Hidden analytic relations for two-loop Higgs amplitudes in QCD

doi:10.1088/1572-9494/ab7ed8

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Communications in Theoretical Physics ›› 2020, Vol. 72 ›› Issue (6): 065201. doi: 10.1088/1572-9494/ab7ed8

• Particle Physics and Quantum Field Theory • Previous Articles Next Articles

Hidden analytic relations for two-loop Higgs amplitudes in QCD

Qingjun Jin^1,^2,(),Gang Yang^1,^3,()

¹CAS Key Laboratory of Theoretical Physics, Institute of Theoretical Physics, Chinese Academy of Sciences, Beijing 100190, China
²Graduate School of China Academy of Engineering Physics, No. 10 Xibeiwang East Road, Haidian District, Beijing, 100193, China
³School of Physical Sciences, University of Chinese Academy of Sciences, No. 19A Yuquan Road, Beijing 100049, China

Received: 2020-02-15 Revised: 2020-03-09 Accepted: 2020-03-09 Published: 2020-06-01

Abstract

Abstract:

We compute the Higgs plus two-quark and one-gluon amplitudes ($H\to q\bar{q}g$) and Higgs plus three-gluon amplitudes ($H\to 3g$) in the Higgs effective theory with a general class of operators. By changing the quadratic Casimir C_F to C_A, the maximally transcendental parts of the $H\to q\bar{q}g$ amplitudes turn out to be equivalent to that of the $H\to 3g$ amplitudes, which also coincide with the counterparts in ${ \mathcal N }=4$ SYM. This generalizes the so-called maximal transcendentality principle to the Higgs amplitudes with external quark states, thus the full QCD theory. We further verify that the correspondence applies also to two-loop form factors of more general operators, in both QCD and scalar-YM theory. Another interesting relation is also observed between the planar $H\to q\bar{q}g$ amplitudes and the minimal density form factors in ${ \mathcal N }=4$ SYM.

Key words: scattering amplitudes, form factors, quantum chromodynamics, Higgs effective field theory

Qingjun Jin, Gang Yang, Commun. Theor. Phys. 72 (2020) 065201.

	Length-2			Length-3		Higher length
Operators
Examples	$\mathrm{tr}({F}^{2})$	$\bar{\psi }\psi $	$\bar{\phi }\phi $	$\begin{array}{c}\mathrm{tr}({F}^{3}),\\ \mathrm{tr}({F}_{\mu }^{\,\nu }{D}_{\sigma }{F}_{\nu }^{\,\rho }{D}^{\sigma }{F}_{\rho }^{\,\mu })\end{array}$	$\begin{array}{c}{F}_{\mu \nu }{D}^{\mu }(\bar{\psi }{\gamma }^{\nu }\psi ),\\ {F}_{\mu \nu }(\bar{\psi }{\gamma }^{\mu \nu }\psi )\end{array}$	$\mathrm{tr}({F}^{L}),L\geqslant 4$	$\bar{\psi }({F}^{L})\psi ,L\geqslant 2$
External Partons	$(g,g,g),(\bar{\psi },\psi ,g)$	$(\bar{\psi },\psi ,g)$	$(\bar{\phi },\phi ,g)$	$(g,g,g)$	$(\bar{\psi },g,\psi )$	$({g}_{1},\ldots ,{g}_{L})$	$(\bar{\psi },{g}_{1},\ldots ,{g}_{L},\psi )$
$\begin{array}{c}{\rm{Max.}}\,{\rm{Trans.}}\\ {\rm{Remainder}}\\ ({\rm{with}}\ {C}_{F}\to {C}_{A})\end{array}$	${R}_{{\rm{L}}2;4}(u,v,w)$			${R}_{\mathrm{len}-3;4}(u,v,w)$		${\sum }_{i}{{ \mathcal R }}_{{\rm{density}};4}^{(2)}({u}_{i},{v}_{i},{w}_{i})$

