 10 GeV and pT(b2) < 10 GeV events, red is the 4 flavour result, green is the 5 flavour result, blue is MC NLO result by MC@NLO.
Figure 3.29: Histogram of invariant mass, m(b1, b2), by the 4, 5 flavour scheme by MadGraph 5 with matching algorithm to MC NLO result by MC@NLO, cutting |η(b1)| > 3, |η(b2)| > 3, pT(b1) < 10 GeV and pT(b2) < 10 GeV events, red is the 4 flavour result, green is the 5 flavour result, blue is MC NLO result by MC@NLO.
28 CHAPTER 3. SIMULATION
Figure 3.30: Histogram of ∆φ of two b-hadrons, Dphi(b1,b2), by the 4, 5 flavour schemes by MadGraph 5 with matching algorithm to MC NLO result by MC@NLO, cutting |η(b1)| > 3, |η(b2)| > 3, pT(b1) < 10 GeV and pT(b2) < 10 GeV events, red is the 4 flavour result, green is by the 5 flavour result, blue is MC NLO result by MC@NLO.
(a) plot of pT(b1) (b) plot of pT(b2)
Figure 3.31: Histogram of comparing pT of b-quark of the 4 flavour scheme (Hb¯b) PL LO by MadGraph 5 with pT of b-quark by PL LO of MC@NLO, red is the PL in MadGraph with matching turn off, green is the PL in MadGraph with matching turn on, blue is PL LO of MC@NLO.
3.4. COMPARISON OF TWO SCHEMES 29
(a) plot of pT(b1) (b) plot of pT(b2)
Figure 3.32: Histogram of comparing pT of b-hadron of the 4 flavour scheme (Hb¯b) MC LO level by MadGraph 5 with pT of b-hadron by LO of MC@NLO, red is the MC in MadGraph with matching turn off, green is the MC in MadGraph with matching turn on, blue is MC LO of MC@NLO.
(a) plot of η(b1) (b) plot of η(b2)
Figure 3.33: Histogram of pseudo rapidity of b-hadron of the 4 flavour scheme (Hb¯b) MC LO by MadGraph 5 with pseudo rapidity of b-hadron by MC LO of MC@NLO, red is the MC in MadGraph with matching turn off, green is the MC in MadGraph with matching turn on, blue is MC LO of MC@NLO.
30 CHAPTER 3. SIMULATION
Figure 3.34: Histogram of comparing ∆R(b1, b2) of b-hadron of the 4 flavour scheme (Hb¯b) MC LO by MadGraph 5 with ∆R(b1, b2) of b-hadron by MC LO of MC@NLO, red is the MC in MadGraph with matching turn off, green is the MC in MadGraph with matching turn on, blue is MC LO of MC@NLO.
Chapter 4 Conclusion
In conclusion, we merge parton shower approach and matrix element method by interfac-ing MadGraph 5 to PYTHIA 6 [24] to study the comparison of the two schemes describinterfac-ing inclusive Higgs production associated with heavy quark (bottom quark) pairs and find that the 4 flavour scheme behaves better than the 5 flavour scheme, since spectra of b-hadron in LO + n jets of the 4 flavour scheme is closer to MC@NLO result (including loop level and radiation level) than those of the 5 flavour scheme. Besides, we find the difference between two schemes is mainly on number of small angle (near the beam direction) b-hadrons. Thanks to parton shower, there are more b-hadrons near the beam direction in the 5 flavour scheme than in the 4 flavour scheme in inclusive Hb¯b production process.
Our result improves our realization of the 4, 5 flavour schemes on Higgs production pro-cess and may help the search for some Beyond the Standard Models (BSMs) that couple strongly to the Higgs boson.
32 CHAPTER 4. CONCLUSION
Bibliography
[1] K. Agashe, H. Davoudiasl, S. Gopalakrishna, T. Han, G.-Y. Huang, et al., Phys. Rev.
D76, 115015 (2007), arXiv:0709.0007 [hep-ph] .
[2] J. Alwall, P. Demin, S. de Visscher, R. Frederix, M. Herquet, et al., JHEP 0709, 028 (2007), arXiv:0706.2334 [hep-ph] .
