Sigma decomposition

Alonso, R.; Brivio, I.; Gavela, M. B.; Merlo, L.; Rigolin, S.

doi:10.1007/JHEP12(2014)034

Sigma decomposition

Journal Article · Tue Dec 02 23:00:00 EST 2014 · Journal of High Energy Physics (Online)

DOI:https://doi.org/10.1007/JHEP12(2014)034· OSTI ID:1454843

Alonso, R. ^[1]; Brivio, I. ^[2]; Gavela, M. B. ^[2]; Merlo, L. ^[2]; Rigolin, S. ^[3]

Univ. of California, San Diego, CA (United States); Department of Physics, University of California at San Diego, 9500 Gilman Drive, La Jolla, CA 92093-0319
Autonomous Univ. of Madrid (Spain)
Univ. of Padova, Padua (Italy)

In composite Higgs models the Higgs is a pseudo-Goldstone boson of a high-energy strong dynamics. We have constructed the effective chiral Lagrangian for a generic symmetric coset, restricting to CP-even bosonic operators up to four momenta which turn out to depend on seven parameters, aside from kinetic terms. Once the same sources of custodial symmetry breaking as in the Standard Model are considered, the total number of operators in the basis increases up to ten, again aside from kinetic terms. Under these assumptions, we have then particularised the discussion to three distinct frameworks: the original SU(5)/SO(5) Georgi-Kaplan model, the minimal custodial-preserving SO(5)/SO(4) model and the minimal SU(3)/(SU(2) × U(1)) model, which intrinsically breaks custodial symmetry. The projection of the high-energy electroweak effective theory into the bosonic sector of the Standard Model is shown to match the low-energy chiral effective Lagrangian for a dynamical Higgs, and it uncovers strong relations between the operator coefficients. Finally, the relation with the bosonic basis of operators describing linear realisations of electroweak symmetry breaking is clarified.

View Accepted Manuscript (DOE)

Research Organization:: Univ. of California, San Diego, CA (United States)

Sponsoring Organization:: USDOE

Grant/Contract Number:: SC0009919

OSTI ID:: 1454843

Journal Information:: Journal of High Energy Physics (Online), Journal Name: Journal of High Energy Physics (Online) Journal Issue: 12 Vol. 2014; ISSN 1029-8479

Publisher:: Springer BerlinCopyright Statement

Country of Publication:: United States

Language:: English

References (66)