1	Parke S J Taylor T R 1986 Phys. Rev. Lett. 56 2459 doi: 10.1103/PhysRevLett.56.2459
2	Del Duca V Duhr C Smirnov V A 2010 J. High Energy Phys. 201084 doi: 10.1007/JHEP05(2010)084
3	Goncharov A B Spradlin M Vergu C Volovich A 2010 Phys. Rev. Lett. 105151605 doi: 10.1103/PhysRevLett.105.151605
4	Gehrmann T Henn J M Lo Presti N A 2016 Phys. Rev. Lett. 116062001 doi: 10.1103/PhysRevLett.116.062001
	Gehrmann T Henn J M Lo Presti N A 2016 Phys. Rev. Lett. 116189903(erratum) doi: 10.1103/PhysRevLett.116.062001
5	Dunbar D C Jehu G R Perkins W B 2016 Phys. Rev. Lett. 117061602 doi: 10.1103/PhysRevLett.117.061602
6	Dunbar D C Godwin J H Jehu G R Perkins W B 2017 Phys. Rev. D 96116013 doi: 10.1103/PhysRevD.96.116013
7	Badger S Brønnum-Hansen C Hartanto H B Peraro T 2019 J. High Energy Phys. 2019186 doi: 10.1007/JHEP01(2019)186
8	Abreu S Dormans J Febres Cordero F Ita H Page B 2019 Phys. Rev. Lett. 122082002 doi: 10.1103/PhysRevLett.122.082002
9	Abreu S Dormans J Febres Cordero F Ita H Page B Sotnikov V 2019 JHEP 2019 84 doi: 10.1007/JHEP05(2019)084
10	Wilczek F 1977 Phys. Rev. Lett. 39 1304 doi: 10.1103/PhysRevLett.39.1304
11	Shifman M A Vainshtein A I Voloshin M B Zakharov V I 1979 Sov. J. Nucl. Phys. 30 711
	Shifman M A Vainshtein A I Voloshin M B Zakharov V I 1979 Yad. Fiz. 30 1368
12	Dawson S 1991 Nucl. Phys. B 359 283 doi: 10.1016/0550-3213(91)90061-2
13	Djouadi A Spira M Zerwas P M 1991 Phys. Lett. B 264 440 doi: 10.1016/0370-2693(91)90375-Z
14	Kniehl B A Spira M 1995 Z. Phys. C 69 77 doi: 10.1007/s002880050007
15	Chetyrkin K G Kniehl B A Steinhauser M 1997 Phys. Rev. Lett. 79 2184 doi: 10.1103/PhysRevLett.79.2184
16	Chetyrkin K G Kniehl B A Steinhauser M 1998 Nucl. Phys. B 510 61
17	Boughezal R Caola F Melnikov K Petriello F Schulze M 2013 J. High Energy Phys. 201372 doi: 10.1007/JHEP06(2013)072
18	Chen X Gehrmann T Glover E W N Jaquier M 2015 Phys. Lett. B 740 147 doi: 10.1016/j.physletb.2014.11.021
19	Boughezal R Caola F Melnikov K Petriello F Schulze M 2015 Phys. Rev. Lett. 115082003 doi: 10.1103/PhysRevLett.115.082003
20	Boughezal R Focke C Giele W Liu X Petriello F 2015 Phys. Lett. B 748 5 doi: 10.1016/j.physletb.2015.06.055
21	Anastasiou C Duhr C Dulat F Furlan E Gehrmann T Herzog F Lazopoulos A Mistlberger B 2016 J. High Energy Phys. 201658 doi: 10.1007/JHEP05(2016)058
22	Harlander R V Liebler S Mantler H 2017 Comput. Phys. Commun. 212 239 doi: 10.1016/j.cpc.2016.10.015
23	Anastasiou C Duhr C Dulat F Furlan E Gehrmann T Herzog F Lazopoulos A Mistlberger B 2016 J. High Energy Phys. 201637 doi: 10.1007/JHEP09(2016)037
24	Chen X Cruz-Martinez J Gehrmann T Glover E W N Jaquier M 2016 J. High Energy Phys. 201666 doi: 10.1007/JHEP10(2016)066
25	Lindert J M Kudashkin K Melnikov K Wever C 2018 Phys. Lett. B 782 210214 doi: 10.1016/j.physletb.2018.05.009
26	Jones S P Kerner M Luisoni G 2018 Phys. Rev. Lett. 120162001 doi: 10.1103/PhysRevLett.120.162001
27	Neumann T 2018 J. Phys. Comm. 2095017 doi: 10.1088/2399-6528/aadfbf
28	Kotikov A V Lipatov L N 2003 Nucl. Phys. B 661 19 doi: 10.1016/S0550-3213(03)00264-5
	Kotikov A V Lipatov L N 2004 Nucl. Phys. B 685 405(erratum) doi: 10.1016/S0550-3213(03)00264-5
29	Kotikov A Lipatov L Onishchenko A Velizhanin V 2004 Phys. Lett. B 595 521 doi: 10.1016/j.physletb.2004.05.078
30	Moch S Vermaseren J A M Vogt A 2004 Nucl. Phys. B 688 101 doi: 10.1016/j.nuclphysb.2004.03.030
31	Brandhuber A Travaglini G Yang G 2012 J. High Energy Phys. 201282 doi: 10.1007/JHEP05(2012)082
32	Gehrmann T Jaquier M Glover E Koukoutsakis A 2012 J. High Energy Phys. 201256 doi: 10.1007/JHEP02(2012)056
33	Jin Q Yang G 2018 Phys. Rev. Lett. 121101603 doi: 10.1103/PhysRevLett.121.101603
