Abstract
We provide expressions for the nonperturbative matching of the effective field theory describing dark matter interactions with quarks and gluons to the effective theory of nonrelativistic dark matter interacting with nonrelativistic nucleons. We give expressions of leading and subleading order in chiral counting. In general, a single partonic operator matches onto several nonrelativistic operators already at leading order in chiral counting. Keeping only one operator at the time in the nonrelativistic effective theory thus does not properly describe the scattering in direct detection. The matching of the axial-axial partonic level operator, as well as the matching of the operators coupling DM to the QCD anomaly term, include naively momentum suppressed terms. However, these are still of leading chiral order due to pion poles and can be numerically important.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
F. Bishara, J. Brod, B. Grinstein and J. Zupan, Chiral Effective Theory of Dark Matter Direct Detection, JCAP 02 (2017) 009 [arXiv:1611.00368] [INSPIRE].
J. Fan, M. Reece and L.-T. Wang, Non-relativistic effective theory of dark matter direct detection, JCAP 11 (2010) 042 [arXiv:1008.1591] [INSPIRE].
A.L. Fitzpatrick, W. Haxton, E. Katz, N. Lubbers and Y. Xu, The Effective Field Theory of Dark Matter Direct Detection, JCAP 02 (2013) 004 [arXiv:1203.3542] [INSPIRE].
A.L. Fitzpatrick, W. Haxton, E. Katz, N. Lubbers and Y. Xu, Model Independent Direct Detection Analyses, arXiv:1211.2818 [INSPIRE].
N. Anand, A.L. Fitzpatrick and W.C. Haxton, Weakly interacting massive particle-nucleus elastic scattering response, Phys. Rev. C 89 (2014) 065501 [arXiv:1308.6288] [INSPIRE].
M. Cirelli, E. Del Nobile and P. Panci, Tools for model-independent bounds in direct dark matter searches, JCAP 10 (2013) 019 [arXiv:1307.5955] [INSPIRE].
G. Barello, S. Chang and C.A. Newby, A Model Independent Approach to Inelastic Dark Matter Scattering, Phys. Rev. D 90 (2014) 094027 [arXiv:1409.0536] [INSPIRE].
R.J. Hill and M.P. Solon, Standard Model anatomy of WIMP dark matter direct detection II: QCD analysis and hadronic matrix elements, Phys. Rev. D 91 (2015) 043505 [arXiv:1409.8290] [INSPIRE].
R. Catena and P. Gondolo, Global fits of the dark matter-nucleon effective interactions, JCAP 09 (2014) 045 [arXiv:1405.2637] [INSPIRE].
J. Kopp, T. Schwetz and J. Zupan, Global interpretation of direct Dark Matter searches after CDMS-II results, JCAP 02 (2010) 014 [arXiv:0912.4264] [INSPIRE].
R.J. Hill and M.P. Solon, WIMP-nucleon scattering with heavy WIMP effective theory, Phys. Rev. Lett. 112 (2014) 211602 [arXiv:1309.4092] [INSPIRE].
R.J. Hill and M.P. Solon, Universal behavior in the scattering of heavy, weakly interacting dark matter on nuclear targets, Phys. Lett. B 707 (2012) 539 [arXiv:1111.0016] [INSPIRE].
A. Kurylov and M. Kamionkowski, Generalized analysis of weakly interacting massive particle searches, Phys. Rev. D 69 (2004) 063503 [hep-ph/0307185] [INSPIRE].
M. Pospelov and T. ter Veldhuis, Direct and indirect limits on the electromagnetic form-factors of WIMPs, Phys. Lett. B 480 (2000) 181 [hep-ph/0003010] [INSPIRE].
J. Bagnasco, M. Dine and S.D. Thomas, Detecting technibaryon dark matter, Phys. Lett. B 320 (1994) 99 [hep-ph/9310290] [INSPIRE].
V. Cirigliano, M.L. Graesser and G. Ovanesyan, WIMP-nucleus scattering in chiral effective theory, JHEP 10 (2012) 025 [arXiv:1205.2695] [INSPIRE].
