Abstract
We analyse the proton Compton-scattering differential cross section for photon energies up to 325 MeV using Chiral Effective Field Theory (χEFT) and extract new values for the electric and magnetic polarisabilities of the proton. Our approach builds in the key physics in two different regimes: photon energies ω ≲ m π (“low energy”), and the higher energies where the Δ(1232) resonance plays a key role. The Compton amplitude is complete at N4LO, \(\mathcal{O}\left( {e^2 \delta ^4 } \right)\), in the low-energy region, and at NLO, \(\mathcal{O}\left( {e^2 \delta ^0 } \right)\), in the resonance region. Throughout, the Delta-pole graphs are dressed with π N loops and γNΔ vertex corrections. A statistically consistent database of proton Compton experiments is used to constrain the free parameters in our amplitude: the M1 γNΔ transition strength b 1 (which is fixed in the resonance region) and the polarisabilities α E1 and β M1 (which are fixed from data below 170 MeV). In order to obtain a reasonable fit, we find it necessary to add the spin polarisability γ M1M1 as a free parameter, even though it is, strictly speaking, predicted in χEFT at the order to which we work. We show that the fit is consistent with the Baldin sum rule, and then use that sum rule to constrain α E1 + β M1. In this way we obtain α E1 = [10.65 ± 0.35(stat) ± 0.2(Baldin) ± 0.3(theory)] × 10−4 fm3 and β M1 = [3.15 ∓ 0.35(state) ± 0.2(Baldin) ∓ 0.3()theory] × 10−4 fm3, with χ2 = 113.2 for 135 degrees of freedom. A detailed rationale for the theoretical uncertainties assigned to this result is provided.
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References
H.W. Grießhammer, J.A. McGovern, D.R. Phillips, G. Feldman, Prog. Part. Nucl. Phys. 67, 841 (2012).
D. Drechsel, B. Pasquini, M. Vanderhaeghen, Phys. Rep. 378, 99 (2003).
M. Schumacher, Prog. Part. Nucl. Phys. 55, 567 (2005).
C.L. Oxley, Phys. Rev. 110, 733 (1958).
L.G. Hyman, R. Ely, D.H. Frisch, M.A. Wahlig, Phys. Rev. Lett. 3, 93 (1959).
V.I. Gol’danskii et al., Sov. Phys. JETP 11, 1223 (1960).
G. Bernardini et al., Nuovo Cimento 18, 1203 (1960).
G. Pugh et al., Phys. Rev. 105, 982 (1957) and references therein, MIT Summer study (1967) p. 555.
P.S. Baranov et al., Phys. Lett. B 52, 122 (1974).
P.S. Baranov et al., Sov. J. Nucl. Phys. 21, 355 (1975).
J.W. DeWire, M. Feldmann, V.L. Highland, R. Littauer, Phys. Rev. 124, 909 (1961).
P.S. Baranov, L.I. Slovokhotov, G.A. Sokol, L.N. Shtarkov, Sov. Phys. JETP 23, 242 (1966).
P.S. Baranov et al., Sov. J. Nucl. Phys. 3, 791 (1966).
E.R. Gray, A.O. Hanson, Phys. Rev. 160, 1212 (1967).
H. Genzel, M. Jung, R. Wedemeyer et al., Z. Phys. A 279, 399 (1976).
S. Weinberg, Physica A 96, 327 (1979).
J. Gasser, H. Leutwyler, Phys. Rep. 87, 77 (1982).
J. Gasser, H. Leutwyler, Ann. Phys. 158, 142 (1984).
E.E. Jenkins, A.V. Manohar, lectures at the Workshop on Effective Field Theories of the Standard Model, Dobogoko, Hungary, Aug 1991, in Dobogokoe 1991, Proceedings, Effective field theories of the standard model, pp. 113-137.
E.E. Jenkins, A.V. Manohar, Phys. Lett. B 259, 353 (1991).