Light top partners for a light composite Higgs Matsedonskyi, Oleksii; Panico, Giuliano; Wulzer, Andrea Journal of High Energy Physics, Vol. 2013, Issue 1 https://doi.org/10.1007/JHEP01(2013)164	journal	January 2013
Strong Higgs interactions at a linear collider Contino, Roberto; Grojean, Christophe; Pappadopulo, Duccio Journal of High Energy Physics, Vol. 2014, Issue 2 https://doi.org/10.1007/JHEP02(2014)006	journal	February 2014
Higgs form factors in associated production Isidori, Gino; Trott, Michael Journal of High Energy Physics, Vol. 2014, Issue 2 https://doi.org/10.1007/JHEP02(2014)082	journal	February 2014
On the tuning and the mass of the composite Higgs Panico, Giuliano; Redi, Michele; Tesi, Andrea Journal of High Energy Physics, Vol. 2013, Issue 3 https://doi.org/10.1007/JHEP03(2013)051	journal	March 2013
Disentangling a dynamical Higgs Brivio, I.; Corbett, T.; Éboli, O. J. P. Journal of High Energy Physics, Vol. 2014, Issue 3 https://doi.org/10.1007/JHEP03(2014)024	journal	March 2014
Model-independent bounds on a light Higgs Azatov, Aleksandr; Contino, Roberto; Galloway, Jamison Journal of High Energy Physics, Vol. 2012, Issue 4 https://doi.org/10.1007/JHEP04(2012)127	journal	April 2012
Composite charge 8/3 resonances at the LHC Matsedonskyi, Oleksii; Riva, Francesco; Vantalon, Thibaud Journal of High Energy Physics, Vol. 2014, Issue 4 https://doi.org/10.1007/JHEP04(2014)059	journal	April 2014
Strong double higgs production at the LHC Contino, Roberto; Grojean, Christophe; Moretti, Mauro Journal of High Energy Physics, Vol. 2010, Issue 5 https://doi.org/10.1007/JHEP05(2010)089	journal	May 2010
Minimal flavour violation with strong Higgs dynamics Alonso, R.; Gavela, M. B.; Merlo, L. Journal of High Energy Physics, Vol. 2012, Issue 6 https://doi.org/10.1007/JHEP06(2012)076	journal	June 2012
Composite scalar dark matter Frigerio, Michele; Pomarol, Alex; Riva, Francesco Journal of High Energy Physics, Vol. 2012, Issue 7 https://doi.org/10.1007/JHEP07(2012)015	journal	July 2012
Effective theory of a dynamically broken electroweak Standard Model at NLO Buchalla, Gerhard; Catà, Oscar Journal of High Energy Physics, Vol. 2012, Issue 7 https://doi.org/10.1007/JHEP07(2012)101	journal	July 2012
A minimally tuned composite Higgs model from an extra dimension Pappadopulo, Duccio; Thamm, Andrea; Torre, Riccardo Journal of High Energy Physics, Vol. 2013, Issue 7 https://doi.org/10.1007/JHEP07(2013)058	journal	July 2013
Composite dark matter and LHC interplay Marzocca, David; Urbano, Alfredo Journal of High Energy Physics, Vol. 2014, Issue 7 https://doi.org/10.1007/JHEP07(2014)107	journal	July 2014
General composite Higgs models Marzocca, David; Serone, Marco; Shu, Jing Journal of High Energy Physics, Vol. 2012, Issue 8 https://doi.org/10.1007/JHEP08(2012)013	journal	August 2012
The composite Higgs and light resonance connection Pomarol, Alex; Riva, Francesco Journal of High Energy Physics, Vol. 2012, Issue 8 https://doi.org/10.1007/JHEP08(2012)135	journal	August 2012
Dimension-six terms in the Standard Model Lagrangian Grzadkowski, B.; Iskrzyński, M.; Misiak, M. Journal of High Energy Physics, Vol. 2010, Issue 10 https://doi.org/10.1007/JHEP10(2010)085	journal	October 2010
On the effect of resonances in composite Higgs phenomenology Contino, Roberto; Pappadopulo, Duccio; Marzocca, David Journal of High Energy Physics, Vol. 2011, Issue 10 https://doi.org/10.1007/JHEP10(2011)081	journal	October 2011
Implications of a light Higgs in composite models Redi, Michele; Tesi, Andrea Journal of High Energy Physics, Vol. 2012, Issue 10 https://doi.org/10.1007/JHEP10(2012)166	journal	October 2012
CP violation with a dynamical Higgs Gavela, M. B.; Gonzalez-Fraile, J.; Gonzalez-Garcia, M. C. Journal of High Energy Physics, Vol. 2014, Issue 10 https://doi.org/10.1007/JHEP10(2014)044	journal	October 2014
Broken symmetries, massless particles and gauge fields Higgs, P. W. Physics Letters, Vol. 12, Issue 2 https://doi.org/10.1016/0031-9163(64)91136-9	journal	September 1964