M. Hoferichter, P. Klos and A. Schwenk, Chiral power counting of one- and two-body currents in direct detection of dark matter, Phys. Lett. B 746 (2015) 410 [arXiv:1503.04811] [INSPIRE].
M. Hoferichter, P. Klos, J. Menéndez and A. Schwenk, Analysis strategies for general spin-independent WIMP-nucleus scattering, Phys. Rev. D 94 (2016) 063505 [arXiv:1605.08043] [INSPIRE].
R. Catena, A. Ibarra and S. Wild, DAMA confronts null searches in the effective theory of dark matter-nucleon interactions, JCAP 05 (2016) 039 [arXiv:1602.04074] [INSPIRE].
S. Weinberg, Nuclear forces from chiral Lagrangians, Phys. Lett. B 251 (1990) 288 [INSPIRE].
S. Weinberg, Effective chiral Lagrangians for nucleon-pion interactions and nuclear forces, Nucl. Phys. B 363 (1991) 3 [INSPIRE].
P.F. Bedaque and U. van Kolck, Effective field theory for few nucleon systems, Ann. Rev. Nucl. Part. Sci. 52 (2002) 339 [nucl-th/0203055] [INSPIRE].
E. Epelbaum, H.-W. Hammer and U.-G. Meißner, Modern Theory of Nuclear Forces, Rev. Mod. Phys. 81 (2009) 1773 [arXiv:0811.1338] [INSPIRE].
E. Epelbaum, Nuclear Forces from Chiral Effective Field Theory: A Primer, arXiv:1001.3229 [INSPIRE].
D. Gazda, R. Catena and C. Forssén, Ab initio nuclear response functions for dark matter searches, Phys. Rev. D 95 (2017) 103011 [arXiv:1612.09165] [INSPIRE].
C. Körber, A. Nogga and J. de Vries, First-principle calculations of Dark Matter scattering off light nuclei, Phys. Rev. C 96 (2017) 035805 [arXiv:1704.01150] [INSPIRE].
J. Brod, A. Gootjes-Dreesbach, M. Tammaro and J. Zupan, Effective Field Theory for Dark Matter Direct Detection up to Dimension Seven, arXiv:1710.10218 [INSPIRE].
PICO collaboration, C. Amole et al., Dark Matter Search Results from the PICO-60 C 3 F 8 Bubble Chamber, Phys. Rev. Lett. 118 (2017) 251301 [arXiv:1702.07666] [INSPIRE].
LUX collaboration, D.S. Akerib et al., Limits on spin-dependent WIMP-nucleon cross section obtained from the complete LUX exposure, Phys. Rev. Lett. 118 (2017) 251302 [arXiv:1705.03380] [INSPIRE].
J. Goodman, M. Ibe, A. Rajaraman, W. Shepherd, T.M.P. Tait and H.-B. Yu, Constraints on Dark Matter from Colliders, Phys. Rev. D 82 (2010) 116010 [arXiv:1008.1783] [INSPIRE].
G. Ovanesyan and L. Vecchi, Direct detection of dark matter polarizability, JHEP 07 (2015) 128 [arXiv:1410.0601] [INSPIRE].
E.E. Jenkins and A.V. Manohar, Baryon chiral perturbation theory using a heavy fermion lagrangian, Phys. Lett. B 255 (1991) 558.
J. Heinonen, R.J. Hill and M.P. Solon, Lorentz invariance in heavy particle effective theories, Phys. Rev. D 86 (2012) 094020 [arXiv:1208.0601] [INSPIRE].
V. Cirigliano, S. Davidson and Y. Kuno, Spin-dependent μ → e conversion, Phys. Lett. B 771 (2017) 242 [arXiv:1703.02057] [INSPIRE].
Particle Data Group collaboration, C. Patrignani et al., Review of Particle Physics, Chin. Phys. C 40 (2016) 100001 [INSPIRE].
D.J. Gross, S.B. Treiman and F. Wilczek, Light Quark Masses and Isospin Violation, Phys. Rev. D 19 (1979) 2188 [INSPIRE].
XENON collaboration, E. Aprile et al., Effective field theory search for high-energy nuclear recoils using the XENON100 dark matter detector, Phys. Rev. D 96 (2017) 042004 [arXiv:1705.02614] [INSPIRE].
