Isospin breaking in nuclear physics: The Nolen-Schiffer effect

Using the QCD sum rules we calculate the neutron-proton mass difference at zero density as a function of the difference in bare quark massm _d—m _u. We confirm results of Hatsuda, Høgaasen and Prakash that the largest term results from the difference in up and down quark condensates, the explicitC(m _d—m _u) entering with the opposite sign. The quark condensates are then extended to finite density to estimate the Nolen-Schiffer effect. The neutron-proton mass difference is extremely density dependent, going to zero at roughly nuclear matter density.The Ioffe formula for the nucleon mass is interpreted as a derivation, within the QCD sum rule approach, of the Nambu-Jona-Lasinio formula. This clarifies theN _c counting and furthermore provides an alternative interpretation of the Borel mass.     

What QCD sum rules tell about the rho meson — A new answer to an old question

First, a historical overview is presented concerning the use of QCD sum rules to learn about the p-meson properties at finite nuclear densities. Second, it is shown that the combination of the sum rule technique with the large-N _c expansion provides new insight. Especially it is possible to determine from the in-medium sum rules a vacuum(!) quantity which is an important ingredient for hadronic in-medium calculations of the p-meson spectral function. This quantity is the coupling strength of the p-nucleon system to the baryonic resonance N^*(1520).     

Quark spin-isospin sum rules and the adler-weisberger relation in nuclei

We use a quark model to extend the classical Gamow-Teller sum rule for the difference of the β^?andβ⁺ strengths to excitations of the nucleon (mainly the Δ isobar).A schematic model illustrates the realization of the new sum rule when a particle-hole force is introduced. We discuss the connection of our result with the model-independent Adler-Weisberger sum rule.     

Probability density function of the sum of N partially correlated speckle patterns

A method is developed which allows exact calculation of the probability density function of the sum of N correlated speckle patterns. To find the density function, it is only necessary to first find the eigenvalues of an N × N coherence matrix. When the eigenvalues are distinct, the density function can be expressed as a simple sum of N exponential terms.     

Parity Projected QCD Sum Rule of the Nucleon with MEM

The nucleon and its negative-parity excited states are examined in a maximum entropy method analysis of QCD sum rules. We derive the parity projected nucleon sum rules with all known first order α _s corrections to the Wilson coefficients of the operator product expansion (OPE). As these corrections have turned out to be large, we suppress them by using a phase-rotated Gaussian kernel. This phase rotation strongly suppresses the continuum contribution and improves the convergence of the OPE. The resulting sum rule has the interesting feature that it is dominated by the term containing the chiral condensate of dimension 3. Analyzing this sum rule by the maximum entropy method, we are able to extract information of both the positive and negative parity states.     

NegativeP′-pole parameters and vanishing total cross sections in high energy πN scattering

In πN forward scattering the conventionalP′-pole can be simulated by two vacuum poles with α(0)<0 and different signs of the residues. In the regions ?0.3≦ α _p ′(0)≦?0.1 and ?0.8≦α _p ′'(0)≦?0.4 the practically identical fits to the πN scattering data from 8 to 65 GeV/c yield 0.98≦α _p (0)<1. The dispersion theoretical sum rule for the scattering lengtha ⁽⁺⁾ is fulfilled because of the negativeP′ residue; it is used as a finite-energy sum rule withN=8 GeV/c.     

A Comparative Analysis of In-Medium Spectral Functions for N(940) and N ∗(1535) in Real-Time Thermal Field Theory

In the real-time thermal field theory, the nucleon self-energy at finite temperature and density is evaluated where an extensive set of pion-baryon (π B) loops are consider. On the other side, the in-medium self-energy of N ^?(1535) for π N and η N loops is also determined in the same framework. The detail branch cut structures for these different π B loops for nucleon N(940) and π N, η N loops for N ^?(1535) are addressed. Using the total self-energy of N(940) and N ^?(1535), which contain the contributions of their corresponding loop diagrams, the complete structures of their in-medium spectral functions have been obtained. The Landau and unitary cut contributions provide two separate peak structures in the nucleon spectral function while N ^?(1535) has a single peak structure in its unitary cuts. At high temperature, the peak structures of both at their individual poles are attenuated while at high density Landau peak structure of nucleon is completely suppressed and its unitary peak structure is tending to be shifted towards the melted peak of N ^?(1535). The non-trivial modifications of these chiral partners may indicate some association of chiral symmetry restoration.     