V. Bernard, N. Kaiser, U.-G. Meißner, Int. J. Mod. Phys. E 4, 193 (1995).
S. Scherer, Adv.. Nucl. Phys. 27, 277 (2003).
V. Bernard, U.-G. Meißner, Annu. Rev. Nucl. Part. Sci. 57, 33 (2007).
V. Bernard, Prog. Part. Nucl. Phys. 60, 82 (2008).
S. Scherer, M.R. Schindler, Quantum chromodynamics and chiral symmetry, in Lect. Notes Phys., Vol. 830 (Springer, 2012) pp. 1.
V. Bernard, N. Kaiser, J. Kambor, U.-G. Meißner, Nucl. Phys. B 388, 315 (1992).
V. Bernard, N. Kaiser, U.-G. Meißner, Phys. Rev. Lett. 67, 1515 (1991).
D. Babusci, G. Giordano, G. Matone, Phys. Rev. C 57, 291 (1998).
F.J. Federspiel, R.A. Eisenstein, M.A. Lucas et al., Phys. Rev. Lett. 67, 1511 (1991).
A. Zieger, R. Van de Vyver, D. Christmann, A. De Graeve, C. Van den Abeele, B. Ziegler, Phys. Lett. B 278, 34 (1992).
E.L. Hallin et al., Phys. Rev. C 48, 1497 (1993).
B.E. MacGibbon, G. Garino, M.A. Lucas, A.M. Nathan, G. Feldman, B. Dolbilkin, Phys. Rev. C 52, 2097 (1995).
V. Olmos de León et al., Eur. Phys. J. A 10, 207 (2001).
C. Molinari et al., Phys. Lett. B 371, 181 (1996).
J. Peise et al., Phys. Lett. B 384, 37 (1996).
A. Hünger et al., Nucl. Phys. A 620, 385 (1997).
F. Wissmann et al., Nucl. Phys. A 660, 232 (1999).
S. Wolf et al., Eur. Phys. J. A 12, 231 (2001).
M. Camen et al., Phys. Rev. C 65, 032202 (2002).
G. Blanpied et al., Phys. Rev. C 64, 025203 (2001).
R. Miskimen, talk at the Conference on Intersections of Particle and Nuclear Physics, St. Petersburg, FL, May 2012, to be published.
R. Miskimen, HIGS Proposal P-06-09, Measuring the Spin Polarizabilities of the Proton in Double-Polarized Real Compton Scattering (2009).
D. Hornidge, talk at the Conference on Intersections of Particle and Nuclear Physics, St. Petersburg, FL, May 2012, to be published.
W. Detmold, B.C. Tiburzi, A. Walker-Loud, Phys. Rev. D 73, 114505 (2006).
W. Detmold, B.C. Tiburzi, A. Walker-Loud, Phys. Rev. D 79, 094505 (2009).
W. Detmold, B.C. Tiburzi, A. Walker-Loud, Phys. Rev. D 81, 054502 (2010).
M. Engelhardt, PoS LATTICE 2011, 153 (2011).
M. Lujan, A. Alexandru, F. Lee, PoS LATTICE 2011, 165 (2011).
K. Pachucki, Phys. Rev. A 60, 3593 (1999).
C.E. Carlson, M. Vanderhaeghen, arXiv:1109.3779 [physics.atom-ph].
M.C. Birse, J.A. McGovern, Eur. Phys. J. A 48, 120 (2012).
D.R. Phillips, J. Phys. G 36, 104004 (2009).
A. Walker-Loud, C.E. Carlson, G.A. Miller, Phys. Rev. Lett. 108, 232301 (2012).
V. Bernard, N. Kaiser, A. Schmidt, U.-G. Meißner, Phys. Lett. B 319, 269 (1993).
S. Ragusa, Phys. Rev. D 47, 3757 (1993).
J.A. McGovern, Phys. Rev. C 63, 064608 (2001).