R.S. Sufian, Y.-B. Yang, A. Alexandru, T. Draper, J. Liang and K.-F. Liu, Strange Quark Magnetic Moment of the Nucleon at the Physical Point, Phys. Rev. Lett. 118 (2017) 042001 [arXiv:1606.07075] [INSPIRE].
J. Green et al., High-precision calculation of the strange nucleon electromagnetic form factors, Phys. Rev. D 92 (2015) 031501 [arXiv:1505.01803] [INSPIRE].
P.J. Mohr, D.B. Newell and B.N. Taylor, CODATA Recommended Values of the Fundamental Physical Constants: 2014, Rev. Mod. Phys. 88 (2016) 035009 [arXiv:1507.07956] [INSPIRE].
F.J. Ernst, R.G. Sachs and K.C. Wali, Electromagnetic form factors of the nucleon, Phys. Rev. 119 (1960) 1105 [INSPIRE].
R.J. Hill and G. Paz, Model independent extraction of the proton charge radius from electron scattering, Phys. Rev. D 82 (2010) 113005 [arXiv:1008.4619] [INSPIRE].
G. Grilli di Cortona, E. Hardy, J. Pardo Vega and G. Villadoro, The QCD axion, precisely, JHEP 01 (2016) 034 [arXiv:1511.02867] [INSPIRE].
QCDSF collaboration, G.S. Bali et al., Strangeness Contribution to the Proton Spin from Lattice QCD, Phys. Rev. Lett. 108 (2012) 222001 [arXiv:1112.3354] [INSPIRE].
M. Engelhardt, Strange quark contributions to nucleon mass and spin from lattice QCD, Phys. Rev. D 86 (2012) 114510 [arXiv:1210.0025] [INSPIRE].
T. Bhattacharya, R. Gupta and B. Yoon, Disconnected Quark Loop Contributions to Nucleon Structure, PoS(LATTICE2014)141 [arXiv:1503.05975] [INSPIRE].
C. Alexandrou et al., Nucleon axial form factors using N f = 2 twisted mass fermions with a physical value of the pion mass, Phys. Rev. D 96 (2017) 054507 [arXiv:1705.03399] [INSPIRE].
HERMES collaboration, A. Airapetian et al., Precise determination of the spin structure function g(1) of the proton, deuteron and neutron, Phys. Rev. D 75 (2007) 012007 [hep-ex/0609039] [INSPIRE].
COMPASS collaboration, V. Yu. Alexakhin et al., The Deuteron Spin-dependent Structure Function g1(d) and its First Moment, Phys. Lett. B 647 (2007) 8 [hep-ex/0609038] [INSPIRE].
A.S. Meyer, M. Betancourt, R. Gran and R.J. Hill, Deuterium target data for precision neutrino-nucleus cross sections, Phys. Rev. D 93 (2016) 113015 [arXiv:1603.03048] [INSPIRE].
V. Bernard, L. Elouadrhiri and U.-G. Meißner, Axial structure of the nucleon: Topical Review, J. Phys. G 28 (2002) R1 [hep-ph/0107088] [INSPIRE].
MiniBooNE collaboration, A.A. Aguilar-Arevalo et al., First Measurement of the Muon Neutrino Charged Current Quasielastic Double Differential Cross Section, Phys. Rev. D 81 (2010) 092005 [arXiv:1002.2680] [INSPIRE].
G. Rajan, J. Yong-Chull, L. Huey-Wen, Y. Boram and B. Tanmoy, Axial Vector Form Factors of the Nucleon from Lattice QCD, arXiv:1705.06834 [INSPIRE].
LHPC collaboration, J.D. Bratt et al., Nucleon structure from mixed action calculations using 2 + 1 flavors of asqtad sea and domain wall valence fermions, Phys. Rev. D 82 (2010) 094502 [arXiv:1001.3620] [INSPIRE].
V. Bernard, H.W. Fearing, T.R. Hemmert and U.G. Meißner, The form-factors of the nucleon at small momentum transfer, Nucl. Phys. A 635 (1998) 121 [Erratum ibid. A 642 (1998) 563] [hep-ph/9801297] [INSPIRE].