QCD sum rules in exclusive kinematics and pion wave function

We suggest a modification of the QCD sum rules for three-point correlation functions that relates hadron expectation values of an operator of interest to properties of the QCD vacuum in alternating external fields. A new sum rule is obtained for the nucleon magnetic moments. Relations are found between the couplings g_πNN , g_ρωπ and the value of the pion wave function at the point with equal momentum carried by the quark and the antiquark. Our results seem to exclude the possibility of having a pronounced dip in the pion wave function in the middle point, as has been assumed on the evidence of a large value of the second moment.     

Pion scattering from a bound nucleon at medium energies

In order to examine the validity of the impulse approximation for pion-nucleus scattering in the 33-resonance energy region, we consider pion-scattering from a “nucleus” which consists of a single nucleon bound in a harmonic oscillator potential. A separable πN interaction is assumed. The oscillator parameter is chosen such that the nuclear sizes are fitted for ⁴He ～ ¹⁶O. The binding effect is found to result in a downward shift of the resonance energy (by about 20 MeV), and an increase (by 50 ～ 70%) of the total cross section near the resonance. The angular distribution is also strongly modified. In connection with the binding effect, the importance of a careful treatment of nucleon recoil is emphasized. It is pointed out that the closure approximation which is often used to sum over intermediate nuclear states leads to very misleading results. The effect of the Pauli principle is also examined by excluding some intermediate states.     

Photonuclear reactions and dispersion relations

We study the photonuclear reaction in the intermediate region. We evaluate the real part of the forward Compton amplitude through the dispersion relation and analyze its structure. The modification of the electromagnetic polarizability of the nucleon, \(\bar \alpha\) , in the nuclear medium is calculated. We show that it affects appreciably the behaviour of the Compton amplitude in the intermediate region, consistent with the experimental data. In the same scheme the enhancement of the photonuclear sum rule,K, is interpreted as an exchange contribution to the nucleon Compton amplitude. We find in lead a value ofK=1.6±0.2 and a quenching of about 20% of \(\bar \alpha\) .     

Nuclear effects in the F3 structure function for finite and asymptotic Q

We study nuclear effects in the structure function F₃ which describes the parity violating part of the charged-current neuitrino nucleon deep inelastic scattering. Starting from a covariant approach we derive a factorized expression for the nuclear structure function in terms of the nuclear spectral function and off-shell nucleon structure functions valid for arbitrary momentum transfer Q and in the limit of weak nuclear binding, i.e. when a nucleus can be treated as a non-relativistic system. We develop a systematic expansion of nuclear structure functions in terms of a Q⁻² series caused by nuclear effects (“nuclear twist” series). Basing ourselves on this expansion we calculate nuclear corrections to the Gross-Llewellyn-Smith sum rule as well as to higher moments of F₃. We show that corrections to the GLS sum rule due to nuclear effects cancel out in the Bjorken limit and calculate the corresponding Q⁻² correction. Special attention is paid to the discussion of the off-shell effects in the structure functions. A sizable impact of these effects both on the Q² and x dependence of nuclear structure functions is found.     

