Abstract
We show how several properties of the QCD axion can be extracted at high precision using only first principle QCD computations. By combining NLO results obtained in chiral perturbation theory with recent Lattice QCD results the full axion potential, its mass and the coupling to photons can be reconstructed with percent precision. Axion couplings to nucleons can also be derived reliably, with uncertainties smaller than ten percent. The approach presented here allows the precision to be further improved as uncertainties on the light quark masses and the effective theory couplings are reduced. We also compute the finite temperature dependence of the axion potential and its mass up to the crossover region. For higher temperature we point out the unreliability of the conventional instanton approach and study its impact on the computation of the axion relic abundance.
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References
R.J. Crewther, P. Di Vecchia, G. Veneziano and E. Witten, Chiral estimate of the electric dipole moment of the neutron in quantum chromodynamics, Phys. Lett. B 88 (1979) 123 [Erratum ibid. B 91 (1980) 487] [INSPIRE].
J. Pendlebury et al., Revised experimental upper limit on the electric dipole moment of the neutron, Phys. Rev. D 92 (2015) 092003 [arXiv:1509.04411] [INSPIRE].
R.D. Peccei and H.R. Quinn, CP conservation in the presence of instantons, Phys. Rev. Lett. 38 (1977) 1440 [INSPIRE].
F. Wilczek, Problem of strong p and t invariance in the presence of instantons, Phys. Rev. Lett. 40 (1978) 279 [INSPIRE].
S. Weinberg, A new light boson?, Phys. Rev. Lett. 40 (1978) 223 [INSPIRE].
J.E. Kim, Weak interaction singlet and strong CP invariance, Phys. Rev. Lett. 43 (1979) 103 [INSPIRE].
M.A. Shifman, A.I. Vainshtein and V.I. Zakharov, Can confinement ensure natural CP invariance of strong interactions?, Nucl. Phys. B 166 (1980) 493 [INSPIRE].
A.R. Zhitnitsky, On possible suppression of the axion hadron interactions (in Russian), Sov. J. Nucl. Phys. 31 (1980) 260 [Yad. Fiz. 31 (1980) 497] [INSPIRE].
M. Dine, W. Fischler and M. Srednicki, A simple solution to the strong CP problem with a harmless axion, Phys. Lett. B 104 (1981) 199 [INSPIRE].
C. Vafa and E. Witten, Parity conservation in QCD, Phys. Rev. Lett. 53 (1984) 535 [INSPIRE].
G.G. Raffelt, Astrophysical axion bounds, Lect. Notes Phys. 741 (2008) 51 [hep-ph/0611350] [INSPIRE].
A. Arvanitaki, S. Dimopoulos, S. Dubovsky, N. Kaloper and J. March-Russell, String axiverse, Phys. Rev. D 81 (2010) 123530 [arXiv:0905.4720] [INSPIRE].
A. Arvanitaki and S. Dubovsky, Exploring the string axiverse with precision black hole physics, Phys. Rev. D 83 (2011) 044026 [arXiv:1004.3558] [INSPIRE].
A. Arvanitaki, M. Baryakhtar and X. Huang, Discovering the QCD axion with black holes and gravitational waves, Phys. Rev. D 91 (2015) 084011 [arXiv:1411.2263] [INSPIRE].
J. Preskill, M.B. Wise and F. Wilczek, Cosmology of the invisible axion, Phys. Lett. B 120 (1983) 127 [INSPIRE].
L.F. Abbott and P. Sikivie, A cosmological bound on the invisible axion, Phys. Lett. B 120 (1983) 133 [INSPIRE].
M. Dine and W. Fischler, The not so harmless axion, Phys. Lett. B 120 (1983) 137 [INSPIRE].
ADMX collaboration, S.J. Asztalos et al., A SQUID-based microwave cavity search for dark-matter axions, Phys. Rev. Lett. 104 (2010) 041301 [arXiv:0910.5914] [INSPIRE].
E. Armengaud et al., Conceptual design of the International AXion Observatory (IAXO), 2014 JINST 9 T05002 [arXiv:1401.3233] [INSPIRE].
D. Horns, J. Jaeckel, A. Lindner, A. Lobanov, J. Redondo and A. Ringwald, Searching for WISPy cold dark matter with a dish antenna, JCAP 04 (2013) 016 [arXiv:1212.2970] [INSPIRE].
D. Budker, P.W. Graham, M. Ledbetter, S. Rajendran and A. Sushkov, Proposal for a Cosmic Axion Spin Precession Experiment (CASPEr), Phys. Rev. X 4 (2014) 021030 [arXiv:1306.6089] [INSPIRE].