P. Junnarkar and A. Walker-Loud, Scalar strange content of the nucleon from lattice QCD, Phys. Rev. D 87 (2013) 114510 [arXiv:1301.1114] [INSPIRE].
xQCD collaboration, Y.-B. Yang, A. Alexandru, T. Draper, J. Liang and K.-F. Liu, πN and strangeness sigma terms at the physical point with chiral fermions, Phys. Rev. D 94 (2016) 054503 [arXiv:1511.09089] [INSPIRE].
S. Dürr et al., Lattice computation of the nucleon scalar quark contents at the physical point, Phys. Rev. Lett. 116 (2016) 172001 [arXiv:1510.08013] [INSPIRE].
J.M. Alarcon, J. Martin Camalich and J.A. Oller, The chiral representation of the πN scattering amplitude and the pion-nucleon sigma term, Phys. Rev. D 85 (2012) 051503 [arXiv:1110.3797] [INSPIRE].
J. Ruiz de Elvira, M. Hoferichter, B. Kubis and U.-G. Meißner, Extracting the sigma-term from low-energy pion-nucleon scattering, arXiv:1706.01465 [INSPIRE].
M. Hoferichter, J. Ruiz de Elvira, B. Kubis and U.-G. Meißner, High-Precision Determination of the Pion-Nucleon σ-term from Roy-Steiner Equations, Phys. Rev. Lett. 115 (2015) 092301 [arXiv:1506.04142] [INSPIRE].
L. Álvarez-Ruso, T. Ledwig, J. Martin Camalich and M.J. Vicente Vacas, Nucleon mass and pion-nucleon sigma term from a chiral analysis of lattice QCD world data, EPJ Web Conf. 73 (2014) 04015 [INSPIRE].
ETM collaboration, A. Abdel-Rehim et al., Direct Evaluation of the Quark Content of Nucleons from Lattice QCD at the Physical Point, Phys. Rev. Lett. 116 (2016) 252001 [arXiv:1601.01624] [INSPIRE].
M. Hoferichter, J. Ruiz de Elvira, B. Kubis and U.-G. Meißner, Remarks on the pion-nucleon σ-term, Phys. Lett. B 760 (2016) 74 [arXiv:1602.07688] [INSPIRE].
A. Crivellin, M. Hoferichter and M. Procura, Accurate evaluation of hadronic uncertainties in spin-independent WIMP-nucleon scattering: Disentangling two- and three-flavor effects, Phys. Rev. D 89 (2014) 054021 [arXiv:1312.4951] [INSPIRE].
C. McNeile et al., Direct determination of the strange and light quark condensates from full lattice QCD, Phys. Rev. D 87 (2013) 034503 [arXiv:1211.6577] [INSPIRE].
UKQCD, QCDSF collaboration, M. Gockeler et al., Quark helicity flip generalized parton distributions from two-flavor lattice QCD, Phys. Lett. B 627 (2005) 113 [hep-lat/0507001] [INSPIRE].
M. Diehl, Generalized parton distributions with helicity flip, Eur. Phys. J. C 19 (2001) 485 [hep-ph/0101335] [INSPIRE].
C. Alexandrou et al., Nucleon scalar and tensor charges using lattice QCD simulations at the physical value of the pion mass, Phys. Rev. D 95 (2017) 114514 [arXiv:1703.08788] [INSPIRE].
T. Bhattacharya, V. Cirigliano, S. Cohen, R. Gupta, H.-W. Lin and B. Yoon, Axial, Scalar and Tensor Charges of the Nucleon from 2 + 1 + 1-flavor Lattice QCD, Phys. Rev. D 94 (2016) 054508 [arXiv:1606.07049] [INSPIRE].
QCDSF/UKQCD collaboration, D. Pleiter et al., Nucleon form factors and structure functions from N f = 2 Clover fermions, PoS(LATTICE 2010)153 [arXiv:1101.2326] [INSPIRE].
G.S. Bali et al., Nucleon isovector couplings from N f = 2 lattice QCD, Phys. Rev. D 91 (2015) 054501 [arXiv:1412.7336] [INSPIRE].