[3] M. Aivazis, J. C. Collins, F. I. Olness, and W.-K. Tung, Phys. Rev. D50, 3102 (1994), arXiv:hep-ph/9312319 [hep-ph] .
[4] J. C. Collins, Phys. Rev. D58, 094002 (1998), arXiv:hep-ph/9806259 [hep-ph] . [5] G. Altarelli and G. Parisi, Nucl. Phys. B126, 298 (1977).
[6] Y. L. Dokshitzer, Sov. Phys. JETP 46, 641 (1977).
[7] V. Gribov and L. Lipatov, Sov. J. Nucl.Phys. 15, 438 (1972).
[8] V. Sudakov, Sov. Phys. JETP 3, 65 (1956).
[9] G. Marchesini and B. Webber, Nucl. Phys. B238, 1 (1984).
[10] T. Sjostrand and P. Z. Skands, Eur. Phys. J. C39, 129 (2005), arXiv:hep-ph/0408302 [hep-ph] .
[11] B. Andersson, G. Gustafson, G. Ingelman, and T. Sjostrand, Phys. Rept. 97, 31 (1983).
[12] B. Webber, Nucl. Phys. B238, 492 (1984).
[13] S. Catani, Y. L. Dokshitzer, M. Seymour, and B. Webber, Nucl. Phys. B406, 187 (1993).
34 BIBLIOGRAPHY [14] S. Catani, F. Krauss, R. Kuhn, and B. Webber, JHEP 0111, 063 (2001),
arXiv:hep-ph/0109231 [hep-ph] .
[15] F. Krauss, JHEP 0208, 015 (2002), arXiv:hep-ph/0205283 [hep-ph] . [16] L. Lonnblad, JHEP 0205, 046 (2002), arXiv:hep-ph/0112284 [hep-ph] .
[17] M. L. Mangano, “Merging multijet matrix elements and shower evolution in hadronic collisions.” http://cern.ch/˜mlm/talks/lund-alpgen.pdf (2004).
[18] M. L. Mangano, M. Moretti, F. Piccinini, and M. Treccani, JHEP 0701, 013 (2007), arXiv:hep-ph/0611129 [hep-ph] .
[19] S. Hoeche, F. Krauss, N. Lavesson, L. Lonnblad, M. Mangano, et al., (2006), arXiv:hep-ph/0602031 [hep-ph] .
[20] T. Stelzer and W. Long, Comput. Phys. Commun. 81, 357 (1994), arXiv:hep-ph/9401258 [hep-ph] .
[21] F. Maltoni and T. Stelzer, JHEP 0302, 027 (2003), arXiv:hep-ph/0208156 [hep-ph] . [22] T. Gleisberg, S. Hoeche, F. Krauss, A. Schalicke, S. Schumann, et al., JHEP 0402,
056 (2004), arXiv:hep-ph/0311263 [hep-ph] .
[23] J. Alwall, S. Hoche, F. Krauss, N. Lavesson, L. Lonnblad, et al., Eur. Phys. J. C53, 473 (2008), arXiv:0706.2569 [hep-ph] .
[24] T. Sjostrand, S. Mrenna, and P. Z. Skands, JHEP 0605, 026 (2006), arXiv:hep-ph/0603175 [hep-ph] .
[25] S. Frixione and B. R. Webber, JHEP 0206, 029 (2002), arXiv:hep-ph/0204244 [hep-ph] .
[26] G. Corcella, I. Knowles, G. Marchesini, S. Moretti, K. Odagiri, et al., JHEP 0101, 010 (2001), arXiv:hep-ph/0011363 [hep-ph] .
[27] A. Martin, W. Stirling, R. Thorne, and G. Watt, Eur. Phys. J. C63, 189 (2009), arXiv:0901.0002 [hep-ph] .
BIBLIOGRAPHY 35 [28] A. Martin, W. Stirling, R. Thorne, and G. Watt, Eur. Phys. J. C64, 653 (2009),
arXiv:0905.3531 [hep-ph] .
[29] A. Martin, W. Stirling, R. Thorne, and G. Watt, Eur. Phys. J. C70, 51 (2010), arXiv:1007.2624 [hep-ph] .