A. Arvanitaki and A.A. Geraci, Resonantly detecting axion-mediated forces with nuclear magnetic resonance, Phys. Rev. Lett. 113 (2014) 161801 [arXiv:1403.1290] [INSPIRE].
P. Sikivie, Experimental tests of the invisible axion, Phys. Rev. Lett. 51 (1983) 1415 [Erratum ibid. 52 (1984) 695] [INSPIRE].
L. Krauss, J. Moody, F. Wilczek and D.E. Morris, Calculations for cosmic axion detection, Phys. Rev. Lett. 55 (1985) 1797 [INSPIRE].
S. Weinberg, Phenomenological Lagrangians, Physica A 96 (1979) 327 [INSPIRE].
J. Gasser and H. Leutwyler, Chiral perturbation theory to one loop, Annals Phys. 158 (1984) 142 [INSPIRE].
J. Gasser and H. Leutwyler, Chiral perturbation theory: expansions in the mass of the strange quark, Nucl. Phys. B 250 (1985) 465 [INSPIRE].
M.I. Buchoff et al., QCD chiral transition, U(1)A symmetry and the Dirac spectrum using domain wall fermions, Phys. Rev. D 89 (2014) 054514 [arXiv:1309.4149] [INSPIRE].
A. Trunin, F. Burger, E.-M. Ilgenfritz, M.P. Lombardo and M. Muller-Preussker, Topological susceptibility from N f = 2 + 1 + 1 lattice QCD at nonzero temperature, arXiv:1510.02265 [INSPIRE].
E. Berkowitz, M.I. Buchoff and E. Rinaldi, Lattice QCD input for axion cosmology, Phys. Rev. D 92 (2015) 034507 [arXiv:1505.07455] [INSPIRE].
S. Borsányi et al., Axion cosmology, lattice QCD and the dilute instanton gas, Phys. Lett. B 752 (2016) 175 [arXiv:1508.06917] [INSPIRE].
P. Di Vecchia and G. Veneziano, Chiral dynamics in the large-N limit, Nucl. Phys. B 171 (1980) 253 [INSPIRE].
H. Georgi, D.B. Kaplan and L. Randall, Manifesting the invisible axion at low-energies, Phys. Lett. B 169 (1986) 73 [INSPIRE].
L. Ubaldi, Effects of theta on the deuteron binding energy and the triple-alpha process, Phys. Rev. D 81 (2010) 025011 [arXiv:0811.1599] [INSPIRE].
M. Spalinski, Chiral corrections to the axion mass, Z. Phys. C 41 (1988) 87 [INSPIRE].
TWQCD collaboration, Y.Y. Mao and T.W. Chiu, Topological susceptibility to the one-loop order in chiral perturbation theory, Phys. Rev. D 80 (2009) 034502 [arXiv:0903.2146] [INSPIRE].
J. Bijnens and G. Ecker, Mesonic low-energy constants, Ann. Rev. Nucl. Part. Sci. 64 (2014) 149 [arXiv:1405.6488] [INSPIRE].
S. Aoki et al., Review of lattice results concerning low-energy particle physics, Eur. Phys. J. C 74 (2014) 2890 [arXiv:1310.8555] [INSPIRE].
D.B. Kaplan and A.V. Manohar, Current mass ratios of the light quarks, Phys. Rev. Lett. 56 (1986) 2004 [INSPIRE].
RM123 collaboration, G.M. de Divitiis et al., Leading isospin breaking effects on the lattice, Phys. Rev. D 87 (2013) 114505 [arXiv:1303.4896] [INSPIRE].
MILC collaboration, S. Basak et al., Electromagnetic effects on the light hadron spectrum, J. Phys. Conf. Ser. 640 (2015) 012052 [arXiv:1510.04997] [INSPIRE].
R. Horsley et al., Isospin splittings of meson and baryon masses from three-flavor lattice QCD + QED, arXiv:1508.06401 [INSPIRE].
Particle Data Group collaboration, K.A. Olive et al., Review of particle physics, Chin. Phys. C 38 (2014) 090001 [INSPIRE].
F.-K. Guo and U.-G. Meißner, Cumulants of the QCD topological charge distribution, Phys. Lett. B 749 (2015) 278 [arXiv:1506.05487] [INSPIRE].
J. Bijnens, L. Girlanda and P. Talavera, The anomalous chiral Lagrangian of order p 6, Eur. Phys. J. C 23 (2002) 539 [hep-ph/0110400] [INSPIRE].