Composite Higgs and custodial SU(2) Georgi, Howard; Kaplan, David B. Physics Letters B, Vol. 145, Issue 3-4 https://doi.org/10.1016/0370-2693(84)90341-1	journal	September 1984
Calculation of the composite Higgs mass Georgi, Howard; Kaplan, David B.; Galison, Peter Physics Letters B, Vol. 143, Issue 1-3 https://doi.org/10.1016/0370-2693(84)90823-2	journal	August 1984
SU(2) × U(1) breaking by vacuum misalignment Kaplan, David B.; Georgi, Howard Physics Letters B, Vol. 136, Issue 3 https://doi.org/10.1016/0370-2693(84)91177-8	journal	March 1984
Composite Higgs scalars Kaplan, David B.; Georgi, Howard; Dimopoulos, Savas Physics Letters B, Vol. 136, Issue 3 https://doi.org/10.1016/0370-2693(84)91178-X	journal	March 1984
Low-energy impact of a heavy Higgs boson sector Longhitano, Anthony C. Nuclear Physics B, Vol. 188, Issue 1 https://doi.org/10.1016/0550-3213(81)90109-7	journal	September 1981
Chiral quarks and the non-relativistic quark model Manohar, Aneesh; Georgi, Howard Nuclear Physics B, Vol. 234, Issue 1 https://doi.org/10.1016/0550-3213(84)90231-1	journal	March 1984
Anatomy of a composite Higgs model Dugan, Michael J.; Georgi, Howard; Kaplan, David B. Nuclear Physics B, Vol. 254 https://doi.org/10.1016/0550-3213(85)90221-4	journal	January 1985
Effective lagrangian analysis of new interactions and flavour conservation Buchmüller, W.; Wyler, D. Nuclear Physics B, Vol. 268, Issue 3-4 https://doi.org/10.1016/0550-3213(86)90262-2	journal	May 1986
Fermionic couplings in an electroweak theory with nonlinear spontaneous symmetry breaking Cvetic̆, Gorazd; Kögerler, Reinhart Nuclear Physics B, Vol. 328, Issue 2 https://doi.org/10.1016/0550-3213(89)90332-5	journal	December 1989
Electroweak symmetry breaking from dimensional deconstruction Arkani-Hamed, Nima; Cohen, Andrew G.; Georgi, Howard Physics Letters B, Vol. 513, Issue 1-2 https://doi.org/10.1016/S0370-2693(01)00741-9	journal	July 2001
Probing non-standard bosonic interactions via W-boson pair production at lepton colliders Hagiwara, K.; Hatsukano, T.; Ishihara, S. Nuclear Physics B, Vol. 496, Issue 1-2 https://doi.org/10.1016/S0550-3213(97)00208-3	journal	July 1997
Higgs as a holographic pseudo-Goldstone boson Contino, Roberto; Nomura, Yasunori; Pomarol, Alex Nuclear Physics B, Vol. 671 https://doi.org/10.1016/j.nuclphysb.2003.08.027	journal	November 2003
The minimal composite Higgs model Agashe, Kaustubh; Contino, Roberto; Pomarol, Alex Nuclear Physics B, Vol. 719, Issue 1-2 https://doi.org/10.1016/j.nuclphysb.2005.04.035	journal	July 2005
Complete electroweak chiral Lagrangian with a light Higgs at NLO Buchalla, Gerhard; Catà, Oscar; Krause, Claudius Nuclear Physics B, Vol. 880 https://doi.org/10.1016/j.nuclphysb.2014.01.018	journal	March 2014
The effective chiral Lagrangian for a light dynamical “Higgs particle” Alonso, R.; Gavela, M. B.; Merlo, L. Physics Letters B, Vol. 722, Issue 4-5 https://doi.org/10.1016/j.physletb.2013.04.037	journal	May 2013
Naive dimensional analysis counting of gauge theory amplitudes and anomalous dimensions Jenkins, Elizabeth E.; Manohar, Aneesh V.; Trott, Michael Physics Letters B, Vol. 726, Issue 4-5 https://doi.org/10.1016/j.physletb.2013.09.020	journal	November 2013
The Littlest Higgs Arkani-Hamed, Nima; Cohen, Andrew G.; Katz, Emanuel Journal of High Energy Physics, Vol. 2002, Issue 07 https://doi.org/10.1088/1126-6708/2002/07/034	journal	July 2002
The strongly-interacting light Higgs Giudice, Gian Francesco; Grojean, Christophe; Pomarol, Alex Journal of High Energy Physics, Vol. 2007, Issue 06 https://doi.org/10.1088/1126-6708/2007/06/045	journal	June 2007
Beyond the minimal composite Higgs model Gripaios, Ben; Pomarol, Alex; Riva, Francesco Journal of High Energy Physics, Vol. 2009, Issue 04 https://doi.org/10.1088/1126-6708/2009/04/070	journal	April 2009
Structure of Phenomenological Lagrangians. I Coleman, S.; Wess, J.; Zumino, Bruno Physical Review, Vol. 177, Issue 5 https://doi.org/10.1103/PhysRev.177.2239	journal	January 1969
Structure of Phenomenological Lagrangians. II Callan, Curtis G.; Coleman, Sidney; Wess, J. Physical Review, Vol. 177, Issue 5 https://doi.org/10.1103/PhysRev.177.2247	journal	January 1969