Photo-absorption sum rules σ<Subscript>–1</Subscript> in different environments (Atoms,nuclei, nucleons)

Combining the spin-dependent dispersion GDH-sum rule, the isotopic-spin-dependent Cabibbo-Radicati sum rule, and the relativistic dipole-moment-fluctuation (i.e. generalized Gottfried) sum rule with the three valence quark configuration of nucleons taken into account for the composition of the ground and the excited states of the nucleon, the relevant moments of the distribution and correlation functions of the quark electric dipole moment operators in the nucleon ground state are expressed via the experimentally measurable nucleon resonance photo-excitation amplitudes.These functions are of interest for checking detailed quark-configuration structure of the nucleon state vector. Within the non-relativistic approach to photo-absorption sum rules for the 3N-nuclei a new σ_–1 sum rule proposed which is based on general charge-symmetry (CS) consequences for the “CS-conjugated” triton and ³He.     

xF_3(x,Q~2) Structure Function and Gross-Llewellyn Smith Sum Rule with Nuclear Effect and Higher Twist Correction

We present an analysis of the xF_3(x,Q~2) structure function and Gross-Llewellyn Smith(GLS) sum rule taking into account the nuclear effects and higher twist correction. This analysis is based on the results presented in[N.M. Nath, et al., Indian J. Phys. 90(2016) 117]. The corrections due to nuclear effects predicted in several earlier analysis are incorporated to our results of xF_3(x,Q~2) structure function and GLS sum rule for free nucleon, corrected upto next-next-to-leading order(NNLO) perturbative order and calculate the nuclear structure function as well as sum rule for nuclei. In addition, by means of a simple model we have extracted the higher twist contributions to the nonsinglet structure function xF_3(x,Q~2) and GLS sum rule in NNLO perturbative orders and then incorporated them to our results. Our NNLO results along with nuclear effect and higher twist corrections are observed to be compatible with corresponding experimental data and other phenomenological analysis.     

Diquarks in nucleons

Under the assumption that a scalar diquark coexists in part of the time with a single quark within a nucleon, which is favored to describe the higher twist effects of both γ and ν induced nucleon structure functions consistently, we consider how its presence affects nucleon properties. It is shown that the sum rule and the magnetic moment constrain its contribution strongly and the asymmetry is quite sensitive to it. In particular, theR=σ _L /σ _T ratio can be explained in terms of the large transverse momentum of the diquark which arises from the consideration on the neutron charge radius value.     

A causal approximation scheme for the commutator of the axial vector-currents

An approximation scheme which fulfils the causality condition is used to compute the matrix elements of the commutator of two axial-vector currents between one proton state. The commutator sum rule is supposed to be saturated by taking into account the nucleon, theN ^*(3/2, 3/2) resonance, and the partially disconnected pion-proton intermediate states. For the axial current form factors pion pole formulas are assumed. It is shown that only the subtraction constants are relevant for the equal time limit of the commutator and so the equivalence with similar earlier methods is proven.     

A computation of Adler's β sum rule II

We improve our previous calculation of Adler's β sum rule by including the Born contributions to the πN states. The result is that the sum rule is only balanced if the weak axial nucleon form factor g_A(q²) and the strong pion-nucleon form factor have roughly the same q² dependance.     

Test of a sum rule for the nucleon magnetic moments

It is shown that the original version of the sum rule relating the isovector part of the nucleon magnetic moment to aπ N scattering amplitude is not consistent with the experimental data. However there is good agreement for the corrected version ofMaiani andPreparata.     

The nuclear Coulomb sum rule in a relativistic model

The nuclear Coulomb sum rule is investigated in a relativistic quantum field theory of the nucleus based on baryons and mesons. First an effective, local, covariant, conserved electromagnetic current operator is constructed for the many-baryon system. It describes the electromagnetic structure of an isolated nucleon; the lowest-mass two-pion contribution to the spectral weight functions of the form factors is contained in it. The sum rule is then evaluated in a model based on baryons and neutral scalar and vector mesons. In the mean-field approximation (MFT) this model correctly describes the saturation properties of nuclear matter. The “one-body” term in the sum rule can be evaluated exactly through the use of the canonical anticommutation relations for the baryon field and the identification of conserved quantities. The remaining relativistic two-body contribution is evaluated in the MFT. Meson contributions to the sum rule at large momentum transfers $\text{q}\text{2k}{}_{\mathrm{<mtext>F</mtext>}}\text{? 1}$ completely dominate anticipated static, short-range, two-nucleon correlation contributions to the non-relativistic Coulomb sum rule. One possible implication is that the nucleus must (at least) be considered as a dynamic system of mesons and baryons.