J.F. Donoghue, B.R. Holstein and Y.C.R. Lin, Chiral Loops in π 0 , η 0 → γγ and ηη′ mixing, Phys. Rev. Lett. 55 (1985) 2766 [Erratum ibid. 61 (1988) 1527] [INSPIRE].
B. Ananthanarayan and B. Moussallam, Electromagnetic corrections in the anomaly sector, JHEP 05 (2002) 052 [hep-ph/0205232] [INSPIRE].
G.F. Giudice, R. Rattazzi and A. Strumia, Unificaxion, Phys. Lett. B 715 (2012) 142 [arXiv:1204.5465] [INSPIRE].
J. Kodaira, QCD higher order effects in polarized electroproduction: flavor singlet coefficient functions, Nucl. Phys. B 165 (1980) 129 [INSPIRE].
E.E. Jenkins and A.V. Manohar, Baryon chiral perturbation theory using a heavy fermion Lagrangian, Phys. Lett. B 255 (1991) 558 [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].
A. Abdel-Rehim et al., Disconnected quark loop contributions to nucleon observables in lattice QCD, Phys. Rev. D 89 (2014) 034501 [arXiv:1310.6339] [INSPIRE].
T. Bhattacharya, R. Gupta and B. Yoon, Disconnected quark loop contributions to nucleon structure, PoS(LATTICE 2014)141 [arXiv:1503.05975] [INSPIRE].
A. Abdel-Rehim et al., Nucleon and pion structure with lattice QCD simulations at physical value of the pion mass, arXiv:1507.04936 [INSPIRE].
A. Abdel-Rehim et al., Disconnected quark loop contributions to nucleon observables using N f = 2 twisted clover fermions at the physical value of the light quark mass, arXiv:1511.00433 [INSPIRE].
T. Bhattacharya et al., Nucleon charges and electromagnetic form factors from 2+1+1-flavor lattice QCD, Phys. Rev. D 89 (2014) 094502 [arXiv:1306.5435] [INSPIRE].
JLQCD collaboraiton, N. Yamanaka et al., Nucleon axial and tensor charges with the overlap fermions, talk presented at 33rd International Symposium on Lattice field theory (LATTICE 2015), July 24–30, Kobe, Japan (2015).
P. Sikivie, Axion cosmology, Lect. Notes Phys. 741 (2008) 19 [astro-ph/0610440] [INSPIRE].
P. Sikivie, Of axions, domain walls and the early universe, Phys. Rev. Lett. 48 (1982) 1156 [INSPIRE].
A. Vilenkin and A.E. Everett, Cosmic strings and domain walls in models with Goldstone and pseudo-Goldstone bosons, Phys. Rev. Lett. 48 (1982) 1867 [INSPIRE].
A. Vilenkin, Cosmic strings and domain walls, Phys. Rept. 121 (1985) 263 [INSPIRE].
R.L. Davis, Cosmic axions from cosmic strings, Phys. Lett. B 180 (1986) 225 [INSPIRE].
D.P. Bennett and F.R. Bouchet, Evidence for a scaling solution in cosmic string evolution, Phys. Rev. Lett. 60 (1988) 257 [INSPIRE].
A. Dabholkar and J.M. Quashnock, Pinning down the axion, Nucl. Phys. B 333 (1990) 815 [INSPIRE].
G.R. Vincent, M. Hindmarsh and M. Sakellariadou, Scaling and small scale structure in cosmic string networks, Phys. Rev. D 56 (1997) 637 [astro-ph/9612135] [INSPIRE].
M. Kawasaki, K. Saikawa and T. Sekiguchi, Axion dark matter from topological defects, Phys. Rev. D 91 (2015) 065014 [arXiv:1412.0789] [INSPIRE].
Z.G. Berezhiani, A.S. Sakharov and M. Yu. Khlopov, Primordial background of cosmological axions, Sov. J. Nucl. Phys. 55 (1992) 1063 [Yad. Fiz. 55 (1992) 1918] [INSPIRE].
E. Masso, F. Rota and G. Zsembinszki, On axion thermalization in the early universe, Phys. Rev. D 66 (2002) 023004 [hep-ph/0203221] [INSPIRE].
P. Graf and F.D. Steffen, Thermal axion production in the primordial quark-gluon plasma, Phys. Rev. D 83 (2011) 075011 [arXiv:1008.4528] [INSPIRE].
A. Salvio, A. Strumia and W. Xue, Thermal axion production, JCAP 01 (2014) 011 [arXiv:1310.6982] [INSPIRE].
J.O. Andersen, L.E. Leganger, M. Strickland and N. Su, Three-loop HTL QCD thermodynamics, JHEP 08 (2011) 053 [arXiv:1103.2528] [INSPIRE].