Broken Symmetry and the Mass of Gauge Vector Mesons Englert, F.; Brout, R. Physical Review Letters, Vol. 13, Issue 9 https://doi.org/10.1103/PhysRevLett.13.321	journal	August 1964
Broken Symmetries and the Masses of Gauge Bosons Higgs, Peter W. Physical Review Letters, Vol. 13, Issue 16 https://doi.org/10.1103/PhysRevLett.13.508	journal	October 1964
The Chiral Approach to the Electroweak Interactions Feruglio, F. International Journal of Modern Physics A, Vol. 08, Issue 28 https://doi.org/10.1142/S0217751X93001946	journal	November 1993
Light top partners for a light composite Higgs Matsedonskyi, Oleksii; Panico, Giuliano; Wulzer, Andrea ETH Zurich https://doi.org/10.3929/ethz-b-000064912	text	January 2013
On the tuning and the mass of the composite Higgs Giuliano, Panico,; Michele, Redi,; Andrea, Tesi, ETH Zurich https://doi.org/10.3929/ethz-b-000065935	text	January 2013
Beyond the Minimal Composite Higgs Model Gripaios, Ben; Pomarol, Alex; Riva, Francesco arXiv https://doi.org/10.48550/arxiv.0902.1483	text	January 2009
Model-Independent Bounds on a Light Higgs Azatov, Aleksandr; Contino, Roberto; Galloway, Jamison arXiv https://doi.org/10.48550/arxiv.1202.3415	text	January 2012
Effective Theory of a Dynamically Broken Electroweak Standard Model at NLO Buchalla, Gerhard; Cata, Oscar arXiv https://doi.org/10.48550/arxiv.1203.6510	text	January 2012
Composite Scalar Dark Matter Frigerio, Michele; Pomarol, Alex; Riva, Francesco arXiv https://doi.org/10.48550/arxiv.1204.2808	text	January 2012
Implications of a Light Higgs in Composite Models Redi, Michele; Tesi, Andrea arXiv https://doi.org/10.48550/arxiv.1205.0232	text	January 2012
General Composite Higgs Models Marzocca, David; Serone, Marco; Shu, Jing arXiv https://doi.org/10.48550/arxiv.1205.0770	text	January 2012
The Composite Higgs and Light Resonance Connection Pomarol, Alex; Riva, Francesco arXiv https://doi.org/10.48550/arxiv.1205.6434	text	January 2012
The Effective Chiral Lagrangian for a Light Dynamical "Higgs Particle" Alonso, R.; Gavela, M. B.; Merlo, L. arXiv https://doi.org/10.48550/arxiv.1212.3305	text	January 2012
A minimally tuned composite Higgs model from an extra dimension Pappadopulo, Duccio; Thamm, Andrea; Torre, Riccardo arXiv https://doi.org/10.48550/arxiv.1303.3062	preprint	January 2013
Higgs form factors in Associated Production Isidori, Gino; Trott, Michael arXiv https://doi.org/10.48550/arxiv.1307.4051	text	January 2013
Naive Dimensional Analysis Counting of Gauge Theory Amplitudes and Anomalous Dimensions Jenkins, Elizabeth E.; Manohar, Aneesh V.; Trott, Michael arXiv https://doi.org/10.48550/arxiv.1309.0819	text	January 2013
Strong Higgs Interactions at a Linear Collider Contino, Roberto; Grojean, Christophe; Pappadopulo, Duccio arXiv https://doi.org/10.48550/arxiv.1309.7038	text	January 2013
Disentangling a dynamical Higgs Brivio, I.; Corbett, T.; Éboli, O. J. P. arXiv https://doi.org/10.48550/arxiv.1311.1823	text	January 2013
Composite Dark Matter and LHC Interplay Marzocca, David; Urbano, Alfredo arXiv https://doi.org/10.48550/arxiv.1404.7419	text	January 2014
CP violation with a dynamical Higgs Gavela, M. B.; Gonzalez-Fraile, J.; Gonzalez-Garcia, M. C. arXiv https://doi.org/10.48550/arxiv.1406.6367	text	January 2014
Electroweak symmetry breaking from dimensional deconstruction Arkani-Hamed, Nima; Cohen, Andrew G.; Georgi, Howard arXiv https://doi.org/10.48550/arxiv.hep-ph/0105239	text	January 2001
The Littlest Higgs Arkani-Hamed, N.; Cohen, A. G.; Katz, E. arXiv https://doi.org/10.48550/arxiv.hep-ph/0206021	text	January 2002
The Minimal Composite Higgs Model Agashe, Kaustubh; Contino, Roberto; Pomarol, Alex arXiv https://doi.org/10.48550/arxiv.hep-ph/0412089	text	January 2004
The Chiral Approach to the Electroweak Interactions Feruglio, Ferruccio arXiv https://doi.org/10.48550/arxiv.hep-ph/9301281	text	January 1993
Higgs form factors in associated production Isidori, Gino; Trott, Michael Springer https://doi.org/10.5167/uzh-107672	text	January 2014

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