Ground-state energy of pionic hydrogen to one loop

Abstract

Abstract. We investigate the ground-state energy of the π − p atom (pionic hydrogen) in the framework of QCD+QED. In particular, we evaluate the strong energy-level shift. We perform the calculation at nextto-leading order in the low-energy expansion in the framework of the relevant effective field theory. The result provides a relation between the strong energy shift and the pion-nucleon S-wave scattering lengths -evaluated in pure QCD -at next-to-leading order in isospin breaking and in the low-energy expansion. We compare our result with available model calculations.

Extraction of S-wave pN scattering lengths from data on pionic atoms

“…Convolving the operators of Tables 1 and 2 with different wave functions derived from chiral and phenomenological NN potentials we find a variation in the results of about 5 %: an independent estimate of the contact term's effect. However, to achieve this accuracy one also has to account for two-body and Using c 1 = (−1.0 ± 0.3) GeV −1 [14], the rough estimate | f 1 | ≤ 1.4 GeV −1 [7], and Eq. (4.1) yields a non-zero a + at better than the 95 % confidence level a + = (7.6 ± 3.1) · 10…”

“…Further, if there are open channels below threshold, the scattering length is complex and the ground state level of a hadronic atom has a non-zero width. The energy shift ε 1s and the line width Γ 1s of the ground state are given by [6,7,8] …”

“…where α = e 2 /4π, µ H is the reduced mass of the hadronic system and the term ∝ O(α 4 ) stands for the corrections at higher order in α [7,8]. In principle, the measurement of the shift and the width of the πH atom [9] is already sufficient to extract both a + and a − .…”

Two-pion exchange electromagnetic current in chiral effective field theory using the method of unitary transformation

“…In particular, one needs to ensure that all appearing ultraviolet divergences are absorbed into redefinition of the LECs d i and l i from L (3) πN and L (4) π , respectively, with already known β-functions, see e.g. [13][14][15][16]. This work is in progress [17].…”

Isospin violation, light quark masses, and all that

“…Interest was rekindled due to the precision measurements of pionic hydrogen and deuterium at PSI [3]. In the framework of covariant baryon CHPT, [4] the elastic π − p amplitude was calculated at threshold to third (leading one-loop) order in the chiral expansion. In Ref.…”