J. Gasser and H. Leutwyler, Light quarks at low temperatures, Phys. Lett. B 184 (1987) 83 [INSPIRE].
J. Gasser and H. Leutwyler, Thermodynamics of chiral symmetry, Phys. Lett. B 188 (1987) 477 [INSPIRE].
F.C. Hansen and H. Leutwyler, Charge correlations and topological susceptibility in QCD, Nucl. Phys. B 350 (1991) 201 [INSPIRE].
P. Gerber and H. Leutwyler, Hadrons below the chiral phase transition, Nucl. Phys. B 321 (1989) 387 [INSPIRE].
D.J. Gross, R.D. Pisarski and L.G. Yaffe, QCD and instantons at finite temperature, Rev. Mod. Phys. 53 (1981) 43 [INSPIRE].
A.D. Linde, Infrared problem in thermodynamics of the Yang-Mills gas, Phys. Lett. B 96 (1980) 289 [INSPIRE].
A.K. Rebhan, The non-Abelian debye mass at next-to-leading order, Phys. Rev. D 48 (1993) 3967 [hep-ph/9308232] [INSPIRE].
P.B. Arnold and L.G. Yaffe, The non-Abelian Debye screening length beyond leading order, Phys. Rev. D 52 (1995) 7208 [hep-ph/9508280] [INSPIRE].
K. Kajantie, M. Laine, J. Peisa, A. Rajantie, K. Rummukainen and M.E. Shaposhnikov, Nonperturbative Debye mass in finite temperature QCD, Phys. Rev. Lett. 79 (1997) 3130 [hep-ph/9708207] [INSPIRE].
O. Philipsen, Debye screening in the QCD plasma, hep-ph/0010327 [INSPIRE].
WHOT-QCD collaboration, Y. Maezawa et al., Heavy-quark free energy, debye mass and spatial string tension at finite temperature in two flavor lattice QCD with Wilson quark action, Phys. Rev. D 75 (2007) 074501 [hep-lat/0702004] [INSPIRE].
O. Wantz and E.P.S. Shellard, The topological susceptibility from grand canonical simulations in the interacting instanton liquid model: chiral phase transition and axion mass, Nucl. Phys. B 829 (2010) 110 [arXiv:0908.0324] [INSPIRE].
O. Philipsen, The QCD equation of state from the lattice, Prog. Part. Nucl. Phys. 70 (2013) 55 [arXiv:1207.5999] [INSPIRE].
S. Borsányi et al., Full result for the QCD equation of state with 2 + 1 flavors, Phys. Lett. B 730 (2014) 99 [arXiv:1309.5258] [INSPIRE].
Planck collaboration, P.A.R. Ade et al., Planck 2015 results. XX. Constraints on inflation, arXiv:1502.02114 [INSPIRE].
A.D. Linde, Generation of isothermal density perturbations in the inflationary universe, Phys. Lett. B 158 (1985) 375 [INSPIRE].
J. Hamann, S. Hannestad, G.G. Raffelt and Y.Y.Y. Wong, Isocurvature forecast in the anthropic axion window, JCAP 06 (2009) 022 [arXiv:0904.0647] [INSPIRE].
F. Sanfilippo, Quark Masses from Lattice QCD, PoS(LATTICE 2014)014 [arXiv:1505.02794] [INSPIRE].
RBC and UKQCD Collaboration, R. Mawhinney, NLO and NNLO low energy constants for SU(3) chiral perturbation theory, talk presented at 33rd International Symposium on Lattice field theory (LATTICE 2015), July 24–30, Kobe, Japan (2015).
P.A. Boyle et al., The low energy constants of SU(2) partially quenched chiral perturbation theory from N f = 2 + 1 domain wall QCD, arXiv:1511.01950 [INSPIRE].
G. Altarelli and G.G. Ross, The anomalous gluon contribution to polarized leptoproduction, Phys. Lett. B 212 (1988) 391 [INSPIRE].
S.A. Larin, The renormalization of the axial anomaly in dimensional regularization, Phys. Lett. B 303 (1993) 113 [hep-ph/9302240] [INSPIRE].
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di Cortona, G.G., Hardy, E., Vega, J.P. et al. The QCD axion, precisely. J. High Energ. Phys. 2016, 34 (2016). https://doi.org/10.1007/JHEP01(2016)034
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DOI: https://doi.org/10.1007/JHEP01(2016)034