S.R. Beane, M. Malheiro, J.A. McGovern, D.R. Phillips, U. van Kolck, Phys. Lett. B 567, 200 (2003) 607.
S.R. Beane, M. Malheiro, J.A. McGovern, D.R. Phillips, U. van Kolck, Nucl. Phys. A 747, 311 (2005).
T.R. Hemmert, B.R. Holstein, J. Kambor, Phys. Lett. B 395, 89 (1997).
T.R. Hemmert, B.R. Holstein, J. Kambor, J. Phys. G 24, 1831 (1998).
T.R. Hemmert, B.R. Holstein, J. Kambor, Phys. Rev. D 55, 5598 (1997).
R.P. Hildebrandt, H.W. Grießhammer, T.R. Hemmert, B. Pasquini, Eur. Phys. J. A 20, 293 (2004).
V. Pascalutsa, D.R. Phillips, Phys. Rev. C 67, 055202 (2003).
T. Becher, H. Leutwyler, Eur. Phys. J. C 9, 643 (1999).
T. Fuchs, J. Gegelia, G. Japaridze, S. Scherer, Phys. Rev. D 68, 056005 (2003).
V. Lensky, V. Pascalutsa, Pisma Zh. Eksp. Teor. Fiz. 89, 127 (2009).
V. Lensky, V. Pascalutsa, Eur. Phys. J. C 65, 195 (2010).
V. Lensky, J.A. McGovern, D.R. Phillips, V. Pascalutsa, Phys. Rev. C 86, 048201 (2012).
J.A. McGovern, H.W. Grießhammer, D.R. Phillips, D. Shukla, PoS CD 09, 059 (2009).
D.R. Phillips, J.A. McGovern, H.W. Grießhammer, talk at the Conference on Intersections of Particle and Nuclear Physics, St. Petersburg, FL, May 2012, to be published (arXiv:1210.3577).
D. Babusci, G. Giordano, A.I. L’vov, G. Matone, A.M. Nathan, Phys. Rev. C 58, 1013 (1998).
H.W. Grießhammer, T.R. Hemmert, Phys. Rev. C 65, 045207 (2002).
N. Fettes, U.-G. Meißner, M. Mojžiš, S. Steininger, Ann. Phys. 283, 273 (2000) 288.
U.-G. Meißner, G. Müller, S. Steininger, Ann. Phys. 279, 1 (2000).
G.C. Gellas, T.R. Hemmert, C.N. Ktorides, G.I. Poulis, Phys. Rev. D 60, 054022 (1999).
T.R. Hemmert, B.R. Holstein, J. Kambor, G. Knochlein, Phys. Rev. D 57, 5746 (1998).
R.P. Hildebrandt, PhD Thesis, TU München (2005) nucl-th/0512064.
V. Pascalutsa, M. Vanderhaeghen, Phys. Rev. D 73, 034003 (2006).
K.M. Watson, Phys. Rev. 95, 228 (1954).
B. Long, U. van Kolck, Nucl. Phys. A 840, 39 (2010).
B. Pasquini, P. Pedroni, D. Drechsel, Phys. Lett. B 687, 160 (2010).
F. Wissmann, Compton Scattering: Investigating the Structure of the Nucleon with Real Photons, in Springer Tracts in Modern Physics, Vol. 200 (Springer, 2004).
P.S. Baranov, A.I. Lvov, V.A. Petrunkin, N.L. Shtarkov, Phys. Part. Nucl. 32, 376 (2001).
Particle Data Group (J. Beringer et al.), Phys. Rev. D 86, 010001 (2012).
M.I. Levchuk, A.I. L’vov, Nucl. Phys. A 674, 449 (2000).
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McGovern, J.A., Phillips, D.R. & Grießhammer, H.W. Compton scattering from the proton in an effective field theory with explicit Delta degrees of freedom. Eur. Phys. J. A 49, 12 (2013). https://doi.org/10.1140/epja/i2013-13012-1
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DOI: https://doi.org/10.1140/epja/i2013-13012-1