34	Brandhuber A Kostacinska M Penante B Travaglini G 2017 Phys. Rev. Lett. 119161601 doi: 10.1103/PhysRevLett.119.161601
35	Brandhuber A Kostacinska M Penante B Travaglini G 2018 J. High Energy Phys. 201876 doi: 10.1007/JHEP12(2018)076
36	Brandhuber A Kostacinska M Penante B Travaglini G 2018 J. High Energy Phys. 201877 doi: 10.1007/JHEP12(2018)077
37	Li Y von Manteuffel A Schabinger R M Zhu H X 2015 Phys. Rev. D 91036008 doi: 10.1103/PhysRevD.91.036008
38	Li Y Zhu H X 2017 Phys. Rev. Lett. 118022004 doi: 10.1103/PhysRevLett.118.022004
39	Dixon L J 2018 J. High Energy Phys. 201875 doi: 10.1007/JHEP01(2018)075
40	Brandhuber A Penante B Travaglini G Wen C 2014 J. High Energy Phys. 2014100 doi: 10.1007/JHEP08(2014)100
41	Loebbert F Nandan D Sieg C Wilhelm M Yang G 2015 J. High Energy Phys. 201512 doi: 10.1007/JHEP10(2015)012
42	Brandhuber A Kostacinska M Penante B Travaglini G Young D 2016 J. High Energy Phys. 2016134 doi: 10.1007/JHEP08(2016)134
43	Loebbert F Sieg C Wilhelm M Yang G 2016 J. High Energy Phys. 201690 doi: 10.1007/JHEP12(2016)090
44	Buchmuller W Wyler D 1986 Nucl. Phys. B 268 621 doi: 10.1016/0550-3213(86)90262-2
45	Gracey J A 2002 Nucl. Phys. B 634 192 doi: 10.1016/S0550-3213(02)00334-6
	Gracey J A 2004 Nucl. Phys. B 696 295(erratum) doi: 10.1016/S0550-3213(02)00334-6
46	Neill D 2009arXiv:0908.1573 [hep-ph]
47	Harlander R V Neumann T 2013 Phys. Rev. D 88074015 doi: 10.1103/PhysRevD.88.074015
48	Dawson S Lewis I M Zeng M 2014 Phys. Rev. D 90093007 doi: 10.1103/PhysRevD.90.093007
49	Bern Z Dixon L J Dunbar D C Kosower D A 1994 Nucl. Phys. B 425 217 doi: 10.1016/0550-3213(94)90179-1
50	Bern Z Dixon L J Dunbar D C Kosower D A 1995 Nucl. Phys. B 435 59 doi: 10.1016/0550-3213(94)00488-Z
51	Britto R Cachazo F Feng B 2005 Nucl. Phys. B 725 275 doi: 10.1016/j.nuclphysb.2005.07.014
52	Chetyrkin K Tkachov F 1981 Nucl. Phys. B 192 159 doi: 10.1016/0550-3213(81)90199-1
53	Tkachov F 1981 Phys. Lett. B 100 65 doi: 10.1016/0370-2693(81)90288-4
54	Hahn T 2001 Comput. Phys. Commun. 140 418 doi: 10.1016/S0010-4655(01)00290-9
55	Boels R H Luo H 2018 J. High Energy Phys. 563 doi: 10.1007/JHEP05(2018)063
56	Boels R H Jin Q Luo H 2018arXiv:1802.06761 [hep-ph]
57	Smirnov A V 2015 Comput. Phys. Commun. 189 182 doi: 10.1016/j.cpc.2014.11.024
58	Lee R N 2014 J. Phys.: Conf. Ser. 523012059 doi: 10.1088/1742-6596/523/1/012059
59	von Manteuffel A Studerus C 2012arXiv:1201.4330 [hep-ph]
60	Maierhoefer P Usovitsch J Uwer P 2018 Comput. Phys. Commun. 230 99112 doi: 10.1016/j.cpc.2018.04.012
61	Gehrmann T Remiddi E 2001 Nucl. Phys. B 601 248 doi: 10.1016/S0550-3213(01)00057-8
62	Gehrmann T Remiddi E 2001 Nucl. Phys. B 601 287 doi: 10.1016/S0550-3213(01)00074-8
63	Gehrmann T Remiddi E 2002 Comput. Phys. Commun. 144 200 doi: 10.1016/S0010-4655(02)00139-X
64	Bardeen W A Buras A J Duke D W Muta T 1978 Phys. Rev. D 18 3998 doi: 10.1103/PhysRevD.18.3998
65	Catani S 1998 Phys. Lett. B 427 161 doi: 10.1016/S0370-2693(98)00332-3
66	Banerjee P Dhani P K Mahakhud M Ravindran V Seth S 2017 J. High Energy Phys. 201785 doi: 10.1007/JHEP05(2017)085
67	Bern Z Dixon L J Smirnov V A 2005 Phys. Rev. D 72085001 doi: 10.1103/PhysRevD.72.085001
68	Duhr C 2012 J. High Energy Phys. 201243 doi: 10.1007/JHEP08(2012)043
69	Banerjee P Dhani P K Ravindran V 2017 J. High Energy Phys. 201767 doi: 10.1007/JHEP10(2017)067
70	Dixon L J Sofianatos Y 2009 J. High Energy Phys. 200958 doi: 10.1088/1126-6708/2009/08/058
71	Badger S Nigel Glover E W Mastrolia P Williams C 2010 J. High Energy Phys. 201036 doi: 10.1007/JHEP01(2010)036
72	Badger S Campbell J M Ellis R K Williams C 2009 J. High Energy Phys. 2009 35 doi: 10.1088/1126-6708/2009/12/035