PNDME collaboration, T. Bhattacharya et al., Iso-vector and Iso-scalar Tensor Charges of the Nucleon from Lattice QCD, Phys. Rev. D 92 (2015) 094511 [arXiv:1506.06411] [INSPIRE].
H.-W. Lin, T. Blum, S. Ohta, S. Sasaki and T. Yamazaki, Nucleon structure with two flavors of dynamical domain-wall fermions, Phys. Rev. D 78 (2008) 014505 [arXiv:0802.0863] [INSPIRE].
J.R. Green, J.W. Negele, A.V. Pochinsky, S.N. Syritsyn, M. Engelhardt and S. Krieg, Nucleon Scalar and Tensor Charges from Lattice QCD with Light Wilson Quarks, Phys. Rev. D 86 (2012) 114509 [arXiv:1206.4527] [INSPIRE].
C. Alexandrou, M. Constantinou, K. Jansen, G. Koutsou and H. Panagopoulos, Nucleon transversity generalized form factors with twisted mass fermions, PoS(LATTICE 2013)294 [arXiv:1311.4670] [INSPIRE].
A. Abdel-Rehim et al., Nucleon and pion structure with lattice QCD simulations at physical value of the pion mass, Phys. Rev. D 92 (2015) 114513 [arXiv:1507.04936] [INSPIRE].
B. Pasquini, M. Pincetti and S. Boffi, Chiral-odd generalized parton distributions in constituent quark models, Phys. Rev. D 72 (2005) 094029 [hep-ph/0510376] [INSPIRE].
H. Gao, T. Liu and Z. Zhao, Nucleon tensor charge and electric dipole moment, arXiv:1704.00113 [INSPIRE].
UKQCD, QCDSF collaboration, M. Gockeler et al., Transverse spin structure of the nucleon from lattice QCD simulations, Phys. Rev. Lett. 98 (2007) 222001 [hep-lat/0612032] [INSPIRE].
I. Schmidt and J. Soffer, Melosh rotation and the nucleon tensor charge, Phys. Lett. B 407 (1997) 331 [hep-ph/9703411] [INSPIRE].
T. Ledwig, A. Silva and H.-C. Kim, Anomalous tensor magnetic moments and form factors of the proton in the self-consistent chiral quark-soliton model, Phys. Rev. D 82 (2010) 054014 [arXiv:1007.1355] [INSPIRE].
T. Ledwig and H.-C. Kim, Transverse strange quark spin structure of the nucleon, Phys. Rev. D 85 (2012) 034041 [arXiv:1107.4952] [INSPIRE].
J. Zanotti et al., Transverse spin densities of octet baryons using Lattice QCD, PoS(LATTICE2016)163.
A.F. Falk, M.E. Luke and M.J. Savage, Nonperturbative contributions to the inclusive rare decays B → X sγ and B → X s l + l −, Phys. Rev. D 49 (1994) 3367 [hep-ph/9308288] [INSPIRE].
A.V. Manohar, The HQET/NRQCD Lagrangian to order α/m − 3, Phys. Rev. D 56 (1997) 230 [hep-ph/9701294] [INSPIRE].
M.E. Luke and A.V. Manohar, Reparametrization invariance constraints on heavy particle effective field theories, Phys. Lett. B 286 (1992) 348 [hep-ph/9205228] [INSPIRE].
Open Access
This article is distributed under the terms of the Creative Commons Attribution License (CC-BY 4.0), which permits any use, distribution and reproduction in any medium, provided the original author(s) and source are credited.
Author information
Authors and Affiliations
Corresponding author
Additional information
ArXiv ePrint: 1707.06998
Rights and permissions
Open Access This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made.
The images or other third party material in this article are included in the article’s Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder.
To view a copy of this licence, visit https://creativecommons.org/licenses/by/4.0/.
About this article
Cite this article
Bishara, F., Brod, J., Grinstein, B. et al. From quarks to nucleons in dark matter direct detection. J. High Energ. Phys. 2017, 59 (2017). https://doi.org/10.1007/JHEP11(2017)059
Received:
Accepted:
Published:
DOI: https://doi.org/10.1007/JHEP11(2017)059