[1]	Zhong-Yi Li,Ju-Jun Xie. Electromagnetic form factors of Σ⁺ and Σ⁻ in the vector-meson dominance model [J]. Commun. Theor. Phys. 73 (2021) 55201.
[2]	Rui-Cheng Li, Xin-Heng Guo. Chiral Extrapolation of Lattice Data of ∧_b → ∧_c Form Factors [J]. Commun. Theor. Phys. 71 (2019) 175.
[3]	Yue-Liang Wu, Rui Zhang. Gravity and Spin Forces in Gravitational Quantum Field Theory [J]. Commun. Theor. Phys. 70 (2018) 161.
[4]	Ali H. Taqi, R. A. Radhi, Adil M. Hussein. Electroexcitation of Low-Lying Particle-Hole RPA States of ¹⁶O with WBP Interaction [J]. Commun. Theor. Phys. 62 (2014) 839.
[5]	LIANG Cui-Ying, DONG Yu-Bing, LIANG Wei-Hong. A Discussion of Deuteron Transverse Charge Densities [J]. Commun. Theor. Phys. 62 (2014) 383.
[6]	ZENG Dai-Min, FANG Zhen-Yun . B_s→f₀(980) Transition Form Factors Within the k_T Factorization Approach [J]. Commun. Theor. Phys. 59 (2013) 457.
[7]	B. Rezaei, G.R. Boroun. Longitudinal Structure Function F_L from Charm Structure Function F₂^c [J]. Commun. Theor. Phys. 59 (2013) 462.
[8]	Stanley J. Brodsky, CAO Fu-Guang, Guy F. de Téramond . AdS/QCD and Applications of Light-Front Holography [J]. Commun. Theor. Phys. 57 (2012) 641.
[9]	Adnan Bashir, CHANG Lei, Ian C. Cloet, Bruno El-Bennich, LIU Yu-Xin, Craig D. Roberts, Peter C. Tandy. Collective Perspective on Advances in Dyson-Schwinger Equation QCD [J]. Commun. Theor. Phys. 58 (2012) 79.
[10]	WANG Hong-Min and ZHANG Ben-Ai. A Diquark-Quark Model with Its Use in Nucleon Form Factors [J]. Commun. Theor. Phys. 44 (2005) 707.
[11]	WANG Hong-Min and ZHANG Ben-Ai. Local Quark-Hadron Duality and Magnetic Form Factors of Bound Proton [J]. Commun. Theor. Phys. 44 (2005) 326.
[12]	WANG Hong-Min and ZHANG Ben-Ai. Contribution of Quark Structure Term in Nucleon Electric and Magnetic Form Factors [J]. Commun. Theor. Phys. 42 (2004) 735.
[13]	WANG Hong-Min and ZHANG Ben-Ai. Electric and Magnetic Form Factors of Proton in Relativistic Constituent Quark Model [J]. Commun. Theor. Phys. 41 (2004) 425.

Hidden analytic relations for two-loop Higgs amplitudes in QCD

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